R8 Taper Specs

# Thread: R8 Taper Specs

1. Cast Iron
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I've seen several charts showing specs for machine tapers, but the ones for R8 have never been too detailed. Anybody know the exact dimensions or taper angle?

2. 16 deg 57 min 28 sec
16.95776330 deg
or 3.5000 inches/foot

Is that exact enough?
JR

3. Aluminum
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" 16 deg 57 min 28 sec
16.95776330 deg
or 3.5000 inches/foot "

I have some trouble with this formulation of the R8 Taper. Let's assume the 3.5000"/foot is the original definition.

Indeed, 3.5/12 = sin(16.95776330). But the underlying construction implied by this calculation is not a right triangle, so using the sine function seems inappropriate to me. A better mental construction for a taper is a pair of identical, mirrored right triangles. Various trig functions can then be used appropriately.

If one is trying to figure out what angle from the centerline defines the R8 taper based on the 3.5/12 taper, I think the correct approximation is 2 * arctan(1.75/12) or 16.594289... degress.

At least, that's what I think today. If someone sees a flaw in my thinking, I'll appreciate correction.

4. Aluminum
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Actualy the calculation should be arctan(3.5/12)= the angle. I get the angle to be 16.26020470831 degrees.

Ray

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Even though it's probably risky to differ with someone whose name includes "carbine", I must. Actually, I'm also trying to judge whether you're in fact just pulling my leg.

A shank taper, such as Morse,B&S,and R8 is a truncated isosceles triangle (2 equal angles). It's geometry is certain not represented by a single right triangle. Using trig functions, whether sine or tangent or arcsin or arctan makes no sense in calculating sides and angles of a single isoceles triangle (implied by the notation arctan(3.5/12)). Thus, one must conceptually cut the isosceles triangle into two mirror image right triangles in order to be using any of these trig functions or to solve the problem correctly.

The "arctan(3.5/12)" solution by definition implies a right triangle with a 3.5" short side and 12" long side. Thus, the hypotenuse is 12.5". I'm unconvinced that this sort of geometry correctly represents a taper shank.

6. Cast Iron
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I'm pretty sure you are correct, Bob. I suspected that discrepancy myself, but being poor at math I just indicated a collet I had and then tweaked things until I got full contact with the shank I was turning in the mill spindle using some spotting compound.

The correct numbers wouldn't have done me any good anyway, though if the shank had turned out to be too hard to cut and I ended up sending it out to be ground it might have been a different story.

7. Aluminum
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I turns out my Machinery's Handbook 26 ed. has a nice table on p. 684 for tapers per foot and corresponding angles that puts the 3.5/12 at 16 35 39 (deg min sec). The next page has the equations. The one we've been addressing is cited as angle = 2 arctan (T/24) where T is the taper in inches.

You'd think this was all an abstract wild hair for me. To the contrary, just before seeing this thread I was trying to calculate how much advance of the compound on my lathe (set at 60 degrees) would move the tool into a B&S taper to move the taper how much closer to an arbitrary shoulder.

I'm trying my hand at turning an arbor for my Tom Senior (with a B&S #9 and an unusal dog design). I could buy an arbor but would still have to deal with the dog on the end of the spindle. So I thought I'd see if my skills were up to making something.

Here I've fit the business end into the spindle taper and I'm getting runout of 0.001 to 0.002. I'm thinking I'll tighten up the drawbar and run the spindle for awhile and remeasure.

Here's a shot of the corresponding arbor dog that fits up against a shoulder on the arbor (the reason for the calculations I was exploring).

I haven't made up my mind how to fix the arbor dog to the arbor yet. Counterbored bolts? Pins that I could peen and then turn smooth?

8. Plastic
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## Incorrect R8 spec?

Originally Posted by JRIowa
16 deg 57 min 28 sec
16.95776330 deg
or 3.5000 inches/foot

Is that exact enough?
JR
Did this change at some point? Every spec I can find says 16 deg 51 min.

9. Originally Posted by kellyb
Did this change at some point? Every spec I can find says 16 deg 51 min.
No, the spec is 3.500"/foot!

OK, I screwed up, I made a mistake, I zigged when I should have zagged.

I used ARCSIN when I should have used ARCTAN

The correct angular conversion is 16.26020470831 degrees, or 16 degrees, 15 min, & 37 sec.
Now, if you look at Machinery's handbook, it gives the angular conversion as 16 degrees 35 min & 41 sec. (pg 1558, 19th ed)
Who's right?

OK, if you convert the MH number to decimal, it's 16.5947222 degrees. I've tried to figure out how they came up with that and can't reproduce the results with 3.500 and 12. That roughly 20 min (1/3 degree) difference is about 0.006" on the taper of a BP collet. What do you do? Indicate a known taper with a tenths indicator.
JR

10. Stainless
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Not sure what this means but I looked up "tapers per foot and corresponding angles" in my 25th edition of Machinery's Handbook
3.5 taper per foot is 16 35' 39" included is 8 17' 50" angle with center line
7.0 taper per foot is 32 31' 13" included is 16 15" 37" angle with center line
I found a couple of references to Bridgeport R 8 spindles and they say 16 51', so maybe the R8 is a special Bridgeport created and not a 3.5 in 12 taper.
Machine taper - Wikipedia
R8 and 5C Collet Dimensions | Metal Arts Press

11. Kind of an interesting mistake. Correct is 16 15' 37" as already stated for 3.5"/ft.

6th Edition:
3.5" taper per foot included 16 35' 41"
7.0" taper per foot angle with centerline 16 15' 37"

26th Edition:
3.5" taper per foot included 16 35' 39"
7.0" taper per foot angle with centerline 16 15' 37"

Edit: I must be overlooking something simple because none of the values for included angle match up with the angle with centerline of the 1/2 value of the taper.
For example,
6th Edition:
2.5" taper per foot included 11 53' 38"
5.0" taper per foot angle with centerline 11 46' 6", which is the answer I get in CAD.

12. Originally Posted by FredC
I found a couple of references to Bridgeport R 8 spindles and they say 16 51', so maybe the R8 is a special Bridgeport created and not a 3.5 in 12 taper.
R8 specifications are 3.5"/foot. Almost all machine tool tapers are spec'd this way. Every time you see something else, it's a conversion done by somebody.

OK, I finally found the numbers that MH is using for the conversion 2 AcrTan (3.5/24) = 16.59428994 or
16 degrees ~ 35 minutes ~ 39.44 seconds.

The formula for the angle of a RA cone is 2*ARCTAN*(r/h). Don't ask me where they came up with 24 (other than is 2 * 12). Don't know, but that's what their using.

That's a lot of thinking for a FOG. Probably hurt myself.
JR

13. Hot Rolled
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Originally Posted by JRIowa
R8 specifications are 3.5"/foot. Almost all machine tool tapers are spec'd this way. Every time you see something else, it's a conversion done by somebody.

OK, I finally found the numbers that MH is using for the conversion 2 AcrTan (3.5/24) = 16.59428994 or
16 degrees ~ 35 minutes ~ 39.44 seconds.

The formula for the angle of a RA cone is 2*ARCTAN*(r/h). Don't ask me where they came up with 24 (other than is 2 * 12). Don't know, but that's what their using.

That's a lot of thinking for a FOG. Probably hurt myself.
JR
r/h is the angle of the taper to the centerline.

3.5/24 is the same as 1.75/12

14. Diamond
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Handy taper site..gives 16" 51' for R-8
http://www.tools-n-gizmos.com/specs/Tapers.html

15. Originally Posted by JRIowa
R8 specifications are 3.5"/foot. Almost all machine tool tapers are spec'd this way. Every time you see something else, it's a conversion done by somebody.

OK, I finally found the numbers that MH is using for the conversion 2 AcrTan (3.5/24) = 16.59428994 or
16 degrees ~ 35 minutes ~ 39.44 seconds.

The formula for the angle of a RA cone is 2*ARCTAN*(r/h). Don't ask me where they came up with 24 (other than is 2 * 12). Don't know, but that's what their using.

That's a lot of thinking for a FOG. Probably hurt myself.
JR
Here is where the difference is, I was thinking about it like the top triangle instead of the bottom triangle.

Edit: I see old Bob already figured this out, but I didn't get what he meant. I haven't seen this guy around for a while (but active a month ago) and this is a 12 year old thread, but I'll give him some credit.

Originally Posted by WoodburnBob
Indeed, 3.5/12 = sin(16.95776330). But the underlying construction implied by this calculation is not a right triangle, so using the sine function seems inappropriate to me. A better mental construction for a taper is a pair of identical, mirrored right triangles.

If one is trying to figure out what angle from the centerline defines the R8 taper based on the 3.5/12 taper, I think the correct approximation is 2 * arctan(1.75/12) or 16.594289... degress.

16. I know this is an old thread, but here's what I found, when I make a drawing in Autodesk Fusion 360.

I make a line 12.000" long. Then a 3.500" line, perpendicular from the end point, I have an angle of 16.260205°.

If I make a line 12" long and then make a line at 16.594289°. The perpendicular line is 3.57605.

If the formula is 3.5" per Ft (12.0"), I'm going with 16.260205°

Mike

17. Anybody know how long the alternate character set has been around? As in, turn number lock on, hold down the Alt key and type 248 to make the degree symbol: ° Was this generally possible in 2005? It sure makes it easier to cuss. There's another forum on PM where that would really be useful.

18. Originally Posted by Mike-Mat
I know this is an old thread, but here's what I found, when I make a drawing in Autodesk Fusion 360.

I make a line 12.000" long. Then a 3.500" line, perpendicular from the end point, I have an angle of 16.260205°.

If I make a line 12" long and then make a line at 16.594289°. The perpendicular line is 3.57605.

If the formula is 3.5" per Ft (12.0"), I'm going with 16.260205°

Mike
You are thinking about it wrong, just as I was Mike. The correct angle is 16.594°..., as shown in the bottom triangle. Photobucket blocked the link to the pictures in my earlier post.

Last edited by Kyle Smith; 07-05-2017 at 10:51 AM.

19. Aluminum
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Originally Posted by Kyle Smith
You are thinking about it wrong, just as I was Mike. The correct angle is 16.594°..., as shown in the bottom triangle. Photobucket blocked the link to the pictures in my earlier post.

Kyle,

If what you are showing here is correct, then the terminology is incorrect. The lower drawing indicates a taper of 1.75"/ft. The upper drawing is 3.5"/ft.

Ted

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## Hardinge R8 Collet Drawing

Don't mean to interrupt the geometry goinz-ons, perhaps posted before, attached is a shop drawing received directly from Hardinge some time ago (8.5 degrees exactly noted). Cheers.

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