On-machine measurement method and geometrical error analysis in a multi-step processing system of an ultra-precision complex spherical surface

In the field of ultra-precision machining, the machining accuracy and the surface quality have increased with the demand. However, due to the varying needs of different fields, the requirements for the surface shapes of workpieces are complicated. Therefore, it is necessary to use multi-process processing methods to process complex curved surfaces. However, determining how to ensure the repeated positioning accuracy of multi-process machining has been an insurmountable problem in the field of ultra-precision machining. In this study, a repeated positioning method for the processing of complex spherical surfaces was designed, and the geometric errors were analyzed. This study was based on an ultra-precise five-axis turning and milling machine. First, the processed workpiece was repeatedly clamped and the workpiece was measured by an on-machine measurement method. By processing the detection data, the position error and the pose error after repeated clamping were obtained. Then, using the detection results of the various geometric errors of the ultra-precise five-axis machine tool, random simulation experiments were performed using the homogeneous transformation matrix (HTM) and multi-body system (MBS) methods. A large number of random simulation experiments predicted the theoretical range of errors in the repeated positioning process. Finally, the processing experiment was carried out according to the designed process. The results showed that this approach could effectively solve the problem of repeated positioning in ultra-precision machining. In addition, the results of the machining experiment were in the range of the calculated error theory, which proved that the calculation model was reliable.