Effects of helix angle and multi-mode on the milling stability prediction using full-discretization method

Regenerative chatter has a negative effect on the quality of machined surfaces in milling and it is thus vital to predict this accurately. The full-discretization method (FDM) is extensively utilized to predict the chatter stability. However, the effects of helix angle and multi-mode usually cause poor prediction by FDM and are often ignored. The existing fourth-order FDM has better computational efficiency and convergence rate than other existing FDMs. In this paper, a fourth-order FDM is optimized to improve prediction accuracy by considering both the helix angle and multi-mode. Based on the numerical stability computation results, it can firstly be observed that the stability lobe diagram (SLD) obtained using the proposed FDM has advantages over the existing SDM in the aspects of both the convergence rate and computational efficiency, and the effect of helix angle on the SLD is determined by both the number of teeth, radial immersion ratio and helix angle of the tool. Furthermore, a detailed investigation on how to detect chatter in milling experiments is made using an integrated method with time-frequency analysis. Finally, comparing the prediction result with the experimental milling results, it can be concluded that the proposed SLD with first three modes excels in prediction accuracy. A quantitative evaluation about the improvement of prediction accuracy is also made. The intention of proposing the updated FDM is to make the chatter prediction more accurate and efficient.