Improved semi-discretization method based on predictor-corrector scheme for milling stability analysis

Abstract

Chatter has a detrimental effect on the milling process, which makes the chatter stability prediction very critical in milling. This paper presents a new semi-discretization method (SDM) based on predictor-corrector scheme to predict the stability of milling process. Firstly, the dynamic of the milling system is modelled by delay-differential equation (DDE), and the forced vibration duration is divided into many parts. Secondly, the DDE is integrated on the small time interval. The time-delay term and the periodic coefficient matrix are taken as an operator and approximated by second-order interpolation polynomial. And then, the state transition matrix is constructed based on predictor-corrector scheme. The proposed method is validated by comparing it with the benchmark. In general, the proposed method is superior compared with the benchmark in terms of the rate of convergence. Besides, the proposed method is also a robust method. The computational efficiency of the proposed method is proved to be good. For a one degree of freedom (1-DOF) milling system under full immersion condition, the stability lobe diagrams obtained by the proposed method are much closer to the reference than those obtained by the PCHDM and UNIM, especially in the peak of the lobes. The proposed method also can be used to predict the stability for a 2-DOF milling system accurately. It is also indicated from this study that the prediction accuracy of the SDM can be improved by combining the predictor-corrector scheme.