Basic Theory on Tooth Contact and Dynamic Loads of Gears. 4th Report. Gear Pairs with Involute Helicoids and Their Conjugate Surfaces.

Abstract

When the location of gear axes, the ratio of angular velocities and a pair of tooth profiles without variation of bearing loads are given, there is the pair of tooth surfaces without variation of bearing loads which has the involute helicoid including one of the tooth profiles for one member and its conjugate tooth surface for the other, and is modified to make contact along the pair of tooth profiles. The involute helicoid, its conjugate tooth surface and the surface of action are presented by the algebraic equation, which enable to analyze the tooth action of all kinds of gears with the pair of tooth surfaces mentioned above, such as helical gears, crossed helical gears, conical gears, face gears, worm gears, bevel gears and hypoid gears, the last two of which are not developed yet but must be useful for quieter power transmissions between non parallel axes.