Floquet theory based approach for stability analysis of the variable speed face-milling process

This paper presents a new method for stability analysis of the variable spindle speed face milling process whose dynamics are described by a set of differential-difference equations with periodic coefficients and time varying time delay. Fourier analysis and Floquet theory applied to the system equations result in a characteristic equation of infinite order with constant coefficients. Its truncated version is used to determine the limit of stability by employing standard techniques of control theory. Analytically predicted stability boundaries are compared with lobes generated by time domain simulations. Experimental results are also presented that validate the proposed analytical method for chatter stability analysis. Finally, an example is presented that demonstrates the advantage of using spindle speed variation when machining a workpiece having multiple modes of vibration.