A non-intrusive interval analysis method for chatter stability of uncertain milling systems

Abstract

A non-intrusive interval analysis method is proposed to evaluate the chatter stability of uncertain milling systems. First, the interval theory is introduced to establish the interval milling system dynamics model. Second, a novel contraction and expansion sampling strategy is proposed to obtain the upper and lower bounds of the stability lobes diagram (SLD) in the solution process inspired by the simplex method. Subsequently, a convergence mechanism is proposed based on the edge detection technique to improve the convergence rate of the bounds calculation of the SLDs. The mean square error and structural similarity of the two iteration results were calculated to control the iteration. In addition, the proposed method is non-intrusive. It can be employed by selecting the corresponding chatter stability analysis method according to the characteristics of different milling systems, without being limited to a specific analysis method. Finally, the accuracy and efficiency are verified by the examples of one and two degrees of freedom milling systems, and the feasibility of the proposed method is validated through experiments.