Profile of bevel gears with concave convex contact surface without backlash

The tooth profile of the driving and driven section of the linear gear pair is shown in the figure. The active tooth profile is composed of a section of circular arc, and the driven tooth profile is composed of two sections of equal radius circular arc. Arc AB is the positive rotating tooth profile, and arc BC is the reverse tooth profile. M1 and M2 are the meshing points corresponding to the positive and negative rotation of the linear gear pair.

According to the contact angle γ and the arc radius ρ, the parameter equation of the profile center line of the driving gear in the coordinate system S1 can be obtained as follows:

In the coordinate system S2, the centerline equations corresponding to the forward and reverse tooth profiles of the driven gear can be expressed as follows: