An internal meshing gear pair that includes double contact points is proposed by the authors. For further performance evaluation and engineering application, special machining cutters for generating tooth surfaces are studied in this paper. General formulas and mathematical models of tooth surfaces of the hobbing cutter for the pinion are derived based on the actual tooth profile. Solid models of the three-dimensional hobbing cutter are established and calculation formulas of deviation conditions between the ideal tooth surface and the generated tooth surface are deduced. Deviation analysis considering the parameters of helical angle and pitch circle radius is discussed. Numerical simulations of the hobbing process are also carried out. While for the internal gear, tooth profile of skiving cutter is designed and forming formulas of tooth surfaces of the skiving cutter are derived. Solid models of the three-dimensional cutter are established, and the deviation calculation method of tooth surfaces is also provided. The research results lay the essential theoretical foundations and engineering analysis for practical applications of the new internal gears.

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.