Mathematical Design and Meshing Analysis of a New Internal Gear Transmission Based on Spatial Involute-Helix Curve

We present a new internal gear transmission based on spatial involute-helix curve in this article. Firstly, the generation principle of spatial involute-helix curve is proposed according to gear geometry theory. Mathematical design model of the spatial conjugate involute-helix curves is provided through establishing the meshing relationship solved by relative velocity and specific normal vector at contact point. The equations of conjugated spatial involute-helix curve and line of action of contact curves are derived, respectively. Secondly, tooth profiles construction with spatial involute-helix curve pair is carried out by isometric offsetting and kinematics methods. General tooth profiles form and numerical example are proposed in terms of given design parameters. Furtherly, meshing analysis of generated tooth profiles are discussed. Center distance separability and axial errors action are discussed according to the theoretical derivation and simulation process. Contact stress analysis and the comparison are studied by finite element method. Finally, the experimental test of the new gear pair manufactured by CNC technology is provided and general transmission efficiency results and contact conditions of tooth profiles under different error conditions are displayed. Research conclusions show that the new internal gear drive has well transmission property and further study on the contact dynamic and error analysis will be carried out.