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math and lathe compound Q

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SE18

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#1
Hi all, I have a bunch of railroad wheels I need to fit axles to. The problem, I just discovered, is the holes are tapered!

So here are the dimensions:

Hole dia. on side facing outboard: 1"
Hole dia. on side facing inboard (where the flange is located) 1 3/16" or 1.1875
Hole depth 1 7/16" or 1.4375

I found an online taper calculator and it said my taper is 1.5652" per foot.

I've got a South Bend 9A lathe but wasn't sure what to set the compound angle to.

After cutting a taper, I'll then need to mill a small keyway, tilting the axle, so I've got some work ahead of me!!

Thanks!
 

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JimDawson

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#2
Since you have the wheel this is an easy one. Chuck up the wheel and get it dialed in. Then put an indicator in the tool holder and run it in and out of the tapered hole with the compound while adjusting the compound angle. When the indicator needle does not move through the travel then the compound is set to the taper angle.

Here I am setting up to grind the bore of a 5C collet chuck, but the same principal applies.
1508689947109.png
 

SE18

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#3
Thanks! I didn't think of that. I just took a look and the wheel just barely fits on the lathe (since it's a SB9". So I lucked out. I've never put anything that big on the lathe before.

(Maybe in the future if something is too big for the lathe, a clay impression of the hole could be made I'm thinking)
 

Dave Paine

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#5
The dial indicator methods in earlier replies are the easiest way.

For folks interested in how to calculate the angle.

1.5652 in per foot infers a tangent, x distance vertically for y distance horizontally. Calculate the ratio which is 1.5652/12 = 0.13043333, then look up the "arc tangent" of this ratio.

An example site for this lookup. In this site arc tangent is shown as "tangent -1".

Tangent calculator site

This gives the angle as 7.43. Very difficult to measure this angle on the compound which is why the dial indicator is easiest.
 

Bamban

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#7
I used this app before, but setting the compound to the angle marks is imprecise.

About the best procedure I can think of if you do not have a sample to indicate, is the one from Joe P.

Watch "Setting the Lathe compound to precision angles" on YouTube
 

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Bob Korves

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#8
For accurate angles on the lathe, set the compound slide to the cross slide by using a sine bar and gage blocks to set the angle. It is not quick, but it is accurate. Using the factory degree scale on your cross slide to set your compound slide is totally hopeless for accurate work.
 

whitmore

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#9
The dial indicator methods in earlier replies are the easiest way.

For folks interested in how to calculate the angle.

1.5652 in per foot infers a tangent, x distance vertically for y distance horizontally. Calculate the ratio which is 1.5652/12 = 0.13043333, then look up the "arc tangent" of this ratio.

This gives the angle as 7.43.
Note, however, that is the approximate CONE angle, and you want THE HALF ANGLE as the compound setting.
The compound is set for the angle from a sidewall to the spin axis, not to the opposite sidewall.
So, you want the arctan of (1.5652/(2*12)), the spin axis-to-sidewall
which is 3.731 degrees.

It's very awkward to get such an angle dialed in, so it is usual to cut a standard, and fit it by
applying blue and seeing what rubs off. And recutting. Then, you mount the standard
and dial in against it instead of squinting at fractions of degrees on a scale.
 
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SE18

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#10
Whitmore: that could make a difference!

Bob: interesting, must be a video somewhere on this as hard to envision.
 

Bob Korves

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#11

Jimsehr

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#12
Hi all, I have a bunch of railroad wheels I need to fit axles to. The problem, I just discovered, is the holes are tapered!

So here are the dimensions:

Hole dia. on side facing outboard: 1"
Hole dia. on side facing inboard (where the flange is located) 1 3/16" or 1.1875
Hole depth 1 7/16" or 1.4375

I found an online taper calculator and it said my taper is 1.5652" per foot.

I've got a South Bend 9A lathe but wasn't sure what to set the compound angle to.

After cutting a taper, I'll then need to mill a small keyway, tilting the axle, so I've got some work ahead of me!!

Thanks!
One thing if you are new at this is to get center of tool dead on. Or your taper will not be true. You should also get your indicator point dead on center.
 
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Asm109

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#13
Another trick to set the compound to an exact angle.
Compute the sine of the 1/2 angle of the taper you want to cut. (Details explained by others above)
Multiply by a convenient travel distance of your compound. Say 2 inches.
Example. say I want a 3 degree 1/2 angle.
sine 3 degrees= .0523
2*.0523 = .1046 inches.
Extend the tailstock ram out fully.
Mount a dial indicator on your tool post and place the tip on the side of the ram.
Move the compound slide exactly 2 inches. The dial indicator should move .1046 inches.
Retract the slide, slightly rotate the compound and repeat.
Its just like tramming in a vise on the mill.
Repeat until you are as close as you desire.
 
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