An efficient approach for milling dynamics modeling and analysis with varying time delay and cutter runout effect

An efficient approach for milling stability and surface location error (SLE) prediction with varying time delay and cutter runout effect is presented in this paper. Firstly, based on the tooth trochoid motion, the paper proposes a varying time delay model during cutter/workpiece engagement with taking cutter runout into account, establishes a milling dynamic model under arbitrary feed direction, and then derives the state transition matrix in one cutter rotation period by using the Cotes numerical integration formula. The milling stability of the dynamics system are obtained by using Floquet theory. According to the fixed point theory, the displacement response of the dynamic system and the method for solving the SLE are both developed. Later, a series of numerical and experimental works are conducted. The numerical verification shows that the proposed method can achieve a faster convergence rate and higher calculation efficiency than other previous methods. Meanwhile, the prediction of stability and SLE are in good agreement with the experimental results, and have a high accuracy for stability prediction when cutter runout and varying time delay considered. In the end, the numerical studies show that the milling stability and SLE strongly depends on the actual milling conditions, including milling parameters, cutter runout, cutter geometric parameters, and asymmetric structural dynamic parameters, which are helpful for milling process optimization.