Effect of speed change on engagement position of fixed-shaft gear drive

It is assumed that the centre of both gears is rigidly supported.In the meshing state of tooth surface, the relationship between pressure angle of meshing point of gear 1 and speed is shown in the figure. In the figure, the origin of coordinate system o1xy is in the theoretical center position of gear 1 and the coordinate axis oy points to the theoretical center position of gear 2.The centre of the rotating coordinate system is the theoretical centre of gear 1 and rotates with the gear.P is the engagement point which varies along the engagement line AB.

As shown in the diagram, the instantaneous velocity at the engagement point is analyzed:

In the formula, Va, Ve and Vr are the absolute speed, the involved speed and the relative speed of the engagement point P respectively; 1 is the speed of gear 1, which defines the counter-clockwise positive and clockwise negative; o1p=r1i and r1i are the radii of the circle where the engagement point P is located.