基于曲线优化提高齿轮弯曲强度的方法
Improving gear bending strength based on curve optimization

为了提高渐开线齿轮齿根的承载能力，结合啮合原理和APDL 语言对齿条型刀具展成的齿轮进行了参数化有限元建模。采用有理二次Bezier曲线替代齿轮原有的齿根过渡曲线，应用ANSYS内嵌的优化方法寻求有理二次Bezier曲线权因子的最优解使齿根弯曲拉应力最小，通过悬臂梁模型对优化结果进行解析计算并对啮合齿轮进行三维有限元接触应力分析。研究结果表明：对于给定参数齿轮，优化齿轮相对未优化齿轮齿根弯曲拉应力降低了约21%，解析计算结果与数值仿真结果基本一致，验证了优化结果的准确性；三维接触分析的等效接触应力基本不变而接触应力稍有减小，由于加载位置和有限元模型的不同，齿根弯曲拉应力降低的百分比有所减小。但综合来看，在齿面接触强度稍有提高的情况下，优化的齿轮比未优化的齿轮表现出较高的齿根弯曲强度，对齿轮的传动非常有利。
Gears are important components on the vehicle. Combined with meshing theory, parameterized finite element model was established by APDL to improve the involute gear bending fatigue strength. The research introduced rational quadratic Bezier curve to describe the gear tooth root fillet. Optimization method in ANSYS was used to optimize the Bezier curve to reduce tooth root bending stress. Analytical method was conducted to verify the results of optimization and three-dimensional contact analysis was used to analyze meshing gear. The results show that: For a given parameter gear, tooth root bending stress of optimized gear is reduced by about 21%, compared to the unoptimized gear. Analytical and numerical simulation results are basically the same and this verifies the optimization results; The equivalent contact stress is basically unchanged and contact stress of three-dimensional analysis is decreased slightly; Due to different load positions and different FEA, reduction percentage of bending stress is less than above. But in the whole, optimized gear exhibits higher bending strength than the unoptimized gear on the condition of slight improvement of contact strength which benefits for gear drive