Voxel-based end milling simulation of machining error induced by elastic deformation of tool and workpiece

Abstract

This study developed a voxel-based method to simulate machining error caused by elastic deformation of the tool and workpiece in end milling. The tool and workpiece shapes are represented by a set of cutting edge points and a voxel model, respectively. The cutting force is calculated based on the collision state between the cutting edge points and workpiece voxels. The elastic deformation is analyzed based on tool and workpiece elastic deformation models and the predicted cutting force. The tool deflection is predicted by a composite model of a cantilever beam and spring. In addition, each voxel representing the workpiece is connected to adjacent voxels using beam elements to build a stiffness matrix for the workpiece. The stiffness matrix and the predicted cutting force are used to predict the workpiece deflection. The predicted workpiece deflection is converted to tool distortion, which keeps the geometric relation between the tool and workpiece equivalent. By considering the tool deflection and distortion corresponding to the workpiece deflection, the cutting edge trajectory is simulated. Machining error can be obtained from the predicted cutting edge trajectory. The change in the workpiece shape is represented by removing voxels. The advantages of this method are that re-meshing is not required to update the workpiece shape change and that re-building the stiffness matrix is not time consuming. Additionally, both models to predict the cutting force and the deflection are linked closely to each other based on the voxel model. It is very important to consider the effect of the elastic deformation on the uncut chip thickness calculation in the cutting force prediction. Especially in the cutting of a thin wall, the effect of the elastic deformation on the uncut chip thickness in the cutting force prediction is quite large. The predicted machining error in the cutting operation of a thin wall had good agreement with the measured one in the experimental verification.

Keywords

• end milling
• thin-walled part
• elastic deformation
• machining error
• simulation
• voxel model