Stability analysis for variable spindle speed milling via the 3^rd-order Newton-Cotes method

Structural chatter vibrations of machine tools are very complex nonlinear dynamic behaviors, which limit the machine tool productivity. Variable spindle speed milling is an efficient way to suppress chatter. This paper proposes a novel method for the stability analysis and parameter optimization of milling processes with periodic spindle speed variation. With the aid of the 3^rd-order Newton-Cotes formula, the time-varying delay differential equation is disassembled into two parts, and the relationship between the two parts is constructed by the transition matrix. The iterative calculation of the transition matrix only depends on the spindle speed. By comparison with other methods, such as the semi-discretization method and the reconstructed semi-discretization method, the proposed method has the advantages of high computational efficiency and prediction accuracy. Finally, milling stability boundaries, chatter frequency analysis, and modulation parameter optimization are carried out to further investigate the dynamic characteristics of variable spindle speed milling proposed in this work.