A novel scheme with high accuracy and high efficiency for surface location error prediction

Surface location error (SLE) caused by the forced vibration is one of the main factors limiting machining accuracy in stable milling. This paper presents a novel scheme with high precision and high efficiency to predict SLE based on the Newton polynomial-Chebyshev nodes. The dynamic model embodying the forced and regenerative excitations is first derived from the simplified milling process. After describing the response of the system with the direct integration format, the Newton polynomial frame is chosen to spread the self-excited and forced-excited elements successively in each equidistant time interval to obtain the separate output of tool vibration displacements with a close form. Then, the coefficient matrix which is not affected by the change of time is established in each spindle speed location to calculate SLE. Three examples which have been verified by the experiments are introduced to capture the optimal approximated order with exhibiting the characteristic of the proposed methods. It is observed that the prediction accuracy of the high-order methods drop seriously for the absence of Runge effect. In order to avoid this unwanted phenomenon, the origin uniform time joints are modified by a nonlinear sampling technique based on Chebyshev nodes to establish the novel coefficient matrix with fewer calculated loads for SLE prediction, and a series of comparisons illuminate the proposed modified method performs satisfactorily.