State dependent regenerative stability and surface location error in peripheral milling of thin-walled parts

Abstract

Chatter avoidance and error control are the core issues accompanying milling processes of thin-walled parts. Owing to the high flexibility of workpiece, the cutting vibrations can easily reach dozens of micrometers and become comparable to the nominal chip thickness. However, the classic dynamic models usually neglect the influence of system state on regenerative stability and surface location error (SLE), which consequently reduces the prediction accuracy. In this paper, the coupling relationships between cutter-workpiece engagement, time delay and system state are modeled by means of analyzing the true teeth trajectories that are composed of tool rotation, feed movement and cutting vibrations. The resultant dynamic model is a state dependent delay differential equation, which is capable of accounting for the fly-over and multi-regeneration nonlinear phenomena too. Afterwards, an efficient numerical algorithm is proposed to accurately compute the dynamic responses. By contrast to classic time domain simulation techniques, the proposed algorithm uses discrete root finding scheme to determine the state dependent time delay and the state dependent cutter-workpiece engagement, which ensures its high computational efficiency. Based on the proposed dynamic model and numerical algorithm, the stability limits and SLE are finally obtained, and experimentally validated on two thin-walled plates using two variable pitch tools. Theoretical comparison and experimental results reveal that the proposed state dependent dynamic model successfully predicts the milling stability and SLE while the classic model fails. The state dependency of regenerative stability and SLE is further investigated and explained in detail.