超短筒谐波齿轮柔轮变厚度杯底的结构最优化设计

Optimum of super-short harmonic drive flexspline with variable thickness bottom

为降低超短筒柔轮的杯底应力,提出基于变厚度杯底的结构优化模型。建立实体单元参数化杯形柔轮模型,计算椭圆波发生器作用下的装配应力;在齿圈中面施加啮合力,求解传动状态的负载应力。通过对装配状态和负载工况下杯底最高应力的参数敏感性分析,找到降低应力的结构参数;提出用三次样条函数表达变厚度杯底的柔轮参数化模型,并编写复合形法APDL优化程序进行杯底断面形状优化,以继续降低杯底应力;应用ANSYS内置的零阶和一阶优化程序对装配应力优化结果进行验证。研究发现:超短筒柔轮的杯底最高应力远超规范规定的齿圈应力值;通过变厚度杯底设计和减小杯底倒圆半径,可降低最高装配应力和负载应力。

In order to reduce stress in the bottom of super short flexspline, a structural optimization model for flexspline with variable thickness is proposed. A parametric model of cup-shaped flexspline with solid element is established to calculate the assembly stress under the action of elliptical wave generator. The transmission stress is solved by applying the meshing forces in the middle plane of the tooth ring. The structural parameters lead to the minimum stress are found by sensitivity analysis of the maximum stresses in the cup bottom under assembly state and transmission state, respectively. A parametric model of the flexspline with variable thickness is presented with cubic spline function, and the shape optimization of the bottom section is built with APDL program of complex method, so as to reduce the bottom stress further. The optimization result of assembly stress is verified by using the built-in zero-order and first-order optimization program of ANSYS. It is found that the maximum stress in the cup bottom is higher than that in the tooth ring in national design specification. The maximum assembly stress and transmission stress can be reduced by designing the variable thickness bottom and smaller fillet radius of the cup bottom.