An efficient and precise stability analysis method for milling process

Regenerative chatter is a detrimental self-excited vibration that significantly impacts machining efficiency and surface quality. This study presents a novel methodology for generating a stability lobe diagram for milling processes, utilizing the Lagrange polynomial and direct integration scheme. The delay and state terms of the milling dynamic equation are iteratively computed using second- and third-order Lagrange polynomials, respectively. Analysis of the convergence rate and fitting error demonstrates that the improved full-discretization algorithm offers superior accuracy compared to alternative approaches. Moreover, the proposed algorithm exhibits a computational speed that is 67.3% faster than the first-order semi-discretization method. The stability of milling, considering a specific combination of cutting parameters, is analyzed in the time domain, frequency domain, and through synchronous sampling. The obtained results consistently align with the stable lobe diagram constructed using the proposed algorithm. Experimental findings validate that the proposed milling dynamic model and algorithm are effective, which can provide a robust theoretical foundation for practical lobe diagram processing.