多项式曲线类二齿差活齿传动齿形设计及活齿动态响应分析

Movable transmission tooth profile design and tooth dynamic response analysis of two-tooth difference with polynomial curve

提出了五次多项式曲线类齿形设计方法,实现了二齿差纯滚动活齿等速共轭传动。建立复直角坐标系,依据凸轮廓线设计基本原理,建立五次多项式类齿形曲线方程,设计激波器廓线。基于转速变换和包络原理,推导出中心轮齿廓方程,并确立中心轮避免齿形干涉的设计条件,对中心轮齿顶凸齿形段最小曲率半径的影响参数进行分析,得到中心轮齿形曲率半径的变化规律。对所设计的活齿传动进行动态响应分析,建立动态响应分析方程,求解出活齿位移、速度、加速度响应,并给出活齿加速度响应谱。研究表明,高次多项式类二齿差纯滚动活齿传动齿形设计方法简单,动态响应快速、平稳。

A new design method of quintic polynomial curve tooth profile was presented to achieve two-tooth difference pure rolling movable tooth conjugate transmission. In the complex rectangular coordinate system, quintic polynomial tooth curve equation was established to design wave generator profile according to the design principle of cam contour. The tooth profile equation of center wheel was derived based on speed conversion and envelope principle. And the parameter design condition avoid interference on center wheel tooth profile was established, and the impact parameters on the minimum curvature radius of the center convex tooth top section was analyzed. Furthermore, the variation of center wheel curvature radius was obtained. The designed movable tooth transmission was analyzed to establish dynamic response equation. The dynamic response of tooth displacement, velocity and acceleration were obtained, and tooth acceleration response spectrum was derived. The study showed that the design method was simple and the new tooth transmission design had a good dynamic response and smooth transmission.