High efficiency and precision approach to milling stability prediction based on predictor-corrector linear multi-step method

Abstract

Regenerative chatter is the most important factor affecting the stability of the milling process. It is core for suppressing chatter and improving production efficiency to accurately and efficiently identify the stable region of milling chatter. Therefore, according to the theory of predictor-corrector, three predictor–corrector methods (PCM) are, respectively, proposed for the milling stability region by applying the fourth-order Adams-Bashforth-Moulton formula, Simpson formula, and Hamming formula. Firstly, the regenerative chatter milling process is described as a second-order time-delay differential equation (DDE) with periodic coefficients. Thus, the forced vibration time can uniformly be discretized as a time node set. Secondly, the fourth-order Adams-Bashforth formula is used to predict the displacement at every time node, whereas the fourth-order Adams-Moulton formula can be employed to correct this predicted value. In addition, the fourth-order Simpson formula and Hamming formula can also correct the predicted value. Thus, a higher precision discrete prediction-correction expansion is constructed for the transformation of DDE into the state transition express. The Floquet theory can be depended on to present the judgment criterion of milling stability. Moreover, finally, under the same milling process parameters, comparisons of both the stability lobe curve and the local discrete error curve show that the PCM has a faster convergence rate than the 1st-SDM (first-order semi-discretization method) and 2nd-FDM (second-order full-discretization method). This shows that the PCM can obtain better computational accuracy under the same discrete number, whereas the PCM is significantly higher computational efficiency over 1st-SDM and 2nd-FDM. Meanwhile, considering the actual machining environment, helix angle effect and multiple modes effect of the tool are analyzed; experimental verification considering multiple modes with helix angle further indicates the applicability of the PCM.