State-dependent delay in regenerative turning processes

Stability of a two degrees of freedom model of the turning process is considered. An accurate modeling of the surface regeneration shows that the regenerative delay, determined by the combination of the workpiece rotation and the tool vibrations, is in fact state-dependent. For that reason, the mathematical model considered in this paper is a delay-differential equation 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.