An Analytical Investigation on the Ratio of Angular Velocity in Spherical Involute Bevel Gearsets

구형 인볼류트 베벨기어쌍의 각속도비에 관한 해석적 연구

The kinematical relationship of bevel gearsets lies at the root of the gear design. As the demand on precision bevel gears is increased in the related industries, the kinematic analysis of a pair of sperical involute bevel gears needs to be exactly evaluated for the computer aided design. Pitch cone angles of bevel gearsets have been calculated under the assumption that the geared system is equivalent to a coned roller system without slipping. But this kinematical model involves some errors in the value of the ratio of angular velocity. In this paper, the ratio of the angular velocity is exactly derived, based on the perfect involute tooth surface. Four nonlinear equations representing the kinematical relationships are numerically solved to obtain the pitch and base cone angles. The ratios of angular volocities according to pressure and shaft angles are calculated and compared with those of the approximate gear model.