View Full Version : How to tell a gears pressure angle?

09-09-2005, 01:03 PM
I have a 33 tooth 12 pitch table elevating gear from a old Walker-Turner 20" drill that looks like a old mans smile...missing lots of teeth. I would like to buy a different one but don't know how to figure out the pressure angle.Any Ideas? James

09-09-2005, 01:39 PM
Well you measure the area of the blood blister you get from being pinched by the matting gears. The smaller the blister higher the face pressure. http://bbs.homeshopmachinist.net//biggrin.gif Ok seriously that info can be found in The Machinist Handbook my copies not handy at the moment but I'm sure someone here will help you out with a through explanation including tips on repairing the gears missing teeth. http://bbs.homeshopmachinist.net//wink.gif

09-09-2005, 02:28 PM
Hi James,

Pressure angle = arc cos( Db / D )

where Db = base circle diameter and D = pitch diameter.

See the section on Spur Gearing in Machinery's Handbook.

You can find tables with gear dimensions in the catalog from Stock Drive Products. They're on the web at http://www.sdp-si.com but the website is pretty difficult to use unless you already know what you want.

[This message has been edited by Leigh (edited 09-09-2005).]

09-09-2005, 05:44 PM
I know the definition. The question is how do you determine the PA when all you have is a gear in hand. I assume there must be some measurement technique, or insturment, but I sure don't know what it is.

09-09-2005, 05:54 PM
Yes that is right. I have the gear in hand and would like to know the pressure angle to order a replacement. Also looking at part of Boston gears web site it looks like 33 teeth might be hard to come by. Any one know of another source?

09-09-2005, 06:01 PM
<font face="Verdana, Arial" size="2">Originally posted by jh:
...Any one know of another source?</font>

If you'd bother to read my previous reply, you'd find a link to Stock Drive Products.

09-09-2005, 06:07 PM
I don't think you can without a gear tooth caliper


not something you'd want to buy, in larger urban centres there may be industrial suppliers specializing in gears that would have one and be willing to measure you up for a replacement. Other than that, start networking until you find one

John Stevenson
09-09-2005, 06:30 PM
It's not easy to tell the pressure angle.
Calculations in Machinery handbook aren't worth a light.
Two main reasons, one is the gear is probably worn and so can't be accurately measured and secondly manufacturers often tweaked pitch sizes to give corrected tooth forms which puts everything off.

Gear calipers only give the correct tooth width on the pitch circle which is the same for 14.5 as 20.


Here's JH's gear, 33 teeth at 12 pitch drawn geometrically correct.
Blue is 14.5, orange is 20 degree.
You can see where the two overlap at the PD.,
this is the width measured by a gear caliper.

There are gear tooth gauges like thread pitch gauges which can measure PA but they are quite rare and very expensive.

I have found that the MK1 human eyeball with a geometrically correct drawing will do 99% of the time.
14.5 tends to be fatter at the top and more undercut than a 20 degree with has a fatter and stronger bottom part.

Historically it normally follows that 14.5 was used solely up to WWI and could even run up to WWII but 20 degrees was more common after WWII.

Machine tool manufacturers tended to stick to 14.5 for things like change gears because of legacy issues.
Myfords for one still run on 14.5 so they still only have to make one type of spare.

John S.

09-09-2005, 06:37 PM
ok John now how do I go about getting a copy of that gear drawing? You are telling me more than any one else has and for that Thanks. As for another source thanks will check into that when I've figured out the pressure angle. James

John Stevenson
09-09-2005, 07:12 PM
Gear drawing at

John S.

09-09-2005, 07:53 PM
Would this gear be meshing into a rack?

John S, would it be easier to measure the angle on the teeth on the rack if this is the case?


09-09-2005, 08:04 PM
Thanks for that diagram John! That is the most enlightening thing I've seen on the matter of PA, which has always been obscure to me.
I take back all the mean, nasty things I've ever said about you. http://bbs.homeshopmachinist.net//biggrin.gif

Rich Carlstedt
09-10-2005, 09:13 PM
What has worked for me in the past was to get another gear of the same pitch, but known PA, and just mate them.
When they are different, you can feel the hangup when meshing.
I know it's not scientific, but it works

George Barnes
09-11-2005, 12:02 AM
In one of my little adventures some years ago, I need to identify a gear and get a cutter to match. I decided that I should go ahead and invest in a gear tooth gage set. I bought one from MSC and the price then was pretty reasonable. the latest catalog that I have says $29.45. It has 14 leaves on a key ring and covers a range from 6 to 80 D.P. After reading this thread, I dug it out to see which pressure angle that this set matched. Surprise! It is not marked anywhere. I looked in MSC's catalog and it doesn't say either. Hmm? I know, ihave a gearback here in the shop. I'll check it and see if it mates up right. I remember that if you have the right D.P. but the wrong pressure angle, the gear will not roll aroung the gage easily. It will try to hang up. O.k. the gear and the gage match up well. the gear is a Browning NSS1636. I'll just check the Browning catalog and find out what angle it's supposed to be. One more little problem, I don't have a Browning catalog, I've got a Martin Gear catalog.

Has anybody got a Browning catalog and could you check and see if the NSS gives a clue as to what pressure angle that is supposed to be. I know that the 16 is for the D.P. and the 36 is the number of teeth. If sombody can fill me in, I'll mark the set so I'll know next time. The gage for 16 D.P. looks like it has a straight side of the teeth and a bevel protractor set at 14.5 degrees looks like it follows the tooth form.

Thanks in advance.

John Stevenson
09-11-2005, 03:46 PM
George, Sounds like you got the cheaper general set.
The proper sets, to use the word loosely, are quite expensive as they cover both the common 14.5 and 20 degree PA's

Here's a link.


Unless you have an ongoing need for these $128 a pop gets expensive.

John s.

09-11-2005, 05:15 PM
Someone posted this site awhile back.

George Barnes
09-11-2005, 10:37 PM
Ya, I'm sure that this is not the top of the line gage set but it has worked well for me so far. Used it just a while ago to try to answer a question.


Since I have gotten fascinatd by this 3-D drawing deal, I have run into several gears that I wanted to draw. I dug out an old drafting book that I had and gradually began to remember how the tooth forms are done. The one question that I have though is in these instructions it shows to use a radius of 1/8 of the pitch diameter for defining the tooth face. I'm just curious how that particular ratio was determined to be appropriate. Is that what you use in your drawings? Just wondering. Maybe it was a WAG on somebody's part. http://bbs.homeshopmachinist.net//smile.gif

09-12-2005, 05:28 AM
I bet your gear tooth gage is made by Fowler Tools, go to their website and look up your gage, all will be revealed. Your gage
is a 14.5 press angle.

09-20-2005, 09:46 PM
Finally found a little time to take the rack off the walker-turner, clean it up, and slap it on the comparator at work. Hey now it is easy to see it is a 14 & one-half degree pressure angle. Thanks for your help one and all. Did look on the Stock drive products web site they don't make any thing that big so have to look around. James

09-20-2005, 10:47 PM
<font face="Verdana, Arial" size="2">Originally posted by George Barnes:
...I have gotten fascinatd by this 3-D drawing deal,...</font>

Hi George,

That's a nice drawing. What program did you use? TIA

Leigh W3NLB

Paul Alciatore
09-21-2005, 12:16 AM

One eighth of the pitch diameter is just an approximation. A gear drawn with pencil and paper is only a representation and only needs to look like the real thing. It would be made to the proper form as specified, not as drawn.

The actual curve is not even an arc, but an imvolute curve. An involute can be thought of as a curve that has a constantly changing radius. That is, the radius is different at each point on the curve so no arc could ever be exact. There is no way to easily draw an invloute curve with pencil and paper or with most CAD programs. I generated one with a series of straight lines that represented successive positions of a hob as it generated a gear. I used a large number of such lines and trimed them to meet. Then I drew a spline curve that was anchored to the center points of each segment. Very tedious. It took several hours to do one tooth face. I then drew an arc that passed through three points on this spline. It matched within +/-0.0002" over the tooth face. That's pretty close. The gear was 18 DP, 14.5 PA and about 50 tooth. Smaller gears would show a larger error.

The one eighth number was simply chosen as a good approximation.

Paul A.