Reliability analysis of chatter stability for milling process system with uncertainties based on neural network and fourth moment method

Abstract

A reliability analysis of the milling system with uncertainties is developed in this paper to predict reliable chatter-free machining parameters. The chatter reliability refers to the probability of no chatter for the dynamic milling system. Then a reliability model is established to predict the chatter vibration, in which the dominant modal parameters of the dynamic milling system are defined as random variables. To solve the reliable model with the second-order fourth-moment (SOFM) method, the limiting axial cutting depth is substituted by an explicit expression obtained using a neural network. Therefore, after distributions of the random parameters are experimentally determined, the reliability of the given machining parameters can be computed with the SOFM method. Furthermore, a reliable stability lobe diagram (RSLD) can be plotted to obtain more reliable and accurate stable region instead of the conventional SLD. A case study is performed to validate the feasibility of the proposed method. The reliability of the milling system was calculated with the SOFM method, the first-order second-moment (FOSM) method and the Monte Carlo simulation (MCS) method. The results from the SOFM method and MCS method were found to be more consistent. Moreover, a RSLD with the reliability level 0.99 was compared with a conventional SLD plotted using the mean values of the random parameters. Chatter tests shown that the RSLD with the higher reliability level was more accurate for predicting the chatter-free machining parameters.