# Modeling of gear drive system with cracks

The centralized parameter method is used to establish the dynamic model of gear transmission system.This method has a small amount of calculation and is easy to iterate with the pre-and post-processing process. It is suitable for studying the time-varying characteristics of dynamic response and meets the research objectives of this paper.The centralized parameter method simplifies the system to a centralized parameter and considers the drive system as a series of springs, dampers and mass blocks connected together.Time-varying meshing stiffness due to crack growth is converted into an excitation applied to the system.

The gear drive system model is shown in Figure 1.The gears are arranged vertically along the engagement line. Gi (i=1, 2, 3, 4) is the theoretical rotation center of the gears respectively. The x-axis is perpendicular to the engagement line of the gears, the y-axis is parallel to the engagement line of the gears, and the z-axis is parallel to the direction of the drive shaft.Gear numbers 1, 2, 3 and 4 represent first-stage master and driven gears, second-stage master and driven gears respectively.

The differential equation of gear system dynamics can be expressed by equation (1):

{S {{{S *x+CxS\929;x+CxS929;x+KxSx=0MS y+CyS_x+KySy=0MS *y+CyS_y+KySy=Ctzezezezezezezezezezezezezezezezezein +KTheta TA Theta ++KTheTheTheta Theta Theta=RiCtzezezezezezezezezezezein 729;Theta+RiKtzezezezezezezezein Thein +RiKtThein Thein+IinThein+cin [in+cin (Theta929cout(theta_out_theta_4)+kout(theta out_theta 4)=Tout(1)

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