# Establishment of three-dimensional geometric model of hypoid gear

In the current automotive hypoid gear processing methods, generally, when the large wheel cone angle is large, the forming method (HFT) or the generating method (HGT) can be used. When the large wheel cone angle is small, the generating method must be used, and the small wheel can be processed by the generating method. The most widely used modeling method of hypoid gear tooth surface is the conjugate surface method proposed by Litvin. Litvin studies the production process of hypoid gear, obtains the points on the hypoid gear surface through spatial transformation of the points generated by tool rotation during gear machining, and interpolates the discrete data points on the hypoid gear surface, High precision tooth surface can be generated. Medium u, θ Is the tooth surface parameter formed by tool rotation, ψ Is the rotation angle of tooth germ. The modeling process is described as follows: firstly, the tool coordinate vector is obtained according to the tool parameters, and then the coordinate transformation of the above vector is carried out to obtain the surface formed by the tool. Then, the tool surface is transformed into the hypoid gear coordinate system according to the machine tool parameters, and the meshing equation is obtained according to the hypoid gear meshing principle. Then, according to the fact that the point on the gear tooth surface must be on the gear tooth embryo, Finally, these discrete points are reconstructed by non-uniform B-spline curve (NURBS), and the three-dimensional digital model of hypoid large and small gears is obtained.

The HFT hypoid gear is analyzed, that is, the pinion is processed by the generation method, the large gear is processed by the forming method, the tooth germ parameters and machine tool processing parameters of the hypoid gear, and finally the three-dimensional CATIA model of the hypoid gear is obtained, as shown in the figure. 