W.-J. CHEN et al.: COLD ROLL FORMING SIMULATION AND ORTHOGONAL EXPERIMENTAL OPTIMIZATION ... 597–607 COLD ROLL FORMING SIMULATION AND ORTHOGONAL EXPERIMENTAL OPTIMIZATION OF SPIRAL CORRUGATED STEEL TUBES SIMULACIJA OBLIKOVANJA S HLADNIM VALJANJEM IN ORTOGONALNA EKSPERIMENTALNA OPTIMIZACIJA [PIRALNO NAGUBANIH JEKLENIH CEVI Wan-Jun Chen, Yi-Ying Zhou, Hua-Min Liu * College of Materials Science and Engineering, Jilin University, Changchun 130025, China; Prejem rokopisa – received: 2024-07-02; sprejem za objavo – accepted for publication: 2024-08-27 doi:10.17222/mit.2024.1234 The cold-roll forming process is capable of producing intricate profiles, and optimizing its parameters can enhance the quality of the final product. This study focuses on analyzing the roll forming of spiral corrugated steel tubes made from galvanized sheet BGH340. The professional roll design software COPRA is utilized to design the rolls, and a three-dimensional finite-ele- ment analysis model for spiral corrugated steel tubes rolls is established. Orthogonal experiments are conducted to investigate the effects of the friction coefficient, line velocity, and rotation angle on the maximum longitudinal strain. The results indicate that increasing the friction coefficient can help reduce the strain, but may also result in defects such as scratches. Line velocity has the most significant impact on strain, with higher line velocities leading to increased strain and resulting in side wave and plate surface inequality defects. The rotation angle has a minimal influence on strain levels. The optimum contour parameters are deduced based on these findings, providing a theoretical foundation that directly contributes to improving the production ef- ficiency and ensuring higher quality in the manufacturing of spiral corrugated steel tubes. Keywords: cold roll forming, spiral corrugated steel tubes, finite-element analysis S postopkom hladnega valjanja lahko izdelujemo razli~ne profilirane izdelke. Z optimiziranjem njegovih procesnih parametrov izbolj{amo tudi kvaliteto kon~nega izdelka. V ~lanku avtorji opisujejo {tudijo, v kateri so se osredoto~ili na analizo hlanega valjanja {piralno nagubanih cevi, izdelanih iz galvanizirane jeklene plo~vine vrste BGH340. Avtorji so uporabili profesionalno programsko orodje COPRA za oblikovanje valjev za nagubane cevi in izdelavo tridimenzionalnega (3-D) modela za analizo s pomo~jo metode kon~nih elementov (FEM). Izvedli so ortogonalne preizkuse, s katerimi so dolo~ili vpliv koeficienta trenja, linijske hitrosti in rotacijskega kota na maksimalno deformacijo v (vzdol`ni) smeri valjanja. Rezultati preizkusov so pokazali, da pove~evanje koeficienta trenja lahko zmanj{a deformacijo, toda tudi povzro~i napake na ceveh, kot so na primer raze. Linijska hitrost ima najve~ji vpliv. Vi{ja hitrost povzro~a ve~jo deformacijo, stranske valove in neenakomerno velikost napak na povr{ini. Kot rotacije ima zanemarljiv vpliv na deformacijo. Parametre optimalne oblike profila so avtorji dobili na osnovi izvedenih preizkusov in teoreti~nih modelnih analiz. S {tudijo so avtorji predstavili temeljne teoreti~ne osnove, ki lahko direktno prispevajo k izbolj{anju u~inkovitosti proizvodnje in izdelavo bolj kvalitetnih {piralno nagubanih cevi. Klju~ne besede: oblikovanje s hladnim valjanjem, {piralno nagubane cevi, analiza s pomo~jo metode kon~nih elementov 1 INTRODUCTION Cold-roll forming technology is an advanced, contin- uous, local cold-working process. It involves applying external force to metal bending areas repeatedly, causing them to bend and deform, thus producing products with predetermined shapes. 1 This technology offers advan- tages over traditional hot-roll forming in terms of pro- duction efficiency, energy consumption, and product quality. 2 Widely used as an efficient and economical forming method for producing corrugated steel pipes, cold-roll forming technology allows for a precise adjust- ment of the parameters in the cold-bending forming equipment, to control the bending radius, rotation angle, and length of the forming process, resulting in corru- gated steel pipes of various shapes. 3 Spiral corrugated steel tubes play an essential role in multiple fields due to their high strength, good flexibil- ity, lightweight structure, rapid construction, long life, excellent ecological and environmental performance, and low comprehensive engineering costs. They are consid- ered an ideal substitute for non-metallic pipe materials and are essential in applications such as underground drainage, urban sewage systems, highway culverts, shared utility tunnels, drilling pipes, irrigation channels, and mine escape passages. 4–7 However, the deformation that occurs during the cold bending process is complex, influenced by material nonlinearity, geometric non- linearity, and boundary nonlinearity. In the cold bending simulation of spiral corrugated steel tubes, accurately simulating the material behavior is crucial to ensuring the finished product’s forming quality and geometric ac- curacy. 8,9 Q. V. Bui explored the impact of material prop- erties, such as yield limit and work-hardening index, on the cold-roll forming process using 3D finite-element Materiali in tehnologije / Materials and technology 58 (2024) 5, 597–607 597 UDK 669.018.255:691.714 ISSN 1580-2949 Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 58(5)597(2024) *Corresponding author's e-mail: liuhm@jlu.edu.cn (Hua-Min Liu) analysis. 10 X. Chen utilized MARC software to investi- gate the importance of material behavior on the forma- tion process, particularly in relation to the precise simu- lation and control of spiral corrugated steel tubes forming. Rotation angle, forming steps, and residual stress were found to have a substantial impact on the overall forming process. Optimizing these parameters can effectively minimize defects during the spiral corru- gated steel tubes forming process, such as edge corruga- tion and buckling, thus improving product quality. 11 Shim used ABAQUS to explore the role of forming pa- rameters in reducing the waviness of the corrugated sheet edges, which is significant for the optimization of spiral corrugated steel tubes forming. 12 Tehrani analyzed the effect of rotation angle and steps on edge buckling during cold-roll forming using ABAQUS, offering valu- able insights for enhancing the spiral corrugated steel tubes forming process. 13 This study employs a digital design approach that in- tegrates theory and experience to facilitate the digital transformation of the spiral corrugated steel tubes roll pressing process design. We developed an optimized roll-pressing process scheme for spiral corrugated steel tubes through simulation analysis and process parameter optimization. The study investigated the main factors af- fecting edge wave defects in spiral corrugated steel tubes roll pressing forming, such as finite-element calculation methods, plate thickness, friction coefficient, line veloc- ity, and rotation angle. The paper primarily focuses on conducting thorough research on the latter three aspects. 2 MATERIAL PROPERTIES AND MESH 2.1 Material characteristics In this study we selected BGH340 galvanized sheet as the key material for our experiments, with some of its material parameters presented in Table 1. This material is widely used in the construction industry due to its ex- cellent corrosion resistance, high strength, and superior rigidity, especially in applications that demand structural integrity and durability. The BGH340 galvanized sheet, treated with hot-dip galvanizing, not only enhances its corrosion resistance but also improves the overall perfor- mance of the material, which is crucial for ensuring the quality of the forming process and the reliability of the finished product. During numerical simulation analysis, we strictly de- fined and controlled the physical dimensions of the BGH340 galvanized sheet. The selected sheet has a width of 308 mm and a thickness of 1.5 mm. These di- mensional parameters were carefully chosen based on typical architectural application requirements and to en- sure the accuracy of the simulation. Such size specifica- tions not only meet our experimental needs but also en- sure that the simulation results are consistent with real-world production environments. 14 Furthermore, we employed the continuous forming method for product modeling. This method not only sim- ulates various aspects of the continuous forming process but also accurately reproduces the material’s behavior during forming, including stress distribution, deforma- tion patterns, and any potential defects. Through this pre- cise modeling approach, we can thoroughly analyze and optimize the cold-roll forming process of spiral corru- gated steel tubes, thereby enhancing the quality and per- formance of the final product. Table 1: Properties of the elastic stage of the material Parameters Units Values Young’s modulus (E) GPa 210 Poisson’s ratio ( ) – 0.3 Yield stress ( s ) MPa 328 Ultimate tensile strength MPa 491 Density Kg/m 3 7850 2.2 Mesh division Our research utilized the mesh adaptive division function within the COPRA system to optimize mesh density in the bending areas, where plastic deformation and stress concentration are critical during the cold-roll W.-J. CHEN et al.: COLD ROLL FORMING SIMULATION AND ORTHOGONAL EXPERIMENTAL OPTIMIZATION ... 598 Materiali in tehnologije / Materials and technology 58 (2024) 5, 597–607 Figure 1: Billet structure diagram Figure 2: Blank grid division forming process. This densification was essential to en- sure accurate simulation of the deformation behavior. We balanced computational efficiency and accuracy by implementing a mesh model with 38,871 nodes and 16,354 elements. While a denser mesh could have pro- vided more detail, it would have greatly increased the computational costs. Conversely, a coarser mesh would have been less computationally demanding but risked losing essential details in areas with complex stress dis- tributions. By adopting a three-dimensional solid mesh in thick- ness, we maintained necessary accuracy without impos- ing excessive computational loads. This approach en- abled us to effectively capture key physical phenomena, while ensuring the process remained computationally ef- ficient. The layout and details of the mesh division are il- lustrated in Figures 1 and 2. 3 ESTABLISHING A FINITE-ELEMENT ANALYSIS MODEL 3.1 Spiral corrugated steel tubes forming method The forming process of spiral corrugated steel tubes is a technically demanding and complex manufacturing procedure, mainly comprising four key stages: the bite-in stage, the cold-roll forming stage, the three-roll bending forming stage, and the spiral tilting stage. This series of carefully designed stages ensures the high standards of spiral corrugated steel tubes regarding shape accuracy and mechanical properties. 19 During the bite-in stage, the strip is precisely intro- duced between the rolls. This stage aims to ensure the stability of the strip, laying the groundwork for the sub- sequent processing steps. At this point, the rolls provide necessary support and apply appropriate boundary con- straints, ensuring that the strip is fixed in width (X-direc- tion) and thickness (Y-direction) and maintains uniform movement in the rolling direction (Z-direction). 20 Then, the process enters the roll-forming stage, where the strip starts forming operations. Unlike the bite-in stage, this stage releases constraints on the thick- ness direction of the strip, allowing it to bend and deform freely in a lateral direction. The constraints in the rolling direction become more complex, closely related to the friction force between the rolls and the strip, often simu- lated precisely using numerical simulation techniques such as the User Sub-Forcdt method in MARC software. Next is the three-roll bending forming stage, where the strip is finally bent and formed through three sets of rollers. These rollers’ intricate design and arrangement directly determine the final shape and dimensional accu- racy of the spiral corrugated steel tubes. In this stage, the initial gap between the first set of upper and lower rolls is 10 mm. As the plate enters the roll gap, its front end is 20 mm ahead of the central line of the upper and lower rolls, and the upper roll is pressed down to initiate the forming process. Finally, the spiral tilting stage gradually forms the strip into a spiral shape by adjusting the rotation angle of the three sets of rolls, as shown from Figure 3a and 3b. To achieve a connection effect, a part of the front end of the plate needs to be cut off after a period. The key in this stage lies in precisely controlling the rotation angle of the rolls and the timing of cutting to ensure the accu- racy of the spiral corrugated steel tubes shape and the tightness of the seam. Throughout the forming process, precise control of various parameters and roll actions is crucial, directly impacting the quality of the final product. These meticu- lous operations and adjustments make spiral corrugated steel tubes precisely manufactured to meet the required physical and geometrical characteristics. 3.2. Rolls design The roll pattern is a schematic cross-sectional view of the roll-forming unit during the sheet-forming process, as shown in Figure 4. The rolling pattern is a crucial ele- ment, depicting the cross-sectional view of the sheet in the roll-forming unit. This pattern is meticulously de- signed using COPRA’s stick-type design module to dem- onstrate the sequence and process of sheet forming. The design specifies the exact steps the sheet undergoes dur- ing the forming process. In this design, we focused on some key parameters: the setback radius was set at 5 mm, the sheet thickness at 1.6 mm, and the total bite an- gle reached 130 degrees, with the entire process divided into four stages. The sectional hole pattern designed based on these requirements is shown in Figure 4. This precise design fully considers the physical prop- erties of the material, especially the spring-back effect. We observed that the spring-back phenomenon is mini- mal in the central part of the material and becomes more pronounced towards the edges. Understanding and con- W.-J. CHEN et al.: COLD ROLL FORMING SIMULATION AND ORTHOGONAL EXPERIMENTAL OPTIMIZATION ... Materiali in tehnologije / Materials and technology 58 (2024) 5, 597–607 599 Figure 3: Spiral tilting stage: a) before spiral and b) after spiral trolling this phenomenon is crucial for optimizing the forming process. 21 After careful planning and design, the entire forming process is completed through 14 stages, successfully forming the desired cross-sectional shape. The precise execution of this series of stages ensures that the final product’s shape meets the design requirements, while maintaining the material’s structural integrity and perfor- mance standards. Through such a refined process, we are able to produce high-quality sheets that meet stringent standards. 22 3.3 Roll optimization based on DTM analysis In this study we utilized the Deformation Technology Module (DTM) of COPRA for an in-depth analysis. Through the DTM we conducted a detailed analysis of the pre-designed roll patterns to measure the steel strip’s strain level accurately under the given roll pattern design. As observed in the DTM analysis shown in Figure 5a, the longitudinal strain on the steel strip is relatively small during horizontal forming. As the depth of forming in- creases, the strain value correspondingly increases, which is in complete agreement with theoretical predic- tions. Figure 5b shows the visual representation of the DTM simulation. In this simulation, the pass interval was set to 250 mm. The black strips in the figure repre- sent the transition areas during the forming process. The tail end of one black strip to the tail end of the next black strip defines the pass interval. From the figure it is clear that the length of the forming transition area is approxi- mately one-third of the pass interval. Therefore, based on the DTM simulation, we can infer that the smooth transi- tion area between adjacent passes is about 300 mm. Based on suggestions from actual production feed- back and to avoid affecting the adjustment of matching rolls and auxiliary mechanisms, we first conducted pre- liminary simulations using DTM before performing ex- tensive simulations. The purpose of this initial simula- tion was to verify the correctness of the roll-pattern design. This approach not only improved the efficiency of the design but also ensured the smooth progress of the forming process, thereby enhancing the quality and con- sistency of the final product. Through such precise pre- diction and analysis, we can effectively guide and opti- mize the production process in the early stages. 3.4 Establishing a finite-element analysis model In this study we used the COPRA2021 software de- veloped by Germany’s Data M company for the precise design of the rolls. We imported the completed roll pat- terns into COPRA FEA for further analysis. COPRA FEA is an advanced finite-element analysis tool inte- grated into MARC software, particularly adept at per- forming complex contact analysis. 23,24 We fully leveraged the powerful capabilities of MARC software, especially in simulating contact pro- cesses. By integrating traditional gap friction elements, MARC can precisely simulate the contact points be- tween the structures. Contact constraints can be applied through Lagrange multipliers or penalty function meth- ods, accurately reflecting actual contact situations in simulations. 25 Additionally, MARC provides advanced contact iteration algorithms based on the direct con- straint method, allowing the software to analyze the con- tact situations automatically between deformable bodies, between deformable and rigid bodies, and within them- selves. When contact occurs, MARC constrains the mov- W.-J. CHEN et al.: COLD ROLL FORMING SIMULATION AND ORTHOGONAL EXPERIMENTAL OPTIMIZATION ... 600 Materiali in tehnologije / Materials and technology 58 (2024) 5, 597–607 Figure 5: a) DTM analysis and b) the visual representation of the DTM Figure 4: Flower pattern ing body by applying boundary conditions, converting motion restrictions into constraints on the nodes’ degrees of freedom and nodal force constraints. Unlike tradi- tional methods, MARC does not require pre-specifica- tion of the reference elements, thus effectively handling complex situations involving large contact areas and un- certain contact regions. To ensure the accuracy of the simulation results and their similarity to actual production, we meticulously set a series of key parameters, including sheet length, mate- rial properties, diameters of the upper and lower rolls, distance between rolls, and contact conditions. The pre- cise setting of these parameters ensures the authenticity and reliability of the simulation results. We performed detailed work using COPRA software to construct the geometrical model of each pass section and roll. First, we imported the profile diagram of the spiral corrugated sheet from AUTOCAD into COPRA and then generated the corresponding roll pattern based on preset parameters. After pre-optimizing the roll pat- tern using DTM, we obtained detailed roll diagrams for each pass section, which are crucial for optimizing and designing the entire forming process. Finally, considering the importance of the spring-back phenomenon, we paid special attention to it in our simulations. The stick comprises 15 stations and is assembled, as shown in Figure 6. Spring back occurs due to the release of stored elastic deformation energy during unloading, which is influenced by many factors. However, the profile’s material properties and bending radius are the most critical. Therefore, we carefully con- sidered these factors in our study to ensure the accuracy and practicality of the simulation results. 4 RESULTS AND DISCUSSION 4.1 Simulation results analysis After defining the roll pattern, we employed an inno- vative Deformation Technology Module (DTM) to opti- mize the initial design. In the roll-forming process, lon- gitudinal strain often occurs at the edges of the sheet due to the need to cover a longer distance than the undeformed area. To effectively address this challenge, we introduced a linear method that considers the forming length. This module integrates finite-element analysis with a wealth of experimental data. By comprehensively con- sidering the geometric deformation and material charac- teristics, it accurately assesses the forming quality. This approach not only resolves potential issues in the design stage but also significantly reduces the workload re- quired for DTM debugging. This method greatly acceler- ates the trial cycle for new products while reducing ma- terial costs. The Von Mises stress calculated by Equation 1 is es- sential for predicting the potential yield points of the ma- terial under combined stresses. As shown in Figure 7a, stress concentrations form along the strip, corresponding to the locations with the highest Von Mises stresses, as predicted by Equation 1. Addionally, Figure 7b provides a front view illustrating how stress is distributed across W.-J. CHEN et al.: COLD ROLL FORMING SIMULATION AND ORTHOGONAL EXPERIMENTAL OPTIMIZATION ... Materiali in tehnologije / Materials and technology 58 (2024) 5, 597–607 601 Figure 7: Variation of the equivalent von Mises stress distribution of strip: a) side view and b) front viewit Figure 6: Assembly of cold-roll forming the entire width of the strip. This comprehensive visual- ization aids in understanding the uniformity of the stress distribution and ensures that the theoretical calculations align with practical outcomes observed in the simula- tions. Equation (1) governs the calculation of the equivalent Von Mises stress: () [ () =+ + ⎧ ⎨ ⎩ − −+++++ 1 2 2 23 222 22 xxz xy yz zx x y y z z TTT () ] } x 2 12 / (1) where represents the equivalent Von Mises stress, x y and z are the normal stresses in the x, y, and z direc- tions and T x , T y and T z are the shear stresses in the xy, yz, and zx planes, respectively. The simulation results revealed the characteristics of the workpiece in the initial stages of bending deforma- tion. In this stage, the plastic equivalent strain at the front end of the workpiece along its length is zero, while the elastic equivalent strain gradually increases. This in- dicates that the workpiece is still in the state of elastic deformation at this stage, without plastic deformation. As the elastic equivalent strain increases to a certain level, its rate of change tends to stabilize and maintains a relatively fixed value. At this point, the plastic equivalent strain begins to increase gradually, marking the transition of the workpiece into the plastic deformation stage. Sub- sequently, the elastic equivalent strain slightly increases, while the plastic equivalent strain continues to rise. When the plastic equivalent strain reaches a specific value, both elastic and plastic equivalent strains tend to stabilize, and the workpiece achieves a stable state of bending deformation. Under the deformation conditions of corrugated pipes, when the equivalent stress reaches a certain threshold, it causes plastic deformation of the material. The stress distribution is primarily concentrated at the contact points between the rolls and the strip, with higher stress near the bending area and reduced stress in the surrounding regions. The cold-roll forming process involves significant de- formation, particularly at the edges of the strip, where the complex stress state increases the likelihood of insta- bility. To gain a better understanding of this phenome- non, we conducted a detailed analysis using specific pa- rameters (spacing 300 mm, friction coefficient 0.05, line velocity 10 min –1 , rotation angle 0.05 rad), focusing on key areas such as the crests and middle of the strip. Figure 8 identifies the measurement positions along the strip and visually depicts the stress distribution through a color gradient. This figure clearly shows that stress is concentrated at the crests, with higher levels in- dicated by warmer colors. This distribution suggests that these areas are more susceptible to deformation and po- tential defects. Figure 9 provides a deeper analysis of these critical points. Figure 9a illustrates the strain curves for differ- ent positions along the strip edge. It is evident that strain is highest at the crests, where the material experiences greater deformation. This increased strain correlates di- rectly with the stress concentrations observed in Fig- ure 8. In Figure 9b, stress curves for same positions are presented. The data confirms that stress peaks at crests with a sharp rise as the material undergoes bending. This stress increase continues until the material reaches its maximum strain capacity, after which it levels off, indi- cating a point of material stability or potential failure. W.-J. CHEN et al.: COLD ROLL FORMING SIMULATION AND ORTHOGONAL EXPERIMENTAL OPTIMIZATION ... 602 Materiali in tehnologije / Materials and technology 58 (2024) 5, 597–607 Figure 9: a) Strain and b) stress curves at different positions of the strip edge Figure 8: Measurement position The combined analysis from Figures 8 and 9 reveals that the crests are the most critical areas during the bend- ing process, where the interplay between stress and strain is most pronounced. This understanding is crucial for optimizing the bending process to reduce the risk of defects, especially in high-stress, high-strain zones. 4.2. Friction coefficient To further investigate the influence of the friction co- efficient on the roll-forming process, we conducted a simulation study with the following parameters: a line velocity of 10 mm/s, a rotation angle of 0.05 rad, and two different friction coefficients (0.05 and 0.08). Fig- ure 10 clearly illustrates the distribution of equivalent strain and stress in the material under varying friction conditions. The findings indicate that distinct sections of the plate exhibit diverse levels of friction, resulting in varying maximum equivalent strain values. It is evident that consistent friction coefficients are maintained across different plate sections due to increased resistance be- tween the roll and plate caused by higher friction coeffi- cients, which hinders smooth flow within the roll. More- over, higher friction coefficients correspond to lower values of the equivalent plastic stress, effectively reduc- ing the rotation angle rebound after elastic recovery oc- curs when exiting the roll. This finding is significant as it helps mitigate the rebound by increasing the forming force during production for materials prone to substantial elastic recovery; thus lubrication may be omitted in favor of dry friction production in such cases. Additionally, moderate increases in roll friction can minimize the rota- tion angle rebound and ensure product quality. 4.3 Line Velocity In order to investigate the influence of line velocity on the roll-forming process, specific parameters were set in our simulation experiments. The line velocity was ad- justed to 10 min –1 and 3 min –1 , with the rotation angle set at 0.05 rad and the friction coefficient fixed at 0.05. Fig- ure 11 illustrates the distribution of equivalent strain and stress under these conditions. It is evident from the fig- ure that the two patterns of change are similar. As shown in the figure, equivalent stress generally increases with the line velocity, but during the molding stage, stress at the Angle frame increases with a higher line velocity. Figure 11 indicates that the line velocity tends to pro- mote strain. In summary, it is clear that a higher line ve- locity generally increases the plate stress and strain, W.-J. CHEN et al.: COLD ROLL FORMING SIMULATION AND ORTHOGONAL EXPERIMENTAL OPTIMIZATION ... Materiali in tehnologije / Materials and technology 58 (2024) 5, 597–607 603 Figure 11: a) Strain and b) stress curves for two different line Velocity Figure 10: a) Strain and b) stress curves for two different friction coefficients which is not conducive to effective molding. Addi- tionally, different design angles exhibit similar changes under n aidentical line velocity. 4.4 Rotation angle To understand the impact of rotation angle on the roll-forming effect, we set the following parameters in our simulation: a line velocity of 10 min –1 , with rotation angles set at 0.05 rad and 0.07 rad, while maintaining the friction coefficient at 0.05. In Figure 12 we displayed the distribution of equivalent strain and stress under these two rotation angles. The simulation results show that at the edge level, the longitudinal strain experiences slight fluctuations as the rotation angle increases. Especially at larger rotation an- gles, with increased depth, there is a sudden change in the edge strains. This indicates that the impact of rotation angle on the edge strain varies with different forming stages. However, this impact is relatively minor overall, suggesting that the rotation angle does not significantly influence the longitudinal strain at the edges. This finding is significant for optimizing the roll-forming process. While the rotation angle does af- fect edge strain to some extent, its rotation angle of im- pact is limited. This means that when setting the forming parameters, the rotation angle can be adjusted within a certain range, without greatly affecting the forming qual- ity. This offers greater flexibility in designing and adjust- ing the roll-forming process. 4.5 Analysis of orthogonal experiment results Using the L8(2^7) orthogonal experimental design, this study analyzed two factors at three levels and con- ducted nine experiments. The relevant parameters and their levels are detailed in Table 2. We calculated the maximum longitudinal strain for each experiment and summarized the results in Table 3. Table 3 shows the or- thogonal array and the maximum strain values and in- cludes the signal-to-noise ratio, which is a key indicator for evaluating the experimental results. Subsequently, we conducted an in-depth analysis of the data in Table 3 using the mean-analysis method. As the goal of this study is to minimize the maximum longi- tudinal strain in each process, we used the šsmaller- the-better’ characteristic formula to calculate the average signal-to-noise ratio for each level of each parameter in the eight experiments. A higher signal-to-noise ratio in- dicates minor strain and, thus, better-forming quality. These analysis results are detailed in Figure 12. Additionally, we performed a range analysis, and the results are presented in Table 4. This analysis shows each parameter’s range R (as shown in Table 4) at differ- ent levels. A parameter with a large R value indicates a significant impact on the experimental indicators; con- versely, a small R value implies a lesser impact. This range analysis helps us better understand the degree of influence of each parameter on the final results, thus pro- viding an important basis for further optimization of the forming process. Equations (2) and (3) are used to calculate the S/N ratios, which quantify the relationship between the input parameters and the resulting strain. Equation (2) is used to determine the S/N ratio for each individual experi- ment, highlighting the impact of each experimental run on the overall process stability. Subsequently, Equation (3) aggregates these individual S/N ratios to assess the overall influence of each parameter. () S/N lg n y ii i n =− × ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ = ∑ 10 1 10 2 1 (2) () () S/N S/N m F i m j = ∑ 1 (3) where y i is the calculated value for each experiment, n is the number of repeated experiments, and (S/N) i is the signal-to-noise ratio. (S/N) Fj represents the level value of parameter F; m is the number of experiments in which the level value of parameter F participates; and (S/N) i is the signal-to-noise ratio of F j . W.-J. CHEN et al.: COLD ROLL FORMING SIMULATION AND ORTHOGONAL EXPERIMENTAL OPTIMIZATION ... 604 Materiali in tehnologije / Materials and technology 58 (2024) 5, 597–607 Figure 12: a) Strain and b) stress curves for two rotation angles Figure 13 illustrates the S/N ratio for different pa- rameter levels, providing a visual representation of their impact on the maximum strain. This figure aids in identi- fying the o; ptimal parameter settings that minimize the strain and maximize the process stability. The analysis reveals that the line velocity and the rotation angle are the most significant factors influencing the strain, as de- picted in the S/N bar chart. Furthermore, Figure 14 supports this by showing the range analysis for these parameters, directly correlating the calculated S/N ratios with observed strain values. The range values in Table 4 complement this visual data, in- dicating each parameter’s degree of influence on the forming process. Through the combined use of Equations (2) and (3), along with graphical representations in Figures 13 and 14, this study provides a comprehensive understanding of how each parameter affects the process outcome. The correlation between theoretical calculations and experi- mental results underscores the importance of optimizing these parameters to improve the cold-roll forming pro- cess quality and efficiency. Table 2: Parameters and their respective levels. Parameter Level 1 Level 2 Friction coefficient (A) 0.05 0.08 Line velocity (B) 3 10 Rotation angle (C) 0.05 0.07 Table 3: Standard orthogonal array for the experiments and results Experi- ments ABC Maximum strain (%) S/N 1 0.05 3 0.05 0.0352 38.1000 2 0.05 3 0.07 0.0776 31.2336 3 0.05 10 0.05 0.1485 25.5963 4 0.05 10 0.07 0.1919 23.3694 5 0.08 10 0.05 0.1119 28.0543 6 0.08 3 0.07 0.1307 26.7053 7 0.08 10 0.07 0.0966 29.3313 8 0.08 3 0.05 0.0710 32.0057 Table 4: The result of a range Results A B C K1 0.4532 0.3145 0.3666 K2 0.4102 0.5489 0.4968 K1 0.2266 0.15725 0.1833 K2 0.2051 0.27445 0.2484 R 0.0215 0.1172 0.0651 In this study the impact of line velocity and rotation angle on the maximum longitudinal strain shows a posi- tive correlation. In contrast, the impact of the friction co- efficient shows a negative correlation. The calculated positive correlation coefficients are 0.1172, and the nega- tive correlation coefficients are 0.0215 and 0.0651, re- spectively. These data indicate a high level of linear cor- relation between the study data. However, the relation- ship between spacing and strain is not linear, suggesting that increased depth and wider distances may hurt the strain. As the contact area between the workpiece and mold expands, the friction correspondingly intensifies, thus stimulating workpiece progression and inducing in- ternal tension that bolsters molding stability. This en- largement of the contact area further facilitates the workpiece advancement; nevertheless, heightened fric- tion may detrimentally impact the surface quality by in- ducing abrasions, smearing, and other defects. To ensure optimal surface quality in practical production settings, strategies such as lubricant application and surface coat- ings are implemented to alleviate frictional effects. Line velocity exerts the most significant influence on strain development; an increase in line velocity escalates strain levels, resulting in side wave formation and uneven plate surfaces. Conversely, the rotation angle exerts minimal influence on this strain. In terms of forming quality, a smaller strain indicates a better forming quality, meaning a larger average signal-to-noise ratio is preferable. The largest average signal-to-noise ratio in Figure 12 indi- cates the best parameters. Therefore, the best parameter combination can be de- termined through a comprehensive analysis of Fig- ures 13 and 14. According to the analysis, the friction W.-J. CHEN et al.: COLD ROLL FORMING SIMULATION AND ORTHOGONAL EXPERIMENTAL OPTIMIZATION ... Materiali in tehnologije / Materials and technology 58 (2024) 5, 597–607 605 Figure 13: S/N under varying parameter Figure 14: Value of R with 3 parameters coefficient is 0.05, the line velocity is 3 min –1 , and the rotation angle is 0.05. Numerical studies show that the equipment of the cold-roll forming production line, as il- lustrated in Figure 15, can meet the requirements for precision and surface quality. Figure 16 shows the final products of the metal strip. These comprehensive analy- ses and comparisons provide strong data support for op- timizing the cold-roll forming process. 5 CONCLUSIONS This paper meticulously designed rolls using the CO- PRA roll-design software and simulated the roll-forming process of spiral corrugated steel tubes using finite-ele- ment modeling software. A comprehensive exploration was conducted on the impact of various process parame- ters on the formation of spiral corrugated steel tubes. Through carefully designed comparative and orthogonal experiments, this study further assessed the specific ef- fects of various process parameters on the forming qual- ity of spiral corrugated steel tubes, thus providing a solid theoretical foundation for the efficient production of spi- ral corrugated steel tubes. The main conclusions can be summarized as follows: (1) The cold-roll forming process of helical corru- gated tubes has shown that the line velocity and friction coefficient have a significant impact on the longitudinal strain of the sheet-metal edges. Specifically, an increase in the friction coefficient from 0.05 to 0.08 resulted in a 35 % decrease in longitudinal strain at the edges. Con- versely, an increase in line velocity from 3 min –1 to 10 min –1 led to a 45 % increase in the longitudinal strain. The rotation angle, ranging from 0.01 rad to 0.05 rad, had only minimal effect on the strain, with changes lim- ited to within 2 %. (2) Optimization Using Orthogonal Experimental Method: The study utilized the L8(2^7) orthogonal ex- periment method to systematically investigate and deter- mine the optimal combination of process parameters. The optimal parameter combination for minimizing the maximum longitudinal strain includes a friction coeffi- cient of 0.05, a line velocity of 3 min –1 , and a rotation an- gle of 0.05 rad. This result has importance for enhancing production efficiency and product quality. (3) According to the optimized process plan, the ac- curacy of the design was verified through production de- bugging and experimental validation. The validation pro- cess comprehensively evaluated the samples against key quality indicators, including dimensional accuracy, sur- face integrity, and structural consistency. All samples met the expected standards, with size deviations within ±1.2 mm (compared to the industry standard of ±2.0 mm), indicating that the optimized parameters sig- nificantly improved the accuracy of the roll-formed prod- ucts. These concrete results confirm the reliability of the optimized design, strongly support the research conclu- sions, and underscore its practicality in enhancing pro- duction efficiency and product quality. Author Contributions WanJun Chen: Methodology, Investigation, Data curation, Writing – original draft. YiYing Zhou: Data curation.Huamin Liu: Conceptualization, Data curation, Writing – review & editing. Funding This research received no external funding. Institutional Review Board Statement Not applicable. Informed Consent Statement Not applicable. Data Availability Statement The datasets used or analyzed during the current study are available from the corresponding author on rea- sonable request. Acknowledgments The authors express their gratitude to the Data M that provided the software COPRA. The authors acknowl- W.-J. CHEN et al.: COLD ROLL FORMING SIMULATION AND ORTHOGONAL EXPERIMENTAL OPTIMIZATION ... 606 Materiali in tehnologije / Materials and technology 58 (2024) 5, 597–607 Figure 15: Production line of roll-forming process Figure 16: Final products of metal strip edge to all the authors who contributed to this article and the teachers who provided the test analysis. Conflicts of Interest The authors declare no conflict of interest. 6 REFERENCES 1 G. Nefussi, L. Proslier, P. Gilormini, Journal of Materials Processing Technology, 95 (1999) 216–221 2 Y. Li, X. Han, J. C. Liang, F. Teng, C. Liang, International Journal of Advanced Manufacturing Technology, 112 (2021) 897–905, doi:10.1007/s00170-020-06574-5 3 J. J. Cheng, J. G. Cao, Q. F. Zhao, J. Liu, N. Yu, R. G. 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