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.

 

[MRSSPOCK]

@occupant

Hi.

Aren't you making the assumption that on my sample gear, the O.D. and / or root diameter are somehow tied up to the involute form and base pitch?

Okay, in certain instances they are, when certain standards are being adhered to.

But the O.D. and root don't define the involute, but rather the inverse, they're defined accordingly.

They have no influence at all on the over teeth measurements until some standard addendum and dedendum values are being adhered to, which should then of course show some correlation.

Compare a gear pump tooth, (as my last referenced sample is), with stub tooth from a gearbox. They're wildly different in form with respect the O.D. and root.

 

[Occupant]

No, that wasn't my point. What I said or at least implied was that what I drew up is a semi-standard gear with a somewhat unconventional profile shift. Yours is just a made up gear that doesn't fit any norm and if that's what you are after then there is no need to ask any questions about it.

 

[MRSSPOCK]

It's actually not made up.

Here it is.

http://i60.tinypic.com/16isikk.jpg[/IMG]]

 

[MRSSPOCK]

As you can see, is quite unconventional, and like you say, with an unconventional profile shift.

I don't understand why people automatically presume things are conventional.

I would tend to presume the opposite to be true, and thereby help ensure something incorrect isn't created purely as a result of presumption.

 

[gearcutter]

So is all the 10-teeth gear data that you have supplied taken from this sample?

 

[MRSSPOCK]

Yip.

The 24T gearbox stub tooth mentioned further up the thread is another real example.

 

[gearcutter]

That gear looks like it's the driven member of a hydraulic pump.
Typically; 22.5 deg pressure angle is used in this application.
How accurate are your BTL measurements +/- ?

 

[MRSSPOCK]

Just as good as a digital vernier.

I guess +/- 0.001"

I was only using this gear as a reference to learn from, so I was happy enough to use just a vernier for the exercise, knowing full well it isn't very accurate.

Though my vernier would need to be pretty much trash, (+/- 0.005") for the gear to be 22.5° at 4.5 Module

My verniers fairly new so it's pretty good.

 

[Occupant]

I didn't mean that you are phantasizing, only that you can't produce this gear with a standard hob and/or the root would
have to be cut afterwards. The sample looks like that anyway with the little bit of undercut it shows.By the way if you
don't have to worry about the O.D. being standard, you could cut this with a profile shift of 0.185 (standard O.D. would
then be 1.3mm smaller), but the measurements would come out to be 21.127 and 34.411 respectively.

 

[Compositepro]

A little off-topic, but I think you mean digital calipers. Verniers are an analog scale.

 

[MRSSPOCK]

@Compositepro

Well spotted.

I've been using that term form about 30 years and never realised how silly it was until now

@Occupant

"with a profile shift of 0.185 (standard O.D. would
then be 1.3mm smaller), but the measurements would come out to be 21.127 and 34.411 respectively."

Sorry, this confuses me.

Could you explain how the O.D. is dependent on profile shift?

How can retracting the cutter make the O.D. smaller?

Forgive my ignorance regarding gear cutting operations.

I created the gear in CAD directly from measured data, then simulated a rack cutter operation, both to the same specifications, and both overlay perfectly, with no impact on the O.D.

You can see the specifications in my parameter tree. (I just created the fillet in the purple manually, i.e.not part of my simulated rack cutter).

http://i62.tinypic.com/296kcc0.jpg[/IMG]]

 

[MRSSPOCK]

I'm maybe not using the proper terminology for the length of arc I'm referring to,

but does anyone know is there a simple equation which lets you determine circular tooth thickness at the base, where the known inputs for the equation are only:

P.A.

Profile Shift

Module

Thanks

 

[Occupant]

Could you explain how the O.D. is dependent on profile shift?

That's not very difficult: Addendum = M * (1+x-k)
"x" is the profile shift, "k" stands for shortening of the addendum - not applicable in your case,
and OD = PD + 2*Addendum

 

[MRSSPOCK]

@ occupant

Okay. I see now what you mean about the O.D.

Thanks.

But, because the sample gear doesn't necessarily follow a standard convention regarding addendum, and the O.D. of a pump gear has quite crucial dimensions with respect to casing clearance, the O.D. is one value that can't deviate at all from the sample, no matter what the resulting addendum is.

Just a few microns undersize and the pump doesn't even work.


I still don't know why you suggest cutting it at 0.185 and ending up with incorrect dimensions, (compared to my sample), when it can be cut at 0.19 correction like I calculated, which provides the correct dimensions as verified by gearcutter.

 

[Occupant]

0.185 results in over 3 teeth: 34.411, over 2 teeth: 21.127
0.190 results in over 3 teeth: 34.427, over 2 teeth: 21.142
you had over 3 teeth: 34.43 and over 2 teeth: 21.12
Since over 2 teeth is the recommended number for this type of gear I thought the number of 21.127 would closer match
the value of 21.12 that you had. If you basing your decision on the value over 3 teeth, then the value from the x = 0.190
profile shift measurement of 34.411 would be closer.

 

[MRSSPOCK]

Phew,

I worked it out, and now someone will probably share an equation with about three terms in it, that does the same job

Here are the Excel equations for anyone interested.

The angular inputs must be radians.

PA = Pressure angle

N = Number of teeth

Mod = Module

X = profile shift

Tooth thickness at baseline before profile shift
=((((TAN(PA)-(PA))*2)+(PI()/N))*Mod*PI()*COS(PA)*N)/(2*PI())


Tooth thickness at baseline after profile shift
=(((((TAN(PA)-(PA))*2)+(PI()/N))*Mod*PI()*COS(PA)*N)/(2*PI()))+(2*(SIN(PA)*X*Mod))

@ Occupant

Thanks for your last post.

I hope your numbers are good, because my Excel sheet provided exactly the same results as your method

Thanks everyone for your patience.