New approach in dynamics of regenerative chatter research of turning

•The models for the chatter dynamics in a turning process is discussed from impulsive dynamical point of view.•To investigate the chatter dynamics on such model, we apply the theory of flow switchability.•Our results give a convenient way to estimate the available parameters to keep the turning process stable.

In this paper, regenerative chatter phenomena in a turning process is discussed from impulsive dynamical point of view. By introducing the instantaneous pulse when vibration occurs and the vibratory condition set, we optimize the models and present a certain kind of second-order impulsive differential systems, which is a specific discontinuous dynamical system. Then we search for the general results of the nonoccurrence of chatter phenomena by discussing the number of the vibration pulse times, utilizing the method of flow theory in discontinuous systems and transversal property at the boundary. Our results give a convenient way to estimate the available parameters to keep the turning process stable.