In fact, the helical gear is installed on the support shaft. When the gear teeth transmit power through the support shaft, the bending deformation of the support shaft under the action of external torque is relatively large. The previous research on the contact strength of helical gears did not take into account the influence of the support shaft, especially when the support shaft is long and flexible. It can be seen that in the process of power transmission, the influence of support shaft stiffness on the whole power transmission can not be ignored. Therefore, the helical gear model with different support shaft stiffness is established to study the influence of support shaft stiffness on the dynamic contact stress of helical gear.

1. Helical gear model supported at both ends

The helical gear pair for contact analysis is the fourth gear pair of a heavy truck transmission. Its power transmission process is that the input helical gear transmits power to the fifth gear through helical gear meshing, the fifth gear transmits power to the fourth gear of the intermediate shaft through the gear shaft, and the fourth gear of the intermediate shaft transmits power to the output gear (second shaft fourth gear) through helical gear meshing. Because the helical gear shaft is connected with the helical gear and the bearing through interference fit, the amount of contact stress calculation of the helical gear is relatively large, so this paper simplifies the helical gear shaft and the helical gear as a whole, and the helical gear model supported at both ends is shown in Figure 1.

2. Helical gear model supported by rigid shaft

Since the helical gear model supported at both ends only defines a part of the shell element at the end of the helical gear shaft as a rigid body element, in order to ignore the influence of the shaft stiffness on the contact stress of the helical gear pair, all the outer rings of all helical gear shafts are defined as rigid body elements, that is, the shaft has only rotational freedom around the Z axis in the meshing process, as shown in Figure 2.

3. Multiple supporting helical gear models

Multiple supported helical gear models add a fixed support in the middle of the helical gear shaft on the basis of the helical gear models supported at both ends, that is, a part of the shell element in the middle of the helical gear shaft is defined as a rigid body element. The specific helical gear model is shown in Figure 3.