In face gear transmission, the curvature radii of cylindrical gears on two orthogonal planes are 1k1 () and K2 () 1 respectively, the curvature radii of the contact points of face gears on two orthogonal planes are 1K (2) and K2 (2), and the intersection lines of the orthogonal main plane and the common section plane are coordinates (x1, Y1) and (X2, Y2), respectively. For the point contact face gear transmission, the contact ellipse is formed at the meshing point. According to the relationship between the main curvature of the contact point and the elasticity coefficient of two elastomers and the contact ellipse area, the long and short half axes X and y of the contact ellipse are respectively:
Where: MI and EI (I = L, 2) are Poisson’s ratio and elastic modulus of two gear materials respectively; coefficients u and V are elliptic integral functions; K (1) 1 and K (2) 1 are two principal curvatures of the tooth surface of the cylindrical gear at the meshing point respectively; K (2) 1 and K (2) are two principal curvatures of the tooth surface of the face gear at the meshing point respectively.
The area of the contact area can be determined by the radius of the ellipse.