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Cutting gear teeth....I need the basics

GregSY

Active member
I need to cut some straight gear teeth in a shaft...and my experience with the math behind this is zero.

The Voest drill is missing the pinion shaft used to crank the horizontal ram. See read arrow in pic. The teeth are about 2.5" long.

I read up on a few sites, including McMaster Carr, and I find myself getting more confused.

The shaft is 28mm (about 1.100") diameter. The rack teeth appear to be 4 teeth per inch (though this does not equate to any round MM value). From the top of the tooth to the bottom is about .140", give or take. The total angle is 60 degrees and the teeth don't look to have any visible curve or profile...they look to be a pretty straight-sided "V", or very close to it.

The McMaster site says to determine pitch, I should divide the number of teeth by 2 then multiply by the shaft diameter. Since I have 3.45 inches of circumference, that indicates I need 13.82 teeth. Since the diameter of the shaft can be smaller, I assume I would want 13 teeth as a round number. So...13/2 = 6.5 x 1.1 = 7.15 which would round down to a 7 pitch. Is that right or?


voest rack.jpg
 

implmex

Active member
Hi GregSY:
Since you have the rack, you have the best possible place to determine the geometry of your pinion too.
You can get all sorts of useful information from it.
First, establish how many teeth per unit length you have.
It's a Voest, (Austrian) so it will be metric unless they did something totally weird for the North American market.
Mark out ten teeth on the rack and then measure how long for those ten teeth.
A simple division and you have the pitch...unambiguously and accurately, rather than implied from a formula and an indirect measurement.
Next, you can measure the pressure angle directly from the rack teeth...it's the same as the flank angle, but only on a rack.

Once you have all that, you can lay out the rack profile, either on paper or with CAD.

Measuring the diameter of the pinion bore in the housing will give you (with formulas) the pinion tooth count, and that will tell you what pinion cutter to buy if you plan to buy the gear cutter, and cut your pinion on a milling machine with a dividing head.

The other way forward, if you have the tools, is to make your own gear cutter and you have two options here.
1) You can make a rack cutter (like a stack of saws with the correct rack teeth copied from the rack profile of your quill) and use a fake called the Sunderland process, whereby you capitalize on the fact that a rack will mesh with a pinion of any tooth count, and if you traverse a rack cutter back and forth across a bar while displacing each the proper amount relative to one another, it will automatically make the correct tooth shapes on the pinion without you ever having to know what that shape actually is.
It just generates it, and that is the beauty of the method.
But it forces you to displace rack cutter vs pinion blank the proper amount for each pass so you have some calculating and other farting about to do to get it to work.

2) The other way, of course, is to make a cutter with the proper profile to allow you to just index the pinion and cut the tooth space in one go, and that means you have to be able to both define the profile and then make the profile, relieving it properly, and hardening it so it will cut.
Hobbyists do that all the time but they don't care how long it takes to make the cutter and they take great pride in doing it all themselves.
Your circumstances will determine which road is more attractive to you.

Other ways have been talked about here fairly often too; you can hob them (or have them hobbed) you can shape them (or have them shaped) you can wire EDM them (or have them wire EDM'ed) or if you're lucky you can buy them from the gear store.

So you have a lot of options, and you can choose between them depending on your inclinations.

One last point; although the teeth on the rack are straight sided, the teeth on the pinion will not be, but they'll still mesh properly.
You cannot just copy the shapes of the teeth of the rack and do the same for the teeth of the pinion...I point this out only because you commented this: the teeth don't look to have any visible curve or profile...they look to be a pretty straight-sided "V", or very close to it.

Remember, a rack can mate with any pinion of any tooth count and any diameter (so long as the pitch and pressure angle are the same for both).
However, the teeth of each will be a totally different shape.

So there's your beginning.
Developing gearing to mate with an unknown existing gear is a fairly involved process, but you happen to have the best possible beginning because you have the rack, and from that you can take direct measurements of the crucial features easily.

As your knowledge of how to tackle it grows, you will find it wasn't all that bad; just don't try to "free hob" it like this poster advocates:
Free hobbing - a rogue method for spur gears

If you do that, we may have to hate you for a bit.:D

Cheers

Marcus
Implant Mechanix • Design & Innovation > HOME
Vancouver Wire EDM -- Wire EDM Machining
 

GregSY

Active member
Thank you Marcus.

I will measure the pitch as you suggested.

Since I only need to make one, and I don't care how long it takes, I will cut one tooth at a time.

This drill is metric, as you note, and I have not found any aspect of it which is not in Metric. The only concession to the US market are the nameplates are in English (though translated to the point of being meaningless!).

I agree, the rack is straight-toothed but the examples of rack/pinion gears I have seen online clearly show the pinion teeth are 'profiled'.

This drill seems very 'exotic' in 2021....no place on the internet have I found any technical information. I'd love a diagram showing the head gears.
 

Peter from Holland

Active member
To determen the modul of the gear devide the pitch of the rack in mm by 3.14
That is usefull information when ordering the tool
A usefull formula is OD of the gear in mm = Modul× (Z+2)
Z=number of teeth
Peter
 

EmanuelGoldstein

Active member
If you could get a little info on the pinion that would be good ...

Frequently, on small pinions like this, they will cut one fewer teeth than you'd calculate from the specs. Gears with small numbers of teeth are weak and often undercut, so it's normal to cut, say, ten teeth on an eleven tooth blank for strength.

Doesn't always happen but often enuogh to look out for.

Measuring your center distance will be a help. DOS Bobcad, btw, will give you a dxf of gear teeth. Maybe not great but should be okay for this.
 

GregSY

Active member
I re-measured the pitch, this time more carefully, but I still am getting a 'funny' number.

250MM / 40 teeth = 6.25 pitch

Does this sound plausible? Or am I doing the math wrong?


If my pitch is 6.25, my module is (basically) 2 then using Peter's formula I would need 12 teeth:

28 = 2(12+2)
 

EmanuelGoldstein

Active member
Does this sound plausible? Or am I doing the math wrong?
Metric doesn't work the same as inch. It's upside down and backwards, so you really should either do it entirely in metric or in inch then translate, but don't try both. Module teeth don't do pitch, they go from the size of the teeth, it's beneath stupid but what can you say ?

(If those are 6DP teeth, that thing must be huge)
 

GregSY

Active member
So 'module' is a metric thing only?

I'd be willing to change my 250MM to 251MM....better light and better eyes are saying 251MM.
 

EmanuelGoldstein

Active member
So 'module' is a metric thing only?

I'd be willing to change my 250MM to 251MM....better light and better eyes are saying 251MM.
This is my own personal opinion, don't want to argue about it, but the metric system of teeth, aka "module" sucks balls. It's upside-down and backwards and inside out and stupid. It is much more logical to do everything in inches and diametral pitch, then convert to metric at the end, than try to do it their stupid way.

Gears work on pitch diameters. That's the foundation for everything. If you try to work from the size of the teeth instead, you are kicking yourself in the head unnecessarily. DP is logical and simple, module is crap.

So when I do something like this I work it all out in inches and diametral pitch, then convert at the end.

Other people are free to do things their own way. I don't really care if people put their shoes on the wrong feet, their pants on backwards, shirt on inside-out and walk on their hands. Not my problem. But logically, I find it unnecessarily inconvenient.
 

pavt

New member
So 'module' is a metric thing only?

I'd be willing to change my 250MM to 251MM....better light and better eyes are saying 251MM.

I do believe "module" is metric only, it is the metric way of calling gears and they tend to use whole numbers.

That is an excellent book, BTW, I have read it a few times and it never gets old.

If you don't feel like making your own, pre-made pinion shafting is a stock manufacturing item nowadays. For example this one, specified in modular units with 12 teeth: KHK SSGS2-12, Module 2, 12 Tooth, Ground Spur Pinion Shafts | Ground Spur Pinion Shafts (SSGS) | KHK USA Metric Gears
 

johansen

Active member
laser cut a 12 tooth 2 modulus gear from 1/8" plywood and see if it fits your machine.

if it does, try buying a 5$ 12 tooth 20mm wide 2 mod gear off of ebay and wait three weeks for it to get here.
 

GregSY

Active member
That's interesting they sell pre-made gears. I think it would work, though the teeth are not as wide as I'd like. My rack has about 2-1/4" or 2-1/2" wide teeth. I know that much contact is not needed, but....

Whatever I make, it will first be cut out of PVC and tested for fit. I have a niece piece of Vasco steel I'll probably use but only after I am sure it's right.
 
I agree, the rack is straight-toothed but the examples of rack/pinion gears I have seen online clearly show the pinion teeth are 'profiled'.

I can smugly add, after digesting a couple of chapters of Ivan Law's book (recommended by pavt on the free hobbing thread), that the rack has straight sided teeth as it is effectively a gear of infinitely large diameter.

Nothing else to add, more chapters to read first..
 

GregSY

Active member
"With anything under 14 teeth there's going to be undercut. Measure the bore and report back. "

I'm not sure how undercut applies here...does that mean the OD of the gear will be lessened?

This did make me realize, in looking at the column and rack, that the horizontal crank feed will only work when the head is in the upright position. If you have the head laid over there will no longer be any mesh between the teeth. It also makes me realize that the pinion must be removed before you can rotate the head...the teeth otherwise would prevent the rotation. This fact is probably why the original pinion shaft is missing....someone removed it to rotate the head and it never made it back.

I can tell you this much...the bore stays at 28MM all the way past the teeth. This means the bottom of the rack teeth are in line with the 28mm plane. The rack teeth don't hang below or above the 28MM bore.voest pinion shaft.jpg
 

pavt

New member
That's interesting they sell pre-made gears. I think it would work, though the teeth are not as wide as I'd like. My rack has about 2-1/4" or 2-1/2" wide teeth. I know that much contact is not needed, but....

I can't find the link right now, but somewhere I had saved the websites for a few companies that make entire shafts with the gear teeth, just saw it off to length to get the width of gear that you need, but dammit I can't find it on my computer!!!!
 

Peter from Holland

Active member
You did your calculation perfectly In spite of all the nonsence comments on going DP first and then convert
12 Teeth Mod 2 will give you a OD of the gear of (12+2)x2=28mm
So order the Mod 2 gear cutter from 12 teeth up
If the pressure angle is 20Dgr undercut will be acceptable


Module system is easy enough if you remember that each modul is Phi (3.14mm) pitch
And if you are used to of measuring in metric
It is a metric system so stick to that
More module gears are made as DP gears I recon

Peter

PS Normally I am very much in favor of a premade gear But in this case itis hard to connect to a rod strong enough With this very low speed application, cut it with a dividing head then
 








 
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