Study on the bifurcation and catastrophe of metal cutting process

Bifurcation and catastrophe would emerge in some unstable process of metal cutting. It's principle and characteristics are analyzed based on a theoretical model of non-free-cutting, and verified through cutting test. The study reveals that: There is a fork domain (g _s1 , g _s2) for geometric parameter of cutting layer, and boundary points g _s1 and g _s2 are in the region of g′ _s = 1. It is the multi-extremum of cutting power that cause the bifurcation of chip ejection angle. The change of chip flow state in fork domain is a typical cusp catastrophe. The catastrophe and its lag phenomenon make a great effect on cutting force and chip form.