Chatter stability analysis of the variable speed face-milling process

In this study, a solution technique based on a discrete time approach is pr esented to the stability, problem for the variable spindle speed face-milli ng process. The process dynamics are described by, a set of differential-di fference equations with time varying periodic coefficients and time delay. A finite difference scheme is used to discretize the system and model it as a linear time varying (LTV) system with multiple time delays. By consideri ng all the states over one period of speed variation, the infinite dimensio nal periodic time-varying discrete system is converted to a finite dimensio nal time-varying discrete system. The eigenvalues of the state transition m atrix of this finite dimensional system are then used to propose criteria f or exponential stability. Predicted stability, boundaries are compared with lobes generated by numerical time-domain simulations and experiments perfo rmed on an industrial grade variable speed face-milling testbed.