The meshing of helical gears can be regarded as line contact, and the load changes and distributes along the contact line. Therefore, the load acting along the contact line can be regarded as the joint action of concentrated load distribution at finite points. The larger deformation will bring about the change of stiffness and cause the vibration of helical gear transmission.
The time-varying meshing stiffness of helical gear pair can be calculated by using the change of contact line length instead of the change of instantaneous meshing stiffness of helical gear. The calculation formula is as follows:
Where: K0 – meshing stiffness of contact line per unit length.
Where:
Un – average deformation of helical gear meshing node（ μ M);
δ I – deformation of node i on contact line（ μ m) ;
F0 – normal force (n) of gear teeth during node meshing;
L0 – total length of contact wire when the driving wheel runs to the node (mm).
Calculate the time-varying meshing stiffness curve of helical gear according to the formula, as shown in Figure 3-10:
It can be seen that the stiffness of helical gear with friction is larger than that without friction, and the variation range is 7.46%.