# Parametric modeling of spiral bevel gear

The tooth profile of spiral bevel gear is a spatial spherical involute, its tooth profile is a circular arc, and the tooth surface is a complex three-dimensional curved surface, so the cylindrical gear tooth profile modeling method is not suitable for spiral bevel gear, and it is difficult to obtain its accurate three-dimensional model, which hinders the development of simulation contact analysis of spiral bevel gear to a certain extent.

Wang Yuqing, Tang Jinyuan and others obtained the three-dimensional coordinates of tooth surface points through coordinate transformation by using the tooth surface meshing principle and the machining principle of spiral bevel gear, and then obtained the tooth surface piece model through a large number of tooth surface point fitting. This method requires a large number of spatial coordinate transformation and matrix operation, so it is more complex. Ran Zhaobo and others use the back cone theory to model with the method of plane involute instead of spherical involute. However, this method can only obtain the approximate tooth profile and can not meet the requirements of high precision. Lin Aiqin et al. Obtained the tooth model by establishing spherical involute on the end face of spiral bevel gear, and then stitching the tooth surface piece. However, this method can not ensure that the tooth profile in the direction of tooth profile is spherical involute. The accuracy of spiral bevel gear tooth surface is low, and it is easy to break the surface when importing the model into ANSYS.

(1) The forming principle of spherical involute of spiral bevel gear is introduced, and the coordinate equations of spherical involute and tooth profile are deduced.

(2) In CATIA, based on the equations of involute and tooth profile, the key points of each curve are established by law command, and then these key points are connected by split command to obtain each curve. Then, the multi section surface function is used to generate the cogging tooth surface sheet, and the cogging solid is obtained by cutting the tooth blank with the tooth surface sheet by split command, Then the whole tooth model is obtained by subtracting the cogging entity from the gear blank entity Boolean, so as to realize the parametric modeling of spiral bevel gear.

(3) Through the virtual assembly and interference inspection of spiral bevel gear in CATIA software, it is known that the three-dimensional model obtained by this modeling method will not produce interference phenomenon, meet the modeling requirements, and lay a foundation for the simulation contact analysis of spiral bevel gear.

The equations of spherical involute and tooth profile of spiral bevel gear are deduced. By adding auxiliary involute on the tooth profile and using multi section scanning, the tooth surface sheet is established to increase the accuracy of tooth surface. Then, the cogging blank is cut with the cogging sheet to obtain the cogging solid, and then the cogging solid is subtracted from the cogging solid to obtain the whole tooth model, so as to avoid the defect of surface breaking when the model is imported into ANSYS.

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