Atlas Shaper Pinion Gear Question

[Wheels17]

Short Version:
Does anybody know the specifications for the Atlas 7B shaper pinion gear? The two most critical numbers I need to confirm are the number of teeth(easy) and the pressure angle(old gears, probably 14.5, but not sure).

I believe it is a modified Boston Gear NF15B. It's fairly expensive, and long lead time:

Teeth:15
Diametral Pitch 10
Pressure Angle: 14.5 degrees
Bore: .750
Face Width: 1.000

Long Version:

When I dismantled my Atlas 7b shaper down to the bull gear and drive pinion, I found the system to turn very roughly. The pinion was extremely chewed up. As I further dismantled the pinion assembly, I found that the taper pins had been replaced with groove straight pins. The bearings on the pinion shaft appeared to be ok once the system was dismantled. Also, the pinion shaft appeared to be turned, not the ground appearance on other shafts I have found on Atlas equipment.

In order to characterize the gear system, I started to use the formulae on https://www.engineersedge.com/gear_formula.htm . After much confusion, I discovered that there are (as of 3/11/2019) a number of errors in the gear formulae on that page. A request for correction has been submitted.

At the very bottom of the Boston Gear application notes, https://www.bostongear.com/-/media/.../p-1930-bg-sections/p-1930-bg_spur-gears.ashx , on page 310, there is a correct set of gear calculations.
Here is the data I have on my shaper, and the symbols for data I need to calculate:

Ng=Number of teeth in gear(Bull Gear) = 80
Np=Number of teeth in pinion = 14
C=Center Distance = 4.7454 inches
Do=Outside Diameter of gear
Dog=Outside Diameter of gear = 8.198
Dop =Diameter of pinion = 1.700
P=Diametral Pitch
D=Pitch Diameter
Dg=Gear Pitch Diameter
Dp=Pinion Pitch Diameter
a=Addendum

Calculate Diametral Pitch (P) using Outside diameter (Do), Pitch Diameter(D), and Addendum(a):
Do=D+2a
a=1/P
D=N/P
Do=N/P+2/P
Do=(N+2)/P
PDo=N+2
P=(N+2)/Do
Bull Gear
P=(80+2)/8.198=10.002
Pinion
P=(14+2)/1.700=9.412
The pinion seems odd. The diameter doesn't match any standard gears in the Boston Gear Catalog. At https://www.engineersedge.com/gear_formula.htm , there's a table linking circular pitches to diametral pitches. There's a 1/3 circular pitch that has a diametrical pitch of 9.4248, which is within .13%. I believe that someone has substituted a gear that is not original.

If I calculate the pitch of a gear with a diameter of 1.700 and 15 teeth, it is 10.000:
P=(15+2)/1.7=10.000

To confirm that this is the right gear, I need to see if the center distances are correct.

Calculate Center Distance(C) using 15 tooth pinion and a Diametral Pitch of 10:
C=(Ng+Np)/2P
C=(80+15)/(2*10)=4.750"
I back calculated a center distance of 4.745" based on a number of measurements of my actual shaper base casting.
This confirms that it is most likely supposed to be a DP10, 15 tooth gear.

I'm not sure of the pressure angle though. Over at https://www.model-engineer.co.uk/forums/postings.asp?th=45514 I found instructions for trying to determine the pressure angle written by Clive Foster.

Firstly you need to know the diametrical pitch, DP, of the gear, basically number of teeth per inch of pitch circle diameter. For practical purposes pitch circle diameter runs round half way up the tooth. As its always a whole number and only a few numbers are used best guess estimation is usually good enough unless you are watch making.

Given the DP take a measurement over any reasonable small number of teeth with whatever equipment you have. 3 to 5 teeth for a chord length of around 1/8 of a circle usually does just fine. Multiply the cosine of the 'PA' by 3.1416 and 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.

Example:-
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."

Obviously 10 DP is easy on the maths.

Doing this measurement suggests that it is a 14.5 degree pressure angle gear.

 

[benmychree]

You should be able to determine pressure angle, just looking at the gear, they are, and look different; take a protractor and sight the apparent angle of the tooth compared to a radial line, so far as the number of teeth, use an inside caliper on the bare pinion shaft to the root of the bull gear, measure that distance and deduct .020 for Clarence and multiply by two, that would be the OD of the pinion. It would be unlikely that it would be CP, given the probable age of the machine, CP has been uncommon for many years. All the dimensions for the pair of gears should be the same whether 14 1/2 degree or 20 degree. only the land width and width at the root would be less on the 20 degree, chordal thickness should be the same.

 

[Wheels17]

I did Clive Foster's calculation, and my measurements of 14 1/2 data was closer than 20.

Then I took a (poor) picture of the teeth on the bull gear. I put it into my CAD program and dropped some lines over the image. The ruler is across the centerline:

So tomorrow I'm ordering the gear with a 14.5 pressure angle. What's the worst that could happen? A gear to sell on ebay...

 

[cjtoombs]

If you have some CAD software with a gear shape generator, you could generate the gear profile, print it out and compare directly by laying it on the gear. Fusion 360 is free and has a gear generator. Even if you are unfamiliar with the program you could get the gear profile made without too much of a learning curve. Good luck.

 

[Wheels17]

I was messaging on another forum about broaching the keyway, and a gentleman over there confirmed my suppositions:

"The Atlas shaper drive pinion is available from McMaster as catalog number 6325K5".

These are the specifications on their product page:

Gear Type Spur
Pressure Angle 14 1/2°
Component Gear
System of Measurement Inch
Bore Type Round
Pitch 10
Number of Teeth 15
Pitch Diameter 1.5"
OD 1.7"
Face Width 1"
Overall Width 1.625"
For Shaft Diameter 3/4"
Material 1144 Carbon Steel
Teeth Heat Treatment Not Hardened
Hub
Diameter 1.219"
Width 0.625"