A pair of hypoid gears refers to a pinion and a gear with skew axes. Hypoid gears are crucial to some power transmission systems, such as those of helicopters, power generation machines and automobiles. However, the design and manufacturing of hypoid gears are quite difficult. Currently, the major parameters of hypoid gears are calculated, but the geometries of the gears are not fully defined. To machine a hypoid gear, parameters of cutting systems are determined according to the gear design, whereas, settings of CNC machine tools with the machining parameters are also computed. The existing hypoid gears machining methods use the simplified blade model of the cutting systems, resulting in large errors in the machined gears. This new work proposes an accurate approach, to determine the parameters of the cutting system blades, for the face-milling of hypoid gears. In this work, a parametric model of the blades is established;​ and according to the hypoid gear parameters, the pressure angle and the cutting system radius are precisely calculated.

Currently, hypoid gear engineers can use special CAD/CAM software to design the gears and to calculate machine settings. Unfortunately, these software are developed only for particular machine tools;​ it cannot be used for hypoid gear machine tools of different configurations. Moreover, few technical articles has been published to clearly address challenges in the CNC programming and post-processing for the multi-axis face-milling of hypoid gears, such as the parameters determination of a cutter system, its location and orientation calculation and CNC programs generation. To solve the current problems, another part of this research proposes a generic approach to CNC programming and post-processing for gear face-milling. The main contributions of this part includes (1) a new mathematical model to calculate the cutter system location and orientation and (2) a generic post-processing method to establish the machine kinematics chain and to compute the coordinates of the machine axes in face-milling. This approach provides a general and accurate methodology for the face-milling of hypoid gears on any machine tools and can be directly applied to the hypoid gear manufacturing for better quality