Spiral bevel gears and hypoid gears are on hypoid machine tools. The design principle of this machine tool is shown in figure 1: the shaking table mechanism on the machine tool simulates an imaginary gear, and the cutting surface of the cutter head installed on the shaking table is a tooth of the illusory gear. When the workpiece, that is, the machined gear rotates around its respective axis with a certain transmission ratio, the cutter head will cut a tooth slot on the workpiece wheel blank. The gear cutting process is like the meshing process of a hyperboloid gear. The cutting surface of the cutter head and the machined tooth surface are a pair of completely conjugate tooth surfaces. This method of machining spiral bevel gears and hypoid gears is called generating method. The false gear represented by the shaking table is called the production wheel.

Commonly used production wheels are divided into plane production wheels and conical production wheels, as shown in figs. 2 (a) and 2 (b). The cutter head axis of the plane production wheel is parallel to the shaking table axis, and the face cone angle of the plane production wheel accounts for δ 090 °. The cutter head axis of the tapered production wheel is not parallel to the shaking table axis, and the face cone angle of the production wheel is not equal to 90 °. The large wheels of spiral bevel gear pairs and hypoid gear pairs are usually machined by plane production wheels. In order to improve the production efficiency, the large wheels are machined by the double-sided method, that is, the double-sided cutters installed with inner and outer cutting blades are used to cut out the tooth surfaces on both sides of the gear at the same time. The methods of machining large wheels are development method and forming method. When the big wheel is machined by the forming method, the shaking table does not move, and the machine tool mechanism can be greatly simplified.

The small wheels of spiral bevel gear pair and hypoid gear pair can be machined not only by plane production wheel but also by conical production wheel. When a small wheel is processed with a tapered production wheel, the transmission ratio of the production wheel to the workpiece is usually constant. Only the machine tool with knife tilting mechanism can form a tapered production wheel, this processing method is called knife tilting method. In order to increase the degree of freedom of the production wheel, the transmission ratio between the production wheel and the workpiece can be changed to adapt to the tooth surface modification of the small wheel. This method needs to be machined on a machine tool with a denatured mechanism, so it is called the denaturalization method. The production wheel that processes the big wheel is called the big wheel, and the production wheel that processes the small wheel is called the small wheel production wheel. The tooth cutting calculation is to determine the nodal plane parameters of the two kinds of production wheel and the relative position between the production wheel and the workpiece, so that the machined wheel and the small wheel can mesh correctly.