A coupling analysis model for chatter prediction of thin-walled workpieces considering the effects of force-induced deflection and material removal

In the milling process of thin-walled workpieces, the material removal can cause their changes in the dynamic parameters and stiffness of the workpiece. Moreover, the weak rigidity of the system itself can also lead to undesired force-induced deflection between the tool and workpiece which will deviate the actual radial depth of cut to from the nominal value. Therefore, it is necessary to consider the force-induced deflection and the variable of workpiece dynamic parameters in predicting accurately the milling stability. Firstly, a multi-point contact dynamic model is established for the flank milling of thin-walled workpieces. At every contact point, the improved calculation method of the tool-workpiece engagement angle is proposed by the force-induced deflection. It is more important that the influence of material removal on the workpiece stiffness is considered in the calculation of workpiece deflection. The elastic thin plate bending theory is first time adopted to efficiently calculate the workpiece deformation. Secondly, the finite element method is applied to deduce the stiffness and mass matrices of the elements and the whole structure. By modifying those of the corresponding elements along the feed path in the stiffness and mass matrices of the whole structure, a rapid approach to predict the time-varying dynamic parameters is proposed for the workpiece in the material removal process. Thirdly, in light of the predictor–corrector numerical solution theory of ordinary differential equations, the stability lobe diagram (SLD) prediction method is suggested to precisely analyze the milling chatter under the condition of the force-induced deflection and time-varying dynamic characteristics of the in-process workpiece (IPW). Finally, the milling experiment results indicate that the proposed method can be effectively used to predict the milling chatter in thin-walled workpieces. The 3D-SLD considering the force-induced deflection and time-varying dynamic characteristics of the IPW has the better prediction accuracy.