This paper presents a systematic approach to enhance the load-bearing capacity of worm gear reducers through parametric optimization and finite element analysis. By establishing mathematical models and leveraging ANSYS simulations, we achieved a 17% improvement in structural load capacity while maintaining original dimensions and materials.
Mathematical Model of Tooth Root Bending Strength
The bending stress calculation for cylindrical gears provides theoretical foundation for worm gear optimization:
$$ \sigma_F = \frac{F_t}{b_m m_n} K_A K_V K_{F\beta} K_{F\alpha} Y_{FS} Y_\beta Y_\varepsilon $$
Where critical coefficients are determined through:
$$ K_V = N(C_{v1}B_p + C_{v2}B_f + C_{v3}B_k) + 1 $$
$$ K_{F\beta} = (K_{H\beta})^{N_f} \quad \text{with} \quad N_f = \frac{1}{1 + h/b + (h/b)^2} $$
$$ Y_\beta = 1 – \frac{\beta}{120^\circ} $$
| Parameter | Pre-optimization | Post-optimization |
|---|---|---|
| Normal Module (mm) | 0.5 | 0.5 |
| Worm Threads (Z₁) | 1 | 1 |
| Wheel Teeth (Z₂) | 40 | 39 |
| Pressure Angle (°) | 20 | 14.5 |
| Contact Ratio (εα) | 1.548 | 3.586 |
Finite Element Analysis and Verification
Critical stress components were analyzed through ANSYS simulations:
$$ \sigma_{contact} = \frac{2F}{\pi b} \left( \frac{1}{\rho_1} + \frac{1}{\rho_2} \right) $$
Mesh generation with 0.05mm element size revealed significant improvements:
| Performance Metric | Original | Optimized | Improvement |
|---|---|---|---|
| Wheel Root Stress (MPa) | 2,225 | 1,845 | 17% |
| Contact Stress (MPa) | 4,404 | 1,689 | 61.7% |
| Tooth Deformation (mm) | 0.0475 | 0.0425 | 10.5% |
Experimental Validation
Prototype testing under 20N·m load demonstrated:
$$ \tau_{output} = \frac{9550P}{n} \geq 20 \text{N·m} $$
Post-test inspection showed only mild wear patterns, confirming the worm gear’s enhanced durability while maintaining 65rpm rotational speed under maximum load.
The optimization strategy successfully balances geometric constraints and mechanical performance through systematic parameter adjustment and advanced simulation techniques, providing valuable insights for worm gear design in precision transmission systems.