Prediction of the Milling Stability Based on the Implicit Adams Method

doi:10.3901/JME.2018.23.223

Abstract

Abstract: In view of the vibration phenomenon in the milling process,an implicit Adams method (IAM) is proposed to predict the stability of the milling process.The dynamic equation of milling process with regenerative chatter can be expressed as a delay linear differential equation.The cutter tooth cycle can be divided into the forced and free vibration stages;The forced vibration stage is discretized and the IAM is used to construct state transition matrix;The stability of the system is determined based on Floquet theory,and the stability lobe diagrams are obtained.Matlab simulation results show that IAM is an effective method to predict the stability of milling process. With the increase of discrete number,the convergence rate of the IAM is faster than the first-order semi-discretization method(1st-SDM) and the second-order full-discretization method(2nd-FDM).The IAM with the less discrete number can reach the local discrete error of the 1st-SDM and the 2nd-FDM with more discrete numbers.In addition,in one and two degree-freedom dynamic model,the stability lobes diagrams of three methods shows that the prediction accuracy of the IAM is better than that of 1st-SDM and 2nd-FDM,and the computation efficiency is much higher than the 1st-SDM,slightly higher than the 2nd-FDM.The results of the cutting test and simulation experimental results show that the prediction accuracy and reliability of the IAM are better than that of the 1st-SDM and the 2nd-FDM.

Key words: Adams method, Floquet theory, milling machine, stability lobe diagrams

CLC Number:

TH113

ZHI Hongying, YAN Xianguo, DU Juan, CAO Qichao, ZHANG Tangsheng. Prediction of the Milling Stability Based on the Implicit Adams Method[J]. Journal of Mechanical Engineering, 2018, 54(23): 223-232.

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