# Calculation of time-varying friction torque of helical gear

According to the previous analysis, the friction perpendicular to the meshing line will cause the friction torque around the rotation center of the driving wheel and the driven wheel. The friction torque is the product of the friction force and the friction force arm. The friction force has been calculated previously. Next, the force arm of the friction force between the meshing teeth of the helical gear driving wheel and driven wheel on each contact line is calculated. Assuming that the friction force is evenly distributed along the contact line, the friction force arm on each contact line is represented by the friction force arm at the midpoint of each contact line. The friction force arm at the left part of the contact line of a single pair of helical gears is expressed as:

Then the friction force arm on the left contact line of pitch line PP ‘at any time in one meshing cycle of helical gear meshing single tooth team is calculated and expressed as:

The friction force arm on the right side of the contact line of a single pair of helical gears is expressed as:

Then the friction force arm on the right contact line of the pitch line PP ‘at any time in one meshing cycle of the helical gear meshing single tooth pair is calculated and expressed as:

According to the friction torque of the meshing teeth of the helical gear driving wheel and driven wheel on each contact line is the friction force and friction torque, the torque expression of the friction force of the meshing teeth of the helical gear driving wheel and driven wheel on each contact line is calculated as follows:

According to the meshing periodicity of the helical gear system, the total friction torque of the pushable helical gear driving wheel and driven wheel in one meshing cycle:

In the process of helical gear meshing, the force on the tooth surface changes due to the existence of friction. The friction perpendicular to the meshing line will cause the friction torque around the rotation center of the driving wheel and driven wheel, and will affect the normal force of the contact teeth of the helical gear on the meshing line. The calculation expression is shown in equation 3.48. Where TP is the input torque of driving wheel.

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