# Load distribution coefficient model of involute spur gear at low speed

When involute spur gear works, it has to go through the process of single tooth meshing and double tooth meshing alternately. In single tooth meshing, the load transmitted by the gear pair is totally borne by one tooth pair, while in double tooth meshing, the load transmitted by the gear pair is jointly borne by two tooth pairs, as shown in Figure 1. In general, it is assumed that the load is evenly distributed between the two tooth pairs, which leads to a certain error in the obtained meshing tooth surface load. For the worn tooth surface, the change of tooth profile makes the tooth profile error, which further affects the load distribution of the meshing tooth pair. Therefore, a load distribution coefficient model considering the tooth surface wear is proposed.

The meshing diagram of Gear Considering wear is shown in Figure 2. Pb is the pitch of ideal base circle, HW is the wear amount of tooth surface, δ When the driven gear is fixed, the driving gear can rotate freely. Because the driving gear is loaded, it is meshed with the driven gear, resulting in the contact deformation of tooth pair 1 and tooth pair 2.

According to figure 2, the relationship between the deformation and meshing force of two pairs of gear teeth can be obtained

Where HW is a positive value (wear causes the material on the meshing tooth surface to be removed), EH is a function of the wear depth of all meshing tooth pairs, and ki (I = 1,2) is the deformation of the meshing tooth pair δ I and rotation angle of driving and driven gears θ Can be expressed as:

Where, Ki（ θ) In order to consider the single tooth meshing stiffness of wear, the energy method is used to calculate the load distribution coefficient of the master-slave gear by bending, shearing, compression and tooth base deformation

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