Determination of the stability lobes with multi-delays considering cutter’s helix angle effect for machining process

Abstract

As a common phenomenon, chatter is one of the most important factors that inhibit the improvement of productivity and deteriorate the machined surface quality in milling process. In this article, the mathematical model of the dynamic machining process is first constructed with multi-delays, in which the effect of the cutter’s helix angle on the chatter is considered. And a new integral interpolation method is proposed to predict the stability lobes. Based on this method, the mathematical model which is divided into two parts is calculated respectively with an interpolation method and an integration method. Using the Floquet theory, the stability limits of the dynamic milling system for an arbitrary point can thus be precisely predicted. Subsequently, the convergence rate of this integral interpolation method is analyzed. In order to verify the mathematical model, the stability lobes with uniform and variable cutter pitch angle are computed and the results show a good agreement with published experimental data; also one experiment is conducted to validate the proposed model and the method. Simultaneously, the simulation of a stability lobe with non-zero helix angle is also performed and the results validate the fact that the proposed method is capable of predicting stability limits with high accuracy. Finally, the influences of the cutter and process parameters such as helix angle, pitch angle, down-milling or up-milling and radial cutting depth on the milling chatter are analyzed.