共轭曲面曲率参数的求解方法及其数值微分的应用

Application of the Solving Methods and Numerical Differentiation for Curvature Parameter of Conjugate Surface

求解共轭曲面的主曲率主方向是共轭曲面原理的一个基本问题。针对常规计算方法涉及中间变量多,求解过程繁琐,容易出错问题,给出了一种数值微分的计算方法。以空间交错轴传动准双曲面齿轮为例,建立了大小轮啮合坐标系,推导了大小轮共轭齿面方程,计算了共轭齿面的主曲率主方向。对常见的LITVIN法、诱导曲率法与数值微分法进行了对比分析。表明数值微分方法求解共轭曲面主方向和主曲率过程清晰明了,易于编程计算,且结果准确。

It is a basic problem to solve the principal curvature and direction of conjugate surface. Aiming at the complex and complicated problem of the conventional method to solve the principal direction and the principal curvature of conjugate tooth surface,a kind of calculation method to solve problem based on numerical differentiation is proposed. The meshing coordinate system is established and the conjugate tooth surface equations are deduced,with a pair of space staggered shaft drive hypoid gear as the research object. The calculation of principal curvatures and directions of conjugate surface of pinion is carried out. The advantages and disadvantages of common methods of numerical differential method,LITVIN method and the method of induced curvature are compared and analyzed. It is shown that the numerical differential method is clear and easy to be used in calculating by the computer,and this result is precise.