The mathematical model of hypoid gear with split cutter face rolling cutting method is established. The three-dimensional model of small wheel is shown in Figure 1, the three-dimensional model of large wheel is shown in Figure 2, and the three-dimensional meshing model of hypoid gear is shown in Figure 3.

According to Litvin f l’s research, the symmetrical parabola transmission error curve can effectively absorb the linear error in the transmission process of spiral bevel gear, so as to reduce the vibration and noise in the transmission process. The ideal contact ellipse and transmission error curve can be obtained by adjusting the design and processing parameters such as the angle of the cutting table and the rotation center offset of the inner and outer cutter heads by the local synthesis method.

The TCA simulation results of the cycloid hypoid gear pair in this example are shown in Figure 4. The contact mark of the tooth surface is in the middle of the tooth surface, and the transmission error is symmetrical, which can meet the meshing transmission performance required by the design.