Hybrid Modeling of Position-Dependent Dynamics of Thin-Walled Parts Using Shell Elements for Milling Simulation

This article presents a hybrid model to update the position-dependent structural dynamic parameters of thin-walled workpieces as the metal is removed during machining. The initial workpiece is modeled by shell elements, and its full stiffness and mass matrices are used to solve the eigenvalues and mode shapes to predict the frequency response function (FRF) at a fixed location. The model is calibrated using the experimentally measured FRF, which reduces the errors contributed by the uncertainties in the material properties and damping values. The optimized finite element (FE) model is then perturbed at discrete cutting locations to obtain the updated natural frequencies and mode shapes of the part without solving the computationally prohibitive eigenvalue problem. The accuracy of the model is further improved by using either full FE solutions or experimental measurements of FRFs at a few intermediate steps which reduce the accumulated perturbation errors along the tool path. The proposed method is verified in five-axis milling of a thin-walled twisted fan blade. It is shown that using shell elements reduces the computation effort by ∼20 times compared to the conventional three-dimensional (3D) cube elements. The experimental calibration of the numerical model at a few discrete locations reduces the prediction error of natural frequencies by about 50%.