Chaotic Vibration of a Simple Model of the Machine Tool-Cutting Process System

Abstract

A study on a simple model of the machine tool—cutting process system is presented. As the system is non-linear and discontinuous, and exhibits intermittent cutting, non-linear dynamics techniques such as constructing bifurcation diagrams and Poincaré maps were employed to ascertain a quality of motion. Untypical routes to chaos and unusual topology of Poincaré sections were observed. New phenomena such as unidirectional bifurcation and births and deaths of periodic solutions were detected. It was also found out that the dynamic responses of the analysed system can be most effectively controlled by a magnitude of the cutting force.