The formation process of the tooth surface of the logarithmic spiral bevel gear can be regarded as that when the meshing surface is pure rolling along the base cone, any logarithmic helix whose rotation center is in the center of the meshing surface will form a curved surface in space, so this curved surface is the tooth surface of the logarithmic spiral bevel gear, as shown in the figure.
The polar radius of logarithmic helix is the increasing or decreasing function of its polar angle. According to differential geometry and gear meshing principle, a mathematical model with unknowns is established θ The tooth surface equation of logarithmic spiral bevel gear is:
For the convenience of use, the vector form of theoretical tooth surface equation of logarithmic spiral bevel gear is obtained as follows:
Of which:
