Geometric Error Modeling, Separation, and Compensation of Tilted Toric Wheel in Fewer-Axis Grinding for Large Complex Optical Mirrors

In ultraprecision grinding, especially for large complex optical mirrors, the geometric accuracy of grinding wheel plays a vital role and almost dominates the success of the entire grinding process. In this paper, a complete set of geometric error modeling, separation, and compensation methods of tilted toric wheel is established for fewer-axis grinding of large complex optical mirrors. Based on the kinematic equations with the assumptions of virtual axes for toric wheel, a mirror surface error model including all wheel error components is established, providing an error prediction for mirror surface. By linearizing the mirror surface error model and using the error information of mirror surface, solving and separating wheel error components are achieved. Then, the mirror surface with highly improved accuracy is obtained after the compensation of wheel trajectories with calculated wheel error components. Finally, the above method is well verified by the simulation.