# Meshing point contact conjugate surface of spiral bevel gear

When two moving surfaces s (1) and S (2

When two moving surfaces s (1) and S (2) are driven, they generally belong to point contact conjugate surfaces. They have only one isolated point on the surface at any time.

Let the equation of surface s (1) be R1, the unit normal vector be N1, the equation of surface s (2) be R2, the unit normal vector be N2, and the radial vector between the origin of two motion coordinate systems be m. the contact trace can be determined by the basic equations. As long as there is no curvature interference, a contact ellipse can be determined at each contact position. The major axis of the contact ellipse is located in the direction of the minimum absolute value of relative normal curvature, and the minor axis of the contact ellipse is located in the direction of the maximum absolute value of relative normal curvature. The instantaneous contact ellipses of all contact points are calculated, and their collection constitutes the contact area on the tooth surface.

The transmission ratio of point contact common roller surface is not constant, which can be determined by the meshing equation. Let the angular velocity of surface s (1) be ω 1= ω 1p1, then the speed V1 of contact R1 on S (1)= ω 1Xr1= ω 1p1Xr1; Let the angular velocity of surface s (2) be ω 2= ω 2P2, then the speed V2 of contact R2 on S (2)= ω 2Xr2= ω 2p2Xr2; Their relative speed:

By substituting the meshing equation v12n = 0, their instantaneous transmission ratio can be obtained: 