Vibration suppression of thin-walled workpiece machining considering external damping properties based on magnetorheological fluids flexible fixture

Milling of the thin-walled workpiece in the aerospace industry is a critical process due to the high flexibility of the workpiece. In this paper, a flexible fixture based on the magnetorheological (MR) fluids is designed to investigate the regenerative chatter suppression during the machining. Based on the analysis of typical structural components in the aerospace industry, a general complex thin-walled workpiece with fixture and damping constraint can be equivalent as a rectangular cantilever beam. On the basis of the equivalent models, natural frequency and mode shape function of the thin-walled workpiece is obtained according to the Euler–Bernoulli beam assumptions. Then, the displacement response function of the bending vibration of the beam is represented by the product of all the mode shape function and the generalized coordinate. Furthermore, a dynamic equation of the workpiece-fixture system considering the external damping factor is proposed using the Lagrangian method in terms of all the mode shape function and the generalized coordinate, and the response of system under the dynamic cutting force is calculated to evaluate the stability of the milling process under damping control. Finally, the feasibility and effectiveness of the proposed approach are validated by the impact hammer experiments and several machining tests.