Frequency response curves of a spindle bearings system with non-linear and non-smooth terms

Abstract

This article presents results of vibrations of spindle system subjected to non-linear and non-smooth ball bearing stiffness. The averaging method, an approximate analytical technique, is applied directly to the non-linear and non-smooth differential equations of motion which ultimately leads to approximate analytical expressions for the frequency response relations of the system. The effects of ball bearing clearance and spindle structural damping on the frequency response curves are investigated. Hardening-type non-linear behaviours are observed in the ranges of base excitation frequency ω near the first, second and third natural frequencies. Crossing and breaking frequency response curves are also observed due to the non-linear and non-smooth properties of ball bearing stiffness. These solutions are clear indications that significant non-linear and non-smooth phenomena are of fundamental importance in the study of spindle bearing system. They also provide direct insight into the relationship between the system parameters and vibration characteristics of the system.