Kinematics of point-conjugate tooth surface couple and its application in mixed mismatched conical worm drive

Abstract

The kinematics is developed and investigated deeply for the point-conjugate tooth surface couple. The formation principle of the conjugate tooth surface couple is studied by means of the kinematics, and the formation mechanism and law are revealed. The kinematic theory is established for the point-conjugate gear drive to measure its motion stability, in which the method to compute the angular acceleration of the driven gear is presented in detail. A novel kind of crossed-axis gearing that is convenient to be machined is proposed and named the mixed mismatched conical worm drive. The kinematic meshing quality is investigated for the worm drive by applying the established kinematic theory. The numerical results reflect that the transmission error of the worm drive is little and the adjacent error curves are intersectant. The angular acceleration of the worm gear is extremely small, and therefore the vibration and impact caused by the mismatch are weak for the worm drive. It is more reasonable that the curve of transmission error of the worm drive is a high-order polynomial curve since the angular acceleration is not constant.