Error calculation for corrective machining with allowance requirements

Abstract

Corrective machining is fundamental to obtain higher precision than the machine tool based on error inspection and calculation techniques. Generally, the error to be corrected is calculated by minimizing the material removal volume. However, there are often constraints for corrective machining, such as nonnegative error and allowance requirements, making it a constrained minimization problem. The basic algorithm for error calculation combines the alternating optimization method and the successive linearization method. Whereas, the sequence of objective function values is not guaranteed monotonously decreasing because of the local validity of linearization. Therefore, in the improved algorithm, the problem is reformulated as an inequality-constrained least square problem. Bound constraints are imposed on the optimization variables to keep local validity. Then, the line search and Palacios-type adjustment strategy are incorporated in each iteration in order to find a better point reducing the value of objective function. This point is chosen as the start of the next iteration. Finally, better convergence of the improved algorithm is verified by numerical simulations and a case of application in optical machining.