An improved full-discretization method for chatter stability prediction

An improved full-discretization method (IFDM) based on the golden search is presented in this brief paper to predict stability lobe diagram (SLD). To begin with, the mathematical model of milling dynamics considering the regenerative chatter is expressed as a state space form. With the time delay being separated equally into a limited amount of elements, the time series expression is obtained by interpolating the integral nonhomogeneous term using linear approximation. Then, 2(N) order algorithm is adopted to resolve the exponential term into a real matrix, which avoids the exponential matrix that has to be calculated each time in scanning the plane comprised of axial cutting depth and spindle speed. Lastly, the golden search instead of traditional sequential search is applied to seek the crucial axial cutting depths corresponding to different spindle speeds, which can improve computational efficiency remarkably. The verifications with two classic benchmark examples demonstrate that the proposed method has higher computational efficiency.