IDENTIFY A GEAR

[MRSSPOCK]

As a newcomer to gears, I have been busy trying to measure an existing gear to try to determine its origin, i.e. the data used to generate it.

I have been studying various forums and reading all sorts of ways to determine what gear you have in hand, and what pressure angle it has etc.

The problem I have with so many discussions is that people assume the O.D. is reliable and that no correction has been added.

I created a CAD file to simulate a rack cutter generating a gear, and also an Excel file to output the tooth data.

What I have discovered is that its possible to have two sets of input parameters, which produce exactly the same gear!

Okay, there might be a tiny bit of difference in the root area, but that's in the clearance zone anyway.

The image below shows two gears generated with completely different data, yet they're identical.

http://i59.tinypic.com/2dan8fs.png[/IMG]]

The purple is obviously generated by the rack cutter simulation, with the data, Module 2.0, 20° deg P.A, 0.295mm offset.

The grey one is from my Excel file, with Module 2.11111, 27.105° P.A, 0.0 offset

I know the Excel data is completely random, but does it not show that gears don't necessarily have an absolute identity?

Does that mean the same gear can be referred to in different terms?

I guess there are application where for example gears don't need to adhere to conventional manufacturing methods, such as EDM manufactured gears, so in such cases do people still try to stick to whole number Modules, or is it okay to create totally random gears if the required application demands it?

I ended up measuring tooth thickness at various displacements from the gear centre using a DTI and milling machine for indexing, then plotting these co-ordinates on CAD, and then driving the best fit involute through the points.

Having the added bonus of the gear pump body at hand to measure the actual centre distance, I was able to use this as a means to check my measured involute. I was surprised how accurate the best fit involute method turned out to be, within a few microns.

This is a gear pump gear so as such I didn't know if it would follow normal gear conventions, and measuring the O.D. at Ø23.25 seemed to confirm it is a bit random.

 

[mfgenggear]

Mrsspock

take the data and the actual gear and have a gear shop inspect it.
ask for for the results to be Din or AGMA class. if the DP and PA are correct the
Involute chart will be acceptable.

also ask them to reverse eng the gear for you. to qualify your data.

a gear can have different DP & PA but must have the same base diameter. in order for it to have correct conjugate tooth action.
when a gear is inspect all the attributes are measure to verify the machined gear is manufactured correctly.

http://www-mdp.eng.cam.ac.uk/web/li...s_dvd_only/DAN/gears/toothForm/toothForm.html

Mfgenggear

 

[3DDave]

What MRSSPOCK is missing is that the data is recorded a certain way for easy of understanding, not 100% uniqueness. As Mfgenggear pointed out, the primary driver is matching pitch at the base circle. This combination isn't where the gears mesh and it is usually difficult to verify, so it offer no clue as to how intermeshable the gear is with other gears.

In particular, the pressure angle changes all along the face of the tooth, starting at 0 degrees at the base diameter. By picking some random diameter one can convert a particular base diameter into one of the infinite values for pressure angle.

The convention is to match gears on a particular pressure angle, one that might be generated with straight-tooth rack, and then pitch diameter so that gear train designers know what the ideal center distance is. Finally, the pitch at the pitch diameter so the size of the teeth is known.

It is possible to create unusual gears. Look at the

http://www.gearotic.com/

website for usual and unusual shaped gears. See the

https://www.youtube.com/watch?v=iTeOrCxqzBs

for "NonCircular Gears" generation.

 

[MRSSPOCK]

Thankyou both for confirming what I deduced while trying to figure out how to tell a gears pressure angle / offset / module.

I originally thought that the pressure angle was a feature of the gear, but once I investigated it, I realised that the involute is just like you say, purely a function of the base diameter, and the same involute can serve different pressure angles / offsets / modules.

I also just noticed that what I thought a random O.D. of Ø23.25 isn't so random at all.

If I calculate (N x m) + (2 x (m x (1 + offset)))

I get (9 x 2) + (2 x (2 x (1.295))) = Ø23.18

or

(9 x 2.1111) + (2 x (2.1111 x (1 + 0))) = Ø23.22


@ mfgenggear, regarding taking it to a gear shop, this is purely an academic exercise at this point. I just want to understand the geometry myself and how to measure it. I want to design some gears eventually for a special one off gear pump, so I really want to get a grounding with regards to gear geometry, so I can know exactly what I want before considering coughing up any money. It could be quite an expensive learning curve I imagine, if I get it wrong for the first few goes :-O

Thanks again

 

[mfgenggear]

Mrsspock

Sorry about that I got the impression you were trying reverse engineer that specific gear.
far as design there are many good experts here that can lead you to the correct method.
gear tooth contact ratios, enlarged pinions (to prevent under cut) , involute & tooth corrections.
efficiency, and and the best material and heat treat type case harden vs core hardening or both.
how
I can help far as manufacturing. the tools use to generate tooth involute, and verified by using standard
gear inspection.

most start with what center distance will the application require. what DP and pressue angle will be required for the
stress and torque loads. many many attributes to consider.

HTH
Mfgenggear

 

[MRSSPOCK]

Hi again.

Here's a couple more questions.

1.

Since the curve generated at the root isn't really a true radius, how is that area of the gear actually inspected?

I haven't come across any information throwing any light on inspecting this area.

As you can see in the attached image, even a sharp corner on the cutter generates a rough curve,

so how on earth do you verify from inspection what rad the cutter tip had on it.

I realise you can assume it was a standard, but surely there must be a way to verify it nevertheless?

2.

I have a gear in my hand with 24T

When I measure it across pins of Ø3.995, I get 57.447mm

When I measure across 3 teeth I get 16.56mm

I am completely confident that the gear is either a standard P.A. and an odd ball module, or a standard module and an odd ball P.A.

It seems a bit bizarre that this is the case, but I am convinced I have measured it absolutely correctly and have verified it with various equations to within 3 decimal places.

I'm convinced it is either a). or b). shown below, each set of data providing exactly the same gear.

a).

Module 2.116666... (i.e. 12 DP)

P.A. 21.5°

Addendum correction of 0.137


or


b). Mod 2.09577

P.A. 20°

Addendum correction of 0.2722


So, the question is, would manufacturers make such an oddball gear?

I wonder is it because this is a motorcycle gearbox stub gear, where a common centre distance has to suit all 5 different ratios.

Do they maybe have to fudge some parameters to make the best compromise as regarding optomised engagement for each of the 5 speeds?


Just for reference, the addendum is 0.833, and the dedendum 1.075 (with regards to the 2.116666... module)

I've also measured it with a tooth vernier which agrees with all of the above.

Finally, it is definitely not a module 2.0 since this would require a pressure angle in the order of 10° and an enormous addendum correction.

Thanks

 

[MikeHalloran]

WRT to the cutter radius, you could make a replica of the tooth root you wish to measure,
section it, and examine it under a microscope, perhaps with a template in the optics,
or just looking at the end of a gage pin placed adjacent the replica.

Even in your CAD system, at some point, starting with a zero corner radius on the cutter and steadily increasing it,
the gullet produced by a single tooth pass will eventually be shallow enough to not resolve on your screen, and a real cutter's
mark will be indistinguishable from a scratch.

Beyond establishing that the cutter had enough of a radius to not leave a terrible stress raiser,
well, why should you care?

Example: The Gleason system generates compound curved hypoid teeth using straight sided cutters,
of generally trapezoidal shape, with a modest edge radius between the three cutting surfaces.
You can see the tracks of the individual cutters in the tooth roots of the finished gears.
Nobody cares.



Mike Halloran
Pembroke Pines, FL, USA

 

[gearguru]

Don't you think that the center distance and no. of teeth of both gears in the mesh also play a little bit in your calculations? Where you calculate the "pressure angle" and the tooth thickness? - on what diameter? The root curve(s) differ by manufacturing methods; they can be broached, hobbed... They can be different and they still can work perfectly in the mesh of those two gears.
Gear box manufacturers use special tooling to make their gears, not necessary the very limiting standard (and which standard?) tools.

 

[MRSSPOCK]

Hi, thanks for your replys.

@ MikeH

"why should you care?"

Clearance.

Suppose, you have a non standard gear, (such as the 24T gear I mention) being manufactured by one manufacturer, and its mating gear being manufactured by another manufacturer, both of which haven't got the convenience of testing the two mating gears together at their working centre distance.

Supposing I as the customer want an inspection report from the individual suppliers to prove they have made the gears to my specifications, one parameter of which is that the tooth generating tool must have a fillet rad of lets say 0.6mm

So, is what you're saying is, there is no way to verify that dimension by inspection?

I think nobody cares in the instance you describe because it doesn't matter, but lets say the application your gear is intended for can't afford too much extra clearance and having a tightly toleranced root fillet is in your best interest, then that's a different situation.

Maybe in such a situation I describe, its just case of getting the gear pair from both suppliers and then inspecting them as a pair, but I just thought it made sense that a gear could be verified to be in agreement with the specification on the drawing, after manufacture, before delivery.


@ gearguru

centre distance and centre distance tolerance, backlash tolerance, runout tolerance, pitch diameter, working pitch diameter and working pressure angle, etc and are all included in my calculations, but none of those are necessary to reverse engineer a gear.

The involute is what it is and has a unique base circle irrespective of its mating gear and its centre distance.

The tooth thickness at various known diameters are all that are required to define the unique involute and hence reverse engineer it, a tooth vernier or a DTI mounted on a two axis measuring device, providing adequate data.

So getting back to my initial question, I presume there is no way to figure out what rad was on the generating cutter?



I suppose maybe a better way at putting my original question might have been,


I have 24T gear in my hand with the following dimensions:

Outside diameter = 54.95

Root diameter = 46.82

And the following data provide an involute which matches exactly the measured involute,

P.A. 21.5°

Module 2.116667

Addendum correction = 0.137

And the measured values, below, are in complete agreement with the gear geometry generated by the above data.

Distance over Ø3.995 rollers = 57.447mm

Distance across 3 teeth flanks = 16.56mm



So, now suppose I want a batch of this gear manufactured. I presume the data supplied is adequate, all expect one value.

How do I stipulate the tip radius that the generating tool must have, or how do I measure the root curve on the gear in my hand in such a way to be able to stipulate its size to a manufacturer?

I hope that makes my question make a bit more sense.

I would just want to be sure that a batch of gears arrived with not enough root rad clearance, because it wasn't stipulated on the gear order correctly.

By the way, at present this is only theoretical but I just want to have confidence as and when I do find my self ordering a batch of gears, that I have defined them correctly.

Thanks again.

 

[MikeHalloran]

You seemed to be asking about the generating cutter's corner radius,
and I told you one way to measure it. You could also get the information from
a sufficiently fancy profilometer.

The tooth root radius is different. You can measure it differently.
For instance, to check for a radius of 0.6mm, you can
lay gage pins of 0.5 and 0.7 mm radius in the root and watch
how they behave. The pin of smaller radius will roll a bit,
touching the root on one line, whereas
the pin of larger radius will touch the root on two lines,
and will not roll. You can verify by touch or optically.

You could even use one of them damn CMM machines to extract the tooth root radius.



Mike Halloran
Pembroke Pines, FL, USA

 

[gearcutter]

I don't think that you have correctly identified your samples.
All you need to know when reverse engineering a standard spur gear tooth profile is;

No. of teeth
Major diam
Minor diam
Base pitch (calculated from 2 base-tangent-length measurements taken over the best fitting no. of teeth)
Center distance

This is assuming that there are no profile modifications such as crowning or tip/root relief.
If you need to know exactly what the sample's profile is; send the part to someone that has a CMM or a gear tooth profile checking machine.

You do not need to specify the root profile and clearance; unless you are trying to do something specific, like maximising tooth strength.
If this is the case; then you are going to require special non-standard cutters.

All standard involute gear tooth profiles will mesh correctly even if generating cutters with different tip radii are used.
A full fillet profile will mesh correctly with a partial radius profile.
For maximum strength; specify that a full fillet cutter be used for both profiles.

There are rare examples where addendum corrections have been applied inappropriately or low number of teeth are used.
In these cases, non involute contact may occur. Generally, to avoid interference in these cases, the teeth are truncated to remedy the situation. This is not a sound design practice though, and shows sloppy work on the part of the designer.

 

[gearguru]

If you know that much about both meshing gears then you for sure know the SAPs on both of them. The root, doesn't matter how created, has to be below it. Are you sure it was hobbed?
And the flank of the tooth is rarely just a perfect involute from the SAP to the tip. There are always some refinements to it especially in the mass production gear boxes.
If you want to replace the gear, replace both of them.
There is a way how to model in the CAD the trochoidal root curve created by hob/basic rack; try different rack profiles and compare it with your gear, if you really need it.

 

[MRSSPOCK]

Thanks for your help everyone.

Its all making much more sense now.


@gearcutter

Just one thing I still can figure out though.

Why do you need the centre distance to copy what you have in your hand?

Surely the data you describe thus:

"No. of teeth
Major diam
Minor diam
Base pitch (calculated from 2 base-tangent-length measurements taken over the best fitting no. of teeth)"


is adequate to replicate the gear you have in hand without having to know the centre distance?

By following your information I was able to create a sample gear in CAD in two minutes, but without a need for the centre distance.

i.e. using,

O.D. 56.96

Minor Diameter 34.67

10T

34.43 over three teeth

21.12 over two teeth

Base pitch, 34.43 - 21.12 = 13.31

Tooth thickness at the base, 34.43 - (2 x 13.31) = 7.81


Am I missing something?

Thanks

 

[gearcutter]

Why do you need the centre distance to copy what you have in your hand?

Because it can help you confirm addendum & backlash corrections to help ensure mating parts will mesh together correctly. It's not so essential for spur gears but an absolute necessity for helicals.

By following your information I was able to create a sample gear in CAD in two minutes, but without a need for the centre distance.

Does that have anything to do with the part you are having trouble identifying?
I fail to see your point here.

 

[gearcutter]

O.D. 56.96

Minor Diameter 34.67

10T

34.43 over three teeth

21.12 over two teeth

Base pitch, 34.43 - 21.12 = 13.31

Tooth thickness at the base, 34.43 - (2 x 13.31) = 7.81

That data fails to match up with any standard pitch/pressure angle combination.

 

[MRSSPOCK]

"Does that have anything to do with the part you are having trouble identifying?
I fail to see your point here."

My point is simply that if I can recreate it in CAD, then it can be recreated without knowing the centre distance.

"That data fails to match up with any standard pitch/pressure angle combination."

I haven't worked it out accurately, but at a glance, it looks to me to be Module 4.5, P.A. 20° with about 0.19 addendum correction.

I will check it again later.

Have to go out right now.

Thanks

 

[gearcutter]

My point is simply that if I can recreate it in CAD, then it can be recreated without knowing the centre distance.

What if the sample you are working to is worn to the point where a significant amount of tooth-cross-section has been reduced?
How do you calculate the original tooth thickness?
Do you work to a standard?
Do you guess what it should be?

Or do you take the mating gear's data and, along with the center distance, use this information to determine precisely what the amount of addendum correction and backlash is required to ensure that the correct assembled clearances are maintained?

If the replacement gear is going to cost something in the order of several thousand dollars to manufacture; I'm quite sure which path I would take as I can't afford to work off guess work alone. I need to be able to prove that my calculations and design will work correctly.

 

[MRSSPOCK]

@gearcutter

100% agree.

That was my point from the very beginning of the thread.

If I want to have a bunch of costly stuff made, I want 100% confidence what I order is an exact replacement of what I have in my hand, regardless of what standard values it might be assumed to be, or regardless of what standard conventions it might assume to adhere to.

But I still reckon that gear data I gave, worn or not, is based on Module 4.5 and P.A. 20° with an addendum correction.

You seemed to suggest it was nowhere close to any standard.

I've modelled both and they can be made to coincide by adjusting the addendum correction.

Thanks again.

Your comments have been really helpful.

I can now do in a few minutes what took me an hour before.

 

[gearcutter]

Base pitch (inches) = Mod x 0.12368 X (cos PA)
4.5 module, 20deg PA, BP = 0.5230"

Your data for BP = 0.5240"

That's close enough even with a 1 thou error.
My mistake...........well done with your calcs.

 

[Occupant]

If you mean by the addendum change that there is a profile shift then that would be x=0.329 to match your O.D., but the root dia. would be wrong and the measurements would come out per attached.