A non-linear theory of machine tool chatter is presented. It is shown that even when the machinetool structure is linear or only slightly non-linear (as appears to be the case), large non-linearity is introduced by two causes. Firstly, by the chatter ampl

基于金属切削中的“最小能量原理”，研究了非自由切削的基本特征，探讨了现代切削加工中普遍存在的排屑干涉和排屑协调的现象与规律，提出以“单元刀具综合法”来建立复杂刀具的切削模型，并由此导出了制约排屑运动的普遍方程，分析了非自由切削的实例，理论分析与预测的结果得到实验数据和事实的验证，还得出了消除排屑干涉，实现自由切削的充要条件，并论述了“自由切削法”的基本思想和技术路线，为现代刀具的改进与优化寻求到一个可行的途径。

A new method for analysing, and calculating angles on cutting tools by means of projective geometry, vector algebra and matrix algebra is suggested. This method makes it possible to turn the solid geometry problem into a plane geometry one, and to deduce

The standard twist drills with curved edges are thoroughly studied in the light of anewly developed technique of displaying and analyzing space angles on cutting toolsin a projection plane [1, 2]. The study leads to a full understanding of the relationsbe