Interaction force between cross-torsion-pendulum coupling gear pairs in involute spur gear drive

Most gear dynamic models assume that the meshing force is evenly distributed along the tooth width direction, but during actual gear meshing, the interaction force between the teeth is along the tooth width direction due to the meshing deviation caused by shaft, bearing deformation and tooth direction error.

Non-uniform load on the meshing surface A1A2-B1B2.The force on gear 2 caused by gear engagement is opposite to the force on the gear in the same direction.When single and double teeth engage, the load distribution diagram acting on the gear along the direction of tooth width is shown in the figure.In order to facilitate dynamic modeling, meshing plane force system of gear pair is equivalent to meshing force Fm and offset torque T perpendicular to meshing plane.In the figure, the X-axis and Y-axis are symmetrical shafts of the meshing plane, the R is offset, and the offset torque T is:

In the formula, r>0 above the Y-axis and r<0 below the y-axis.