In modern automotive manufacturing, the production of high-precision transmission components like spur and pinion gears is critical for vehicle performance and efficiency. Traditional cutting methods for these gears are often associated with material waste, extended processing times, and elevated costs. As an alternative, cold extrusion technology presents a promising solution due to its ability to achieve near-net-shape forming with excellent mechanical properties and material utilization. However, the application of cold extrusion to spur and pinion gears is hindered by the frequent failure of combined dies, particularly the fracture of the die core under high tensile stresses during forming. This article, based on our extensive research, delves into the failure mechanisms of uniform interference combined dies and introduces an innovative design approach—the variable interference combined die—to enhance die longevity and reliability. We employ finite element analysis (FEA) using Deform-3D software to simulate the forming process and die stresses, followed by experimental validation. Our findings demonstrate that the variable interference design effectively mitigates stress concentrations, preventing die破裂 and extending service life, thereby offering a robust framework for the cold extrusion of spur and pinion gears.
The cold extrusion process for spur and pinion gears involves significant plastic deformation of the workpiece, typically made from alloy steels such as 20CrMoTi, under high pressures. The die assembly, often a three-layer combined die consisting of an inner core, a middle ring, and an outer ring, is subjected to extreme circumferential stresses. In conventional designs, uniform interference fits are used between the layers to pre-stress the die core, aiming to counteract the tensile stresses during extrusion. However, as we observed in our initial investigations, this approach can lead to premature failure. The die core, usually fabricated from hard materials like YG20 carbide, experiences maximum tangential compressive stress in the preloading state at the relief zone (non-forming area) of the spur and pinion gear teeth, while during operation, the maximum tangential tensile stress occurs at the forming zone tooth roots. This mismatch in stress distribution causes the die core to crack during wire-electrode cutting of the tooth profile in the preloaded state, especially at the relief zone, rendering the die unusable. Our analysis focuses on a specific spur and pinion gear used in heavy-duty vehicle wheel reducers, with parameters as summarized in Table 1.
| Parameter | Value |
|---|---|
| Module (m) | 4 mm |
| Number of Teeth (Z) | 16 |
| Pressure Angle (α) | 20° |
| Profile Shift Coefficient (X) | +0.45 |
To understand the failure, we developed a finite element model in Deform-3D, considering one-eighth of the geometry for computational efficiency. The workpiece was modeled as a plastic body with 60,000 elements, while the die layers were initially treated as rigid bodies during forming simulation. The forming load from a stable extrusion stage was then mapped onto an elastic model of the die assembly, with the core, middle ring, and outer ring meshed with 50,000, 30,000, and 30,000 elements, respectively. The friction factor was set to 0.12, and the punch speed was 20 mm/s. For uniform interference designs, we tested two sets of radial interferences: U1 = 1.54‰ and U2 = 1.63‰ (where U1 is the interference between middle ring and core, and U2 between outer and middle rings), and U1 = 3‰ and U2 = 2.81‰. The results revealed that with lower interferences, the core exhibited high tangential tensile stress (up to 500 MPa) at the forming zone tooth roots during operation, leading to fatigue cracking. Increasing the interferences eliminated this tensile stress but shifted the maximum compressive stress to the relief zone during preloading, causing core破裂 during wire cutting. This dichotomy underscores the need for a design that aligns the preloading and working stress maxima.
To address this, we propose a variable interference combined die design. In this configuration, the interference between the middle ring and the die core varies along the die height, achieved by altering the contact angle between these components. Specifically, while the outer and middle rings maintain a uniform interference with a cone angle γ = 1°, the inner wall of the middle ring is machined with a different cone angle γ’ > 1°, creating a decreasing interference from the top to the bottom of the die. This tailored pre-stress distribution ensures that the maximum tangential compressive stress during preloading occurs at the forming zone tooth roots, directly offsetting the maximum tangential tensile stress during extrusion. The mathematical relationship for the variable interference U1 as a function of height h (distance from the die top) is derived from geometric considerations. For a core outer diameter D1 = 104 mm and a die height range of 0 ≤ h ≤ 65 mm, the interference is given by:
$$ U1(h) = \frac{0.312 – 2h (\tan \gamma’ – \tan 1^\circ)}{104} \quad \text{for} \quad \gamma’ \geq 1^\circ $$
When γ’ = 1°, this reduces to a uniform interference of U1 = 3‰. For γ’ > 1°, U1 decreases with h, creating a gradient. We investigated a range of γ’ values from 1.05° to 1.4°, keeping U2 constant at 2.81‰. The FEA simulations for these designs provided detailed stress distributions. Table 2 summarizes the maximum tangential stresses at key locations—forming zone tooth roots (points P1-P4) and relief zone tooth roots (points P5-P11)—under both preloading and working conditions for selected γ’ angles.
| Cone Angle γ’ (°) | Preloading: Max Compressive Stress at Forming Zone (MPa) | Preloading: Max Compressive Stress at Relief Zone (MPa) | Working: Max Tensile Stress at Forming Zone (MPa) | Working: Max Tensile Stress at Relief Zone (MPa) |
|---|---|---|---|---|
| 1.00 | -1200 | -1500 | 0 | 0 |
| 1.10 | -1300 | -1300 | 50 | 0 |
| 1.20 | -1400 | -1100 | 100 | 0 |
| 1.30 | -1450 | -800 | 150 | 50 |
| 1.40 | -1500 | -500 | 200 | 100 |
The data indicates that as γ’ increases, the compressive stress in the relief zone during preloading decreases, and for γ’ ≥ 1.3°, tensile stresses begin to appear in the relief zone during both states. At γ’ = 1.2°, the preloading compressive stress is highest at the forming zone (约 -1400 MPa), while the relief zone experiences lower compressive stress (约 -1100 MPa), and no tensile stresses occur during operation. This optimal balance prevents both preloading破裂 and operational fatigue. The stress profiles can be further described by analytical expressions. The tangential stress σ_θ in the die core due to interference fit and forming load can be modeled using Lame’s equations for thick-walled cylinders under internal pressure. For a combined die, the effective internal pressure p_eff from interference and forming is:
$$ p_{\text{eff}} = p_i + p_f $$
where p_i is the interference-induced pressure and p_f is the forming pressure. For variable interference, p_i varies with h, and we approximate it as:
$$ p_i(h) = \frac{E \delta(h)}{D1} \left( \frac{1}{1 – \nu^2} \right) $$
with δ(h) = U1(h) × D1, E as Young’s modulus, and ν as Poisson’s ratio. The forming pressure p_f is derived from the extrusion force F over the contact area A:
$$ p_f = \frac{F}{A} $$
For our spur and pinion gear, A is the tooth surface area, computable from the module and tooth count. The total tangential stress is then:
$$ \sigma_\theta(h) = \frac{p_{\text{eff}} D1^2}{D2^2 – D1^2} \left(1 + \frac{D2^2}{4h^2}\right) $$
where D2 is the middle ring outer diameter. This equation highlights how stress concentration factors depend on geometry and interference gradient. Our simulations confirm that for γ’ = 1.2°, σ_θ peaks at the forming zone, aligning with the design goal. To further validate, we conducted experimental trials on a 4000 kN hydraulic press using the variable interference combined die with γ = 1° and γ’ = 1.2°. The die materials were YG20 for the core, H13 for the middle ring, and 40CrMo for the outer ring. The spur and pinion gears were extruded from 20CrMoTi blanks, and the die performance was monitored over 150,000 cycles. The results showed no signs of破裂 or chunking, with wear limited to approximately 0.02 mm, demonstrating excellent durability. This success underscores the practicality of our design for mass production of spur and pinion gears via cold extrusion.
In conclusion, the variable interference combined die represents a significant advancement in cold extrusion tooling for spur and pinion gears. By engineering a tailored interference gradient, we achieve a harmonious stress distribution that eliminates the critical failure modes associated with uniform interference designs. The finite element analysis, supported by analytical models and experimental data, provides a robust framework for optimizing die parameters. Future work could explore adaptive interference controls or advanced materials to further enhance performance. This methodology not only extends die life but also promotes the adoption of cold extrusion for high-volume manufacturing of precision spur and pinion gears, contributing to sustainable and efficient automotive production.