# Normal load and normal contact stiffness model of gear transmission system with rough tooth surface

Let A1 be the contact area of the largest single asperity, and the contact of the tooth surface can be equivalent to that of two cylinders. Because the number of contact asperities of two cylinders is different from that of the plane contact, the area distribution function n (a) of the contact point of the tooth surface is: 1

Where:

L-contact length of cylinder;

R1, R2 – curvature radius of cylinder.

When A1 > AC, the contact point of asperity presents elastic-plastic contact state, and the total normal load is composed of elastic load and plastic load

When A1 < AC, the contact point of asperity presents plastic contact state, and the total normal load only contains plastic load

According to the relationship between the elastic load and the contact deformation of a single asperity in Hertz contact theory, the normal contact stiffness can be obtained by the differential of the elastic load on the contact deformation

The relationship between the total normal contact stiffness and the contact area is obtained by substituting the formula and combining the contact area distribution function

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