双圆弧谐波齿廓设计方法  

Design of Harmonic Drive with Double-Circular-Arc Tooth Profile

作　　者：杨玉虎[1] 何渠 解然 周国成 Yang Yuhu;He Qu;Xie Ran;Zhou Guocheng(School of Mechanical Engineering,Tianjin University,Tianjin 300350,China)

机构地区：[1]天津大学机械工程学院,天津300350

出　　处：《天津大学学报（自然科学与工程技术版）》2023年第4期346-354,共9页Journal of Tianjin University：Science and Technology

基　　金：国家自然科学基金资助项目(52075363).

摘　　要：针对双圆弧齿廓参数表征量多、圆弧尺度与设计参数关联度低的不足,提出一种根据柔轮齿与刚轮齿的相对运动特征设计双圆弧谐波齿廓的方法.首先,根据工况参数与柔轮中线变形曲线函数特征,分别在固定刚轮与固定柔轮两种形式下分析柔轮齿廓公切点的运动轨迹,提取其最大切向位移量作为齿顶圆弧的参数特征,并建立齿顶齿廓连续共轭条件及设计公切点倾角;在此基础上,根据给定的齿厚比与分度圆,分析切向位移量系数与公切线倾角对共轭啮合区间的影响,并结合连续共轭条件遴选合理的齿廓重要参数.其次,结合算例分析了传动比分别为80和100时柔轮齿与刚轮齿的啮合状态及性能,结果显示共轭齿廓能够实现连续啮合且不存在干涉.最后,结合有限元仿真校验齿廓啮合特性,结果表明:共轭存在角度为68.31°、单侧共轭齿对数为37对、啮合侧隙最大值小于10µm,有限元仿真与数值算例分析结果基本吻合,验证了本文设计方法的有效性.This study proposes a method for designing the double-circular-arc tooth profile of the harmonic drive,considering the relative motion characteristics between flexspline and circular spline teeth to address the problems of complex parametric characterization and low correlation between circular-arc and design parameters.First,according to the working parameters and deformed neutral curve function,the moving trajectories of the common tangent point of the flexspline tooth profile are analyzed for the fixed circular spline and fixed flexspline.On this basis,the maximum tangential displacement of the flexspline tooth is calculated as the parameter reference of the tooth top arc,and the continuous conjugate conditions for the top tooth profile are established for designing the obliquity angle of the common tangent point.The effects of the displacement coefficient and the obliquity angle on the conjugate-existing domain are researched with a given tooth thickness ratio and reference diameter.The important parameters of the tooth profile are selected according to the continuous conjugate condition.Secondly,the meshing condition between flexspline and circular spline teeth is demonstrated for the transmission ratios of 80 and 100.The calculation results show that the conjugate tooth profile can mesh continuously without interference.Finally,combined with finite element simulation to check tooth profile meshing characteristics,the extant conjugate domain is 68.31°,the number of conjugate teeth pairs is 37,the backlash is less than 10µm,and the finite element simulation and numerical example are consistent,validating the design method.

关 键 词：谐波传动 双圆弧齿廓 运动学分析 啮合特性 

分 类 号：TH132.43[机械工程—机械制造及自动化]