Theoretical Approximation of the Vibration in a Regenerative Cutting Process

ABSTRACT In this paper, the phenomenon of chatter vibration in metal cutting is investigated. For this purpose, a theoretical one-degree of freedom model of the vibrations generated in an orthogonal cutting process is developed. The dynamic cutting forces are strongly affected by the variations of the cutting process parameters, and the model is based on the mechanical theoretical prediction of the cutting zone. The developed model considers the variation of the rake angle, depth of cut, and a nonlinear model of the cutting force. An analysis of the differential equation obtained enables to determine the different types of oscillatory patterns that develop. A numerical solution by means of the fourth-order Runge-Kutta method allows the determination of the variation of the cutting force and rake angle as a function of time.