Stability prediction of variable pitch milling based on extended Hamming linear multistep method

Milling chatter is a main problem that reduces the quality and productivity of the workpiece. The variable pitch milling cutter, as an effective method for vibration reduction during the milling process, has attracted widespread attention. Therefore, predicting the stability of variable pitch milling stands as a pivotal issue in contemporary research. Aiming at the problem of multi-delay caused by variable pitch, this paper extends the Hamming linear multistep method (EHAMM) to predict the stability of milling systems with multiple delays. Firstly, the milling dynamic model considering the regeneration effect is transformed into state space form through Cauchy transformation. Then, the delay terms are linearly interpolated, the state transition matrix is constructed based on the Hamming linear multistep method, and the optimal critical cutting depths are solved by dichotomy. Finally, the stable lobe diagram (SLD) is obtained according to Floquet theory. The accuracy and effectiveness of the method were validated through comparison with existing methods. The results indicate that the algorithm exhibits high computational accuracy and computational efficiency