designing parametric helica

Designing parametrichelical gears with Catia V5

Published at http://gtrebaol.free.fr/doc/catia/helical_gear.html

Written by Gildas Trébaol on July 1st, 2005.Zipped part: gearbox.zip (728 KB).VRML97 model: helical_gear.wrl (414 KB).

A helical gear can be used with a worm,in a worm / worm wheel gearbox

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

1 Sources, credits and links

The helical gear can be coupled with a worm part.The helical gear is close to the standard spur gear part.The main difference is the inclination angle of the teeth relative to the rotation axis:

On a spur gear, the tooth is parallel to the gear axis.On an helical gear, the angle between the teeth and the axis is named ψ . (i.e. the Greek letter "psi").The ψ angle of the helical wheel must match the ψ angle of the worm.

The lead L of the helix screw corresponds to the formula: L = π * D / tan( ψ ) .The dimension of the helical gear and the worm shown in this tutorial are takenfrom the page #358 of the part catalog Engrenages H.P.C, June 1999 edition.

2 How to use the same parametric part for spur gears and helical gears

The standard spur gear coresponds to a ψ = 0 .In that case, L = π * D / tan( 0 ) = ∞ .

Designing parametric helical gears with Catia V5 http://gtrebaol.free.fr/doc/catia/helical_gear.html

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So we cannot use the helix curve provided by Catia when ψ = 0 .However, whe can use a zero angle when the helix is replaced by a straight line:

For ψ = 4.50deg we have L/D = π / tan( 4.50deg ) ≈ 39 .For ψ = 20.0deg we have L/D = π / tan( 20.0deg ) ≈ 9 .

Since the L/D ratio is large, a straight line is a good approximation of the helix.Then the spur gear and the helical gear can be generated both by the same parametric part.

3 Make the tooth profile

The tooth profile is built using the Catia part shown in the spur_gear.html tutorial:

4 Make the rotated tooth section and the inclined guides

The tooth template is a multi-section surface:

The first section is the tooth profile built previously in the spur_gear.html tutorial.The second section is a translation and a rotation of the first section on the Z axis.The translation length corresponds to the wheel thickness e .The rotation angle φ corresponds to a fraction of the helical lead L :φ = 360deg * e/L = 360deg/π * tan( ψ ) * e/D .The inclined guides are two line segments connected to the ends of the tooth sections.

5 Make the gear surface with a circular repetition of the tooth


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6 Make a part body with a filled teeth surface

7 Assemble or intersect it with the main part body

The intesection of the second part body with the main body is advantageouswhen the main part body is a beveled cylinder.

8 Check that we can generate a spur gear

When ψ = 0deg , the helical gear becomes a standard spur gear.


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9 Make a toy gearbox

With the worm shown in the worm.html tutorial, you can make a reduction gearbox:I theory, we should use a worm wheel instead of an helical wheel,but I don't know how to design a worm wheel...So I use an helical wheel having the same ψ angle as the worm.The distance between the two shafts is the sum of the pitch radius of the worm and the worm gear.For a pitch m = 1.5mm , a worm pitch diameter D = 20mm and an helical wheel having Z = 22 teeth,that distance is (D + m * Z) / 2 = (20 + 1.5 * 22) / 2 = 26.5 mm .

End of File


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designing parametric helica

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