Time varying contact line load model for spur gears

The load distribution rate of spur gear in the double tooth meshing area near the root of the tooth is between 0.346~0.657, and that near the top of the tooth is between 0.334~0.666. The load distribution rate of single tooth meshing is 1. The load distribution of spur gears is related to the position of the meshing point of the tooth profile, but is not affected by the basic parameters of gears such as module and pressure angle.

The helical gear is divided into slice gears of unit length along the direction perpendicular to the axial direction of the gear. Each slice gear is considered as a spur gear. The tooth profile parameter variation d along the axial direction between the two slice spur gears ξ The relationship with the change DL of contact line length along the contact line direction is shown in the formula:

Then the load expression on the kth slice of the ith pair of teeth can be written as:

FIK load per unit length on the kth slice of the tooth, the expression is as follows: