How to determine a gear's PA?
Hi guys, I have some gears I understood to be 20 degree PA however there is significant debate as to whether they are actually 14.5. As I don't presently have the cutter, is there any way I can measure the gears and determine the PA?
I believe the formula to determine the DP = number of teeth/pitch circle diameter. However the PCD is less than the overall gear diameter and I'm not sure how that's determined.
DP: Add two to tooth count and divide by OD of gear.
32 tooth gear, 2.125" OD
34 divided by 2.125 = 16 DP
Concerning pressure angle I lifted this "calculate from measurements" method from somewhere I (presumably) considered reliable.
"as long as you know the 'DP' of the gear the following will give you a good guide to the pressure angle 'PA'.
Take a measurement over any number of teeth with whatever equipment you have, multiply the cosine of the 'PA' by 3.1416 and the divide by the 'DP' add this to your measurement, this should be the measurement over one more tooth if its not the same, change the the 'PA' and try again.
10dp 14.5 pa, 30 teeth,
Measurement over 3 teeth .776,
Cos 14.5° = 0.986147
(0.986147 x 3.1416) = 3.04
3.04/10 = 0.304
0.304 + 0.776 = 1.080 which will be the measurement over 4 teeth if the gear is 14.5° PA."
In practice you only have 14.5° and 20° pressure angles to choose from for general purpose gears so the difference is pretty conclusive.
I'd be very careful with gears having heavily modified addendum and dedendum tho'. Its quite possible to modify the gear sufficiently to make one tooth difference in the tooth count when compared to a standard gear of the same nominal size. Which can be confusing. Japanese motorcycle gearbox designers frequently exploit this. Fortunately such tricks are mostly restricted to very special purpose jobs or serious mass production things where the tooling and design costs can be accommodated.
I believe the Boston Gear Catalogue illustrates the standard tooth shapes so its worth comparing if you get a strange result.
If you have a Cad system with a gear tooth drawing function, you could try drawing one gear with each PA, print them out to full scale and compare the sample gear. The 20 degree PA has a sustantially wider looking root to each tooth, and a pointier looking tip.
It would be great if there were a formula for calculating the tooth thickness at, say addendum depth/2 so a person could figure out which pin gauge would be tangent to the teeth at those depths.
One could do this by construction with a Cad system as well.
maybe not what you want to hear, because it involves a purchase....but i have this neat gear tooth set of gauges, leafs sort of like thread gauge. it has 14.4 an 20 PA gauges - when you use it there is absolutely no doubt which is which....may has HuFlung suggests a cut-out of a print out of the right DP would accomplish the same
If they are non standard gears, the spreadsheets in this thread and a little drawing software will tell you exactly what you have - Spline Chart?
If the gear is small enough and you have a flat bed scanner, scan the gear at high resolution and print a section of the gear image. Use a protractor and pencil and draw a rack such that the teeth of the rack are drawn at 20º and 14.5º, and meshed with the image of your gear's teeth. It should be pretty obvious which is the better fit. You can also draw the rack and cut it out with scissors.
One could also roll the gear along the surface of some modelling clay thereby 'generating' a rack, then measure the included angle of the teeth that way.
or: find your local industrial supplier that sells gears. They have "gear pitch gauges" that look like screw pitch gauges except for gear teeth and will identify them for you, tell you if its a stock gear( or something close that can be modded into what you need) and how much.
Thanks guys, some great suggestions here. It's on a lathe so, assuming all the gears have the same PA, I have a rack to work with. The trouble is I've tried to measure it with the rack in situ and with them being relatively small it's not immediately obvious. They certainly look like 20 to me, but swinging the protractor around to 14.5 it can be a bit difficult to tell for absolute certain. I will need to take the rack off soon anyway, and it may be easier to see once I can get a bit closer to the action, but in the meanwhile had hoped there was some formulae etc I could measure with something and come up with a definitive answer. Sadly I don't use any CAD software, but wish I did ... I'm always in too big a hurry to start cutting metal; measure once cut thrice
Clive, from the information you and John have given me I should be able to sit down with some of the gears tonight and work it out. Cheers
Edit: incidentally the application is on a locally produced SB clone. I was always on the understanding the SB and Hercus (locally produced) were virtually interchangeable, with the exception of the threads (local one is whitworth), and the change gears (local one uses 20 degree PA instead of SB's 14.5). However I've seen somebody producing change gear sets locally with a 14.5 PA and I'm pretty sure that's wrong. Before I start buying expensive cutters I want to be sure!
Originally Posted by Pete F
Do as Johnoder suggests to find the D.P. of the gear then measure the whole depth of a tooth (O/D - Root Ø)/2. Your answer for a 14.5° P.A. should be approximately equal to 2.157/D.P. and 2.25/D.P. for a 20°(or greater) P.A.
e.g. 14.5° 10 D.P. depth should be about 0.2157" and 20° 10 D.P. should be about 0.225"
Last edited by stroker; 05-06-2010 at 08:42 PM.
Reason: Hi not Ho!
Hi, hey who ho?
Originally Posted by stroker
Where did you come up with that, Mike?
e.g. 14.5° 10 D.P. depth should be about 0.2157" and 20° 10 D.P. should be about 0.225"
Both 14.5 and 20 degree P.A. full depth involute per ASA-B6b are the same Minimum Total Depth, 2.157 divided by DP
For what it is worth,the gears on a Hercus "SB clone" are 14.5, at least the ones on a friends one are. However if you have a Sheraton "SB clone "and it is a later model with the taper roller headstock the gears are 20 degrees. Another friend has one of this models Sheraton, it came with a damaged bull gear, the 600 Group wanted about $600 for a new one, we tried a Hercus one on it but found it was not compatable, so I repaired the damaged gear with nickel bronze and re-cut the filled section with a 20 PA cutter. The lathe is still going strong. I don't know if the early plain bearing headstock Sheratons are 20 degrees but I would suggest that they might well be.
As has been posted above, the use of "Base Pitch", is the most effective method if one has no gear testing gauges. A simple dial/digital caliper, measure the difference between the "span measurements" of one tooth difference, [3~4. 6~7, bigger gear more teeth] gives the "Base Pitch" from which the Pressure Angle can be determined accurately, this works on all gears/splines even with modified addendum's.
Base Pitch = (Pi/Diametral Pitch)x(Cos of Pressure Angle).
Base Pitch for unit one, (1 Diametral Pitch):
14.50° = 3.0415
17.50° = 2.9962
20° = 2.9521
22.50° = 2.9025
25° = 2.8472
27.5° = 2.7866
30° = 2.7207
Circular Pitch gears:
Base Pitch = Circular Pitch x (Cos of Pressure Angle).
Metric Module Gears:
Base Pitch = [Metric Module x Pi] x (Cos Pressure Angle) (in millimeters )
Divide by 25.4 to get inch equivalent.
Theoretically the tooth depth for an involute is a specified fraction of the circular pitch (i.e distance between teeth). This changes (slightly) with pressure angle so given two perfect involutes cut with zero clearance on their correct PCD for the same number of teeth it "should" be possible to identify the pressure angle by measuring the tooth depth. In the real world teeth are cut with addendum, dedendum and clearances to, hopefully, a recognised specification. The permitted variations usually being more than enough to scupper any chances of a reliable ID by this method.
In practice, as you say, the basic specification refers simply to minimum total depth without worrying about the slight theoretical differences due to pressure angle. Which hardly matter anyway as those parts are "in the wind" and don't actually do any driving.
As the OP is talking about lathe change gears, presumably cast, the tips will almost certainly have been cut back by several thou to make setting up on the quadrant a bit easier and to ensure that hard tip to root contact is unlikely even when the gears wear.
Profile projector works pretty well, if you can gain access to one for a few minutes.
to approximate pressure angle
If certain of pitch, select a pair of measuring wires using the standard pin size formula of 1.728/DP for externals.
Closely measure gear over pins and calculate CTT for both 14.5 deg and 20 deg values. Choose pin pairs of .005, .010 and .015 both larger and smaller then standard size. Again calculate CTT for both pressure angles. Compare values. CTT should remain constant for sample's PA.
Or buy a 12M instrument and roll for base circle dia. I usually do both almost daily.
Yes I checked 2 change gears using the above technique and came up with 14.5 degrees, not what I was expecting! However the spindle gear came out closer to 20 and I doubt they would mix 14.5 and 20 in the same machine.
Originally Posted by Peter F
One I did have trouble with was the pinion gear on the rack, as it's that gear that's most worn, an why this whole thing came up. While the PA may be different to SB's, the DP almost certainly won't be. The gear is 13 tooth and I measured it at approximately 1.125, that gave a DP of 13.3???? Is that possible?
In the Hercus Gears you have 16,18 and 20 DP,as far as I know all Gears are 14.5 PA.