THE MATHEMATICAL MODEL AND TOOTH SURFACE DEVIATIONS OF INTERNAL CONICAL GEARS

摘要

The internal conical gear investigated in this paper is generated by a shaping machine by inclining the shaper-arbor with respect to the gear axis. Applying the theory of gear meshing and differential geometry, the mathematical model of the internal conical gear is developed according to the gear shaping mechanism. Due to the tapered tooth thickness, the backlash of an internal conical gear pair can be easily controlled by axial adjustments without affecting its center distance. Besides, crowning effect can be observed on the generated tooth surface, which makes the bearing contact of an internal conical gear pair exhibits a point contact. The investigation shows that the tooth surface varies with the number of teeth of the shaper. Computer graphs of the internal conical gear are presented according to the developed gear mathematical model, and the tooth surface deviations due to the number of teeth of the shaper are also investigated.