The Coulomb friction model with time-varying friction coefficient is given and introduced into the dynamic model of gear system, in which μ AVG is the average friction coefficient of tooth surface.

The friction coefficient of gear tooth surface is related to surface roughness, normal load per unit length of tooth surface, dynamic viscosity of lubricating oil, and so on. With the pitting failure of gear tooth surface and the deterioration of tooth surface pitting fault, the surface roughness of gear will increase, so the friction coefficient will also increase. The average friction coefficient of healthy gear is usually in the range of (0.03-0.06); in addition, the range of instantaneous friction coefficient of healthy gear is also given (0.01-0.06). In practice, it is difficult to measure the surface roughness and dynamic viscosity of lubricating oil, so the friction coefficient of healthy gear is set as 0.05.

As a result, the fault occurs only on the tooth surface of the other tooth surface where the friction coefficient of the tooth surface increases. The friction coefficient of pitting-1, pitting-2 and pitting-3 are set to 0.1, 0.15 and 0.2 respectively, and the friction coefficient increment is 0.05.