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cutting spur gears on a mill

a rogue method?

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Andrew Johnston11/10/2021 11:04:15
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Posted by Pete Rimmer on 10/10/2021 21:20:16:

It produces facets it just doesn't produce flat ones......

Unfortunately that is mathematically incorrect. A facet is a feature of a polyhedron, generally of one dimension less than the original object. Assuming that we're discussing 3D Euclidian geometry then a facet will be 2D. By definition that means it exists on a plane and so will be planar, ie, flat.

Here's a thought experiment. Let's assume we hob a spur gear of zero width, so the hob teeth only cut when they cross the plane of the blank. As the hob enters the plane of the blank, and exits the other side, it will cut a reproduction of its shape, ie, straight sided. Since the blank is of zero thickness the cut time is also zero, so there is no rotation of the blank during the cut to consider. What will the resultant shape of the cut space be; a series of straight lines, or a smooth curve?

Andrew

Martin Kyte11/10/2021 11:16:22
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Posted by Dave S on 11/10/2021 10:48:54:

From a pendants point of view Hobs approximate (closely or not depending on the hob parameters) the involute curve with a series of straight lines.

This is not a surface roughness thing, its an approximation thing.

Dave

Please don't call me a pedant. Turning marks on a lathe turned cylinder would be referred to as surface roughness. Taper would be the approximation to the correct geometery. Unless you produce a form tool for each tooth count some of the gears are going to be approximations of the curve. Thats geometry. Hobbs will generate the right geometery but create machining facets which is surface finish. Lumping surface finish and geometrical errors into the same bucket makes the discussion woolly.

regards Martin

duncan webster11/10/2021 11:41:33
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Taking Andrews thought experiment, his zero thickness gear will be a series of flats, but if there is another one alongside the flats will have an angular offset, so for a real case there will be a series of spirals. The repeat rate is the same as the cut per tooth, ie a few thou.

Dave S11/10/2021 12:53:17
257 forum posts
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Firstly I was mostly calling myself a pedant - for insisting that the hobbed profile is actually a series of facets.

Apologies if that came across as insulting to anyone.

In the case of a Lathe turned cylinder, assuming the lathe is in good order the cross section of that cylinder will be circular. (the intended form). There is a helical groove running down the cylinder, which does affect the cylindrical size - crests are larger than troughs. but it does not make the cylinder none circular.* Hence the helix can be described as surface roughness - now close to size (not form) is the cylinder.

The hobbed gear has both surface roughness issues (its a cutting process and will leave tooth marks after all) AND form issues. The faceting is a departure from the ideal surface form, and hence is more appropriately termed an approximation, just as using a circular form tool cutter is a departure from the idea from, and hence an approximation.

Gear grinding has 2 benefits. Firstly the cutting tools are capable of taking a much smaller cut - so can leave the surface roughness at a lower level, and secondly there are millions of cutting tools operating all the time - equivalent to a hob with millions of gashes - so the form produced is much more perfect than it would be with the limited number of cuts a hob makes.

Dave

*actually it does if you cross section you get an oval with the DOC as you go peak to trough.

Martin Kyte11/10/2021 13:05:38
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Thanks Dave.

I do understand what you are getting at. Any deviation from the ideal surface could be termed an approximation to form but as I say lumping everything into one term is not helpfull to any discussion. I think you have answered the question really when you equate the grinding wheel to a hobb with millions of gashes. All that changes is the surface finish.

regards Martin

Michael Gilligan11/10/2021 13:11:08
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Posted by Martin Kyte on 11/10/2021 11:16:22:
Posted by Dave S on 11/10/2021 10:48:54:

From a pendants point of view […]

Please don't call me a pedant. […]

.

He didn’t … he called you a pendant

[ perhaps hanging on your every word ]


angel MichaelG.

Dave S11/10/2021 13:15:36
257 forum posts
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As a thought experiment imagine a hob with a single gash.
We will have to assume that the formed cutting tooth is smalle enough to escape fromt he nascent gear during the hobbing rotation, to line it up with the next tooth.
As a basis for this Tony Jeffrey has a nice picture on his site on the page about rackform hobs. http://www.jeffree.co.uk/pages/multi-tooth-gear-cutter.htm

Tonys nice picture

If you visualise the hob as having a single gash then the top of the picture shows all the places that you are cutting on a single hob rotation.
Then the blank rotates in the helix and you make another cut. With a single gash the blank has to rotate a full tooth space before the next cut is made.
The end tooth form you will achieve is that of the tooth form detail - an obviously faceted shape.

Further down the page Tony illustrates how by 4 cuts per tooth (in other words a hob with 4 gashes) gets much closer to the correct form - to the point that although the tooth must have flats on it - it can be no other way with a straight sided cutter - the approximation to a curve is such that it would be easy to miss, and for all practical purposes is an involute.

Dave

Martin Kyte11/10/2021 13:43:19
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But there is always one point on the rack where the cutter is exactly on the involute. With three cuts there will be three points on each flank where the cut and the involute touch. So the rack exactly follows the path of the involute. Increasing the number of cuts per degree of rotation is just the same as dialing in a finer feed on the lathe.

regards Martin

SillyOldDuffer11/10/2021 15:47:35
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7686 forum posts
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Duncan Webster helped me out last month by writing a program in Python3 to draw involute gears. (I was and still am struggling with the maths!) Duncan's code, which requires the easygraphics module, is here on Dropbox.

Duncan's teeth aren't drawn with curves, instead the involute is approximated by drawing a series of straight lines, i.e. facets. By default, the teeth are drawn with 12 facets, so a 20 tooth Mod 1 gear looks like this:

fullgear20.jpg

I bodged Duncan's code to draw only one tooth with 1,2,3,4 and 8 facets, all scaled up so the eye can see the facets.

Single facet teeth are obviously notchy:

onefacet.jpg

Two facets are a considerable improvement:

twofacets.jpg

Four facets are quite good:

fourfacets.jpg

And at this scale, eight facets are almost indistinguishable from a true curve.

eightfacets.jpg

All of these 'involutes' are approximations because of the way they are generated by drawing straight lines, but there are more issues to come.

Duncan's program could be modified to produce G-code to make subtractive gears with a CNC mill or additive gears with a 3D printer. In both cases his mathematical involute could be an excellent approximation, say 24 facets or more, but the resulting gear will be degraded by the production process. Although both gears can be improved by cleaning up if necessary, the plastic and metal versions differ in strength while the metal version could also be greatly improved by polishing and hardening. The properties of a Duncan gear depend on the maths, the material, the basic production process, and the finishing. It's possible for Duncan gears to be either cheaply or better made as required. Most engineering objects are like this. They can be made up to an advanced specification or down to a price. Both useful, but don't waste money on uneccessarily expensive gear or on on cheap junk. It's the engineer's job to make cost effective choices.

My general point was lathe change-gears ain't anything special, and that it doesn't matter as long as they do the job.

Dave

Dave S11/10/2021 17:05:08
257 forum posts
56 photos

Indeed more cuts is a bit like a finer lathe feed, but the difference is that the lathe will still turn round (form) with either.

The hob with “courser feed” (1 gash in extremity) creates a different, more approximate form.

The other difference is that the hobs “feed” is set at manufacture but the number of gashes.

The thing to remember is that even a couple of gashes gets you a very close approximation of the correct form, and by the time you have a typical number of gashes in a commercial hob the form is essentially perfect, and other factors in machining are likely to have at least as big an effect on the perfection of form.

Dave

John Haine11/10/2021 17:06:32
4272 forum posts
251 photos

Nice! And thanks for the link to the code, and Duncan thanks for generating it. I am wondering about writing a Python wizard for gears, this will be very useful to get me started I think.

Michael Gilligan11/10/2021 17:09:04
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19285 forum posts
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Very useful, Dave [and Duncan] yes

MichaelG.

.

P.S. __ Your final point is valid, Dave ... but it does depend a little on 'the job'

... See my earlier link to the Bryant-Symons lathe

... Some people use[d] lathes to do very serious screw-cutting

Pete Rimmer11/10/2021 18:39:07
1096 forum posts
69 photos
Posted by Andrew Johnston on 11/10/2021 11:04:15:
Posted by Pete Rimmer on 10/10/2021 21:20:16:

It produces facets it just doesn't produce flat ones......

Unfortunately that is mathematically incorrect. A facet is a feature of a polyhedron, generally of one dimension less than the original object. Assuming that we're discussing 3D Euclidian geometry then a facet will be 2D. By definition that means it exists on a plane and so will be planar, ie, flat.

Here's a thought experiment. Let's assume we hob a spur gear of zero width, so the hob teeth only cut when they cross the plane of the blank. As the hob enters the plane of the blank, and exits the other side, it will cut a reproduction of its shape, ie, straight sided. Since the blank is of zero thickness the cut time is also zero, so there is no rotation of the blank during the cut to consider. What will the resultant shape of the cut space be; a series of straight lines, or a smooth curve?

Andrew

I don't do theroetical debate very well I see it as wasted energy. I take your point about the use of the term 'facet' but it's the most fitting terminology I could come up with.

Basically my hobber when it's feeding has very little infeed in fact the feed handle moves like clock's minute hand. Almost all of the 'movement' is the hob teeth passing the blank whilst the blank is constantly rolling so whilst a zero-thickness blank might theoretically receive a flat facet cut ANY thickness of blank will be cut via a simultaeneous action of helical-motion teeth passing through the part whilst it's rolling. It will generate a curve, not a flat.

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