Enhanced numerical integration methods for stability analysis of milling processes

This paper presents enhanced numerical integration methods for the stability analysis of milling processes within the integral equation framework. The dynamic equation governing the milling process, which accounts for the regenerative effect, is expressed in the form of an integral equation. The tooth passing period is divided into two distinct phases: free vibration and forced vibration. The time interval corresponding to the forced vibration phase is discretized into equal segments, each of which is further subdivided into two sub-intervals. Within each segment, the second-degree Lagrange polynomial is employed to interpolate the state term and the time-delay terms, respectively. By applying Simpson’s rule to approximate the integral term in the equation, the state transition matrix over one period is constructed. Milling stability is then analyzed using Floquet theory, and two computational schemes are provided. The effectiveness and computational efficiency of the proposed methods are demonstrated through benchmark examples. Additionally, milling experiments are performed to validate the methods.