Abstract:  In order to accurately evaluate the meshing characteristics and differences between the two meshing regions of nutated double-arc bevel gear pairs, the curvature and relative motion parameters that characterized the quality of gear transmission were theoretically calculated and studied. Firstly, the tooth surface mathematical equations of double circular-arc internal and external bevel gears were derived based on gear spatial meshing theory of gear meshing. Secondly, a meshing coordinate system of nutation drive was established and the meshing contact points under ideal installation conditions were obtained by using tooth contact analysis (TCA). Then, the mathematical expressions of the curvature and velocity at the contact point were derived based on differential geometry, and the contact region was determined with Hertz elastic contact theory. Finally, the principal curvature, induced normal curvature, entrainment velocity, relative sliding velocity and slide-roll ratio of the meshing gear pair were analyzed by an example. The results indicate that the induced normal curvature of the elliptic long-axis direction is close to 0, and the absolute value of the induced normal curvature of the short-axis direction is small, combining with the public law vector direction of the tooth flank, it is known that the curvature interference phenomenon doesn't occur in the meshing process and the gear pair has good contact strength. Meanwhile, the relative sliding velocity is much smaller in value than the entrainment velocity, which is beneficial to reduce wear of tooth. The slide-roll ratio in both meshing areas approaches 0, indicating that the transmission is approximately pure rolling. The contact points and regions are located in the middle of the tooth surface and distributed along the direction of the tooth width; the finite element results are consistent with the theoretical calculations. The results of this study provide a theoretical basis for the elastohydrodynamic lubrication and wear analysis of nutated double-arc bevel gears.
Key words: gear transmission; double circulararc tooth profile; nutation drive; tooth contact analysis (TCA); induced normal curvature; slideroll ratio; meshing characteristics