The extrusion forming process of cylindrical gears significantly improves production efficiency and mechanical strength compared to traditional machining methods. This study establishes a comprehensive framework combining finite element simulation, experimental verification, and material optimization to address critical challenges in gear manufacturing.
1. Metal Flow Characteristics and Strain Evolution
The radial displacement distribution of billet material during cylindrical gear extrusion follows:
$$ \Delta r = \frac{1}{E} \int_{0}^{t} \sigma_{\theta} dt $$
where Δr represents radial displacement, E elastic modulus, and σθ tangential stress. Numerical simulations reveal uniform displacement distribution across gear teeth regions (variation < 2.3%), confirming complete mold filling.
2. Die Wear Analysis and Process Optimization
The modified Archard wear model for cylindrical gear extrusion dies:
$$ W(T) = \frac{K(T)P(T)L(T)}{H(T)} $$
where temperature-dependent parameters include:
$$ K(T) = 29.29 \ln T – 168.73 \times 10^{-6} $$
$$ H(T) = 9216.4T^{-0.505} $$
| Upper Die Fillet (mm) | Billet Volume (mm³) | Max Wear Depth (10⁻⁶mm) |
|---|---|---|
| 4 | 215,432 | 2.41 |
| 6 | 221,567 | 1.83 |
| 8 | 228,912 | 2.15 |
Response surface optimization yields optimal parameters:
$$ \text{Minimize } W = 52.37 – 0.01885T – 98.255\mu – 4.0593V + 0.026T\mu + … $$
3. Advanced Die Material Development
The (Ti,W)C-based cermet composition demonstrates superior performance:
$$ \sigma_f = \frac{3FL}{2bh^2} $$
where σf represents flexural strength, F fracture load, and b/h specimen dimensions.
| Al₂O₃ Content (wt%) | Hardness (GPa) | Fracture Toughness (MPa·m⁰·⁵) |
|---|---|---|
| 0 | 18.02 ± 0.63 | 7.2 ± 0.31 |
| 15 | 19.01 ± 0.35 | 8.9 ± 0.29 |
| 30 | 17.15 ± 0.41 | 6.8 ± 0.27 |
4. Precision Die Manufacturing Technology
The reverse forming process achieves dimensional accuracy:
$$ \Delta D = \sqrt{\sum_{i=1}^{n} (d_{i,actual} – d_{i,design})^2} $$
With maximum tooth profile deviation < 0.83% and average dimensional tolerance of 0.47%.
5. Industrial Application Potential
The optimized cylindrical gear extrusion process demonstrates:
- Material utilization rate improvement: 22-28%
- Die service life prediction: ~11,000 cycles
- Production efficiency increase: 35-40%
This comprehensive research establishes a scientific foundation for high-precision cylindrical gear manufacturing, with significant implications for automotive transmission systems and precision machinery applications.