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

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