A prediction method based on the voxel model and the finite cell method for cutting force-induced deformation in the five-axis milling process

Abstract

When milling a thin-walled workpiece, knowledge of machining error due to the workpiece deformation induced by cutting force is crucial to ensuring the quality of the final machined part. In the current research of deformation prediction, the finite element method (FEM) is the dominant tool for calculating the deformation induced by the cutting force. However, FEM needs tremendous manual effort to generate a mesh of the in-process workpiece (IPW) and cannot be directly applied to discrete structured models such as the voxel or dexel models that are widely used for its advantage on parallel computation. In addition, a very fine mesh is needed for FEM to preserve the geometry of IPW, but it will lead to a huge global stiffness matrix. Therefore, it calls for a new method of fast deformation prediction in the milling of thin-walled workpieces. In this paper, aiming at the fast prediction of the deformation error of five-axis milling directly and efficiently on the voxel model, we present a prediction algorithm based on a combination of the finite cell method (FCM) and the voxel model. Specifically, in this study, a pipeline of FCM combined with the voxel model is specially designed for the efficient analysis of IPW deformation along a continuous tool path in the five-axis milling of thin-walled workpieces. By introducing a technique of partially updating the global stiffness matrix and the cells’ stiffness matrices, the proposed algorithm can tremendously reduce the FCM calculation time per sample point on the tool path, by as much as 19 times in our test examples. Both computer simulation and physical cutting experiments performed by us have convincingly verified the accuracy of the proposed deformation prediction algorithm. To our best knowledge, this is the first work of introducing FCM on the voxel model to the prediction of deformation induced by cutting force in milling problems, which enables customized tool path design and optimization in the five-axis milling of free-form surfaces.