Two novel prediction methods for milling stability analysis based on piecewise polynomial interpolations

Abstract

Chatter has been one of the major limiting factors leading to poor productivity and surface finish. The prediction of the stable cutting zones of cutting parameters is thus vital in machining. On the basis of piecewise polynomial interpolations, two efficient and accurate methods are developed in this paper for calculating the stability lobes. Firstly, the dynamic milling process with regenerative effect is modeled by delay differential equations (DDEs) with time-periodic coefficients. The principal period of system is easily separated based on the existence of any non-zero elements of coefficient matrix, and the forced vibration phase is equally discretized into a series of subintervals. Piecewise polynomial interpolations are adopted in two contiguous subintervals to estimate all parts of the DDEs. Secondly, the state transition matrix is formed to search for the borderline of stable cutting region based on Floquet theory. Thirdly, the convergence rates of the two proposed methods are analyzed through comparison with four existing algorithms. The results validate that the two proposed approaches achieve higher convergence rate, accuracy, and efficiency than the others within the same time intervals. Finally, the operability of the two proposed methods is verified by cutting tests, which indicate that the two proposed methods are of effectiveness and practicability.