Since the geometry of a spur gear is controlled by a few parameters,
we can design a generic gear controlled by the following parameters:
● The pressure angle a.
● The modulus m.
● The number of teeth Z.
This tutorial shows how to make a basic gear that you can freely re-use in your assemblies.
1 Sources, credits and links
● Most of my tutorial is based on a nice tutorial on helical gears
in English at http://ggajic.sbb.co.yu/pub/catia/.
● I improved it a little for making an exactly symmetric tooth.
● The mathematic description of the involute curve is visually explained
in French at http://serge.mehl.free.fr/courbes/developC.html.
● The gear technology is explained
in French at http://casm.insa-lyon.fr/engrenag/.
● The conventional formulas and their names in French
come from the pocket catalog Engrenages H.P.C, June 1999 edition.
2 Table of gear parameters and formulas
Here is a table containing the parameters and formulas used later in this tutorial.
The table is given first so that you can use it for further copy/paste operations.
All the units are defined in the metric system.
2.1 Notes about the formulas (in French)
Formule N°11: explication de l'équation rb = d * cos( a ) / 2:
ttp://gtrebaol.free.fr/doc/catia/spur_gear.html（第 4／31 页）2006-2-28 14:10:44
● La crémaillère de taillage est tangente au cercle primitif.
● Au point de contact, a définit l'angle de pression de la ligne d'action.
● La ligne d'action est tangente au cerce de base.
● On a donc un triangle rectangle à résoudre.
Formule N°12:
● Entre le cercle de pied et les flancs des dents,
prévoir un petit congé de raccordement pour atténuer l'usure en fatigue.
Formule N°14: explication de x = rb * cos( t ) + rb * t * sin( t ):
● Le premier terme correspond à une rotation suivant le cercle de base.
● Le second correspond au déroulement de la développante.
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