螺旋锥齿轮齿面加载性能多目标优化

Multi-objective optimization of loaded spiral bevel and hypoid gears

针对螺旋锥齿轮齿面设计需进行多次试算的问题,提出了齿面加载性能多目标优化问题数学模型的建立及求解方法。建立了包含最大接触应力、加载传动误差、加载接触区范围和齿根弯曲应力的齿面加载性能多目标优化问题的数学模型;建立了考虑齿根弯曲应力计算的加载接触分析模型,用于计算优化问题中的目标函数和约束函数;采用Kriging代理模型结合多目标遗传算法对该优化问题进行求解;通过对驱动桥螺旋锥齿轮副进行多目标优化,实现了接触区完全位于理想接触区且无边缘接触,最大接触应力降低11.7%,加载传动误差降低27.9%,大小轮最大齿根弯曲应力分别降低2.0%和12.6%。通过对优化后的齿面进行驱动桥加载接触印迹台架试验,对接触区进行了验证,结果显示优化得到的接触区与试验结果吻合良好,验证了优化方法的可行性和正确性。

The loaded stresses in the tooth flank of spiral bevel and hypoid gears were optimized without a trial-and-error procedure in a multi-objective optimization model. The multi-objective optimization model was developed considering the maximum contact pressure, load transmission error, load contact pattern and the maximum bending stress. A semi-analytical loaded tooth contact analysis model for the root bending stress was developed to calculate the objectives and constraints. Kriging surrogate models of the objectives and constraints together with a multi-objective genetic algorithm were used to solve the optimization model. The model was then used to optimize a spiral bevel gear pair for a drive axle. The loaded contactpattern was completely in the ideal zone with the maximum contact pressure decreased by 11.7-, the loaded transmission error decreased by 27. 9% and the maximum bending stresses in the wheel and pinion decreased by 2.0%and 12.6%. The optimal design was installed in a drive axle for loaded contact tests that showed that the actual loaded contact pattern coincided well with the predicted loaded contact pattern, which verified the accuracy ofthe optimization approach.