Investigation of manufacturing bilayer gears using flow forming process to enhance the strength of gears

Abstract

Due to the widespread industrial use of gears, a mass production method with high economic efficiency is essential. Flow forming is a novel manufacturing technique that not only forms the gear but also performs hardening by adding a thin layer of desired metal simultaneously. In this process, a copper tube is placed concentrically inside a steel tube, and the assembly is inserted into a mandrel with an internal gear profile. Both the tube assembly and mandrel rotate simultaneously during internal flow forming. A roller induces plastic deformation in the copper tube, reducing its wall thickness and forming gear-like teeth matching the mandrel’s geometry. The geometry of the teeth and required forming forces were analyzed and compared between forward and backward flow forming methods. Crush forces needed to deform the teeth were also evaluated. Results showed that flow-formed copper gears have double the crush resistance compared to non-flow formed ones. Additionally, a hardened steel 304 L layer on the gear further doubles the strength against crushing. This study demonstrates a simple process to effectively form and strengthen gears.

Introduction

Gears play a crucial role in today’s advanced industries. Nearly every machine relies on gears to function. They are widely used in gearboxes, differentials, and engines, serving key functions such as changing the direction of rotation, adjusting rotational speed, and transmitting rotational motion between shafts. Given the extensive use of gears in industrial applications, there is a growing demand for efficient manufacturing methods that can produce high volumes of gears at a cost-effective rate. However, gears are constantly subjected to various stresses and must be designed to withstand these forces. Traditional manufacturing methods, such as milling and turning, can compromise the strength of gears, making them less resistant to stress. Additionally, these processes generate significant material waste, further increasing production costs. In contrast, forming methods like forging and extrusion can enhance the strength of gears, offering superior resistance to stresses compared to machined gears. However, these methods typically require greater force for shaping¹. One promising alternative is the flow forming process (FP), which can also be used to manufacture gears. In the gear flow forming process (GFP), a mandrel with an internal gear design is placed inside a tubular workpiece. By increasing the inner diameter of the tube, the outer wall is wrapped around the mandrel’s teeth, effectively creating the gear profile. The key advantages of this process include the formation of teeth in a single step—eliminating the need for additional cutting operations—requiring less force than forging or broaching, and achieving a high-quality surface finish. These benefits distinguish GFP from other forming methods and make it an attractive option for gear production.

In the FP, by decreasing the wall thickness of cylindrical pieces, the parts’ strength and rigidity are increased. This process is one of the most used techniques for manufacturing thin-walled pressure vessels in the aerospace and aviation industry^2,3. This method involves mounting a tubular preform on a mandrel and rotating it at a steady angular velocity⁴. The material is locally yielded as a result of the part’s rotation and the roller’s movement; the yielding area produces the entire part by moving in a spiral pattern⁵. This process can be carried out either internally or externally. This process’s inherent benefits of flexibility, ease of tooling, and low forming force have contributed to its growing application in the automobile industry^2,6. Gears are typically made via machining procedures, which lengthens production times and wastes materials⁷. Furthermore, the gears’ strength needs to be adequate to endure the stresses placed on them. The strength of gears made with machining techniques is low¹. Gears can be made using flow forming techniques to get around these problems^8–12.

A number of studies have focused on flow forming of internal gears, employing both numerical and experimental methods. Groche and Fritsche¹³ demonstrated that mandrel wear is considerably reduced when multiple rollers are employed; tool life is thereby extended, with the ring method regarded as the most favorable solution. In the work of Xia et al.¹⁴, it was confirmed that using three rollers, rather than a single one, minimizes elongation, enhances tooth cavity filling, and yields a more uniform tooth height. Xu et al.¹⁵ emphasized the critical role of initial thickness and reduction in improving the filling ratio, although excessive reduction or too low a feed rate was found to trigger circumferential cracking. A detailed analysis of strain and force distribution by Zhao et al.¹⁶ revealed radial compressive strain and radial force as dominant; their study further indicated that higher feed and larger roller size improve cavity filling, albeit at the cost of increased resistance to material flow. Abd-Eltwab et al.¹⁷ reported that while greater reduction and feed raise forming force and filling ratio, they also deteriorate surface quality. Their findings also showed that enlarging the roller diameter increases process force, whereas a greater number of spline teeth reduces radial force without affecting the axial one. In the study of Zeng et al.¹⁸, differences in rib filling mechanisms were clarified: axial strain was linked to lower longitudinal rib height, while radial strain promoted higher transverse rib height; improvements in rib filling were achieved by applying greater thickness reduction and feed ratio. Finally, Khodadadi et al.^8–12 demonstrated that roller diameter, reduction, feed rate, and attack angle strongly influence force, tooth height, pile-up, and temperature. Their results showed that forming force and tooth height rise with roller diameter up to 40 mm before declining, and while greater reductions enhance tooth height, they also lead to higher force, pile-up, and temperature. Increased feed and attack angle were associated with reduced tooth height but intensified pile-up, with process temperature showing a rise–fall trend as these parameters increased.

Previous studies have highlighted several challenges in applying flow forming to gear production, including mandrel teeth wear and breakage¹³, uneven tooth height¹⁴, tooth cracking¹⁵, and built-up edge formation¹⁶. These issues indicate that the tooth-forming process is highly complex, as it requires precise control of material flow in both longitudinal and tangential directions. Notably, while extensive work has been carried out on internal gears, the application of flow forming to external gear manufacturing has not yet been explored, and the governing parameters remain unidentified. Moreover, the potential to simultaneously form gears and develop a hardened surface layer has not been addressed in the literature. In this context, the present study investigates the feasibility of applying flow forming to external gear production.

Materials and methods

In the present study, the gear flow forming process (GFP-manufacturing of spur gear by flow forming) was investigated through numerical simulation. For this purpose, an internal flow forming process was employed to produce the spur gear. In this process, the roller moves along the inner surface of the tubular preform at a low constant velocity, while the preform is mounted on the mandrel and rotates with it around its axis of symmetry at a constant angular velocity. The roller applies pressure on the preform, inducing plastic deformation. This deformation propagates along the preform’s length as the roller advances longitudinally, resulting in an increase in length and diameter, thereby forming the spur gear. Although the main focus is on external gear manufacturing, the absence of experimental facilities limited the possibility of direct experimental validation for this case. To address this limitation, the developed FE model was validated using the author’s previously conducted experimental and numerical studies on internal gear flow forming process (IGFP)^8–12, as shown in Fig. 1. Since both internal and external gears are produced by the same flow forming principle, and the deformation mechanisms (roller–preform contact, material flow, and plastic strain distribution) are governed by similar process parameters, the internal gear results provide a reliable reference for validation. For this purpose, the finite element model was first applied to the internal gear case and the obtained numerical results were compared with the corresponding experimental measurements reported in my previous work^8–12. A good agreement was observed in terms of dimensional accuracy, strain distribution, and forming forces, confirming the accuracy of the model. After this validation step, the model was extended to predict the forming behavior of external spur gears. Thus, the validated simulation framework ensures the reliability of the results for external gear forming, despite the absence of direct experimental data.

Fig. 1.

Experiment setup of internal gear flow forming process (IGFP).

Three spur gears were produced by this technique. First, a spur gear with 44 teeth and a modulus of 1 mm was produced by backward internal flow forming. The preform was a tube made from C12200 copper alloy with 3 mm thickness (Fig. 2-a) and was inserted in the mandrel, which was an internal gear with 44 teeth and a modulus of 1 mm (Fig. 2-b). The gear was produced in two steps so that the thickness reduction percent was 30% in step1, and 25% in step2. The second process was the manufacturing of this gear by a forward internal FP. In the third process, the manufacturing of a bilayer gear by a backward internal FP was investigated. Four parts are used in this process: A gear with 44 teeth and a modulus of 1 mm was used as a mandrel. The preform was a dual-layer tube constructed from alloys of copper and steel. As shown in Fig. 2-c, a stainless steel304L tube (thickness = 0.5 mm and inner diameter = 40.5 mm) is assembled on a Cu12200 tube (thickness = 2.5 mm and inner diameter = 35.5 mm), and this set is inserted into the mandrel.

Fig. 2.

Dimension of a) copper preform, b) mandrel, and c) bilayer preform.

The mandrel and preform rotated at a velocity of 500 rpm, and a roller was used to reduce the thickness and form the teeth of the bilayer gear in a backward FP. The gear was produced in three steps of thickness reduction: step1: 30%, step2: 25%, and step3: 20%. Because the hard layer of steel prevents the material flow, one more step is needed to complete tooth formation. ABAQUS/Explicit finite element software was used to simulate the manufacturing gear using FP. In the three-dimensional finite element modeling (FEM), the mandrel and roller were assumed to be rigid, and preforms were considered elastic-plastic models. The tensile test is employed to determine the plastic behavior of the preforms’ material. The test was carried out on a Zwick/Roell tensile test machine with a maximum load of 650 kN with a servo motor control. The tensile test machine and stress-strain diagrams of steel304L and C12200 are shown in Fig. 3. A thermomechanical analysis was performed, and 99,900 C3D8RT type elements with the ALE formulation were employed to mesh. The contact surfaces were defined using the Coulomb friction model, and the friction coefficient was ascertained using the friction test. The test was conducted in temperatures of 25, 60, 100, and 150 degrees Celsius because temperature affects the friction coefficient and rises during the FP. The test samples were rings with a standard geometrical ratio of 2:3:6 (thickness of 8 mm, an internal diameter of 12 mm, and an external diameter of 24 mm). Figure 4 presents the ring compression sample and its dimensions. The tests were conducted using a Zwick/Roel compression test equipment, as seen in Fig. 4, which has a maximum load of 650 kN. The final dimensions of the samples were measured after tests, and the friction coefficient was determined. Table 1 shows the friction coefficient used in finite element simulation. In the procedure of simulation, the mandrel was fixed and its degrees of freedom was constraint in all directions. The roller was a ball with a diameter of 10 mm and has a spiral movement on the preform. Due to high deformation and complicated contact conditions in the FP, the dynamic explicit solving procedure and ALE procedure were used because of the numerical robustness and computational efficiency in the case of highly non-linear and large-scale applications¹⁹. The FEM model is shown in Fig. 5. Finally, to validate the simulation model, the tooth height was compared in two experimental and simulation results.

Fig. 3.

Stress-strain diagram for C12200 and Steel304L.

Fig. 4.

Setup of ring compression test.

Table 1.

Friction coefficient between steel and copper at different temperatures.

Temperature(ºC)	30	60	90	130
Friction coefficient	0.05	0.07	0.1	0.13

Fig. 5.

Schematic of the gear flow forming process (GFP) in the FEM model.

Results

The results of simulation and experiments are presented in this section. First, a comparison was done between simulation and experimental results of IGFP, which is shown in Fig. 6. The height of teeth was compared in simulation and experiment and according to Fig. 6 there was a good agreement between them. Following the verifying of FEM model in IGFP, the FP was simulated to produce spur gear.

Fig. 6.

Comparison between simulation and experimental results in IGFP.

The copper gear was formed in two steps of backward internal FP. The preform thickness decreases by 30% and 25%, in steps 1 and 2, respectively. Figure 7 displays the simulation results and the two steps of tooth form alteration. The deformation is concentrated along the tips of the forming teeth, particularly on the outer edges in the first step. The internal sections and the root of the teeth exhibit minimal displacement. This initial forming pass primarily initiates the tooth profile formation, with limited material flow toward the mandrel geometry. Plastic deformation is localized, and the contact between the roller and the copper tube is not yet maximized. A significant increase in deformation is observed across the entire tooth geometry in the second step. The displacement field covers a larger area, and more pronounced material flow is evident along the full tooth depth. The second pass effectively completes the forming process. Material has conformed more closely to the mandrel geometry, and the teeth have attained their final shape. The higher displacement magnitudes suggest deeper plastic flow and full engagement of the roller.

Fig. 7.

Formation of a C12200 copper gear in two steps through the backward gear flow forming process.

Additionally, a comparison between the forward and backward FP has been made in Fig. 8; in the backward, the gear is fully formed in two passes, while in the forward, approximately half of the tooth height is completed. This is because in the backward method, the material flows in the opposite direction to the roller movement after striking the end of the mandrel, and the roller itself obstructs the movement of material, forcing it to move radially and in the direction of filling the mandrel teeth. The forces of the two methods have also been compared in Fig. 8. In the forward forming method, the absence of flow restrictions allows the material to deform with minimal resistance, thereby requiring comparatively lower forming forces. In contrast, the backward forming process involves the roller acting as an impediment to material flow, resulting in a pronounced increase in forming force. As depicted in Fig. 8, the forming force during backward groove forming is more than double that observed in the forward method. This substantial increase necessitates the use of stiffer and more robust equipment to effectively withstand the augmented mechanical loads.

Fig. 8.

Comparison of tooth height and force in backward and forward gear flow forming process.

The multi-pass forming process plays a critical role in ensuring accurate and uniform internal gear formation. The simulation results of total displacement clearly demonstrate the progressive nature of material flow during internal flow forming. In pass 1, deformation is mostly localized at the crest of the teeth, with only partial contact between the roller and the inner surface of the copper tube. This indicates that the first pass functions primarily as a pre-forming stage, initiating plastic deformation but not achieving full die conformity. The lower displacement values and limited affected area support this interpretation. In contrast, pass 2 reveals a substantial increase in displacement across the entire inner profile. The tooth roots, flanks, and crests exhibit significant deformation, confirming that material flow is now fully developed. The results suggest complete mechanical engagement with the mandrel, and the geometry closely matches the intended internal gear profile. This pass finalizes the forming process by filling in under formed regions and refining the tooth geometry. From a mechanical perspective, the increased displacement magnitude in Pass 2 also implies higher forming forces and stresses (Fig. 8). While beneficial for full profile formation, it raises concerns about material thinning or potential failure if process parameters are not properly optimized. This underscores the need for careful control of roller feed rate, rotational speed, and lubrication during the second pass to avoid defects such as cracking, folding, or excessive residual stress.

The stress distribution in the first pass along the circumferential direction for both the inner and outer surfaces is illustrated in Fig. 9-a. The inner surface exhibits significantly higher stresses due to its direct contact with the roller, which stretches the material and imposes greater mechanical constraints. In contrast, the outer surface behaves like a free boundary in the mandrel tooth region, allowing partial stress relaxation and therefore experiencing considerably lower stress levels. In Region II (mandrel tooth), the material is forced into the tooth cavity under the action of the roller to form the gear shape. Here, the maximum stress discrepancy occurs: the inner surface reaches tensile stresses up to 500–550 MPa, while the outer surface decreases sharply to below 120 MPa. In Region III, located between two mandrel teeth, both surfaces are subjected to compressive loading, resulting in nearly equal stress levels (~ 400 MPa). After the roller passes through this region, partial stress relaxation occurs due to elastic spring back. Figure 9-b shows the stress distribution in the second pass. Once the mandrel tooth is filled, the outer surface no longer behaves as a free boundary but is constrained by the mandrel tooth and roller, leading to a substantial increase in its stress level. Consequently, the stresses on the inner and outer surfaces become comparable, and in the regions between two mandrel teeth, both surfaces share nearly equal compressive stresses. Overall, these results highlight that the stress distribution strongly depends on the forming stage:

Fig. 9.

Stress distribution along the circumferential direction a) in the first pass b) in the second pass.

• Before tooth filling (first pass): the inner surface dominates the load-bearing role.

• After tooth filling (second passes): the outer surface also sustains high stresses, leading to a more balanced stress state across the thickness.

This transition plays a critical role in material flow, tooth filling, and the dimensional accuracy of the formed gear, and must be considered in both process design and failure analysis.

The plastic strain evolution for inner and outer surface is presented in Fig. 10. This graph was compared with external flow forming process to produce longitudinal inner ribs¹⁸. A clear distinction can be observed between the two forming modes in terms of strain magnitude, dominant strain components, and the surface layer most affected by deformation. In internal flow forming, the roller acts on the inner surface of the tube. As a result, the circumferential strain component (PE22) on the inner surface reaches large negative values (up to − 0.55), indicating intense compressive deformation. Meanwhile, the axial (PE11) and radial (PE33) strain components exhibit positive values (~ 0.3 and ~ 0.15, respectively), reflecting tensile stretching caused by material displacement along the forming direction and toward the mandrel cavity. This behavior confirms that the inner surface is the most deformed layer, while the outer surface experiences comparatively smaller strain levels. In contrast, during external flow forming, the roller acts directly on the outer surface. In this case, the circumferential strain (PE22) still remains compressive. Instead, the axial and radial strain components (PE11 and PE33) show significantly higher positive values, highlighting the dominance of tensile stretching in these directions. Consequently, the outer surface becomes the most deformed region, while the inner surface shows more moderate strain levels¹⁸. A stage-wise comparison also reveals distinct deformation mechanisms. In both processes, four characteristic regions (I–IV) can be distinguished:

Fig. 10.

Plastic strain distribution on the a) inner surface and b) outer surface in the first pass.

• Region I (0–2 s): there is no contact between the roller and the element.

• Region II (2–3 s): roller indentation, with sharp compressive strain development in PE22.

• Region III (3–4 s): progressive filling of the tooth cavity and bulk material displacement, leading to rapid growth of PE11 and PE33 (tensile strains).

• Region IV (4–10 s): stabilization stage, where strain values reach steady-state after the roller passes.

Overall, the comparison indicates that internal flow forming localizes deformation mainly on the inner surface with dominant circumferential compression, while external flow forming shifts the deformation toward the outer surface, where axial and radial tensile strains govern the process¹⁸. Finally, by comparing the strain evolution in both forming modes, it can be concluded that the deformation behavior of the roller-contacted surface is essentially similar in nature. In internal flow forming, the inner surface is directly in contact with the roller, while in external flow forming the outer surface plays the same role. In both cases, the contacted surface undergoes circumferential compression (negative PE22) accompanied by tensile axial and radial strains (PE11 and PE33). This confirms that the roller-contacted layer governs the main deformation mechanism, regardless of whether the process is performed internally or externally.

Figure 11 presents the radial displacement profiles along the tube axis for three consecutive forming passes. The results can be divided into three distinct regions, namely the dead zone, the effective forming zone, and the edge roll-back zone. In the dead zone (0–10 mm), the radial displacement is nearly negligible for all passes. This part corresponds to the free tube end, where insufficient tool contact and the lack of boundary constraints result in no significant plastic deformation. Consequently, this section does not contribute to the tooth formation and is considered a non-effective region. Beyond ~ 10 mm (Effective forming zone (10–30 mm), the radial displacement increases rapidly, marking the onset of plastic deformation and tooth formation. In the first pass (Step 1), the maximum radial displacement reaches only about 1.5 mm, followed by a gradual decrease. This limited deformation indicates localized strain concentration and restricted plastic flow during the initial loading. In the second pass (Step 2), the maximum tooth depth significantly increases to approximately 2.3 mm, and a relatively stable plateau region appears. At the beginning of the roller movement, the materials are pushed forward, and after a while, due to the return of the material from the end of the workpiece, a larger amount of material is placed in front of the roller, and therefore the tooth height becomes greater than the initial value. In the third pass (Step 3), although the maximum displacement remains similar to Step 2, the plateau extends further with a more uniform distribution. Therefore, the third pass primarily serves to homogenize and stabilize the tooth profile rather than further increasing its depth. These observations clearly indicate that the multi pass forming strategy enhances strain distribution and improves the dimensional stability of the tooth. At the tube entrance (30–40 mm), the radial displacement decreases as the tool exits the forming region. This phenomenon, known as edge roll-back, arises from elastic spring back of the free edge, which is the nature of the backward FP. Therefore, to achieve the desired length of the gear, the amount of longitudinal movement of the roller must be greater than the length of the gear. The roll-back is most severe in Step 1 and becomes progressively less pronounced in Steps 2 and 3, owing to strain hardening and a more balanced residual stress field developed during successive passes. In industrial applications, edge roll-back can be compensated through strategies such as intentional over-forming, applying a calibration (restrike) pass, or trimming the tube end after forming. Accordingly, adopting a multi pass forming approach is essential for producing geometrically stable and defect-free teeth in the GFP processes (see Fig. 11). In the backward FP, the external gear is manufactured in two steps, but an additional step is also performed to achieve the desired dimensions (length and diameter), which can be seen in Fig. 11.

Fig. 11.

Tooth height and length formed in three stages of the gear flow forming (GFP) process.

Three steps of internal FP were employed to produce a bilayer gear with 44 teeth and a modulus of 1 m. Each step reduces the thickness of the preform by 30%, 25%, and 20%, respectively. Figure 12 illustrates the progressive development of the tooth profile in three steps. All profiles show a nearly parabolic and symmetric shape, confirming high precision in manufacturing and uniform stress distribution. The maximum tooth height increases from about 0.8 mm in step1 to 2.2 mm in step3, reflecting a stepwise improvement in geometry through forming of the gear. The observed geometric symmetry across all steps further confirms the precision of the process, which is critical for minimizing vibration, noise, and premature wear. These characteristics are particularly important in high-performance mechanical systems, where small deviations in geometry can significantly impact efficiency and reliability.

Fig. 12.

Formation of the bilayer gear in three steps of backward GFP.

Figure 13 shows how much force is needed for forming teeth at each step in forming composite gear. As can be seen, one factor contributing to the gradual increase of force is the work hardening of the preform. Another reason can be the narrowing of the tooth tip, which makes filling more difficult. These forces can be used to design and select the appropriate tool to perform the process correctly. Figure 13 complements the findings in Fig. 12 by showing the forming force required at each step. The force increases consistently with roller displacement, while the maximum values rise substantially from ~ 15 kN in step1 to ~ 40 kN in step3. This trend demonstrates that as the profile develops and the amount of displaced material grows, the forming process demands higher force and energy input. Taken together, the two datasets reveal an inherent trade-off in the forming process. On one hand, the stepwise development of the profile ensures improved dimensional precision and overall mechanical performance of the final component. On the other hand, these improvements are achieved at the expense of significantly increased forming forces, higher energy consumption, and greater demand on the forming equipment. Therefore, the findings highlight the necessity of process optimization strategies that balance geometric accuracy with manufacturability.

Fig. 13.

Forming force of the bilayer gear over three steps.

To better understand the benefits of the GFP process, the strength of teeth against crush was compared in Fig. 14. The presented diagram illustrates the crush resistance of gears manufactured from different materials and processes, including non-flow formed Cu, flow-formed Cu, non-flow formed St304L, and a flow-formed bilayer gear. The force–rotation curves reveal distinct trends reflecting both the intrinsic material properties and the effect of the forming process. In the crush test, the flow formed gear was engaged with another gear, and the force yielded to crush the tooth is recorded. In this study, once the teeth are formed inside the mandrel, the gear rotates about its axis while the mandrel is fixed. During rotation, repeated impacts between the gear teeth and the mandrel teeth induce bending stresses, leading to progressive tooth deformation, crushing, and eventual failure after a certain duration. The non-flow formed Cu gear exhibits the lowest crush resistance, with peak forces below 100 kN. When subjected to flow forming, Cu shows a significant improvement in crush resistance (≈ 150 kN), which can be attributed to strain hardening, grain refinement, and texture evolution induced during the forming process^8–12. These microstructural changes enhance the yield strength, thereby improving crush performance despite possible local thinning. The non-flow formed St304L gear demonstrates the highest crush resistance (~ 370 kN), which is consistent with the inherently higher strength and work-hardening capacity of austenitic stainless steels. The flow-formed bilayer gear exhibits intermediate resistance, ranging from 200 to 310 kN. This behavior reflects the composite nature of the structure, where the harder layer positioned farther from the neutral axis increases the section modulus and crush moment capacity. Such hybrid designs provide a compromise between the high resistance of stainless steel and the lower forming effort of copper. Oscillations present in all curves can be explained by stick–slip phenomena, localized elastic–plastic transitions, or variations in roller–gear contact conditions. In summary, the results establish the following ranking of crush resistance: St304L (non-flow) > flow-formed bilayer > flow-formed Cu > non-flow Cu. Flow forming markedly improves the mechanical performance of Cu by inducing strain hardening, while the bilayer approach provides a practical balance between strength and manufacturability. The findings confirm that both material selection and forming process optimization are critical for achieving high-performance gears with enhanced crush resistance.

Fig. 14.

Comparison of crush force among four gear types.

Conclusion

The feasibility of external gear manufacturing through flow forming was investigated in this study. The gear flow forming process (GFP) was first simulated, and the results were validated experimentally, confirming the accuracy of the finite element model and the applicability of flow forming for external gear production. A comparison between backward and forward FP revealed that while the backward process requires higher forming forces, it can produce gears in fewer passes. The force increased progressively with each step, reaching its maximum during the final pass to fully fill the mandrel teeth. Stress analysis showed that during the initial pass, the inner surface bears most of the load due to direct roller contact. Once tooth filling is completed, however, stresses become more evenly distributed across the thickness, with both inner and outer surfaces sustaining comparable levels. Regardless of whether the process is internal or external, the roller-contacted surface governs the dominant deformation mechanism. Radial displacement analysis further demonstrated that multi-pass forming is essential for stable tooth formation. While the first pass produces limited deformation, subsequent passes improve depth uniformity and reduce edge roll-back, ensuring dimensional accuracy in GFP processes. In addition, the feasibility of manufacturing bilayer gears was examined. Crush tests revealed that St304L gears exhibited the highest resistance, while incorporating a steel304L layer approximately doubled the strength of copper gears. Overall, the results indicate that flow forming markedly enhances the crush resistance of Cu through strain hardening, and the bilayer design provides a practical balance between strength and manufacturability. These findings highlight that both material selection and process optimization are critical for producing high-performance gears.

Author contributions

All steps in writing this paper were carried out by the corresponding author (Majid Khodadadi).

Data availability

The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.