Manual Generation of Involute profile

I was just reading an article in a British magazine regarding the manual generation of an involute gear profile using a V profile rack tool, by firstly cutting just the V, then rotating the gear blank a specific amount and correspondingly moving the cutter in/out a specific amount, indexing around the whole gear and repeating. The author says that 4 passes on each tooth side provide a step free tooth profile. I can see this would be a very handy method for one-off gears, where it's not worth buying a full set of cutters, and on gears with a small number of teeth it probably isn't as time consuming as it sounds. I normally just set up the power feed and stops to cut each tooth, so it's semi-automated anyway.

I'm curious as to whether anyone here has tried this method, and if so how to determine the relative angular rotation and in/out feed required for each pass? I can see it would also be possible to generate undercut teeth using this process, and would this allow a lower tooth count gear as compared to using horizontal involute profile cutters?

Pete F said:

I was just reading an article in a British magazine regarding the manual generation of an involute gear profile using a V profile rack tool, by firstly cutting just the V, then rotating the gear blank a specific amount and correspondingly moving the cutter in/out a specific amount, indexing around the whole gear and repeating. The author says that 4 passes on each tooth side provide a step free tooth profile. I can see this would be a very handy method for one-off gears, where it's not worth buying a full set of cutters, and on gears with a small number of teeth it probably isn't as time consuming as it sounds. I normally just set up the power feed and stops to cut each tooth, so it's semi-automated anyway.

I'm curious as to whether anyone here has tried this method, and if so how to determine the relative angular rotation and in/out feed required for each pass? I can see it would also be possible to generate undercut teeth using this process, and would this allow a lower tooth count gear as compared to using horizontal involute profile cutters?

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Cannot answer all your questions, what I do know is, that this is an old model engineering technique known to produce useable gears with dirt cheap tooling you can make yourself. Obviously not ideal, but known to be a working method.

It sounds like a neat process but full sets of 20 deg cutters can be found on eBay for about $100 these days. If one needed some weird pressure angle it might be practical method but in that case, I might just grind a lathe tool and sort of fly cut the thing - hobbyists do that all the time apparently with success.

Was the article online and if so, can you post it here ?

Thanks -

If you think about how the hob cutter works its profile just advancing linearly at a consistent rate, the hob arbor is then geared to the work arbor in an oversimplification.

The biggest pain might be making, hardening, sharpening the rack cutter. Next, indexing the blank in an accurate manner. I don't think the face of a dividing head can take the load of a non-gashed full depth single tooth cut but I could be wrong.

Exactly

Found my source:


This is entirely in Kraut and way too much for me to translate. Not an economic use of my time, sorry. But the pictures alone tell the story. It works quite well and even on unmentionable machines

Zahnräder fräsen mit dem Gear Hobber

I wish i had the quality shop time to try it myself. But since the museum got its new building in 2013 it has been one huge push forward. The shop time i get is spent fixing stuff, not making tools to make gears and then have to come up with a third project to actually use the gears

If you have a CNC vertical mill with a 4th axis, you just need a cutter with teeth at the pressure angle. Start with the cutter above the blank and feed down and rotate the blank at the same time. Move over a little and repeat. Making each one at a time tooth in several passes will take a while but you will have true involutes generated the same way a hob does it.

Bill

I was typing when Zonko posted. If you want to make a hob like that, then you can turn a CNC mill into a hobbing machine. I was thinking in terms of buying a V cutter, although you might have trouble getting a 40 degree one and need to regrind a 45.

Zonko said:

...This is entirely in Kraut and way too much for me to translate. Not an economic use of my time, sorry. But the pictures alone tell the story. It works quite well and even on unmentionable machines ...

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Thanks, you're right - it's quite easy to absorb and it is a very interesting process !

Pete F said:

I'm curious as to whether anyone here has tried this method

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Well, it's just another variation on gear shaping or gear hobbing. From your description, I would call it closer to gear shaping, and I seem to recall a commercial piece of machinery that used a rack with straight-sided teeth (section of an infinite diameter involute profile) rather than a finite diameter involute profile cutter.

I think 4 passes per tooth-side would be a fairly crude approximation. I think normal shaping and hobbing take more like 30 to 50 "bites" per tooth-side. (That number is off-hand, and an experienced gear shaper hand could give a very tight number.)

how to determine the relative angular rotation and in/out feed required for each pass?

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Exactly and precisely the same relative motions between cutter and part as between a rack and a gear in mesh, if you ignore the parallel-to-tooth traverse needed for the cutting action.

I can see it would also be possible to generate undercut teeth using this process, and would this allow a lower tooth count gear as compared to using horizontal involute profile cutters?

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Not really, no. Standard involute cutters can give you a 12 tooth pinion, and that's as small as is practical regardless of production method.

No the article wasn't online it was in a magazine. $100 a set of cutters may be chicken feed for some, but it sure as heck isn't for me, and it starts to add up. For a one-off application it would be good to know the liklihood of success in just buying a single rack cutter and using this technique.

No it's not shaping, nor is it hobbing. The German article was very interesting, sadly however had nothing to do with the question as it was just an article on hobbing.

It's been a while since I've looked at gear theory, but iirc a low tooth number involute gear should technically be undercut slightly, and that's not possible with involute cutters. The only way to achieve this normally is by either hobbing or shaping or (by the looks of things) this technique.

Matt I take full depth passes in steel gear blanks without a problem. A slow feed but not an issue. A mentioned above, I just drop the power feed on and it takes an average of a minute per tooth (actually less, but that's what I bank on). I do something else while that's happening.

In the meanwhile it at least prompted me to drag out my gear hobbing attachment for the lathe and blow off the dust

No it's not shaping, nor is it hobbing. The German article was very interesting, sadly however had nothing to do with the question as it was just an article on hobbing.

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imo that german article wasn't hobbing (despite the title)- Its a simple form cutter, there is no helix on the cutter and its rotation and the blank are not synchronized.

When you first posted, what was described in the German article was what I thought you meant. If thats not it, I confess do not really understanding what the artcile is describing to do - can you clarify?

As was described in the German article, it works well enough for non demanding gears, ie low speed, low load....good to have in the bag of tricks but its a facetted face not a smooth involute.

matt_isserstedt said:

I don't think the face of a dividing head can take the load of a non-gashed full depth single tooth cut but I could be wrong.

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hmmmm...imo thats not a concern, how else would you gash a gear blank if not in the dividing head? The ones I've had apart had massive plain bearings on the business end that would have no trouble taking substantial forces

Pete F said:

No it's not shaping, nor is it hobbing.

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Call it what you will, but it's pretty clear that using reciprocating a rack cutter with straight-sided teeth is just a minor variation on the more common setups for gear shaping and gear hobbing. Hobs have straight-sided teeth, and a rack is just the degenerate case of an infinite pitch diameter involute tooth form. In all three cases, you're using an involute formed tooth cutter taking multiple cuts on a workpiece held "in mesh" with the cutter. It just the involute generation process, very slightly complicated by the need to cut teeth of non-zero face width.

Same comment applies to using a single tooth fly cutter. It's just a smaller piece of rack.

Reciprocating (as in gear shaping) or traversing (as in hobbing or fly-cutting) makes no never mind, so long as the cutter tooth forms are held in the proper "mesh" relationship with the workpiece.

randyc said:

full sets of 20 deg cutters can be found on eBay for about $100 these days.

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Randy, I don't know what you're buying, but a single cutter in a useful DP runs me closer to $80. I suppose if you are after module 0.5 or something like that, you can get a cheap Chinese set for $100. Can't say the same for DP8, DP12, DP16, etc.

sfriedberg said:

Call it what you will, but it's pretty clear that using reciprocating a rack cutter with straight-sided teeth is just a minor variation on the more common setups for gear shaping and gear hobbing.

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I think one would be pretty upset if a hob was bargained for and a form cutter showed up. We practice a craft of precision so nomenclature matters - at the sme I confess no one has elected me to the board of the machinists dictionary ..... but IMO if the cutter and work aren't rotating and synchronized its incorrect to call it hobbing.

sfriedberg said:

...Randy, I don't know what you're buying, but a single cutter in a useful DP runs me closer to $80. I suppose if you are after module 0.5 or something like that, you can get a cheap Chinese set for $100. Can't say the same for DP8, DP12, DP16, etc...

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I'm grateful for that advice since I have a set of cutters on my E Bay watch list. I guess I'll stick to the flycutter method with a form tool but dang that's a lot of pounding !

Mcgyver said:

IMO if the cutter and work aren't rotating and synchronized its incorrect to call it hobbing.

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To quote myself,

Well, it's just another variation on gear shaping or gear hobbing. From your description, I would call it closer to gear shaping

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So I really don't see that you have any objection to what I actually wrote.

but IMO if the cutter and work aren't rotating and synchronized its incorrect to call it hobbing.

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Just so. It either IS or it ISN'T

sfriedberg said:

Call it what you will, but it's pretty clear that using reciprocating a rack cutter with straight-sided teeth is just a minor variation on the more common setups for gear shaping and gear hobbing.

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Ummmm...


No.


It appears that you've somehow managed to overlook the very basic reality ( and requirement ) of generative formation - that both tool and work are moving, in unison. If they are not, then it quite simply is NOT generative. ( and not Hobbing or Shaping ) What you are seeing and ( seemingly ) failing to recognize is that anything less is simple form cutting. The exact same way that Bevel gears are milled with an indexer ( or dividing head ) in multiple passes, utilizing offsetting cuts.

Now, to the OP's question. What I think he is after is the process of using a single toothed, flat sided tool in a Shaper arrangement that ties the blank to the table's movement, as described in this article - http://neme-s.org/Shaper Books/Michael_Moore/shaper gear cut.pdf

I did this out of curiosity and trying to learn more and it works the treat. A friend and I later did another version doing the same thing but using a servo slaved to an encoder, instead of the wire and wheel. Note that a Rack tool could just as easily be used in place of a single tooth tool.

Also akin to this - http://www.homemodelenginemachinist...rams_Bevel_Gear_Cutter_Am._Mach._9May1885.pdf

Zahnrad Kopf said:

It appears that you've somehow managed to overlook the very basic reality ( and requirement ) of generative formation - that both tool and work are moving, in unison.

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No, I have been really quite clear and consistent in the thread, stating that the cutter and the workpiece are constrained by the relative motions of gears in mesh. I have said so repeatedly. Go. Look above, and read what I actually wrote, not someone else's lazy synopsis of what they think I wrote.

As I don't care for aimless pissing contests, this will be my final contribution to this particular thread. I don't believe we are in any substantial disagreement about the actual mechanical process involved.

Interesting thread.
I have used the principal successfully, but by milling rather than shaping, on a 4 axis CNC mill. I got the local tool grinder to make a 40 deg endmill, and wrote a nested macro with a formula including pi to rotate the blank the correct amount for each increment of y axis. The increment was arbitrary, and the number of cuts (and smoothness of the curve) only limited by what we considered a sensible cycle time. The process was slow, but since my usual gear cutting shop did not have cutters for the stub profile required (this was a one off repair) and was going to have to do offset cuts it worked out to be our cheapest option. The gears were 4140 and came out great with a smooth looking face. We also did some helical gears the same way. One of the benefits for a job shop is unusual stub ratios can be cut like this. A good example is gears for quick change rear ends, since the centre distance is fixed, some ratios require non-standard tooth profiles to mesh. If all you have to do is grind a shaper tool to a specific root width of pressure angle for that matter, (if you are using the method described in the op) the tooling outlay is pretty small.

Another thing to ponder, we can say this method is inferior to hobbing since we are leaving a series of flats and therefore not a genuine involute, but surely a hob leaves material behind too? Each cutting edge follows a geometrically correct path, but what about between each edge as the cutter advances? Is it not the same as a helical milling cutter, a fine finish only resulting from a fine feed, and even then when magnified enough will show a series of ridges?

Oh yes, lets not also forget, the form cutters many of us rely on will cut several numbers of teeth, but are only geometrically correct for one of the numbers of teeth in the stated range. This means that the method described by the op can potentially produce a better profile than a more expensive form cutter. (But more than four passes would be required!)

ADFToolmaker said:

Another thing to ponder, we can say this method is inferior to hobbing since we are leaving a series of flats and therefore not a genuine involute, but surely a hob leaves material behind too? Each cutting edge follows a geometrically correct path, but what about between each edge as the cutter advances? Is it not the same as a helical milling cutter, a fine finish only resulting from a fine feed, and even then when magnified enough will show a series of ridges?

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I think your points are correct, but with enough magnification a lapped surface is furrows and hedgerows. So the difference is partially a matter of degree, but really the big difference is the that the imperfections of the form cutter idea are perfectly axial whereas from hobbing they're almost curving up toward radial - there might be forrows but each is on an involute curve vs the hard change between facets contacting. If you picture how gears come in and out of contact that strikes me as a massive difference in how smooth things will be. Have made gears by this facetted method, they are somewhat clunky especially with smaller tooth counts.