Nonlinear dynamic modeling of trochoidal milling with engagement loss-induced time-varying delay

Abstract

Engagement loss is a geometric-temporal switching mechanism that renders the chip thickness evolution nonsmooth and the delay state dependent and time-varying, thereby acting as a system nonlinearity. However, prior research has predominantly relied on regenerative chatter theory while neglecting the effect of cutter-workpiece engagement loss, resulting in inaccurate dynamic models for trochoidal milling. This paper develops a precise dynamic model for trochoidal milling that incorporates engagement loss effects and enables analysis of process nonlinear dynamics. First, the characteristics of the double trochoidal path are analyzed, and the mechanism by which engagement loss arises during milling is elucidated. On the basis of the above analysis, a novel numerical method is proposed to accurately calculate engagement loss rate resulting from variations in cutter-workpiece engagement conditions. Subsequently, a nonlinear dynamic model for trochoidal milling is developed using a time-domain simulation approach, which incorporates both time-varying delay and engagement loss effects. An adaptive prediction time-domain algorithm is then introduced, utilizing slope guidance to iteratively predict the initial axial depth of cut. The algorithm significantly narrows the search range for stability boundaries and enhances computational efficiency. Finally, the proposed model is validated through horizontal spiral and trochoidal milling experiments and compared with classical stability predictions. Results indicate that engagement loss reduces the overlap of regenerative waviness and modulates the effective delay, which weakens or intermittently breaks the regenerative loop and thereby raises the stability limit. The proposed time-varying mixed-delay dynamic model predicts milling stability with high accuracy.