Abstract: Aiming at the problem of principle error of non-developable ruled surface, the error determination function of single tool axis position is proposed as the objective function, that is, the distance from each point on a single tool axis to the non-developable straight surface minus the square of the tool axis radius is minimum. In MATLAB, the SA-PSO (simulated annealing algorithm and particle swarm optimization) hybrid algorithm is used to solve it. The hybrid algorithm solves the problem of finding the optimal position of tool axis in the case of single tool position. By comparing the envelope errors of PSO algorithm and SA-PSO algorithm, it is shown that the undercutting and overcutting errors of SA-PSO hybrid algorithm are 14.7% less than the single particle swarm optimization algorithm. The feasibility of the method is verified by actual machining and surface error detection of blade finishing.