基于瞬心线的谐波传动双圆弧齿形设计方法

Double circular arc tooth profile design method of harmonic drives based on centrodes

为提高谐波传动的啮合性能,提出一种基于轮齿瞬心线的成对双圆弧齿形设计方法.根据谐波传动轮齿瞬心线与其共轭啮合点的相伴运动建立齿形共轭、二次共轭及双共轭条件式,并依据瞬心线与双圆弧曲率特性推导出瞬心线、齿形曲率及其拐点相关的共轭区间连续条件式.以齿廓的起止啮合点与拐点为特定共轭点,将谐波传动双圆弧齿形设计问题转化为特定点共轭约束的成对同时设计问题,建立设计方法,并设计了一对三个特定共轭点的双圆弧新齿形,实现了共轭区间连续不间断.该设计方法几何意义明确,从原理上避免谐波传动齿顶干涉,不再需要圆弧拟合与齿形优化.啮合仿真表明所设计的一对双圆弧齿形在非共轭点位置有很好的啮合性能.

A method for a pair of double circular arc(DCA)tooth profile based on gear teeth centrodes was presented to improve the engagement quality of harmonic drives(HDs).Based on the adjoint motion between the gear teeth centrodes and conjugate meshing point of a HD,the conjugate condition,twice conjugate and double conjugate condition were established.Based on the centrodes and curvature characteristics of DCA,the tooth meshing continuous conditions in the range of conjugate points,related to the centrodes,tooth curvature and its inflection point were deduced.Tanking the beginning,end meshing point and inflection point as specific conjugate points,a pair of DCA tooth profile design problem was converted into that with the conjugate constraint of the specific points,and the design method was established.A pair of DCA new tooth profile was then designed with the three specific conjugate points to realize continuous meshing in the conjugation interval.This proposed method has clear geometric meaning,avoiding tip interference from mesh principle,without arc fitting and tooth profile optimization.The meshing simulation shows that the meshing performance of the designed pair of DCA tooth profile exhibits a good performance even at non-conjugate points.