State-dependent delay in regenerative turning processes

Abstract Stability of a two degrees of freedom model of the turning process is considered. An accurate mod-eling of the surface regeneration shows that the regener-ative delay, determined by the combination of the work-piece rotation and the tool vibrations, is in fact state-dependent. For that reason, the mathematical model considered in this paper is a delay-differential equa-tion with state-dependent time delay. In order to study linearized stability of stationary cutting processes, an associated linear system, corresponding to the state-dependent delay equation, is derived. Stability analysis of this linear system is performed analytically. A comparison between the state-dependent delay model and the previously used constant or time-periodic delay models shows that the incorporation of the state-dependent delay into the model slightly affects the linear stability properties of the system in certain parameter domains