# Modeling of hypoid gear blank and tooth contact analysis

The large wheel of the hypoid gear is processed by generating method, and the small wheel is processed by denaturing method. For spiral bevel gears processed by any method, the tooth surface equations of large and small gears must be obtained before tooth surface contact analysis (TCA), and the establishment of gear tooth surface model is the basis for modern CAE analysis software such as analysis to deeply analyze gear characteristics. Based on the gear meshing principle and spatial transformation matrix, this chapter deduces the mathematical model of the tooth surface equation of large and small teeth, solves the tooth surface equation in MATLAB to obtain the point coordinates of the tooth surface grid, uses the point coordinates to display the tooth surface in SolidWorks, and finally establishes the three-dimensional solid model of the gear.

In the machining of hypoid gears, whether the machining parameters are reasonable or not is very important, which directly determines the gear transmission performance. In the traditional gear cutting calculation process, the processing parameters are adjusted according to the experience of the gear contact area. To obtain a gear pair that meets the performance requirements, it may need many times of trial cutting and detection, and it will take a lot of time. Using the computer to carry out the virtual tooth contact analysis (TCA) on the gear pair can greatly improve the productivity and reduce the workload. On the premise of determining the equations of large and small tooth surfaces, the tooth surface contact under different installation conditions is analyzed. If the tooth surface contact is not ideal, the machining parameters are adjusted to obtain the tooth surface that meets the performance requirements.

The transformation formula of coordinate system is given, and the machining coordinate system of large wheel and small wheel is decomposed and analyzed in detail. Through coordinate transformation, the tooth surface equations of large wheel and small wheel are finally established. By solving the tooth surface equations, the tooth surface coordinates of large and small wheels are obtained, and the wheel blank model of large and small wheels is established by using the Three-dimensional Modeling Software Solidworks. According to the tooth surface contact analysis principle of Gleason spiral bevel gear, the initial value problem of TCA solution is studied in detail, and a method to quickly determine the initial value is proposed. Finally, a complete TCA analysis is carried out on the concave surface of the big wheel and the convex surface of the small wheel of an aligned hyperbolic gear.