Arched transmissions teeth geometry within offset of initial profile

Abstract

There has been researched teeth geometry of cylindrical arched teeth gears, cut with rod instrument, teeth of which profiled by arbitrary curve in normal cross-section and in linear direction within initial profile offset. Toothing of instrumental rod with arched teeth with gears within initial profile offset is an analogue of the process of cutting teeth with rod instrument by means of enveloping. Surfaces of gear teeth within toothing with rod are enveloping of teeth surfaces of the last one. If teeth surfaces of instrumental rods for cutting pinion teeth and gear are non-congruous, then we have case of dotty toothing of pinion and gear. If initial profiles are non-congruous, then contact dot moves from one side of the tooth to another. It was obtained equations of teeth surfaces, while writing down coordinates of toothing surfaces in coordinate systems X1Y1Z1 and X2Y2Z2, connected with pinion and gear. While making such a transition, we have equations of surfaces of convex side of pinion teeth and concave side of gear teeth. In common case those equations are equations of helical lines of variable pitch. These equations can be used within the determination of toothing field borders, appropriate to the tops of the pinion and the gear teeth. Within this case two types of toothed gears with arched teeth will differ: gears with symmetric arched teeth (teeth are symmetric relatively to the plane XOZ and asymmetric arched teeth (working area of teeth surface is situated from one side of plane). Received results can be used within the determination of indices of loading ability and other characteristics of cylindrical arched transmissions with generalized teeth geometry within initial profile offset.