Helical gear as solid

[fuccaro]

Someone asked my advice (by e-mail) for a solid helical gear. He referred at THIS article where I showed a helical gear surface. I created and sent him a PDF file but I think that some of the Forum readers could find it useful too. So HERE is the document. Sure, your comments are welcomed.

[a1harps]

Fuccaro,
As usual I am amazed at your mastery over geometry!!
-Frank

[neal69]

Very Impressed...........I've tried so many times and failed at this.

[CADbug]

hi..thats really nice to see. but how do you do that?
pls let me know the process.

[fuccaro]

Hello CADbug

In my first post the words in UPPER CASE are hyperlinks. Just click them and a PDF will open in your browser.
Probable I will re-post the construction of the helical gear model in "normal" way -with some changes. For the moment it was the easiest way to post a document I already had...

[fuccaro]

It seems that some of you can not open the PDF . For me it works fine. I will create a "normal" post these days...

[hyposmurf]

I remember having a similar problems,sometimes it can be that your using acrobat version 6 rather than 5.

[fuccaro]

I used the free pdf writer PDF995. Sorry if I caused problems to any of you

[fuccaro]

It seems I choused wrong when I uploaded the PDF I refer in the first post. The uploaded documents are not so popular. Also some users reported difficulties to open the PDF .So here is the "normal" version with some minor changes. Sorry for the delay.

1 Draw the active profile in 2D –or just a part of the profile. You can use a lisp or approximate the profile with arcs. I will not detail this step because it is not the subject of this article.


2 Draw the two opposite profiles of the same teeth. Make them a bit longer if you can.


3 Copy the profiles. Move the copies in Z direction and rotate them with the desired angle.


4 Using the two profile pairs (marked with red and yellow in my image) draw the twisted profiles as surfaces (command: RULESURF)


5 Download the M2S lisp routine. You will find it HERE
If you need help in using the lisp click HERE and say a big "thank you" to CADTutor!
Rotate the UCS as in the image. Use the M2S lisp to convert the first surface to solid. The orientation of the UCS is critical; the solid will "grow" in Z- direction.


6 Slice the solid careful; the reminder part must not exceed the yellow surface but the red surface must remain untouched. ***** see the end note to make this step easier *****


7 Now rotate the UCS and construct the "other" solid…


8 …than slice it using the same points as you used when slicing the red one.


9 Union together the two solids and you get a tooth. Intersect it with a cylinder having the base radius Re (see the first image)
The green arrows are pointing geometrical imperfections. You can avoid them if you start from longer profiles (see point 2). Also you can edit the solid to correct the imperfections.



10 From now it is simple; Polar Array the solid, draw a cylinder with base radius Ri and union the solids.
Possible problems: if the surfaces are "very twisted" you can not slice the solid as showed at points 6 and 8. If the gear twists even more, the M2S will generate a strange solid but we are not talking about this case now. So if you can not slice the solid without to "touch" the active surfaces you may try to reduce to half the height of the gear (the Z coord). Sure you will reduce the twist angle to half too. So you will end up with a half long gear. Copy it in axial direction and rotate the copy to keep the continuity of the helical profiles. Union together the half gears to get a full one.

***** The following is the contribution of our friend ABJ
Don’t draw the yellow half profile nor the yellow mesh and solid. Draw just the red ones.
We refer at the point 6 (see the image).
It might be difficult to slice the half profile. So after you used the M2S to solidify the first mesh you may mirror it. At first use the MIRROR3D command, the mirror plane is XOY with Z=0 and don’t delete the original object. Now mirror the last solid (the MIRROR command in 2D). The mirror line is perpendicular to the middle of the gear axis. In the MIRROR command choose to be deleted the source object. The resulted solid must mach with the yellow surface in the image. Now intersect the two solids and you should get the common part: a twisted tooth. Continue with the intersection described at point 10.

- Thank you ABJ!

[mohstar]

2 Draw the two opposite profiles of the same teeth. Make them a bit longer if you can.
sorry i dont get it >> please any body say how ?