The non-linear phenomena in vibration cutting system: The establishment of dynamic model

Abstract

It is well-known that vibration cutting is an effective method to cut materials with accuracy. However, it often suffers from unevenness of surface roughness caused by the non-linear vibration phenomena in tool–work vibration system. To solve this problem, we propose a vibration cutting model described by two-dimensional differential equations to analyze the non-linear phenomena. This non-linear model reproduces the basic features of the real vibration cutting systems, that is, the reduction of the cutting force and the displacement of work by pulsing of the cutting force. In this report, our experiment shows that various non-linear phenomena exist in the vibration cutting system. Our non-linear model for the vibration cutting produce behaviors which qualitatively agree with these various non-linear phenomena. These behaviors can be classified by the Lyapunov exponents.