Prediction of the milling stability based on the Hamming linear multistep method

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Journal of Vibration and Shock ›› 2018, Vol. 37 ›› Issue (22) : 67-74.

ZHI Hongying1, YAN Xianguo2,DU Juan2,CAO Qichao2

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Abstract

To address the vibration phenomenon in milling process, the Hamming linear multistep method (HAMM) was proposed to predict the stability of milling process.The dynamic equation for milling process with regenerative chatter was expressed as a delay linear differential equation .The cutter tooth cycle was divided into forced and free vibration stages.The forced vibration stage was discretized and the HAMM was used to construct a state transition matrix.The stability of the system was determined based on the Floquet theory, and the corresponding stability lobe diagrams were obtained.The matlab simulation results show that the HAMM is an effective method to predict the stability of milling.With the increase of discretization number, the convergence rate of HAMMis faster than that of the first-order semi-discretization method(1st-SDM) and second-order full-discretization method(2nd-FDM).The HAMM with less discretization number can already reach the local discrete error of 1st-SDM and 2nd-FDM with more discretization numbers.In addition, for one and two degree-freedom dynamic models, the stability lobes diagrams by the three methods show that the prediction accuracy of the HAMM is better than that of the 1st-SDM and 2nd-FDM, and the computation efficiency of the HAMM is much higher than that of the 1st-SDM and 2nd-FDM.The experimental results also show that the HAAM method is effective for predicting the milling stability.

Key words

/ milling ；linear multistep method；stability lobe diagrams；Floquet theory

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ZHI Hongying1, YAN Xianguo2,DU Juan2,CAO Qichao2. Prediction of the milling stability based on the Hamming linear multistep method[J]. Journal of Vibration and Shock, 2018, 37(22): 67-74

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