Mathematical model and deviation analysis of machining cutters for internal gears with double contact points

Abstract

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.