Geodesic
Modeling of teeth surfaces of contacting details of a hypoid gear
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 48 (2017), pp. 30-35

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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.
Mots-clés : hypoid gear
Keywords: envelope of a family of surfaces. 
N. R. Shcherbakov; A. A. Shchegoleva. Modeling of teeth surfaces of contacting details of a hypoid gear. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 48 (2017), pp. 30-35. http://geodesic.mathdoc.fr/item/VTGU_2017_48_a2/
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[1] Shcherbakov N. R., Shchegoleva A. A., “Tangency of one-sheeted hyperboloids as axsoids of the hypoid gearing”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mechanika - Tomsk State University Journal of Mathematics and Mechanics, 2017, no. 47, 37–42

[2] Ljukchin W. S., Teorija ogibajushej semejistwa poverchnosteji, M., 1963, 267 pp.

[3] Shcherbakov N. R., Zakharkin N. V., “Geometrical simulation oft the surface of the detail oft he driving gear as envelope”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mechanika - Tomsk State University Journal of Mathematics and Mechanics, 2012, no. 4(20), 50–55

[4] Zalgaller W. A., Envelope theory, Nauka, M., 1975, 104 pp.