A Method of General Stiffness Modeling for Multi-Axis Machine Tool

In this paper, a new method for computing general stiffness model at tool tip for multi-axis machine tool is presented. The formula of general stiffness model at tool tip is derived from virtual-work principle and point transformation matrix method. Point transformation matrix method indicates the transformation relationship of elastic displacement on both ends of flexible axes as well as the transformation relationship of force. By multiplying the point transformation matrix, the final stiffness matrix at tool tip will be obtained efficiently. In this modeling method, the final stiffness matrix is composed of local compliance matrixes according to their contribution to the final stiffness matrix.