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Tooth effects on assembling bending stress of flexible tooth rim in harmonic drive
Mechanism and Machine Theory ( IF 5.2 ) Pub Date : 2020-08-01 , DOI: 10.1016/j.mechmachtheory.2020.103871
Yunpeng Yao , Xiaoxia Chen , Jingzhong Xing

Abstract The maximum assembling stress in tooth rim mainly determines the ultra-high-cycle fatigue life of harmonic drive, which is a strength index in design. The present investigation aims to analyze the tooth effects on tooth rim's bending stiffness and stress concentration that affect the assembling bending stress. An analytical rack with detailed tooth geometries is constructed for calculating the bending stiffness of the rack via the integration of the second moment of varying-cross-area over an entire tooth pitch. The unknown equivalent tooth depth is determined by finite element analysis. Orthogonal simulations of stiffness coefficient and stress concentration factor are carried out numerically over rack models with two dimensionless parameters: relative root thickness and relative dedendum arc radius. The results show that the stress concentration factor varies parabolically with the relative dedendum arc radius and exponentially with the relative root thickness while the stiffness coefficient changes linearly with both parameters. Ultimately, characteristic formulae which provide general approaches to stiffness coefficient and stress concentration factor are concluded, and then verified by stress simulation of two-dimensional tooth rims and three-dimensional cup-shaped flexsplines, respectively.

中文翻译:

齿对谐波传动柔性齿圈装配弯曲应力的影响

摘要 齿圈最大装配应力主要决定谐波传动的超高周疲劳寿命,是设计中的一个强度指标。本研究旨在分析齿对齿缘弯曲刚度和应力集中的影响,这些影响会影响装配弯曲应力。构建了具有详细齿几何形状的分析齿条,用于通过在整个齿距上对不同横截面的二阶矩进行积分来计算齿条的弯曲刚度。未知的等效齿深由有限元分析确定。刚度系数和应力集中系数的正交模拟在具有两个无量纲参数的齿条模型上进行数值模拟:相对根厚度和相对齿根圆弧半径。结果表明,应力集中因子随相对齿根圆弧半径呈抛物线状变化,随相对齿根厚度呈指数变化,而刚度系数随两个参数呈线性变化。最后,得出了刚度系数和应力集中系数的通用方法的特征公式,然后分别通过二维齿圈和三维杯形柔轮的应力模拟进行验证。
更新日期:2020-08-01
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