Spiral tool path optimization method for fast/slow tool servo-assisted diamond turning of freeform surfaces with highly form accuracy

Spiral tool path generation methods for ultra-precision diamond turning of freeform surfaces can significantly affect form accuracy and machining efficiency. However, there is no previous research treating the tool path generation as a multi-objective optimization problem. In this study, a multi-objective optimization method for tool path generation based on a novel surface analysis model was proposed for the first time. In this method, spiral tool path generation methods were uniformly described on the basis of the newly established surface analysis model. The relation between cutting point sampling details and the resulting form error of freeform surfaces was analyzed and simulated. Then, corresponding fitness function and constraint function models were established, and the non-dominated sorting genetic algorithm (NSGA-II) was used to solve the path optimization problem to obtain the pareto optimal solution of the cutting point sampling parameters. Next, based on the optimization results of tool path, machining simulations with experimental parameters were performed to evaluate the quality of optimized tool path. To demonstrate the effectiveness of the proposed method, turning tests of near-rotational freeform surfaces were attempted on single-crystal germanium using the optimization method and the measurement results demonstrated that the optimized tool path can achieve sub-micron form accuracy, which further verified the effectiveness of the proposed optimization method. The proposed optimization method has been further applied in the machining of larger diameter freeform optics.