内齿轮剃齿刀齿向最小修形量的计算

本文采用单自由度线接触的方法和共轭曲面的运动学原理建立了计算内齿轮剃齿刀齿向最小修形量的数学模型,并进行了实例计算。由计算结果分析可知:内齿轮剃齿刀的齿向曲线已经不是螺旋线了,而是一个中凸的空间曲线,即是说,刀齿在齿长方向是变齿厚的。因此,内齿轮剃齿刀的齿面已不是螺旋面了。但由计算的结果可知:理论的内齿轮剃齿刀的齿向曲线与标准的螺旋线的偏离是很小的。因此,内齿轮剃齿刀的齿向曲线完全可以由标准的渐开螺旋面修磨而得到,从而为内齿轮剃齿刀的设计与制造提供了理论依据。

THE CALCULATION OF THE MINIMUM LONGITUDINAL MODIFICATION OF AN IN-TERNAL CEAR SHAVING CUTTER TOOTH

This paper presents a mathematical model for calculating the minmum value of longitudinal modification of the tooth surface of an internal gear shaving cutter using the ? single freedom degree and line contact method based on the kinetic principles of conjugating surfaces . A calculation example has been performed . From the analysis of the results calculated it is known that longitudinal curve of an internal gear shaving cutter tooth is not a spiral but a three dimensional convex curve , i.e. the thickness of the tooth is variable along its length Therefore , the surface of an internal gear shaving cutter tooth is not a spiral surface . But from the calculation results it is shown that the deviation of the thcoretical curve of the internal gear shaving cutter tooth from the standard spiral is so small that the longitudinal curve of the shaving cutter can be easily obtained by grinding the standard involute spiral surface . From this point of view , this paper provides thcoretical bases for the design and manufacture of internal gear shaving cutters .