Considering flexible manufacturing of large gears in small and medium batch productions, a five-axis CNC machine is a good choice because it is cheaper and easier to be obtained compared to a dedicated bevel gear cutting machine. Company Heller recently released a new cutting method for bevel gears on its five-axis machines. In this method, a disk milling cutter replaces a dedicated face-milling cutterhead. However, its mathematical model is not revealed due to commercial considerations. This research aims to establish a mathematical model of disk tool cutting method based on the target tooth surface. The tooth surface is first approximated using B-Spline surface fitting method for refining cutter-contact (CC) points. The mathematical model of cutting tool is established. The five-axis coordinates of table-table type five-axis machines are then derived through the inverse kinematics. Finally, an experiment is done to verify the correctness of the proposed mathematical models.
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