In modern automotive manufacturing, the hollow gear shaft plays a critical role in transmission systems, where it transmits power and motion through gear meshing. The demanding operational conditions, including continuous cyclic loading, necessitate high forming quality and mechanical performance. Traditional manufacturing processes such as casting, machining, open-die forging, and multi-stage die forging have been employed, but they often suffer from limitations like poor material utilization, low production efficiency, and high模具 costs. To address these issues, we propose the use of closed-die forging, a process that involves applying a clamping force to a separable die to form a封闭 cavity, followed by multi-directional punching to achieve complex geometries in a single deformation. This method enhances material flow, refines grain structures, and improves overall part quality. In this article, we explore the simulation and optimization of the closed forging process for a hollow gear shaft, focusing on die structure design, punch movement strategies, and their effects on forming quality and模具寿命.
The hollow gear shaft, as illustrated in the design, features helical teeth, through-holes, and stepped shafts, with significant cross-sectional variations—the minimum diameter is 53 mm, less than half of the maximum size. This complexity, combined with a high depth-to-diameter ratio for the holes, poses challenges for conventional forming methods. We designed the forging process with a vertical orientation to facilitate part ejection and die manufacturing, selecting the largest projected area as the parting surface. The billet, made of 42CrMo alloy steel, was sized to Φ53.0 mm × 250.5 mm based on volume conservation principles to prevent underfilling or模具 damage. The process flow involves sawing, weight screening, heating, preheating, closed forging, piercing, and annealing. Two die structure schemes were considered: a three-punch and a four-punch configuration. Finite element analysis (FEA) was employed to simulate the forming process, using a rigid-plastic model with thermo-mechanical coupling to assess material flow, temperature distribution, and stress states.
To establish the FEA model, we simplified the die assemblies in Solidworks, importing half-models into Deform for computational efficiency. The workpiece material, 42CrMo, was characterized by its high-temperature flow stress behavior, described by the following constitutive equation derived from compression tests:
$$ \dot{\epsilon} = 1.34 \times 10^{18} \left[ \sinh(8.198 \times 10^{-3} \sigma)^{8.1434} \right] \cdot \exp\left[ -\frac{4.6334 \times 10^{-5}}{R T} \right] $$
where $\dot{\epsilon}$ is the strain rate in s-1, $\sigma$ is the flow stress in MPa, $R$ is the gas constant (8.314 J·mol-1·K-1), and $T$ is the absolute temperature in K. The模具 were treated as rigid bodies, preheated to 380°C, while the billet was heated to 1050°C. Mesh sizes were set to 42,000 elements for the upper and lower dies, 12,000 for the punches, and 50,000 for the billet. Thermal boundary conditions included a constant heat transfer coefficient of 11 N·s-1·mm-1·°C-1, and friction was modeled with a coefficient of 0.3 under lubricated conditions. Punch movements were programmed as per the schemes: for the three-punch structure, upper punches moved downward while the lower punch moved upward; for the four-punch structure, all punches moved symmetrically toward the center.
Simulation results for the three-punch structure revealed issues with material flow, where metal tended to escape into gaps between the lower die and punch, forming flash and leading to incomplete filling of the helical teeth. In contrast, the four-punch structure demonstrated superior performance, with simultaneous bidirectional punching promoting uniform material flow toward the central cavity, minimizing flash and ensuring complete filling. The following table summarizes the key observations from the FEA for both die structures:
| Die Structure | Material Flow Behavior | Filling Completeness | Risk of Defects |
|---|---|---|---|
| Three-Punch | Uneven, with flash formation | Incomplete at teeth | High |
| Four-Punch | Uniform, minimal flash | Complete | Low |
Based on these findings, we selected the four-punch structure for further optimization. The volume ratio between the upper and lower sections of the gear shaft was approximately 2.5, indicating a need for preferential material accumulation in the upper region during early forming stages to reduce resistance and enhance tooth formation. We investigated three punch movement schemes: Scheme A (symmetric movement), Scheme B (asymmetric with upper punches leading), and Scheme C (modified asymmetric). The temperature distribution post-forging was analyzed to assess the risk of cooling cracks, which occur due to thermal stresses exceeding the material’s tensile strength. The temperature gradient $\Delta T$ across the gear shaft can be estimated using Fourier’s law of heat conduction:
$$ q = -k \nabla T $$
where $q$ is the heat flux and $k$ is the thermal conductivity. Results showed that Scheme B resulted in the smallest maximum temperature difference (818°C vs. 923°C in Scheme A), reducing the likelihood of crack initiation. The table below compares the temperature extremes and differentials for each scheme:
| Scheme | Min Temperature (°C) | Max Temperature (°C) | Temperature Difference (°C) |
|---|---|---|---|
| A | 523 | 923 | 400 |
| B | 520 | 818 | 298 |
| C | 521 | 852 | 331 |
Furthermore, we evaluated the impact of punch movement on模具 loading and longevity. The minimum clamping force $F_c$ required to prevent material leakage is critical; excessive force demands higher equipment tonnage and accelerates模具 wear, while insufficient force leads to flash. Using the FEA results, we calculated the loads on each punch and the corresponding minimum clamping forces. The data indicate that Scheme B required the lowest clamping force and punch loads, thereby extending模具 life. The following table presents the载荷 data in units of 105 N:
| Scheme | Upper Punch 1 Load | Upper Punch 2 Load | Lower Punch 1 Load | Lower Punch 2 Load | Min Clamping Force |
|---|---|---|---|---|---|
| A | 2.21 | 5.01 | 2.26 | 4.69 | 13.32 |
| B | 1.43 | 4.11 | 1.67 | 3.72 | 8.61 |
| C | 1.79 | 4.78 | 1.82 | 4.42 | 10.69 |
Surface temperature rise on the模具 is another factor affecting hardness and wear. Scheme B exhibited the least pronounced temperature increase, as shown in the table below, which lists surface temperatures in °C for various模具 components:
| Scheme | Upper Punch 1 | Upper Punch 2 | Lower Punch 1 | Lower Punch 2 | Upper Die | Lower Die |
|---|---|---|---|---|---|---|
| A | 497 | 793 | 497 | 738 | 626 | 640 |
| B | 460 | 727 | 425 | 666 | 611 | 620 |
| C | 467 | 765 | 434 | 701 | 615 | 625 |
To validate the optimized process, we conducted trial productions using a hot die forging setup with the four-punch structure and Scheme B movement parameters. The billet, heated to 1050°C for 10 minutes, was forged under continuous lubrication with water-based graphite. The resulting hollow gear shaft forgings exhibited complete filling, high-quality helical teeth, and no flash at the parting surface. Key dimensions were measured and found to comply with design specifications: upper and lower hole diameters of Φ36.03 mm, shaft outer diameters of Φ52.99 mm, overall height of 170.04 mm, maximum tooth轮廓尺寸 of 123.08 mm, and web thickness of 10.01 mm, all within tolerance ranges (e.g., Φ36+0.0390 mm, Φ530-0.019 mm). Sectional analysis revealed continuous forging streamlines without cracks or folds, confirming the integrity of the gear shaft.
The success of this approach underscores the advantages of closed-die forging for complex components like the hollow gear shaft. By leveraging FEA, we optimized die design and process parameters, achieving a balance between forming quality,模具 life, and efficiency. Future work could explore advanced material models or real-time control systems to further enhance the process for automotive applications.