Design and meshing characteristics of curvilinear cylindrical gears with asymmetric teeth

Current research on curvilinear cylindrical gears primarily focuses on symmetric teeth, with little attention given to curvilinear cylindrical gears with asymmetric teeth. To investigate the impact of asymmetric tooth design on the meshing performance of curvilinear cylindrical gears. Two types of curvilinear cylindrical gear with asymmetric tooth are proposed. one is generated by a spread-blade cutter, and the other uses two different types of fixed-setting cutters to generate the concave and convex tooth surfaces of the gear respectively. The tooth profiles on both sides of the tooth of the proposed gear have unequal pressure angles, and the gear is asymmetric in the longitudinal direction. Two mathematical models of the gear tooth surfaces were derived based on the enveloping theory. A quasi-static finite element model of the gear pair was established for stress analysis, based on the mathematical model of the tooth surface. The influence of asymmetrical parameters, milling cutter radius, and other factors on the contact pattern, working pressure, bending stress, transmission error, and load distribution coefficient was investigated. The research shows that when the longitudinal asymmetry coefficient is 10 mm, the root bending stress increases by 21.5%, and the axial thrust force rises to 2.23 N. Reducing the pressure angle from 25° to 15° decreases root bending stress by 35%, transmission error fluctuation by 52%, and eliminates single-tooth contact. Smaller contact patterns reduce thrust force and improve gear performance. Larger contact patterns increase edge contact pressure and transmission error amplitude. The study suggests avoiding longitudinally asymmetric curvilinear gears and recommends gears with smaller pressure angles for smoother operation.