Tooth surface equation of bevel gear without backlash

Take the point on the center line as the coordinate origin, fix the base vectors of the coordinate systems S0 and SP, and construct the main and driven section coordinate systems SC1, Sr1 and Sr2 for the x-axis, Y-axis and z-axis respectively. In the section coordinate system, the tooth profile equation is as follows:

In the formula, U1, ur1 and UR2 are parameter variables; ρ 1 and ρ 2 are tooth radius.

The positive and negative tooth surfaces of the driving gear pair and the driven gear pair can be expressed by the formula, namely:

Equation (9) – equation (11) is a function of parameters T and μ; μ is a parameter of circular section equation; t is a parameter of contact line equation, also known as the sweep parameter. In the process of generating tooth surface, each t corresponds to a unique circular section, and the set of all circular sections constitutes the driving and driven tooth surfaces.