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Designing parametric
worms with Catia V5

Published at http://gtrebaol.free.fr/doc/catia/worm.html
Written by Gildas Trébaol on June 26, 2005.
Zipped part: worm.zip (306 KB).
VRML97 model: worm.wrl (304 KB).

The worm is a part of a worm / worm wheel reduction gear

This tutorial shows how to make a basic worm that you can freely re-use in your assemblies.

1 Sources, credits and links

• The worm can be coupled with a worm gear or with an helical gear.
• The principle for designing a worm consists in drawing a thread helix that cuts a cylinder.
• The worm dimension is taken from the part catalog Engrenages H.P.C, June 1999 edition.
• The worm above corresponds to the part ref. W1,5-1 page 358.

2 Table of worm parameters and formulas

#	Parameter	Type or unit	Formula	Description	Name in French
1	a	angular degree	20deg	Pressure angle: technologic constant (10deg ≤ a ≤ 20deg)	Angle de pression.
2	m	millimeter	—	Modulus.	Module.
3	N	real	—	Number of turns of the thread (3 ≤ N ≤ 15).	Nombre de tours du filet de la vis.
4	D	millimeter	—	Diameter of the pitch cylinder.	Diamètre du cylindre primitif.
5	L	millimeter	p * (N + 1)	Length of the thread.	Longueur du filetage.
6	ψ (psi)	angular degree	atan( m / D )	Angle of the worm helix. Must match the angle of the worm wheel helix.	Angle d'hélice de la vis. Doit être égal à l'angle d'hélice de la roue correspondante.
7	dZ	millimeter	-L/2	Translation offset of the worm surface on the Z axis.	Décalage de la surface de la vis suivant l'axe Z.
8	p	millimeter	m * π	Pitch of the teeth on a straight generative rack.	Pas de la denture sur une crémaillère génératrice rectiligne.
9	e	millimeter	p / 2	Tooth thickness, measured on the pitch circle.	Epaisseur d'une dent mesurée sur le cercle primitif.
10	ha	millimeter	m	Addendum = height of a tooth above the pitch circle.	Saillie d'une dent.
11	hf	millimeter	m * 1.25	Dedendum = depth of a tooth below the pitch circle.	Creux d'une dent.
12	rr	millimeter	m * 0.38	Radius of the root concave corner. (m * 0.38) is a normative formula.	Congé de raccordement à la racine d'une dent. (m * 0.38) vient de la norme.

1 Make the pitch helix

2 Add straight segments at each end of the thread

3 Draw the thread profile

4 Make the helical thread

5 Make the thread extremities

6 Insert a cylinder tangent to the outside circle

7 Intersect both surfaces

8 Fill the worm surface and add a hub

ψ angle of t

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End of File

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