In the field of power transmission, the manufacturing of gears has always been a critical process that directly influences the performance, durability, and cost of mechanical systems. Among the various methods available, such as cutting, casting, and forging, the gear forging process stands out due to its high material utilization, superior strength, and long service life. When applied to the production of motor spline gears for sports cars, gear forging offers significant advantages in terms of mechanical properties and fatigue resistance. However, one of the most persistent challenges in gear forging is the excessive wear of the die, particularly at the tooth top of the female die, which leads to a shortened die service life and increased production costs. In this study, I aimed to address this issue by systematically analyzing the wear behavior of the forging die used for a motor spline gear, optimizing the process parameters, and validating the results through actual production trials. The entire investigation was conducted using numerical simulation, orthogonal experiments, and production tests, with a strong focus on the gear forging process.
The gear under consideration is a straight cylindrical gear with a spline structure, specifically designed for a sports car motor. Its primary geometric parameters are summarized in Table 1. The gear has 18 teeth, a module of 1.5 mm, a pressure angle of 20°, a tooth width of 24 mm, and an inner hole with a spline configuration. The complex geometry of the spline and the tight tolerances required for automotive applications make the gear forging process particularly demanding. The die material selected for this study was 4Cr5MoSiV1 steel, a common hot-work die steel known for its excellent thermal fatigue resistance and hardness retention at elevated temperatures. The billet material was 45 steel, which is widely used for gears due to its good machinability and hardenability.
| Parameter | Value |
|---|---|
| Number of teeth | 18 |
| Module (mm) | 1.5 |
| Pressure angle (°) | 20 |
| Tooth width (mm) | 24 |
| Inner hole | Spline structure |
| Gear material | 45 steel |
| Die material | 4Cr5MoSiV1 steel |
To determine the most suitable gear forging process, I designed three different hot extrusion schemes and established corresponding CAE models. Each scheme involved a distinct billet geometry, die configuration, and metal flow pattern. The goal was to evaluate the forming quality, die wear distribution, and load requirements for each scheme, and then select the optimal one for further optimization. The three schemes are described in detail below.
Scheme 1: The billet had an outer diameter of Φ23 mm and a height of 21 mm. The process sequence included blanking, vacuum heat treatment, water-based graphite lubricant application, closed composite extrusion (where metal flows in three directions: along the punch motion direction, opposite to the punch motion, and radially), punching of the connecting web, vacuum heat treatment, tooth profile finishing, and spline cutting. This scheme was designed to produce a near-net shape gear with minimal material waste.
Scheme 2: The billet had an outer diameter of Φ23 mm, an inner diameter of Φ18 mm, and a height of 48 mm. The process sequence was blanking, vacuum heat treatment, water-based graphite lubricant, closed radial extrusion (where metal flows primarily in the radial direction), vacuum heat treatment, tooth profile finishing, and spline cutting. This scheme aimed to improve the radial filling of the die cavity and reduce the forming load.
Scheme 3: The billet had an outer diameter of Φ29 mm and a height of 30 mm. The process sequence included blanking, vacuum heat treatment, water-based graphite lubricant, open forward extrusion (where metal flows in the same direction as the punch motion), vacuum heat treatment, tooth profile finishing, cutting off, and spline cutting. This scheme was intended to simplify the tooling but often results in poorer dimensional accuracy.
For Schemes 1 and 2, the tooth profile finishing step only required changing the female die, while the other die components remained unchanged. This approach was adopted to improve production efficiency and assembly accuracy. Since the main forming operation occurs during the hot extrusion stage, I focused my analysis on this critical step. Table 2 compares the key characteristics of the three schemes.
| Feature | Scheme 1 | Scheme 2 | Scheme 3 |
|---|---|---|---|
| Billet outer diameter (mm) | Φ23 | Φ23 | Φ29 |
| Billet inner diameter (mm) | — | Φ18 | — |
| Billet height (mm) | 21 | 48 | 30 |
| Extrusion type | Closed composite | Closed radial | Open forward |
| Metal flow direction | Three directions | Radial | Axial |
| Die replacement | Only female die | Only female die | Full die set |
To perform the numerical simulations, I used DEFORM-3D, a widely accepted finite element analysis software for metal forming processes. The initial conditions, boundary conditions, and material constitutive models were carefully defined to reflect the actual gear forging conditions. The initial conditions included a billet temperature of 1150 °C, a die preheating temperature of 250 °C, an initial die hardness of 50 HRC, and a punch downward speed of 50 mm·s⁻¹. The gear material was modeled as a plastic body, while the die was treated as a rigid body. The boundary conditions specified fixed supports for the die, a shear friction model with a friction factor of 0.25, and heat exchange coefficients between the die and billet. The termination conditions were set based on the punch displacement for each scheme: 17.2 mm for Scheme 1, 23.5 mm for Scheme 2, and 19.5 mm for Scheme 3, with a step increment of 0.1 mm. The flow stress-strain curves of the billet material were taken from the built-in material library, which provides accurate temperature- and strain-rate-dependent behavior for 45 steel.
The simulation results for the three schemes were analyzed in terms of equivalent strain distribution, die wear distribution, and load-stroke curves. For a successful gear forging operation, the equivalent strain should generally exceed 0.69 to 1.10 to ensure adequate material deformation and proper filling of the die cavity. In Scheme 1, the equivalent strain values ranged from 1.52 to 4.86 at the lower tooth face and root regions, while the tooth top and upper tooth face exhibited values between 0.80 and 1.52, indicating difficulty in forming these areas. In Scheme 2, the difficult-to-form region was significantly reduced, and the overall strain distribution on the tooth face ranged from 0.8 to 3.4 with a more uniform, banded pattern. In Scheme 3, the difficult-to-form region increased markedly, and the strain distribution was highly non-uniform with large variations, which would likely lead to uneven gear formation and complex subsequent correction processes. Based on these observations, Scheme 2 was identified as the optimal scheme for gear forging.
The die wear distribution further supported this conclusion. In Scheme 1, the most severe wear occurred at the tooth top of the female die, with a maximum wear amount of 2.18 × 10⁻⁵ mm. The entire tooth face and core die positions also experienced wear, resulting in a large repair area. In Scheme 2, the wear area was noticeably reduced, with wear concentrated only at certain tooth top regions, making die repair more convenient. The maximum wear amount was similar to that of Scheme 1. In Scheme 3, the most severe wear occurred at the die entry half-angle, with a wear area that was larger and a maximum wear amount that was two to three times greater than those of Schemes 1 and 2. Considering the overall die wear, Scheme 2 offered the smallest wear area and the most favorable wear location, thus confirming its superiority.
The load-stroke curves for Schemes 1 and 2 exhibited nearly identical trends. In the first stage, the material underwent plastic deformation under the external force of the punch, flowing into the tooth space, and the load began to increase. In the second stage, as the punch continued to descend, the material gradually filled the tooth bottom, and the load change became more gradual. In the third stage, a sharp deformation stage occurred, where the remaining space in the tooth space became small, the material flow resistance increased dramatically, and the forming load increased exponentially. In contrast, Scheme 3 showed only two stages, with no sharp deformation stage, indicating that the gear deformation mainly occurred at the die entry half-angle and that the forming accuracy was relatively low. The maximum load for Scheme 2 was 47.6 kN for two teeth, which implies that a hydraulic press of at least 428.4 kN would be required for the entire gear.
The cavity filling degree, which describes the gap between the formed gear and the die cavity, was also evaluated. Schemes 1 and 2 produced gears that fit the die cavity with almost no gap, meeting the forming requirements. Scheme 3, however, showed a noticeable gap between the formed gear and the die cavity, resulting in poor forming quality and complex subsequent processing. Therefore, Scheme 2 was definitively selected as the optimal gear forging process.
After selecting Scheme 2, I proceeded to analyze the die wear in greater detail using a point tracking method. The wear on the female die was localized and magnified, and six representative points were selected for tracking. The coordinates of these points are listed in Table 3. The points were distributed along the tooth top region of the female die, with P1 near the upper end and P6 near the middle. Based on the Archard modified wear model, which accounts for the correlation between die hardness, wear coefficient, and temperature, I predicted the wear amount at each point. The Archard model is expressed as:
$$ W = \int_{0}^{t} K \frac{p v}{H} \, dt $$
where \( W \) is the wear depth, \( K \) is the wear coefficient, \( p \) is the contact pressure, \( v \) is the relative sliding velocity, \( H \) is the die hardness, and \( t \) is the time. The point tracking results showed that the maximum wear amount in the neighborhood of each point followed the order: P6 > P5 > P4 > P3 > P2 > P1. The P6 region, located at the middle of the tooth top, exhibited the highest wear amount of 2.78 × 10⁻⁵ mm. This can be attributed to the fact that when the punch presses the billet, the material at both ends is compressed simultaneously, causing the initial deformation to take a barrel shape. Consequently, the closer a region is to the middle of the die, the longer it remains in contact with the billet, the faster the die temperature rises, and the higher the relative velocity between the material and the die, leading to increased wear. In contrast, the material at the ends first forms a collapse angle, and as the punch descends, the material flows toward the tooth space, reducing the wear at the ends. Therefore, the middle of the tooth top experiences the most severe wear, and special attention must be paid to this region during die maintenance.
| Point | X (mm) | Y (mm) | Z (mm) |
|---|---|---|---|
| P1 | 7.864 | 23.208 | 60.583 |
| P2 | 7.790 | 23.227 | 58.452 |
| P3 | 7.810 | 23.225 | 56.231 |
| P4 | 7.791 | 23.226 | 54.084 |
| P5 | 7.831 | 23.217 | 51.826 |
| P6 | 7.767 | 23.232 | 49.413 |
To optimize the die wear and extend the die service life, I conducted an orthogonal experiment with four factors and three levels. The factors considered were the friction factor \( Y \), the initial die hardness \( X \), the die preheating temperature \( Z \), and the punch downward speed \( T \). The levels for each factor are presented in Table 4. The friction factor was varied from 0.25 to 0.35, the initial die hardness from 45 to 55 HRC, the die preheating temperature from 250 to 350 °C, and the punch downward speed from 50 to 100 mm·s⁻¹. These ranges were chosen based on practical constraints and previous experience in gear forging.
| Level | X (HRC) | Y | Z (°C) | T (mm·s⁻¹) |
|---|---|---|---|---|
| 1 | 45 | 0.25 | 250 | 50 |
| 2 | 50 | 0.30 | 300 | 75 |
| 3 | 55 | 0.35 | 350 | 100 |
A total of nine representative parameter combinations were selected according to the orthogonal array, and the corresponding wear amounts in the P6 region of the gear die were simulated. The results are shown in Table 5. The wear depth \( W \) was recorded for each combination. The simulation results clearly indicate that the combination with the highest die hardness and the lowest punch speed yields the smallest wear amount.
| Run | X (HRC) | Y | Z (°C) | T (mm·s⁻¹) | W (×10⁻⁵ mm) |
|---|---|---|---|---|---|
| 1# | 45 | 0.25 | 250 | 50 | 3.43 |
| 2# | 45 | 0.30 | 300 | 75 | 3.54 |
| 3# | 45 | 0.35 | 350 | 100 | 3.63 |
| 4# | 50 | 0.25 | 300 | 100 | 3.00 |
| 5# | 50 | 0.30 | 350 | 50 | 2.71 |
| 6# | 50 | 0.35 | 250 | 75 | 2.85 |
| 7# | 55 | 0.25 | 350 | 75 | 2.38 |
| 8# | 55 | 0.30 | 250 | 100 | 2.46 |
| 9# | 55 | 0.35 | 300 | 50 | 2.21 |
The significance analysis of the orthogonal experiment results is presented in Table 6. The sum of the wear amounts for each level of each factor, denoted as \( N_{jk} \), was calculated, where \( j \) is the factor and \( k \) is the level. The range \( R_j \) for each factor was determined using the following equation:
$$ R_j = \max\left(\frac{N_{j1}}{3}, \frac{N_{j2}}{3}, \frac{N_{j3}}{3}\right) – \min\left(\frac{N_{j1}}{3}, \frac{N_{j2}}{3}, \frac{N_{j3}}{3}\right) $$
The sum of squares \( S_j \) for each factor, the degrees of freedom \( f \), the mean square, and the \( F \)-value were also computed. The significance level \( \alpha \) was used to judge the influence of each factor, with \( \alpha < 0.01 \) indicating a highly significant factor and \( \alpha > 0.05 \) indicating a non-significant factor.
| Source | X | Y | Z | T | Model |
|---|---|---|---|---|---|
| \( N_{j1} \) (×10⁻⁵ mm) | 10.6 | 8.81 | 8.74 | 8.35 | — |
| \( N_{j2} \) (×10⁻⁵ mm) | 8.56 | 8.71 | 8.75 | 8.77 | — |
| \( N_{j3} \) (×10⁻⁵ mm) | 7.05 | 8.69 | 8.72 | 9.09 | — |
| \( R_j \) (×10⁻⁵ mm) | 1.18 | 0.04 | 0.01 | 0.25 | — |
| \( S_j \) (×10⁻¹³ mm²) | 2100 | 2.4 | 0.067 | 91.27 | 2194 |
| \( f \) | 1 | 1 | 1 | 1 | 4 |
| \( F \)-value | 506 | 0.58 | 0.016 | 21.98 | 132 |
| \( \alpha \) | <10⁻⁴ | 0.49 | 0.905 | 0.009 | 2×10⁻⁴ |
From the significance analysis, the factors affecting the wear amount in the P6 region of the gear die, in descending order of influence, are: initial die hardness \( X \) > punch downward speed \( T \) > friction factor \( Y \) > die preheating temperature \( Z \). The initial die hardness and the punch downward speed are both highly significant factors, with \( \alpha < 0.01 \), indicating a confidence level greater than 99%. The friction factor and die preheating temperature have negligible effects on the wear amount and are considered non-significant factors. Therefore, the optimal levels for the significant factors are \( X_3 T_1 \), which correspond to an initial die hardness of 55 HRC and a punch downward speed of 50 mm·s⁻¹. The non-significant factors can be selected based on cost and process complexity, but for the purpose of this study, they were kept at their mid-levels.
The final regression equation for the die wear depth \( W \) is given by:
$$ W = 2.912 \times 10^{-5} – 5.917 \times 10^{-6}X – 2 \times 10^{-7}Y – 3.333 \times 10^{-8}Z + 1.233 \times 10^{-6}T $$
This equation quantifies the individual contributions of each factor to the wear depth. The negative coefficients for \( X \), \( Y \), and \( Z \) indicate that increasing the initial die hardness, friction factor, and die preheating temperature reduces the wear depth, while the positive coefficient for \( T \) indicates that increasing the punch downward speed increases the wear depth. The regression model is highly significant, with an \( \alpha \)-value less than 0.01, confirming the reliability of the model and the predicted data.
To further illustrate the combined effect of the two significant factors, a response surface was constructed for the die wear amount as a function of initial die hardness and punch downward speed, while keeping the friction factor at 0.35 and the die preheating temperature at 300 °C. The response surface shows that as the initial die hardness increases, the wear amount in the P6 region decreases. Conversely, as the punch downward speed increases, the wear amount increases. The slope of the surface is steeper for the initial die hardness than for the punch downward speed, confirming that the initial die hardness has a greater influence on the wear amount. The minimum wear amount predicted by the response surface is 2.21 × 10⁻⁵ mm, which is consistent with the orthogonal experiment results.
Based on the orthogonal experiment results, the optimal wear amount in the P6 region of the gear die is 2.21 × 10⁻⁵ mm, which represents a 20.5% reduction compared to the unoptimized value of 2.78 × 10⁻⁵ mm. Using the allowable unilateral wear of 0.5 mm as specified by the gear production requirements, the die service life can be calculated. The unoptimized die life was approximately 17,985 pieces, while the optimized die life is approximately 22,624 pieces. In actual production, the die service life exceeded 20,000 pieces, meeting the production target and demonstrating the effectiveness of the parameter optimization. The gear forging process with the optimized parameters not only improves the die service life but also reduces maintenance costs and increases production efficiency.
The actual gear parts produced using the optimized parameters are shown in the figure. The gear teeth are clearly formed, and no visible defects are present. This confirms that the optimized parameters, particularly the increased initial die hardness and the reduced punch downward speed, are effective in enhancing the die service life without compromising the gear forming quality. The gear forging process has been successfully validated through production trials, and the optimized parameter combination can be readily applied to industrial production.
In conclusion, I have conducted a comprehensive study on the die wear behavior of a motor spline gear during the gear forging process. Three hot extrusion schemes were designed and simulated, and Scheme 2 was identified as the optimal scheme based on equivalent strain, die wear, and load-stroke characteristics. The point tracking method revealed that the most severe wear occurs at the P6 region of the female die, located at the middle of the tooth top. Through orthogonal experiments, the initial die hardness and punch downward speed were identified as the most significant factors affecting the die wear. The optimal parameter combination was determined to be an initial die hardness of 55 HRC and a punch downward speed of 50 mm·s⁻¹, which reduced the wear amount by 20.5% and extended the die service life to over 20,000 pieces. The regression equation and response surface provided a reliable model for predicting die wear. The production trials confirmed the accuracy of the optimization, and the gear forgings exhibited full filling and good quality. This study provides a theoretical basis and practical guidance for improving die service life in the gear forging of motor spline gears for sports cars.
The findings of this research have significant implications for the gear forging industry. By optimizing the process parameters, manufacturers can achieve substantial cost savings through reduced die replacement and maintenance. The methodology presented here, combining numerical simulation, point tracking, and orthogonal experiments, can be adapted to other gear forging applications. Future work could involve investigating the effects of other parameters, such as billet temperature and lubrication conditions, and exploring advanced die materials and surface treatments to further enhance die performance. The continuous improvement of gear forging processes is essential for meeting the increasing demands for high-performance gears in automotive and other demanding applications.
| Parameter | Unoptimized | Optimized | Improvement |
|---|---|---|---|
| Initial die hardness (HRC) | 50 | 55 | +5 |
| Punch downward speed (mm·s⁻¹) | 50 | 50 | — |
| Friction factor | 0.25 | 0.35 | +0.10 |
| Die preheating temperature (°C) | 250 | 300 | +50 |
| Maximum wear in P6 (×10⁻⁵ mm) | 2.78 | 2.21 | -20.5% |
| Die service life (pieces) | 17,985 | 22,624 | +25.8% |
The relationship between the die wear depth and the process parameters can be further analyzed using the regression equation. For instance, if the initial die hardness is increased from 50 to 55 HRC while keeping other factors constant, the wear depth decreases by approximately \( 5.917 \times 10^{-6} \times 5 = 2.959 \times 10^{-5} \) mm, which is a significant reduction. Similarly, reducing the punch downward speed from 100 to 50 mm·s⁻¹ decreases the wear depth by \( 1.233 \times 10^{-6} \times 50 = 6.165 \times 10^{-5} \) mm. These quantitative insights are valuable for process engineers aiming to fine-tune the gear forging parameters.
In the actual gear forging production, the die life is not only influenced by the parameters studied here but also by factors such as the cooling rate, the lubrication method, and the die surface treatment. However, the current study has demonstrated that by focusing on the most significant factors, substantial improvements can be achieved. The optimized parameters have been implemented in the production line, and the die life has consistently exceeded 20,000 pieces, which is a significant improvement over the previous life of less than 18,000 pieces. The gear forgings produced with the optimized parameters have met all dimensional and quality requirements, and no premature die failures have been observed.
Overall, this research contributes to the understanding of die wear in gear forging and provides a practical approach for optimizing the process. The use of numerical simulation and orthogonal experiments allows for efficient exploration of the parameter space without the need for extensive physical trials. The point tracking method is particularly useful for identifying the critical wear regions on the die, which can guide targeted maintenance and design improvements. The findings underscore the importance of die hardness and punch speed in controlling wear, and they highlight the potential for further optimization through advanced materials and coatings.
The gear forging process for motor spline gears is a complex interplay of material flow, thermal effects, and mechanical stresses. By systematically analyzing the process and optimizing the key parameters, I have demonstrated that the die service life can be significantly extended, leading to reduced costs and improved productivity. This work serves as a foundation for future studies aimed at further enhancing the gear forging process and die performance.