Generation of bevel gears - how?
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# Thread: Generation of bevel gears - how?

1. Stainless
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## Generation of bevel gears - how?

I'm trying to get my head around the purely academic question of generation of bevel gears with correct tooth form.

Is there actually a way of doing this, in the same way that hobbing or shaping with sufficeintly small incremental rotation of the cutter and work will generate the correct tooth form for ordinary spur gears?

Or is every method an approximation with some approximations coming slightly closer to correct form than others?

And if every method is a dirty approximation, are the methods for improving that approximation equally dirty - for example running pairs of gears together with abrasive in order to average out deviations from correct form.

I was running through the geometry of hobbing in my head, but come up against the geometrical problem of the hob (as a continuous rack) having infinite diameter, so it's pitch circle cannot intersect the projected intersection of the shafts, and the hob has a fixed pitch rather than pitch increasing going towards the centre of the work.

Reason I'm asking in the OID forum rather than General, Is that the contributors here generally have a much longer perspective of what has been tried in the past and why - as opposed to this is what we use in the shop now.

Many thanks.

2. Titanium
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The usual method still used today is with special shapers. As johnoder linked to one.

I do mill my gears with a saw-blade shaped mill. Just with the sides at 20° (pressure angle) and a side relief for nice cutting (a saw blade geometry won't work).
That process is generative.
I thought about how this process could be used to generate bevel gears. It does work, but requires a second rotary axis. So a 5 axis mill. The movement is quite odd. But as I don't have a second rotary, I never actually tried it. I'm quite sure the process doesn't just work in my (gear)head.

Nick

3. Diamond
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Alpacca 45, there's more than one tooth form used for bevel gears, even if you restrict yourself to "straight" teeth. If you allow curved or asymmetric teeth, probably a couple of dozen different systems have been used in the last 150 years.

Generally speaking, shaping will work but hobbing will not, for (nearly) all of these tooth forms.

The two forms I think (not an expert in this area) are most common for bevel gears are the octoid tooth (an extremely close relative of the involute) and the parallel depth or constant depth tooth. Both of these can be generated (nominally perfectly) but the parallel depth tooth is especially suited for cutting with non-specialist machines.

4. Diamond
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A Gleason bevel gear generator is pretty much just a shaper that can have the ram set to cut a taper with a tracer for the tooth form and a built in rotary table. A straight tooth bevel gear is is just a straight tooth gear, but the tooth tapers from say a 5dp to a 7 from the outside edge to the center. Look up Gleason bevel gear cutter on Youtube and you can see several videos of some in action. Now, the helical bevel gear generators are a totally different animal.

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6. Titanium
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Here is a drawing of an older Bilgram machine .
https://archive.org/stream/internati.../n126/mode/1up
If you scroll back and forward a few pages there is some more discussion about cutting bevel gears on this and other machines .
Regards,
Jim

7. Hot Rolled
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Going way back, I believe it was fiat that used a bevel herringbone ring and pinion in their cars.

THAT is a mind bending thing trying to figure out how in the heck they were able to do that without some bajillion axis CNC and magical CAD stuff.

EDIT: it was citroen
Last edited by [486]; 06-27-2014 at 12:45 AM.

8. Diamond
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Think I've seen pictures of such a thing, did not realize it was ever actually made as a production assembly!

smt

9. Hot Rolled
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Just edited it in, it was citroen.

Google brings up some really interesting pictures.

10. Stainless
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Thanks for so many replies.

I'll be taking a good look at those Bilgram shaper refs, and looking into the Gleason shapers too. The connections were a little slow when I looked, so I'll try again when the net is faster.

486, I did a quick search for Citroen herringbone gears, and found a good old thread started by Peter S, with some pictures. Herringbone gears - Citroen The snide political comments from the time of the Iraq invasion are an interesting time capsule too.

It's interesting the the Citroen gears left the apex of the herringbones in place, I wonder whether they designed for directional running (as the picture which Peter S shows would suggest) so that the lubricating oil was expelled out of the sides rather than trapped at the apex to cause all sorts of havoc there?

11. Diamond
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In keeping with the original question and that this is the antique forum I thought you might want to see this video from ZF corp.

It is from the 1930s and has some very good photography of various types of gear generating equipment. Although the shots are pretty short as it is not a gearmaking training film. You may wish to skip the first part, although I found it nicely done, as the machining starts around 4:20 and the bevel gears around 6min in.

ZF in den 1930er Jahren - YouTube

Charles

12. Cast Iron
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Originally Posted by Alpacca Fortyfive
And if every method is a dirty approximation, are the methods for improving that approximation equally dirty - for example running pairs of gears together with abrasive in order to average out deviations from correct form.
Not likely to help. Sliding velocity between teeth varies from entry through zero at centerline to exit. This means the abrasive will probably make the geometry worse, not better. Wear will selectively occur near roots and tips, and not at pitch diameter.

13. They thought this abrasive method above would work in the 18th. C.,when they had not yet figured out how to make smooth running gear teeth. The gears wore OUT instead of wearing IN.

14. Diamond
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Also, for a slow moving bevel gear, like for the knee on a mill or shaper, you can cut a very close approximation to a proper tooth by using a straight tooth gear cutter and off setting the table, then "rolling in" the blank on a horizontal mil or shaper with the dividing head set up vertical to the proper taper angle. I have done this, myself. It works well enough even for drive gears on a radial drill, but I would not try it with something subjected to heavy, constant loads.

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The final op on a spiral bevel is a lapping op (there lapped to each other)

That is why there sold as a set.

16. Here is a link to a thread in another forum about a beautiful 1860 French bevel gear shaper: Something French, including some speculation about how it might work. In the 2nd last post (#28) there's a link to an old book on the subject, including that particular machine.

17. Here is the link to the book mentioned by Lofty. The 1909 book, written by Ralph E. Flanders, titled "Gear-cutting machinery, comprising a complete review of contemporary American and European practice, together with a logical classification and explanation of the principles involved". It has a great detailed description of the various methods and machines used, including the operations for cutting bevel gears. It's available here:
https://archive.org/details/gearcuttingmachi00flanuoft

I thought I'd mention it by itself in case you don't read the "Something French" thread. The pictures there are not viewable unless you register on that forum.

Irby
Last edited by IrbyJones; 06-28-2014 at 09:02 AM. Reason: Rewording

18. Diamond
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Oh yeah, the method for milling/shaping a bevel gear was in a Colvin and Stanley Machinists Handbook from 1927. Later editions of similar books just said you couldn't make one, lol.

19. Originally Posted by IrbyJones
I thought I'd mention it by itself in case you don't read the "Something French" thread. The pictures there are not viewable unless you register on that forum.
Sorry I forgot about that. The discussion won't make much sense without the pics, which BTW are numerous and very good. Maybe we can entice Anorak Bob to repost some of them here?

Thanks for the link Irby. I should have done that. The Flanders book is well worth a read for anyone interested in gears and old machines. This is a grab from it - a cross section of the aforesaid French machine.

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