Design and kinematics evaluation of a gear pair with asymmetric parabolic teeth

This paper presents design of imaginary spur and skew rack cutters having teeth of asymmetric parabolic profiles to generate spur and helical gear pairs, respectively. First, a mathematical model of the imaginary rack cutter having teeth of an asymmetric parabolic profile is derived using geometric relations and coordinate transformation. After the relationship between the coordinate system of the imaginary rack cutter and that of the gear pair is set up, a family of imaginary rack cutter surfaces is obtained using the homogeneous coordinate transformation matrix to transfer the coordinate system of the rack cutter to that of the gear pair. Substituting the equations of meshing into the family of imaginary rack cutter surfaces, a pinion and a gear are generated and their geometries are plotted using an in-house software package. Based on the derived mathematical model of the gear pair with assumed assembly errors, tooth contact analysis is performed to determine the influences of kinematic errors and the asymmetric tooth profile. A helical gear pair made by CNC machining is used to verify the influences of asymmetric parabolic tooth profiles on contact conditions and kinematic performance.