A spline-based method for stability analysis of milling processes

Based on the idea of collocation methods, a spline-based integration method for the stability prediction of systems governed by time-periodic delay differential equations (DDEs) is presented. A B-spline curve is adopted to approximate the solution of the DDEs using the direct integration technique. The stability of the dynamic system is then predicted using the Floquet theory based on the established state transition matrix. The proposed method can apply to time-periodic DDEs where the delay and the period are incommensurate, and the proposed method is extended to study the stability of milling processes as well. For stability analysis of variable pitch cutters, the proposed method use one or multiple B-spline curves to approximate the solution of the DDEs according to the relationship between the cutter angles and the radial immersion, which can describe exactly the free vibration of the cutter. Compared with the numerical integration method and the Chebyshev collocation method, the simulation results demonstrate that the proposed technique is more efficient and accurate for stability prediction at low radial immersion cases in milling processes with variable pitch cutters.