Ball-end milling is widely used in five-axis high-speed machining. The abrupt change of tool orientations or rotary axes movements will scrap the workpiece. This research presents a smoothing method of rotary axes movements within the feasible domains of the rotary-axes space. Most existing smoothing methods of tool orientation or rotary axes movements employ the Dijkstra's shortest path algorithm. However, this algorithm requires extensive computations if the number of the cutter locations is large or the sampling resolution in the feasible regions is high. Moreover, jumps in the results obtained with the Dijkstra's shortest path algorithm may occur, because the optimization problem has to be converted from a continuous problem into a discrete problem when using this algorithm. The progressive iterative approximation (PIA) method incorporating smoothness terms is established as a gradient-based optimization method to smooth the rotary axes movements in this research. Then a gradient-based differential evolution (DE) algorithm, combining the global exploration feature of the DE algorithm and the local searching ability of the gradient-based optimization method, is developed to solve the smoothing model. The validity and effectiveness of the proposed approach are confirmed by numerical examples.

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