Dynamic model of spur gear pair considering random error and tooth surface friction

As shown in Figure 1, the 3-DOF bending torsion coupling dynamic model of spur gear pair is established by using the mass concentration method. The displacement of spur gear in the X direction is Xi (I = P, g), the displacement in the Y direction is Yi (I = P, g), and the displacement in the rotation direction around the spur gear shaft is θ I (I = P, g), X direction, Y direction and θ The direction is shown in Figure 1. The subscript p is the driving wheel and G is the driven wheel.

The displacement vector of mass point is:

Considering the tooth surface friction, time-varying meshing stiffness and random error, the corresponding bending torsional vibration equation shown in Figure 1 is:

Where, KXI is the equivalent support stiffness of the main driven gear in the X direction; Kyi is the equivalent support stiffness of the main driven gear in Y direction; Km (T) is the time-varying meshing stiffness of the spur gear; Ti (T) torque of main driven gear; RI (T) meshing curvature radius of the main driven gear along the contact line; Mi the mass of the main driven gear; II is moment of inertia; F (T) is the time-varying friction force under the random roughness of spur gear teeth; α Is the pressure angle of the spur gear pair; E (T) is the spur gear error.

ParameterDriving wheelDriven wheel
Number of teeth3326
Accuracy class6GJ6GJ
Mass / kg10.67.43
Modulus / mm77
Moment of inertia (/ kg ⋅ mm2)147 67061 426
Pressure angle (/ °)2020
Tooth width / mm6969
Input speed (/ R / min)2 0002 000
Input torque (/ N ⋅ m)2 340.72 340.7

The spur gear pair for a transmission is taken as the research object, and its parameters are shown in the table.

(a) Time domain curve of meshing stiffness
(b) Amplitude frequency characteristics of meshing stiffness

The time-varying meshing stiffness curve is calculated according to the numerical integration formula of Weber energy method, as shown in Figure 2.

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