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.