Measuring for the PA of an ordinary involute pinion gear

[Adam HarrisParticipant @adamharris13683]

I have a gear I would like to know the PA of (in order to cut a replica) but it is next to impossible to draw the PA on paper to measure with a protractor . I have read about taking a photo, enlarging, and measuring from the print. Is that really the only way to go about it? Since the gear is quite thick I cannot see how a photo could produce an accurate 2D image. Is there a set of distance measurements I can take with digital calipers that can be used to calculate the PA. How do gear manufacturers do this? Thanks for any thoughts. Adam

[Adam HarrisParticipant @adamharris13683]

[Neil WyattModerator @neilwyatt]

Roll it over a piece of blu-tac. It;''s imprint should be a more-or-less straight sided rack that will be much easier to measure. You may need to section the blu-tac with a sharp blade.

Neil

[Johnboy25Participant @johnboy25]

I've got the same problem but with a worm and gear for my Warco bandsaw. Think it's the same as a Clarke CBS45 looking at the pictures. I suppose the easy way out is to try to purchase a set. Had thought about using the gearbox components from a Belle cement mixer. I would like to remake the gear as a bit of a challenge but I really want the bandsaw working!

John

[Adam HarrisParticipant @adamharris13683]

Thanks Neil, that does sound a better idea!!! So when i look at the cross section of the imprinted rack, i take the midpoints of the tooth heights, draw a line and measure the angle of that line, from the intersection of that line with the side of a tooth, drawn to the top side/corner of the adjacent tooth's side ?

[Adam HarrisParticipant @adamharris13683]

but looking at the useful diagram in http://www.bostongear.com/pdf/gear_theory.pdf , it seems unclear as to where that midpoint line should be taken as there is a Clearance gap at the trough, which means presumably that the midpoint line is not half way between the top and bottom of the tooth?

[Adam HarrisParticipant @adamharris13683]

If I understand correctly , the midpoint line is the midpoint of the "Working Depth" which is the Addendum times two, or the total tooth height minus the Clearance gap. How do I get that???

[Adam HarrisParticipant @adamharris13683]

Sorry I meant a Spur gear not a Pinion gear, although I believe the principles are exactly the same…

[Michael GilliganParticipant @michaelgilligan61133]

A couple of thoughts, Adam

1. The image from a flatbed scanner is surprisingly good … Poor Man's ShadowGraph.
2. Draw [or grab from elsewhere] the theoretical shape for one or more standard pressure angles, and compare your scan with these. It will almost certainly be one of just a few standard options; so that's much easier than trying to measure it.

MichaelG.

[Keith LongParticipant @keithlong89920]

Adam

Depending on what measuring gear you've got you can determine the pa by measuring the gear with two pins or balls sitting between the teeth. I've NOT tried it but saw the method referred to by Graham Meek in his article about the screwcutting clutch. I've just located the following pdf which I think gives sufficient information for you to have a stab at it. Drill shanks come to mind for the pins as you can easily check the diameter of those. The measurement combined with the methods outlined above should give the pa to a fair degree of confidence, as Michael above points out it will one value of a very few possibles.

Keith

[Michael GilliganParticipant @michaelgilligan61133]

That's a very useful reference, Keith

Thanks for the link.

MichaelG.

[Adam HarrisParticipant @adamharris13683]

Keith, thanks – i suppose it is tortuously logical that one can work backwards from the calculations to find the PA but those calculations offered are all using the PA to find other measurements. I think the maths is somewhat beyond my flight range!

[John Stevenson 1Participant @johnstevenson1]

That link only works if the gear is a standard gear and follows all the text book formulae. As soon as you modify one thing that pin method goes out of the window.

These three gears are all the same OD, they have all been hobbed with the same hob but only the 22T is a correct text book gear. The 20 and 21 have been corrected so they will interchange between any shown.

The 20 and 21 will not measure correctly across pins but all three will give the same PA [ 20 degrees BTW ] when rolled into blue-tak or plasticine.

[Adam HarrisParticipant @adamharris13683]

Michael, i have the theoretical shape of 20 and 14.5 deg DP16 teeth from the bostongear website but I can assure you it is not at all easy to see the difference! And even less easy to compare the profile with my teeth, as one has no idea of how many toothed gear they are using for their profile, and as i understand it , the profile becomes flatter/longer the more toothed the gear is…

Edited By Adam Harris on 19/03/2015 12:58:00

[Adam HarrisParticipant @adamharris13683]

So John could you please tell me exactly what I need to measure on the plasticene imprint to get the PA?

[Adam HarrisParticipant @adamharris13683]

Incidentally I have contacted the well known HPC gears and they said they would match up the sample gear to their different cutters to get the PA (written on whichever cutter that best fits) which is clearly not much help to me. They are not offering to tell me my PA, if presented with my gear in the post, but rather a quote for making a replica themselves of course.

Edited By Adam Harris on 19/03/2015 13:05:11

[Michael Cox 1Participant @michaelcox1]

Here is another way of determining the pressure angle:

http://mikesworkshop.weebly.com/change-gear-pressure-angle.html

Mike

[BazyleParticipant @bazyle]

Take a punt on your favourite number and buy/make the cutter. You have 50% chance of being right and can always sell the cutter if wrong.

[Johnboy25Participant @johnboy25]

Interesting thread… Thanks for the useful links – they'll certainly advance my repair.

John

[Adam HarrisParticipant @adamharris13683]

Bazyle that is assuming it is 20 or 14.5, but Ivan Law's book mentions PA's of 30 so I think my chance of losing £30+ on the cutter is higher than 50%, and it does not solve the problem of gear replication of other gears in the future

[John Stevenson 1Participant @johnstevenson1]

Forget 30 degrees, don't know why Ivan mentions it. Involute splines are usually 30 degrees [ some are 22.5 just the muddy the waters a bit ] but involute splines are usually half size in that they are shallow.

Can you tell us what the gear is off, maybe someone knows ?

[Adam HarrisParticipant @adamharris13683]

John yes indeed – it is out of a Meddings Drill but that does not help me with learning the principle for future replacement of different worn gears. Meddings themselves are treating the PA as proprietary information and not willing to divulge it.

[Neil WyattModerator @neilwyatt]

Adam,

Have you had a go at the blu-tac method yet?

You don't have to faff around with mid points, as the gear should generate a 'rack' which has (more or less) straight-sided teeth. OK it will be a rather mangy looking and distorted rack but the difference between 14.5 degrees and 20 degrees should be obvious.

Neil

P.S. 'other angles are available':

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Adam Harris on 19/03/2015 11:44:40:

… Since the gear is quite thick I cannot see how a photo could produce an accurate 2D image.

.

Adam,

Just returning to this comment in your original post. ^^^

[unless the gear has chamfered ends, which could make it tricky] … If you can photograph the gear exactly end-on, there should be no problem: The combination of perspective and depth of field will hide most of the confusing details, and it is a simple matter to identify the edges on the plane surface.

The worst you are likely to get is some lens distortion [barrel, or pincushion], but you can easily check the performance of the lens by photographing a sheet of graph paper.

Alternatively, as I said before; if it's flat, put it on a flat-bed scanner.

MichaelG.

.

P.S. … Here is a photo that I took a while back; showing one tooth of a cutter … The lighting was awkward, but the image is certainly fit-for-purpose.

Edited By Michael Gilligan on 19/03/2015 14:45:48

[MuzzerParticipant @muzzer]

Dunno if this is of any use to you. It's imperial of course.

Bottom line, you are going to have to measure something and then determine if it's what you'd expect to see, or simply guess it's 20 degrees or whatever by eye and live dangerously. I don't suppose anyone would die if you got it wrong, worst case it may be a bit noisy perhaps?

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