Dynamic response prediction model of thin-wall workpiece-fixture system with magnetorheological damping in milling

In aerospace industry, the machining vibration of the thin-walled workpiece is a major factor affected the machining accuracy of the final part. Based on the analysis of the geometric structure features and vibration of thin-walled blade in milling, a complex compressor blade can be equivalent with a thin-walled plate with complex magnetorheological (MR) damping support and fixture edges constraints. Then, the inherent properties of the equivalent plate are calculated exactly considering the external damping effect. Further, a dynamic equation of the MR damping support fixture-workpiece system considering complex constraints is proposed using the Lagrangian method in terms of the calculated mode shape functions. Finally, the feasibility and effectiveness of the proposed approach is validated by experiments, and from the experimental results, it is shown that the average and variance of the predicted vibration displacement under 1A current are 0.1058 μm and 45.6711 μm² compared with that of measured value 0.3320 μm, 63.116 μm² without damping effect, and the prediction accuracy of the proposed model with damping effect is improved by 26.43%.