求解共轭齿形的轮转曲线等距偏移法

针对传统共轭齿形求解方法无法解决奇异点的问题,提出轮转曲线等距偏移法。分析了共轭曲线的等距偏移特性,推导出轮转曲线等距偏移线方程,基于该方程进行了圆弧齿廓的共轭齿形计算;采用圆弧逼近方式,以轮转曲线等距偏移线族求解任意齿廓的共轭齿形,并以含齿顶尖点的渐开线齿廓曲线为例进行共轭齿形计算;讨论了该方法的原理性误差,优化了该方法的求解精度。计算验证表明:相比于传统共轭齿形求解方法,轮转曲线等距偏移法能解决奇异点问题,且无需求解啮合方程,在齿廓曲线曲率半径变化率较小且存在奇异点时,用该方法求解共轭齿形优势明显。

An equidistant offset algorithm of rotation curve to solve conjugate gear profile

In order to solve the problem of singular point in the traditional algorithm for solving conjugate gear profile, an equidistant offset algorithm of rotation curve was proposed. The equidistant offset characteristics of conjugate curves were analyzed and the equations of equidistant offset line of rotation curve were derived. By way of arc approximation, equidistant offset line family of rotation curve was used to solve conjugate curves of any gear profile, and the involute profile curve with a cuspidal point of addendum was taken as an example. The principle error of this algorithm was analyzed, and a method to solve precise conjugate points was proposed. Compared with the traditional method of solving conjugate gear profile, the equidistant offset algorithm of rotation curve has no singular point problem, and there is no need to solve the meshing equation. It has obvious advantages in solving conjugate gear profile with singular points and small change rate of curvature radius.