Experimental Verification of a Stability Theory for Periodic Cutting Operations

Abstract

The stability of periodic cutting operations, the dynamics of which are described by linear differential-difference equations with periodic coefficients, is studied. A new stability theory that uses parametric transfer functions and Fourier analysis to obtain the characteristic equation of such systems is experimentally verified. The theory is applied to single-point turning of a compliant work piece with two degrees-of-freedom. The theoretical predictions of both the critical depth of cut for chatter-free turning and the corresponding chatter frequency were found to be in good agreement with the measurements obtained from actual chatter tests under various surface speeds.

Simple Stability Analyses of a Regenerative Chatter Problem and of a Time-Delayed Displacement Feedback Sdof System

“…Most common techniques use the Nyquist criterion to establish whether a certain cutting configuration is stable or unstable [1,2].…”

Stability Analysis of Spinning Stepped-Shaft Workpieces in a Turning Process

“…This model can be used to explain the following three types of chatter: Arnold-type chatter, regenerative chatter, and mode-coupling chatter. Based on the model of Wu and Liu, Minis and Tembo [4] provided a set of cutting force equations to describe the variation of the cutting force as a function of the change in the inner and outer chip surface shape. In stability analysis, the cutting force is usually assumed to be proportional to the cross-sectional area of the chip for steady state cutting.…”