An Updated Method for Stability Analysis of Milling Process with Multiple and Distributed Time Delays and Its Application

Abstract

Predicting and avoiding the onset of milling chatter are desirable to reduce its harm to machine tools, workpieces, and cutters. This paper presents an updated method to complete the stability prediction for the milling process with multiple and distributed time delays. After the dynamic of the combination milling process with variable helix cutter (VHC) and variable spindle speed (VSS) is modeled as linear delay differential equations with multiple and distributed time delays, the presented method is applied to carrying out its stability prediction for the first time. By comparing with the existing researches and time-domain simulations, the effectiveness of the presented method has been validated. The influence and feasibility of the combination process on chatter suppression are explored and investigated for the associated one- and two-degree-of-freedom systems. Results show that the application of the combination process can realize a further suppression of milling chatter in practice. It can result in nearly 2-fold as high as the minimum depth of cut for the traditional milling or VSS milling and about 1.3-fold for VHC milling for some special domain, and can respectively lead to the average increase of stable area by 30.4%, 23.5%, and 1.5% for the adopted simulations. However, consider the contribution, the combination process is actually one process in which VHC plays an absolutely leading role but VSS plays an auxiliary role, in terms of milling stability.