平面凸轮廓线分析中牛顿插值法的应用及其误差探讨

关于平面凸轮廓线设计,现有文献中推出的凸轮廓线方程式,一般均是以凸轮转角为参数的函数。但生产实践中要求凸轮廓线的向径是以向径角为参数的函数。本文讨论了应用牛顿插值函数解决这个问题。该法简便灵活,易于进行误差估算。通过设计实例,探讨了线性插值、抛物插值、三次插值和四次插值的精确度,进行了误差分析计算,为高速凸轮设计提供依据;还分析了凸轮廓线误差对从动件运动规律的影响,为凸轮廓线设计中制定向径公差和凸轮廓线测绘分析中制定向径测量精度提供依据。

THE APPLICATION OF NEWTON'S METHOD OF INTERPOLATION AND ITS ERROR ESTIMATION IN THE ANALYSIS OF PLATE CAM PROFILES

In the design of plate cam profiles, the cam profile equation generally takes the an- gle of cam rotation as the independent parameter. But the requirement of production practice rather takes the cam angle of radius vector as the independent parameter. In this paper, the problem is solved by using Newton's Method of interpolation, which is concise, easy and effective in error estimation. As for examples,the accuracy of linear, parabolic, cubic and quartic interpolations has been discussed, and tbe error analysis has been made. It provides the basis for the high-speed cam design. It analyzes the effect of the cam profile error on the motion of the cam follower. It also provides the basis for determining the radius vector tolerance of cam profile in cam design and the accuracy requirement of radius vector measurement in measuring the cam profiles.