Machining systems stability analysis for chatter suppression and detection.

Abstract

One of the most significant factors adversely affecting the performance of machining processes is chatter. Variable spindle speed machining, mainly sinusoidal spindle speed variation (S<super>3</super>V) has been demonstrated to be effective in suppressing chatter. However, this technique has not been implemented widely in industry because there is no systematic way to select the proper amplitude and frequency of the aforementioned sinusoidal signal. As an alternative to S<super>3</super>V, multi-level random spindle speed variation (MRSSV) where the spindle speed is varied in random fashion within the maximum amplitude ratio allowed by the spindle drive, has been recently introduced. In this research, a new analysis method, based on Lyapunov Exponent for discrete time-varying systems, is developed to analyze the stability of machining systems with variable spindle speed, including S<super>3</super>V and MRSSV techniques. Next, a novel method to program an S<super>3</super>V signal for machine tool chatter suppression is presented. This method is based on varying the spindle speed for minimum energy input. The work done by the cutting force during sinusoidal spindle speed variation is computed numerically over a wide range of spindle speeds to generate charts from which the optimum S<super> 3</super>V amplitude ratio can be selected. For on-line application, a simple criterion to select the optimum amplitude S<super>3</super>V ratio based on the knowledge of the spindle speed and the chatter frequency is developed. A heuristic criterion to select the minimum effective S<super>3</super>V frequency is also proposed. Since on-line chatter detection and frequency estimation are critical for implementing spindle speed variation techniques, a normalized chatter detection index, which is independent of the cutting conditions and has excellent prediction accuracy and speed, is introduced. This technique utilizes the relation between the Teager-Kaiser nonlinear energy operator (NEO) and time-frequency (Wigner) distribution to characterize the significant transition in the cutting dynamics during the onset of chatter by the changes in the instantaneous energy of the machining system. In addition to chatter detection, this energy operator gives rise to a very efficient algorithm for computing the chatter frequency by estimating the frequency of the mode with highest energy in the time-frequency plane.