Abstract:
Hypoid gears are intended for transmitting the rotation between skew shafts and are characterized by higher loading capacity, ease of movement, and operation quietness. Base surfaces (axoids) of such a gear are hyperboloids of revolution of one sheet. The surface of the tooth of the input component $S$ is obtained by helical motion of a circumference around the detail axis of rotation with a simultaneous decrease in the radius of this circumference; at the same time, centers of circumferences of the family must lie on the axoid of the input component, i.e., form a helical line on this hyperboloid. In this work, exact analytical equations of the surface $S$ are obtained and the input component tooth surface is found as an envelope of the family of surfaces $S$. This family is formed by rotations of the surface S around the axis of rotation of the input detail with a simultaneous rotation around the axis of the output detail (after a shift to the distance between the axes). The first and second rotations are performed at angles $\tau$ and $-\tau/i$, respectively, where $i$ is the gearing ratio. Parametric equations of the tooth contact line as a regular curve along which the envelope is tangential to the surface of the family (the characteristic) are obtained.
Keywords:hypoid gear, envelope of a family of surfaces.
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