Time varying meshing stiffness principle of helical gear

When the potential energy method is used to solve the time-varying meshing stiffness of spur gear, the meshing stiffness mainly includes bending stiffness BK, radial compression stiffness AK, shear stiffness SK and Hertz contact stiffness HK The total meshing stiffness of the gear pair is composed of various parts in series. The expression of the meshing stiffness is shown in the following equations (1) and (2). The contact surface of the helical gear is different from that of the spur gear due to the effect of the helix angle, so the bevel gear is divided into the helical gear and the spur gear The gear is cut into n pieces of very thin pinion along the axial direction, and each pinion can be regarded as a spur gear. By establishing boundary conditions, the time-varying meshing stiffness of each piece of pinion is offset and superimposed to obtain the total time-varying meshing stiffness of helical gear.

The expression of the time-varying meshing stiffness of a single pair of gears is as follows:

The total time-varying meshing stiffness can be expressed as follows: