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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{VTGU_2017_48_a2,
     author = {N. R. Shcherbakov and A. A. Shchegoleva},
     title = {Modeling of teeth surfaces of contacting details of a hypoid gear},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {30--35},
     publisher = {mathdoc},
     number = {48},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTGU_2017_48_a2/}
}
TY  - JOUR
AU  - N. R. Shcherbakov
AU  - A. A. Shchegoleva
TI  - Modeling of teeth surfaces of contacting details of a hypoid gear
JO  - Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
PY  - 2017
SP  - 30
EP  - 35
IS  - 48
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VTGU_2017_48_a2/
LA  - ru
ID  - VTGU_2017_48_a2
ER  - 
%0 Journal Article
%A N. R. Shcherbakov
%A A. A. Shchegoleva
%T Modeling of teeth surfaces of contacting details of a hypoid gear
%J Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika
%D 2017
%P 30-35
%N 48
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VTGU_2017_48_a2/
%G ru
%F VTGU_2017_48_a2
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/