Since 1955 „ > Strojniški vestnik Journal of Mechanical Engineering 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 250 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 Mitjan Kalin University of Ljubljana, Faculty of Mechanical Engineering, Slovenia Vice-President of Publishing Council Bojan Dolšak University of Maribor, Faculty of Mechanical Engineering, Slovenia Strojniški vestnik -t!'^ Journal of Mechanical ' Engineering Cover: The self-excited pulsed air-water jet offers many advantages over other jets and has a large number of practical and industrial applications. Experimental testing of it's cleaning performance is necessary. The cleaned area ratio was calculated from acquired images by using image analysis software through image pre-processing, greying, image segmentation, calibration, and area calculation. Image courtesy: Research Center of Fluid Machinery Engineering and Technology, Jiangsu University, Zhenjiang, China ISSN 0039-2480, ISSN 2536-2948 (online) International Editorial Board Kamil Arslan, Karabuk University, Turkey Hafiz Muhammad Ali, King Fahd U. of Petroleum & Minerals, Saudi Arabia Josep M. Bergada, Politechnical University of Catalonia, Spain Anton Bergant, Litostroj Power, Slovenia Miha Boltežar, University of Ljubljana, Slovenia Filippo Cianetti, University of Perugia, Italy Janez Diaci, University of Ljubljana, Slovenia Anselmo Eduardo Diniz, State University of Campinas, Brazil Igor Emri, University of Ljubljana, Slovenia Imre Felde, Obuda University, Faculty of Informatics, Hungary Imre Horvath, Delft University of Technology, The Netherlands Aleš Hribernik, University of Maribor, Slovenia Soichi Ibaraki, Kyoto University, Department of Micro Eng., Japan Julius Kaplunov, Brunel University, West London, UK Iyas Khader, Fraunhofer Institute for Mechanics of Materials, Germany Jernej Klemenc, University of Ljubljana, Slovenia Milan Kljajin, J.J. Strossmayer University of Osijek, Croatia Peter Krajnik, Chalmers University of Technology, Sweden Janez Kušar, University of Ljubljana, Slovenia Gorazd Lojen, University of Maribor, Slovenia Darko Lovrec, University of Maribor, Slovenia Thomas Lubben, University of Bremen, Germany George K. Nikas, KADMOS Engineering, UK Tomaž Pepelnjak, University of Ljubljana, Slovenia Vladimir Popovič, University of Belgrade, Serbia Franci Pušavec, University of Ljubljana, Slovenia Mohammad Reza Safaei, Florida International University, USA Marco Sortino, University of Udine, Italy Branko Vasič, University of Belgrade, Serbia Arkady Voloshin, Lehigh University, Bethlehem, USA General information Strojniški vestnik - Journal of Mechanical Engineering is published in 11 issues per year (July and August is a double issue). Institutional prices include print & online access: institutional subscription price and foreign subscription €100,00 (the price of a single issue is €10,00); general public subscription and student subscription €50,00 (the price of a single issue is €5,00). Prices are exclusive of tax. Delivery is included in the price. The recipient is responsible for paying any import duties or taxes. Legal title passes to the customer on dispatch by our distributor. Single issues from current and recent volumes are available at the current single-issue price. To order the journal, please complete the form on our website. For submissions, subscriptions and all other information please visit: http:// www.sv-jme.eu. You can advertise on the inner and outer side of the back cover of the journal. The authors of the published papers are invited to send photos or pictures with short explanation for cover content. We would like to thank the reviewers who have taken part in the peer-review process. © 2021 Strojniški vestnik - Journal of Mechanical Engineering. All rights reserved. SV-JME is indexed / abstracted in: SCI-Expanded, Compendex, Inspec, ProQuest-CSA, SCOPUS, TEMA. The list of the remaining bases, in which SV-JME is indexed, is available on the website. The journal is subsidized by Slovenian Research Agency. Strojniški vestnik - Journal of Mechanical Engineering is available on https://www.sv-jme.eu. Strojniški vestnik- Journal of Mechanical Engineering 67(2021)3 Contents Contents Strojniški vestnik - Journal of Mechanical Engineering volume 67( 202J , number 3 Ljubljana, March 2021 ISSN 0039-2480 Published monthly Papers Yong Wang, Xiaolin Wang, Zilong Zhang, Yu Li, Houlin Liu, Xiang Zhang, Marko Hocevar: Optimization of a Self-Excited Pulsed Air-Water Jet Nozzle Based on the Response Surface Methodology 75 Manuel Javier Rosel Solis, José Omar Dávalos Ramírez, Javier Molina Salazar, Juan Antonio Ruiz Ochoa, Antonio Gómez Roa: Optimization of Running Blade Prosthetics Utilizing Crow Search Algorithm Assisted by Artificial Neural Networks 88 Omar Dávalos, Uzziel Caldiño-Herrera, Delfino Cornejo-Monroy, Oscar Tenango-Pirin, Juan Carlos Garcia, MA. Basurto-Pensado: Reduction of Stresses and Mass of an Engine Rubber Mount Subject to Mechanical Vibrations 101 Bin Wang, Chenxiao Yan, Jubo Li, Peiyao Feng, Shuaipu Wang, Shuo Chen, Jianxin Su: Residual Stress and Deformation Analysis in Machining Split Straight Bevel Gears 114 Sandino Torres, Roberto Ortega, Pablo Acosta, Edisson Calderón: Hot Incremental Forming of Biocomposites Developed from Linen Fibres and a Thermoplastic Matrix 123 Strojniški vestnik- Journal of Mechanical Engineering 67(2021)3, 75-87 © 2021 Journal of Mechanical Engineering. All rights reserved. D0l:10.5545/sv-jme.2020.6995 Original Scientific Paper Received for review: 2020-10-17 Received revised form: 2021-02-11 Accepted for publication: 2021-03-01 Optimization of a Self-Es ited Pulsed Air-W er Jet Nozzle Based on the Response Surface Methodology Yong Wang1 - Xiaolin Wang1 - Zilong Zhang1 - Yu Li1 - Houlin Liu1 * - Xiang Zhang2 - Marko Hocevar3 1 Jiangsu University, Research Center of Fluid Machinery Engineering and Lechnology, China 2Xihua University, Key Laboratory of Fluid and Power Machinery, China 3University of Ljubljana, Faculty of Mechanical Engineering, Slovenia A self-excited pulsed air-water jet (SEPAWJj offers many advantages over other jets and has a large number of practical and industrial applications. In order to take better advantage of the SEPAWJ, response surface methodology (RSM) models were established with the experimental impact force characteristics as the dependent variable and three key nozzle parameters as the independent variable. Single and coupling factor effects of these three parameters (oscillation chamber length, oscillation chamber height, and diameter of the downstream nozzle) on performance of nozzle are analysed, and the structural parameters of optimum performance are calculated using RSM models. The external flow field, impact force and cleaning performance of SEPAWJ before and after optimization are analysed and compared experimentally. It is found that the significance levels of established average impact force and impact force amplitude RSM models are lower than 0.05, and their error ratios between calculation and experiment under the optimum construction are both less than 5 %, which confirms their considerable reliability. Meanwhile, the final large water mass of optimized SEPAWJ is formed much earlier, and is more intensive and more concentrated. Compared with the original SEPAWJ nozzle, the impact force and impact force amplitude of optimized SEPAWJ nozzle are increased by 52.00 % and 38.26%, respectively. In addition, the cleaned area ratio of nozzle before and after optimization is 76% and 100 % at 50 seconds, respectively, with an increase of 22.4 %. Keywords: multiphase flow, impact force, cleaning performance, optimization, pulsed jet Highlights • The collapse of air bubbles and water surface tension transform continuous air-water mixed jet to discrete water masses with different speeds. • At the same mass flow rate and time duration, bigger water masses from a pulsed jet offer larger volume and less number water masses which improves impact force amplitude and lowers impact force frequency. • Multiphase periodic flow in the oscillation chamber of the pulsed air-water jet nozzle consists of shear layer flow formation, air suction from holes, air-water vorticity ring formation, air bubble breakage, and air mixing with the main stream. • A self-excited pulsed air-water jet nozzle is optimized on the basis of Response Surface Methodology. • Models are established with the experimental impact force characteristics as the dependent variable and three geometric dimensions as the independent variable. 0 INTRODUCTION The high energy enabled by breaking of a continuous jet into a series of pulses lias been widely used. Guha et al. [1] experimentally, numerically and theoretically investigated the very high speed water jet (80 m/s to 200 m/s) cleaning process, and the pressure distribution on the cleaning surface was assessed. Li et al. [2] investigated the effects of nozzle inner surface roughness on the cavitation erosion characteristics of submerged cavitating jets through experiments to push the erosion capability to a maximum, Chahine et al. [3] studied the Helmholtz nozzle and concluded that when the jet pulse frequency is consistent with the cavity's natural frequency, resonance will occur and the jet intensity will be improved. Scholars have studied the mechanism of pulsed jets through theoretical and experimental methods. Its most significant characteristic is periodic ejected water mass rather than continuous flow. Labus and Savanick determined that the peak value of pulsed air-water jet dynamic pressure is several times that of the steady and continuous water jet under the same working conditions, which greatly improves the cleaning effect. Researchers created many mechanical methods for producing high-energy water pulses repeatedly, such as rotating, reciprocating, or wobbling mechanisms. Glenn [5] mentioned an impulsive water cannon that can produce high energy. Grinspan and Gnanamoorthy [6] studied the high efficiency pulsed water jet acting on rock targets. Although these devices could drive large scale oscillations of the water flow and improve the erosion effect, they required high levels of mechanical maintenance which limits durability in harsh industrial enviromnents. The complexity-related short life-time of the mentioned mechanical devices have prevented the development of a high-pressure pulsed water jet systems. However, "self-resonating *Corr. Author's Address: Jiangsu University, Research Center of Fluid Machinery Engineering and Technology, Zhengjiang, China, 1429685398@qq.com 75 Strojniški vestnik - Journal of Mechanical Engineering 67(2021)3, 75-87 jet" can be generated by the instability of shear flow, which could produce pulsed jets. Dehkhoda and Hood [7] mentioned the Helmholtz oscillator, which can form self-excited pulsed water jets. The vortices generated by the disturbed shear layer are continuously formed, enhanced, and weakened. The energy of the oscillation disturbance will increase significantly when the frequency of the process equals the natural frequency of the oscillator. Many researchers have studied the self-excited water pulsed jet in many aspects. Tang et al. [8] built an oscillation frequency model of jet on the basis of hydro-acoustics and fluid dynamics for better understanding the principle of increasing jet pressure amplitude. He found that the oscillation frequency increased while increasing pump pressure and decreased while increasing cavity length, while there was an optimum cavity-length corresponding to the pressure peak value of the SEPAWJ. Hu [9] discussed the correlation of time-frequency distribution between the cervix cavity pressure pulsation signal and the shock pressure pulse signal in self-excited pulsed jet nozzle. He focused on the time-frequency rule of the pressure pulse signal, especially the inherent characteristic of frequency component. In order to improve the performance of the self-resonating cavitating waterjet under ambient pressures, Li et al. [10] experimentally studied the effects of the nozzle inner surface roughness by impinging the jets on pure aluminium specimens at various standoff distances. In addition, Chen et al. [11] investigated and compared the spray atomization properties and droplet turbulence characteristics of a twin-fluid nozzle with and without a self-excited vibrating cavity though a phase doppler particle analyser. He found that the self-excited vibrating cavity profoundly influenced the droplet turbulence characteristics by affecting the variation of droplet oscillation. In the presence of a self-excited vibrating cavity, the spray cone angle and the droplet number concentration increased significantly. The results indicated the significant role of the self-excited vibrating cavity in promoting fluid atomization. Furthermore, Hall and Ewing [12] estimated the instantaneous turbulent velocity field in a three-dimensional wall jet from the fluctuating wall pressure though a spectral linear stochastic estimation technique and found that the passage of the large-scale structures caused large, coherent lateral sweeps of fluid across the entire span of the wall jet. Besides, Li et al. [13] analysed effects of area discontinuity at nozzle inlet of Helmholtz oscillator and experimentally investigated it with respect to the axial pressure oscillations. It was found that area discontinuity had a capacity of enhancing their peak, which largely depended on the inlet pressure and standoff distance. The enhancement decreased with increasing inlet pressure and only happened within small standoff distances. Oh and Cho [14] carried out experimental cutting tests with water pressure, traverse speed of nozzle, and abrasive feed rate, and the energy loss was expressed by the energy term. Thakur and Singh [15] summarized the research progress and integrated function of abrasive waterjet machining in terms of mechanism and machining performances by using mathematical modelling and optimization methods. Alsoufi et al. [16] studied the effect of abrasive waterjet machining parameters on the surface texture quality of Carrara marble, and determined that the abrasive waterjet cutting process offers better cut surface texture quality of Carrara marble when the parameter conditions are constant. With the wider application of pulsed water jet in engineering, scholars found that the self-excited pulsed air-water jet performed better in some fields. Wang and Zhou [17] used out the air-water and pulsed jets to break rock by combination. They optimized the parameters of pulsed jet device structure and the results show that erosion effect had increased significantly. Hu et al. [18] described a new way of generating pulsed air-water jet by entraining and mixing air into the cavity of a pulsed water jet nozzle based on the theory of hydro-acoustics and fluid dynamics. A theoretical model was built, which described the frequency characteristic of the pulsed air-water jet and aiming at gaining a better understanding of the nozzle for generating pulses. In addition, the experimental results on specimens impinged by the pulsed water jet and pulsed air-water jet showed that the erosion rate increased slightly with air addition within a certain range of cavity length. It can be seen from the above that the self-excited pulsed air-water jet is a new type of efficient cleaning jet, which combines the advantages of different kinds of jets. The periodic high-intensity impact of self-excited pulsed air-water jet can quickly remove stains and its impact distribution is much wider, which significantly improves the cleaning effect. In addition, the RSM is a statistical method to determine the optimum parameters, to solve the multivariate problems by using reasonable experimental design method, to obtain data through experiments and by using multivariate quadratic regression equation to obtain the functional relationship between factors. RSM was first proposed by Box and Wilson [19]. It is widely used in the fitting 76 Wang Y - Wang, X L. - Zhang, Z.L. - Li, Y. - Liu, H.L. - Zhang, X. - Hočevar, M. Strojnlskl vestnik - Journal of Mechanical Engineering 67(2021)3, 75-87 field of physical experiments in medicine, chemical industry, food and mechanical engineering. Vyavaharc et al. [20] studied the effects of dye concentration, time, pH, and temperature on sorption of malachite green (MG) dye using response surface methodology (RSM). Tang et al. [21] used the central composite design (CCD) and response surface methodology to optimize the working parameters of the sprinkler, and established multiple regression models, so that the vertical rocker sprinkler can achieve the best hydraulic performance in operation. Siddhant and Jignasa [22] investigated the optimum deposition conditions for preparation of copper zinc tin sulphur compounds (CZTS) thin films using the spray pyrolysis method based on the response surface methodology. Qi et al. [23] adopted box Behnken's design combined with response surface methodology to investigate the effect of pH value, contact time, initial concentration, and other adsorption parameters on Th(IV) adsorption capacity. Khoshnamvand et al. [24] used response surface methodology to study the effects of Ciprofloxacin (CIP) concentration, CuO dosage and pH value on Chemical Oxygen Demand (COD) removal rate, and established a second-order model based on CIP concentration, CuO dosage and pH value. Oztiirk and Kahraman [25] analysed and determined the best grinding parameters of glass by response surface method, and studied the relationship between grinding characteristics and surface roughness by Box Behnken design (BBD) to design the experiment. Gnanavelbabu and Saravanan [26] studied the abrasive water jet machining (AWIM) process for the machining of Grade 5 Titanium alloy through response surface methodology (RSM) and adopted BBD to optimize the abrasive water jet machining process. Especially, in the aspect of the AWJ cutting, many scholars also use response surface method to study. Dani and Shah [27] used response surface methodology to study the effects of transverse velocity, water pressure, and tool spacing on the removal rate and surface roughness. Karakurt et al. [28] studied the effects of the abrasive wateijet operating variables on the kerf angle and the material properties were correlated with the kerf angle through response surface methodology. Gupta et al. [29] adopted the abrasive water jet cutting (AWJ) process to study experimental investigation parameters on kerf taper angles of makrana white marble through changing the water pressure, nozzle transverse speed and abrasive flow rate; analysis of variance (ANOVA) was used to determine the main statistically significant process factors affecting the kerf taper angle. Mohammad and Jabari [30] studied the cooling of photovoltaic modules through multi-nozzle jet impingement cooling (JIC) system. The effects of the number of nozzles, their sizes (diameter), and the dimensionless nozzle-to-photovoltaic (PV) spacing on the overall performance of the JIC system were studied using a response surface methodology. Many experiments are needed to study the influence of various factors on the performance of self-excited pulsed air-water jet nozzle and their relationship. The response surface methodology can shorten the optimizationprocess with less experimental time compared with traditional optimization methods. In the present paper, SEPAWJ was applied to toilet nozzle, and the second-order mathematical model of RSM was established for the SEPAWJ characteristics of impact force characteristics (average impact force /•'. impact force amplitude AF) under different chamber and downstream nozzle parameters measured by experiments. The significance of the coefficients of the model and regression equation was tested. The influence of interaction items and single factors on the SEPAWJ impact characteristics was obtained. Structural parameters for optimum performance were calculated with RSM equations and the performance of the nozzle before and after optimization was compared experimentally. Comparison supplements the previous related research and provides useful information for better applications of SEPAWJ. 1 OPERATING PRINCIPLES OF A SEPAWJ NOZZLE The SEPAWJ lias a more pronounced cleaning effect than the continuous jet because of its periodic water mass delivery. The peak value of jet-forced pressure of the pulsed air-water jet is several times that of the continuous water jet under the same working conditions. Fig. 1 shows the operating principles of a nozzle producing SEPAWJ. As shown in Fig. 1, the shear layer flow flows to the air holes on both sides of the chamber, which reduces the holes pressure to lower than atmospheric pressure. Air is sucked from the air holes and forms a series of discrete bubbles. The inclusion of bubbles to the fluids shear layer enables formation of air-water vorticity rings due to the confinement by the chamber wall. Some bubbles in air-water vorticity rings break up and produce pressure pulses. This results in small bubbles mixing into the main stream flow and causing pressure and velocity fluctuations. The air-mixed main stream flow passes through the downstream nozzle and eventually forms an air-water pulsed jet. As discussed, the series phenomena: "shear layer Optimization of a Self-Excited Pulsed Air-Water Jet Nozzle Based on the Response Surface Methodology 77 Strojniški vestnik - Journal of Mechanical Engineering 67(2021)3, 75-87 Fig. 1. Schematic diagram of a SEPAWJ nozzle and its operating principles flow formation", "air suction from holes", "air-water vorticity rings formation", "air bubble breakage", and "air mixing with main stream" develop quasi-periodic operations of the pulsating air-water jet under certain working conditions. ajH Wm b) Fig. 2. Visualization of continuous jet and EPAWJ; a) continuous jet; b) EPAWJ Fig. 2 shows visualization of the continuous jet and SEPAWJ. As shown in Fig. 2a, the continuous water jet is thin, straight, and stable for the entire observation length. Because of its stability, its cleaning area and the impact force amplitude are small. As shown in Fig. 2b, the air bubbles in the air-water jet collapse and the jet becomes unstable at 6 cm. Because non-stationary and random phenomena, like the uneven distribution of air bubbles in the entire jet, unstable and turbulent flow within the jet, pressure instabilities within the water jet, surface tension and the random air bubble collapse, the continuous air-water jet breaks into small discrete water segments at around 10 cm distance from the downstream. All of this results in different speeds of individual segments. The faster segments catch up with the slower segments and eventually form a large water segment at around 15 cm from the downstream nozzle. Continuous occurrence of pulsed large water segments forms the SEPAWJ. 2 EXPERIMENTAL SETUP AND PROCEDURES The design of the experimental SEPAWJ nozzle is shown in Fig. 3. The experimental SEPAWJ nozzle parameters before optimization are shown in Table 1. The nozzle is 3D-printed with photosensitive resin as material, which is waterproof and not easy to deform. The performance parameters of material are shown in Table 2. Fig. 3. Schematic diagram of the SEPAWJ nozzle 78 Wang Y - Wang, X L. - Zhang, Z.L. - Li, Y. - Liu, H.L. - Zhang, X. - Hočevar, M. Strojnlskl vestnik - Journal of Mechanical Engineering 67(2021)3, 75-87 Table 1. The main structural parameters of the SEPAWJ nozzle before optimization Parameter Name Size ch Outlet diameter of upstream nozzle 1 mm d2 Inlet diameter of downstream nozzle 1.4 mm ch Outlet diameter of downstream nozzle 1.7 mm He Oscillation chamber height 5.5 mm Lc Oscillation chamber length 16 mm a Inclination angle of oscillation chamber side wall 60° P Inclination angle of oscillation chamber bottom wall 4° Table 2. The main performance parameters of the resin material Heat distortion temperature 47 °C Hardness 87 Tensile strength (fracture) 56 MPa Tensile modulus 2800 MPa Ductility (tensile) 4 % Impact strength 25 J/m Bending strength 84 MPa Bending modulus 2490 MPa Poisson's ratio 0.41 The experimental setup is arranged from several subsystems, indicated by different colours in Fig. 4; water supply and conditioning, nozzle, SEPAWJ cleaning evaluation, force measurement, flow visualization, and control systems. As impact force is the most important evaluating indicator of a jet, its average impact force and impact force amplitude, as well as impact force frequency of fluctuations are essential to be measured and analysed for SEPAWJ performance evaluation under different working conditions and parameters. A miniature impact force sensor (model: LH-S09A) was used to measure the SEPAWJ impact force. It was mounted at a distance 150 mm away from the downstream nozzle outlet. The size and shape of the discrete water segments formed within the discrete jet from the downstream nozzle outlet have a great influence on the cleaning performance. Therefore, flow field visualization was used to provide better understanding of the SEPAWJ characteristics LH-S09A performance under different nozzle structure parameters. A high-speed image acquisition system (camera model: MotionPro Y4) for capturing flow field was used for the SEPAWJ jet evaluation. Experimental testing of the cleaning performance of the SEPAWJ is necessary and the steps to do so are as follows: 1. Evenly apply 10 g soybean paste as a dirt on a 100 mm x 20 mm water-resistant sandpaper (model: P1500). 2. The direction of nozzle outlet is at 25 degrees angle relative to the paper surface placed horizontally. The distance between nozzle outlet and sandpaper is 15 cm. i__________________________________i Fig. 4. Schematic diagram of the experimental setup Optimization of a Self-Excited Pulsed Air-Water Jet Nozzle Based on the Response Surface Methodology 79 Strojniški vestnik - Journal of Mechanical Engineering 67(2021)3, 75-87 3. The image of residual dirt is acquired every 10 seconds for measurement of cleaned area ratio. 4. The cleaned area ratio was calculated from acquired images by using image analysis software through image pre-processing, greying, image segmentation, calibration, and area calculation. Fig. 5 shows residual dirt image before and after the grey level thresholding by image analysis software. Furthermore, in order to reduce the influence of testing system pressure amplitude, a centrifugal pump is used as pumping device and a surge tank and two accumulators are installed. The pressure controlled valve in upstream of the nozzle ensures that the dynamic pressure of the nozzle inlet is stable at 0.12 MPa. Fig. 5. Before and after the gray processing of residual dirt area by Image analysis software; a) before the grey processing of residual dirt area; b) after the grey processing of residual dirt area 3 RESULTS AND ANALYSIS 3.1 Design of Experiment and Measurement Results Tang et al. [8] compared self-excited oscillation pulsed jet and continuous jet for time domain impact characteristics under the same inlet pressure and mass flow rate. They found that the impact force amplitude of continuous jet is small and that of the self-excited oscillation pulsed jet is such significant, although the average impact force of self-excited oscillation pulsed jet is slightly smaller because of energy lost from gas bubbles breakings and associated turbulent losses. The average impact force and impact force amplitude are important parameters in evaluating a jet nozzle. Based on our previous research it was found that the oscillation chamber length oscillation chamber height and diameter of the downstream nozzle each have a sensitive effect on the average impact force and impact force amplitude of the jet nozzle separately. However, single factor analysis lias some disadvantages in the optimization; for example, it needs a lot of experiments and the coupling effect of three parameters are unknown. The RSM enables seeing how changes to each input parameter affect a selected output parameter, showing the coupling relationship between variables and responses. The RSM, especially the BBD used in this research is a technique in which orthogonal arrays are used to investigate design parameters. Table 3. Initial design parameters and constraint values Quantity Lower value [mm] Base value [mm] Largest value [mm] Inlet diameter of upstream nozzle 1.2 1.4 1.6 Chamber length 12 16 18 Chamber height 5.1 5.5 5.9 As a result, in this paper, the average impact force F and impact force amplitude AF were selected as target dependent variables to establish RSM model respectively and oscillation chamber length oscillation chamber height and diameter of the downstream nozzle are taken as experimental variables. The initial design parameters and constraint values are shown in Table 3. According to the initial design parameters and selected constraint values presented in Table 3, 17 test cases were obtained by Box-Behnken method in Software Design-Expert 10.0, and the average impact force F and impact force amplitude AF for each test scheme were obtained experimentally, as shown in Table 4. 3.2 Average Impact Force RSM Model An ANOVA, which a data mining technique, is carried out to differentiate the contributions to the variance of the response surface from the model. To evaluate the effect of each design variable, the total variance of the model is decomposed into that of each design variable and their interactions. This method is used to identify unnecessary terms in model function. Table 5 shows the RSM summary of the RSM model and ANOVA for average impact force. For the established average impact force of the RSM model, the significance levels of inlet diameter of downstream nozzle (J) and chamber length (B) are less than 0.01, which means that these two single factors have a very significant effect on average impact force F. Similarly, the significant level of the interaction term (AB) is less than 0.05, which indicates that it has a significant coupling effect on the average impact force F. The significance level of a certain item is inversely proportional to the influence level of the item on the average strike force. Therefore, the order 80 Wang Y - Wang, X L. - Zhang, Z.L. - Li, Y. - Liu, H.L. - Zhang, X. - Hočevar, M. Strojnlskl vestnik - Journal of Mechanical Engineering 67(2021)3, 75-87 Table 4. Experimental variables and obtained results No. Downstream nozzle inlet diameter^ [mm] Chamber length B [mm] Chamber height C [mm] Average impact force F [N] Impact force amplitude aF[N] 1 1.6 20 5.5 0.0942 0.0121 2 1.4 16 5.5 0.1361 0.0163 3 1.4 12 5.9 0.1145 0.0103 4 1.2 16 5.1 0.1013 0.0148 5 1.2 16 5.9 0.0948 0.0131 6 1.6 12 5.5 0.0545 0.0088 7 1.6 16 5.9 0.0923 0.0115 8 1.4 12 5.1 0.1184 0.0113 9 1.4 16 5.5 0.1361 0.0163 10 1.4 16 5.5 0.1361 0.0163 11 1.6 16 5.1 0.0939 0.0124 12 1.4 20 5.1 0.1348 0.0159 13 1.4 16 5.5 0.1361 0.0163 14 1.2 20 5.5 0.1074 0.0143 15 1.4 20 5.9 0.1194 0.0151 16 1.4 16 5.5 0.1361 0.0163 17 1.2 12 5.5 0.0895 0.0095 of the influence of single factors the average impact force F is: chamber length (B) > inlet diameter of downstream nozzle (J) > chamber height (C)- The order of the influence of interaction items on the average impact force F is: downstream nozzle and chamber height (AC) > chamber length and chamber height {BC) > downstream nozzle and chamber length (A B). Table 5. Summary of RSM model and ANOVA for average impact force Source Sum of squares Degrees of freedom Mean square Significance level (P-value) Model 8.225E-003 9 9.139E-004 0.0002 A 6.680E-004 1 6.680E-004 0.0039 B 6.827E-004 1 6.827E-004 0.0037 B 1.748E-004 1 1.748E-004 0.0472 AB 1.796E-004 1 1.796E-004 0.0444 AC 5.550E-005 1 5.550E-005 0.2622 BC 3.306E-005 1 3.306E-005 0.3779 Residual 2.613E-004 7 3.732E-005 Lack of fit 2.613E-004 3 8.708E-005 Pure error 0.000 4 0.000 Cor Total 8.486E-003 16 Fig. 6 shows the average impact force as a function of interaction items consisting of the downstream nozzle inlet diameter, chamber length, and chamber height. The interaction term (AB) consisting of the length of downstream nozzle and chamber length has a very significant effect on the average impact force, while the other two interaction terms are less significant. Therefore, the parameters of downstream nozzle inlet diameter and chamber length are more critical for obtaining larger average impact force. According to the response surface regression equation when the downstream nozzle inlet diameter is 1.37 mm, the chamber length is 18.12 mm, and the chamber height is 4.80 mm, the average impact force is expected to reach the maximum value of 0.1434 N. The RSM equation of average impact force F is as follows: F = +0.14-0.009138,4 + 0.0092385 -0.004675C + 0.0067AB + 0.003725,4 C -0.0028755C - 0.036A2 -0.012B2 -0.00195C2. (1) It can be seen from Table 5 that the regression model P = 0.0002 < 0.01 shows that the model has a very significant impact on the impact force /•'. and can well describe the relationship between the structural parameters and the impact force F. 3.3 Average Impact Force Amplitude of the RSM Model The response surface regression equation of impact force amplitude AF is as follows: Optimization of a Self-Excited Pulsed Air-Water Jet Nozzle Based on the Response Surface Methodology 81 Strojniški vestnik - Journal of Mechanical Engineering 67(2021)3, 75-87 BO O Chamber height Downstream nozz c ( [mm] mlet diameter, A [mm] o.us Chamber length, Chamber height, B [mm] C [mm] Fig. 6. Average impact force Fas a function of interaction items; a) interaction item of A and B; b) interaction item of A and C; c) interaction item ofB and C Chamber length Downstream nozzle Is mm inlet diameter, A [mm] AF = +0.016 - 0.0008625,4 + 0.0021885 -0.00055C - 0.000375,45 + 0.0002,4C +0.000055C - 0.002663,42 - 0.00246352 -0.0006875C2, (2) It can be seen from Table 6 that the regression model P < 0.0001 shows that the model has a very significant impact on the impact force amplitude, and can well describe the relationship between the structural parameters and the impact amplitude . Table 6. Summary of RSM model and ANOVA for impact force amplitude Source Sum of squares Degrees of freedom Mean square Significance level Model 1.098E-004 9 1.220E-005 < 0.0001 A 5.951E-006 1 5.951E-006 < 0.0001 B 3.828E-005 1 3.828E-005 < 0.0001 B 2.420E-006 1 2.420E-006 0.0005 AB 5.625E-007 1 5.625E-007 0.0204 AC 1.600E-007 1 1.600E-007 0.1557 BC 1.000E-008 1 1.000E-008 0.7027 Residual 4.425E-007 7 6.321E-008 Lack of fit 4.425E-007 3 1.475E-007 Pure error 0.000 4 0.000 Cor Total 1.103E-004 16 Table 6 shows the summary of RSM model and ANOVA for impact force amplitude. For the established impact force amplitude RSM model, the significant level of inlet diameter of downstream nozzle (.4), chamber length (B) and chamber height (O are less than 0.01 which means that these three single factors have a very significant effect on impact force amplitude AP. Similarly, the significant level of the interaction terms (AB) is less than 0.05, which indicates that only it has a significant effect on the impact force amplitude AP. The significance level of a certain item is inversely proportional to the influence level of the item on the average impact force. Therefore, the order of the influence of single factors the impact force amplitude AF is: inlet diameter of downstream nozzle (A) = chamber length (B) > chamber height (O- The order of the influence of interaction items on the average impact force F is: inlet diameter of downstream nozzle and chamber length (.45) > inlet diameter of downstream nozzle and chamber height (AC) > chamber length and chamber height (BC). Fig. 7 shows the impact force amplitude as a function of interaction items consisting of the downstream nozzle inlet diameter, chamber length and chamber height. The interaction term (AB) consisting of the length of downstream nozzle and combustor has a very significant effect on the average impact force, while the other interaction terms are less significant. Therefore, the parameters of downstream nozzle inlet diameter and chamber length are more critical for obtaining larger average impact force. 82 Wang Y. - Wang, XL - Zhang ZL - Li, Y. - Liu, HI. - Zhang, X. - Hocevar, M. Strojnlskl vestnik - Journal of Mechanical Engineering 67(2021)3, 75-87 D • 0.011 ll.DliS Chamber Downstream nozzle length. B [mm] inlet diameter, A [mm] Z to p 0.01 ü ä a ^ o «Î ï ^ Q. 3 £ = - & £ « 0.008 0.011 Chamber height, "-v Downstream nozzle 5 112 cj (1 [mm] inlet diameter, A [mm] Fig. 7. Impact force amplitude AF as a function of interaction Items; a) Interaction item of A and B; b) Interaction item ofB and C; c) Interaction item of A and C g. 3 0.011 £ 5 0.008 Chamber length. Chamber height. B [mm] ( [mm] According to the response surface regression equation, when the downstream nozzle inlet diameter is 1.36 mm, the chamber length is 17.82 mm, and the chamber height is 5.33 mm, the impact force amplitude is expected to reach the maximum value of 0.0167 N. 3.4 Optimized Design Parameters To optimize both the average impact force value and the impact force amplitude value, the average value of chamber lengths when the average impact force value and the impact force amplitude value reach their maximum is taken as the optimized dimension of chamber length. The chamber height and the diameter of downstream nozzle are obtained by the same method, as shown in Table 7. Table 7. Optimized dimensions Parameters Maximum average impact force Maximum impact force amplitude Average Outlet diameter of upstream nozzle [mm] 1.37 1.36 1.365 Chamber length [mm] 18.12 17.82 17.97 Chamber height [mm] 4.80 5.33 5.065 3.5 Flow Visualization The pulsed water mass formed by SEPAWJ can cause strong strike force pulse, which greatly improves the cleaning performance. Fig. 8 shows the external flow field diagram of SEPAWJ before and after optimization. b) Fig. 8. External flow field diagram of SEPAWJ before and after optimization; a) flow visualization of original SEPAWJ nozzle; b) flow visualization of optimized SEPAWJ nozzle Optimization of a Self-Excited Pulsed Air-Water Jet Nozzle Based on the Response Surface Methodology 83 Strojnlskl vestnik - Journal of Mechanical Engineering 67(2021)3, 75-87 Because air bubbles mixed in the jet collapse and water has surface tension in the air environment the continuous air-water jet gradually forms small discrete water masses with different speeds. The faster small water masses will catch up with the slower small water masses and form to one large water mass. As can be seen from the external flow field diagram of original SEPAWJ in Fig. 8a, the final large water mass is formed near 16 cm from the nozzle exit, and it is not really concentrated and does not form a spherical shape. As shown in Fig. 8a, in the external flow field diagram of optimized SEPAWJ nozzle, the large water mass is formed close to the nozzle outlet at around 12 cm from the nozzle exit. As it continues downstream, the water mass becomes concentrated and ultimately forms near spherical water mass in location around 14.5 cm from the nozzle exit with possessing improved cleaning capabilities. 3.6 Analysis of Impact Force Fig. 9 shows the time and frequency domain diagram of SEPAWJ impact force before and after optimization; it can be seen that the value of average impact force and impact force amplitude are obviously improved for the optimized nozzle, which indicates that the cleaning performance of the optimized nozzle should be greater. Furthermore, for the optimized nozzle, the impact force intensity of fluctuations exhibits a peak in a lower frequency region around 40 Hz. At the same mass flow rate and duration, bigger water masses definitely means less number of water masses which improves impact force amplitude and lower impact force frequency. Table 8 shows the comparison of average impact force and impact force amplitude before and after optimization. For the SEPAWJ optimized nozzle, the average impact force is 0.1403 N and the impact force amplitude is 0.0159, which are 52.00 % and 38.26 % higher than that of the original nozzle, respectively. This means that the impact performance of the SEPAWJ nozzle lias been remarkably improved. Table 8. Comparison of average impact force and impact force amplitude before and after optimization Value Average impact force F Impact force amplitude AF Original [N] 0.0923 0.0115 Optimized [N] 0.1403 0.0159 Increase [%] 52.00 38.26 Table 9. Comparison of impact force between the experiment and RSM Result Average impact force F Impact force amplitude AF RSM model value [N] 0.1426 0.0167 Experimental value [N] 0.1403 0.0159 Error [%] 1.64 4.79 Comparison between experimental and predicted values of the average impact force value and the impact force amplitude value are shown in Table 9. The impact force and impact force amplitude errors of prediction and experiment are both less than 5 %, which means that the response surface functions are basically accurate. 3.6 Analysis of Impact Force The cleamng performance of SEPAWJ before and after optimization of SEPAWJ nozzle were tested. Fig. 10 is a comparison of cleaning process before and after optimization. IklorL' opiumism ion ¿)J Frequency,/[H?,] Fig. 9. Time and frequency domain diagram of SEPAWJ impact force before and after optimization; a) time domain diagram; b) frequency domain diagram 84 Wang Y. - Wang, X.L. - Zhang ZL. - Li, Y. - Liu, H.L. - Zhang X. - Hocevar, M. Strojnlskl vestnik - Journal of Mechanical Engineering 67(2021)3, 75-87 Fig. 10. Comparison of cleaning process before and after optimization; a) original nozzle; b) optimized nozzle Time [s] Fig. 11. Comparison of the cleaned area ratio ofSEPAWJ before and after optimization Fig. 11 shows a comparison of the cleaned area ratio of SEPAWJ before and after optimization. From the figure, it can be seen that the cleaning performance of optimized SEPAWJ on soybean paste is better than that of original SEPAWJ. At 40 seconds, the cleaned area ratio of optimized SEPAWJ reaches 96 %, and finally 100 % at 50 seconds. However, the cleaned area ratio of original SEPAWJ reaches only 76 % at 50 seconds, and the difference between them is 22.4 %. In the first 20 seconds, the cleaned area ratio of the optimized and original SEPAWJ increases rapidly, and that of the original SEPAWJ increases much faster. After 20 seconds, the difference of the growth rate of the cleaned area ratio between the two SEPAWJ decreases gradually and is zero at 50 seconds. During the entire cleaning process, the cleaned area ratio of the optimized SEPAWJ is always higher than that of the original SEPAWJ. At 50 seconds, the cleaned area ratios of the two SEPAWJ do not change much more, and the difference of the cleaned area ratios between the two SEPAWJ reached the maximum of 22.4 %. 4 CONCLUSION The second-order mathematical RSM were established for the jet characteristics of average impact force F and impact force amplitude AF for different chamber and downstream nozzle parameters. The significance of the coefficients of the model and regression equation were tested. Single and coupling factor effects of three parameters (oscillation chamber length, oscillation chamber height and diameter of the downstream nozzle) on performance of nozzle were analysed and parameters of optimum performance were calculated using RSM. The performance of the nozzle before and after optimization was compared experimentally. The result are follows: 1. The RSM model significance levels of average impact force and impact force amplitude are both lower than 0.05, which means that they have high significance. The most significant single factor affecting the average impact force and impact force amplitude of the SEPAWJ is the chamber length. The interactive item of the downstream nozzle inlet diameter and the chamber length has the most significant coupling effect on the SEPAWJ average impact force and impact force amplitude. 2. To maximize both modelled variables, the maximum value of parameters (average impact force and the impact force amplitude) are taken as the optimal nozzle parameters, as follows: the diameter of the upper nozzle inlet is 1.365, the Optimization of a Self-Excited Pulsed Air-Water Jet Nozzle Based on the Response Surface Methodology 85 Strojniski vestnik - Journal of Mechanical Engineering 67(2021)3, 75-87 chamber length is 17.97 mm, and the chamber height is 5.065 mm. 3. The predicted values of RSM under optimized parameters are as follows: impact force is 0.1426 N and impact force amplitude is 0.0167 N. The experimental values under optimized parameters are as follows: the impact force is 0.1484 N and the impact force amplitude is 0.0187 N. The impact force and impact force amplitude errors of prediction and experiment are both less than 5 %, which means the response surface functions are basically accurate. 4. Flow visualization by high speed image acquisition shows the final large water mass of optimized SEPAWJ was formed much earlier, providing for more intensive and intermittent cleaning in comparison with original SEPAWJ. 5. Compared with original SEPAWJ, the average impact force and impact force amplitude of optimized SEPAWJ are increased by 52.00 % and 38.26 %, respectively, and the impact force intensity of fluctuations exhibits peak in the low frequency region around 40 Hz. 6. In the cleaning experiment at 40 seconds, the cleaned area ratio of optimized SEPAWJ reaches 96 %, and finally 100 % at 50 seconds. However, the cleaned area ratio of original SEPAWJ reaches only 76 % at 50 seconds, and the difference between them is 22.4 %, further showing that the optimized SEPAWJ cleaning performance is much higher in comparison with original design. 7. Although the multi-parameter optimization of self-excited pulsed air-water jet nozzle was carried out, only a few key parameters of the nozzle were selected as the optimization variables. In the future, the multi-parameter combination optimization of the self-excited pulsed air-water jet nozzle can be studied by taking into account the tilt angle of the two ends of the mixing chamber, the location and layout of the pores and the aperture of the nozzle as the optimization variables. 5 ACKNOWLEDGEMENTS The authors would like to thank the support by the National Natural Science Foundation of China (51779106 and 51979126), a project funded by the Priority Academic Programme Development of Jiangsu Higher Education Institutions, Ministry of Education Xihua University (szjj2016-068). The authors would like to thank Slovenian Research Agency (ARRS) for providing support under research programme Energy engineering P2-0401. 6 NOMENCLATURES c/, Outlet diameter of upstream nozzle, [mm] cl2 Inlet diameter of downstream nozzle, [mm] i/, Outlet diameter of downstream nozzle, [mm] IIc Oscillation chamber height, [mm] Lc Oscillation chamber length, [mm] a Inclination angle of oscillation chamber side wall, [°] /; Inclination angle of oscillation chamber bottom wall, [°] F Average impact force, [N] AF Impact force amplitude, [N] 7 REFERENCES [1] Guha, A, Barron, R.M, Balachandar, R. (2011). An experimental and numerical study of water jet cleaning process. Journal of Materials Processing Technology, vol. 211, no 4, p. 610 618, D0l:10.1016/j.jmatprotec.2010.11.017 [2] LI, D„ Kang, Y., Wang X., Ding X., Fang Z. (2016). Effects of nozzle Inner surface roughness on the cavitation erosion characteristics of high speed submerged jets. Experimental Thermal and Fluid Science, vol. 74, p. 444-452, D0l:10.1016/j. expthermflusci.2016.01.009 [3] Chahlne, G.L., Kapahl, A., Choi, J.-K., Hsiao, C.-T. (2016). Modeling of surface cleaning by cavitation bubble dynamics and collapse. UltrasonicsSonochemistry, vol. 29, p. 528-549, D0l:10.1016/j.ultsonch.2015.04.026 [4] Labus, T.J.,Savanlck, G .A. (2001). An Overview of Waterjet Fundamental and Application. Waterjet Technology Association, Saint Louis. [5] Glenn, L.A. (1975). The mechanics of the Impulsive water cannon. Computers and Fluids, vol. 3, no. 2-3, p. 197-215, 001:10.1016/0045-7930(75)90018-3 [6] Grlnspan, A.S., Gnanamoorthy, R. (2010). Impact force of low velocity liquid droplets measured using piezoelectric PVDF film. Colloids and Surfaces A: Physicochemical and Engineering Aspects, vol. 356, no. 1-3, p. 162-168, D0l:10.1016/j.colsurfa.2010.01.005 [7] Dehkhoda, S, Hood, M. (2013). An experimental study of surface and sub-surface damage In pulsed water-jet breakage of rocks. International Journal of Rock Mechanics and Mining Sciences, vol. 63, p. 138-147, D0l:10.1016/j. ijrmms.2013.08.013 [8] Tang C.L, Hu, D, Zhang F.H. (2011). Study on the frequency characteristic of self-excited oscillation pulsed water jet. Advanced Materials Research, p. 317-319, 1456-1461, DOI:10.4028/www.scientific.net/AMR.317-319.1456 [9] Hu, Y.Z. (2016). Time-Frequency Feature Analysis of the Pulsed Liquid Gas Jet of the Self-Excited Inspiration Nozzle in Deep Water Conditions. MSc. Thesis, North China University of Water Resources and Hydropower, Zhengzhou. Wang Y. - Wang. XI. - Zhang ZI. - Li, Y - Liu, H.L. - Zhang X. - Hocevar, M. Strojnlskl vestnik - Journal of Mechanical Engineering 67(2021)3, 75-87 [10] Li, D., Kang, Y., Ding, X., Wang, X., Fang, Z. (2017). Effects of nozzle inner surface roughness on the performance of self-resonating cavitating waterjets under different ambient pressures. Strojniški vestnik - Journal of Mechanical Engineering, vol. 63, no. 2, p. 92-102, D0I:10.5545/sv-jme.2016.3563. [11] Chen, B., Gao, D.R., Liang, Y.N., Zhao, J.H., Sun, Y.N. (2018). Experimental investigation of atomization and droplet turbulence characteristics of a twin-fluid nozzle with different self-excited vibrating cavity structures. Experimental Thermal and Fluid Science, vol. 99, p. 525-536, D0I:10.1016/j. expthermflusci.2018.08.017. [12] Hall, J., Ewing, D. (2010). Spectral linear stochastic estimation of the turbulent velocity in a square three-dimensional wall jet. Journal of Fluids Engineering, vol. 132, no. 5, p. 1-9, D0I:10.1115/1.4001490. [13] Li, D., Kang, Y., Ding, X., Wang, X., Fang, Z. (2016). Effects of area discontinuity at nozzle inlet on the characteristics of high speed self-excited oscillation pulsed waterjets. Experimental Thermal and Fluid Science, vol. 79, p. 254-265, D0I:10.1016/j.expthermflusci.2016.07.013. [14] Oh, T.M., Cho, G.C. (2011). Energy loss from an abrasive waterjet for rock cutting. WJTA-IMCA Conference and Expo, Houston. [15] Thakur, R.K., Singh, K.K. (2020). Abrasive waterjet machining of fiber-reinforced composites: A state-of-the-art review. Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 42, no. 7, p. 1-25, D0I:10.1007/s40430-020-02463-7. [16] Alsoufi, M.S., Suker, D.K., Alhazmi, M.W., Azam S. (2017). Influence of abrasive waterjet machining parameters on the surface texture quality of Carrara marble. Journal of Surface Engineered Materials and Advanced Technology, vol. 7, no. 2, p. 25-37, D0I:10.4236/jsemat.2017.72003. [17] Wang, W., Zhou, Z. (1988). Rock breaking device with pulse gas-liquid jet. Mining Technology, vol.36, p. 23-24, D0I:10.13828/j.cnki.ckjs.1988.36.015. (in Chinese) [18] Hu, D., Li, X.-H., Tang, C.L., Kang, Y. (2015). Analytical and experimental investigations of the pulsated air-water jet. Journal of Fluids And Structures, vol. 54, p. 88-102, D0I:10.1016/j.jfluidstructs.2014.10.010. [19] Box, G.E.P., Wilson, K. (1992). On the experimental attainment of optimum conditions. Journal of the Royal Statistical Society, vol. 8, no. 1, p. 1-38, D0I:10.1007/978-1-4612-4380-9_23. [20] Vyavahare, G.D., Gurav, R.G., Jadhav, P.P., Patil, R.R, Aware, C.B., Jadhav, J.P. (2018). Response surface methodology optimization for sorption of malachite green dye on sugarcane bagasse biochar and evaluating the residual dye for phyto and cytogenotoxicity. Chemosphere, vol. 194, p. 306-315, D0I:10.1016/j.chemosphere.2017.11.180. [21] Tang, P., Li, H., Chen, C., Sun, C. Z. (2016). Optimization and experiment of adjustable structural parameters for vertical impact sprinkler with working pressure. Transactions of the Chinese Society of Agricultural Engineering, vol. 32, no. 20, p. 99-107, D0l:10.11975/j.issn.1002-6819.2016.20.013. (in Chinese) [22] Siddhant, B.P., Jignasa, V.G. (2018). Enhanced solar cell performance by optimization of spray coated CZTs thin film using taguchi and response surface method. Journal of Materials Science Materials in Electronics, vol. 29, p. 56135623, D0I:10.1007/s10854-018-8530-5. [23] Qi, C.X., Liu, H.J., Deng, S.X., Yang, A.H., Li, Z.D. (2018). A modeling study by response surface methodology (RSM) on Th(IV) adsorption optimization using a sulfated p-cyclodextrin inclusion complex. Research on Chemical Intermediates, vol. 44, p. 2889-911, D0I:10.1007/s11164-018-3286-3. [24] Khoshnamvand, N., Kord, F.M., Mohammadi, A., Faraji, M. (2018). Response surface methodology (RSM) modeling to improve removal of ciprofloxacin from aqueous solutions in photocatalytic process using copper oxide nanoparticles (CuO/UV). AMB Express, vol. 8, p. 48, D0I:10.1186/s13568-018-0579-2. [25] Oztürk, S., Kahraman. M.F. (2019). Modeling and optimization of machining parameters during grinding of flat glass using response surface methodology and probabilistic uncertainty analysis based on Monte Carlo simulation. Measurement, vol. 145, p. 274-291, D0I:10.1016/j.measurement.2019.05.098. [26] Gnanavelbabu, A., Saravanan, P. (2020). Experimental investigations of abrasive waterjet machining parameters on titanium alloy Ti-6Al-4V using RSM and evolutionary computational techniques. Advances in Unconventional Machining and Composites, p. 413-425, D0I:10.1007/978-981-32-9471-4_33. [27] Dani, D.N., Shah H.N. (2016). An experimental investigation of abrasive water jet machining on granite. International Journal for Innovative Research in Science & Technology, vol. 3, no. 5, p. 26-31. [28] Karakurt, I., Aydin G., Aydiner K. (2012). A study on the prediction of kerf angle in abrasive waterjet machining of rocks. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, vol. 226, no. 9, p. 1489-1499, D0I:10.1177/0954405412454395. [29] Gupta, V., Garg, M. P., Batra, N.K., Khanna R. (2013). Analysis of kerf taper angle in abrasive water jet cutting of Makrana white marble. Asian Journal of Engineering and Applied Technology, vol. 2, no. 2, p. 35-39. [30] Javidan, M., Moghadam, A.J. (2021). Experimental investigation on thermal management of a photovoltaic module using water-jet impingement cooling. Energy Conversion and Management, vol. 228, no. 15, art. ID 113686, D0I:10.1016/j.enconman.2020.113686. Optimization of a Self-Excited Pulsed Air-Water Jet Nozzle Based on the Response Surface Methodology 87 Strojniški vestnik - Journal of Mechanical Engineering 67(2021)3, 88-100 © 2021 Journal of Mechanical Engineering. All rights reserved. D0l:10.5545/sv-jme.2020.6990 Original Scientific Paper Received for review: 2020-10-12 Received revised form: 2021-01-29 Accepted for publication: 2021-02-05 Optimization of Running Blade Prosthetics Utilizing Crow Search Algorithm Assisted bjA rtifícial Neural Networks Manuel Javier Rosel Solis1 - José Omar Dávalos Ramirez2 * - Javier Molina Salazar2 -Juan Antonio Ruiz Ochoa1 - Antonio Gómez Roa1 1 Autonomous University of Baja California, México 2Autonomous University of Ciudad Juárez, México A crow search algorithm (CSA) was applied to perform the optimization of a running blade prosthetics (RBP) made of composite materials like carbon fibre layers and cores of acrylonitrile butadiene styrene (ABS). Optimization aims to increase the RBP displacement limited by the Tsai-Wu failure criterion. Both displacement and the Tsai-Wu criterion are predicted using artificial neural networks (ANN) trained with a database constructed from finite element method (FEM) simulations. Three different cases are optimized varying the carbon fibre layers orientations: -45 °/45 0 °/90 and a case with the two-fibre layer orientations intercalated. Five geometric parameters and a number of carbon fibre layers are selected as design parameters. A sensitivity analysis is performed using the Garzón equation. The best balance between displacement and failure criterion was found with fibre layers oriented at 0 °/90 The optimal candidate with -45 °/45 ° orientation presents higher displacement; however, the Tsai-Wu criterion was less than 0.5 and not suitable for RBP design. The case with intercalated fibres presented a minimal displacement being the stiffer RBP design. The damage concentrates mostly in the zone that contacts the ground. The sensitivity study found that the number of layers and width were the most important design parameters. Keywords: optimization, crow search algorithm, artificial neural networks, running blade prosthetics, Tsai-Wu criterion, finite element method Highlights • An optimization methodology was proposed for the RBP design. • A new technique for RBP manufacturing was evaluated. • Carbon fibre layers with layers oriented 0 °/90 ° were the best option for the design of the RBP. • The proposed methodologies reduce the manufacturing costs of the RBP. 0 INTRODUCTION A prosthesis is an artificial element integrated into the human body to replace an internal or external organ. The most common prostheses are those that replace upper and lower limbs. With the use of new materials and better manufacturing techniques, it has been possible to optimize prosthetic models to replace amputated arms and legs [1] to [3], Regarding leg prostheses, the applications are diverse; everyday cosmetic prostheses have been created that allow an amputated person to lead a normal life, thereby improving their living conditions. Furthermore, advanced prostheses have been developed that have allowed an athlete with amputations in one or both lower limbs took take part in sports activities almost at the level of a non-amputee athlete. An example is the blade type prostheses used by the South African athlete Oscar Pistorius made with carbon fibre, a composite material with applications in the automotive and aerospace industry, which has properties similar to steel but with little weight, which makes it ideal for prosthetic applications. Manufacturers of these sports implement, for low and high impact activities, such as Osur and Ottobock, offer various blade-type sports prostheses, but the high cost of these makes them inaccessible to the general public [4] An alternative in the manufacture of sports prostheses, like running blade prosthetics (RBP), is the inclusion of additive manufacturing in the process of developing a human prosthesis, in particular, fused deposition modelling, which is one of the most widely used processes due to its simplicity and ease of operation. Therefore, the mechanical properties that composite materials offer can be combined with the advantages of fused deposition modelling, mainly in small-scale production, with the option of manufacturing highly personalized products and, at the same time, with shorter prototypes development times [5], Turk et al. [6] evaluate the mechanical performance of lower limb prostheses manufactured combining additive manufacturing with carbon fibre-reinforced polymers. They found that by using this technique, the mechanical strength increases by around 40 %, and the weight decreases by 28 %. Tavangarian et al. [7] studied the mechanical strength of the pylon section of a lower limb prosthetic 88 *Corr. Author'sAddress: Universidad Autónoma de Ciudad Juárez, Av. del Charro 450, Ciudad Juárez, Chihuahua, México, jóse.davalos@uacj.mx Strojniski vestnik - Journal of Mechanical Engineering 67(2021)3, 88-100 manufactured with 3D printing using polylactic acid polymers. They found that this material meets the standards set by ISO 1038:2016 [8] regarding the structural requirements of lower-limb prostheses. Ouarhim et al. [9] perform the characterization and numerical simulation of laminated glass fibre-polyester composites applied to running blade prosthetics. They used software to simulate the composite materials. Its results show that the number of layers impacts in bending and buckling. Its results show a good agreement between experimental and numerical. A good balance between displacement and mechanical resistance guarantees the good performance of an RBP. During the change of length or displacement of an RBP, energy is stored and returned, increasing the forward propulsion [10]. However, increasing the displacement can lead to the mechanical failure of RBP, mainly in the sections with a curved shape. To achieve an optimal design of an RBP, advanced tools as optimization algorithms are required. These types of algorithms are widely used to solve diverse problems in engineering fields [11] to [14]. A common characteristic of optimization algorithms is the large number of objective function evaluations required to find an optimal solution. When experimental or finite element method (FEM) calculations are employed to perform objective function evaluations, the computational cost increases, making the optimization process infeasible. In these cases, surrogated methods are an option to reduce the optimization time [15] to [17]. An example of an optimization strategy assisted by surrogated methods applied to lower limb prosthesis manufactured with composite materials can be found in [18], focusing on the optimization of the pylon tube made of isogrid structures. Due to optimization, they achieved a reduction of 13.3 % and 70.59 % in the mass and the Tsai-Wu index under compression effects. Unlike previous optimization work, the present investigation is applied to a lower-limb sport prosthetics which can be used to reintegrate people with lower-limb amputations into sport activities. Also, optimization methodology employs artificial neural networks (ANN) with two intentions: to evaluate the objective function and to use the ANN coefficients in the calculation of relative importance of design parameters. This work employs an optimization strategy to improve the design of an RBP. This strategy integrates crow search algorithm (CSA), and ANN and FEM calculations. The objective of the optimization was to find a design that has better resistance to failure without decreasing its capability to displace in order to maintain its functionality. The failure criterion used for determining the resistance of the RBP was the Tsai-Wu criterion. To reduce the computational cost, displacements and the Tsai-Wu failure criterion were calculated by means of ANN. The ANN was trained with a database constructed from FEM calculations of displacement and Tsai-Wu failure. The manufacturing process, modelled using commercial FEM software, is a lay-up process with carbon fibre layers stacked around acrylonitrile butadiene styrene (ABS) cores. Three carbon fibre orientations were tested to find the better design option: -45745°, 0790°, and a combined case with -45745° and 0790° orientations. Using the ANN coefficients, a sensitivity analysis was performed to know the relative importance of the design parameters in each orientation. 1 METHODS 1.1 RBP Design and Manufacturing An RBP is a hook-shaped artefact made primarily of composite materials from epoxy matrix carbon fibres. The manufacturing processes used for its manufacture are the lay-up process and the pre-impregnated fibre process. The first consists of applying or mixing epoxy resin with a brush or roller into the carbon fibre layers that are stacked until reaching the thickness based on the desired resistance. Another manufacturing process consists of the use of pre-impregnated carbon fibre layers that, after being stacked, must undergo a thermal treatment in an autoclave for the activation of the resin [19]. The RBPs have a spring-like mechanical behaviour; during the first gait cycle, the prosthesis is compressed by the effect of the dynamic load of the body storing energy. In the second stage of the gait cycle, that stored energy is released, generating a thrust forward, just as the heel joint of the human foot does. The maximum efficiency in this energy return of a high-performance RPB ranges between 63 % and 95 % of the accumulated energy [20]. 1.2 Optimization Methodology A bio-inspired method used in optimization is the CSA. This novel algorithm, developed by Askarzadeh [21], is based in the behaviour of crows, considered the most intelligent birds. A characteristic of the crow's behaviour is the way they store food in hideouts to prevent that other crows from stealing it; at the same time, they look for opportunities to steal Optimization of Running Blade Prosthetics Utilizing Crow Search Algorithm Assisted by Artificial Neural Networks 89 Strojnlskl vestnik - Journal of Mechanical Engineering 67(2021)3,88-100 the food of other members of the flock. Crows use the gained experience stealing food to deceive potential plunderers, employing diverse strategies [22], Crows, always try to find optimal food places. This intelligent behaviour is replied in the CSA in which the optimal place is analogous to the global optima into the search space. In CSA, it is assumed that the crows live in flocks, can memorize the places where they hide their food, a crow follows another to try to steal its food and protect its hideouts from other crows via a probability reason [22], In the CSA optimization process, during a iteration iter, a crow /', from a flock of size TV, occupy a position defined by the vector x'>" = [xf', ,..., x*f ] , where / = 1,2,...,7V, it= 1,2, ...,;'imax, ;imax is the maximum number of iterations, and d is the dimension of the problem or the number of variables in the design. The position, in1", of the hideout it is stored in the crow memory and represents the best position at it, the far. For the next iterations, the crow will try to find better positions. Two situations may occur when, at iteration it, a crow j visits the hideout where it stores its food and a crow i is on the lookout attempting to steal it: (1) the crow j does not realize that crow i followed it and reveals its hideout to the thief crow; (2) the crow j detects the presence of the crow i and changes its trajectory to avoid revealing the location of its hideout. In the first situation, the new position of crow i is defined by: xU,+l = xu, + r x jji.it x (,„• ••• _ v •)_ (1) where 0' + rt x fl''" x(w ' - x''") r. > .!/' a random position otherwise (2) where 0