Tool position control for three-coordinates NC milling with ball-end cutter considering geometric errors of machine tools

The important factors affecting the machining accuracy of machine tools are various errors of machine tools, among which the geometric error of machine tools is one of the main error sources. In order to eliminate the influence of geometric errors of machine tools on machining accuracy, the homogeneous coordinate transformation theory, rigid body kinematics method and topological structure analysis of machine tool kinematic chain are used to map the geometric errors of machine tools to the position errors of the ball head cutter center, taking the ball-end cutter three-coordinates NC milling as the research background.Based on the principle of forming the surface of a workpiece by milling with a ball-end cutter, a forward and reverse calculation model between the tool centre curved surfaces and the workpiece surface/design surface is constructed, taking into account the mapping between the geometric error of the machine tools and the tool centre position. The model is used to solve for a programmed tool centre curved surfaces that eliminates machine geometric errors, which is then imported into CAM software to obtain an NC machining program that eliminates machine geometric errors. The feasibility of the method is verified by the calculation and simulation of surface examples.