Design of noncircular gears to minimise shaft accelerations

This paper presents a novel pair of noncircular gear profiles for minimising shaft accelerations of the driven gear. The proposed profiles are developed based on an "exponential" function that is valid for a portion of gear rotation, and this function is extended to the remaining parts of the rotation of both gears. The exact shapes of the centrodes of the toothed bodies, which depend on a "smoothness" parameter, b, constitute a trade-off between the maximum shaft acceleration and the smoothness of the centrodes, so as to control the maximum tooth dynamic forces and stresses. A comparison between the derived noncircular gears and a gear pair that provides a sinusoidal variation of the angular velocity is presented. Results indicate that, for two-lobule gears, the maximum and minimum values of the polar radii, the velocity at the contact point, and the gear ratio are the same for both profiles. In contrast, there are significant differences in the angular acceleration of the driven gear, the tangential acceleration at the contact point, and the pressure angle, especially in the first one. It is concluded that the derived pair not only can provide low shaft accelerations, but also low tangential accelerations and small pressure angles.