A Voxel-Based End Milling Simulation Method to Analyze the Elastic Deformation of a Workpiece

Abstract

A new method to analyze the elastic deformation of a workpiece during end milling is proposed. One of the advantages of this method is the possibility of easily combining it with a voxel-based milling simulation, which is often used to predict cutting force, and to predict machining error due to workpiece deflection. With this method, the workpiece is discretely represented by voxels connected to their neighboring voxels with beam elements. Although the finite element method (FEM) is generally used for deformation analysis, it requires substantial time to analyze the deformation. In contrast, the proposed method does not require much time for remeshing, as the workpiece shape change is represented by removing voxels, and the stiffness matrix can be easily updated from the stiffness matrix obtained before the shape change. By conducting the preliminary analysis using coarse voxels and estimating the initial value of the solution, our method also reduces the number of iterations required to determine the deformation. The proposed method was integrated into the voxel-based cutting force prediction method in order to simulate the workpiece deformation caused by the cutting force. Therefore, the cutting force and the resulting workpiece deflection are seamlessly predicted using a voxel model. The results of a verification experiment showed that the analyzed workpiece deformation was in rough agreement with the measured deformation. Our future work is to predict the machining error induced by the workpiece elastic deformation based on this method and to integrate it with our previous work on the prediction of machining error induced by elastic deformation of the tool.