A method of identifying geometric errors for machine tools with 3 axes based on a set of sine functions using double ballbar

Geometric error is an important error source of machine tools. Quick, accurate, and convenient measurement of machine tool geometric errors is an urgent need to improve the accuracy of machine tools. Based on the ballbar’s circular trajectory test principle, this paper proposes a machine tool error identification method based on a collection of sine functions. Based on the multi-body system theory and the homogeneous coordinate transformation method, a mathematical model of the circular path error and geometric error of the machine tool with 3 axes is established. Using a collection of sine functions to fit geometric errors has a higher fitting accuracy than traditional polynomial function fitting methods. By designing five circular motion trajectories of the same radius with different centers in the test area, and assuming that each geometric error is a collection of sine functions, a parametric identification model for machine tool geometric errors based on the circular trajectory is derived. The particle swarm algorithm is used to search and solve the various parameters of the sine function collection, and finally, 9 linear errors and 5 angular errors of the machine tool are obtained. In order to verify the effectiveness of the method, simulation and test comparison experiments were carried out. The experimental results show that 4 linear errors and 1 angular error of the machine tools can be effectively obtained. The verification experiment results show that, compared with the measurement results of the laser interferometer, the maximum deviation of the measurement and identification results proposed in this paper is within 2.5 μm.