Bifurcation analyses on the chatter vibrations of a turning process with state-dependent delay

Abstract

Bifurcation analyses are performed using the methods of multiple scales and harmonic balance in order to investigate the chatter vibration characteristics of a nonlinear turning system with state-dependent delay. In this study, the tool of the turning system is modeled as a two degrees of freedom oscillator and both the nonlinear stiffness and the nonlinear cutting force are considered. Prior to performing the bifurcation analyses, the nonlinear cutting force is appropriately expanded using a Taylor series, and an eigenanalysis is performed on the linearized system to obtain the linear stability boundaries. The bifurcation analyses are then performed and examined to explain the effect of state-dependent delay on the small- and large-amplitude behavior of the turning system. Analytic results derived from this study are validated through direct comparison with numerical results.