70 (2024) 1-2 http://www.sv-jme.eu Since 1955 Strojniški vestnik Journal of Mechanical Engineering Contents Papers 20 Samo Zupan, Robert Kunc: Overview of Principles and Rules of Geometrical Product Specifications According to the Current ISO Standards tolerancing Zhengfang Li, Xudong Di, Zhengyuan Gao, Zhiguo An, Ling Chen, Yuhang Zhang, Shihong Lu: Improvement of the Dimensional Accuracy of a Ti-6Al-4V Ripple Disc During Electric Hot Incremental Sheet Forming 27 Ireneusz Zagórski, Monika Kulisz, Anna Szczepaniak: Roughness Parameters with Statistical Analysis and Modelling Using Artificial Neural Networks After Finish Milling of Magnesium Alloys with Different Edge Helix Angle Tools 42 Tat-Khoa Doan, Trung-Thanh Nguyen, An-Le Van: Multi-performance Optimization of the Rotary Turning Operation for Environmental and Quality Indicators 55 Xin Tian, Guangjian Wang, Yujiang Jiang: A New Calculation Method for Instantaneous Efficiency and Torque Fluctuation of Spur Gears 70 Grzegorz Struzikiewicz: Investigation of the Titanium Alloy Turning Process with Prime A Tools under High-Pressure Cooling Conditions 80 Berat Gürcan Şentürk, Mahmut Cüneyt Fetvacı: A Modified Approach to the Rack Generation of Beveloid Gears 92 Oktay Adıyaman: Investigation on the Application of Worn Cutting Tool Inserts as Burnishing Tools ISO standard Journal of Mechanical Engineering - Strojniški vestnik 3 1-2 year 2024 volume 70 no. geometrical product specification verification Strojniški vestnik – Journal of Mechanical Engineering (SV-JME) Aim and Scope The international journal publishes original and (mini)review articles covering the concepts of materials science, mechanics, kinematics, thermodynamics, energy and environment, mechatronics and robotics, fluid mechanics, tribology, cybernetics, industrial engineering and structural analysis. The journal follows new trends and progress proven practice in the mechanical engineering and also in the closely related sciences as are electrical, civil and process engineering, medicine, microbiology, ecology, agriculture, transport systems, aviation, and others, thus creating a unique forum for interdisciplinary or multidisciplinary dialogue. The international conferences selected papers are welcome for publishing as a special issue of SV-JME with invited co-editor(s). Editor in Chief Vincenc Butala University of Ljubljana, Faculty of Mechanical Engineering, Slovenia Technical Editor Pika Škraba University of Ljubljana, Faculty of Mechanical Engineering, Slovenia Founding Editor Bojan Kraut University of Ljubljana, Faculty of Mechanical Engineering, Slovenia Editorial Office University of Ljubljana, Faculty of Mechanical Engineering SV-JME, Aškerčeva 6, SI-1000 Ljubljana, Slovenia Phone: 386 (0)1 4771 137 Fax: 386 (0)1 2518 567 info@sv-jme.eu, http://www.sv-jme.eu Print: Demat d.o.o., printed in 240 copies Founders and Publishers University of Ljubljana, Faculty of Mechanical Engineering, Slovenia University of Maribor, Faculty of Mechanical Engineering, Slovenia Association of Mechanical Engineers of Slovenia Chamber of Commerce and Industry of Slovenia, Metal Processing Industry Association President of Publishing Council Mihael Sekavčnik University of Ljubljana, Faculty of Mechanical Engineering, Slovenia Vice-President of Publishing Council Matej Vesenjak http://www.sv-jme.eu 70 (2024) 1-2 University of Maribor, Faculty of Mechanical Engineering, Slovenia Since 1955 Strojniški vestnik Journal of Mechanical Engineering ts bert Kunc: nciples and Rules of Geometrical Product Specifications Current ISO Standards tolerancing dong Di, Zhengyuan Gao, Zhiguo An, Ling Chen, Yuhang Zhang, the Dimensional Accuracy of a Ti-6Al-4V Ripple Disc Hot Incremental Sheet Forming ISO standard Trung-Thanh Nguyen, An-Le Van: nce Optimization of the Rotary Turning Operation for and Quality Indicators an Wang, Yujiang Jiang: on Method for Instantaneous Efficiency and Torque Fluctuation kiewicz: the Titanium Alloy Turning Process with Prime A Tools under Cooling Conditions ntürk, Mahmut Cüneyt Fetvacı: oach to the Rack Generation of Beveloid Gears the Application of Worn Cutting Tool Inserts as Burnishing Journal of Mechanical Engineering - Strojniški vestnik ki, Monika Kulisz, Anna Szczepaniak: meters with Statistical Analysis and Modelling Using Artificial s After Finish Milling of Magnesium Alloys with Different Edge s 1-2 2024 70 no. year volume geometrical product specification verification Cover: The geometrical product specifications (GPS) are, in addition to material specifications, a key component of effective planning and production of mechanical products as well as communication between partners in these processes. The principles and basic rules for precise and unambiguous specification of all requirements are embodied in a series of ISO GPS standards. 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One of the principles that it appropriate be established from the real features of to ensure, using form and orientation GTs, (modifications) datums based errors. One ofwith the principles isgeometry thatand it is permissible appropriate are typically w the product all (modifications) Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 3-19 Datums are stated on technical drawings or models (MBD) which display the TEG and whose siz es correspond to the dimensioned nominal dimensions. Datums can be individual (e.g., A) or common (e.g., A-B), and both types can form datum systems. H owever, for verification, datums need to be established from the real geometry features of the product with all possible and permissible errors. One of the principles is that it is appropriate to first ensure, using the form and orientation G Ts, that these features also have suitable quality (flatness, straightness, etc.) after manufacturing. A C artesian coordinate system is most easily created with three planar datums that are orthogonally oriented to each other, but other combinations are also possible. Such a datum system locks all degrees of freedom of movement (three translations, three rotations) of a rigid body, which is a necessary condition when needing to control all geometrical features, primarily with location. W hen only orientation needs to be controlled, it is enough that four or five degrees of freedom are locked. W hen using datum systems, the sequence (primary, secondary, tertiary) in the tolerance frame is crucial as it also allows for repeatable insertion of the product into the gauge, thus ensuring repeatable and comparable measurements. Datums for verification can be established using mechanical measuring tools and accessories (tables, support elements, etc.). At least one suitable primary datum system defined on the product should be of such a type that it can be used to position products in measuring devices. The primary single datum in the datum system should ideally support the weight of the product. Datums can also be established mathematically from clouds of measured points. In doing so, various operations previously described in the characteristic specifications can be used to determine a proper mathematical feature from a cloud of points that will be used to establish the datum. The current standard allows for the use of operations similar to those applicable for toleranced features (filtering [24], ISO 160 [37] series, associations, etc.). It also offers several ways to limit the extent of features used for datums (datum targets). If a derived feature (e.g., an axis) is chosen for an individual datum, it is also possible to use material requirements and the appropriate simulation of the datum (e.g., with fixed mechanical aids in the case of MMR ). It can also be set which characteristics each datum can be used for and which degrees of freedom it should lock. 14 All these possibilities are foreseen in the current version of the standard, which today allows for an unambiguous definition of practically useful datums based on the state of measurement technology. Various additional requirements (modifications) that need to be taken into account are typically written in the definition and use datums with appropriate indicators written in square brackets (e.g., [ C F ] , [ DV] , [ VA] , etc. F ig. 4) and new symbols used on the drawing or 3 D model (e.g., movable datum targets). Fig. 4. Example of datum system specification using a movable datum target and contacting feature [CF] 3.8 General Tolerances The general principles of ISO G P S (ISO 8015 [14]) also include the general specification principle and the definitive drawing principle. The first speaks to the fact that for each product it is possible to explicitly specify every one of its characteristics, while the second indicates that general specifications (dimension tolerances, G T, surface conditions, edge states) must be determined for all characteristics without explicit specifications. The second principle speaks to the fact that we cannot demand the executor (workshop) to make anything that is not unambiguously defined on the drawing in an explicit or general way. G eneral specifications are therefore a very important part of technical documentation. In ISO G P S, this issue is regulated with a series of general standards, which must be appropriately listed or used in the documentation: ISO 22081: 2021 [38] is a new standard that sets out the principles and rules on how to specify general dimensional tolerances and general geometrical tolerances on documentation. It is recommended that this standard is explicitly mentioned in the documentation and that it is detailed within this mention whether the general tolerances are: Zupan, S. – Kunc, R. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 3-19 linear siz e dimension tolerances; angular siz e dimension tolerances; or geometrical tolerances (it recommends the exclusive use of surface profile tolerance with a complete reference system of plane datum system; R , S, T). Fig. 5. Example of general tolerances specification [38] Each of these can be determined individually and with their own constant values or own table for a larger siz e range, or we can refer to another appropriate standard in which the values are already determined according to the selected quality class defined in this standard. ISO 2768-1:1 8 [39] is the basic standard for general tolerances of linear and angular dimensions (siz es) of products, which are mainly produced using cutting technologies (machining). Typically, the permitted deviations depend on the siz e of the dimension (eight intervals from 0.5 mm to 3150 mm) and on the required quality (four classes: fine, medium, coarse, and very coarse). As with all general tolerances, the tolerance interval is centred around the nominal value of the dimension. This, of course, means that dimensions controlled by general tolerances are entirely unsuitable for forming various fits between parts (shafts and holes), as the fit is impossible to predict. The second part of this standard governed certain general geometrical tolerances and was outdated and therefore withdrawn in 2021. ISO 80 62 [40] to [43] specifies general specifications for castings made from metal alloys. The standard is issued in several parts and regulates vocabulary, rules, general tolerances for linear dimensions (DC TG in 16 quality grades), general geometrical tolerances (G C TG – surface profile tolerance based on the full general datum system R , S, T in 15 grades) and siz es of required machining allowances for subsequent mechanical processing (R MAG in 10 quality grades). The siz e measurement interval is in sub-intervals up to 10,000 mm, and the corresponding quality levels depend on the type of material and casting technology. [44] is a standard that sets ISO 20457: 2018 general tolerances for general plastic castings and is very similar to ISO 8062 in principles and rules. H owever, it also provides guidance on product acceptability conditions and allows the selection of suitable specifications that correspond to the chosen type of material and plastic casting technology. The standard is issued under the auspices of ISO/ TC 61/ SC 2. ISO 13 20:2023 [45] is a standard that sets general tolerances for length and angle measurements as well as form and orientation (flatness, straightness, parallelism), and positions of parts of welded constructions. The standard is issued under the auspices of ISO/ TC 44/ SC 10 and is conceptually somewhat different from what is presented in the current principles and rules of ISO G P S. It focuses on the main errors that occur in welding technology. 4 OTHER GPS STANDARDS In addition to the standards described earlier in the paper, it is necessary to mention several commonly and widely used standards and specific ISO G P S standards from the group of general geometrical specification standards which are less frequently used but contain certain useful and effective principles and rules. ISO 167 2:2021 [66] is a standard that falls into the TP D group and operates under the auspices of ISO/ TC 10. H owever, it is inextricably linked with the group of G P S standards as it sets out the principles and rules on how to specify geometrical specifications in accordance with the MBD philosophy directly in 3D C AD models of products. ISO 1057 :2010 [50] is a global G P S standard that sets out principles and rules for tolerancing parts that are not rigid and deform during verification under the influence of gravity differently in different orientations. Overview of Principles and Rules of Geometrical Product Specifications According to the Current ISO Standards 15 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 3-19 ISO 21 20:2021 [46] to [48] is a new standard in three parts that sets out profile specifications for the texture and condition of surfaces (roughness, waviness) and replaces ISO 1302, which has been withdrawn. ISO 1375 : 2017 [49] is a standard under the auspices of ISO/ TC 10 that specifies allowable conditions (“ chamfering or rounding” ) of sharp edges (external and internal) that are modelled as ideal. L ess frequently used standards include, for example, standards used to specify and control certain characteristics on workpieces produced using special technological processes (e.g., castings [51]), local and limited imperfections on surfaces [52], conical and pyramidal (wedge) shapes [53] to [56], patterns [57] etc. ISO 20170:201 [67] is a new and important standard from the group of fundamental ISO G P S standards. It describes principles and tools to control a manufacturing process in accordance with a G P S specification. F or this purpose, a set of one or more complementary, independent characteristics (siz e, form, orientation, and location characteristics independent to each other) that correlate to the manufacturing process parameters and to the manufacturing process coordinate system established from the manufacturing datum system are used. This standard describes the concept of decomposition of the macro-geometrical part of the G P S specification. It does not cover the micro-geometry, i.e., surface texture. The objective of the decomposition is to define correction values for manufacturing control or to perform a statistical analysis of the process. In order to carry out SP C , it is inevitable to monitor the selected and most influential siz e dimensions and also geometrical tolerances on the basis of calculated statistical process capability indices (such as Cp, Cpk , etc.), and not merely based on verification whether the toleranced features are within the tolerance z one or not (classic tolerance definition). F or siz e dimensions, which behave as independent scalar statistical variables during verification, these indices are easy to calculate (also with the help of new statistical operators of siz e definition according to ISO 14405) . H owever, geometrical tolerances can be complex specifications (operations) that cannot be mathematically represented by a single scalar statistical variable. F or SP C , it is necessary to mathematically 16 decompose each G T into a list (vector) of scalar statistical components. This standard is the first to provide clear starting points, a mathematical basis (geometrical transformations), methods and rules for this decomposition. In this way, each geometrical specification can be fully monitored according to the principles of SP C . 5 CONCLUSIONS This paper provides an overview of the philosophy of geometrical product specifications which is embodied in the ISO series of G P S (ISO/ TC 213 ) standards. The principles and basic rules for clear and unambiguous specification of all requirements related to the geometrical features of products are divided into fundamental, general and complementary ISO G P S standards. A clear and unambiguous geometrical specification which belongs to the basic pillar of G P S enables unambiguous product verification based on the principle of duality, thus facilitating the negotiation and communication process between the parties, i.e., the client and the supplier, in the process of designing and manufacturing mechanical products. In the last two decades, ISO has made comprehensive and significant progress in this area, with many standards being amended and improved. The regulated specification of geometrical requirements with innovations in standards also enables a clear and unambiguous definition of necessary operations in verification, which better correspond to modern measurement methods and measurement technology based on the absolute measurement of the location of individual points in the cloud of extracted points on geometrical features of real products (C MM, optical and laser scanning, etc.). Since these are important basics of technical communication, users should be well acquainted with them. This is often not the case, as it is a rather extensive topic with many novelties and frequent changes, causing considerable effort and thus problems for practical users in training. Due to the vast and varied scope of standards, engineers find it difficult to keep up with their dynamics in practice. Another issue is the accessibility, or the cost, of standards for users. This causes numerous problems since the communication between partners (client and supplier) often does not occur on the same basis. In this paper, we focused primarily on geometrical specifications and the standards that regulate the geometry and siz es of products. There Zupan, S. – Kunc, R. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 3-19 are also novelties in the field of surface texture and edge state specifications, which are mentioned but not explained in detail. L ikewise, the entire parallel pillar of verification is omitted from the discussion. According to the ISO G P S matrix, the verification pillar contains an even larger number of standards that regulate verification in more detail. 8 REFERENCES [1] Nielsen, H.S. (2012). The ISO Geometrical Product Specifications Handbook, ISO/Danish Standards, International Organization for Standardization, Geneva. [2] Charpentier, F. (2012). Handbook for the geometrical specification of products, The ISO-GPS standards. [3] Krulikowski, A. (2015). ISO GPS Ultimate Pocket Guide (A companion to ISO 1101:2012 and related Geometrical Tolerancing Standards), 2015 Effective Training Inc. an SAE INTERNATIONAL company, from www.etinews.com, accessed on 2023-08-06, DOI:10.4271/pd027104. [4] Henzold, G. (2020). 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[12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] alter, . . ., lein, ., eling, B., artzack, . . Statistical Tolerance Analysis-A survey on awareness, use and need in German industry. Applied Sciences, vol. 11, no. 6, art. ID 2622, DOI:10.3390/app11062622. ISO 14638:2015. Geometrical product specifications (GPS) — Matrix model. International Organization for Standardization, Geneva. ISO 8015:2011. Geometrical product specifications (GPS) — Fundamentals — Concepts, principles and rules. International Organization for Standardization, Geneva. ISO 14253-1:2017. Geometrical product specifications (GPS) — Inspection by measurement of workpieces and measuring equipment — Part 1: Decision rules for verifying conformity or nonconformity with specifications. International Organization for Standardization, Geneva. ISO 14253-2:2011. Geometrical product specifications (GPS) — Inspection by measurement of workpieces and measuring equipment — Part 2: Guidance for the estimation of uncertainty in GPS measurement, in calibration of measuring equipment and in product verification. International Organization for Standardization, Geneva. ISO 14405-1:2016. Geometrical product specifications (GPS) — Dimensional tolerancing — Part 1: Linear sizes. International Organization for Standardization, Geneva. ISO 14405-2:2018. Geometrical product specifications (GPS) — Dimensional tolerancing — Part 2: Dimensions other than linear or angular sizes. International Organization for Standardization, Geneva. ISO 14405-3:2016. Geometrical product specifications (GPS) — Dimensional tolerancing — Part 3: Angular sizes. International Organization for Standardization, Geneva. ISO 128-1:2020. Technical product documentation (TPD) — General principles of representation — Part 1: Introduction and fundamental requirements. International Organization for Standardization, Geneva. ISO 129-1:2018. Technical product documentation (TPD) — Presentation of dimensions and tolerances — Part 1: General principles. International Organization for Standardization, Geneva. ISO 286-1:2010. Geometrical product specifications (GPS) — ISO code system for tolerances on linear sizes — Part 1: Basis of tolerances, deviations and fits. International Organization for Standardization, Geneva. ISO 286-2:2010. Geometrical product specifications (GPS) — ISO code system for tolerances on linear sizes — Part 2: Tables of standard tolerance classes and limit deviations for holes and shafts. International Organization for Standardization, Geneva. ISO 1101:2017. Geometrical product specifications (GPS) — Geometrical tolerancing — Tolerances of form, orientation, location and run-out. International Organization for Standardization, Geneva. ISO 14406:2010. Geometrical product specifications (GPS) — Extraction. International Organization for Standardization, Geneva. ISO 12180-1:2011. Geometrical product specifications (GPS) — Cylindricity — Part 1: Vocabulary and parameters of Overview of Principles and Rules of Geometrical Product Specifications According to the Current ISO Standards 17 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 3-19 [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] 18 cylindrical form. International Organization for Standardization, Geneva. ISO 12180-2:2011. Geometrical product specifications (GPS) — Cylindricity — Part 2: Specification operators. International Organization for Standardization, Geneva. ISO 12181-1:2011. Geometrical product specifications (GPS) — Roundness — Part 1: Vocabulary and parameters of roundness. International Organization for Standardization, Geneva. ISO 12181-2:2011. Geometrical product specifications (GPS) — Roundness — Part 2: Specification operators. International Organization for Standardization, Geneva. ISO 12780-1:2011. Geometrical product specifications (GPS) — Straightness — Part 1: Vocabulary and parameters of straightness. International Organization for Standardization, Geneva. ISO 12780-2:2011. Geometrical product specifications (GPS) — Straightness — Part 2: Specification operators. International Organization for Standardization, Geneva. ISO 12781-1:2011. Geometrical product specifications (GPS) — Flatness — Part 1: Vocabulary and parameters of flatness. International Organization for Standardization, Geneva. ISO 12781-2:2011. Geometrical product specifications (GPS) — Flatness — Part 2: Specification operators. International Organization for Standardization, Geneva. ISO 1660:2017. Geometrical product specifications (GPS) — Geometrical tolerancing — Profile tolerancing. International Organization for Standardization, Geneva. ISO 2692:2021. Geometrical product specifications (GPS) — Geometrical tolerancing — Maximum material requirement (MMR), least material requirement (LMR) and reciprocity requirement (RPR). International Organization for Standardization, Geneva. ISO 5459:2011. Geometrical product specifications (GPS) — Geometrical tolerancing — Datums and datum systems. International Organization for Standardization, Geneva. ISO 16610-1:2015. Geometrical product specifications (GPS) — Filtration — Part 1: Overview and basic concepts. International Organization for Standardization, Geneva. ISO 22081:2021. Geometrical product specifications (GPS) — Geometrical tolerancing — General geometrical specifications and general size specifications. International Organization for Standardization, Geneva. ISO 2768-1:1989. General tolerances — Part 1: Tolerances for linear and angular dimensions without individual tolerance indications. International Organization for Standardization, Geneva. ISO 8062-1:2007. Geometrical product specifications (GPS) — Dimensional and geometrical tolerances for moulded parts — Part 1: Vocabulary. International Organization for Standardization, Geneva. ISO/TS 8062-2:2013. Geometrical product specifications (GPS) — Dimensional and geometrical tolerances for moulded parts — Part 2: Rules. International Organization for Standardization, Geneva. ISO 8062-3:2023. Geometrical product specifications (GPS) — Dimensional and geometrical tolerances for moulded parts — Part 3: General dimensional and geometrical tolerances [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] Zupan, S. – Kunc, R. and machining allowances for castings using ± tolerances for indicated dimensions. International Organization for Standardization, Geneva. ISO 8062-4:2023. Geometrical product specifications (GPS) — Dimensional and geometrical tolerances for moulded parts — Part 4: Rules and general tolerances for castings using profile tolerancing in a general datum system. International Organization for Standardization, Geneva. ISO 20457:2018. Plastics moulded parts — Tolerances and acceptance conditions. International Organization for Standardization, Geneva. ISO 13920:2023. Welding — General tolerances for welded constructions — Dimensions for lengths and angles, shape and position. International Organization for Standardization, Geneva. ISO 21920-1:2021. Geometrical product specifications (GPS) — Surface texture: Profile — Part 1: Indication of surface texture. International Organization for Standardization, Geneva. ISO 21920-2:2021. Geometrical product specifications (GPS) — Surface texture: Profile — Part 2: Terms, definitions and surface texture parameters. International Organization for Standardization, Geneva. ISO 21920-3:2021. 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Geometrical product specifications (GPS) — Population specification. International Organization for Standardization, Geneva. [65] ISO 21204:2020. Geometrical product specifications (GPS) — Transition specification. International Organization for Standardization, Geneva. [66] ISO 16792:2021. Technical product documentation — Digital product definition data practices. International Organization for Standardization, Geneva. [67] ISO 20170:2019. Geometrical product specifications (GPS) — Decomposition of geometrical characteristics for manufacturing control. International Organization for Standardization, Geneva. Overview of Principles and Rules of Geometrical Product Specifications According to the Current ISO Standards 19 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 20-26 © 2024 The Authors. CC BY 4.0 Int. Licensee: SV-JME DOI:10.5545/sv-jme.2023.545 Original Scientific Paper Received for review: 2023-02-06 Received revised form: 2023-07-19 Accepted for publication: 2023-09-25 Improvement of the D imensional Accuracy of a Ti-6Al-4V R ipple D isc D uring Electric H ot Incremental Sheet Forming L i, Z . – Di, X . – G ao, Z . – An, Z . – C hen, L . – Z hang, Y. – L u, S. Z hengfang L i1 – X udong Di2 – Z hengyuan G ao3,* – Z higuo An3 – L ing C hen4 – Yuhang Z hang1 – Shihong L u5 Kunming U niversity, School of Mechanical and Electrical Engineering, C hina G roup C o., L td., P assenger C ar R esearch Institute of Technology C enter, C hina 3 C hongqing Jiaotong U niversity, School of Mechanotronics and Vehicle Engineering, C hina 4 Kunming U niversity, Office of Science and Technology, C hina N anjing U niversity of Aeronautics and Astronautics, C ollege of Mechanical & Electrical Engineering, C hina 1 2 Jianghuai Automobile 5 The edge warpage of a Ti-6Al-4V ripple disc is a major forming defect during electric hot incremental forming, which can lead to a significant dimensional error. In this paper, a novel manufacturing method, namely the combination of electric hot incremental forming and electrically assisted sizing, has been proposed to improve the forming defect. The effect of process parameters on forming fracture was analysed in detail, and then an optimal combination of process parameters was obtained to ensure the successful forming of a Ti-6Al-4V ripple disc. On this basis, a sizing device and a sizing current were separately designed and analysed to eliminate the warpage defect of Ti-6Al-4V ripple discs. According to the experimental result, Ti-6Al-4V ripple discs can be satisfactorily fabricated through the method proposed. Keywords: incremental sheet forming, electric hot forming, electrically assisted sizing, edge warpage, ripple disc Highlights • A novel forming process that combines electric hot incremental forming and electrically assisted sizing of Ti-6Al-4V ripple discs is proposed to fabricate the part. • The suitable current value is obtained to fabricate Ti-6Al-4V ripple discs in electric hot forming. • The effect of main forming parameters, such as feed rates and step size, on the forming quality of the part is analysed in detail. • A sizing device and a sizing current are separately designed and analysed to improve the forming accuracy of Ti-6Al-4V ripple discs. 0 INTRODUCTION The formability of materials is enhanced during incremental sheet forming, and the lower forming accuracy of parts is also obtained due to the local forming characteristics, namely that the forming region between the tool and the sheet has a springback with the removal of the tool; consequently, the application of this technology can be restricted. To solve this problem, various efforts, in Taguchi desirability function analysis [1], process optimiz ation [2], optimal forming strategies [3], grey relation analysis [4], and considering tool deformation [5], are executed to improve the forming accuracy of parts The sum of clamping, non-clamping, and final errors is the manufacturing error of parts in incremental sheet forming and it is often less than or equal to ± 3 mm according to the study of Oleksik et al. [2] C urrently, auxiliary support, path compensation, and process optimiz ation are separately adopted to reduce the fabricating error of parts [6] to [9]. Although some assistant forming schemes [10] are proposed to enhance the dimensional accuracy of parts in the forming process, the manufacturing cost is increased due to the fact that the complexity of the whole 20 process can be improved. Therefore, the latter two methods remain major ways of enhancing the forming quality of parts during incremental sheet forming. The deformation mechanism of materials is more complex in electric hot incremental forming (EH IF ), and the effect factors of dimensional accuracy are mainly process parameters, thermal expansion, and residual stress [11]. Saidi et al. adopted the cartridge heater to fabricate the part of titanium alloy Ti-6A l4V below the recrystalliz ation temperature [12]. X u et al. adopted the self-lubricating method to improve the surface quality of TA1 sheet [13]. Mohanraj et al. proposed a thermal model to predict the forming region temperature during the electric heating incremental sheet forming [14]. W u et al. further analysed the characteriz ation of material flow for the hot incremental sheet-forming process of dissimilar sheet metals [15]. Ajay adopted the optimal method of process parameters to improve the forming quality of titanium alloy in incremental sheet forming [16]. F an et al. [17] employed a composite process, namely reverse drawing and EH IF , to enhance the axial forming accuracy of parts with Ti-6A l-4V. On this basis, Ambrogio et al. [18] further adopted an energy density function to analyse the energy level of *Corr. Author’s Address: Chongqing Jiaotong University, No.66, Xuefu Road, Nan’ an District, Chongqing, China, zhengyuangao@cqjtu.edu.cn Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 20-26 different alloys, such as AA2024-T3, AZ 31 B-O, and Ti-6A l-4V alloys, and then the mapping relationship between forming angle and minimum energy level was established. F urthermore, Skjoedt et al. [19] and Shi et al. [20] separately proposed a modified spiral forming path to enhance the manufacturing accuracy of parts. According to the above studies, some typical parts, such as cone and square cone, are adopted to analyse the optimal method of dimensional accuracy [21] to [23]. H owever, the heteromorphic part, namely a ripple disc, is still rarely reported in recent studies, and its forming defect, namely that is obtained due to the interaction between residual stress and thermal expansion, is shown in F ig. 1. In this paper, a novel manufacturing method, the combination of EH IF and electrically assisted siz ing (EAS), was proposed to improve forming defects of the ripple disc. The effect of process parameters on forming fracture was analysed in detail, and then an optimal combination Fig. 1. Forming defects of a ripple dis of process parameters was obtained to ensure the successful forming of Ti-6A l-4V ripple discs. On this basis, a siz ing device and a siz ing current were separately designed and analysed to eliminate the warpage defect of Ti-6A l-4V ripple discs. The Fig. 2. Sketch of the forming profile of parts; units in mm Fig. 3. The test setup of the ripple disc in EHIF Improvement of the Dimensional Accuracy of a Ti-6Al-4V Ripple Disc During Electric Hot Incremental Sheet Forming 21 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 20-26 Fig. 4. The sizing process of the ripple disc proposed novel method can be used to rapidly fabricate the ripple disc for the aerospace field and be also further expanded to the forming of other similar parts for other fields, such as the automotive industry, biomedicine, rail transit, and the like. 1 METHODS A ripple disc with Ti-6A l-4V titanium alloy is fabricated to analyse the effect of forming and siz ing process parameters on forming quality, the dimension of which is shown in F ig. 2. The part with 0.8 mm thickness is fabricated in a numerical control machine (P roducer: L N C Technology C O., L td., Taiwan; Type: L N C -M700; Machine range: 1400 mm for x -axis, 700 mm for y-axis, and 700 mm for z -axis). Meanwhile, a direct-current power (current range of 0 A to 1500 A) and a thermal imager (P roducer: Shenz hen C etemp Technology C o., L td., C hina; Type: P I1M P I80x; R ange: –20 º C to 1500 º C ; Error: ± 0.1 º C ) are separately adopted to provide the heat and to collect temperature for the forming region, which is shown in F ig. 3. The warpage defect of parts remain, and then an electrically assisted siz ing process, as shown in F ig. 4, is designed to improve the forming defect. The four stages (i.e., heating, clamping, pressure-maintaining, and insulating) are designed in the siz ing process, in which the last three stages are used to ensure the 22 siz ing force and the siz ing time, and the first stage is used to provide a reliable siz ing temperature. 2 EXPERIMENTAL 2.1 Electric Hot Incremental Forming Experiments F ig. 5 shows the forming strategy of ripple disc, and the two stages are adopted to fabricate the part. The first forming path is designed to obtain the lateral wall of ripple disc, and the opposite wall is fabricated according to the second forming path. Meanwhile, some process parameters, such as current, feed rate and step siz e, are selected to analyse the forming quality of ripple disc, and the corresponding experimental scheme is shown in Table 1. In the siz ing stage, the heating method, namely electrically assisted integral heating, is different from the local heating method of forming stage. Therefore, a high-power Fig. 5. The forming strategy of the ripple disc Li, Z. – Di, X. – Gao, Z. – An, Z. – Chen, L. – Zhang, Y. – Lu, S. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 20-26 pulse power (current range of 0 A to 150 00 A) is adopted to realiz e the integral heating of sheet metal. C urrent values from 2200 A to 3000 A are separately used to heat the sheet, and the max holding time is 35 min in order to reduce the oxidation phenomenon of Ti-6A l-4V titanium alloy. Table 1. The forming experimental scheme of the ripple disc No. 1 2 3 4 5 6 7 8 Current [A] 75 202 220 350 220 220 220 220 Feed rate [mm/min] 900 900 900 900 300 1500 900 900 Step size [mm] 0.2 0.2 0.2 0.2 0.2 0.2 0.4 0.6 Fig. 6. The thermal imaging photo of the isothermal surface of parts 3 RESULTS AND DISCUSSION 3.1 Effect of Current Intensity on Forming Quality 2.2 Electrically Assisted Sizing Experiments The reference annealing temperature of Ti-6A l-4V titanium alloy is 600 ° C to 650 ° C , and the keep-warm time is 60 min to 240 min in the traditional annealing process. In the electrically assisted siz ing process, five current values, (2200 A, 2400 A, 2600 A, 2800 A, and 3000 A) are designed according to the traditional annealing process, and the isothermal surface of parts is viewed as a saturated temperature of the annealing process, as shown in F ig. 6. The corresponding saturated temperatures are 563.7 C, 5 3.6 C, 623.5 ° C , 652.3 ° C , and 684.1 ° C , respectively. Meanwhile, the heating time for the electrically assisted siz ing process should be less than the keep-warm time of the traditional annealing process due to the hightemperature oxidation defect of Ti-6A l-4V titanium alloy. Therefore, 10 min, 15 min, 20 min, 25 min, 30 min, and 35 min are respectively used to analyse the change of h, in which h is the warpage height of the part edge. C urrent [ A] C urrent: 75 A F our experimental groups (no. 1 to no. 4) are adopted to analyse the effect of current intensity on forming quality according to Table 1. The height (h) of the warpage is viewed as a major forming defect, and the crack and the bump are further used to estimate the feasibility of the parameters designed. F ig. 7 shows the effect of current intensities on forming defects, and the value of h increases with the increase of current intensity when the current intensity is less than 200 A. Meanwhile, the value of h is basically unchanged in the range of 202 A to 350 A, the springback is significant under the action of 75 A current, the crack is obtained under the action of 202 A current, and the bump is acquired under the action of 350 A current. According to the above analysis, the springback is a major defect when the current intensity is lower, and the interaction of thermal stress and springback is a major factor when the current value is greater than 200 A, in which the thermal stress is a main inducing factor of forming defects. Therefore, the current of C urrent: 202 A C urrent: 350 A Fig. 7. The effect of current intensity on forming defects Improvement of the Dimensional Accuracy of a Ti-6Al-4V Ripple Disc During Electric Hot Incremental Sheet Forming 23 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 20-26 220 A is a suitable current parameter in the EH IF of ripple disc. 3.2 Effect of Feed Rates on Forming Quality F ig. 8 shows the effect of feed rate on forming quality, in which the warpage of parts is both existent under the action of each feed rate. Meanwhile, the bump is obtained at the centre of parts when the feed rate is 300 mm/ min, which is caused due to the effect of thermal stress. The springback is significant under the action of 15 00 mm/ min feed rate because a large deformation resistance is obtained due to the fact that the forming temperature is lower than the other two experiments. Therefore, a feed rate of 00 mm/min is selected to fabricate the part according to the above analysis. 3.3 Effect of Step Size on Forming Quality Based on the current of 220 A and the feed rate of 00 mm/ min, three step siz es (0.2 mm, 0.4 mm, and 0.6 mm) are separately used to analyse the forming quality of parts. Fig. shows the effect of step size on forming quality, and the warpage of parts is still obtained in the three experiments. Meanwhile, the forming part a) would produce a crack under the action of 0.4 mm and 0.6 mm, and the crack increases with the increase of step siz e. The contact area between tools and sheets increases with the increase of step siz e, which leads to the actual forming temperature being less than the temperature planned. Therefore, the plasticity of materials is reducing with the increase of step siz e, and then the crack defect is easily obtained when the step siz e is large. 3.4 Improvement on Warpage Defect According to the aforementioned analysis, the combination of process parameters (220 A, 00 mm/ min, and 0.2 mm) is adopted to obtain a ripple disc without crack- and bump-defect. H owever, the warpage defect of the parts remains, and then an electrically assisted siz ing process is adopted to eliminate the defect. F ig. 10 shows the effect of siz ing current and time on h, in which the value of h is negatively correlated with time and current. The effect of siz ing time on h is less than that of the siz ing current. h is 30.6 mm under the interaction of 2200 A and 10 min to 15 min, and it is a maximum in siz ing experiments. In each current, the value of h from 20 min to 25 min is both b) c) Fig. 8. The effect of feed rates on forming defects; a) 300 mm/min, b) 900 mm/min, c) 1500 mm/min a) b) c) Fig. 9. The effect of step sizes on forming defects; a) 0.2 mm, b) 0.4 mm, c) 0.6 mm 24 Li, Z. – Di, X. – Gao, Z. – An, Z. – Chen, L. – Zhang, Y. – Lu, S. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 20-26 between 15 min and 30 min. Meanwhile, h of 2.1 mm is obtained under the interaction of 3000 A and 30 min to 35 min, and the value of h is far less than the blank holder distance (53.5 mm). According to Saint Venant’ s principle, the distribution of stresses or displacements in a structure remains nearly unchanged at a sufficiently distant point from the region of interest, as long as the external loads or boundary conditions remain the same. Therefore, an h of 2.1 mm has no influence on the dimensional accuracy of ripple disc according to the above principle. In addition to this, a long heating time can easily lead to the oxidation defect of Ti-6A l-4V titanium alloy. C onsequently, the setup of 3000 A and 30 min is an optimal combination of siz ing parameters, which can significantly eliminate the warpage defect caused by the forming stage. containing 3000 A and 30 min, is set to eliminate the warpage defect of ripple disc in the siz ing stage. N NT This work was supported by the N ational N atural Science F oundation of C hina (grant N o. 52205374 and 22272013) , and the Special Basic C ooperative R esearch P rograms of Yunnan P rovincial U ndergraduate U niversities’ Association (grant N o. 202101B A070001- 260 and 202101B A070001158) , and the F rontier R esearch Team of Kunming U niversity 2023, and the Scientific and Technological R esearch P rogram of C hongqing Science and Technology Bureau (grant N o. cstc2021j cyjmsxm2 10). 8 REFERENCES Fig. 10. Difference between different sizing parameters 4 CONCLUSIONS Aiming to eliminate the forming defect of ripple disc, a novel manufacturing scheme, namely the combination of EH IF and electrically assisted siz ing, is proposed to improve fabricating defects, such as crack, bump, and warpage. The crack and the bump are improved through optimiz ing process parameters in the forming stage, the warpage is an inherent forming defect of Ti6A l-4V ripple disc, and it is not eliminated through adjusting process parameters. Therefore, an optimal combination of forming process parameters, namely 220 A, 00 mm/min, and 0.2 mm, is selected to fabricate the part according to experimental analysis results. On this basis, the effect of siz ing current and time on h is further analysed in detail, and h is negatively correlated with time and current, and the effect of siz ing time on h is less than that of the siz ing current. F inally, the combination of siz ing parameters, [1] Bishnoi, P., Chandna, P. 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Licensee: SV-JME DOI:10.5545/sv-jme.2023.596 Original Scientific Paper Received for review: 2023-04-05 Received revised form: 2023-07-03 Accepted for publication: 2023-10-05 R oughness Parameters w ith Statistical Analys is and Modelling U sing Artificial Neural Netw orks After Finish Milling of Magnesium Alloys w ith D ifferent Edge H elix A ngle Tools Z agór ski, I. – Kulisz , M. – Sz cz epaniak, A. Ireneusz Z agór ski1,* – Monika Kulisz 2 – Anna Sz cz epaniak1 1 L ublin U niversity of Technology, Mechanical Engineering F aculty, P oland 2 L ublin U niversity of Technology, Management F aculty, P oland The paper presents the results of a study investigating the roughness parameters Rq, Rt, Rv, and Rp of finished-milled magnesium alloys AZ91D and AZ31B. Carbide end mills with varying edge helix angles were used in the study. Statistical analysis was additionally performed for selected machining conditions. In addition, modelling of selected roughness parameters on the end face for the AZ91D alloy was carried out using artificial neural networks. Results have shown that the tool with λs = 20° is more suitable for the finish milling of magnesium alloys because its use leads to a significant reduction in surface roughness parameters with increased cutting speed. Increased feed per tooth leads to increased surface roughness parameters. Both radial and axial depth of cut has an insignificant effect on surface roughness parameters. It has been proven that finish milling is an effective finishing treatment for magnesium alloys. In addition, it was shown that artificial neural networks are a good tool for the prediction of selected surface roughness parameters after finishing milling of the magnesium alloy AZ91D. Keywords: magnesium alloys, finish milling, roughness, surface quality, statistical analysis, artificial neural networks Highlights • Finish milling of magnesium alloys AZ31B and AZ91D is an effective kind of machining method. • The surface roughness (Rq, Rt, Rv, and Rp) depends on the geometry of the different edge helix angles. • The tool with λs = 20° is more suitable for the finish milling of magnesium alloys. • The change of cutting speed vc and feed per tooth fz has a significant influence on the surface roughness parameters during finish milling. • Both the radial and axial depths of cut (ae and ap) have an insignificant effect on surface roughness parameters. • Artificial neural networks are a good tool for the prediction of selected surface roughness parameters after finishing milling of the magnesium alloy AZ91D. 0 INTRODUCTION The machinability of a material is described by machinability indices, one of which is surface quality. G eometric structure is defined as the general surface condition, and it is the end result of the technological process for a given workpiece. The geometric structure consists of all surface texture irregularities that are formed due to material wear and machining. The evaluation of the condition of this structure includes considering shape deviations, waviness, and surface roughness. To compare and verify surface roughness requirements for constructional materials after machining, studies use parameters describing surface conditions in quantitative terms. These include two-dimensional (2D) and 3D surface roughness parameters, where 2D measurements are made on the profile, i.e., in the cross-section of a given workpiece, and 3D measurements, known as stereometric, are made on the surface. The fundamental and most widely analysed surface roughness parameter is R a; however, surface roughness evaluation that is based on this parameter only is far from being exhaustive. The R a parameter is widely used in industry even though it does not provide data about many significant roughness profile features. Therefore, additional parameters must be considered, such as R q , R t, R v, and R p. The R q parameter is usually considered together with R a, with the value of R q being greater than the value of R a (by approx. 25 % for random profiles). This relationship for random profiles can be expressed as R q 1.25 R a [1]. Another common parameter used for surface quality evaluation is the maximum height of the profile, R z . G iven the fact that single profile peaks and valleys are partly taken into account, this parameter should primarily be analysed for bearing or sliding surfaces and measurement areas [1] and [2]. The R z parameter is often analysed together with another surface roughness parameter, R t. These two parameters should also be analysed in combination with other parameters such as R p (maximum profile peak height) and R v (maximum profile valley depth). The R t parameter (total height of profile) may affect *Corr. Author’s Address: University of Technology, Mechanical Engineering Faculty, Department of Production Engineering, Nadbystrzycka 36, 20-618 Lublin, Poland, i.zagorski@pollub.pl 27 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 27-41 the so-called functional properties of a given surface (e.g., fatigue strength, wear and tear, lubrication etc.) [3]. This parameter is the vertical distance between the maximum profile peak height and the maximum profile valley depth along the evaluation length between (it belongs to the group of so-called amplitude parameters). The R p parameter provides information about, e.g., profile shape. Moreover (by analysing the R p parameter), it is possible to assess the surface in terms of abrasion resistance. A surface with poor abrasion resistance is characteriz ed by high values of R p compared to R v. Depending on the values of R p and R z and their ratio, it is possible to obtain data about profile shape and, thus the abrasion resistance of the analysed surface. If the R p/ R z ratio considerably exceeds a value of 0.5, this means that the profile has sharp peaks and the surface is less abrasion-resistant. The use of the above parameters is recommended for evaluating sliding surfaces, bearings, and pre-coated surfaces, as well as for analysing close fits in terms of shrink behaviour [1] and [3]. Measurements and research of surface roughness parameters are important due to such surface features as friction and wear, lubrication, assembly tolerances, contact deformations, load capacity, contact stresses and other surface features related to the physical or functional properties of a given surface. P revious studies on the machinability of materials by milling have predominantly investigated the surface roughness parameter R a. A comparison of machining methods and evaluated roughness parameters used in previous studies is given in Table 1. Table 1. Comparison of machining methods and roughness parameters under evaluation in milling of magnesium alloys Machining method milling milling high-speed dry face milling dry milling and low plasticity burnishing milling milling dry end milling dry milling and low plasticity burnishing milling dry face milling milling milling face milling (DRY, MQL) high speed milling dry milling by air pressure coolant milling precision milling Roughness parameters Ra, Rq, Rz, RzDIN, Rt, Ry, RSm Ra Ra Ra Ra Ra Ra Ra, Rt, Rv, Rp Rku, Rsk, RSm, Sa, Sv, Sp, St, Ssk, Sku Ra Ra, Sa, RSm, Ssk, Sku Ra Sa Ra Ra Ra Ra, Rv, Rp, Rt, Rvk, Rk, Rpk Summing up, surface roughness analysis is particularly important in terms of the quality of finished components of machines and devices. L ight alloys, including magnesium and aluminium alloys [21] and [22], occupy a special place among construction materials. Surface quality and roughness are even more important when it comes to finishing treatments and operations. Therefore, it seems that the finish milling of light alloys (aluminium and magnesium) is significant not only from the practical and implementation-related points of view but also due to knowledge-related reasons, as there is a lack of comprehensive studies devoted to this problem. 28 Material / Alloy grade AZ91D/HP Mg-SiC/B4C Mg-Ca0.8 Mg-Ca0.8 Mg-Ca0.8 Mg-Ca1.0 AM60 Mg-Ca0.8 AZ91D ZE41 AZ91D AZ61 AZ61 AZ91D AZ31B AZ91D AZ91D Year 2016 2017 2010 2011 2018 2017 2017 2011 2019 2018 2021 2017 2019 2016 2010 2016 2023 Reference [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] 1 METHODS The objective of this study was to evaluate the surface roughness of two magnesium alloys, A 1D and AZ 31, after milling depending on the value of the technological parameters and tools with variable helix angle. The employed research scheme is shown in F ig. 1. Milling was conducted on the vertical machining centre AVIA VMC 800H S with H eidenhain iTN C 530 control and maximum spindle speed of 24000 [ rev/ min] . In the study, we used two carbide 3- edge end mills with a diameter of 16 mm and a variable helix angle λs (λs = 20° , λs = 50° ). U sing the ISG 2200 Zagórski, I. – Kulisz, M. – Szczepaniak, A. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 27-41 shrink-fit machine from H . Diebold G mbH & C O (Jungingen, G ermany), the end mills were mounted in the CELSIO HSK-A63 16 5 tool holder from SC H U N K (L auffen am N eckar, G ermany). According to the ISO 21 40 11:2016 standard [23], the tool with the tool holder was balanced to G 2.5 (residual unbalance was 0.25 g mm) with a C IMAT R T 610 balancing machine (Bydgosz cz , P oland). The milling process was conducted using the following ranges of technological parameters: cutting speed vc = 400 m/ min to 1200 m/ min, feed per tooth f z = 0.05 mm/ tooth to 0.3 mm/ tooth, axial depth of cut ap = 0.1 mm to 0.5 mm, radial depth of cut ae = 0.5 mm to 3.5 mm. The following surface roughness parameters were analysed: R q , R t, R v, and R p. Surface roughness measurements were made on both lateral and end faces with the use of a contact-type roughness tester, H OMMEL TESTER T1000, from ITA-K. P ollak, M. W iecz orowski Sp. J. (Pozna , Poland). The measurement parameters were as follows: total measuring length l t = 4.8 mm, sampling length l r = 0.8 mm, a) b) c) Fig. 1. Research scheme: a) the test set-up, b) the measurement equipment (end mill, milling machine and 2D profilographometer), and c) milling visualization with the roughness measurement model with end face and lateral face on the workpiece surfaces Roughness Parameters with Statistical Analysis and Modelling Using ANN After Finish Milling of Magnesium Alloys with Different Edge Helix Angle Tools 29 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 27-41 scanning speed vt = 0.5 mm/ s and measuring range/ resolution M = ± 320 µ m (range) / 0.04 µ m (resolution). Every measurement was repeated five times per each surface. Data from surface roughness measurements were subjected to statistical verification. The assumed level of significance was α = 0.05. There exist several criteria that must be taken into account when selecting a statistical test. In this study, output data were treated as independent quantitative variables. As shown in the scheme, results of the Shapiro-W ilk test for checking the normality of distribution were used to decide whether further tests had to performed. If the normal distribution was not confirmed, the nonparametric Mann-W hitney U test was performed. If the z ero hypothesis saying that “ the distributions are not different from the normal distribution in a statistically significant way” was accepted, the significance of differences had to be assessed by one of two parametric tests: Student’ s t-test or C ochran’ s Q test. The test type was selected by assessing the equality of variances, which was made based on the results of L evene’ s test and the Brown and F orsythe test. It should be noted that the selected test type and the end result depended on the p-value. All statistical tests were conducted using Statistica 13 [24] and [25]. N ext, the modelling of selected roughness parameters (R q and R t) on the face of the magnesium alloy A 1D after finishing milling was carried out with variable helix angle λs (λs = 20° , λs = 50° ) using Matlab software. The input parameters for network learning were machining parameters such as cutting speed vc = 400 m/ min to 1200 m/ min, feed per tooth f z = 0.05 mm/ tooth to 0.3 mm/ tooth and axial depth of cut ap = 0.1 mm to 0.5 mm. At the output from network learning, the appropriate roughness parameter (R q , R t) was obtained for the specified tool (λs = 20° , λs = 50° ). A shallow neural network with one hidden layer was used for modelling. The learning algorithm L evenberg-Marquardt was used. The number of neurons was selected experimentally in the range of 5 to 10. The dataset was split in a proportion of 80 % : 20 % (for training and validation data, respectively) putting aside the test set due to the small amount of data. N etwork quality was assessed based on the value of the correlation coefficient R , Mean Squared Error (M SE ) and root mean square error (R M SE ). The correlation coefficient R that was calculated in accordance with the Eq. (1) : Fig. 2. Statistical test selection scheme [20] 30 Zagórski, I. – Kulisz, M. – Szczepaniak, A.   R y , y*   cov y , y*  y  y* , (1 ) Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 27-41 where σy is the standard deviation of values of the analysed roughness parameter obtained as a result of experimental tests, σy* standard deviation of values obtained as a result of the model predicting the value of the analysed roughness parameter. R is a real number in the interval between 0 and 1. In addition, the value of the MSE, calculated according to Eq. (2), was taken into account: MSE   1 n   y i  yi n n 1 , 2 (2) as well as R MSE, calculated according to the Eq. (3) : RMSE   1 n   y i  yi n n 1 , 2 (3) where yi is value of the analysed roughness parameter obtained as a result of experimental tests and y i is values obtained as a result of the model predicting the value of the analysed roughness parameter. 2 EXPERIMENTAL RESULTS AND DISCUSSIONS This section of the paper presents experimental results of surface roughness evaluation for two magnesium alloys: A 1D and A 31, obtained with the use of tools with varying helix angles (λs = 20° , λs = 50° ). The surface roughness of AZ 31 was evaluated for the extreme values of the technological parameters. F ig. 3 shows the relationship between cutting speed vc and surface roughness parameters. It can be a) b) c) d) e) f) Fig. 3. Cutting speed versus surface roughness parameters: a) R q of AZ91D, b) R q of AZ31 c) R t of AZ91D, d) R t of AZ31, e) R v, R p of AZ91D, f) R v, R p of AZ31; f z = 0.15 mm/tooth, lateral face: ae = 2 mm, ap = 8 mm, end face: ae = 14 mm, ap = 0.3 mm Roughness Parameters with Statistical Analysis and Modelling Using ANN After Finish Milling of Magnesium Alloys with Different Edge Helix Angle Tools 31 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 27-41 observed that the milling process for A 1D alloy conducted with the cutting speed vc ranging from 600 m/ min to 1 200 m/ min results in a clear decrease in the values of R q and R t with increasing the cutting speed. The surface roughness parameters only increased on the lateral face after milling with the λs = 50 ° tool and increasing the cutting speed value from vc = 800 m/ min to 1000 m/ min. It should be stressed that the surface roughness parameters are lower on the lateral face. The lowest values of these parameters were obtained with λs = 50° at vc = 1200 m/ min (R q = 0.2 m, R t = 2.02 m). The lowest values of the parameters were obtained with λs = 50° on the end face for the milling process conducted with vc = 600 m/ min (R q = 5.54 m, R t = 18.04 m). The values of a) c) e) 32 R v and R p on the lateral face are similar for all tested cutting speeds and range from 0.8 m to 3.44 m. On the end face the parameters R v and R p clearly decreased with increasing the cutting speed and their values range 3.2 m to .61 m. An increase in cutting speed leads to decreased values of the surface roughness parameters R q , R t, R v and R p for both A 1D and A 31. The greatest differences between these surface parameters can be observed on the end face for the λs = 50° tool. The parameter R q value decreased by 3.14 m and that of R t by 13.87 m. Regarding the parameters R v and R p, increasing the cutting speed from 400 m/ min to 120 0 m/ min had the greatest impact on these parameter b) d) f) Fig. 4. Feed per tooth f z versus surface roughness parameters: a) R q of AZ91D, b) R q of AZ31, c) R t of AZ91D, d) R t of AZ31, e) R v, R p of AZ91D, f) R v, R p of AZ31; vc = 800 m/min, lateral face: ae = 2 mm, ap = 8 mm, end face: ae = 14 mm, ap = 0.3 mm Zagórski, I. – Kulisz, M. – Szczepaniak, A. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 27-41 values on the end face for the λs = 50° tool, the value of R v decreased by 6.57 µ m and that of R p by 7.3 µ m. C omparing, for example, the machinability of both magnesium alloys for the highest cutting speed value, it can be seen that for the R q parameter, a lower value roughness was obtained on the end face for the AZ 31B alloy (R q = 1.45 m), while for the A 1D alloy (R q = 1.67 m). F ig. 4 shows the relationship between feed per tooth f z and surface roughness parameters. R egardless of the tool used, increased feed per tooth has no significant effect on the surface roughness parameters on the lateral face of magnesium alloy A 1D, and the values of these parameters range as follows: R q 0.32 µ m to 0.72 µ m, R t 1. 5 m to 4.28 m, R v 0. 6 m to 1. 4 m, R p 0. m to 2.45 m. However, the roughness parameters show a sudden increase on the end face with increasing the feed per tooth value from f z = 0.05 mm/ tooth to f z = 0.1 mm/ tooth. In the range f z = 0.1 mm/ tooth to –0.3 mm/ tooth, the feed per tooth increases. The highest values of the surface roughness parameters were observed for f z = 0.3 mm/ tooth. The highest values of R q = 3.5 m and R t = 15. 1 m are obtained on the end face for λs = 50° at f z = 0.3 mm/ tooth. Moreover, for the feed per tooth range f z = 0.1 mm/ tooth to 0.25 mm/ tooth (λs = 50, end face), the values of R p are higher than those of R v, which means that the surface has poor abrasion resistance [1]. R egarding magnesium alloy AZ 31, increased feed per tooth results in a slight increase in the values of R q and R t. The values of R q and R t range: R 0.17 m to 0.65 m and R t 1.25 m to 3.77 m. F or λs = 20° , the values of the parameters R q and R t are higher on the end face, both at vc = 400 m/ min (R q = 1.08 m, R t = 5.18 m) and at vc = 1200 m/ min (R q = 1. m, R t = 8. 6 m). Increasing the feed per tooth value from 0.05 mm/ tooth to 0.3 mm/ tooth also causes an increase in the values of R v and R p. The highest values are obtained on the end face with the λs = 20° tool, both at f z = 0.05 mm/ tooth (R v = 2.41 m, R p = 2.76 m) and at f z = 0.3 mm/ tooth (R v = 3.58 m, R p = 5.21 m). C omparing both magnesium alloys on the example of the results for the R q parameter, it can be seen that at f z = 0.3 mm/ tooth (similarly to the cutting speed analysis) a lower value of the R q parameter was recorded on the end face for the AZ 31B alloy (R q = 1. m), than for A 1D alloy (R q = 2.17 m). F ig. 5 illustrates the relationship between axial depth of cut and surface roughness parameters. F or alloy A 1D, no significant changes in the parameters R q , R t, R v, R p are observed in the entire tested axial depth of cut range. The values of the surface roughness parameters are similar and range as follows: for λs = 20° : R q (1.8 m to 2.13 m), R t (8.43 m to 10. m), R v (3. 7 m to 4.66 m), R p (4.47 m to 6.53 m), and for λs = 50° : R q (1.6 m to 3.36 m), R t (8.56 m to 12. m) R v (3. 6 m to 5.57 m), R p (4.71 m to 7.33 m). However, it should be noted that the differences between the values of the above parameters depending on the tool can particularly be observed for ap = 0.2 mm to 0.5 mm. The results demonstrate that the above axial depth of cut range leads to higher values of R p compared to R v. The increased axial depth of cut has no significant effect on the surface roughness parameters of both A 1D and A 31. It is noteworthy that the roughness parameters obtained with the λs = 50° tool are smaller than the values of these parameters obtained after milling with the λs = 20° tool (AZ 31) . An inverse relationship can be observed by analysing the change in the axial depth of cut on the end face, the value of the R q parameter in the conditions when ap = 0.5 mm, for the AZ 31B alloy is higher (R q = 1. m), than for the A 1D alloy (R q = 1.81 m). F ig. 6 shows the relationship between the radial depth of cut ae and surface roughness parameters. The results demonstrate that the radial depth of cut has no significant effect on the roughness parameters R q , R t, R v, R p of both A 1D (λs = 20° ) and AZ 31 (λs = 20° and λs = 50° ). The obtained values are similar and range as follows: R q (0.53 m to 0.73 m), R t (2.4 m to 4.24 m), R v (1.08 m to 2.07 m), R p (1.53 m to 2.17 m). In contrast, for the tool with λs = 50° one can observe a sharp increase in the values of R q (by 2.56 m) and R t (by 13.3 m), R v (by 6.5 m), R p (by 6.8 m) when the radial depth of cut value is changed from ae = 1.5 m m to 2.5 m m. Similarly, analysing the radial depth of cut on the end face, it can be seen that for ae = 3.5 mm, the machining results are better (lower value of the R q parameter) for the A 1D alloy (R q = 0.56 m), while for the AZ 31B alloy (R q = 0.70 m). Thus, comparing the results obtained using carbide cutters for roughing and the analysis of the surface of the end face of the workpiece A 1HP/D [4] and [12], the following conclusions can be drawn: when employing a carbide cutter coated with titanium aluminium nitride (TiAlN ), higher values of the parameters R q , R p, and R v were recorded, specifically: 1. for the variable parameter vc , the parameters R v and R p range between 6.8 m to 8.32 m, while the parameter R t spans from 14.24 m to 17.72 m; Roughness Parameters with Statistical Analysis and Modelling Using ANN After Finish Milling of Magnesium Alloys with Different Edge Helix Angle Tools 33 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 27-41 a) b) c) d) e) f) Fig. 5. Axial depth of cut ap versus surface roughness parameters: a) R q of AZ91D, b) R q of AZ31 c) R t of AZ91D, d) R t of AZ31, e) R v, R p of AZ91D f) R v, R p of AZ31; vc = 800 m/min, f z = 0.15 mm/tooth, ae = 14 mm 2. considering the variable parameter f z , the parameters R v and R p lie within the spectrum of 1. 4 m to 15.84 m, with the parameter R t standing at 4 m to 31.04 m; for the variable parameter ap, the values of R v and R p present remarkable similarity, recorded within the interval of 5.26 m to 7.78 m, and for R t the values range from 12.02 m to 24.82 m; in instances of machining with cutters of diverse blade geometry (different rake angles γ), the parameters R q and R t were investigated: for the variable parameter vc , the parameter R q did not surpass 4 m, with R t recorded within the range of 10 m to 15 m, in relation to the variable parameter f z , the R q parameter ascends to a maximum value of 3. 1. 2. 34 approximately 3 m, with the R t parameter spanning from 10 m to 15 m, 3. concerning the variable parameter ap, the R q parameter consistently approximates 3 m, while the value of R t does not exceed approximately 1 5 m. Therefore, these values are much higher than those observed in the present experiment. This is due to the larger cross-sections of the cutting layer obtained during roughing. H owever, as the literature lacks a broader analysis of surface roughness parameters, especially after finishing machining while roughing mainly analyses the basic surface roughness parameters (usually mainly R a), it seems advisable to extend the state of knowledge in this area. Zagórski, I. – Kulisz, M. – Szczepaniak, A. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 27-41 a) b) c) d) e) f) Fig. 6. Radial depth of cut ae versus surface roughness parameters: a) R q of AZ91D, b) R q of AZ31, c) R t of AZ91D, d) R t of AZ31, e) R v, R p of AZ91D, f) R v, R p of AZ31; vc = 800 m/min, f z = 0.15 mm/tooth, ap = 8 mm 3 STATISTICAL ANALYSIS The experiments were followed by statistical analysis. Significance tests were performed to determine if the following technological parameters: cutting speed vc , feed per tooth f z , axial depth of cut ap and radial depth of cut ae affected the mean values of surface roughness parameters. The statistical analysis made it possible to determine whether the differences were statistically significant for the assumed level of confidence. H ypotheses were tested taking account of the extreme values of the technological parameters, i.e., cutting speed vc = 400 m/ min, and 1200 m/ min, feed per tooth f z = 0.05 mm/ tooth, and, 0.3 mm/ tooth, axial depth of cut ap = 0.1 mm, and 0.5 mm, radial depth of cut ae = 0.5 mm, and 3.5 mm. In this paper, we report the final test results, i.e. the median and mean values from the tests. F ig. 7 shows an example of results obtained by the Student’ s t-test for the z ero hypothesis of normal distribution and the equality of variance hypothesis. Tables 2 and 3 give the results of the MannW hitney U test, Student’ s t-test, and C ochran’ s Q test. The results make it possible to statistically assess the significance of differences between the mean and median values obtained for the compared groups. The statistical analysis results demonstrate that, irrespective of the magnesium alloy grade, for the tool with λs = 20° increased cutting speed has, in most cases, the greatest impact on the mean and median values of the surface roughness parameters. F eed per tooth also has a significant impact on the surface roughness parameters for the tool with Roughness Parameters with Statistical Analysis and Modelling Using ANN After Finish Milling of Magnesium Alloys with Different Edge Helix Angle Tools 35 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 27-41 Fig. 7. Student’s t-test results Table 2. Results of Mann-Whitney U test, Student’s t-test, Cochran’s Q test for the roughness parameters of magnesium alloy AZ91D after milling λs = 20° Lateral face p-value End face p-value vc R q R t R v R p Table 3. Results of Mann-Whitney U test, Student’s t-test, Cochran’s Q test for the roughness parameters of magnesium alloy AZ31 after milling λs = 50° Lateral face p-value λs = 20° End face p-value Lateral face p-value [m/min] 400 vs. 1200 vc R t R v R p End face p-value [m/min] 400 vs. 1200 0.01354 0.09172 0.00124 R q 0.00794* 0.00093 0.00362 0.00088 0.00794* 0.00384 0.18904 0.00794* 0.000004 0.00287 0.159 0.00443 0.15079* 0.06089 0.22089 0.00794* 0.00018 0.00126 0.35012 0.00435 0.00009 0.21357 0.00794* R t R v R p 0.02907 0.19048* 0.00507 0.01587* 0.00003 f s [mm/tooth] 0.05 vs. 0.3 0.22222* 0.00466 0.03175* 0.00004 R q 0.00813 0.00022 0.01372 1* 0.00902 0.06349* 0.00028 0.01587* 0.00953 0.07128 0.51158 0.84127* 0.0007 0.06349* 0.00794* 0.05556* 0.00052 0.15926 0.966295 0.78555 0.03114 0.03175* 0.00422 R t R v R p 0.00794* 0.054187 0.02645 0.278767 ae [mm] 0.5 vs. 3.5 ae [mm] 0.1 vs. 0.5 ae [mm] 0.5 vs. 3.5 ae [mm] 0.1 vs. 0.5 ae [mm] 0.5 vs. 3.5 ae [mm] 0.1 vs. 0.5 ae [mm] 0.5 vs. 3.5 ae [mm] 0.1 vs. 0.5 0.06349* R q 0.17048 0.95209 0.00149 0.0001 R q R t R v R p 0.35526 0.69048* 0.00103 0.00536 0.43513 0.40148 0.00282 0.150794* R t R v R p 0.27617 0.97658 0.01587* 0.03102 * Mann-Whitney U test for checking the equality of the medians 36 λs = 50° Lateral face p-value 0.0008 f s [mm/tooth] 0.05 vs. 0.3 R q End face p-value 0.13088 0.3862 0.77097 0.76164 0.84127* 0.42063* 0.61483 0.12539 0.38109 0.55077 0.94354 0.195110 0.12928 0.92479 0.42396 0.087671 * Mann-Whitney U test for checking the equality of the medians Zagórski, I. – Kulisz, M. – Szczepaniak, A. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 27-41 λs = 20° . The only exception are the results obtained for the lateral end of A 1D, as they show that changing the feed per tooth value from 0.05 mm/ tooth to 0.3 mm/ tooth does not result in statistically significant differences between the values of the surface roughness parameters. The opposite can be observed for the tool with λs = 50° , where the p-values are either smaller than the assumed confidence level or verge on the statistically significant limit. For alloy A 1D, the differences in the mean and median values of the surface roughness parameters are affected by the radial and axial depth of cut, and depend on the tool. F or alloy AZ 31, irrespective of the tool used, the radial and axial depth of cut has no effect on the mean and median values of the surface roughness parameters R q , R t, R v, R p (on the statistical level). N T N U N T Artificial neural networks were trained for the magnesium alloy A 1D in order to build four models showing the relationship between the technological parameters (cutting speed vc , feed per tooth f z and axial depth of cut ap) and the predicted roughness on the face surface of the R q and R t parameters, respectively, after machining with the tool with variable helix angle (λs = 20° , λs = 50° ). Approximately 100 networks were trained for each model. The quality of the obtained models was assessed on the correlation coefficient R , value of M SE and R M SE . Table 4 presents four different models obtained from an artificial neuron network (AN N .) The best modelling results for the R q and R t parameters after machining with a tool with a helix Table 4. Network parameters Model No. Roughness parameter 1 R q R t R v R p 2 3 4 a) c) Helix angle λs 20 50 M SE R M SE R training data set R validation data set 0.0022 0.0467 0.99999 0.99029 R all data set 0.99563 0.1058 0.3252 0.99999 0.9989 0.99358 0.0193 0.1391 0.99999 0.96648 0.99263 0.3424 0.5851 0.99999 0.95309 0.98741 b) d) Fig. 8. ANN best training performance for a) parameter R q , λs = 20°, b) parameter R t, λs = 20°, c) parameter R q , λs = 50°, d) parameter R t, λs = 50° Roughness Parameters with Statistical Analysis and Modelling Using ANN After Finish Milling of Magnesium Alloys with Different Edge Helix Angle Tools 37 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 27-41 angle λs = 20° were obtained for the network with 10 neurons in the hidden layer. The network for the R q parameter was obtained in five iterations, and for the R t parameter in ten iterations. In the case of the tool with the helix angle λs = 50° , for the R q parameter, it was also a network with 10 neurons (obtained in 6 iterations), and for the R t parameter a network with eight neurons in the hidden layer (obtained in 5 iterations). The best validation performance was obtained respectively for iteration 5 (for R q parameter when machined with helix angle λs = 20° ), which is shown in F ig. 8a , for iteration 6 (for R t parameter when machined with helix angle λs = 20° ); F ig. 8b, for iteration 10 (for the R q parameter when machining a) with a helix angle λs = 50° ); F ig. 8c and for iteration 5 (for the R t parameter when machining with a helix angle λs = 50° ); F ig. 8d. AN N regression statistics for individual sets and the total set was presented in Fig. . Respectively for parameter R q when machining with tool with helix angle λs = 20 ; Fig. a, for parameter R t when machining with tool with helix angle λs = 20 ; Fig. b, for parameter R q when machining with tool with helix angle λs = 50 ; Fig. c and for parameter R t when machining with tool with helix angle λs = 50 ; Fig. d. Taking into account the quality of the presented models measured by the level of M SE , R M SE and the R value (R in each case is a value greater than 0. 5), b) c) d) Fig. 9. ANN regression statistics for individual sets and the total set: a) parameter R q , λs = 20°, b) parameter R t, λs = 20°, c) parameter R q , λs = 50°, c) parameter R t, λs = 50° 38 Zagórski, I. – Kulisz, M. – Szczepaniak, A. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 27-41 a) b) Fig. 10. Simulation results of the R q surface roughness parameter after machining with tool with helix angle λs = 20° a) for the vc and f z , and b) for the vc and ap a) b) Fig. 11. Simulation results of the R t surface roughness parameter after machining with tool with helix angle λs = 20° a) for the vc and f z , and b) for the vc and ap a) b) Fig. 12. Simulation results of the R q surface roughness parameter after machining with tool with helix angle λs = 50° a) for the vc and f z , and b) for the vc and ap Roughness Parameters with Statistical Analysis and Modelling Using ANN After Finish Milling of Magnesium Alloys with Different Edge Helix Angle Tools 39 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 27-41 a) b) Fig. 13. Simulation results of the R t surface roughness parameter after machining with tool with helix angle λs = 50° a) for the vc and f z , and b) for the vc and ap it can be concluded that the presented AN N models show an acceptable level of error and can be used to predict approximate values of roughness parameters. The simulation results of the appropriate roughness parameters R q / R t of the A 1D alloy for the appropriate tool with helix angle λs = 20° , and 50° , for the assumed range of cutting speed vc , feed per tooth f z and axial depth of cut ap parameters are shown in F igs. 10 to 13. The simulation results for each model are presented in two graphs, depending on cutting speed vc and feed per tooth f z or cutting speed vc and axial depth of cut ap. 5 CONCLUSIONS The experimental and statistical analysis results of the study leads to the following conclusions: for the λs = 20° tool increased cutting speed leads to a considerable decrease in surface roughness parameters, whereas for the tool with λs = 50° increased cutting speed has no significant effect on lateral face surface roughness parameters; increased feed per tooth leads to increased surface roughness, which was particularly visible when the feed per tooth f z = 0.05 mm/ tooth was changed to f z = 0.1 mm/tooth for A 1D alloy; irrespective of the magnesium alloy grade, for the tool with λs = 20° both axial and radial depth of cut has an insignificant effect on surface roughness parameters; the statistical analysis results show that for the tool with λs = 20° increased cutting speed has, in most cases, the greatest effect on the mean and 40 median values of the roughness parameters for both A 1D and A 31; the statistical analysis results for the tool with λs = 50° show that the roughness parameters of magnesium alloy A 1D are most affected by varying feed per tooth as well as axial and radial depth of cut; as a result of modelling the R q and R t parameters after machining with a variable helix angle λs tool (λs = 20° , λs = 50° ), the best models were obtained primarily for the network with 1 0 neurons in the hidden layer, only in the case of the R t parameter with helix angle λs = 50° the best model had 8 neurons in the hidden layer; networks obtained as a result of modelling surface roughness parameters show a satisfactory predictive ability, as evidenced by the obtained regression values R : R q (λs= 20° ) = 0. 563, R t(λs= 20° ) = 0. 358, R q (λs= 50° ) = 0. 263 and R t(λs= 50° ) = 0. 8741; as a result of the conducted modelling of neural networks, it can be concluded that they are an effective tool that can be used to predict surface roughness parameters. 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Statsoft Polska, Kraków, p. 75-86. Montgomery, D.C., Runger, G.C. (2003). Applied Statistics and Probability for Engineers. o n iley ons, nc., oboken. Roughness Parameters with Statistical Analysis and Modelling Using ANN After Finish Milling of Magnesium Alloys with Different Edge Helix Angle Tools 41 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 42-54 © 2024 The Authors. CC BY 4.0 Int. Licensee: SV-JME DOI:10.5545/sv-jme.2023.692 Original Scientific Paper Received for review: 2023-06-15 Received revised form: 2023-10-02 Accepted for publication: 2023-11-15 Multi-performance O ptimiz ation of the R otary T urning O peration for Environmental and Q uality I ndicators Doan, T.-K. – N guyen, T.-T. – Van, A.-L . Tat-Khoa Doan1 , Trung-Thanh N guyen1 , An-L e Van2,* 1 L e Q uy Don Technical U niversity, F aculty of Mechanical Engineering, Vietnam guyen Tat Thanh U niversity, F aculty of Engineering and Technology, Vietnam 2N In this investigation, two environmental metrics (the comprehensive energy used (TU) and turning noise (TN)) and a quality metric (surface roughness (SR)) of the rotary turning process for the Ti6Al4V were optimized and reduced using the optimal factors (the inclined angle-i, depth of cut-d, feed-f, and turning speed-V). The TU model was proposed comprising the embodied energy of the insert and lubricant. The method based on the removal effects of criteria (MEREC), an improved quantum-behaved particle swarm optimization algorithm (IQPSO), and TOPSIS were applied to select weight values and the best optimal solution. The machining cost (MC) was proposed in terms of process parameters. The outcomes presented that the optimal values of the i, d, f, and V were 35 deg., 0.30 mm, 0.40 mm/rev., and 190 m/min, respectively, while the TU, SR, TN, and MC were saved by 6.7 %, 22.3 %, 23.5 %, and 8.5 %, respectively. The turning responses were primarily affected by the feed rate and turning speed, respectively. The developed turning process could be employed for machining hard-to-cut alloys. The developed approach could be applied to deal with optimization problems for other machining operations. Keywords: rotary turning, total energy consumption, surface roughness, noise emission, IQPSO Highlights • A new rotary turning tool was designed and fabricated. • Process parameters, including the spindle speed, depth of penetration, feed rate, and inclination angle were optimized. • The total energy consumption, surface roughness, and turning noise were enhanced. • An improved quantum-behaved particle swarm optimization algorithm was proposed. 0 INTRODUCTION The machining operation using rotary inserts is an effective solution to deal with hard-to-cut materials. The cutting temperature, force components, and pressure at the nose are reduced with the support of the rotational motion of the round piece. Additionally, a higher tool life is obtained due to the even distribution of the cutting temperature, leading to higher productivity and quality indicators, as compared to the conventional processes. Different milling and turning operations having rotary inserts have been developed and optimiz ed by many investigators. Karaguz el et al. [1] indicated that the rotary turning and milling processes provide 10- and 40-times longer tool life than conventional operations. The optimal cutting speed, feed, depth of cut, and inclination angle were selected to decrease the surface roughness and improve the material removal rate [2]. The ultrasonic vibration-based rotary turning was developed to machine decrease the machining forces and average roughness of the turned AA 7075 [3]. The results indicated the tool speed of 8.63 m/ min and the feed of 0.08 mm/ min were optimal data. A simulation model was developed to predict the tool wear in the rotary turning [4]. The authors stated that the tool wear was effectively decreased due to the 42 disengagement duration. The energy efficiency and surface roughness were enhanced by 8. and 24.8 % , respectively using the optimal process parameters [5]. N guyen emphasiz ed that the energy consumption, surface roughness, and material removal rate of the turned SKD1 1 were affected by the speed, feed, depth of cut, and inclination angle [6]. U mer et al. indicated that an increased speed and/ or depth caused a higher temperature of the turned 51200 steel [7]. Ahmed et al. stated that surface roughness and tool wear of the turned AISI 4140 were decreased by 24.6% and 32 .6 % , respectively using optimal process parameters [8]. N ieslony et al. [9] indicated that a higher speed caused a decrease in the surface roughness and a stable turning operation, while an increased depth led to a higher intensity of the vibration. A rotary milling process was developed to machine the titanium alloy, in which a low speed was recommended to reduce the tool wear rate [10]. Ahmed et al. [11] emphasiz ed that low process parameters (speed, feed, and depth of cut) and high inclination angle decreased the temperature of the rotary turning. Similarly, C hen et al. [12] emphasiz ed that the surface roughness produced by the rotary process was lower than the conventional one. A novel simulation model was developed to forecast the temperature of the turned nickel and titanium alloys [13]. The authors stated that low process parameters *Corr. Author’s Address: Nguyen Tat Thanh University, 300A Nguyen Tat Thanh, Ho Chi Minh, Vietnam, lvan@ntt.edu.vn Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 42-54 (speed, feed, and depth of cut) and high inclination angle decreased the temperature. U mer et al. [14] revealed that a lower depth of cut was recommended to reduce the temperature and forces. The total energy consumed and machining time of the turned SKD61 were decreased by 1 7.0 % and 17.8 % , respectively, using the optimal factors [15]. Additionally, the carbon emission of the rotary turning operation was reduced by 5.0 % using the P SO [16]. H e et al. revealed that the cutting temperature of the turned K417 alloy decreased with a higher inclination angle and cutting speed [17]. H owever, the shortcomings of the aforementioned works can be expressed as follows. An efficient self-propelled rotary tool having high stiffness to machine high-hardness steels has not been designed and fabricated to replace the fixed turning one. L ow rigidity is a primary drawback of the proposed tools in previous publications. The noise emission damages the inner ear and causes occupational hearing loss as well as chronic stress; hence, minimiz ing the sound intensity of the rotary turning operation is a necessary requirement. Moreover, the optimal process variables have not been determined to make reductions in energy consumed, roughness, and noise emission. The next section presents the framework. The experimental setting and discussions are then shown. F inally, the obtained findings are drawn. a) b) Fig. 1. The concept of the rotary turning process; a) the schematic principle, and b) the fabricated rotary tool (1. the screws; 2. the bolts; 3. the round insert, 4. the base; and 5. the holder) The E C is computed as: TE  Est  Esb  Etn  Eat  Et  Etc , (2) where E st, E sb , E tn , E at, E t, E tc are energy consumed in the startup, standby, transition, air-turning, turning, and tool change stages (F ig. 2). 1 THE CONCEPT OF THE ROTARY TURNING OPERATION The principle of the rotary turning process to produce external surfaces of hardened materials is presented in F ig. 1a . The workpiece is rotated around its axis, while the motion of the round piece is conducted using the friction between the body and specimen. The manufactured tool is shown in F ig. 1b, including the screws, bolts, the round insert, the base, and the holder. The milled grooves on the base are utiliz ed to change the inclination angle. The round insert is conducted self-rotation using two bearings. The round inserts having a rake angle of 1 1 o and a hardness of 2 H R C are utiliz ed for all tests. 2 OPTIMIZATION APPROACH The T U consists of the turning energy (T E ), embodied energy for the insert (E I), and embodied energy for the coolant (E C). TU  TE  EI  EC. (1) Fig. 2. The machining load of the rotary turning process The start-up state presents the shortest period for turning on the lathe. The standby state denotes the stable period, which starts with turning on the machine tool and stops with the spindle rotation. The transition state refers to the short period for increasing and decreasing the spindle speed. The air-turning state presents the duration with spindle rotation but no material cutting. The turning state refers to the steady period for material removal. Multi-performance Optimization of the Rotary Turning Operation for Environmental and Quality Indicators 43 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 42-54 0.4 mm/rev f 0 m/min V TE  Po to  Psb tsb  aV 2  bV  c t   ( Pst  c1V  c2 )ta  Pc tc  Pst ttc  c  ,  TT  (3) where P o, P sb , and P c are the power used in the startup, standby, and turning states, respectively. to, tsb , ta, and tc are the startup, standby, air-cutting, and turning time, respectively. a, b , and c denote the experimental coefficients. ttc and T T are the tool change time and tool life, respectively. The T T is expressed as: A TT     , (4) V f d 0.8 mm/rev; 1 0 m/min. Table 1. Process parameters of the rotary turning Symbol i d f V Parameters Inclination angle [deg] Turning depth [mm] Feed rate [mm/rev] Turning speed [m/min] 1 20 0.3 0.4 90 2 35 0.5 0.6 140 3 50 0.7 0.8 190 3.2 Optimization Framework The optimiz ing approach is depicted in F ig. 3. where A , α, β, and γ are the experimental coefficients. The E I is computed as: EI = tc SEi I v , TT (5) where SE i and Iv are the fabricating energy and volume of each insert, respectively. The E C is computed as: EC  tc Vu EL , TL (6) where T L and E L denote the cycle time and fabricating energy of the lubricant, respectively. V u is the lubricant volume. ρ and η are the density and concentration of the lubricant, respectively. The SR is computed as: n SR   i 1 Rai , n where R ai is the average roughness at the ith measured point. The T N is computed as: TN i , i 1 n n TN   (8) where T N i is the turning noise at the i th measured time. In this study, the characteristics of the coolant system, cutting piece, and specimen are named as constants. The factors considered and their levels are presented in Table 1. The ranges are determined based on the specifications of the lathe. Moreover, these values are confirmed with the published works related to the rotary turning processes. The optimiz ation issue is presented as: F ind X = [ i , V , f , and d ] . Minimiz ing T U , SR , and T N ; Constraints: 20 deg i 50 deg; 0.3 mm d 0.7 mm; 44 Fig. 3. Systematic optimizing procedure (7) St ep 1 : P erforming experimental tests using the Box-Behnken design [18] and [19]. The Box-Behnken design requires three levels for each factor, which presents the lowest, middle, and highest ranges. The design points are placed on the middle points of the edge and the centre of the block. The advantages of the Box-Behnken design are the low number of tests and ensuring predictive accuracy. The number of experiments (N E ) in the Box-Behnken design is computed as [20]: NE  2n(n  1)  N c , ( ) where n and N c are the number of variables and the number of centre points, respectively. In this work, 2 experiments are performed for 4 process parameters and 5 r eplications. St ep 2 : Developing regression models for energy components, SR , and T N [21]. Doan, T.-K. – Nguyen, T.-T. – Van, A.-L. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 42-54 St ep 3 : The MER EC is utiliz ed to compute the weights. F or the maximiz ing aim, the normaliz ed response (n i j) is computed as: min yi (10) . nij = yi F or the minimiz ing aim, the n yi . nij = max yi is computed as: ij (1 1) The performance of the alternatives S computed as:   Si  ln 1 1  j ln( nij )   ,  n is i (12)  where n is the number of responses. The performance of i th alternative is computed as:   Sij'  ln 1 1  k ,k  j ln( nij )   . f ( x, xo ,  )    1 ,  2 2    ( x  xo )    (20) where x o and γ are the locations of the peak of the distribution and scale parameter, respectively. In the mutation stage, each vector is added by a C auchy-L orentz random value (D (.)) and expressed: x '  x   D(.), (21) where x is the new location after mutatation with random value to x . The convergence of the Q P SO-C L is enhanced with the aid of natural selection, which is expressed as: F ( X (t ))  F ( x1 (t )),..., F ( xN (t )) , (22) The removal effect of the jth response (E j) is computed as: where X (t) and F (X (t)) are the position vector of particles and fitness function of swarm, respectively. The particles are sorted based on fitness values, which is expressed as: E j   i Sij'  Si . F ( X' (t ))  F ( x1' (t ))...F ( x N ' (t )) ,  n  (13) (14) X' (t )  x1' (t ),... x N ' (t ) , The weight (ωi ) is computed as: Ej i  .  Ek (15) k (23) The operating steps of the IQ P SO are illustrated in Fig. 4. Matlab 201 commercial software entitled is used to conduct the IQ P SO. St ep 4 : G eneration of the optimality using the IQ P SO. In the Q P SO, the updated position of each particle is expressed as: [22] and [23]: xi , j (t  1)  pi , j (t )   (mbest i , j (t ) 1  xi , j (t )) ln   If k  0.5, u (16) xi , j (t  1)  Pi , j (t ) 1   mbest i , j (t )  xi , j (t ) ln   u If k  0.5, (17)   pi , j (t  1)   Pi , j (t )  (1   )G j (t ), mbest i , j (t )  1 N N ,M  i 1, j 1 Pi , j (t ). (18) (1 ) In this work, the IQ P SO combining the Q P SO and theC auchy-L orentz distribution is proposed to expand the perturbation [24]. The probability density function (f (x )) of the C auchy-L orentz distribution is given as: Fig. 4. The operating procedure of the IQPSO Multi-performance Optimization of the Rotary Turning Operation for Environmental and Quality Indicators 45 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 42-54 St ep 4 : The best solution is selected by the TOP SIS. The normaliz ed value of each alternative (gi j) is computed as: eij (24) gij  , m A KEW 6305 electrical sensor, Mitutoyo SJ-301, and EX TEC H 407730 sound meter are employed to obtain the power components, machined roughness, and turning noise. e i 1 2 ij where ei j presents the value of the alternative jth. The positive ideal solution (P + ) and the negative idea solution (N – ) are computed as:  P  N  m 2  vij v j , j 1 (25) 2 m  vij  v j . j 1 (26)     The best point is found with the highest selection index (S i ), which is calculated as: Si  N . P  N  (27) Fig. 5. The turned specimens Table 2. Chemical compositions of the Ti6Al4V Elements [%] Al Ti V 6.01 83.74 3.26 Fe 0.16 C 0.28 O 5.08 Others Allowance 3 EXPERIMENTAL SETTING A turning machine entitled EMC OTU R N E45 is utiliz ed to execute the turning trials. The Ti6A l4V bar with an outside diameter of 60 and a length of 400 mm is utiliz ed as the specimen (F ig. 5) . The chemical compositions of the Ti6A l4V produced by EDX results are presented in Table 2 and F ig. 6. The outside diameter, inside diameter, and thickness of the round insert are 12 mm, 4.4 mm, and 4.76 mm, respectively. The representative data of the rotary turning operation are depicted in F ig. 7. F ig. 7a presents the power used at the experimental N o. 1 6, while the roughness profile and SEM image are shown in F igs. 7b and c, respectively. The wear and fracture have not been found on the edges of round inserts, as shown in F ig. 7d. The noise profile is presented in F ig. 7e . a) b) Fig. 6. Investigation of a) the microstructure, and b) chemical compositions of Ti6Al4V; produced by EDX results Table 3. Regression models of the energy consumed in the transition state and operational power No. Regression model 1 E Cts = 0.000025V 2 – 0.0014V + 0.4682 P op = 0.0025V + 0.03682 2 46 0.9882 Adjusted R 2 0.9794 Predicted R 2 0.9654 0.9924 0.9826 0.9758 R 2 Doan, T.-K. – Nguyen, T.-T. – Van, A.-L. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 42-54 a) b) c) d) e) Fig. 7. Representative experiments at experimental No. 16; a) power consumed, b) average roughness, c) the SEM image, d) the SEM image of the round insert, e) turning noise 4 RESULTS AND DISCUSSIONS 4.1 Development of E The E Cts and P op Cts and P op Models models are shown in Table 3. 4.2 Development of E t, SR , and TN models The obtained data for the E t, SR , and T N are presented in Table 4. The AN OVA results of the E t, SR , and T N are shown in Tables 5 to 7, respectively. The values of the R 2, the adjusted R 2, and the predicted R 2 values indicate that the E t, SR , and T N correlations are significant. F or the E t model, the contributions of the i , d , f , and V are 2.11 , 6.04 , 22.7 , and 27.33 , respectively. The contributions of the i f , df , dV , and f V are 1.22 , 2.44 , 2.8 , and 4.23 , respectively. 2 , .33 The contributions of the i , f 2, and V 2 are 6.8 % , and 13.2 % , respectively. F or the SR model, the contributions of the i , d , f , and V are 6.37 % , 18.18 % , 22.15 % , and 23.36 % , respectively. The contributions of the i d , i V , dV , and f V are 1.06 , 2.42 , 3.34 , and 2.5 , respectively. The contributions of the i 2 and d 2 are 15.22 % and 3.38 % respectively. Multi-performance Optimization of the Rotary Turning Operation for Environmental and Quality Indicators 47 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 42-54 F or the T N model, the contributions of the i , d , f , and V are 17.37 , 15. 1 , 16.82 , and 18.0 % , respectively. The contributions of the i f , dV , and f V are 1.64 % , 1 .44 % , and 1.04 % , respectively. The contributions of the i 2, d 2, f 2, and V 2 are 21.23 % , 1.82 % , 1.35 % , and 2.22 % respectively. The deviations between the actual and predictive to values of the E t, SR , and T N change from 0. 1.26 , from 0. 7 to 0.80, and 1.26 to 0.47 , respectively (Table 8) . Therefore, the E t, SR , and T N models are significant. The probability plots of three responses are presented in F ig. 8. It can be stated that observed data are distributed on straight lines, indicating the goodness of the fit of the proposed models. Table 4. Experimental data for developing the E t , SR models No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 48 i d f V E t Table 5. ANOVA results for the E So. Mo. i SS MS 249.1 17.8 37.4 37.4 107.1 107.1 404.0 404.0 484.4 484.4 21.6 21.6 51.2 51.2 75.0 75.0 122.1 122.1 165.4 165.4 234.0 234.0 5.5 0.5 254.6 R 2 = 0.9784; Adj. R d f V if dV fV i2 f 2 V 2 Re. To. t model F -value 35.6 74.8 214.1 807.9 968.9 43.2 102.5 150.0 244.3 330.8 467.9 2 p-value < 0.0001 0.003 < 0.0001 < 0.0001 < 0.0001 0.007 0.003 0.002 < 0.0001 < 0.0001 < 0.0001 = 0.9692; Pred. R 2 Con. [%] 2.11 6.04 22.79 27.33 1.22 2.89 4.23 6.89 9.33 13.2 = 0.9578 , and T N Table 6. ANOVA results for the SR SR T N Experimental data for developing models 50 0.5 0.6 190 8.75 2.17 20 0.3 0.6 140 9.69 2.04 35 0.3 0.8 140 7.57 2.24 20 0.5 0.8 140 8.67 2.78 50 0.5 0.4 140 14.90 2.16 20 0.7 0.6 140 10.78 2.75 50 0.5 0.6 90 15.73 2.99 35 0.7 0.4 140 14.24 2.19 20 0.5 0.4 140 13.98 1.97 35 0.5 0.6 140 9.60 2.18 50 0.3 0.6 140 9.99 2.31 35 0.5 0.4 90 19.34 2.14 20 0.5 0.6 190 8.36 1.81 35 0.5 0.6 140 9.62 2.16 35 0.3 0.4 140 12.08 1.41 35 0.5 0.4 190 11.47 1.37 35 0.5 0.8 190 6.52 2.11 35 0.7 0.6 190 8.52 2.22 50 0.5 0.8 140 8.99 3.02 50 0.7 0.6 140 11.29 2.94 35 0.5 0.8 90 12.32 3.07 35 0.3 0.6 190 7.55 1.49 20 0.5 0.6 90 15.09 2.81 35 0.7 0.6 90 15.56 2.94 35 0.7 0.8 140 8.53 2.99 35 0.3 0.6 90 13.18 2.46 Experimental data for testing developed models 25 0.5 0.4 100 17.72 2.15 30 0.4 0.5 120 14.57 2.17 40 0.6 0.7 140 8.95 2.63 25 0.7 0.5 130 13.08 2.51 40 0.5 0.7 150 8.11 2.36 45 0.4 0.6 160 8.73 2.06 98.1 78.2 78.2 91.4 79.4 92.1 81.4 73.3 77.4 76.3 80.1 59.8 96.5 76.8 58.8 76.7 94.9 93.4 96.7 94.2 75.9 77.3 79.2 74.1 91.4 60.9 65.7 63.3 85.7 80.7 84.3 81.9 model Con. [%] So. SS MS F -value p-value Mo. 6.33 0.45 38.90 < 0.0001 6.37 i 0.42 0.42 154.86 < 0.0001 18.18 1.19 1.19 441.98 < 0.0001 22.15 1.45 1.45 538.49 < 0.0001 23.36 V 1.53 1.53 567.91 < 0.0001 1.06 id iV 0.07 0.07 25.77 0.010 6.37 0.16 0.16 58.83 0.007 2.42 0.22 0.22 81.20 0.009 3.34 fV i2 0.17 0.17 62.97 0.007 2.59 1.00 1.00 370.02 < 0.0001 15.22 2 0.22 0.22 82.17 0.009 3.38 Re. To. 0.13 6.45 0.01 d f dV d R = 0.9802; Adj. R 2 2 = 0.9784; pred. R 2 = 0.9662 Table 7. ANOVA results for the T N model So. Mo. i SS 3168.7 2729.5 2500.1 2643.0 2842.6 257.7 226.3 163.4 3336.0 286.0 212.1 348.8 56.1 3224.8 d f V if dV fV i2 d f 2 V 2 2 Re. To. R 2 Doan, T.-K. – Nguyen, T.-T. – Van, A.-L. MS 226.3 2729.5 2500.1 2643.0 2842.6 257.7 226.3 163.4 3336.0 286.0 212.1 348.8 5.1 = 0.9826; Adj. R 2 F -value 44.4 535.1 490.1 518.1 557.3 50.5 44.4 32.0 654.0 56.1 41.6 68.4 p-value < 0.0001 0.0010 < 0.0001 < 0.0001 < 0.0001 0.0068 0.0075 0.0078 < 0.0001 0.0066 0.0074 0.0062 = 0.9794; pred. R 2 Con. [%] 17.37 15.91 16.82 18.09 1.64 1.44 1.04 21.23 1.82 1.35 2.22 = 0.9685 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 42-54 a) a) b) c) b) Fig. 8. The probability plots of three responses; a) for E t model, b) for SR model, c) for T N model The residuals versus the observations of three responses are presented in Fig. . The errors of the responses are systematically distributed, presenting constant errors for each model. 4.3 Parametric Impacts The E t is first reduced by 2.8 % with a higher i (F ig. with 10a ). H owever, the E t is increased by 7. a further i . An increased i causes a reduction in the cutting volume, leading to a decrease in the resistance; hence, the E t reduces. A higher i increases the cutting c) Fig. 9. The residuals versus the observations for three responses; a) for E t model, b) for SR model, c) for T N model volume due to the perpendicular tool, resulting in higher friction; hence, the E t increases. with an increment The E t is increased by 14. in the d (F ig. 10a ). A higher d increases the thickness of the chip; hence, the E t increases. % with an increment The E t is decreased by 3.6 in the f (F ig. 10b) . A higher f reduces the turning time; hence, the E t increases. with an increment The E t is decreased by 38. in the V (F ig. 10b) . W hen the V increases, the turning time reduces; hence, the energy consumption decreases. Multi-performance Optimization of the Rotary Turning Operation for Environmental and Quality Indicators 49 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 42-54 Table 8. Confirmations of the precision of the developed models E No. Exp. 17.72 14.57 8.95 13.08 8.11 8.73 27 28 29 30 31 32 t [kJ] Pred. 17.86 14.62 9.04 13.16 8.19 8.62 SR Err. -0.79 -0.34 -1.01 -0.61 -0.99 1.26 Exp. 2.15 2.17 2.63 2.51 2.36 2.06 The SR is first decreased by 1 1.2 % with an increment in the i (F ig. 1 1a ). H owever, the SR is increased by 21. with a further i . An increased i decreases the turning volume, resulting in a low resistance; hence, a low SR is produced. A higher i causes an increased turning volume, leading to a hard turning; hence, a rough surface is generated. The SR is increased by 30. with a higher d (F ig. 1 1a ). A higher d causes an increase in the turning volume, leading to higher resistance; hence, a higher SR is produced. The SR is increased by 47.6 % with an increment in the f (F ig. 1 1b) . A higher f causes an increase in the turning volume, leading to a higher friction; hence, the a) a) 50 [µm] Pred. 2.16 2.18 2.62 2.49 2.38 2.08 T N Err. -0.47 -0.46 0.38 0.80 -0.85 -0.97 Exp. 65.7 63.3 85.7 80.7 84.3 81.9 [dB] Pred. 66.1 64.1 86.1 81.2 84.9 82.6 Err. -0.61 -1.26 -0.47 -0.62 -0.71 -0.85 SR increases. Moreover, A higher f causes an increase in the turning marks, resulting in a higher roughness. The SR is decreased by 47.6 % with an increment in the V (F ig. 1 1b) . The cutting temperature increases with an increment in the V , resulting in softer specimen; hence, the SR reduces. The T N is decreased by 8.72 % with an increment in the i (F ig. 12a ). H owever, the T N is increased by 47.5 % with further i . A higher i decreases the material removal volume, resulting in low friction between the turning insert and workpiece; hence, the T N decreases. In contrast, a further i increases the material removal volume, leading to greater resistance; hence, the T N increases. b) Fig. 10. Interactions of process parameters on the E t; a) E b) Fig. 11. Interactions of process parameters on the SR ; a) SR Doan, T.-K. – Nguyen, T.-T. – Van, A.-L. t vs. i and d , b) E vs. i and d , b) SR t vs. V and f vs. V and f Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 42-54 a) b) Fig. 12. Interactions of process parameters on the T N ; a) T N vs. A and D , b) T N vs. V and f The T N is increased by 27.6 % with an increment in the d (F ig. 12a ). A higher D increases the material removal to be cut, leading to higher friction; hence, the T N increases. Moreover, a higher d causes greater resistance, resulting in higher turning noise. The T N is increased by 28.2 % with an increment in the f (F ig. 12b) . An increased f causes higher material removal to be cut, leading to higher friction; hence, the T N increases. Additionally, a higher f increases the machining power of the drive system; hence, a higher T N is produced. The T N is increased by 2 .3 with an increment in the V (F ig. 12b) . A higher V increases the engagement frequency of the spindle system; hence, the T N increases. Additionally, an increased V causes higher material removal to be cut, leading to higher friction; hence, the T N increases. The E t, S R , and T N are expressed as: – 0.21 18 i 14.0 801d 4 .8 73f E t = 0.43126 – 0.2573 V 0.017 43i d 0.04 7 i f – 0.000085 i V 2 – 7.46871 d f – 0.0353 d V + 0.0517 + 0.00374 i 2 2 2 f + 0.00064 V (28) – 1.60143 d + 28.51704 = 3.2 271 0.08815i – 0.4125 d + 2.7712 5 f – 0.0126 V – 0.0066 i d + 0.00416 i f + 0.00006 i V 2 – 0.1875 df + 0.00625 dV – 0.00475 f V + 0.00126 i 2 2 2 0.072 2f + 0.0000053 V (2 ) + 1.583 d SR T N = 56.38004 – 2.88317 i + 57.05417 d 4 .7375f – 0.00301 V + 0.016 i d + 0.275 i f – 0.0002i V – 8.125 df + 0.0725 d V + 0.0525 f V + 0.04743 i 2 16. 7 17f 2+ 0.00044V 2 (30) 22. 1667d 4.4 Optimizing Outcomes Produced by the IQPSO Table shows the coefficients for turning objectives. The values of the T U , SR , and T N are presented in Table 10. The weight values of the T E , SR , and T N are 0.43, 0.37, a nd 0.20, respectively. The P areto fronts generated by IQ P SO are exhibited in F ig. 13. As a result, turning objectives have contradictory trends. The reduction in the SR leads to a higher T U (F ig. 13a ). Similarly, a decreased T U leads to a higher T N (F ig. 13b) . The TOP SIS is utiliz ed to select the best point among feasible solutions. The optimum values of the i , d , f , and V are 35 deg, 0.30 mm, 0.40 mm/ rev., and 1 0 m/min, respectively. The reductions in the T E , SR , and T N are 6.7 % , 22.3 % , and 23.5 % , respectively in comparison with the initial values (Table 1 1) . 4.5 Comparisons with the Optimization Results Produced by the MOPSO The optimum findings generated by the MOP SO of the i , d , f , and V are 2 deg, 0.30 mm, 0.40 mm/ rev, and 172 m/ min, respectively. The reductions in the T U , SR , and T N are 6.0 , 20. , and 23.0 , respectively, as compared to the initial values. The number of feasible solutions generated by the IQ P SO and MOP SO are 426 and 286, respectively. It can be stated that the IQ P SO provides better optimiz ation results than the MOP SO. 4.6 Evaluation of the Total Turning Cost The comprehensive model for the M C is expressed as: t MC  keTU  kc c  klabor (to  tst  ta  ttc  tc ) TT  klabor tch tc (k fp  k fd )(to  tst  ta  ttc  tc )Vu  TT TL  (kmd  kmr )(to  tst  ta  ttc  tc ) Tm  kn (to  tst  ta  ttc  tc ) , TW Multi-performance Optimization of the Rotary Turning Operation for Environmental and Quality Indicators (31) 51 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 42-54 Table 9. Experimental coefficients for the rotary turning process po [kW] to [s] 0.48 4 γ 0.37 U m [kJ/m3] P st TL [month] 9.16×103 a) [kW] tst [s] ta [s] ttc [s] 6 8 8 16.2×105 H [%] ρ [g/cm3] 5 0.92 0.72 1 V 3 i n [cm ] V 8.5 3 ad [cm ] 4.5 b) Fig. 13. Pareto fronts generated by IQPSO; a) T E and SR A α β 2.65 0.27 L [J/g) E 422984 U 3 m [kJ/m ] 9.16x103 , b) T N and SR Table 10. The values of total energy consumption, average roughness, and turning noise No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 i [deg] D [mm] f [mm/rev] V [m/min] T U [kJ] 20 50 20 50 35 35 35 35 35 35 35 35 20 20 50 50 35 35 35 35 20 20 50 50 35 35 0.3 0.3 0.7 0.7 0.5 0.5 0.5 0.5 0.3 0.3 0.7 0.7 0.5 0.5 0.5 0.5 0.3 0.3 0.7 0.7 0.5 0.5 0.5 0.5 0.5 0.3 0.6 0.6 0.6 0.6 0.4 0.4 0.8 0.8 0.6 0.6 0.6 0.6 0.4 0.8 0.4 0.8 0.4 0.8 0.4 0.8 0.6 0.6 0.6 0.6 0.6 0.4 140 140 140 140 90 190 90 190 90 190 90 190 140 140 140 140 140 140 140 140 90 190 90 190 140 190 25.31 25.72 26.69 27.31 33.65 28.52 27.05 23.98 28.05 24.65 30.24 25.43 29.84 24.57 30.66 24.79 28.31 23.33 30.38 24.21 29.73 25.75 30.37 26.14 25.48 27.77 where k e, k c k l abor are the costs of energy, tool, and labour, respectively. V u is the lubricant volume. k f p and k f d present the cost for the lubricant preparation 52 SR [µm] 2.04 2.32 2.76 2.96 2.16 1.38 3.08 2.11 2.41 1.41 2.96 2.21 1.93 2.73 2.14 3.00 1.47 2.31 2.16 2.98 2.83 1.87 2.98 2.20 2.17 1.03 T N [dB] 73.6 90.9 89.5 107.2 63.9 81.3 79.8 992 64.3 81.1 78.9 98.5 74.1 89.4 89.9 108.5 62.1 79.7 78.8 95.3 74.3 92.8 92.1 109.9 80.5 71.1 and disposal, respectively. k md , k mr, and T m are the cost of the degradation and remanufacturing for the lathe, respectively. T m is the service life of the machine. k n Doan, T.-K. – Nguyen, T.-T. – Van, A.-L. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 42-54 Table 11. The optimality produced by the IQPSO and MOPSO Method Initial values Optimal values by IQPSO Reductions by IQPSO [%] Optimal values by MOPSO Improvement by MOPSO [%] i [deg] d [mm] f [mm/rev] V [m/min] T U [kJ] 50 35 0.30 0.30 0.40 0.40 140 190 29 0.30 0.40 172 28.89 26.95 6.7 27.08 6.0 SR [µm] 1.48 1.15 22.3 1.17 20.9 T N [dB] 89.5 68.5 23.5 68.9 23.0 S i 0.8624 Table 12. Experimental coefficients for the turning cost model k e [USD/kWh] k c [VND/piece] k 0.15 l ab our [USD/h] 16.62 V 8.40 u [l] 20 k fp [USD/l] k 0.14 and T w are the noise tax and working hours per month, respectively. The empirical coefficients of the M C are shown in Table 12. It can be stated that, the M C is saved by 8.5 % at the selected point (Table 13) . Table 13. Comparative values of the total cost Optimization parameters Method Initial values Optimal results Reduction [%] i d [deg] [mm] 50 35 f Response V M C [m/min] 140 [USD] 0.30 [mm/rev] 0.40 0.30 0.40 190 4.48 4.91 8.5 4.7 The Contribution Analysis The proposed cutting tool could be used in the practical rotary turning process for other hard-to-cut alloys. The new rotary turning tool could be developed based on the current device. The empirical correlations of the performance measures could be effectively employed to forecast the total energy, turned roughness, and noise emission. The optimiz ing outcomes could be used in the practical operation to improve the technological data. The proposed turning process could be applied to produce external surfaces for other difficult-to-cut alloys. The develop optimiz ation approach could be applied to deal with other issues of different machining operations. The turning expense model could be used to compute total cost. 5 CONCLUSIONS In the current work, the T U , SR , and T N of the rotary turning process were optimiz ed, while optimal inputs fd [USD/l] T 0.45 L [month] k md [USD] k mr [USD] T 1 41244.75 1649.79 m [year] k n [USD] 14 2.68 were the i , d , f , and V . The MER EC and IQ P SO were utiliz ed to select optimal outcomes. The findings are expressed as below: 1. To save the T U , the low data of the i and D were used, while the highest data of the f and V were utiliz ed. To decrease the SR , the low d and f were utiliz ed, while the high i and V were employed. F or reducing the T N , the lowest process parameters could be applied. 2. The T U and SR models were primarily affected by the f and V , followed by the d and I, respectively. F or the T N model, the V had the highest contribution, followed by the f , i , and d , respectively. 3. The optimal i , d , f , and V were 35 deg, 0.30 mm, 0.40 mm/rev, and 1 0 m/min, respectively. 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ID 773, DOI:10.3390/ photonics10070773. Doan, T.-K. – Nguyen, T.-T. – Van, A.-L. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 55-69 © 2024 The Authors. CC BY-NC 4.0 Int. Licensee: SV-JME DOI:10.5545/sv-jme.2023.709 Original Scientific Paper Received for review: 2023-06-28 Received revised form: 2023-09-26 Accepted for publication: 2023-09-28 A New Calculation Method for Instantaneous Efficiency an d Torq ue Fluctuation of Spur Gears Tian, X . – W ang, G . – Jiang, Y. X in Tian1,2 – G uangjian W ang1,2,* – Yujiang Jiang1,2 1 C hongqing U niversity, State Key L aboratory of Mechanical Transmissions, C hina 2 C hongqing U niversity, C ollege of Mechanical and Vehicle Engineering, C hina As a critical component of the joint gearbox, spur gear pairs play a crucial role in energy conversion, limiting the performance of a collaborative robot. Accurately assessing their instantaneous efficiency and torque fluctuation is essential for developing high-precision robot joint control models. This study proposes a computational model to predict the instantaneous efficiency and torque fluctuation of spur gears under typical operating conditions. The model incorporates a torque balance model, a load distribution model, and a friction model to reflect the relationship between gear meshing position and efficiency. The instantaneous efficiency and torque fluctuation of gear pairs were compared with the Coulomb friction model with an average friction coefficient and the elastohydrodynamic lubrication model with a time-varying friction coefficient. The effect of gear contact ratio on efficiency is analysed, while the instantaneous efficiency and torque fluctuation of gears are studied under varying operating conditions. The results indicate a maximum efficiency difference of 1.86 % between the two friction coefficient models. Under specific operating conditions, the instantaneous efficiency variation of the gear pair can reach 3.34 %, and the torque fluctuation can reach 5.19 Nm. Finally, this study demonstrates the effectiveness and accuracy of the proposed method through comparative analysis. Keywords: collaborative robot, instantaneous efficiency, torque fluctuation, friction coefficient, load distribution Highlights • A new model to predict instantaneous efficiency and torque fluctuation of spur gears. • The model includes torque balance, load distribution, and friction models. • Instantaneous efficiency of gear pairs is examined under different friction coefficient models. • Torque fluctuation of gear pairs under different friction coefficient models. • Gear efficiency and torque trends are analysed under varying operating conditions. 0 INTRODUCTION C ollaborative robots are widely used in manufacturing, assembly, rehabilitation, and medical treatment and have become a research hotspot in recent years. To achieve high-precision force/ position control of collaborative robots, it is necessary to establish an accurate control model of the joint reducer. H owever, the commonly used harmonic drive has many disadvantages, such as low efficiency and stiffness, large speed and torque fluctuations, and complex hysteresis characteristics [1] to [3], which directly affect the control precision of collaborative robots. To overcome the limitations of the harmonic drive, many researchers have recently started to study the 3K planetary joint reducer with high efficiency and stiffness to meet the high-precision force/ position control requirements of collaborative robots [1] and [4] to [6]. H owever, these studies mainly focus on efficiency optimiz ation design and less on the research of instantaneous efficiency characteristics. The torque fluctuation caused by instantaneous efficiency will directly affect the control performance of collaborative robots. As the basic transmission unit of the joint reducer, the instantaneous efficiency and torque fluctuation of gear pairs have a direct effect on the stability and lifespan of collaborative robot joints. Therefore, studying the instantaneous efficiency and torque fluctuation characteristics of the gear pair is of great significance for improving the friction characteristics and control model of the joint reducer of collaborative robots. Energy consumption has drawn much attention in recent years due to the global energy crisis and increasingly stringent environmental regulations. Therefore, improving the efficiency of transmission devices has become an important indicator for evaluating the performance of collaborative robots’ joint reducers and other transmission devices in the future [5], and [7] to [9]. In order to accurately evaluate the instantaneous efficiency of planetary gear reducers, it is necessary to study the dynamic changes in the instantaneous efficiency of gear pairs at different meshing positions and contact ratios. As a basic component of planetary transmission systems, the meshing efficiency of gear pairs directly affects the performance of joint reducers in collaborative robots. F or example, a 1 % increase in gear meshing *Corr. Author’s Address: Chongqing University, State Key Laboratory of Mechanical Transmissions, Chongqing, 400044, China, gjwang@cqu.edu.cn 55 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 55-69 efficiency can improve the efficiency of a compound gear train by 30 % [10]. The existing literature focuses more on the average efficiency of gears. W hen calculating the average efficiency of gear pairs, H öhn [11] introduced a loss factor based on the C oulomb friction model, considering the influence of gear geometry. Baglioni et al. [12] analysed the effects of different friction coefficient calculation models, transmission ratios, addendum modification coefficients, loads, and speeds on the average efficiency of gear pairs. P leguez uelos et al. [13] calculated the average efficiency of gear pairs based on a load distribution model and a friction model that remained constant along the contact path and studied the effects of transmission ratio and pressure angle on efficiency. Marques et al. [14] investigated the effects of rigid and elastic load distribution models on the average efficiency of gear pairs while analysing the average power loss of gears under local and constant friction coefficients. Diez -Ibarbia et al. [15] proposed an average efficiency evaluation model for gear pairs that simultaneously considers the C oulomb friction model and load distribution and analysed the effects of addendum modification coefficient, different friction coefficient calculation formulas [16], and tooth profile modification [17] on gear efficiency. P etry-Johnson et al. [18] analysed the changing trends of the average meshing efficiency of gear transmission systems and the average efficiency of gearboxes under different speeds and load torque through experiments. The instantaneous efficiency of a compound gear train can vary by more than ± 20 % from the average efficiency [19], while there are relatively few studies on the instantaneous efficiency of gear pairs. C ao et al. [20] found that the instantaneous efficiency variation of bevel gears can reach up to 8 % . L i and Kahraman [21] proposed a model for predicting the mechanical power loss related to a load of a gear pair based on the elastohydrodynamic lubrication (EH L ) theory. The model predicts the instantaneous mechanical power loss at each tooth contact and the overall power loss at gear engagement based on the pressure and film thickness of the lubricating oil. H owever, this model is analytically difficult, neglects the load distribution between the teeth, and cannot be used to investigate the torque fluctuation of gear pairs. X u et al. [22] modelled the time-varying friction coefficient (TF C ) at the gear contact point to predict the mechanical power loss caused by gear friction, and analysed the effects of geometric parameters, tooth profile modifications, operating conditions, surface roughness, and lubricant performance on mechanical efficiency loss. H owever, they only calculated the average efficiency without 56 delving into the instantaneous efficiency in depth. W ang et al. [19] proposed a method for analysing instantaneous efficiency using a load distribution model. H owever, this method cannot accurately evaluate the instantaneous efficiency of gears and ignores the relationship between the instantaneous efficiency of gear pairs and torque fluctuation. Therefore, there is an urgent need to propose a calculation model that can accurately evaluate the instantaneous efficiency of gear pairs. In studying the instantaneous transmission efficiency of gear pairs under constant speed and load, it is generally desirable to have a stable torque for the output side shafting [9]. The strong nonlinearity and time-varying nature of internal friction characteristics in gear pairs cause torque fluctuation not only to vary with the meshing position of the gears but also to be affected by various factors, such as operating temperature [9], [23], and [24], load torque [18], and contact surface roughness [25]. These fluctuations reduce system stability, leading to significant noise and vibration problems [26]. At present, many scholars have carried out modelling and compensation studies on the friction torque of robot harmonic reducers. L u et al. [27] proposed a method to compensate for the torque fluctuation of a harmonic reducer by using a torque sensor. Tadese et al. [24] used a dynamic friction model that considers temperature fluctuations to predict the joint torque variations of a collaborative robot mechanical arm driven by a harmonic reducer. Although the torque fluctuation and friction model of harmonic reducers have been extensively studied, there are relatively few studies on the torque fluctuation of gear pairs. F or collaborative robots employing 3K planetary transmissions, an in-depth investigation into their friction models and torque fluctuations is crucial for achieving precise force and position control. Therefore, studying the torque fluctuations of gear pairs is essential in enhancing the accuracy and reliability of the system. Accurately assessing torque fluctuations in gear pairs is crucial to improving the accuracy and reliability of a system. In summary, this paper proposes a computational model for predicting the instantaneous efficiency and torque fluctuation of gear pairs, considering the torque balance at the meshing point, the load distribution between teeth, and the friction coefficient models. The instantaneous efficiency and torque fluctuation of gear pairs under the average friction coefficient (AF C ) based on C oulomb friction and the TF C based on EH L are compared. Additionally, the relationship between gear instantaneous efficiency and torque fluctuation is analysed, and the influence of contact ratio on Tian, X. – Wang, G. – Jiang, Y. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 55-69 efficiency is discussed. C ompared with existing research, which mainly focuses on the influence of output torque and speed on the average efficiency of gears [12], [15] to [17], and [28], this paper not only considers load and speed conditions but also explores the influence of surface roughness and lubricating oil operating temperature on the instantaneous efficiency and torque fluctuation of gears. F inally, the effectiveness and accuracy of the proposed method were verified through comparative analysis. The paper is organiz ed as follows. Section 1 develops a model for calculating the instantaneous efficiency of gears based on the torque balance, load distribution model, and friction coefficient model. Section 2 presents a study on the instantaneous efficiency and torque fluctuation of gears under different friction coefficient models with given parameters (geometric parameters and operating conditions). Section 3 discusses the evaluation results of gear efficiency and torque fluctuation under four operating conditions, validating the effectiveness and accuracy of the proposed method. Section 4 is the research conclusion. a) b) 1 METHODS 1.1 Instantaneous Efficiency Model of Gears In gear transmission, it has been found through numerous experiments and numerical analyses that load-dependent power losses are the main cause of changes in system efficiency [11], [16], [18], and [28]. In addition, losses due to sliding friction under adverse load conditions account for approximately 5 of the losses [17]. Therefore, this paper focuses on the effect of sliding friction on the instantaneous efficiency of gears. To determine the instantaneous efficiency of gears, it is crucial to have a comprehensive understanding of the meshing process; for gears with a contact ratio between 1 and 2, they will sequentially cross the double-tooth meshing area, single-tooth meshing area, and double-tooth meshing area as they mesh in and out along the actual meshing line B1 B2. F ig. 1 describes the three key moments of the meshing of a pair of gear wheels with a contact ratio between 1 and 2. There are three pairs of gears involved in the entire meshing process in a single cycle from the in-mesh to the out-mesh. F ig. 1a shows gear pair 2 meshing in the double-tooth meshing area B1 Blpstc while gear pair 3 meshes out in the doubletooth meshing area BhpstcB2. At this time, there are two meshing points on the meshing line B1 B2. F ig. 1b shows the situation of gear pair 2 entering the c) Fig. 1. Gear meshing process; a) MMGP in double-tooth meshing area B1Blsptc b) MMGP in single-tooth meshing area BlsptcBhsptc, and c) MMGP in double-tooth meshing out area single-tooth meshing area BlpstcBhpstc from the doubletooth meshing area B1 Blpstc. At this time, there is only one meshing point in the meshing area B1 B2. F ig. 1 c shows gear pair 2 entering the double-tooth meshing rea BhpstcB2 while gear 1 meshes in the double-tooth meshing area B1 Blpstc. There are two meshing points on the meshing line B1 B2, and gear pair 2 gradually exits the meshing area, completing one gear meshing cycle. F or ease of discussion, the gear pair that completes one gear meshing cycle on the meshing line B1 B2 is defined as the main meshing gear pair (MMG P ), such as gear pair 2 mentioned above. W hen the MMG P is in the double-tooth meshing area, other gear pairs participating in the meshing process are defined as secondary meshing gear pairs (SMG P ). It should be noted that there are two gear pairs in the SMG P during A New Calculation Method for Instantaneous Efficiency and Torque Fluctuation of Spur Gears 57 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 55-69 a single gear meshing cycle of the MMG P , such as gear 3 when gear pair 2 appears in B1 Blpstc and gear pair 1 when gear pair 2 appears in BhpstcB2. W hen calculating the instantaneous efficiency of the gear pair along the line of contact, the torque balance at different mesh positions, load distribution between teeth, and friction coefficients must be considered. The force analysis of the gear along the contact line is shown in F ig. 2, where P is the meshing node, N 1 N 2 is the theoretical contact line, B1 B2 is the actual contact line, and K1 and K2 are the meshing points of the gear profiles of the MMG P and SMG P during the gear transmission process, respectively. The input torque of the driving gear is defined as positive, and the output torque of the driven gear is defined as negative. The gear friction torque is not always in the same direction because the direction of the sliding velocity of the contact point changes up and down at the node, which causes the direction of the friction torque to change. In addition, in the double-tooth meshing area, the parameters such as contact force, sliding velocity, and curvature radius of different meshing points are different, so the friction coefficient and load distribution of each meshing point must be considered separately. Based on the torque balance model at the meshing point, load distribution between teeth, and friction coefficient, this paper proposes the instantaneous efficiency calculation model for gears. The instantaneous input torque of the gear in the doubletooth meshing area at any moment is expressed as follows: a) Tin  Fn Rb1  1 Fn Rb1 tan  K 1  1     2 Fn Rb1 tan  K 2 , (1) where F n is the contact force, R b 1 is the base circle radius of the driving gear, λ is the load distribution factor (be discussed in a subsequent section), μ1 and μ2 are the friction coefficients of MMG P and SMG P , respectively (to be discussed in a subsequent section), αK 1 and αK 2 are the instantaneous meshing positions of MMG P and SMG P on the driving gear, respectively. The output torque of the gear at any instant in the double-tooth meshing area are as follows: b) Fig. 2. Gear force analysis; a) forces and friction on a driving gear, and b) forces and friction on a driven wheel In summary, the instantaneous calculation model of the gear is Eq. (3) :  Tout   Fn Rb 2  1 Fn Rb 2 tan  K 1  1    2 Fn Rb 2 tan  K 2 , (2) where R b 2 is the base circle radius of the driven wheel, βK 1 and βK 2 are the instantaneous meshing positions of MMG P and SMG P on the driven wheel, respectively. 58 Tian, X. – Wang, G. – Jiang, Y. efficiency Tout 2 Tin1 1  1 tan   K 1   1     2 tan   K 2  ,  1  1 tan  K 1   1     2 tan  K 2   when 0  B K  B P 1 1 1  1   1   tan  K 1      2 tan   K 2  1  1   tan    1     tan   , 1 K1 2 K2   when B1 P  B1 K1  B1 B2 (3) Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 55-69 where B1 K1 = R b 1 tan αK1 – N 1 B1 , ω1 and ω2 are the angular velocity of the driving and driven wheel. W hen B1 P < B1 K1 < B1 B1hs ptc, it is the instantaneous efficiency of single-tooth meshing area. In addition to the above method of using torque balance to obtain the instantaneous efficiency of the gear, the efficiency of the gear can also be obtained through the friction power loss of the gear. The calculation of load-dependent power losses in gear is based on C oulomb friction Eq. (4): FR   FN (4) Ploss  FRVg   FN Vg , (5) where P l oss is power loss, μ is coefficient of friction, F N is normal force, V g is sliding speed. Eq. (5) calculates the friction power loss of the gear only for a single-point contact [11], ignoring the alternate meshing process of single and double teeth and leading to an inaccurate evaluation of the power loss over one meshing cycle. Based on the concept presented in this section, this paper modifies Eq. (5) considering the load distribution between gear teeth at the double-tooth meshing position, as well as the friction coefficient and sliding velocity, to obtain the instantaneous friction power loss of the gear is as follows: Ploss ,i  Fn ,i i 1,i vs1 ,i  1  i   2,i vs2 ,i . (6) The calculation model of average friction loss power is as follows:  Blsptc   B1 i 1,i vs1 ,i  1  i   2,i vs0 ,i dx   F  Bhsptc  . (7) Ploss = n ,i    i 1,i vs1 ,i dx B1 B2  Blsptc   B2    B i 1,i vs1 ,i  1  i   2,i vs2 ,i dx   hsptc  In this paper, a novel average friction loss calculation model is proposed. Eq. (7) is related not only to the gear parameters themselves but also to the sliding velocity, load, and friction coefficient at the gear meshing point. More importantly, based on the dynamic process of gear on the meshing line, the coupling relationship between different meshing points is considered, and the loss power of single and double teeth meshing is separated. F inally, the gear efficiency is Eq. (8) :  Pout . Pout  Ploss (8) C ombining Eqs. (6) and (8) , the instantaneous efficiency calculated from the equations is consistent with the result obtained from Eq. (3) , which mutually validates the two proposed models for calculating instantaneous efficiency. To facilitate comparison and highlight the instantaneous fluctuation, the terms “ average efficiency η ” and “ efficiency fluctuation η ” will be used to represent the instantaneous efficiency variation of the gear in the subsequent text, while the terms “ average input torque T in ” and “ torque fluctuation Tin ” will be used to replace the influence of the gear’ s instantaneous input torque. Efficiency fluctuations η and torque fluctuations Tin are defined as follows:    max   min , Tin  Tin _ max  Tin _ min , ( ) (10) where ηmax and T i n _ max are the maximum value of instantaneous efficiency and instantaneous input torque, ηmin and T i n _ min are the minimum value of instantaneous efficiency and instantaneous input torque. 1.2 Load Distribution Coefficient Considering Hertz Contact Stiffness F rom Eq. (6) , it can be seen that the factors affecting the instantaneous friction power loss of the gear include the contact force, load distribution coefficient, and friction coefficient. The load distribution between the teeth of spur gears is not distributed evenly but is closely related to the contact stiffness at the contact point. In this paper, the load distribution coefficient adopts a widely accepted simplified linear calculation model proposed in [29], as follows:  0.28 B1 K1 , 0.36    1   when 0  B1 K1  B1 Blsptc    1, when B1 Blsptc  B1 K1  B1 Bhsptc ,  0.36  0.28  B1 K1     ,    1  when B1 Bhsptc  B1 K1  B1 B2  (1 1) where εα is contact ratio, 1 εα 2. This model uses a linear function to represent the relationship between the load distribution coefficient in two double-tooth meshing areas and the displacement of the meshing point, with a simple calculation process, a small amount of computation, and accurate results. The maximum error between the calculation results of this model and the finite element simulation results is within 6 % . A New Calculation Method for Instantaneous Efficiency and Torque Fluctuation of Spur Gears 59 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 55-69 1.3 Average Friction Coefficient and Time-Varying Friction Coefficient Models The friction coefficient is an indispensable factor in evaluating the efficiency of gears, and it is a function of many variables [30], such as normal load, sliding velocity, relative curvature radius, surface roughness, oil viscosity, sliding-to-rolling ratio, and temperature. The selection of the friction coefficient greatly affects the accuracy of the gear efficiency calculation. This section will focus on the average friction coefficient and time-varying friction coefficient used in the calculation of instantaneous efficiency and torque fluctuation. 1.3.1 Method I: Average Friction Coefficient As the coefficient of friction only changes slightly with the variable operating conditions on the path of contact, it can be assumed to be constant for approximation purposes. In this paper, the most commonly used average friction coefficient in the international standard [31] is as follows:  AFC  F /b  0.048  bt v    C redC Fn max = 0.2  0.25 0.05  oil Ra X L .  (12) 1.3.2 Method II: Time-varying Coefficient of Friction The friction coefficient calculation formula proposed by X u et al. [22] under EH L conditions was adopted in this study. This formula was obtained by performing multivariate linear regression analysis on a large number of EH L predictions under various contact conditions. C ompared to traditional methods, this formula is simpler to calculate, and the calculated friction coefficient based on the EH L formula matches well with the measured traction data. The calculation equation is as follows: TFC  e f  SR,Ph , 0 ,S  Phb2 SR 3 Veb6 0b7 R b8 , b (13) f  SR,Ph , 0 ,S   b1  b4 SR Ph log10  0  b5 e  SR Ph log10  0   b9 e S . W hen calculating the gear transmission efficiency under constant speed and load, if the friction effect is ignored, the maximum contact force of the gear can be obtained by Eq. (15) . The contact force acts on the 2Tout . d2 (15 ) F or the force analysis of the driven gear under constant speed and load conditions, as shown in F ig. 2, after balancing the output torque, the magnitude of the contact force acting on the contact point is derived from Eq. (2): Fn   1   tan  1 Tout K1   1     2 tan  K2 Rb 2 . (16 ) Since the friction coefficient μ1 and μ2 are function of the contact force, the contact force F n during the gear meshing process cannot be directly obtained from this formula when the gear output torque is known. Therefore, this paper uses a numerical iteration method to solve for the contact force F n and Eq. (15) . is set as the initial value of the contact force F n iteration. Set the iteration termination condition as follows: Fni 1  Fni    , (14) 1.4 Calculation of Gear Contact Force Based on Torque Balance Method 60 contact point with a constant direction relative to the rotation axis of the meshing gear, the friction force acts on the tangent surface of the meshing tooth flank, and the friction coefficient is a function of the contact force. Therefore, there is a coupling relationship between the friction coefficient and the contact force, and their numerical changes will affect each other. H owever, Eq. (15) cannot reflect this relationship. Therefore, in efficiency calculation, the gear contact force and friction coefficient are still the focus of discussion [30]. In this paper, the balance between input torque, output torque, and friction torque at the gear meshing point is considered as the entry point. Through the torque balance method, it establishes the relationship expression between output torque, friction coefficient, and contact force, and solves and calculates the contact force of each meshing point of the gear. This is achieved through an iterative process to calculate the torque generated by contact force and friction force and make them equal to the output torque applied to the system. (17 ) where ε = 0.001 is the convergence accuracy, and i is the iteration number. To describe the variation of contact force along the contact line under different friction coefficients visually, the ratio of the contact force for different models to the maximum contact force obtained without considering friction is compared. The ratio of the contact forces obtained from different models after Tian, X. – Wang, G. – Jiang, Y. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 55-69 torque balance is calculated using Eq. (18) , and the result is shown in F ig. 5.  Fni . Fn max (18) 2 CASE OF APPLICATION The specific calculation process is shown in F ig. 3. The parameters of the spur gear are shown in Table 1, the 75W 0-A lubricating oil parameters in reference [32], and the operating conditions are shown in Table 2. U nder the same operating conditions, the intertooth friction coefficients obtained by considering different friction coefficient calculation models and satisfying the torque balance condition from meshing to disengagement for one cycle of MMG P are shown in F ig. 4. In the single-tooth meshing area BlpstcBhpstc, the time-varying friction coefficient in Method II quickly decreases to 0 as MMG P approaches node P and increases as MMG P moves away from node P . This is a clear local variation process, while the average friction coefficient calculated by Method I in this area is almost a straight line and a constant value. In other double-tooth meshing areas, the value of the time-varying friction coefficient is significantly larger than that of the average friction coefficient. The friction coefficient of SMG P only exists in the doubletooth meshing area, which is due to the different gears involved in the meshing and disengagement processes. C onsidering the friction and torque balance, the ratio of the contact forces of the MMG P along the actual contact line is shown in F ig. 5 at different meshing positions. In the double-tooth meshing area B1 Blpstc of the SMG R , the contact force is proportional to the meshing distance, while in the double-tooth meshing area BhpstcB2, the change in contact force is opposite to the trend in the B1 Blpstc meshing area and is inversely proportional to the meshing distance. At this time, MMG P is in the meshing-out process, and the load is gradually borne by SMG R . In these two double-tooth meshing areas, the contact force obtained by Method I is greater than the contact force without friction, and the contact force obtained by Method II is greater than that obtained by Method I. These three methods are almost identical in siz e when entering the double-tooth meshing area, and the difference between them becomes significant as the double-tooth meshing distance increases. At the points Blpstc and Bhpstc, the contact force of the gear pair will produce a step change because the gear pair undergoes a single-double tooth meshing transition, which will cause impact and vibration at this moment. Fig. 3. The calculation flowchart of the mathematical model of the gear instantaneous efficiency model Table 1. Pinion/gear parameters Parameters Teeth number of pinion 1 = 18 Z Teeth number of wheel Z 2= 36 α= 20 β= 0 m= 3 Pressure angle [°] Helix angle [°] Module [mm] Face width [mm] b Centre distance [mm] = 26.7 a= 81 εα = 1.611 Transverse contact ratio Table 2. Operating conditions Operating Output torque Input speed conditions T out [Nm] n 1 [rpm] case 1 case 2 case 3 case 4 case 5 159 159 159 159 Surface roughness R a [µm] 1500 1500 1500 1500 0.8 0.8 0.8 Lubricant operating temperature θoi l [°C] 55 55 55 55 0.8 Symbol : this value will change in Section 3. A New Calculation Method for Instantaneous Efficiency and Torque Fluctuation of Spur Gears 61 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 55-69 a) Fig. 4. The friction coefficient of the gear pair at case 1: μA F C1 and μT F C1 are the friction coefficients of MMGP at different meshing positions, μA F C2 and μT F C2 are the friction coefficients of SMGR in the double-tooth meshing area b) Fig. 6. Gear instantaneous efficiency at case 1: a) The variation of instantaneous efficiency with time in the gear meshing process, b) Instantaneous efficiency at one meshing cycle, ηA F C is the instantaneous efficiency obtained by Method I, ηT F C is the instantaneous efficiency obtained by Method II Fig. 5. The ratio of the contact force of the MMPG gear during the engagement cycle at case 1: without friction ( βN F ), with average friction coefficient ( βA F C ), and with time-varying friction coefficients ( βT F C ) In the single-tooth meshing area BlpstcBhpstc, the contact force obtained by Method I undergoes a sudden change at node P . The reason for this phenomenon is that the sliding velocity direction of the meshing points on the left and right of node P changes, and the frictional force is related to the sliding velocity which leads to a change in the direction of the frictional torque before and after the node. The contact force obtained by Method II in the single-tooth meshing area will decrease smoothly with the meshing position and will not produce a jump phenomenon. The phenomenon in F ig. 5 is consistent with the previous research [15] to [17]. It can be seen that the siz e of the tooth surface contact force calculated by different friction coefficient calculation models is different. 62 The instantaneous meshing efficiency of the gear under different friction coefficient calculation methods is shown in F ig. 6. F ig. 6a represents the change in the instantaneous efficiency of the gear over time. The instantaneous meshing efficiency obtained by Method I (ηA F C) changes from .18 to 100 , and the fluctuation range of instantaneous efficiency is 0.82 % . The instantaneous meshing efficiency obtained by Method II (ηT F C) changes from 7.53 to 100 % , and the fluctuation range of instantaneous efficiency is 2.47 % . At the same time, the value of TF C is lower than the value of AF C at the same meshing position. F ig. 6b can more clearly reflect the instantaneous meshing efficiency of the gear at any meshing point on the meshing line. R egardless of AF C or TF C , there will be a significant abrupt change in instantaneous efficiency in the process of single-todouble tooth alternation. At the double-tooth meshing area, the instantaneous efficiency is lower than that in the single-tooth meshing area. This is because the Tian, X. – Wang, G. – Jiang, Y. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 55-69 relative sliding velocity generated by the gear in the double-tooth meshing area is greater than that in the single-tooth meshing area. The instantaneous meshing efficiency at node P is the highest. Although different methods have different friction coefficients at the nodes, the same results can be obtained. For TF C , there is no relative sliding between the driving and driven wheels at the node, and the friction coefficient is 0, so the efficiency is the highest. For AF C , although the friction coefficient at the node is not 0, the actual meshing angle at the node is the same, which produces the same result as TF C . This explains why the numerical values of the different friction coefficient models are different at the node, but their instantaneous efficiency is consistent. and changes in the meshing position, as shown in F ig. 7. F ig. 7a shows the variation of the instantaneous input torque with time, with T i n _ A F C changes from 7 .50 Nm to 80.16 Nm with a tor ue fluctuation range of 0.66 N m, and T i n _ T F C changes from 7 .50 Nm to 80.52 N m with a torque fluctuation range of 2.02 N m. F ig. 7b shows the variation of the instantaneous input torque with the meshing position of the gear, where the instantaneous input torque in the double-tooth meshing area is higher than that in the single-tooth meshing area, and T i n _ T F C is higher than T i n _ A F C at the same meshing position. Method I has a smaller torque fluctuation than Method II. Fig. 8. The instantaneous efficiency and instantaneous input torque of the gear at case 1 a) b) Fig. 7. Gear instantaneous input torque at case 1: a) the variation of instantaneous input torque with time in gear meshing process; b) Instantaneous input torque at one meshing cycle, T i n _ A F C is the instantaneous input torque obtained by Method I, T i n _ T F C is the instantaneous input torque obtained by Method II U nder constant speed and load conditions, where a constant output torque is maintained on the driven gear, the instantaneous input torque of the driving gear fluctuates due to the existence of tooth friction F ig. 8 shows that the instantaneous efficiency of the gear decreases as the instantaneous input torque increases. The greater the fluctuation in gear efficiency, the greater the resulting torque fluctuation. The increase in input torque fluctuation not only reduces stability but also creates significant noise and vibration problems, making it difficult to model and compensate for. This also poses a challenge to the original engine. W ithout changing the gear ratio, increasing the proportion of single-tooth meshing in the actual meshing area, i.e., reducing the contact ratios of the gear, can improve gear transmission efficiency and reduce tor ue fluctuation. Fig. shows the average efficiency and the efficiency fluctuation of the gear for different contact ratios, showing that decreasing the contact ratio can improve the gear efficiency. H owever, it should be noted that reducing the gear contact ratio also affects gear transmission capacity, load capacity, and service life. Therefore, in practical applications, a balance and selection should be made based on specific circumstances, ensuring continuous gear transmission while minimiz ing contact ratio to achieve maximum gear efficiency. A New Calculation Method for Instantaneous Efficiency and Torque Fluctuation of Spur Gears 63 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 55-69 design of gear surface roughness and lubricant operating temperature can lead to more friction power loss, reducing gear meshing efficiency and increasing input torque fluctuation. This section focuses on the variability of gear efficiency and torque fluctuations under four different operating conditions: different output torque, input speed, gear surface roughness, and lubricant operating temperature. 3.1 Gear Instantaneous Efficiency under Different Operating Conditions Fig. 9. Influence of gear contact ratio at case 1 on efficiency The meshing efficiency and efficiency fluctuation for gears under different operating conditions are shown in F ig. 10. η AFC and ηTFC represent the average efficiency under Method I and Method II, respectively. η AFC and ηTFC represent the instantaneous efficiency fluctuation under Method I and Method II, respectively. F ig. 10a shows the influence of different output torques on the average efficiency and efficiency fluctuation. The average efficiency obtained by Method I decreases as the input torque increases, while Method II shows the opposite trend. The difference in the results obtained by the two methods is mainly due to the fact that the friction coefficient calculation formula in Method I increases with the increase of the output torque, causing an increase in 3 RESULTS The efficiency of a gear pair is not only related to factors such as friction coefficient and tooth load distribution but also to operating conditions. P revious research has focused on the effects of friction coefficient calculation models, gear ratios, addendum modification coefficients, loads, and speeds on gear efficiency [12], [15], and [16], neglecting the effects of gear surface roughness and lubricant operating temperature on gear efficiency and lacking exploration of the effects of different operating conditions on torque fluctuations during gear meshing. Improper a) b) c) d) Fig. 10. Efficiency and efficiency fluctuation of gears; a) at case 2, b) at case 3, c) at case 4, and d) at case 5 64 Tian, X. – Wang, G. – Jiang, Y. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 55-69 oil film in the gear contact area becomes difficult, leading to an increase in friction losses and a decrease in efficiency. F rom F ig. 10d, with the increase in lubricating oil temperature, the gear efficiency of Method I decreases by 0.06 % , and the gear efficiency of Method II increases by 1.32 % . The result shows that the AF C is not sensitive to lubricant operating temperature, which is consistent with the results obtained in [33]. W hen the oil temperature increases, the viscosity of the lubricant decreases, which significantly improves efficiency. H owever, in Method II, when the oil temperature rises, the viscosity of the lubricant decreases and the efficiency improves significantly. Therefore, in gear design, it is necessary to select a reasonable operating temperature range for the lubricant according to the actual operating conditions, to fully utiliz e the properties of the lubricant, reduce the frictional power loss of gears, and improve the efficiency of the robot joint reducer. frictional losses, resulting in a decrease in efficiency. H owever, the effect of the efficiency decrease is not significant, only 0.1 . In contrast, the friction coefficient formula in Method II results in a decrease in instantaneous friction coefficient with the increase of the output torque, resulting in a decrease in frictional losses and an increase in efficiency. The amplitude of the efficiency fluctuation is greater than that of the efficiency obtained by Method I. The difference in gear meshing efficiency values obtained by the two methods is at most 1.44 % . The main reason for the difference in calculation results is that the friction coefficient at each contact point in Method II is a local variable that varies with time, while the friction coefficient in Method I is an average value along the contact line. The effect of input speed on gear efficiency is shown in F ig.10b. W hen the speed increases from 1000 rpm to 100 00 rpm, the efficiency obtained by both methods increases with the speed. The average efficiency under Method I and Method II increased by 0.25 % and 0.4 % , respectively. F rom F ig. 10c , gear efficiency decreases with increasing surface roughness, by 0.2 for Method I and 1.5 for Method II. This indicates that the TF C is highly sensitive to surface roughness, because as the roughness increases, the formation of the lubricating a) c) 3.2 Gear Instantaneous Input Torque Under Different Operating Conditions In this section, the input torque fluctuations due to instantaneous efficiency fluctuations are discussed under constant load torque conditions. F ig. 1 1a shows b) d) Fig. 11. Input torque and torque fluctuation of gears; a) at case 2, b) at case 3, c) at case 4, and d) at case 5 A New Calculation Method for Instantaneous Efficiency and Torque Fluctuation of Spur Gears 65 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 55-69 the influence of different output torques on the input torque fluctuations of the gear. Tin _ AFC and Tin _ TFC represent the average input torque under Method I and Method II respectively. Tin _ AFC and Tin _ TFC represent the instantaneous torque fluctuation under Method I and Method II, respectively. It can be seen that when the output torque increases, the torque fluctuation will increase with the increase of output torque, whether the AF C or the TF C is used. Therefore, it is necessary to choose a suitable output torque range according to the actual operating conditions in gear design, to reduce the torque power loss and improve the working smoothly of the robot joint reducer. As F ig. 1 1b shows, increasing the rpm from 1000 rpm to 1000 rpm reduced torque fluctuation by 36 % and 20 % for Method I and Method II, respectively. F ig. 1 1c shows that gear input torque fluctuation increases with surface roughness, especially under EH L conditions. Therefore, in design, it is necessary to ensure the smoothness of the gear contact surface as much as possible to promote the formation of oil film on the meshing surface and reduce the torque fluctuation during gear meshing. F rom F ig. 1 1d, as the lubricating oil temperature increases from 40 º C to 100 º C , the gear input torque fluctuation of Method I increases from 0.64 N m to 0.70 N m, and the gear input torque fluctuation of Method II decreases from 2.63 N m to 1.22 N m. U nder EH L conditions, the lubricating oil operating temperature is one of the important factors affecting gear efficiency and torque fluctuation. As the temperature rises, the viscosity of the lubricating oil decreases, which can reduce the viscous resistance of the oil and improve the meshing efficiency of the gear, thereby reducing the input torque fluctuation. Through the analysis of gear efficiency and torque fluctuation under the same operating conditions in F igs. 10b and 1 1b, F igs. 10c and 1 1c , F igs. 10 d and 1 1d, it was found that regardless of using Method I or Method II, the average input torque of the gear will decrease as the average efficiency increases. At the same time, the input torque fluctuation of the gear increases with the increase of efficiency fluctuation. Therefore, studying the laws of gear efficiency and torque fluctuation is conducive to establishing a more accurate friction model and torque fluctuation compensation method for the joint reducer of collaborative robots. 4 DISCUSSION The gear transmission efficiency and torque fluctuation are influenced by various factors, 66 including gear output torque, input speed, tooth surface roughness, and temperature, among which the friction coefficient has the greatest impact. In Method I, decreasing the output torque and gear roughness and increasing the input speed can improve gear efficiency, with roughness and speed having the greatest influence on efficiency, while lubricating oil temperature has little effect. In Method II, increasing the output torque, rotational speed, and lubricating oil temperature, and decreasing gear roughness can enhance gear efficiency, with suitable roughness and lubricating oil temperature contributing to around 1 .5 % efficiency improvement. The average efficiency calculated by Method I and Method II differs by a maximum of 1.86 % . U nder case 4, the instantaneous efficiency variation of the gear can reach 3.34 % . R egarding the input torque fluctuation, both Method I and Method II can reduce the torque fluctuation amplitude by lowering the output torque, and the gear surface roughness, and increasing the speed, resulting in smoother gear operation. In addition, in Method II, raising the lubricating oil temperature can reduce torque fluctuation by 53.6 % . U nder case 2, the torque fluctuation of the gear can reach 5.1 Nm. Method I assumes a constant friction coefficient along the meshing line, neglecting the influence of lubricating oil temperature, and is often used to calculate the average efficiency of gears or roughly evaluate gear performance in spur gear transmission design. The friction coefficient of Method II varies along the meshing line and is based on the instantaneous efficiency calculation model presented in this study, so the combination of the two provides a good evaluation of the real-time efficiency at each meshing position in the spur gear pair. F or an accurate calculation of the instantaneous efficiency of the gear, the time-varying friction coefficient is recommended in this study. To evaluate the accuracy of the calculation method proposed in this paper, the numerical results obtained by the present method were compared with those reported in previous studies under the same conditions as described in the reference [15]. Table 3 and F ig. 12 presents the factors considered and the corresponding results from the efficiency calculation models described in the literature. The comparison showed that the average efficiency calculated using the present method I was consistent with the results reported by H öhn [11] and Diez -Ibarbia et al. [15], with a difference of only 0.01 % . This can be attributed to the fact that the present study did not treat the friction coefficient as a constant but allowed it to vary with the changing contact conditions at different mesh positions, as shown in F ig. 4. Through comparative Tian, X. – Wang, G. – Jiang, Y. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 55-69 a) b) Fig. 12. Gear efficiency comparison; a) average efficiency under different methods, and b) instantaneous efficiency under different methods Table 3. Comparison of results between different methods under the same conditions Method Höhn [11] Diez-Ibarbia et al. [15] Proposed Method I Wang et al. [19] Proposed Method II Instantaneous efficiency Average efficiency ✓ ✓ ✓ ✓ ✓ symbol ✓: the method has this characteristic. analysis, the effectiveness and accuracy of the proposed method in this paper have been verified. This paper proposes a more accurate calculation model for the instantaneous efficiency of gear pairs compared to the model proposed in reference [19], by considering the meshing position, load distribution, and both average and time-varying friction coefficient models of the gear pair. 5 CONCLUSIONS In this paper, through the analysis of the meshing characteristics of the external meshing gear pair, a numerical calculation model for the instantaneous efficiency of the gear is established under the comprehensive consideration of the friction coefficient model, the load distribution model between the teeth and the torque balance of the meshing point. This model can calculate the instantaneous efficiency of the gear and its corresponding input torque fluctuations. Then, two different friction coefficient models are used to compare the change laws of gear instantaneous efficiency and instantaneous input torque along the meshing position under the same Method I ✓ ✓ ✓ Method II ✓ Load distribution ✓ ✓ ✓ ✓ ✓ Torque balance ✓ ✓ η [%] 99.21 99.22 99.32 98.03 99.01 operating conditions, and also studies the changing law of gear efficiency and efficiency fluctuation, input torque and input torque fluctuation under different load, speed, roughness, and temperature conditions. The following conclusions can be drawn: The instantaneous efficiency of gears in the double-tooth meshing area is lower than that in the single-tooth meshing area. Ensuring continuous and stable transmission of gears, the gear transmission efficiency can be improved by reducing the degree of contact ratio. Different friction coefficient models have a significant impact on the efficiency and efficiency fluctuation of gears. The efficiency calculated using the time-varying friction coefficient model is lower than that calculated using the average friction coefficient model, and the maximum difference between the two is 1.86 % . In contrast, the value of the torque fluctuation under the average friction coefficient is smaller than that under the time-varying friction coefficient. The instantaneous efficiency of the gear increases and the instantaneous input torque decreases under constant load. The gear efficiency A New Calculation Method for Instantaneous Efficiency and Torque Fluctuation of Spur Gears 67 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 55-69 fluctuation increases, and the torque fluctuation at the input end also increases. U nder specific operating conditions, the gear pair’ s instantaneous efficiency variation can reach 3.34 % , and the tor ue fluctuation can reach 5.1 Nm. Increasing the input speed, raising the operating temperature of the lubricating oil, and reducing the surface roughness of the gear can improve the gear transmission efficiency and reduce the torque fluctuation during meshing. In addition, an increase in output torque will increase the torque fluctuation. This paper presents numerical calculations of the instantaneous efficiency and torque fluctuation of an external meshing gear pair using theoretical analysis. Some of the computed results are consistent with previous studies. H owever, the presented model only considered the instantaneous efficiency and torque fluctuation of gears under sliding friction, while neglecting the effects of rolling friction losses and non-load-related losses on gear efficiency and torque fluctuation. In addition, the precision and manufacturing errors of gear are also ignored. Therefore, experimental verification of the model is still necessary in future research. 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Tribology Internationa, vol. 106, p. 109-122, DOI:10.1016/j.triboint.2016.05.051. Fernandes, C.M.C.G., Martins, R.C., Seabra, J.H.O. (2016). Coefficient of friction equation for gears based on a modified Hersey parameter. Tribology Interntional, vol. 101, p. 204-217, DOI:10.1016/j.triboint.2016.03.02. A New Calculation Method for Instantaneous Efficiency and Torque Fluctuation of Spur Gears 69 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 70-79 © 2024 The Authors. CC BY 4.0 Int. Licensee: SV-JME DOI:10.5545/sv-jme.2023.718 Original Scientific Paper Received for review: 2023-07-05 Received revised form: 2023-10-10 Accepted for publication: 2023-11-07 Investigation of the Titanium Alloy T urning Process w ith Prime A Tools under H igh-Pressure Cooling Conditions Struz ikiewicz , G . G rz egorz Struz ikiewicz * AG H U niversity of Science and Technology, P oland When turning titanium alloys, it is difficult to ensure the required quality with maximum machining efficiency. A typical problem in the turning process of titanium alloys is to achieve effective breaking and removal of chips from the machining zone. The combination of the new construction of cutting tools and machining methods in the machining of titanium alloys increases the efficiency of the machining. For this reason, the use of tools typical for the Prime Turning method in combination with the high-pressure cooling (HPC) method was analysed. The longitudinal turning of the Ti6Al4V ELI titanium alloy was performed using Sandvik Coromant grade 1115 carbide tools. An increase in the pressure of the cutting fluid to p = 70 bar was used. Measurements of the components of the total cutting force for finishing machining with variable cutting parameters in the range of: feed rates f = <0.1;0.4> mm/rev, cutting depth ap = <0.25;1.0> mm and cutting speed vc = <40;80> m/min were performed. It has been shown that the values of cutting force are mainly dependent on the feed and the depth of cut. An analysis of the forms of chips obtained is presented. The dependence of the applied cutting parameters on the value of the chip breakage coefficient Cch was determined. The method of searching for the maximum efficiency of the turning process was determined, taking into account the desired value of the chip breakage coefficient. Keywords: turning, titanium alloy, cutting forces, chip form, chip breakage index Highlights • Using the carbide cutting insert CP-A1104-L5 and the HPC method is an effective means of improving productivity in the turning process of the Ti6Al4V ELI titanium alloy. • The cutting parameters have a significant impact on the values of the components of the total cutting force and the chip breakage index. • It is possible to increase the efficiency of the machining process by maintaining the required chip form. 0 INTRODUCTION The optimiz ation of existing titanium alloy machining processes and the use of new machining techniques enable the achievement of the expected efficiency and quality of machining at low cost [1]. This is particularly significant for the machining of expensive materials or demanding materials. Titanium alloys, next to nickel alloys and heat-resistant steels, are difficult-to-cut materials. This is due to the specific mechanical and chemical properties that characteriz e this group of materials [2] and [3]. Due to their high strength, corrosion resistance and inertness, titanium alloys are most often used by the automotive, aerospace, chemical and medical industries [4]. On-going research broadens knowledge in the field of machining titanium alloys. The area of research described in the literature concerns the influence of cutting parameters on the roughness of the machined surface and the determination of the value of forces or temperature in the cutting z one [5]. Another important issue is the process of breaking chips during machining and the use of calculation methods that enable the simulation of cutting processes [6] and [7]. Accelerated wear of cutting tools 70 due to high temperatures in the cutting z one and stress concentration at the edge of the cutting insert are also frequently analysed issues [1] and [8]. The machinability of titanium alloys can be increased as a result of the use or combination of different techniques and machining methods. F or example, the use of various cooling methods in the cutting processes of titanium alloys yields measurable results. The literature describes the results of research on machining under dry cutting conditions, with minimal quantity or high pressure of the cutting fluid, as well as cryo-machining [8] to [12]. Increasing the efficiency of the titanium alloy machining process can be achieved using the high-pressure cooling (H P C ) method. C urrently, the pressure range recommended by cutting tool manufacturers to work with titanium alloys is 50 bar to 300 bar. This method allows faster heat dissipation and lower temperatures in the cutting z one. C ompared to typical cooling, this results in a longer cutting tool life of up to 15 times. H P C machining greatly supports the chip-breaking process and chip removal outside the machining z one [4] and [10]. This is particularly important for turning and drilling processes [13]. *Corr. Author’s Address: Faculty of Mechanical Engineering and Robotics, AGH University of Science and Technology, 30-059 Cracow, Poland, gstruzik@agh.edu.pl Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 70-79 In the case of turning titanium alloys under H P C conditions, the selection of tool materials is important. P alanisamy et al. [15] described the results of experimental studies on the machining of inserts made of cemented carbide. The authors showed that H P C machining increases tool life by almost three times compared to conventional cooling. F urthermore, they showed that the mechanical effect of the liquid jet on the chips supports the process of breaking and removing chips from the cutting z one. H P C machining has been shown to produce short, segmented chips. In turn, Ez ugwu et al. [16] analysed the machinability of titanium alloys under conventional and high-pressure cooling conditions with tools made of cemented carbides and coated with various coatings. They also demonstrated reduced cutting tool wear under H P C machining conditions. Da Silva et al. [17] analysed the mechanism of tool wear during high-speed machining of titanium alloys. They showed that tool life decreased with increasing cutting speed, and increased productivity was achieved during high-pressure cooling. In turn, Stolf et al. [18] analysed the method of tool wear due to tool-chip contact conditions during H P C machining of the Ti6A l4V alloy. They found that the coolant pressure and the maximum wear on the flank surface are inversely proportional. This is due to the effect on the process of abrasion of heat acting on the surface of the cutting tool application. The authors also pointed out that H P C machining has a positive effect on lowering the temperature of the tool and on the chip breakage process. Kaminski and Alvelid [19] showed that high coolant pressure causes fluid to enter the slip z one, reducing friction and temperature. In addition, the high-pressure cutting fluid stream reduces the chip winding radius and shortens the contact time between the tool and the chips. In turn, L iang et al. [20] performed Ti6A l4V surface integrity tests at different cooling pressures and injection positions of cutting fluid. The researchers examined three injection positions, i.e., only injection in the rake face, only in the flank face, and injection in both rake/ flank face directions. They observed that compared to dry cutting and H P C conditions, 3D surface roughness parameters were reduced during high-pressure jet-assisted machining. Masek et al. [21] analysed the influence of the direction of liquid supply to the cutting z one during polycrystalline diamond (P C D) machining. Their study showed that double cooling is strongly recommended when machining titanium alloys, both on the rake surface and on the flank surface, and the results showed that the appropriate H P C intensity was around 60 bar. This results in an increase in the efficiency of the chip- breaking process with reduced tool wear. Ç olak [22] optimiz ed the H P C machining process using genetic algorithms due to the desired surface roughness. Surface roughness and chip breaking were selected as optimisation criteria due to their importance for the finishing turning process. One of the recently developed concepts for increasing the efficiency of the machining process is the so-called P rime Turning method. This concept takes into account the changed geometry of the cutting tool. These cutting inserts have three edges for longitudinal, face and profiling turning. This ensures efficient use of the edges and a longer tool life. Krajčoviech et al. wrote about the use of this type of tool for steel machining [23]. The authors showed that the depth of cut has the most significant impact on the values of cutting forces. According to a review of the literature presented, researchers investigated various H P C strategies with the common goal of reducing tool wear or increasing process efficiency. H owever, the impact of machining efficiency of various cutting conditions is connected with different cutting parameter values and tool geometry, methods of cutting liquid delivery, etc. F urthermore, analysis of the quality of the cutting process could be realiz ed from different points of view. In this regard, there are still few analyses that take chip forms into account. Due to the problems described above for obtaining effective machining of titanium alloys, Ti6A l4V EL I alloy turning tests were carried out under conditions of feeding the cutting fluid with increased pressure and using P rime A turning tools. The experimental research plan took into account three variables, i.e., feed, depth, and cutting speed. During the experiments, the processes of cutting forces were recorded, microscopic analysis of the chip form was carried out and the chip breakage coefficient was determined. The concept of maximising machining efficiency is presented, taking into account the favourable form of the chips. 1 METHODS The experimental research plan was developed according to the Taguchi method [24] for three variables, i.e., feed f , depth of cut ap and cutting speed vc . The 16t h test systems were designated. F or statistical analysis, every group of the experimental run was done three times, for a total of 48 trials (16 3 runs). Table 1 shows the assumed ranges of cutting data values. The values of the cutting parameters are within the range of cutting parameters recommended by the tool manufacturer for turning titanium alloys. Investigation of the Titanium Alloy Turning Process with Prime A Tools under High-Pressure Cooling Conditions 71 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 70-79 Table 1. The variables values in the research plan No. Coded parameter Real parameter 1 A f 2 B 3 C ap [mm] vc [m/min] [mm/rev] Value 0.1 0.2 0.3 0.4 0.25 0.50 0.75 1.0 40 80 The signal-to-noise (S / N ) ratio analysis strategy was adopted as “ the lowest-best” according to Eq. (1) [24]. 1 n  S / N  10  log   yi2  . (1)  n i 1  A modified classification and characteristics of the chips presented by F ang et al. [25] and L ee et al. [26] were adopted. The aim of the modification was to adapt the classification of chips to practical industrial use. In general, chips can be described using words and numbers. In practice, a typical approach is to characteriz e chips using language terms such as “ good” , “ weak” , etc. The authors of the paper presented a concept in which there are four different types of chip shapes, i.e., arch/ bulky, spiral/ circular, helical/ tubular and ribbon. F or each chip type, two main dimensional characteristics of the chips were assigned, which in turn were converted into numerical values. These values can be used to classify and determine the chip breakage coefficient [27]. During the investigation, the analysis of the form of the chips and their classification and evaluation were carried out. Only two forms of chips obtained during machining tests were observed, i.e., arc/ bulky and helical/ tubular type chips. F or these types of chips, the dimensional characteristics were adopted according to Table 2. simplified method of chip classification was adopted, according to which the chip breakage index Cc h takes values from 0 to 1 and is described by Eq. (2). L ower Cc h values represent better chip breakability. 0.01  Dimch if 0  Dimch  Dimch _ limit 2 Cch  Dim    , ,(2) if Dimch  Dimch _ limit 2  1 where • D i mc h_l i mi t1 5 mm; correct chips (0 < Cc h 0.2); • D i mc h_l i mi t 1 > 5 mm and D i mc h_l i mi t 2 20 mm; acceptable chips (0.2 < Cc h < 1.0) ; • D i mc h_l i mi t 2 > 20 mm; unfavourable chips (Cc h = const. = 1.0) . W here D i mc h were described for arc/ bulky chips by Eq. (3) and for helical/ tubular chips by Eq. (4): Dimch  Wch  H ch , (3 ) Dimch  Lch  Dch . (4) Table 2. Dimensional features of chips obtained during cutting tests Group Chip index characterization Helical/Tubular Arc/Bulky W c h - W idth L H ch - H eight c h - L ength D Fig. 1. Sample of chips photographs for parameters: a) f = 0.4 mm/rev, ap = 0.50 mm, vc = 40 m/min, b) f = 0.4 mm/rev, ap = 0.75 mm, vc = 80 m/min, and c) f = 0.1 mm/rev, ap = 1.00 mm, vc = 40 m/min c h - Diameter Based on the dimensions of the measured chip, the chip breakage coefficient Cc h was determined according to Eqs. (2) to (4). In the investigation, a 72 The main criterion for the assessment of chip form was the chip dimensions, i.e., length and height for arc chips or length and spiral diameters for tubular Struzikiewicz, G. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 70-79 chips. A three-stage assessment of the chip form was assumed, i.e., correct chips up to 5 mm, acceptable chips up to 5 mm to 20 mm and incorrect chips over 20 mm. The following markings were adopted when assessing the form of chips: “ + ” chips correct (good); “ –” chips unfavourable (poor); “ 0” chips acceptable (fair). Example photographs of chips are shown in F ig. 1. edge was used in each machining test. The impact of cutting-edge wear was not analysed. A constant cutting liquid pressure of p = 70 bar was used, and Blaser’ s 10 % Blasocut 2000 universal emulsion was used as the cutting fluid. The selected cutting parameters were within the range of finishing titanium alloys. The tests were carried out on a conventional lathe, equipped with a 150 ba r pressure high-pressure plunger pump. 2 EXPERIMENTAL Ti6A l4V-EL I (extra low interstitials) titanium alloy contains less oxygen, nitrogen, carbon, and iron than a typical Ti6A l4V alloy. This improves the ductility and resistance to cracking of the material, which means that this alloy is used in dentistry and medicine, for example, for orthopaedic implants [27]. The material to be processed was a shaft with a diameter of D c = 50 mm. The mechanical properties of the alloy were as follows: tensile strength = 02 MPa, hardness = 2 HRc, elongation 13 , ield MP a. C hemical composition ware: strength0.2% = 815 Al 6.1 % , V 4.13 % , F e 0.05 % , O 0.1 % , N 0.01 % , C < 0.01 % , H 0.003 % and Ti remainder. The longitudinal turning process was analysed under conditions of coolant supply with increased pressure. The cutting fluid was fed to the rake face by the cutting tool through the tool holder noz z le. In cutting tests, cutting inserts of type P rime A turning (F ig. 2) type C P -A1 10 4-L 5 grade 1 1 15 and the tool holder Q S-C P -30A R -2020-1 1C from Sandvik C oromant were used. The value of the corner radius of the cutting insert was rƐ = 0.4 mm. A new cutting Table 3. Test results for measurements of cutting force F No A B C 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 1 1 1 2 3 4 1 1 2 2 1 1 1 2 c Fig. 2. Cutting tool Prime A During the research, measurements of the components of the total cutting force and microscopic measurements of the chip dimensions were carried out. To record and analyse the components of the cutting forces, a measuring track system consisting of a 257B dynamometer and a Kistler 5070B amplifier was used. C hip analysis was carried out using a Keyence VH X -7000 type 3D microscope with dedicated measurement software. and chip breakage coefficient Cc f [mm/rev] ap [mm] vc [m/min] F 0.1 0.1 0.1 0.1 0.2 1.00 0.75 0.50 0.25 1.00 40 40 80 80 40 h [N] 255.4 208.7 140.0 68.2 462.3 c _m ean S/NFc –48.2 –46.4 –42.9 –36.7 –53.3 2 2 1 0.2 0.75 40 395.3 –52.0 2 3 2 0.2 0.50 80 210.6 122.0 610.0 445.9 285.4 152.3 776.0 545.0 –46.5 –41.7 –55.7 –53.0 –49.1 –43.7 –57.8 –54.7 2 4 2 0.2 0.25 80 3 1 2 0.3 1.00 0.75 0.50 0.25 1.00 0.75 80 80 40 40 80 80 3 2 2 0.3 3 3 1 1 2 2 0.3 0.3 0.4 0.4 3 4 4 4 1 2 Cc h_m ean 1.00 0.17 0.07 0.05 0.41 0.13 0.07 0.05 0.42 0.14 0.05 0.04 0.20 0.10 4 3 1 0.4 0.50 40 351.2 –50.9 0.06 4 4 1 0.4 0.25 40 184.1 -45.3 0.05 Investigation of the Titanium Alloy Turning Process with Prime A Tools under High-Pressure Cooling Conditions S/NCch 0.0 15.2 22.9 26.6 7.5 17.6 23.2 26.4 7.4 17.2 25.2 27.3 14.0 19.6 24.8 25.9 73 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 70-79 3 RESULTS In accordance with the adopted research plan, measurements of the components of the total cutting force and geometrical dimensions of the chips obtained were made. The influence of the assumed variables, i.e., feed values f [ mm/ rev] and depth ap [ mm] and cutting speed vc [ m/ min] on the values of components of the total cutting force, i.e., main cutting force F c [ N ] , feed force F f [ N ] and resistive F p [ N ] was analysed. Table 3 presents the results of the average values of the cutting force F c _m ean , and the chip breakage coefficient Cc h_m ean and the values of a) the SN parameter obtained in individual test systems. Tables 4 and 5 present a statistical analysis of the results. F igs. 3 and 4 show the influence of individual variables on the average value of the main cutting force F c and the values of the chip breakage coefficient Cc h. 4 DISCUSSION The analysis of the measurement results showed a linear dependence of the values of all components of the total cutting force on the assumed values of the b) c) d) Fig. 3. Influence of the analysed cutting parameters on the mean values of the cutting force F c ; a) each parameter in separate graphs: feed f , depth of cut ap and cutting speed vc ; b) only depth of cut ap; c) only depth of cut ap and feed f ; and d) only cutting speed vc and feed f 74 Struzikiewicz, G. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 70-79 a) b) c) d) Fig. 4. Influence of the analysed cutting parameters on the mean values of the chip breakability index Cc h; a) each parameter in separate graphs: feed f , depth of cut ap and cutting speed vc ; b) only depth of cut ap; and c) only cutting speed vc ; and d) only feed f and depth of cut ap cutting parameters during the H P C turning of the titanium alloy Ti6A l4V EL I. The most significant factors (F ig. 3) on the value of the cutting force F c were depth of cut ap and feed f . The depth of cut contributed 58 % and the feed rate contributed 30 % in the F c response of the cutting force during the machining of the alloy. This was due to the increase in the cross section of the cut layer, which required the cutting process to use higher cutting forces. A fourfold increase in feed value or cutting depth results in about a fourfold increase in the average cutting force. In turn, a twofold increase in cutting speed, that is, from vc = 40 m/ min to vc = 80 m/ min, resulted in an increase (by about 50 N ) in the average cutting force F c . F or cutting speed vc = 8 0 m/ min, an increase in the intensity of increase in cutting forces was observed, both as a function of depth of cut ap and feed f (F ig. 3c and d). The analysis of the data obtained showed that the chip form and average values of the chip breakage coefficient in the longitudinal turning process are significantly influenced by the tested cutting parameters (F ig. 4a), with the cutting depth ap most significantly. The depth of cut contributed 70 % in chip breakage coefficient Cc h responses during the turning of the tested alloy. The cutting speed vc and Investigation of the Titanium Alloy Turning Process with Prime A Tools under High-Pressure Cooling Conditions 75 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 70-79 Table 4. Analysis of variance for mean values for cutting force F c Source DF SeqSS AdjSS AdjMS F P f 3 188287 188287 62762 18.96 0.001 ap vc 3 357200 357200 119067 35.96 0.000 58 1 24255 24255 24255 7.33 0.027 12 Residual Error Total 8 15 26486 596228 26486 3311 Table 5. Analysis of variance for mean values for chip breakability index Cc % Contribution 30 h Source DF SeqSS AdjSS AdjMS F P f 3 0.107 0.107 0.036 1.36 0.323 % Contribution 14 ap vc 3 0.558 0.558 0.186 7.09 0.012 70 1 0.042 0.042 0.042 1.61 0.240 16 Residual Error Total 8 15 0.210 0.917 0.210 0.026 the feed rate f contributed, respectively, 16 % and 14 % . In this case, the correct and acceptable form of chips results from the simultaneous action of the pressure of the cutting fluid and the shape of the chip groove on the rake surface of the insert. F or increasing depth of cut and feed values, the chip groove is filled with the chip material to a greater degree. The chip winding radius is also reduced (more short arc chips). The pressure of the cutting fluid additionally supports the process of chip winding and cracking. The chipcracking process may also be supported by the impact of the chip formed against the unfinished surface of the workpiece or the flank surface of the cutting insert. In contrast, increasing values of depth of cut cause a much faster increase in the average values of the chip breakage coefficient Cc h (F ig. 4b). An increase in the depth of cut value causes an increase in the width of the created chip. The chip strength are increased. The pressure of the cutting fluid may not be sufficient to initiate the chip cracking process. The determined regression equations F c (f ,ap,vc ) and Cc h(f ,ap,vc ) are shown below.     Fc f , a p , vc  366  964  f  534  a p  1.95  vc , (5) Cch f , a p , vc  0.711  1.899  f  1.192  a p It was also observed that for the cutting speed vc = 80 m/ min, lower values of the Cc h coefficient and thus a more correct form of chips were obtained (F ig. 4c). The unacceptable form of chips (F ig. 4d) was obtained for low feed values (e.g., f = 0.1 mm/ min) and large depth of cut values (e.g., ap = 1.0 mm). It is a prerequisite to look for an increase in the efficiency of the machining process, taking into account the correct form of the chips. This is particularly important for the finishing machining titanium alloys. Analysing the results obtained, it can be concluded that increased machining efficiency should be sought by selecting higher values of depth or cutting speed. It is well-known that the feed value has a significant and negative effect on the surface roughness. Therefore, for finishing machining, it may be difficult to increase productivity by increasing feed value. An example illustrating the method is shown in F ig. 5. In the analysed case, F c 200 N and Cc h 0.2 (correct form of chips) were adopted as limiting criteria to not exceed the cutting force value. The cutting force diagrams F c and Cc h were determined on the basis of the regression equations presented in Eqs. (5) and (6) . The material removal rate Q v was established according to Eq. (7) :  A confirmatory test was performed to verify the predicted values compared to the experimental values. The results obtained (Table 6) showed a good precision of the predicted cutting force values and the classification of chips based on the chip breakability index Cc h. 76  Qv f , a p , vc  f  a p  vc . [ cm3 / min] . 0.00257  vc  2.479  f 2  1.418  a 2p .(6) (7 ) Taking into account the limiting criteria, it can be noted that the adoption of a higher cutting speed value (i.e., vc = 80 m/ min) results in an increase in the material removal rate, from Q v = 4 cm3 / min to Q v = 6.2 cm3 /min, which is an increase of more than 50 % in efficiency. Despite the reduction in depth of Struzikiewicz, G. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 70-79 Table 6. Results for confirmation test No F c _ mean [N] F c _ an ti c i pated [N] F c perc ent age error [%] 3 255.4 208.7 140.0 342.4 208.9 153.4 34.1 0.1 9.6 4 68.2 19.9 70.8 5 462.3 395.3 210.6 122.0 438.8 305.3 249.8 116.3 5.1 22.8 18.6 4.7 1 2 6 7 8 9 610.0 613.2 0.5 10 445.9 285.4 152.3 776.0 479.7 268.2 134.7 709.6 7.6 6.0 11.6 8.6 11 12 13 14 545.0 576.1 5.7 15 351.2 184.1 364.6 231.1 3.8 25.5 16 Cc cut ap resulting from the limitation of the permissible value of the cutting force F c . It should be noted that an increase in the cutting speed may accelerate the wear of the cutting tools. This may result in higher manufacturing costs. The presented method does not take into account the tool life of the cutting edge. Fig. 5. Method of searching for an increase in material removal rate Q v 5 CONCLUSIONS The purpose of the experimental research was to analyse the machinability of the Ti6A l4V EL I titanium alloy with P rime A turning tools made of h_ mean 1.00 0.17 0.07 0.05 0.41 0.13 0.07 0.05 0.42 0.14 0.05 0.04 0.20 0.10 0.06 0.05 Chi ps c l ass. unfavo. correct correct correct accept. correct correct correct accept. correct correct correct correct correct correct correct Cc h_ mean _ an ti c i pated 0.67 0.35 0.10 0.13 0.55 0.23 0.00 0.02 0.38 0.06 0.02 0.05 0.37 0.05 0.00 0.04 A nt i c i p. c hi ps c l ass. accept.. accept. correct correct accept. accept. correct correct accept. correct correct correct accept. correct correct correct cemented carbides under machining conditions with increased pressure of the cutting fluid. The main area of analysis was to determine the influence of the cutting parameters (f , ap, vc ) on the values of the cutting forces, as well as the chip breakage coefficient Cc h and the form of the chips. The results of the analysis showed that: the values of the cutting force F c depend linearly on the cutting parameters adopted. According to the statistical analysis, the cutting depth ap was the most significant parameter, followed by feed f , which affects the cutting force. The cutting speed vc affected the mean cutting force to a much lesser extent. the cutting depth ap was the most significant parameter which affects the chip breakability index Cc h. The obtained form of chips (correct, acceptable, and incorrect) depends on the range of cutting parameters used. On average, for the tested ranges of cutting parameter values, a correct chip form was obtained for: ap 0.75 mm, f 0.2 mm/rev. A higher cutting speed value, that is, for vc = 80 m/ min, reduced the chip breakage coefficient value. obtaining a correct form of chips in the finishing turning of titanium alloy Ti6A l4V under H P C machining conditions depends on the synergistic impact of factors such as the values of cutting parameters, the shape and degree of filling of the chip breaker on the rake face, as well as the pressure of the cutting fluid. U nder these Investigation of the Titanium Alloy Turning Process with Prime A Tools under High-Pressure Cooling Conditions 77 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 70-79 conditions, it is possible to increase the machining efficiency by selecting the cutting speed. In the case presented, the increase in the material removal rate Q v of the machining was more than 50 % . [12] 8 REFERENCES [1] Saini, A., Pabla, B.S., Dhami, S.S. (2016). Developments in cutting tool technology in improving machinability of Ti6Al4V alloy: A review. 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Journal of Materials Processing Technology, vol. 173, no. 2, p. 166-171, DOI:10.1016/j.matprotec.2005.05.057. [27] Festas, A., Ramos, A., Davim, J.P. (2021). Machining of titanium alloys for medical application - a review. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, vol. 236, no. 4, p. 309-318, DOI:10.1177/09544054211028531. Investigation of the Titanium Alloy Turning Process with Prime A Tools under High-Pressure Cooling Conditions 79 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 80-91 © 2024 The Authors. CC BY 4.0 Int. Licensee: SV-JME DOI:10.5545/sv-jme.2023.722 Received for review: 2023-07-12 Received revised form: 2023-10-17 Accepted for publication: 2023-10-30 Original Scientific Paper A Modified Approach to the R ack Generation of Beveloid Gears entürk, B.G. Fetvac , M.C. Berat Gürcan entürk1,* Mahmut Cüneyt Fetvac 2 1 Dogus U niversity, Turkey U niversity-C errahpasa, Turkey 2Istanbul The purpose of this paper is to present an easier and more efficient method for the determination of the geometry of a bevelled gear tooth. Based on a method that provides an easier way for the rack generation of involute helical gears, the mathematical model of a beveloid gear is studied. The mathematical procedure for developing two-dimensional cross-sections has been extended to three-dimensional gear models. A computer programme is developed to obtain generating and generated surfaces. The proposed algorithm is compared with the previous studies for verification and validation. The results demonstrate that the coordinates obtained from the given method are nearly the same on the start and end points of the main gear parts, such as the involute and root fillets regions. Also, between the limits, the values can be considered acceptable. A coordinate deviation of the gear profile has been observed in the mathematical model, because of the profile shift. Modifications have been developed in the equations to eliminate these cases. The main advantage of the proposed method is to obtain mathematical models without carrying out some of the calculation steps used in previous studies. Eventually, this feature will provide an easier and faster method to develop computer-aided models of the beveloid gear types. Keywords: beveloid gears, mathematical modelling, rack-type cutters, parametric modelling, involute profile Highlights • An extended mathematical model for involute gears generated by rack-type cutters. • Implementation differences between the given method and the previous methods have been compared. • Avoiding the deviation of the profile caused by the profile shift. • Coordinates of the critical points on the roots are analysed. 0 INTRODUCTION G ear wheels, which are widely used in power transmission, have a wide range of applications from watches to automobiles, from printers to helicopters. In applications requiring high reliability, high strength, and low weight, simulating the physical behaviour of gear wheels in operating conditions before manufacturing saves time and material in the product development stage. N umerical tools, such as the finite element method, are widely used to calculate the bending strength, contact stress, and transmission error of gear wheels. An accurate representation of the gear tooth geometry is essential for a reliable numerical analysis. R ack-type cutters are widely used in the mass production of involute gears. A rack cutter is composed of three generating sections: involute, tip fillet, and topland. The corresponding generated surfaces of a gear are the involute flank, trochoidal root fillet, and root bottomland [1] and [2]. The mathematical equations of a gear tooth profile can be obtained based on the profile of the generating cutter, the manufacturing process, and gear meshing theory [3]. There are many studies on the mathematical modelling of gear wheels manufactured by rack 80 cutters in the literature [3], [4] and [5]. To mention some other studies as rack cutter modelling examples, Yang et al. have proposed a mathematical model for helical gears with asymmetric teeth [6]. Element construction and dynamic analysis have been made by H uang et al. for involute spur and helical gears [7]. F igliolini and R ea proposed a general algorithm for the kinematic synthesis of spur and helical gears and analysed the effects of the design parameters on the undercutting [8]. An approach for a mathematical model and contact analysis of helical gears was developed by Z eyin et.al. [9]. Another parameteriz ed approach to establish a high precision three-dimension finite element model of involute helical gears is proposed by L iu et.al. [10]. In that study, a refinement methodology of the elements has been developed to improve the mesh quality and accuracy. A new tooth surface modelling method for beveloid gears has been proposed, and influences of the design parameters on the contact behaviours of parallel beveloid gears have been studied by Sun et al. [11]. entürk and Fetvac have developed a mathematical method to prevent undercutting on the beveloid gear models [12]. Mesh stiffness is also a frequently studied topic for computeriz ed gear modeling. A potential energy-based method was proposed by Song et al. to calculate the * orr. ut or s ddress: o u University, epartment o ec anical ngineering, stanbul, Turkey, bsenturk@dogus.edu.tr Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 80-91 mesh stiffness for straight beveloid gears with parallel axes. The effects of parameters, such as the pressure angle, pitch cone angle, and profile shift coefficient on the mesh stiffness were investigated [13]. Another mesh stiffness model has been generated by Z hou et al., which considers the direction variation of the tooth friction and wear influence on single gear–rack tooth pair mesh stiffness [14]. In another significant study, a calculation method of tooth profile modification for tooth contact analysis technology is proposed by W ang et al. [15]. In all the studies mentioned, the rack cutter generating method has been used in the modelling of gear geometries. L itvin’ s Vector Approach, which also takes into account functional or production-required modifications, is widely used in the mathematical modelling of gear wheels. This approach also can be extended to all gear wheel modifications such as concave, crowning [16], parabolic modifications [17] and [18], non-circular gears [19] and cylindrical gears [20]. The mathematical model of the concave beveloid gears given, and contact simulations have been performed in [21]. C oncave beveloid gears are also modelled and analysed in [22], [23] and [24]. The research on gear tooth modifications continues, such as the research on the external non-involute gear profiles. A review is made on this topic by Okorn et al. [25]. Also, experimental research investigates the characteristics and increases the performance of the gear systems, such as the electrical control anti backlash method proposed by W ang et al. [26] and the experimental study and numerical analysis on aviation spiral bevel gear made by L i et.al. [27]. By generaliz ing the mathematical model for parallel axis gears, a model including spur, helical, straight beveloid, and helical beveloid gears can be obtained [4], [5] and [7]. A beveloid gear can be generated by a basic rack whose pitch plane intersects with the axis of the gear and forms an angle equal to the generating cone angle [4]. In the computer simulation of gear wheels, the vector representation of the generating tool is first established. U sually, equations are expressed in the normal section. C oordinate transformation is performed in the case of helical and/ or conical geometries. Then, the cutter geometry at the transverse section is expressed in the coordinate system of the gear to be manufactured. The next step is to establish the equation of meshing by using differential geometry and gear theory. Thus, the mathematical model of the gear wheel is obtained. In the publications mentioned above, the coordinate systems used for determining the tool geometries may be oriented differently. The right-hand type of a cartesian coordinate system is preferred. Analytical description of the rack tooth geometry and intervals of curvilinear parameters may change due to the orientation of the coordinate system attached to the generating cutter. In most of the papers engineering approach to differential geometry proposed by L itvin is used to establish the equation of meshing. In Batista' s study [28], the origin of the coordinate system, unlike with other researchers, is located at the point where the pitch line intersects the involute edge, as illustrated in F ig. 1 compared to other studies, Batista did not use the directional cosines of the cutter surface vector in the determination of the equation of meshing. The steps followed in modelling provide ease of computer programming. Fig. 1. Different coordinate systems for normal section of rack cutter The mathematical models of beveloid gears generated by rack-type cutters are studied in various research works [7], [11] and [12]. The aim of this study is to extend the mathematical model proposed by Batista to beveloid (involute conical) gearing. This way, when compared to the previous studies, the gear tooth geometry can be expressed in a much simpler form, depending on the roll angle. Also, the gear simulation process will be less time consuming by shortening the modelling algorithm. In scope of this work, the design steps of the proposed modelling method are given clearly, by showing the mathematical equations of the design parameters, including the modifications for the conical and beveloid gear geometries. G ear tooth profiles drawn by the previous studies and the present method are compared, and finally, the modelling algorithms are shown. 1 METHODS According to one of the previous methods proposed by L iu et.al. [4], a beveloid gear can be modelled by defining the rack cutter geometry and simulating the translation and rotation of the cutter around the global A Modified Approach to the Rack Generation of Beveloid Gears 81 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 80-91  u   xL    tan(  n1, 2 ) yL    2 2  yL 0  ( 1, 2 )  ( xL 0  xL )   mn  cn   mn  xL  u tan( n1, 2 ) 4 u tan( n1, 2 )  xL  mn tan( n1, 2 ) , (1 ) mn tan( n1, 2 )  xL  xL 0 xL 0  xL  coordinate system origin, S C. Dimensions of the rack cutter design parameters are given in F ig. 2. Also, the figure shows the asymmetrical state, in which both tapered and helical hobbing conditions exist in the gear model. 1, 2  cn mn 4 1  sin  n1, 2  , xL 0  mn tan  n1, 2   1, 2 cos  n1, 2  , yL 0  mn  1, 2 sin  n1, 2  . (2) F or plotting, we can define the tool geometry in the global cartesian coordinate system S 0, as written in Eq. (3) .  xN   xL   0.25 mn  y   y    . 0   N  L  In Eq. (1) , the equations that define the beveloid tooth profile can be simplified according to the position of this chosen coordinate system. Because of this orientation, intervals of the design parameters can be changed when compared to previous studies [4], [6], [12]. F ig. 2 shows that the rack cutter coordinate system is placed over the involute section. The angles β and δ are the helical and cone angles of the gear tooth, respectively. F rom F ig. 2, the coordinates can be defined analytically by Eq. (1) . H ere, the radius of the root fillets ρ1 and ρ2 and the origin coordinates x L 0 and yL 0 of the rack coordinate system S L can be expressed as: 82 On Eq. (3 ). the + and – signs are for the left and right side of the rack, respectively. Eq. (3) draws only one of the rack cutter profiles for the z ero position in 2D. The rack cutter crosssection is translated by ri φ and rolled by an angle which is one of the major design parameters φ. After the translation and rotation processes, twodimensional cross-section of the beveloid gear, which has an asymmetrical profile due to the helix and cone angles, is drawn by the imaginary motion of the inclined rack cutter cross-sections (see F ig. 3) . y [ mm] Fig. 2. The configuration of rack cutter and reference coordinate system (3 ) x [ mm] Fig. 3. The rack cutter generation process for beveloid gears Şentürk, B.G. – Fetvacı, M.C. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 80-91 Because of the helix and cone angles, the position of the rack cutter should be turned around the horiz ontal and vertical axis X N and Y N , by the amount of δ and β, respectively. The rotation matrices are given in Eq. (4). M CP M PN 0 0 1 0 cos( )  sin( )  0 sin( ) cos( )  0 0 0 cos(  )  0   sin(  )   0 0 1 0 0 0 0  , 0  1  sin(  )  sin(  )   0 0 . cos(  )  cos(  )   0 1  If the third row of Eq. (5) is rearranged for z C = z , the parameter λ can be calculated as in Eq. (6) . W ith the help of this parameter, a two-dimensional crosssection of the rack can be defined.  (4)  xC  R C   yC    zC  xN cos      sin          xN sin   sin     y N cos     sin   cos     . (5)   y N sin    xN cos   sin      cos  ²  cos    z  y N sin    xN cos   sin    cos    cos   . (6) On the analytical definitions, different from the formulations given in the previous studies, normal vectors are not used. Instead, the meshing condition is simulated with the help of partial derivatives. F inally, the parametric equations for the geometric positions of the rack cutter have been derived. As explained earlier, the global and rack coordinate systems are defined and can be seen in F ig. 4. The relation between these systems can be expressed as: X  X 0  xN sin    y N cos   , (7) Y  Y0  xN cos    y N sin   . (8) The involute of the circle, which described by the origin of the rack coordinate system S 0, can be defined as: X 0  R0 cos    R0 sin   , Y0  R0 sin    R0 cos   . ( ) (10) The vertical position of the rack cutter should be redefined due to the profile shift e. The equation of the generated gear tooth surface at the transverse section can be explained by Eq. (12) . y N  y N  e, (1 1) X   R0  e  yC  cos     R0  xC  sin   , (12) Y   R0  e  yC  sin     R0  xC  cos   . (13) In Eqs. (1 1) to (13) , parameters x C and yC can be defined as x C = x C(s) and yC = yC(s) . H ere s is defined as an arbitrary continuous parameter. To be able to calculate the roll angle φ, the condition during the meshing of the gears in contact can be written as in Eq. (14) , Fig. 4. Relations among the coordinate systems By applying these coordinate transformations, we can obtain tooth geometry in the S C coordinate system. The term λ states the translation of the origin O c and is integrated into the matrix MPN.  X Y Y  X   0.   s   s (14) After the parameters in Eqs. (12) and (13) are differentiated, and plugged, in Eq. (14) the roll angle φ can be calculated as, A Modified Approach to the Rack Generation of Beveloid Gears 83 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 80-91   xC    dy 1  xC  e  yC  dxC . R0 L (15) dyC can be H ere, the value for the derivative dxL written as in Eq. (16) :     dyC   dxL      0 1  tan  t1, 2  xL 0  xL    x 2 1, 2 L0 tan  n1, 2  , (16) 2  xL  tan  t1, 2  Fig. 6. Generating rack and generated gear in mesh 0 By using Eqs. (5) , (6) , (12) , (13 ), (15) and (16) , we can obtain generated gear geometry in the plane of rotation (in transverse section). In this manner, a three-dimensional beveloid gear tooth can be modelled with the help of changed cross-sections with respect to coordinate z . In Eq. (16) , αt1,2 is included in the formulation to state the pressure angle on the transverse plane. If not, because of the helical and conical properties, this condition will cause geometric irregularities on the involute section and the root fillets. This modification is one of the major changes made in the mathematical models proposed by Batista [28]. This relationship can be seen in F ig. 5. The equations of “ αt1,2 ” on each side of the rack can be written as in Eqs. (1 7) and (18) . These expressions are proposed on the previous works by L iu and Tsay [4]. It has been observed in the present mathematical model that the conventional profil shift causes coordinate deviation of the generated helical beveloid gear. To compensate for this deviation, gear blank is re-rotated by the angle γ. e   e tan    sin   R0 en , cos   or   en tan    (1 ) tan   R . (20) F ig. 6 shows this effect for the parameters, mn = 1 mm, z = 40, δ = 14° , β = 24° , en = 0.5 mn . F or this case, the deflection is 2.53527e -03 rad (0.1452603° ). R0  mn z cos    . 2 (21 ) After defining the deflection angle, the correction can be made by following Fig. 5. Generating rack and generated gear in mesh 1  cos   sin  n1   cos  n1  sin    sin      t1   tan    , (17)  cos  n1  cos      1  cos   sin  n 2   cos  n 2  sin    sin     t 2   tan    . (18)  cos  n 2  cos       X G   cos    sin    0   X c    R G   YG    sin    cos    0   Yc  .  Z G   0 0 1   Z c  (22) After multiplying the gear profile coordinates by the correction matrix in Eq. (22), gear coordinates with the profile shift, X G , Y G and Z G can be obtained. 1.1 Gear Generation After generating the tooth profiles in two dimensions, cross-section geometries can be combined using 84 Şentürk, B.G. – Fetvacı, M.C. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 80-91 geometric methods offered by computer-aided design (C AD) software. After modelling the single gear tooth, the 3D geometries can be duplicated. F ig. 7a displays the change in geometry through the tooth width. By using these cross-section geometries, solid models of beveloid gears can be built. C onsecutive cross-sections form the tooth surfaces as seen in F igs. 7b and in c the complete model is seen. F ig. 8a displays the geometric parameters of the designed beveloid gear pair, such as the centre distance, tip and root diameters and the tooth thickness. The design parameters are: mn = 3 mm, a) for both pinion z = 24, αn 1 = αn 2 = 20° , δ = 15° , β = 15° and gear. The 3D models of the gear geometries has been produced by 3 D printer using, fused deposition modelling (F DM) technique. It can be seen on F igs. 8b and c that the tooth thickness is becoming smaller, and undercutting can start to occur on the side where the height of the root region is the greatest and becoming larger on the other side where the root height is the smallest. G ear geometries in both F igs. 8b and c are the same, but the gears are flipped. Fig. displays the generation algorithms of previous studies in Fig. a and the proposed method b) Fig. 7. Beveloid gear generation steps c) a) b) c) Fig. 8. Geometric parameters of the gear pair and generated beveloid gears; a) beveloid gear pair on parallel axes, b) and c) views form the front and back sides of the beveloid gear model respectively A Modified Approach to the Rack Generation of Beveloid Gears 85 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 80-91 Fig. 9. Gear generation algorithms a) previous studies, b) proposed method in Fig. b. It has seen that the calculating algorithm is shortened. F or this reason, the modelling process for the proposed model becomes much simpler and less time consuming. F or the cross-section generation, values for the roll angle “ φi ” is calculated by meshing equation Eq. (1 5) . In this manner, the definition of normal vectors will not be necessary. As seen in Eq. (A8) the normal vector equation is a function of both the “ l R ” and “ λ” parameters. The symbolic definition of a normal vector becomes large and hard to calculate after the cross multiplication operations. W ith the help of the new proposed method, gear cross-sections can be drawn directly from coordinate definitons “ X and Y ” as in Eqs. (5) and (6) . 2 RESULTS Based on the proposed mathematical model, a program is developed to obtain generating and generated surfaces. F ig. 10 displays cross-section geometries of beveloid gears for design parameters ... mn = 4 mm, z 86 = 25, αn 1 = αn 2 = 20° , δ = 20° , β = 0° for F ig. 10 a and δ = 20° , β = 20° for F ig. 10b. The same parameters are also used in F igs. 1 1 to 13. F ig. 1 1 shows the comparison of the gear tooth geometries drawn by the previous and the new proposed method. It is clearly seen that the position coordinates are nearly the same. H ere, the helical and cone angles are the same as in F ig. 10b. After the mathematical model for the twodimensional cross-sections has been completed, the involute and root fillet regions are compared with the previous models. F igs. 1 1 and 12 show the change in the root fillets due to tooth width and cone angle respectively. As seen in F ig. 12, the distance between the position coordinates of the root fillet regions is sensitive to the excessive undercut cases. These situations can occur either with the increase in the cone angle or the change in the tooth width through undercut sections. Mathematically, this inconsistency is caused by the square root terms in the root fillet definitions of the proposed model. Şentürk, B.G. – Fetvacı, M.C. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 80-91 Fig. 10. 2D cross-sections of conical and beveloid gear models; a) non-helical, b) helical beveloid gear models Fig. 11. Comparison of conventional method and the method proposed by Batista [28] in 2D; a) the side with no undercut, and b) undercut side Fig. 12. The root fillet coordinates of 2D beveloid gear models generated by previous and new developed methods; a) δ = 10°, β = 10° and z = 15 mm to 25 mm, and b) δ = 15° to 30°, β = 20° F ig. 1 3 indicates the same result, by comparing the radius values R , which is the square root of sum of square values of horiz ontal and vertical position coordinates. The coordinate values are chosen from the regions where the root fillets are connected to the involute sections. At high cone angle values, undercutting starts to occur. The patterns do not follow the geometric A Modified Approach to the Rack Generation of Beveloid Gears 87 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 80-91 a) b) Fig. 13. The change in radius values R based on the change in a) tooth width, and b) cone angle δ contour around the undercut regions of the models drawn by previous methods. N evertheless, the twodimensional geometries are compatible with the previous ones on the end points of the root fillets.In general applications, cone angles are not selected as high values to cause undercutting problems (mostly up to 15° ). Because of that, deviation cases do not cause serious modelling errors. C onsequently, the variation between the calculation algorithms cause a relatively small difference in the coordinates when undercutting status is concerned. This condition can be fixed by practical geometric techniques offered by C AD programs. Also, the results shows that the differences between the coordinate values are within acceptable limits. It is obvious that the modelling technique proposed by Batista [28] makes it easier to define the gear cross-section geometries and enables the designers to avoid time-consuming techniques. In this way, especially for the computer simulations of gears, modelling the point clouds and tooth surfaces of the involute, root fillet, bottom land, and tip regions of the beveloid gears will be easier and less time-consuming. The mathematical model proposed in this study, can be extended to different gear geometries such as non-circular, cylindrical gears, and curvilinear gear teeth [19], [20] and [29], and internal gears [30]. Also parabolic modification [17] and [18] and generating cutter can be considered [31] to [33]. 3 CONCLUSION 4 NOMENCLATURES In this study, Batista’ s mathematical model for rack generation [28] has been extended to beveloid gears. That model was developed for 2D cross-sections; the modified equations in the proposed method allows for model gear geometries in three dimensions by changing the cross-section accurately, considering the effect of the cone angle. The mathematical equations are given briefly, and the modelling algorithms are compared with the previous method proposed by L iu and Tsay [4]. It has seen that the gear tooth profiles generated by the two methods overlap very closely with each other. Also, while adapting of the equations, it has been observed that the profile shift parameters cause the cross-sections to rotate by a small angle around the tooth width axis for beveloid geometries. To avoid that, a modification angle has been developed and included in the equations. The detailed investigation on the root fillet regions for helical and conical cases showed that the change in the position coordinates is within acceptable limits. 88 δ cone angle, [ ° ] β helix angle, [ ° ] ρ1,2 root fillet radius, [ mm] c n clearance, [ mm] u addendum, [ mm] mn normal module, [ mm] αn 1,2 pressure angle on normal plane, [ ° ] αt1,2 pressure angle on transverse plane, [ ° ] z gear tooth width, [ mm] φ roll angle, [ ° ] e profile shift in transverse section, [ mm] en profile shift in normal section, [ mm] γ deflection angle, [ ° ] R 0 pitch circle radius, [ mm] 5 REFERENCES [1] elaska, . . ears and ear rives. o n iley ons, Chichester, DOI:10.1002/9781118392393. [2] Vullo, V. (2020). Gears. Spinger, Cham, DOI:10.1007/978-3030-40164-1. Şentürk, B.G. – Fetvacı, M.C. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 80-91 [3] Litvin, F.L., Fuentes, A. (2004). Gear Geometry and Applied Theory. 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M cn  cos(  ) 0  sin(  )  sin(  )     sin(  ) sin( ) cos( )  cos(  ) sin( )  cos(  ) sin( )    ,(A5)  cos( ) sin(  ) sin( ) cos(  ) cos( )  cos(  ) cos( )    0 0 0 1   The position vector R ci can be obtained as: R ci =  M cn  R ni , The components of the vector are: xci  xni cos      sin    , yci  yni cos     cos    sin   6 APPENDIX  xni sin   sin    , zci  yni sin     cos    cos   Comparison of Mathematical Models The calculation process due to the generation method proposed by L iu and Tsay [4] is explained in detail. The coordinates of the involute section is:  xnR  bc  lR sin  n1   c y mn      R nR   ynR    lR cos  n1   . (A1)   zR   0  n    xni cos   sin    . cos(  ) 0  sin(  )  sin(  )   0  0 0 1  . (A4) M pn    sin(  ) 0 cos(  )  cos(  )    0 0 1  0  By multiplying Mcp with Mpn, Mcn can be written as: 90 nci  (A2) where ac and at are addendum and dedendum values respectively and equal to normal module mn and b c = 0.25 πmn . The value c y can be determined as 0, 1, 2, … so that the rack cutter and generated gear can be modeled with desired number of teeth. The rotation matrices for the cone and helix angles can be written as: 0 0 0 1 0 cos( )  sin( ) 0  , M cp   (A3) 0 sin( ) cos( ) 0    0 0 1 0 (A7 ) H ere, λ is the same offset parameter which is given in Eq. (6) . In this way, coordinates of the 2D gear cross-sections can be calculated for an arbitrary value of tooth thickness in the axis of z . In the next step, the normal vectors of the cutting tool surfaces nci should be calculated as: H ere l R is the coordinates of the involute section of the rack, where: ac at  lR  , cos  n1  cos  n1  (A6 ) Rci Rci  lR 1 Rci Rci  lR 1 . (A8 ) C onsidering the rolling process, the relation between the rack cutter and the generated gear can be specified with the matrix M1c . M1c......  ... ... ... 1 ) sin(1 )  cos(   sin( ) cos( ) 1 1   0 0  0  0 0 r1 (sin(1 )  1 cos(1 ))  0 r1 (cos(1 )  1 sin(1 ))  . (A )  1 0  0 1  The roll angle of the generated gear φ1 can be calculated by considering the fundamental law of gearing. X ci  xci Yci  yci Z ci  zci   , nxci niyc nzci (A10 ) where X ci , Yci and Z ci are the coordinates of an arbitrary point on the instant center of rotation I-I. i Detailed explanation is given in [6]. H ere, nxci , n yc i and nzc are the direction cosines of the unit normal Şentürk, B.G. – Fetvacı, M.C. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 80-91 nci . U sing this relation, the angle φ1 can be obtained as: 1 y n  i c i xc i p  xci niyc rn i xc . (A1 1) After calculating the related parameters as specified, coordinates of the generated gear can be obtained by calculating the coordinate vector R1 i . R1i   M1c  Rci . The calculation steps shows that, the position vector can not be obtained without calculating the roll angle ϕ1 . Eq. (A1 1) requires the calculation of the unit normal nci . The proposed mathematical method in this study, enables to complete the process without this calculation. The roll angle φ can be calculated directly by Eq. (14) and the gear coordinates can be obtained by Eq. (12) . (A12) A Modified Approach to the Rack Generation of Beveloid Gears 91 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 92-102 © 2024 The Authors. CC BY 4.0 Int. Licensee: SV-JME DOI:10.5545/sv-jme.2023.781 Original Scientific Paper Received for review: 2023-09-01 Received revised form: 2023-11-30 Accepted for publication: 2023-12-13 Investigation on the Application of Wor n Cutting Tool Inserts as Burnishing Tools Ad yaman, O. Oktay Ad yaman* 1 Batman U niversity, Besiri Organiz ed Industrial Z one Vocational School, Turkey The amount of wear in cutting tools used in all machining processes is around 1 % to 2 % evaluation of the non-wearing areas of the inserts is economically beneficial. This study aims to test the usability of the non-wearing regions of the waste tungsten carbide (WC), cubic boron nitride (CBN) and ceramic inserts as a rolling tool in the deep rolling method and to observe their performance. The turned workpieces were deep rolled with three different types of waste-cutting tools (WC, CBN and ceramic) in different machining parameters (rolling force, number of passes, and feed rate). As a result, surface roughness and microhardness values obtained in deep rolling operations with these inserts were similar to those in deep rolling operations with other rolling tools. It has been determined that ceramic inserts perform better in deep rolling processes in terms of microhardness, and WC inserts perform better in terms of surface roughness. Thus, it has been determined that waste WC, CBN and ceramic inserts can be used in the deep rolling method. Keywords: deep rolling, ball burnishing, microhardness, tribology, surface roughness Highlights • Deep rolling process is a surface treatment process that has been studied in recent years. • The inserts (WC, ceramic, CBN, etc.) used in machining processes have areas that are largely (≈ 98 % to 99 %) non-worn after use. • The use of non-worn areas of these tools is very valuable from economic and environmental points of view. • The use of these waste inserts in deep rolling processes is an alternative. 0 INTRODUCTION The cutting insert wear occurs at a rate of 1 % to 2 % in machining applications, and after this damage, they are junked [1], which is a great loss in terms of economy and environment. R ecycled W C makes up nearly 20 % and 30 % of the total production according to statistics. R etrieving tungsten carbide decreases the raw material cost between 15 % and 50 % [2]. All these reasons make the studies related to re-evaluation of these cutting tools that have become wasted very significant. The increasing metal demand throughout the world has encouraged intensive studies for extracting metals from low grade ores and/ or from secondary sources [3]. Among these metals, the main raw materials of cutting tools such as tungsten carbide (W C ), cubic boron nitride (C BN ) and ceramic, are the most important materials in industrial applications [3]. Since the production of cutting inserts is a very costly process, regaining these inserts through recycling makes the process more important [4]. Besides the benefit that recycling studies bring together with them [5], it is an expensive process, which encourages seeking different alternatives. This makes the reuse of waste-cutting inserts important. The deep rolling process is a surface treatment process. Deep rolling that F ord C ompany first applied to axle shafts dates back to the 1 30s [6]. The basic 92 mechanism in this method is the surface pressure effect created between a workpiece and a spherical ball end in the contacted area, as explained through H ertz ian theory [7]. As a result of this surface pressure, residual tensions and micro structural deformations (hardening/ softening) occur since the yield force of the material is exceeded [8], [9], and [6]. Studies about deep rolling are still continuing in various ways, such as simulation works about deep rolling [10], deep rolling analysis through finite elements method [11], and [12], trials of deep rolling in different work conditions (for example: cryogenic) [13], and deep rolling analysis through regression methods etc.. It is seen that hardness, corrosion resistance and fatigue life have been obtained as a result of press residual stress formed on the surfaces by deep rolling [14]. The good surface quality obtained and the spreading possibility of fatigue cracks are counteracted by residual press stresses [14]. Deep rolling nitration, similar to that of induction hardening and hardening with laser processes, has effects on the surface of the workpiece at values close to the values of surface penetration depth [6]. The cutting tools used in machining processes have areas that are largely ( 8 to ) non-worn after use. Except for the studies on recycling cutting tools, no studies were found in the literature on the evaluation of unused surfaces of inserts. In order to *Corr. Author’s Address: Besiri Organized Industrial Zone Vocational School, Batman University, Batman, Turkey, oktay.adiyaman@batman.edu.tr Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 92-102 achieve this aim, the non-worn insert areas on the surfaces of cutting tools were used as the crushing edge in the deep rolling method, and thus, it was recovered again. In this context, three different cutting insert types (W C , C BN and and ceramic) that had become waste were selected and processed by a deeprolling method with different processing parameters of AISI 1050 steel. Thus, the applicability of the deep rolling method in the recycling of these inserts was investigated. The performances of the inserts used were compared in terms of microhardness, surface roughness ( R a) and the resulting surface appearance. The aim of this article is not to analyse deep rolling, but to detail whether the waste inserts achieve the results in deep rolling or not. a) 1 MATERIALS AND METHODS A SMAR C brand C AK616B X 200 model computer numerical control (C N C ) lathe was used in all turning operations (F ig. 1a ). In the cutting process in general turning operations, the upper surface of the cutting tool is aligned with the workpiece axis. In this study, in the deep rolling process, the middle region of the used and worn cutting edge was aligned in the same direction of the workpiece axis (F ig. 1b ). H enceforth, the used waste insert will be called the roll insert. The roll insert was mounted on the C N C lathe turret with a specially designed tool holder (F ig. 1c ). In order to adjust the pressure force of the cutting tool and the tool holder, the pressure force was adjusted by changing the spring length as a result of the connection apparatus that was specially designed and connected to the turret. Three different clamping force values adjusted according to the spring pressure lengths in the spring catalogue [15] were selected (F ig. 1c ). The pressure forces were not separately measured during the experiment, yet the table values were taken as reference. H ere, the basic aim is to investigate and measure the effects according to force increase rather than measuring the forces. In all deep rolling processes, three different roll inserts were used. The inserts were chosen from different types of each group, such as the P VD-coated M30 series (W C ) (82 % W C + 5 % titanium carbide (TiC ) + 10 % C o), (C BN ) and ceramic. All cutting inserts chosen were previously used and became waste materials (F ig. 2). AISI 1050 steel (20 mm diameter and 70 mm long) was used in the experiments. The work piece with an 18 mm diameter was primarily finish applied material. The average hardness of the material before rolling was measured as 220 H V0.5 t o -240 H V0.5. b) c) Fig. 1. Schematic representation of conducting deep rolling and aligning waste cutting tool with workpiece a) All operations b) tool alignment c) tool holder a) b) c) Fig. 2. Different waste inserts a) WC, b) CBN, and c) ceramic In the experiments, three pressure forces (143 N , 30 N and 4 5 N), three passes (1, 2 and 3) and three feed rate values (0.04 mm/ rev, 0.08 mm/ rev and 0.12 mm/ rev) were selected. Thus, for each inserts, 27 experiments (Table 1) , 81 experiments in total were performed for all inserts. N o cooling was used in the experiments. Variance analysis was performed to examine the effect of process parameters on the results for both microhardness and R a. Investigation on the Application of Worn Cutting Tool Inserts as Burnishing Tools 93 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 92-102 Table 1. The design matrix for the experiments WC –CBN-Ceramic Exp. Insert Number of passes Feed rate [mm/rev] No 1 1 0.04 2 1 0.08 3 1 0.12 4 2 0.04 5 2 0.08 6 2 0.12 7 3 0.04 8 3 0.08 9 3 0.12 10 1 0.04 11 1 0.08 12 1 0.12 13 2 0.04 14 2 0.08 15 2 0.12 16 3 0.04 17 3 0.08 18 3 0.12 19 1 0.04 20 1 0.08 21 1 0.12 22 2 0.04 23 2 0.08 24 2 0.12 25 3 0.04 26 3 0.08 27 3 0.12 27 for each insert, 81 total experiments Force [N] 143 143 143 143 143 143 143 143 143 330 330 330 330 330 330 330 330 330 495 495 495 495 495 495 495 495 495 Fig. 3. The worn areas in inserts Three different types of roll inserts shown in F ig. 6 were calculated as both insert wear length ( V bm ax ) and the worn area (A ), and the results are shown in Table 2. F or each pass, an equal 0.04 mm depth of pass was applied. F or the microhardness, 27 pieces from the parts with a feed rate of 0.08 mm/ rev were selected. Microhardness was measured from at three different points of the cylindrical surface of each selected part and was assigned by calculating the arithmetic average of the three values measured. F or the face microhardness, the microhardness was measured as 10 values by shifting 70 µ m from the edge to the axis of the part. F or the surface roughness, the arithmetic mean of R a values measured from three different areas of each cylindrical surface was accepted as the surface R a of the experiment sample. 2 RESULTS AND DISCUSSION 2.1 Tool Wear The purpose of the study to re-evaluate waste-cutting tools by using them in the rolling process. The 94 damages occurring in the nose part of the cutting tools are shown in F ig. 3. Table 2. Worn area values Tool type WC insert CBN Ceramic [mm] 1.1525 1.236 1.339 V bm ax Area, A [mm2] 1.059 0.910 0.758 In the observations, no significant wear was observed on the surface of all three insert types. In the W N MG and C BN insert types, it was observed that the coating layer was erased, but no trace of abrasion was formed on the surface (F ig. 6a and b). Only a black z one has formed due to heat and abrasion. Of the insert types used, the ceramic tip is uncoated. As seen in F ig. 6c group, there was no significant wearrelated damage on this insert type; only a black area was caused by heat and dirt. W hat is expressed as V bm ax here is not actually the wear value in the real sense but is expressed only as the dimensional length of the trace formed. F rom the results obtained, it is Adıyaman, O. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 92-102 possible to say that every insert type can be used in deep rolling. C onsidering Table 2 data, it is seen that the dimensional lengths of the traces (here as the edge wear length ( V bm ax ) ) are close to each other. W hen the siz es of the areas formed by the traces are examined, it is seen that the largest area is with the W C -type insert, and the smallest area is with the ceramic-type insert. 2.2 Microhardness Microhardness measurements were carried out to examine the number of passes in the radial direction on the face surface of the simples, and the microhardness values graph of values from cylindrical surfaces are seen in F ig. 4a. W hen the graph of F ig. 4a is examined, it is seen that there is an increase in the hardness caused by deep rolling on the surface of the workpiece. This situation presents parallelism with the results of many studies in the literature [16] to [18]. the most important factors in microhardness [22]. As can be seen in F ig. 4a, the highest hardness value was obtained in the experiment with three passes, and the lowest value was obtained in one pass. There is a difference in surface hardness up to 500 µ m below the surface. Studies on deep rolling show that the depth of the affected area varies between 500 µ m to –1 µ m [13], [16] and [20]. This depth varies according to material type, process parameters and application environment (cryogenic, etc.). W hen each insert type was analysed according to the values, the graphic in F ig. 5 w ere obtained. a) a) b) b) c) Fig. 4. a) Microhardness graph in radial direction, b) status of traces, and c) surface distribution of traces It was also stated that the highest hardness occurred on the surface and the hardness decreased from the surface to the centre [12], [14], [18] and [19]. Abrã o et al. [20] stated that for AISI 10 60 steel, with the increase of rolling pressure and the number of passes, the intensity of the plastic stress under the surface increased, resulting in an increase in both the microhardness value and the depth of the affected z one. L oh et al. [21] found that the surface hardness of medium carbon steel increased by an average of 5 % after deep rolling with tungsten carbide balls. Also, rolling pressure and feed rate were found to be c) Fig. 5. Microhardness graphs according to insert types; a) WC, b) ceramic, and c) CBN This effect is also seen in other studies [12]. P arallel to this, the increase in the number of passes at all inserts also causes an increase in hardness. It is seen that the highest hardness values are obtained with the ceramic insert, and the lowest hardness values are obtained with the W C insert. Investigation on the Application of Worn Cutting Tool Inserts as Burnishing Tools 95 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 92-102 W hen the values in F ig. 5c are evaluated, it can be said that the use of ceramic inserts in deep rolling is more convenient in terms of microhardness. In applications for which hardness is required, ceramic inserts and high pass numbers are recommended. In general, it is seen from the graphs that instabilities in the C BN inserts occur with the increase in the pressing force. It is estimated that these instabilities are due to the instabilities on the surface of the work piece. In general terms, it is possible to say that the hardness increases in both the surface and radial directions in the deep rolling method for all inserts. This did not change in the use of waste inserts. It should also be noted that compared to previous studies, hardness values can be quite misleading in evaluating the hardening state because increases in hardness values are also induced by compressive residual stresses [23]. W hen F ig. 5 is examined, it is seen that the hardness of all inserts increases with the increase of the pressure force. Depending on the material, deep rolling can result in the formation of dislocation cell structures [24], nanocrystals [9] and [25], twinning [18] or martensitic transformations [18]. W hen the surfaces with microhardness values are examined, it is seen that quite different structures are formed within the same region (F ig. 6) . In deep rolling, temperature is one of the most important criteria. The main source of formations on the surface is temperature [13] and [19]. As a result of plastic deformation of the surface (with changes in parameters such as feed rate, number of passes etc.), increases in temperature occur. Also, with effects such as a high feed rate, more force (partially converted to heat in the ball-work piece contact z one) is required for rolling [12]. In addition, the increased heat from the wear mechanism causes the structure to transform from ferrite to perlite or martensite. Accordingly, it is observed that carbide bands are formed (F ig. 6) . Maximov expresses the work obtained in the thermodynamic explanation of the tool and workpiece in the deep rolling process in Eq. (1) [19]. e dA  dAQe  dAel  dApl . is seen that the hardest structure is the ceramic tip, followed by the C BN and W C tips, respectively. Since the thermal conductivity of W C -type and C BN -type inserts (60 W / (m K) to –80 W / (m K)) is higher than the thermal conductivity of ceramic inserts (10 W / (m K) to –20 W / (m K)) [26], W C and C BN inserts take most of the heat generated on themselves and do not transfer it to the material surface. U nlike W C and C BN inserts, since ceramic inserts have (1) e H ere dA the external (input) work, dAQe the work converted into heat and dAel + dApl are the elementary works of the external and the internal surface forces for the elastic and plastic deformation of the workpiece, respectively. Accordingly, the rise in temperature is an important parameter of the work achieved in deep rolling. Temperature increases on the workpiece thermodynamically have an improving effect on the work obtained. In the graphs in F ig. 8, it 96 Adıyaman, O. Fig. 6. Images of structures on surfaces Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 92-102 lower thermal conductivity, most of the heat generated in deep rolling is transferred to the workpiece. It is thought that [19] phase transformations occur thermodynamically as a result of the heat staying more on the workpiece, and as a result, the hardness increases. It is thought that the reason for the high hardness values in deep rolling with ceramic-type inserts is in this direction. Similar to this idea, in their study of carbon steels, Abrã o et al. and other researches [17], [20] and [27] stated that partial annealing, full annealing or quenching and tempering occur on AISI 1060 steel material. In particular, it was stated that the pressure force and the number of passes significantly increase the hardness [20]. In contrast, since the ferrite layers are transformed into perlite in the heat transfer, it was observed that the microhardness increases accordingly [19]. a) d) g) b) e) The results in Table 3 were obtained as a result of the AN OVA analysis performed to investigate to what extent the process parameters affected the microhardness. W hen the variance analysis table is examined, the values under the column shown with the P -value indicate whether the independent variables are statistically significant on the dependent variables. The fact that the P -value is less than 0.05 indicates that this value is statistically significant. In this regard, it can be seen that the insert type, force, and number of pass parameters on microhardness are statistically significant. It is the “ C ontribution” value that shows the effect of independent variables on dependent variables. Accordingly, it can be seen that the number of passes, insert type, and force are effective on microhardness by 44.77 % , 23.70 % and 13.53 % , respectively. This shows that deep rolling of c) f) h) j) Fig. 7. R a values measured according to feed rate and number of passes Investigation on the Application of Worn Cutting Tool Inserts as Burnishing Tools 97 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 92-102 Table 3. ANOVA for microhardness Source Insert type Force [N] Number of passes Error Total DF 2 2 2 20 26 Seq SS 33670 19218 63616 25578 142081 Contribution [%] 23.70 13.53 44.77 18.00 100.00 waste insert inserts produces a result parallel to the literature [17], [19] and [28]. W hen the graphs in F ig. 5 and the images in F ig. 6 are evaluated together with variance analysis, it is seen that the insert type is also effective as the number of passes increases. Each pass causes more deformation on the surface, resulting in a tougher structure and more carbide formation on the material surface, which is observed as an increase in microhardness. W ith each pass, the peaks on the surface fill into the valleys on the surface. If more passes are applied after a certain stage, a mechanism similar to slidingrubbing occurs between the material and the crushing tip. This situation causes the formation of debris and carbide bands similar to the one in F ig. 6. The number of passes having the greatest impact here is perhaps due to the filling of the valleys on the surface after the 1 st or 2nd pass and the burnishing turning into slidingrubbing after this stage. Therefore, more work is needed to obtain optimum values. W hen an excessive number of passes or rolling force is applied, the surface turns into a mechanism similar to ploughing, as in the grinding process. The fact that some of the slopes in F ig. 5 do not occur linearly or logarithmically can be defined as a result of the unstable structures formed. 2.3 Surface Roughness Each insert was separately examined according to R a values and relevant rolling force obtained, and the results are shown in F ig. 7. W hen F ig. 7 is examined, it is seen that the lowest R a values are obtained when f = 0.08 mm/ rev according to the different feed values selected. L ow and high feed rates have a negative effect on R a. This shows that optimum feed rates must be achieved in deep rolling. Data showing a direct relationship between progress and R a could not be obtained from the graphs in F ig. 7. P rabhu et al. found the coefficient effect of progress on R a very low in their regression and AN OVA analysis in deep rolling of AISI 4140 steel [29]. 98 Adj SS 33670 19218 63616 25578 Adj MS 16835 9609 31808 1279 F-value 13.16 7.51 24.87 P-value 0.000 0.004 0.000 In deep rolling, the surface of the workpiece is exposed to more heat as the time to reach the maximum temperature increases with the decrease of the feed value. In F igs. 7g, h and j graphs, higher R a values were obtained in ceramic inserts. H ere too, we believe that the temperature factor is effective. It is thought that the surface structure deteriorates due to the heat accumulated on the surface formed at the ceramic inserts, and as a result, increases in R a values occur. Similarly, in another study, it is stated that the decrease in feed causes the deformation of the surface layers near the roll insert, resulting in higher workpiece temperatures. It is stated that at higher feed rates, more power (partially converted to heat in the ball-work piece contact area) is required for deep rolling [12]. The low and high progress therefore, causes negative effects on the surface in terms of R a. F rom all this, we are of the opinion that optimum values should be applied for progress rather than low or high. In all graphs in F ig. 7, the R a value was mostly obtained at 0.08 mm/ rev as the optimum value. C onsidering the situations where the rolling force is low, it is seen that lower R a values are obtained in W C inserts than in C BN inserts (F igs. 7a , and d). H owever, when the rolling force is increased (F igs. 7b, c, d, and e), it is seen that C BN inserts have a more positive effect on R a. H ere, it can be concluded that the best R a values are obtained in W C inserts with low rolling forces and in C BN inserts with high rolling forces. In addition, according to these results, it can be said that the use of ceramic inserts in deep rolling applications where R a values are intended to be low is not appropriate compared to other insert types. It is observed that R a values generally increase with the increase in the number of passes in the W C insert (F igs. 7a , b, and c). H owever, the same trend cannot be said for C BN (F igs. 7d, e, and f) and ceramic (F igs. 7g, h, and j) inserts. In this respect, it can be said that the insert type, which is parallel to the literature in terms of R a values to be obtained, is W C -type inserts. Studies show that R a values decrease with the increase in the Adıyaman, O. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 92-102 number of passes [28] and [29] and the most effective parameter on R a is the number of passes [29]. The graphs obtained in order that the effect of the rolling force in connection with feed rate on R a can be better understood are presented in F ig. 8. Although it is said that the increase in the rolling force causes an increase in R a [20] and [29], there are also studies indicating that the increase in the rolling force leads to worse surface quality [28]. W hile interpreting this situation, some studies stated that when the rolling force exceeds a certain value, deterioration occurs as a result of overloading the material. Abrã o et al. found that for AISI 1060 steel, high-pressure values produced higher R a values than more moderatepressure values [28]. In deep rolling, the surface of the workpiece is exposed to more heat [12] and [29] as the time to reach the maximum temperature increases with the decrease of the feed rate value. This causes unstable R a values to occur in W C -type inserts at a low feed rate, depending on the rolling force and the number of passes (F ig. 8a ). At higher feed rates, a more balanced distribution and an increase in R a values are observed with the increase in rolling force (F igs. 8b, a nd c). a) b) c) d) e) f) g) h) j) Fig. 8. Display of the relation between rolling force and feed rate values according to inserts a,b and c) WC, d, e and f) CBN, and g, h and j) ceramic inserts Table 4. ANOVA for surface roughness (R a) Source DF Seq SS Contribution [%] Adj SS Adj MS F-value P-value Insert type 2 1.50865 18.23 1.50865 0.75433 12.18 0.000 Force [N] 2 0.37534 4.54 0.37534 0.18767 3.03 0.054 Number of passes 2 0.06379 0.77 0.06379 0.03189 0.52 0.600 Feed rate [mm/rev] 2 1.87061 22.60 1.87061 0.93531 15.11 0.000 Error 72 4.45776 53.86 4.45776 0.06191 Total 80 8.27616 100.00 Investigation on the Application of Worn Cutting Tool Inserts as Burnishing Tools 99 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 92-102 W hen F igs. 8a , b and c are examined, it is seen that the lowest R a values are f = 0.08 mm/ rev for W C type inserts, and R a values close to each other are obtained when the number of passes is two and three. Abrã o et al. [28] stated that there is a decrease in R a value after 50 bar pressure value, and deterioration occurs after 100 bar for AISI 1060 steel. They stated that the reason for this is the deterioration and spalling in the plastic flow. In F igs. 8b and c, it is understood that the compression value of 143 N for AISI 1050 steel is the most appropriate rolling force value for low R a values in W C -type inserts. L ooking at the C BN insert type, it is seen that the most stable and ideal feed is f = 0.08 mm/ rev, similar to the W C insert type (F ig. 8 e). H owever, here, unlike the W C insert type, R a values decrease with increasing rolling force (F ig. 8e ). In this insert type, it is understood that the most unstable and highest R a values are f = 0.12 mm/ rev (F ig. 8 f). R a values at low (f = 0.04 mm/ rev) and medium feeds (f = 0.08 mm/ rev) are quite low for this insert type (F igs. 8d, and e). In this type of insert, the ideal conditions for R a are low pass number, medium feed value (f = 0.08 m m/ rev) and high rolling force values. W hen looking at the ceramic insert type, it is seen that higher R a values occur in all cases compared to W C and C BN insert types (F igs. 8g, h and j). In this insert type, an increase in R a values is observed with an increase in rolling force. As explained, it was concluded that the formed high temperature remains on the workpiece due to the low thermal conductivity coefficient of the ceramic insert, and as a result, both instability and surface deterioration occur. It is seen that the ideal feed rate is f = 0.08 mm/ rev in the ceramic insert type as in the other insert types (F ig. 8h) . W hen this type of insert is used, low rolling force, low pass number and medium feed values should be chosen. Variance analysis was performed to see the interaction of R a and process parameters, to determine the effect rate of the parameters on R a, and to examine the issue statistically. As a result of the variance analysis, the values in Table 4 were obtained. W hen the variance analysis table (Table 4) for R a is examined, it is seen that the insert type and feed rate values on surface roughness are statistically significant. W hen the “ C ontribution” values, which reveal the effect of independent variables on the dependent variable R a, are examined, it is seen that the most effective parameter on R a is the feed rate. The effect ranking on the dependent variable R a was obtained as 22.6 0 % , 18.23 % , 4.54 % and 0.77 % for feed rate, insert type, force and number of passes, 100 respectively. The fact that the effect percentage rates here are not significantly different from each other prevents reaching a very clear conclusion for federate and insert types, which have a significant effect on R a. Even in the research referenced in the evaluations made for F ig. 8 above, no definite conclusions in machining could be reached. In this respect, more studies are needed to form certain opinions and formulations on deep rolling. 3 CONCLUSIONS and SUGGESTIONS The following conclusions and suggestions have been listed for W C , C BN and ceramic inserts used in the deep rolling process in order to have wasted cutting tools regained: In the deep rolling process with waste inserts, good results are obtained with W C and C BN type inserts in terms of surface roughness, and ceramic inserts in terms of microhardness. W hen the rolling force and pass numbers increased, it was seen that the microhardness in all types of inserts increased. The increase in microhardness is due to the increase in subsurface plastic stress intensity as a result of the increase in pressing force and number of passes. It was observed that the highest hardness values were obtained from ceramic inserts, while the lowest values were obtained from W C inserts. This situation is explained by the higher temperature increase on the surface due to the low thermal conductivity of ceramic tips. Medium feed rates are suitable for all insert types for AISI 1050 steel, and in this study, this value was established as f = 0.08 mm/ rev. In W C cutting inserts, unstable R a values formed with regard to rolling force and number of passes in low feed rates. It is thought that the high thermal conductivity of this insert type and the temperature increase on the surface at low feed are the sources of the unstable structure formed. In ceramic type insert, it was seen that in general, R a values increased with the increase in rolling force. Thus, when this type of insert is used, low rolling force, pass numbers, and medium feed should be chosen. In C BN -type inserts, it was seen that R a values decreased with the increase in rolling force. F or this type of insert, the ideal conditions for R a values occur at low pass numbers, medium feed value (f = 0.08 m m/ rev) and high rolling force. It was determined that the 143 N rolling value for AISI 1050 steel was the most suitable rolling force Adıyaman, O. Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 92-102 for low R a values in W C -type cutting inserts. W C inserts give good results in low rolling forces. This is due to reduced surface deterioration combined with lower heat generation. In all conditions, optimum values of process parameters must be obtained in terms of surface deformation, temperature, and stress. 8 REFERENCES [1] Ustel, F., Turk, A., Yildiz, K., Kurt, A.O. (2022). 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Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 103-104 List of reviewers L ist of review ers w ho review ed manuscripts in 2023 H usam Jawad Abdulsamad, Iraq Alexandre M. Abrã o, Brasil Abuzer A kg z, Turkey P aulo Sergio Afonso, P ortugal H assan Afshari, Iran Siddique Akbar, Austria Marwan Alakhras, U K Salman Aldriasawi, Iraq Jorge Enrique Araque Isidro, Italy Mohammad Arefi, Iran Muhammad U sman Asad, C anada F rank Baginski, U SA Jani Barle, C roatia Anmol Bathia, India Micha Batsch, Poland H edi Belhadjsalah, Tunisia Jure Berce, Slovenia Anton Bergant, Slovenia Tomaž Berlec, Slovenia C ristina Biris, R omania Miha Boltežar, Slovenia Andrej Bombač, Slovenia É d C laudio Bordinassi, Brasil Marek Boryga, P oland R ajmohan Bose, India Jaros aw Brodny, Poland Tomasz Bulz ak, P oland Michele C alì , Italy Bing C ao, C hina C aterina C apponi, Italy G eorge C arutasu, R omania G regor C epon, Slovenia F erdinand C erbe, G ermany H imadri C hattopadhyay, India Alfredo C há vez , Mexico P eng C heng, U S Bogdan C hirita, R omania F ilippo C ianetti, Italy Marco C irelli, Italy Marco C occoncelli, Italy F ranco C oncli, Italy Martin esnik, Slovenia Omar Dá valos, Mexico J. P aulo Davim, P oland L uis de L acalle Marcaide, Spain Krisz tiá n Deá k, H ungary H amed Aghajani Deraz kola, Spain eljko V. Despotović, Serbia Jiang Ding, C hina J n Dižo, Slovakia C hangbin Dong, C hina David B. Dooner, P uerto R ico Mateja Dovjak, Slovenia X ing Du, C hina N guyen Dinh Duc, Vietnam L . C anan Dül ger, Turkey Pawe Dunaj, Poland Radomir okić, Serbia R une Elvik, N orway Igor Emri, Slovenia Kaan Emre Engin, Turkey Mohammad A. F araj, Iraq H amed F arz aneh, Iran C uneyt F etvaci, Turkey G rz egorz F ilo, P oland Jür gen F leischer, G ermany Alexey F omin, R ussia P aolo F ranceschi, Italy F rederico Miguel F reire R odrigues, P ortugal Juan C arlos G arcí a, Mexico Rok Gašperšič, Slovenia Jabbar G attmah, Turkey Vijay G autam, India Srečko Glodež, Slovenia Adam G lowacz , P oland F . G ó mez -Silva, Spain Domen G orjup, Slovenia C hristoph G reb, G ermany Damir G rguraš, Slovenia Alec G roysman, Israel Tarahom Mesri G undoshmian, Itran L eo G usel, Slovenia H amid H aghshenas G organi, Iran Ali H ajnayeb, C anada R H alicioglu, Turkey Miroslav Halilovič, Slovenia P atricia H abib H allak, Brasil Anis H amz a, Tunisia Boštjan H arl, Slovenia Mikihito H irohata, Japan Sergej H loch, Slovakia Z bigniew H umienny, P oland Z bigniew H umienny, P oland Soichi Ibaraki, Japan Musa Alhaji Ibrahim, N igeria Jamshed Iqbal, P akistan H ajro Ismar, Bosnia and H erz egovina Špiro Ivošević, Montenegro Adam Jacso, H ungary Goran Janjić, Bosnia and H erz egovina Juliana Javorova, Bolgariy Boris Jerman, Slovenia Matija Jez eršek, Slovenia H ongxiang Jiang, C hina Jihailiu Jihai, C hina N ikolaos Karkalos, G rece Masashi Kashiwagi, Japan Z denka Keran, C roatia N icole Kessissoglou, Australia Mohammed-El-Amine Khodja, Algeria Kyo-Seon Kim, South Korea P ino Koc, Slovenia Borut Kosec, Slovenia R obert Kosturek, P oland Nataša Kovač, Montenegro G yör gy Ková cs, H ungary G rz egorz Krolcz yk, P oland Vivek Kumar, India 103 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, 103-104 R obert Kunc, Slovenia Amanendra K. Kushwaha, U SA Janez Kušar, Slovenia Marz ena L achowicz , P oland Andrej L ebar, Slovenia Stanislaw L egutko, P oland H irpa L emu, N orway C hanghe L i, C hina X in L iao, C hina Mathias L iewald, G ermany Edgar L ópe z , Mexico Darko L ovrec, Slovenia L iteng Ma, C hina Miloš Madić, Serbia Olasumbo Makinde, South Africa P etr Masek, C z ech R epublic N icolae Medan, R omania Marc Medrano, Spain N . Muthu Mekala, India G iovanni Meneghetti, Italy Andrijana Milinović, Croatia Mladomir Milutinović, Serbia Sergey Mironov, R ussia Ava Mohammed, Iraq R . Mohanraj, India N ikolaj Mole, Slovenia G onz alo Moreno, Brasil Essam B. Moustafa, Saudi Arabia Manuel Moya, Spain Matic Može, Slovenia Jacek Mucha, P oland Andrzej My li ski, Poland Balaz s N emeth, H ungy Trung-Thanh N guyen, Vietnam Johann N icolics, Austria Anatolij N ikonov, Slovenia Milosav Ognjanović, Serbia Ivan Okorn, Slovenia Simon Oman, Slovenia Ashraf Omar, Maroko S. Omprakasam, India Sabri Oz turk, Turkey Srinivasa P . P ai, India Massimiliano P almieri, Italy C handan P andey, India Branislav Panić, Slovenia P arth Sarathi P anigrahy, U SA Yong-H wa P ark, South Korea Ji P ei, C hina Tomaž Pepelnjak, Slovenia Tomas P etr, C z ech R epublic Igor Petrović, Slovenia Vu N goc P i, Vietnam Miha P ipan, Slovenia Bojan Podgornik, Sloveniaž P avel P olach, C z ech R epublic Marko P olajnar, Slovenia Milton L uiz P olli, Brasil Antonio P osa, U SA R adu-Emil P recup, R omania C hand R . P rem, India F ranci P ušavec, Slovenia S. Suresh, India R óbe rt Sz abolcsi, H ungary R iad R amadani, Kosovo Matjaž Ramšak, Slovenia Dunja R avnikar, Slovenia Sunil R aykar, India Dragan R odic, Serbia Andreas R osenkranz , C hile Michal R uz ek, F rance W im Van H elden, Austria J. A. Velasco-P arra, C olombia Aleksandar Vencl, Serbia Simone Venturini, Italy Arkady Voloshin, U SA G oran Vorotovic, Serbia Rok Vrabič, Slovenia eljko Vukelić, Slovenia Mohammad R ez a Safaei, Saudi Arabia serdar ahin, Turkey R afael Sanchez C respo, U K Manel Sbayti, Tunisia Dieter Schuöc ker, Austria Sathish Kumar Selvaperumal, Malesia V. Serbez ov, Bolgaria H useyin Sevinc, Turkey Yujie Shen, C hina X ia Sheng, C hina Krz ysz tof Sicz ek, P oland Silvio Simani, Italy Vilmos Simon, H ungary N oan Tonini Simonassi, Brasil R abesh kumar Singh, India Jasjeevan Singh, India L idija Slemenik P erše, Slovenia L uigi Solaz z i, Italy F ikret Sönm ez , Turkey Mohsen Soori, Turkey Marco Sortino, Italy U roš Stritih, Slovenia Idawu Yakubu Suleiman, N igeria W enjing Sun, C hina Domen Š eruga, Slovenia Tatjana Š ibalija, Serbia Marko Š imic, Slovenia Graciela Šterpin Valić, Croatia R oman Š turm, Slovenia Titus Thankachan, India Stefano Tornincasa, Italy X uan Bo Tran, Vietnam Anastasios Tz otz is, G reece C uneyt U ysal, Turkey a r Uzay, Turkey Erdem U z unsoy, Turkey Z henshuai W an, C hina Z henqian W ang, C hina X uhao W ang, C hina Yueyong W ang, C hina Shunli W ang, C hina C henxue W ang, C hina Jür gen W eber, G ermany Jerz y Adam W incz ek, P oland H ongwei Yan, C hina Yuewei Yu, C hina Yang Yu, Australia Daniel Z abek, U K Binglong Z hang, C hina W anjie Z hang, C hina X iaohong Z hang, C hina W ei Z hao, C hina Bo Z hou, C hina Youhang Z hou, C hina Shuaidong Z ou, C hina Samo Z upan, Slovenia Uroš uperl, Slovenia The Editorial would like to thank all the reviewers in participating in reviewing process. W e appreciate the time and effort and greatly value the assistance as a manuscript reviewer for Strojniški vestnik – Journal of Mechanical Engineering. 104 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2 Vsebina Vsebina Strojniški vestnik - Journal of Mechanical Engineering letnik 70, ( 2024), številka 1- 2 L jubljana, januar-februar 2024 ISSN 0039-2480 a ad o e e o R az širjeni povz etki (extended abstracts) Samo upan, Robert Kunc: Pregled načel in pravil za geometrijske specifikacije izdelkov v skladu z aktualnimi ISO standardi Z hengfang L i, X udong Di, Z hengyuan G ao, Z higuo An, L ing C hen, Yuhang Z hang, Shihong L u: Izboljšanje dimenzijske točnosti valovitega diska iz materiala Ti-6Al-4V po električnem inkrementalnem preoblikovanju pločevine v vročem Ireneusz ag rski, Monika Kulisz, Anna Szczepaniak: Uporaba statistične analize in modeliranja za določitev parametrov hrapavosti po končni obdelavi magnezijevih zlitin z orodji z variabilnim kotom vijačnice Tat-Khoa Doan, Trung-Thanh Nguyen, An-Le Van: Večkriterijska optimizacija procesa struženja z gnanim orodjem glede na okoljske in kakovostne kaz alnike in Tian, Guangjian Wang, ujiang Jiang: Nova metoda za računanje trenutnega izkoristka in nihanj momenta pri čelnih zobniških gonilih Grzegorz Struzikiewicz: Raziskava struženja titanovih zlitin z orodji Prime A v pogojih visokotlačnega hlajenja Berat Gürcan entürk, Mahmut Cüneyt Fetvac : Prilagojen pristop h generiranju zobnic za beveloidne zobnike Oktay Ad yaman: Študija možnosti uporabe izrabljenih rezalnih ploščic za gladilno valjanje SI 3 SI 4 SI 5 SI 6 SI 7 SI 8 SI SI 10 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, SI 3 © 2024 Avtorji Prejeto v recenzijo: 2023-08-06 Prejeto popravljeno: 2023-10-04 Odobreno za objavo: 2023-10-11 re led a el i ra il a eo etri e eci i aci e i del o v skladu z aktualnimi ISO standardi Samo Z upan* – R obert Kunc U niverz a v L jubljani, F akulteta z a strojništvo, Slovenija V članku smo pregledali filozofijo načel in pravil v ozadju serije ISO standardov za področje geometrijskih specifikacij proizvodov (GPS), ki so ob materialnih specifikacijah ključna sestavina posredovanih informacij pri učinkovitem načrtovanju in izdelavi mehanskih izdelkov ter tudi pri komunikacijah med partnerji, ki sodelujejo v teh procesih. Področje GPS, za katerega skrbi ISO tehnični komite š t. 213, vključuje š tevi l ne standarde (trenutno 144) , ki opisujejo zahtevano natančnost geometrijskih značilnosti » velikosti« (tolerance mer) in geometrijskih toleranc, ki se uporabljajo za zagotavljanje natančnosti oblike, orientacije in lokacije geometrijskih značilnosti v 3D prostoru. Opravljen je pregled temeljnih načel in pravil, ki jih določajo aktualni standardi ISO GPS. Opisana je organizacija sistema ISO GPS standardov in povzetek vsebine bolj relevantnih standardov, ki so nedavno doživeli več revizij ali so povsem novi. Standardi ISO GPS temeljijo na načelu dvojnosti: geometrijskim specifikacijam neizogibno sledijo ustrezni postopki verifikacije. V tem prispevku smo se osredotočili predvsem na steber geometrijskih specifikacij, izpustili pa smo celotni vzporedni steber verifikacije, ki v skladu z modelom matrike ISO GPS standardov vsebuje še večje število dokumentov (standardov o merjenju oziroma preverjanju). Področje GPS je torej zelo obsežno in v stebru specifikacij zajema poglavja toleranc kotiranih mer, geometrijske tolerance ter definicije in omejitve stanja površin (nov standard ISO 21 20:2021) in robov (čemur smo se v tem prispevku prav tako izognili). Načela in osnovna pravila za jasen in nedvoumen zapis vseh zahtev za geometrijske značilnosti izdelkov so raz deljena v skupine temeljnih, splošnih in dopolnilnih standardov ISO G P S. Organiz acija standardov je prikaz ana s pomočjo matrike GPS, ki je definirana v temeljnem ISO 14638:2015 standardu. Glavna načela področja so dana večinoma v ISO 8015:2011 in v drugih temeljnih standardih, ki podajajo osnovne definicije. Načela in pravila za praktično rabo pri določanju in uporabi toleranc mer linearnih velikosti zunanjih in notranjih oblik (premeri oz. širine čepov in lukenj) so podrobno določena v seriji ISO 14405 standardov (trije deli). Standardi prinašajo številne nove definicije pomena linearne (1. del) in kotne (3. del) velikosti čepov in lukenj, kjer so mnoge specifikacije povezane z novimi tehnologijami in metodami verifikacije. Definicije velikosti geometrijske značilnosti često temeljijo na matematičnem obravnavanju izmerkov v oblaku točk podanih z absolutnimi prostorskimi koordinatami. Bistvena novost so definicije velikosti s pomočjo statističnih cenilk, ki jih pogosto uporabljamo pri statističnem nadzoru procesov (SPC). Hkrati ISO 144052 definira kotirane mere, ki ne predstavljajo značilnih velikosti čepov in lukenj in predlaga, da vse take značilnosti toleriramo dosledno z uporabo geometrijskih toleranc oblike, orientacije, lege in teka v skladu s povezanimi pravili (več standardov). Najbolj obsežnemu poglavju geometrijskih toleranc (GT) so posvečeni številni ISO GPS standardi in večina jih je bila v zadnjem obdobju pomembno posodobljena in nadgrajena. V članku so ključni aktualni standardi našteti v virih. Temeljni standard z a geometrijske tolerance je ISO 1 101: 2017, ki pa ne vsebuje vsega potrebnega z a obvladovanje področja. Pomembne vsebine imajo tudi drugi ISO standardi za GT (definicije toleranc oblike, profila, teka, materialni pogoji (ključni npr. za izdelavo kalibrov), reference oziroma baze itd. lanek daje pregled in glavne povzetke o teh ISO GT standardih ter daje nekaj primerov, ki prikazujejo tudi najbolj opazne novosti pri grafičnem simbolnem jeziku. ISO 167 2:2021 definira načela in pravila v skladu z sodobnimi potrebami in filozofijo Model Based Definitions« ( M B D ) posredovanja vseh geometrijskih informacij o izdelkih že s prostorskimi virtualnimi (3D CAD) modeli. Obsežen standard vsebuje vsa potrebna načela in pravila, po katerih lahko geometrijske definicije in zahteve z uporabo ISO simbolov vnesemo bodisi v 3D virtualne model izdelkov in po enakih načelih in pravilih se ti lahko dedujejo tudi na 2D delavniške risbe. Dalje članek obravnava tudi pomembno GPS načelo, po katerem je na delavniških risbah možno in potrebno podati vse zahteve o tolerancah na splošen ali na izrecen način, pravila o tem pa so urejena v več ISO standardih glede na tehnologijo iz delave iz delkov. Ker gre za pomembne osnove tehnične komunikacije, bi morali uporabniki (inženirji) dobro poznati te standarde. Pogosto pa ni tako, saj gre za obsežno tematiko s pogostimi spremembami in novostmi, kar povzroča znaten napor in s tem težave praktičnim uporabnikom pri usposabljanju. aradi velikega obsega standardov inženirji pri delu v praksi težko sledijo tej dinamiki, težava pa je tudi v dostopnosti standardov za uporabnike, saj je ta pogosto povezana z znatnimi stroški. To povzroča številne težave v praksi, saj komunikacija med partnerji (naročniki in dobavitelji in tudi v podjetju) pogosto ne poteka na istih izhodiščih. l e e ede O ta dard eo etri e eci i aci e roi odo eo etri e tolera ce a ela pravila, velikost, toleranca, verifikacija *Naslov avtorja za dopisovanje: Univerza v jubljani, akulteta za strojništvo, škerčeva , jubljana, lovenija, samo.zupan@ s.uni lj.si SI 3 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, SI 4 © 2024 Avtorji Prejeto v recenzijo: 2023-02-06 Prejeto popravljeno: 2023-07-19 Odobreno za objavo: 2023-09-25 ol a e di e i e to o ti alo ite a di a i ateriala i l o ele tri e i re e tal e reo li o a lo e i e ro e Z hengfang L i1 – X udong Di2 – Z hengyuan G ao3,* – Z higuo An3 – L ing C hen4 – Yuhang Z hang1 – Shihong L u5 1 U niverz a Kunming, Š ola z a strojništvo in elektrotehniko, Kitajska 2 Jianghuai Automobile G roup C o., L td., R az iskovalni inštitut z a tehnologijo osebnih voz il, Kitajska 3 U niverz a C hongqing Jiaotong, Š ola z a mehatroniko in avtomobilsko tehniko, Kitajska 4 U niverz a Kunming, Oddelek z a z nanost in tehnologijo, Kitajska 5 Univerza za aeronavtiko in astronavtiko v Nanjingu, Kolidž za strojništvo in elektrotehniko, Kitajska Veganje robov predstavlja veliko težavo pri električnem inkrementalnem preoblikovanju valovitih diskov iz materiala Ti-6Al-4V v vročem in lahko privede do znatnih dimenzijskih napak. V članku je zato predstavljen predlog novega postopka z a odpravo napak pri preoblikovanju valovitih diskov iz materiala Ti-6A l-4V, ki kombinira električno inkrementalno preoblikovanje v vročem z električno podprtim kalibriranjem. P redstavljen je tudi eksperimentalen proiz vodni postopek z a analiz o vpliva parametrov preoblikovalnega procesa in kalibriranja na dimenzijsko točnost diska. Veganje na robu izdelka kot ciljni parameter (h) je bilo izmerjeno z inštrumentom za meritve višine. Valoviti disk je bil izdelan na numerično krmiljenem stroju, uporabljena pa sta bila tudi iz vor enosmernega toka (od 0 A do 1500 A) z a segrevanje in termoviz ijska kamera (proizvajalec: Shenzhen Ce-temp Technology Co., Ltd; tip: PI1M-PI80x; merilno območje: 20 C do 1500 C; napaka: ± 0,1 º C ) z a meritve temperature v coni preoblikovanja. Disk je bil izdelan v dveh korakih. Prva pot preoblikovalnega orodja je bila uporabljena za izdelavo bočne stene valovitega diska, nasprotna stena pa je bila iz delana z drugo potjo. Z a analiz o kakovosti preoblikovanja valovitega diska po metodi kontrolnih spremenljivk so bili iz brani procesni parametri tok, podajalna hitrost in velikost koraka. Referenčna temperatura žarjenja titanove zlitine Ti-6Al-4V glede na mehanizem popuščanja napetosti je 600 do ° C 650 ° C . Iz branih je bilo pet vrednosti toka (2200 A, 2400 A, 2600 A, 2800 A in 3000 A) ustrezno tradicionalnim postopkom žarjenja. Ustrezne temperature znašajo 563,7 C, 5 3,6 C, 623,5 C, 652,3 C in 684,1 C. Uporabljeni so bili časi 10 min, 15 min, 20 min, 25 min, 30 min in 35 min za analizo sprememb ciljne vrednosti ob upoštevanju napak zaradi visokotemperaturne oksidacije titanove zlitine Ti-6Al-4V. lanek obravnava tematsko področje preoblikovanja pločevine. Eksperimenti so pokaz ali, da je iz delani valoviti disk brez raz pok in iz boklin pri kombinaciji parametrov 220 A, 00 mm/min in 0,2 mm. Vrednosti 3000 A in 30 min sta optimalni za kalibriranje, pri katerem so v veliki meri odpravljene napake veganja iz faz e preoblikovanja. C iljna vrednost pri optimalnih procesnih parametrih še vedno z naša 2,1 mm, nadaljnje z manjšanje višine pa bo lahko predmet prihodnjih raz iskav. V članku je predstavljen predlog novega postopka za odpravo napak pri preoblikovanju valovitih diskov iz materiala Ti-6Al-4V, ki kombinira električno inkrementalno preoblikovanje v vročem z električno podprtim kalibriranjem. Podrobno je preučen vpliv parametrov procesa na nastanek razpok med preoblikovanjem in določena je optimalna kombinacija parametrov za uspešno preoblikovanje valovitega diska iz materiala Ti-6Al-4V. Na tej podlagi sta bila ločeno izbrana in analizirana naprava za kalibriranje in vrednost el. toka za odpravo napak veganja. Eksperimenti so dokaz ali uporabnost predlaganega iz delovalnega postopka. R ez ultati raz iskave bodo uporabni z a hitro iz delavo valovitih diskov v letalski in vesoljski industriji, postopek pa bo z dopolnitvami uporaben tudi z a avtomobilsko industrijo, biomedicino, industrijo tirnih voz il idr. l e e ede i re e tal o reo li o a e lo e i e ele tri o reo li o a e ro e ele tri o podprto kalibriranje, veganje robov, valoviti disk, optimiz acija velikosti SI 4 * orr. ut or s ddress: Univerza ong ing iaotong, , No. , ue u oad, Nan an kro je, ong ing, itajska, z engyuangao@c jtu.edu.cn Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, SI 5 © 2023 Avtorji. Prejeto v recenzijo: 2023-04-05 Prejeto popravljeno: 2023-07-03 Odobreno za objavo: 2023-10-05 ora a tati ti e a ali e i odelira a a dolo ite ara etro ra a o ti o o i o dela i a e i e i liti orod i aria il i oto i a ice Ireneusz Z agór ski1,* – Monika Kulisz 1 2 – Anna Sz cz epaniak1 Tehniška univerz a v L ublinu, F akulteta z a strojništvo, P oljska univerz a v L ublinu, F akulteta z a management, P oljska 2 Tehniška Obstaja pomanjkanje objav na področju analize končnih obdelav magnezijevih zlitin, zlasti z rezkanjem. Cilj raziskave je bila zato analiza procesa končne obdelave magnezijevih zlitin A 1D in A 31 z rezkanjem. Analiz iran je bil vpliv sprememb tehnoloških parametrov rez kanja na 2D-parametre površinske hrapavosti, kot so R q , R t, R v in R p, kakor tudi vpliv spremembe variabilnega kota vijačnice steblastega rezkarja λs (λs = 20° , λs = 50 ). Opravljene so bile statistične analize in numerične simulacije s pomočjo umetnih nevronskih mrež. Definicija problema: obravnavani problem je izbira ustreznih tehnoloških parametrov končne obdelave, ki bo zagotavljal visoko kakovost končne površine obdelovancev. Uporabljena je bila enofaktorska metoda načrtovanja eksperimentov. R ez kanje je bilo opravljeno na vertikalnem obdelovalnem centru AVIA VMC 800H S. U porabljena sta bila dva trdokovinska steblasta rezkarja s tremi rezalnimi robi premera 16 mm in variabilnim kotom vijačnice λs (λs = 20° , λs = 50 ). a vpenjanje steblastih rezkarjev v orodno držalo je bila uporabljena naprava za nakrčevanje. Orodje v držalu je bilo na ustreznem stroju centrirano do preostale neuravnoteženosti 0,25 g mm (G2.5). Nato je bilo opravljeno rez kanje v naslednjem raz ponu tehnoloških parametrov: rez alna hitrost vc = 400 m/ min do 1200 m/ min, podajanje na z ob f z = 0,05 mm/ z ob do 0,3 mm/ z ob, aksialna globina rez a ap = 0,1 mm do 0,5 mm, radialna globina rez a ae = 0,5 mm do 3,5 mm. Meritve površinske hrapavosti so bile izvedene na bočnih in čelnih površinah s kontaktnim merilnikom hrapavosti HOMMEL TESTER T1000. Opravljene so bile tudi statistične analize (s paketom Statistica 13) in numerične simulacije s pomočjo umetnih nevronskih mrež (s paketom Matlab). Na hrapavost obdelane površine vplivajo tako sprememba kota vijačnice kakor tudi izbrani tehnološki parametri rezkanja. Najboljše modele je dalo omrežje z 10 nevroni v skritem sloju. Mreže, ustvarjene z modeliranjem parametrov površinske hrapavosti, imajo glede na izračunane vrednosti regresijskih parametrov zadovoljivo prediktivno zmogljivost. Rezultati modeliranja z nevronskimi mrežami kažejo, da so le-te učinkovito orodje z a napovedovanje parametrov površinske hrapavosti. Možnosti za prihodnje raziskave in identificirane omejitve pri raziskavi: nadaljevanje raziskav na področju končne in precizne obdelave magnezijevih zlitin, edina potencialna omejitev je nagnjenost manjših odrezkov k vžigu med obdelavo. Analiz a površinske hrapavosti je še posebej pomembna z a kakovost obdelanih komponent strojev in naprav. Kakovost in hrapavost površin sta še pomembnejši v kontekstu končnih obdelav. Končna obdelava lahkih zlitin (aluminija in magnezija) je pomembna s praktičnega vidika, obstaja pa pomanjkanje celovitih študij omenjene tematike. l e e ede a e i e e liti e o a o dela a ra a o t a o o t o r i tati ti a a ali a et e e ro e re e *Naslov avtorja za dopisovanje: Tehniška univerza v Lublinu, Fakulteta za strojništvo, Nadbystrzycka 36, 20-618 Lublin, Poljska, i.zagorski@pollub.pl SI 5 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, SI 6 © 2023 Avtorji. e riteri Prejeto v recenzijo: 2023-06-15 Prejeto popravljeno: 2023-10-02 Odobreno za objavo: 2023-11-15 a o ti i aci a roce a tr e a a i glede na okoljske in kakovostne kaz alnike orod e Tat-Khoa Doan1 , Trung-Thanh N guyen1 , An-L e Van2,* 1 Tehniška univerz a L e Q uy Don, F akulteta z a strojništvo, H a N oi, Vietnam niverz a N guyen Tat Thanh, Tehniška fakulteta, H o C hi Minh, Vietnam 2U Cilj predstavljene študije je optimizacija parametrov procesa struženja materiala Ti6Al4V z gnanim orodjem nagibni kot, globina rez a, hitrost podajanja in vrtilna frekvenca – z a z manjšanje skupne rabe energije, hrupa med obdelavo in površinske hrapavosti. Učinkovita gnana rotacijska orodja z visoko togostjo za obdelavo trdih jekel še niso bila zasnovana in izdelana, da bi lahko zamenjala fiksna stružna orodja. Glavna slabost orodij, ki so predstavljena v obstoječi literaturi, je majhna togost. Glasen hrup lahko povzroči okvare sluha in kroničen stres, zato mora biti pri struženju z gnanimi orodji poskrbljeno z a z manjšanje obremenitve s prahom. P rav tako še niso bili opredeljeni optimalni parametri procesa z a z manjšanje rabe energije, hrapavosti in emisij hrupa. Prediktivni modeli so bili postavljeni na podlagi regresijske metode. Pri izbiri vrednosti uteži in optimalnih rešitev so bili uporabljeni metoda na podlagi vpliva odstranitve kriterijev, iz boljšan optimiz acijski algoritem z rojem delcev s kvantnim vedenjem in TOP SIS. G lavni rez ultati: Raba energije, površinska hrapavost, hrup med struženjem in celotni stroški so se zmanjšali za 6,7 , 22,3 , 23,5 % oz . 8,5 % . Na odziv pri struženju sta vplivali predvsem podajalna hitrost in vrtilna frekvenca. Vpliv dejavnikov struženja z gnanim orodjem na zmogljivost proizvodnje in ogljični odtis bo raziskan v prihodnje. P redstavljeno rez alno orodje je primerno tudi z a obdelavo drugih z litin, ki so z ahtevne z a odrez avanje. Iz trenutne izvedbe bi bilo mogoče razviti nova stružna orodja. empiričnimi korelacijami kriterijev zmogljivosti je mogoče napovedovati rabo energije, hrapavost po struženju in emisijo hrupa. Rezultate optimizacije je mogoče uveljaviti za izboljšanje tehnoloških parametrov v praksi. Predstavljeni stružni proces je mogoče uporabiti tudi za obdelavo zunanjih površin izdelkov iz drugih zlitin, ki so težavne za odrezavanje. Opisani pristop k optimizaciji je poleg tega primeren za odpravo težav pri drugih obdelovalnih postopkih. a izračun celotnih stroškov je mogoče uporabiti model stroškov struženja. l e e ede tr e e a i rotaci i orod e celot a ra a e er i e o r i a ra a o t emisija hrupa, IQ PSO SI 6 *Naslov avtorja za dopisovanje: Univerza Nguyen Tat Thanh, Tehniška fakulteta, 300A Nguyen Tat Thanh, Ho Chi Minh, Vietnam, lvan@ntt.edu.vn Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, SI 7 © 2024 Avtorji. Prejeto v recenzijo: 2023-06-28 Prejeto popravljeno: 2023-09-26 Odobreno za objavo: 2023-09-28 o a etoda a ra a e tre t e a i ori t a i i a o e ta ri el i o i i o ili X in Tian1,2 – G uangjian W ang1,2,* – Yujiang Jiang1,2 1 2 Univerza v ongčingu, Kolidž za strojništvo in avtomobilsko tehniko, Kitajska Kolaborativni roboti so pomembni z a sodobno industrijo, oz ko grlo pri uporabi teh robotov pa predstavlja izkoristek sklepnih reduktorjev. Trenutna nihanja izkoristka in momenta pri čelnih zobniških dvojicah v sklepnih reduktorjih neposredno vplivajo na njihovo zmogljivost pomika in točnost. V članku je predstavljen računski model z a napovedovanje trenutnega iz koristka in nihanj momenta pri z obniških dvojicah ob upoštevanju ravnovesja momentov v točki ubiranja, porazdelitve sil med zobmi in modelov količnika trenja. Nihanja momenta pri z obniških dvojicah do sedaj še niso bila obravnavana v z nanstveni literaturi. P redstavljena je primerjava trenutnega izkoristka in nihanj momenta pri zobniških dvojicah ob upoštevanju povprečnega količnika trenja (AFC) na podlagi Coulombovega trenja in časovno spremenljivega količnika trenja (TFC) na podlagi elastohidrodinamičnega maz anja. Analiz irana je odvisnost med trenutnim iz koristkom in nihanjem momenta gonila in obravnavan je vpliv kontaktnega razmerja na izkoristek. a razliko od obstoječih raziskav, ki se osredotočajo predvsem na vpliv izhodnega momenta in hitrosti na povprečni izkoristek zobniških gonil, ta članek preučuje tako obremenitvene in hitrostne raz mere kakor tudi vpliv površinske hrapavosti in delovne temperature maz alnega olja na trenutni izkoristek in nihanja momenta. Učinkovitost in točnost predlagane metode v danih obratovalnih pogojih je bila potrjena s primerjavo s tehnikami za računanje izkoristka iz literature. Rezultati kažejo, da je trenutni izkoristek zobniškega gonila v območju ubiranja dveh zob manjši kot v območju ubiranja enega zoba. Izkoristek je za neprekinjen in stabilen prenos mogoče izboljšati z zmanjšanjem kontaktnega razmerja. Različni modeli količnika trenja signifikantno vplivajo na izkoristek in nihanja izkoristka zobniških gonil. Izkoristek, izračunan po modelu časovno spremenljivega količnika trenja, je manjši od izkoristka, izračunanega po modelu povprečnega količnika trenja, največja razlika med obema pa znaša 1,86 . Vrednost nihanja momenta pri povprečnem količniku trenja je manjša kot pri časovno spremenljivem količniku trenja. Trenutni iz koristek z obniškega gonila in trenutni vhodni moment se z manjšata pod konstantno obremenitvijo. Nihanje izkoristka se poveča, prav tako pa se poveča nihanje vhodnega momenta. Variabilnost trenutnega izkoristka zobniškega gonila v danih obratovalnih pogojih lahko doseže 3,34 , nihanja momenta pa 5,1 Nm. Ob porastu hitrosti na vhodu se poviša obratovalna temperatura maz alnega olja, z manjšanje površinske hrapavosti zobniškega gonila pa lahko izboljša izkoristek prenosa in zmanjša nihanja momenta med ubiranjem. Povečanje izhodnega momenta poveča nihanja momenta. Raziskava tako izpolnjuje vrzel na področju nihanja momenta pri zobniških dvojicah ter predstavlja nov prediktivni in računski model za trenutni izkoristek in nihanja momenta pri zobniških dvojicah. Model zagotavlja solidno podporo raz iskavam in aplikacijam sklepnih reduktorjev kolaborativnih robotov ter prinaša nove z amisli in metode za preučevanje trenutnega izkoristka in nihanj momenta. V članku je predstavljena metoda za numerično računanje takojšnjega izkoristka in nihanj momenta pri zobniških dvojicah z zunanjim ubiranjem na podlagi teoretične analize. Nekateri rezultati izračunov se ujemajo s predhodnimi študijami. Predstavljeni model upošteva samo trenutni iz koristek in nihanja momenta pri z obniških gonilih v pogojih drsnega trenja, ne z ajema pa vpliva izgub zaradi kotalnega trenja in izgub, ki niso povezane z obremenitvijo. Prezrte so tudi natančnost in napake v iz delavi z obniških gonil, z ato bo v prihodnje potrebna eksperimentalna verifikacija modela. P rihodnje raz iskave bodo usmerjene v raz voj modela trenutnega iz koristka in nihanj momenta v sklepnih reduktorjih kolaborativnih robotov, sestavljenih iz z obniških dvojic. l e e ede ola orati i ro ot tre t i i ori te i a e o e ta oli i tre a ora delite obremenitev *Naslov avtorja za dopisovanje: Univerza v ongčingu, r avni laboratorij za me anske prenose, ong ing, , itajska, gj ang@c u.edu.cn SI 7 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, SI 8 © 2024 Avtorji. a i a a tr e a tita o i o o i i o otla Prejeto v recenzijo: 2023-07-05 Prejeto popravljeno: 2023-10-10 Odobreno za objavo: 2023-11-07 liti orod i ri e e a la e a G rz egorz Struz ikiewicz * Z nanstveno-tehniška univerz a AG H , F akulteta z a strojništvo in robotiko, P oljska Na področju strojne obdelave poteka stalen razvoj novih metod za izboljšanje kakovosti in učinkovitosti obdelovalnih postopkov. Glavna motivacija za pripravo pričujočega članka je bilo zagotavljanje zahtevane kakovosti procesa struženja titanove zlitine z največjo učinkovitostjo ob upoštevanju oblike odrezkov. načilna težava pri struženju titanovih zlitin je učinkovitost lomljenja in odstranjevanja odrezkov iz cone obdelave. Novost v predstavljeni raz iskavi je kombinacija nove z asnove rez alnega orodja in postopkov z a obdelavo titanovih z litin, ki izboljšuje učinkovitost obdelave. V ta namen je bila analizirana uporaba značilnih stružnih orodij tipa Prime v kombinaciji z visokotlačnim hlajenjem (HPC). G lavna tema analiz e je bila opredelitev vpliva rez alnih parametrov (f , ap, vc ) na vrednosti rez alnih sil, kakor tudi količnika lomljenja odrezkov Cc h in oblike odrezkov. a vzdolžno struženje titanove zlitine Ti6Al4V ELI so bila uporabljena trdokovinska orodja Sandvik C oromant kvalitete 1 1 15. U porabljen je bil povišan tlak hladilnomazalne tekočine p = 70 bar. Izmerjene so bile komponente skupne rezalne sile pri končni obdelavi z variabilnimi rez alnimi parametri v naslednjih raz ponih: podajalna hitrost f = 0,1 mm/ vrt do 0,4 mm/ vrt, globina rez anja ap = 0,25 mm do 1,0 mm in rez alna hitrost vc = 40 m/ min do 80 m/ min. Iz kaz alo se je, da je rez alna sila odvisna predvsem od podajanja in od globine rez a. P redstavljena je analiz a oblike ustvarjenih odrez kov in opredeljena je odvisnost vrednosti količnika lomljenja odrezkov Cc h od rez alnih parametrov. Opredeljena je tudi metoda z a iskanje največje učinkovitosti procesa struženja ob upoštevanju želene vrednosti količnika lomljenja odrezkov. R ez ultati analiz e so predstavljeni v nadaljevanju. R ez alna sila F c je v linearni povezavi z obravnavanimi rezalnimi parametri. Statistično najbolj signifikanten parameter pri tem je globina rez a ap, sledi pa ji podajanje f . Vpliv rez alne hitrosti vc na srednjo rez alno silo je bistveno manjši. G lobina rez a ap je najpomembnejši dejavnik, ki vpliva na količnik lomljivosti odrezkov Cc h. Oblika nastalih odrez kov (pravilna, sprejemljiva in nepravilna) je odvisna od raz pona rez alnih parametrov. Odrez ki prave oblike so bili v preizkušenem razponu rezalnih parametrov v povprečju doseženi pri vrednostih ap 0,75 mm, f 0,2 mm/vrt. Pri višji vrednosti rezalne hitrosti vc = 80 m/min se je zmanjšal količnik lomljenja odrezkov. Doseganje prave oblike odrezkov pri končni obdelavi titanove zlitine Ti6Al4V v pogojih obdelave HPC je odvisna od sinergije med dejavniki, kot so vrednosti rez alnih parametrov, oblika in stopnja iz polnitve lomilca odrezkov na cepilni ploskvi ter tlak hladilno-mazalne tekočine. V opisanih pogojih je mogoče izboljšati učinkovitost obdelave z izbiro rezalne hitrosti. V nadaljevanju bo mogoče nadaljevati z razvojem in simulacijo procesa struženja zlitine Ti6Al4V z orodji tipa P rime ter raz iskati obrabljanje teh orodij pri obdelavi materialov, ki so z ahtevni z a odrez avanje. l e e ede tr e e orod a ri e tita o a liti a i l re al e ile o li a odre a i de lomljenja odrez kov SI 8 *Naslov avtorja za dopisovanje: Znanstveno-tehniška univerza AGH, Fakulteta za strojništvo in robotiko, 30-059 Krakow, Poljska, gstruzik@agh.edu.pl Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, SI 9 © 2024 Avtorji. Prejeto v recenzijo: 2023-07-12 Prejeto popravljeno: 2023-10-17 Odobreno za objavo: 2023-10-30 Prilagojen pristop h generiranju z obnic z a beveloidne z obnike Berat Gürcan entürk1,* 1 Mahmut Cüneyt Fetvac 2 Univerza Dogus, Turčija v Istanbulu Cerrahpasa, Turčija 2Univerza Namen pričujoče študije je predstavitev poenostavljene in učinkovite metode za opredelitev geometrije ozobja beveloidnih zobnikov. Avtorji so med pregledom literature odkrili metodo Milana Batiste, ki omogoča preprostejšo matematično opredelitev geometrije ravnih in spiralnih zob v dveh razsežnostih. Cilj je razširitev njegovih formul na beveloidne zobnike v treh razsežnostih in nova metoda tako vključuje risanje različnih 2D-prerezov po globini z oba, ki sestavljeni oblikujejo 3D -model z oba. Z a beveloidne z obnike je predstavljena tehnika modeliranja z orodji v obliki z obnice, ki namesto na metodi avtorja Liu temelji na Batistinem modelu. Vrednosti kotalnega kota pri generiranju prerezov so izračunane z enačbo ubiranja. P redstavljena je primerjava geometrij z ob, ustvarjenih s prejšnjo in novo metodo. R az vidne so manjše raz like v vrednostih koordinat. P rototipni z obniki so bili iz delani z dodajalno tehnologijo ciljnega nalaganja (F DM) in nato sestavljeni. U gotovljeno je bilo odstopanje koordinat z aradi profilnega pomika, ki se kompenz ira z z asukom surovca z a določen kot. Kot je navedeno v razdelku Rezultati in ugotovitve, so pri nekaterih vrednostih parametrov zobnika možna odstopanja koordinat v korenu. To je značilno za modele s kotom stožca, ki presega 15 , in lahko predstavlja omejitev uporabnosti predlagane metode. Kot stožca pri izdelanih prototipih je znašal 15 . V prihodnje bo mogoče prilagoditi formule, ki opredeljujejo ovojnično krivuljo. Matematični model bo prav tako mogoče razširiti na druge vrste zobnikov, kot so eliptični ali neokrogli zobniki, ter na geometrije zobnikov s paraboličnimi, konkavnimi, konveksnimi ali kronskimi modifikacijami. Predlagana nova metoda omogoča generiranje evolvente, korena in medzobne vrzeli, tehnike za modifikacijo zob pa je mogoče prilagoditi formulam. Matematični model, ki ga je predstavil Batista za dvorazsežnostne prereze, je bil v pričujoči študiji razširjen na trirazsežnostne modele beveloidnih zobnikov. Predlagani modelirni algoritem je krajši, generirani zobniški profili pa se tesno prekrivajo. Pri prilagajanju enačb je bilo ugotovljeno, da parametri profilnega pomika pri beveloidnih geometrijah povzročijo zasuk prerezov po širini osi zoba za manjši kot. V izogib temu je bil izpeljan prilagoditveni kot, ki je vključen v enačbah. V rezultatih so prikazani zobni profili z odstopanji in korigirani zobni profili. Opravljena je bila podrobna analiza področja zaokrožitve korena zoba za spiralne in konične zobnike. Podana je primerjava položajnih koordinat za različne kote stožca in širine zoba. Rezultati so pokazali, da so spremembe položajnih koordinat v sprejemljivih mejah. P redstavljena tehnika modeliranja tako poenostavlja opredelitev geometrije v prerez u, konstruktorjem pa so pripravljene zamudne tehnike, saj formule ne zahtevajo računanja normalnih vektorjev. l e e ede e eloid i o i i ate ati o odelira e orod a o li i o ice ara etri o modeliranje, evolventni profil, analiz a spodrez anja *Naslov avtorja za dopisovanje: Univerza ogus, , ddelek za strojništvo, stanbul, Turčija, bsenturk@dogus.edu.tr SI 9 Strojniški vestnik - Journal of Mechanical Engineering 70(2024)1-2, SI 10 © 2024 Avtorji. t di a o o ti Prejeto v recenzijo: 2023-09-01 Prejeto popravljeno: 2023-11-30 Odobreno za objavo: 2023-12-13 ora e i ra l e i re al i z a gladilno valjanje lo ic Oktay Ad yaman* Univerza Batman, Turčija Namen pričujoče študije je preveriti uporabnost in zmogljivost neobrabljenih delov odsluženih rezalnih ploščic iz materialov W C , C BN in keramike v funkciji orodja z a globoko valjanje. Rezalna orodja za strojno obdelavo (iz karbidne trdine, CBN, keramike itd.) so ključnega pomena v industriji, narejena pa so iz dragocenih kovin. Rezalne ploščice se običajno zavržejo, ko dosežejo stopnjo obrabe 1 do 2 , kar je povezano s stroški in obremenitvijo za okolje. Po statističnih podatkih se reciklira med 20 in 30 W C . R ecikliranje je sicer koristen, vendar tudi drag postopek. Z ato obstaja potreba po iskanju alternativ in v tem kontekstu je pomembna ponovna uporaba izrabljenih rezalnih ploščic. Neobrabljeni deli rezalnih ploščic (iz WC, CBN in keramike) so bili preizkušeni pri gladilnem valjanju jekla AISI 1050 po metodi globokega valjanja z različnimi parametri. Na ta način so bile preučene možnosti za ponovno uporabo omenjenih ploščic za globoko valjanje. mogljivost ploščic je bila ovrednotena na podlagi mikrotrdote, hrapavosti (R a) in videz a nastalih površin. Z a eksperimente brez hlajenja so bile iz brane tri sile valjanja (143 N, 330 N in 4 5 N), tri števila prehodov (1, 2 in 3) in tri podajalne hitrosti (0,04 mm/vrt, 0,08 mm/vrt in 0,12 mm/vrt). Opravljenih je bilo torej 27 eksperimentov z vsako ploščico, skupaj 81 eksperimentov. Vpliv procesnih parametrov na vrednosti mikrotrdote in R a je bil določen z analizo variance. Po globokem valjanju ni bilo mogoče opaziti signifikantne obrabe na površini nobene od rezalnih ploščic. Pri ploščicah iz materialov WC in CBN je bilo ugotovljeno, da je sicer izginila prevleka, na površini pa ni bilo sledov abrazije. aradi toplote in abrazije se je oblikovala le črna cona. Proces globokega valjanja je povzročil porast mikrotrdote. Trdota je največja na površini in od tam pada proti sredini. Največja vrednost trdote je bila izmerjena po eksperimentih s tremi prehodi, najmanjša pa po enem prehodu. Trdota je bila največja pri keramični ploščici in najmanjša pri ploščici iz materiala WC. Analiza variance je pokazala, da so statistično signifikantni dejavniki za mikrotrdoto tip ploščice, sila in število prehodov. Prispevek števila prehodov, vrste ploščic in sile k mikrotrdoti znaša 44,77 , 23,70 oz. 13,53 . N iz ke in visoke vrednosti podajanja negativno vplivajo na hrapavost površine (vrednost R a), podajanje pa naj bi z agotovilo optimalne vrednosti R a. V razmerah z manjšo silo valjanja so bile pri ploščicah iz WC dosežene nižje vrednosti R a kot pri ploščicah iz CBN. Pri večjih silah valjanja ima material CBN bolj pozitiven vpliv na R a. N ajboljše vrednosti R a so bile dosežene pri ploščicah iz WC pri majhnih silah, pri ploščicah iz materiala CBN pa pri velikih silah valjanja. Vrednost R a pri ploščicah iz materiala WC na splošno narašča s številom prehodov. Dosežene vrednosti R a pri ploščici iz materiala WC se ujemajo s podatki iz literature. Glede na analizo variance imata statistično signifikanten vpliv na R a tip ploščice in hitrost podajanja. Največji vpliv na vrednost R a ima podajanje, sledijo pa mu vrsta ploščice, sila in število prehodov s prispevki 22,60 , 18,23 , 4,54 oz. 0,77 . V literaturi je mogoče najti študije na temo recikliranja rezalnih orodij, medtem ko izkoriščanje neizrabljenih površin rezalnih ploščic še ni bilo obravnavano. Pričujoča študija predstavlja alternativo za ponovno uporabo odpadnih (izrabljenih) ploščic v funkciji orodja za globoko gladilno valjanje, s čimer je bilo odprto tudi novo raziskovalno področje. l e e ede lo o o al a e ladil o al a e ro lo i rotrdota tri olo i a o r i a ra a o t integriteta površine SI 10 *Naslov avtorja za dopisovanje: Univerza Batman, Poklicna šola organizirane industrijske cone Besiri, Batman, Turčija, oktay.adiyaman@batman.edu.tr Strojniški vestnik – Journal of Mechanical Engineering (SV-JME) Aim and Scope The international journal publishes original and (mini)review articles covering the concepts of materials science, mechanics, kinematics, thermodynamics, energy and environment, mechatronics and robotics, fluid mechanics, tribology, cybernetics, industrial engineering and structural analysis. The journal follows new trends and progress proven practice in the mechanical engineering and also in the closely related sciences as are electrical, civil and process engineering, medicine, microbiology, ecology, agriculture, transport systems, aviation, and others, thus creating a unique forum for interdisciplinary or multidisciplinary dialogue. The international conferences selected papers are welcome for publishing as a special issue of SV-JME with invited co-editor(s). Editor in Chief Vincenc Butala University of Ljubljana, Faculty of Mechanical Engineering, Slovenia Technical Editor Pika Škraba University of Ljubljana, Faculty of Mechanical Engineering, Slovenia Founding Editor Bojan Kraut University of Ljubljana, Faculty of Mechanical Engineering, Slovenia Editorial Office University of Ljubljana, Faculty of Mechanical Engineering SV-JME, Aškerčeva 6, SI-1000 Ljubljana, Slovenia Phone: 386 (0)1 4771 137 Fax: 386 (0)1 2518 567 info@sv-jme.eu, http://www.sv-jme.eu Print: Demat d.o.o., printed in 240 copies Founders and Publishers University of Ljubljana, Faculty of Mechanical Engineering, Slovenia University of Maribor, Faculty of Mechanical Engineering, Slovenia Association of Mechanical Engineers of Slovenia Chamber of Commerce and Industry of Slovenia, Metal Processing Industry Association President of Publishing Council Mihael Sekavčnik University of Ljubljana, Faculty of Mechanical Engineering, Slovenia Vice-President of Publishing Council Matej Vesenjak http://www.sv-jme.eu 70 (2024) 1-2 University of Maribor, Faculty of Mechanical Engineering, Slovenia Since 1955 Strojniški vestnik Journal of Mechanical Engineering ts bert Kunc: nciples and Rules of Geometrical Product Specifications Current ISO Standards tolerancing dong Di, Zhengyuan Gao, Zhiguo An, Ling Chen, Yuhang Zhang, the Dimensional Accuracy of a Ti-6Al-4V Ripple Disc Hot Incremental Sheet Forming ISO standard Trung-Thanh Nguyen, An-Le Van: nce Optimization of the Rotary Turning Operation for and Quality Indicators an Wang, Yujiang Jiang: on Method for Instantaneous Efficiency and Torque Fluctuation kiewicz: the Titanium Alloy Turning Process with Prime A Tools under Cooling Conditions ntürk, Mahmut Cüneyt Fetvacı: oach to the Rack Generation of Beveloid Gears the Application of Worn Cutting Tool Inserts as Burnishing Journal of Mechanical Engineering - Strojniški vestnik ki, Monika Kulisz, Anna Szczepaniak: meters with Statistical Analysis and Modelling Using Artificial s After Finish Milling of Magnesium Alloys with Different Edge s 1-2 2024 70 no. year volume geometrical product specification verification Cover: The geometrical product specifications (GPS) are, in addition to material specifications, a key component of effective planning and production of mechanical products as well as communication between partners in these processes. The principles and basic rules for precise and unambiguous specification of all requirements are embodied in a series of ISO GPS standards. Image Courtesy: Photo by