到锥面的射影变换及其在切削弧长锥齿轮的铣刀的性能研究中的应用(英文)

On Generating Catastrophe Circle and Generating Discontinuous Lines of AFace-Mill Cutter for Cutting Spiral Bevel Gears with Teeth of Constant Depth

文中借助于形象思维把齿轮的啮合几何化,提出了一种研究按滚切法工作的切齿刀具的方法,从节曲面到齿曲面的射影变换.这一方法与被加工的齿轮的特殊性无关,只与刀具和机床本身的结构有关。因而,计算和推导是简捷的,得到的结果对刀具和机床是固有的.文中还应用了奇异理论,着重于不存在、不连续、不可微、不正则的点集的分析,这虽带来无法应用成熟的数学工具的困难,但往往能发现渐变和突变的界限.应用以上方法和概念,文中得到了关于园锥形刀具的以下结果:(1)这种刀具被称为展成间断线的二母线和称为突变园的正截园划分四个不同功能的区域;(2)这种刀具具有加工出三种且只三种类型的齿曲面的本领。目前为止,人们只知道和应用了其中的两种;这里指出了一种新的尚待开发应用的性能,文中给出了其实施方案;(3)求出了目前通用的各种刀具加工范围。

In this paper we propose a method of projective transformation from pitch surface to cutter surface for studying face mill cutters.It is a short cut and intrinsic method because it is independent of the special features of produced gears and only dependent of the cutter and its pitch cone.Using this method and the catastrophe theory. We obtain the results: a face mill cutter has the abilities to produce three types of tooth surfaces and only the three, one of these remains to be used.The capacities of inside blade outside blade atlernate blade face mill cutters for cutting generated gears.