# Example of time-varying equivalent meshing of hypoid gears

At 3 000 n · The equivalent time-varying meshing parameters of hypoid gear in one cycle are calculated according to the above formula.

## 1. Time varying equivalent meshing point position

The position change of the equivalent meshing point is obtained, as shown in Figure 1. It can be seen that with the change of the meshing state of the hypoid gear, the equivalent meshing point moves on a small spatial curve near the middle of the width of the big gear tooth. Because the meshing parameters have periodic characteristics, the trajectory is a closed curve.

Further study the change curve of each coordinate component of the equivalent meshing point. As shown in Figure 2, the change of X coordinate is greater than that in the other two directions, because the distance of the meshing area moving along the long direction of the big gear tooth is greater than the tooth height direction in the meshing process of hypoid gear, and the tooth length direction of the big gear tooth in the meshing state is mainly along the x-axis direction of the global coordinate system.

## 2. Action direction of time-varying equivalent meshing force

It can be seen from Figure 3 that the action direction of equivalent meshing force of hypoid gear at each time is basically the same, and the specific change curve of each component in one cycle is shown in Figure 4, which changes with the rotation angle cycle of small wheel.

## 3. Linear displacement transmission error

The linear displacement transmission error curve in the action direction of the meshing force in the next cycle of the torque is further obtained, as shown in Fig. 5. The loading linear displacement transmission error is the main excitation causing the vibration and noise of the hypoid gear system.

## 4. Time varying equivalent meshing stiffness

The comparison curve of time-varying equivalent secant stiffness and tangent stiffness under this working condition is shown in Figure 6. The tangent meshing stiffness is larger than the secant stiffness obtained by the traditional method, which is consistent with the theoretical analysis in Figure 7. In the dynamic analysis of hypoid gears, the tangent meshing stiffness in the real meshing state should be used. 