# Calculation principle of stiffness excitation of spiral bevel gear

Stiffness excitation is the phenomenon that the time-varying meshing stiffness of the gear produces the dynamic meshing force of the gear and dynamically excites the gear transmission:

K (T) represents the dynamic comprehensive meshing stiffness in the process of gear transmission, and E (T) represents the transmission error. In order to continuously transmit power, the coincidence degree of spiral bevel gears is usually greater than 1, so there will be multiple teeth meshing at the same time.

Ki (T) is the meshing stiffness of a single tooth, and N is the number of teeth participating in meshing at a certain time. In order to accurately solve the dynamic comprehensive meshing stiffness, it is necessary to accurately solve the meshing stiffness of single tooth and the number of teeth participating in meshing at each instant. The mathematical expression of single tooth meshing stiffness is:

Where FN is the normal contact force acting on the tooth surface; UN is the comprehensive deformation of a single pair of teeth, which is the comprehensive influence of the contact elastic deformation UHI caused by local Hertz contact and the displacement UBI of the tooth contact position caused by tooth bending:

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