Boundary conditions between sliced gears

When calculating the meshing stiffness of helical gear by slicing method, because the tooth surface of helical gear is helical, the meshing process of a pair of gears is in the form of “point line point”. After splitting the gear, each piece of gear is offset relative to the initial gear. The angle change of the nth gear after offset is shown in the expansion diagram of indexing circle cylinder shown in the figure below The angle of the disc gear after offset can be expressed as follows:

Therefore, the total time-varying meshing stiffness of Helical Gear Considering spalling feature is: 1

The units of β, θ and θ n in the above formula are rad, and R is the radius of dividing circle of driving wheel.