Optimal sequencing of rotation angles for five-axis machining

In this paper, we propose two new algorithms to correct the trajectories of the tool tip of a five-axis milling machine by adjusting the rotation angles in such a way that the kinematics error is reduced. The first algorithm is based on the shortest-path optimization with regards to feasible rotations of the inverse kinematics. The cost function is represented in terms of the total angle variation. We show that such an optimization increases the accuracy of machining and is the most appropriate in the case of a rough cut. The shortest-path procedure applies to either the entire set of trajectories or to only the most inappropriate undercuts inside the workpiece. In the latter case, the algorithm generates an interesting family of solutions characterized by smaller undercuts obtained at the expense of increased overcuts. The second algorithm also exploits the idea of the minimization of the angle variation. It is based on the uniform distribution of the cutter contact points with regards to the rotation angles. The method inserts additional tool positions by numerically finding a grid of points distributed uniformly in the angular space. We prove that the proposed algorithm in the neighborhood of stationary points requires 3-4 times fewer additional points than the conventional scheme. Also, if a maximum angular speed has been exceeded, the controller detects this event and reduces the angular speed. Our correction algorithms minimize the total angle variation, thus, reducing the probability of such an event. Finally, the efficiency of the two algorithms has been verified by a five-axis machine MAHO600E at the CIM Lab of the Asian Institute of Technology of Thailand and HERMLE UWF920H at the CIM Lab of the Kasetsart University of Thailand.