Chatter reliability of milling system based on first-order second-moment method

Abstract

In this paper, reliability analysis for dynamic structural system is presented to predict chatter vibration in a milling system. Chatter reliability is defined to represent the probability of stability (no chatter occurs) of milling system. Probability model (reliability model) of chatter vibration is established to predict milling chatter vibration, in which structural parameters and spindle speed are considered as random variables. Choosing chatter frequency as an intermediate variable, the reliability model is built. The first-order second-moment method is adopted to solve the reliability model of the milling process system to obtain the reliability level of the system. The reliability lobe diagram (RLD), which is a contour line with a specified reliability level as a function of spindle speed and cutting depth, is presented to designate the reliable region for chatter vibration prediction. A numerical example is used to demonstrate the method for reliability analysis. The reliability of milling chatter system was calculated using first-order second-moment (FOSM) method and compared to the Monte Carlo simulation method. The results from the FOSM method and Monte Carlo method were found to be similar. Comparing the results with the traditional stability lobe digram (SLD) method, chatter reliability of milling process system can be used to judge the probability of stability of milling process system. It can be concluded that RLD can be efficiently used to predict reliability in workshop applications.