Analysis and Design of Machine Tool Chatter Control Systems Using the Regeneration Spectrum

This paper introduces a new concept in the analysis and design of machine tool chatter control systems, the regeneration spectrum. This development follows from a recognition of the fact that the stability analysis of time delayed systems such as machining systems is considerably simplified for large values of the time delay. The regeneration spectrum is a function of frequency whose definition is based on the system characteristic equation. Features of the distribution of the system characteristic roots in the s-plane are related quantitatively to the regeneration spectrum. Moreover, a quantitative measure of the degree of system stability is provided by the closeness of the regeneration spectrum peak to unity. Minimization of the regeneration spectrum peak is therefore the basis for determining controller parameters. The application of the regeneration spectrum to prior chatter control systems is illustrated. The use of the regeneration spectrum enables the formulation of the controller design problem as a multi-parameter optimization problem. Experimental work was performed to demonstrate the efficacy of this design methodology.