In modern manufacturing, the precision forging of a straight spur gear has become a critical process due to its high material utilization, excellent dimensional accuracy, and superior mechanical properties. Among various forging methods, closed-die forging, also known as flashless forging, is widely adopted for producing straight spur gears because it eliminates flash, reduces subsequent machining, and enhances productivity. However, this technique often suffers from excessively high forming loads, rapid tool wear, and premature die failure. To address these challenges, my research focuses on two innovative improvements: the floating die method and the hole split method. Using the finite element software DEFORM-3D, I conducted a systematic numerical simulation of the entire forging cycle for a straight spur gear made from 20CrMnMo steel. The objective was to compare the forming load, stress distribution, and die load characteristics among three process variants: conventional closed-die forging, floating die forging, and hole split forging. The results demonstrate that both improvements significantly reduce die loads while maintaining full tooth filling. Specifically, the floating die method reduces the peak die load by approximately 10%, and the hole split method achieves a reduction of up to 25%. This article presents detailed quantitative data through tables and mathematical formulas, providing a robust reference for the industrial production of high-quality straight spur gears.
The straight spur gear under investigation has a pitch circle diameter of 60 mm, a face width of 30 mm, a pressure angle of 20°, a module of 3, and 20 teeth. The material selected is 20CrMnMo steel, a low-alloy steel widely used for transmission gears due to its excellent hardenability and wear resistance. Table 1 summarizes its mechanical properties, which are essential for determining the forming force and die stress.
| Property | Value |
|---|---|
| Tensile strength / MPa | 1250 |
| Yield strength / MPa | 958 |
| Elongation / % | ≥10 |
| Reduction of area / % | ≥45 |
| Impact energy / J | ≥55 |
| Hardness / HB | ≤217 |
| Poisson’s ratio | 0.27 |
| Elastic modulus / GPa | 207 |
Given the symmetry of the straight spur gear, I constructed a one-fifth sector model in SolidWorks to enhance computational efficiency. The assembly includes the upper punch, lower punch, die (or floating die), and billet (solid cylindrical or ring-shaped). The model was imported into DEFORM-3D, where the material library provided AISI-4120, equivalent to 20CrMnMo. Mesh refinement was applied to the outer region of the billet that forms the tooth profile. Symmetry boundary conditions were set on the two cut faces. The upper punch, die, and lower punch were defined as rigid bodies. A constant shear friction model with a friction factor of 0.1 was adopted. The simulation step size was set to one-third of the smallest element size, and the termination condition was defined by the upper punch stroke. The detailed simulation parameters are listed in Table 2.
| Parameter | Value |
|---|---|
| Workpiece material | 20CrMnMo (AISI-4120) |
| Initial billet dimensions (solid) / mm | Φ50 × 40 |
| Initial billet dimensions (ring, hole split) / mm | Φ50 × 40, hole Φ20 |
| Friction type | Constant shear |
| Friction factor | 0.1 |
| Mesh type | Solid tetrahedral |
| Element count (1/5 model) | ~80,000 |
| Punch speed / mm·s⁻¹ | 1 (quasi-static) |
| Initial temperature / °C | 20 (cold forging) |
During the conventional closed-die forging process, the die and lower punch remain fixed while the upper punch descends. The material first upsets, then flows radially into the die cavity to form the tooth profile. The frictional force between the billet and the die wall opposes the material flow, leading to a high forming load. The simulation captured three distinct stages: upsetting, steady tooth formation, and final filling. The effective stress distribution indicates that the maximum stress occurs at the tooth root during the middle stage and at the tooth tip during the final stage. The load-stroke curve in Figure 1 shows a peak load of 778 kN. The load rises sharply near the end because the remaining unfilled volume becomes very small.
To mitigate the high die load, I proposed the floating die method. In this configuration, the lower punch is stationary, while the die moves downward together with the upper punch under an applied force (e.g., spring or hydraulic pressure). As the die descends, the frictional force between the billet and the die wall reverses direction from resisting to assisting the material flow. This “active friction” promotes metal movement toward the lower tooth region, improving fillability and reducing the required forming force. The simulated effective stress distribution shows that the maximum stress is lower than in the conventional process. The peak load recorded was 705 kN, representing a reduction of about 10%. The underlying mechanism can be expressed by the friction force relation:
$$ F_f = \mu \sigma_n A $$
where \( \mu \) is the friction coefficient, \( \sigma_n \) is the normal contact stress, and \( A \) is the contact area. When the die velocity \( v_d \) exceeds the material flow velocity \( v_m \), the relative motion of the billet with respect to the die is upward, generating a downward friction force that aids deformation. Conversely, if \( v_d < v_m \), the friction force opposes deformation. The ideal condition for minimizing the forming load \( F \) is \( v_d > v_m \). Through careful control of the die motion, the floating die method converts the frictional resistance into a driving force, thereby reducing the overall load requirement.
The second improvement, the hole split method, involves using a ring-shaped billet with a central hole. During forming, a portion of the metal flows radially outward to fill the tooth cavities, while the remaining metal flows inward into the central hole. This “hole split” effect alleviates the hydrostatic pressure in the closed cavity, significantly lowering the die load. The central hole acts as a pressure relief valve. However, the hole diameter must be optimized: too small and the hole closes prematurely, nullifying the benefit; too large and insufficient metal remains for complete tooth filling. Through iterative simulations, I determined that a central hole diameter between Φ19 mm and Φ22 mm yields optimal results. The simulated effective stress distribution shows reduced peak values compared to the conventional process. The peak load for a Φ20 mm hole was 589 kN, which is 24.3% lower than the 778 kN of the conventional process. Table 3 compares the key results for all three processes.
| Process | Peak die load / kN | Max effective stress / MPa | Load reduction / % | Tooth filling quality |
|---|---|---|---|---|
| Conventional closed-die | 778 | 921 | – | Incomplete at lower teeth |
| Floating die | 705 | 862 | 9.4 | Complete, uniform |
| Hole split (Φ20 mm) | 589 | 805 | 24.3 | Complete, good |
The load-stroke behavior of each process can be analyzed through the plastic work equation. The total forming load \( P \) is the sum of the ideal deformation load \( P_i \) and the friction load \( P_f \). For the conventional process, \( P_f \) is positive (resisting). For the floating die, \( P_f \) can become negative (assisting), reducing the total. For the hole split, the internal pressure is lowered because the central orifice allows radial flow, which reduces the hydrostatic component. An approximate expression for the peak load in hole split forging is:
$$ P_{hole} = P_{solid} – \Delta P_{split} $$
where \( \Delta P_{split} \) is proportional to the cross-sectional area of the central hole and inversely proportional to the current hole diameter during forging. The exact relationship requires numerical calibration, but the simulation provides a reliable estimate.
The actual die trials were conducted on a hydraulic press. The floating die process used a solid cylindrical billet, while the hole split process used a ring billet with a pre-drilled central hole of Φ20 mm. Both processes produced straight spur gear preforms with fully filled teeth, smooth surfaces, and no defects such as underfilling or cracking. The measured peak loads were 658 kN for the floating die and 534 kN for the hole split process, deviating from the simulation by less than 10%. This confirms the accuracy and reliability of the finite element model.
In summary, my numerical and experimental investigation into the precision forging of a straight spur gear has demonstrated that both the floating die and hole split methods effectively reduce die loads while maintaining high part quality. The floating die method reduces the peak load by about 10% by converting friction from resistance to assistance. The hole split method achieves a 25% reduction by providing a central relief path for metal flow. These findings offer practical guidance for die design and process selection in the mass production of straight spur gears. Future work will focus on optimizing the hole diameter and die velocity profiles to further enhance die life and process stability.