# Calculation method of time-varying friction force of helical gear

The friction force on the contact line of the helical gear. When the helical gear meshes through the node P, the direction of the relative sliding speed of the contact point of the gear teeth will be reversed, resulting in the change of the friction force direction between the tooth surfaces, as shown in the figure. According to the relative movement speed direction of the contact tooth to the tooth surface, the friction direction of the contact line on the left side of the pitch line acting on the driving wheel is assumed to be positive, then the friction on the right contact line is negative, that is, the friction direction on the left side of the pitch line PP ‘is the same, and the defined direction is positive; On the right side of the pitch line PP ‘, the friction direction is the same, and the defined direction is negative. The contact line at any time is divided into two parts, lleft and lright, bounded by the pitch line. They are in the area where the friction is positive and negative respectively. The total friction force received by the helical gear is the difference between the friction forces generated by the two parts of the line segment.

The length of single pair of tooth contact lines on the left of pitch line PP ‘can be expressed as:

Then the calculation expression of the length of the left contact line of the pitch line PP ‘of a single pair of helical gears at any t time is as follows:

The length of single pair of tooth contact lines on the left of pitch line PP ‘can be expressed as:

Then the length of the contact line on the right side of the pitch line PP ‘of a single pair of helical gears at any time t is calculated and expressed as:

Assuming that the load is evenly distributed along the length of the meshing line when the helical gear meshing pair is engaged, the contact line at any time is divided into two parts, lleft and lright, which are in the positive and negative regions of friction force respectively. The total friction force received by the helical gear is the difference between the friction forces generated by the two segments. The friction calculation formula of single pair of teeth is:

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

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