# Taper turning with Boring Head in lathe



## Brian Rupnow

I just read on another post how Marv Klotz suggested using a boring head mounted in the tailstock with a "dummy center" mounted in it to do taper turning in the lathe. --WITHOUT setting the tailstock over. (Because its always a bugger to get set back to zero!!!) I have heard about doing this before, but today I decided to try it myself. It works like a charm!!! Thanks Marv. I took a couple of quick pics so others could see the set-up. ----Brian


----------



## Metal Butcher

Brian, did you line up the work piece before offsetting it to create the taper? And what was the off set?

What is the degree of taper your creating, and what is the formula for calculating the offset. I need to learn this stuff!

Thanks

-MB


----------



## Blogwitch

Brian,

It is a very good system, and saves buying the plans for ones you can make yourself. Unfortunately, the one thing you must do when using this system is to ensure the boring head is totally level. Otherwise the centre point is liable to either raise or lower, depending which way it is tilted, and that will throw out where the tool tip sits on the job, and any problems that will arise, cutting a curve, bad surface finishes etc. 
You must also take into account any rotation of the tailstock ram, that has to be taken out first by turning fully one way (usually towards you), and the ram locked up solid, then level the boring head. After levelling, the ram can be loosened for locating into the bar centre, but once into position, the ram must be turned to full one way again, and locked up.

An easy way to level it, if you have an engineers level, is to take the setting from across the lathe bed (just in case the bed isn't perfectly level), and two accurate bars mounted in the tool holes in the boring head, as far apart as possible, or preferably, a bar sticking out of the horizontal hole (if the head has one). Then with the level sitting on the bar/bars, turn the boring head until it has the same setting as the bed. You should then be spot on for use.

An easier method, rather than relying on the morse taper not moving, is to make a fitting that clamps around the tailstock nose, that your boring head screws onto.
The head is levelled by slackening and tightening the nose clamp. 

That is one of my many tuit jobs to do.

Blogs


----------



## Twmaster

I just read an email from HSM magazine. It outlined that very same tip. Brilliant!


----------



## Brian Rupnow

Metal Butcher  said:
			
		

> Brian, did you line up the work piece before offsetting it to create the taper? And what was the off set?
> 
> What is the degree of taper your creating, and what is the formula for calculating the offset. I need to learn this stuff!
> 
> Thanks
> 
> -MB



Wiser heads than mine can probably answer all your questions. I have no idea what the offset amount is, nor the taper. I was trying out the method, thats all. As Blogwitch pointed out, to maintain any degree of accuracy, the boring head would have to be kept level. If I wanted to set up for a specific taper per inch, I could calculate it, but this was just a quickt 'Try it and see how well it works" thing.---Brian


----------



## mklotz

Metal Butcher  said:
			
		

> What is the degree of taper your creating, and what is the formula for calculating the offset. I need to learn this stuff!
> 
> Thanks
> 
> -MB



MB, 

The mathematics relating the critical parameters are:

phi = taper half angle (half the included angle)
L = length of workpiece
os = offset dialed into boring head 

tan(phi) = os/L


----------



## kvom

Seems the taper depends on which way you move the head; toward the tool means small end is at tailstock, away has large end at tailstock.


----------



## Metal Butcher

mklotz  said:
			
		

> MB,
> 
> The mathematics relating the critical parameters are:
> 
> phi = taper half angle (half the included angle)
> L = length of workpiece
> os = offset dialed into boring head
> 
> tan(phi) = os/L



Thanks Marv. With out a specific examples I don't know how to use the formula you provide. I don't have any math education other than plus, minus, and divide.
Taper half angle = 1/2 of an angle shown a print? What does "included" mean?
I add to work pieces for a later cut off. Would this effect the resulting angle?
Boring head offset. Wouldn't the length of the center and boring head have the same effect as above?
What is "tan" and what does it mean?
Try to put yourself in my shoes when you try to help out. I know you mean well.

Maybe every body else on this forum understands what the formula means, and knows how to use it, but I don't.

With a better explanation and a specific part or drawing used as an example the formula could probably be learned, and used by others like myself that don't understand it, but are willing to learn.

Thanks.

-MB


----------



## Brian Rupnow

Metalbutcher---Thats why I didn't try to explain it to you. Tan is short for Tangent, which is a trigonometry function. You either have to have the math to even begin to understand the formula, or a damn good CAD system to draw it out and it will give you the answer. This is one of those situations where "Add and subtract" isn't going to be a lot of help. Included angle means the total angle of two diametrically opposed (straight across from each other) sides of the tapered piece. If you add to the length for "some extra" it does affect it. If ya don't understand trig, don't feel bad----Neither does the other 98% of the human race. It something from the realm of engineers, mathemeticians, and scientists. We all struggled though it in high school math, then immediately forgot everything we had learned as soon as we graduated----unless we happened to work in a field that required the knowledge and it got used every day for the next 20 or 30 years. Tangent, Sine, Cosine, ---all trig speak.


----------



## mklotz

A 60 degree lathe center has a 60 degree included angle. If you wanted to turn a 60 degree center, you would turn your compound to 30 degrees, the taper half angle.

Often a print will specify the included angle. If it does, you must first find the half angle in order to calculate the required offset.

'tan' refers to the tangent function, one of the key functions of trigonometry. In a right triangle, the tangent of the angle is the ratio of the side opposite the angle to the side adjacent to the angle. While tables of tangents exist in most machinery handbooks, it's far simpler to buy a $10 scientific calculator at the local drug store, punch in the angle and then press the key marked 'tan' to get the required value.

Solving the equation for 'os', we have:

os = L * tan(phi)

(where the asterisk denotes multiplication). After calculating tan(phi) with your calculator, enter the value for 'L' and press the multiply key. The result will be the offset you need to dial into the boring head.


----------



## Metal Butcher

Thanks for all the help Brian and Marv.
 I think I under stand for the most part. I'm still a little confused on the part where the length of the work piece dosen't matter. It seems to me that a 6" work piece offset .050 at the boring head would not end up with the same angle as a 12" piece offset the same .050" at the boring head. I can't picture it being the same angle in my mind.

I'll figure it out even if I have to go to the library and get a book on it.

Thanks guys. 

-MB


----------



## 1hand

MB 

Just a second, I'll get my 14yr old in here. He should know how to figure it out. The home work he brings home for 8th grade, would give ya a headache for sure. The only thing I can help him with is his name at the top of the paper.. ???..............Sometimes I've been known to misspell that too.


----------



## Metal Butcher

1hand  said:
			
		

> MB
> 
> Just a second, I'll get my 14yr old in here. He should know how to figure it out. The home work he brings home for 8th grade, would give ya a headache for sure. The only thing I can help him with is his name at the top of the paper.. ???..............Sometimes I've been known to misspell that too.



LOL..... :big:

Ain't that the truth!

Good news! I got it all figured out! I think. ;D

A simple drawing would have been sufficient to explain to this old bugger how the formula works. L= length of work piece, this is where the problem started. Not the length of the tapered area!!! That why the length dosen't matter. The rest is simply to use the formula that Marv provided to get the offset needed to create the specified angle. 

However I think I found a minor flaw in this set up using a boring head for the off set. I think you need to add the distance from the end of the work piece to the sliding area on the boring head, to the length of the work piece (L), for the formula to give an accurate off set to give a true angle.

Sorry Marv. ;D

Nice knowing you Matt. I might get the "boot" for this one.

-MB


----------



## mklotz

Metal Butcher  said:
			
		

> I think I under stand for the most part. I'm still a little confused on the part where the length of the work piece dosen't matter. It seems to me that a 6" work piece offset .050 at the boring head would not end up with the same angle as a 12" piece offset the same .050" at the boring head. I can't picture it being the same angle in my mind.
> 
> I'll figure it out even if I have to go to the library and get a book on it.
> 
> Thanks guys.
> 
> -MB



MB,

You're right. The angles will be different...

tan(phi) = 0.05/6 = 0.00833... implies phi = 0.47745 deg

while

tan(phi) = 0.05/12 = 0.00417... implies phi = 0.23873 deg

The offset and the length work together to determine the angle of the taper. (The equation describes *how* they work together.)

If you're going to study any mathematics with the view to simplifying your shop work, some time spent learning elementary geometry and trigonometry will be time well spent, indeed. I encourage you to give it a try. Both of these subjects have the advantage of being very visual and simple to relate to the real world experience you already have. This makes them ideal for self study. If you get hung up, feel free to call on us to provide clarification.


----------



## Metal Butcher

Thanks Marv. Your very kind. 

I appreciate all the time you spent helping me out.

And also your patience.

-MB


----------



## mklotz

> However I think I found a minor flaw in this set up using a boring head for the off set. I think you need to add the distance from the end of the work piece to the sliding area on the boring head, to the length of the work piece (L), for the formula to give an accurate off set to give a true angle.
> 
> Sorry Marv. Grin



L is the distance between the two *pivot points* of the workpiece. Any distance from the pivot point to the sliding part of the boring head doesn't enter into the calculation. Convince yourself of this by imagining making the boring head center twice as long with the same boring head offset. The taper turned would not change.

The real reason for using the boring head is to dispense with the annoyance of tweaking the tailstock and getting it back into line after making the part.

When I do this, I seldom bother with the calculation. Instead, I set up a sine bar (another trigonometry calculation) with the required angle on top of the compound, then adjust the boring head until the stock matches the sine bar angle.

Another nuance of this technique is to make a ball center to put in the boring head if the angle turned is appreciable. A conical center will not be a good match to a center hole with a large offset whereas a ball center will match nicely.


----------



## 1hand

Just to make sure I'm tracking.

If I had a 8" long piece, and I wanted a 5 deg. taper. I would offset the tailstock/boring bar .70 ?

Matt


----------



## kvom

1hand  said:
			
		

> Just to make sure I'm tracking.
> 
> If I had a 8" long piece, and I wanted a 5 deg. taper. I would offset the tailstock/boring bar .70 ?
> 
> Matt



Yes, if 5 degrees is the "half angle". Otherwise .035 (half angle 2.5).


----------



## Metal Butcher

1hand  said:
			
		

> Just to make sure I'm tracking.
> 
> If I had a 8" long piece, and I wanted a 5 deg. taper. I would offset the tailstock/boring bar .70 ?
> 
> Matt



Hey Matt. With out the calculator that Marv suggests I can't tell you if your correct. I assume the 5 degree's you indicate is half the included angle (phi). I tried looking at the Machinery's Handbook to get the Tangent (tan) and found myself up against a brick wall (again). At the top of one of the pages and on the left is a large '5' degree, and on the top right is '174' degree. The fourth column shows Tangent's, and the first column (on the left, marked "M") is numbered from 0 to 60? The last column ("M") on the right is numbered from 60 to 0? 

What does the "M" marking the column mean? I'm on page 184 of the 15th edition.
Its an old 1955 edition that "Honey" picked up for me at a garage sale. I finally took the time to take a good look at the content, and it looks like the basis for the entire Industrial Revolution! :big:

It should still be good since math doesn't change, just the amount of people that need to use it (or know how to use it). : 

-MB


----------



## Tin Falcon

M would be Minutes of angle or 1/60th of a degree. degrees can be expressed as decimal degrees or in the Degree Minute second system.
Your scientific calculator should have a degree setting Usually radians , dd and ,dms there may also be a dd > dms  dms>dd conversion keys. 
Tin


----------



## Metal Butcher

Tin Falcon  said:
			
		

> M would be Minutes of angle or 1/60th of a degree. degrees can be expressed as decimal degrees or in the Degree Minute second system.
> Your scientific calculator should have a degree setting Usually radians , dd and ,dms there may also be a dd > dms  dms>dd conversion keys.
> Tin



Thanks Tin.

So then the tan for exactly 5 degrees would be in the horizontal "0" of the vertical 'M' column.

And the bottom last number 60 (under "M") line means + 60 minutes, and that equals 6 degrees.


----------



## putputman

MB, I think most computers with versions of Windows have a scientific calculator in the accessories. It can be jumped back & forth between standard & scientific.

Once you find it, type in 5 and press the TAN key. You will get a long list of numbers that are TAN for 5 degrees. Multiply that times (*) 8. Hit (=). The answer should be .69999 which rounds out to .7.


----------



## Metal Butcher

putputman  said:
			
		

> MB, I think most computers with versions of Windows have a scientific calculator in the accessories. It can be jumped back & forth between standard & scientific.
> 
> Once you find it, type in 5 and press the TAN key. You will get a long list of numbers that are TAN for 5 degrees. Multiply that times (*) 8. Hit (=). The answer should be .69999 which rounds out to .7.



Thanks.

I'm challenged with using a computer too. I know how to access the forum, Google search, and that's about it.

But, I did it with paper and pencil, and came up with .69992.

I'll be getting a scientific calculator real soon.

-MB


----------



## mklotz

MB,

The tangent of 5 degrees is 0.087488... 5 degrees implies 5 degrees and 0 (zero) minutes
(i.e., exactly 5 degrees). On the '5' page look in the zero 'M' row, across to the tangent column and you should find the number 0.087488, perhaps with fewer significant places (I don't know how far out your book carries the tables).

Now, just for practice, look up the following tangents...

tan(5.25 deg) = tan(5 deg and 15 minutes) = 0.09188...
tan(5.75 deg) = tan(5 deg and 45 minutes) = 0.10069...

and see if you find the values given above.

Once you've used the tables in MH a few times, I'm pretty sure that you'll agree with me that pressing the 'tan' button on a cheap scientific calculator is a hell of a lot easier and far less prone to error.

Some time ago, I wrote up a treatise on this subject for our club members. I've reproduced it below. If you're interested in learning more on the subject or you've run out of sleeping pills, try reading it. You may not get everything the first time round but keep at it. The subject isn't impenetrable and it is relevant to many aspects of metalworking, e.g., sine bars and dividing calculations.


			GETTING AN ANGLE ON ANGLES

The ancient Babylonians counted using a base sixty system. Unfortunately,
this system has survived to today in the numerics we use to count time and
angle. We write time as h:m:s where sixty seconds (s) = one minute (m) and
sixty minutes = one hour (h). Similarly, angles are written as d:m:s with the
same relationships (60 arcseconds = 1 arcminute, 60 arcminutes = 1 degree). 
Mathematicians normally add the prefix 'arc' to distinguish the fact that
they're talking about angle and not time. (There really ought to be a special
circle in hell for anyone who uses the same term for two completely disparate
units or, like the American gallon, redefines an existing unit.)

For most practical applications it's much more convenient to express angles as
decimal numbers. This raises the problem of converting between the two
notations.

Going from d:m:s to decimal notation is straightforward. Consider converting
12:34:56 (12 degrees, 34 arcmin, 56 arcsec) to decimal degrees. We know that
34 arcmin is 34/60 of a degree. We also know that there are 60*60 = 3600
arcsec in a degree. So the 56 arcsec is 56/3600 degrees. Adding them, we
have:

12 deg + 34/60 deg + 56/3600 deg = 12.582221... degrees

or, in general form:

d:m:s = d + m/60 + s/3600 decimal degrees

If your print calls out 12:34:56 d:m:s and you need the tangent of that angle
you'll need to perform the above calculation to get the decimal degrees
to feed to the tangent function. (Better scientific calculators have this
conversion built-in but the less expensive ones often lack it.)

Converting from decimal to d:m:s isn't very difficult. Using 12.582221
decimal degrees as an example:

Extract the integer degrees:

	12.582221 = 12 + 0.582221		12 degrees

Multiply the remainder by 60 (arcmin/deg):

	60 * 0.582221 = 34.93326

Extract the integer arcmins:

	34.93326 = 34 + 0.93326			34 arcminutes

Multiply the remainder by 60 (arcsec/arcmin):

	60 * 0.93326 = 55.9956			~56 arcseconds

Again, better scientific calculators have a single key to do this conversion.
However, if yours lacks it, no worry. You won't be doing it frequently and
the procedure above is straightforward.

Most scientific calculators can deal with angles in decimal degree notation,
radian notation and grad notation. So, the question arises:

What the hell are radians and why do we need them? Isn't d:m:s notation
confusing enough? Now you're telling me that we need two more ways of
expressing angles?

When doing mathematics, it's much more useful to express angles in a
notation such that the angle so expressed, when multiplied by the radius of a
circle, yields the length of the arc on the circle subtended by that angle.

Consider a 90 deg angle. It subtends one-quarter of the circumference of a
circle or an arc length of 2*pi*r/4 (2*pi*r = the circumference of a circle
whose radius is 'r'). We want this angle (we'll call it 'A') expressed in
radians to satisfy:

	A (rad) * r = 2 * pi * r / 4

That is, the angle in this radian notation, multiplied by the radius of the
circle, equals the length of the arc on said circle subtended by this angle.

Cancelling the 'r's, we have:

	A (rad) = pi/2 radians

Since we assumed that A=90 deg, we now have a relationship between degrees and
radians.

		90 deg = pi/2 radians
or:
		1 deg = pi/180 radians =~ 0.017453 rad
or:
		1 radian = 180/pi degrees =~ 57.295831 deg

Which makes things pretty simple. If we have degrees and want radians,
multiply degrees by 180/pi. If we have radians and want degrees, multiply
radians by pi/180. Rather than trying to memorize that, simply remember that
a full rotation, 360 deg, equals 2*pi radians.

-------------------------------
For completeness, a brief note about grads.

The French are never happy with any measurement system they didn't personally
invent. They thought that 90 degrees was an awkward number for a right angle
so they 'metricized' it to be 100 grads. I don't remember the details but
their argument for this aberration revolved around the fact that slopes
expressed in percent (as we express the slope of hills in road-building) would
then convert directly to grads without the need to do any calculation. 

Don't worry about grads. They're only used by the French and a few other
Europeans. In 30+ years of doing mathematics for a living,
I *never* had to convert any angles to grads. Should you ever need to do so,
the relationships are:

	100 grads = 90 degrees = pi/2 radians
-------------------------------


----------



## Metal Butcher

Quote from Marv.
"Now, just for practice, look up the following tangents...

tan(5.25 deg) = tan(5 deg and 15 minutes) = 0.09188...
tan(5.75 deg) = tan(5 deg and 45 minutes) = 0.10069..."

Unquote.

Marv, I got, .09189 and .10069.

Is the book wrong? (.09189).

I think that I learned something important here, between yesterday and today.

Thanks again Marv, and also to all the other members that posted replies.

I'm going down to the shop now and do something that's a little easier for me, like making a part or two for my current build, before I forget what it is I'm building! :big:

-MB


----------



## mklotz

tan(5.25)= 0.091887091 to the limit of my calculator's readout.

The ellipsis (...) in my post indicates that I truncated, rather than rounding, the value.

MH rounded their value to five places to obtain 0.09189.

Most (but not all) trig functions (sine, cosine, tangent, etc.) of angles are irrational numbers. That means that their value cannot be expressed as the ratio of two integers and therefore the decimal representation is infinitely long.

You can round such numbers to a value consistent with whatever precision you need but that raises yet another possibility for what I'll euphemistically term 'operator error'.

The beauty of using a calculator is that it'll happily and accurately carry all those decimal places through a long chain of calculations with no effort at all for the operator. Then, once you arrive at your ten place answer, you can do the final round off to whatever precision your measuring gear will accommodate.

Given the ubiquity of cheap scientific calculators, I marvel that machinist's handbooks still include trig tables. MH could use all that paper to finally publish standards for the R8 taper.


----------



## Twmaster

mklotz  said:
			
		

> Given the ubiquity of cheap scientific calculators, I marvel that machinist's handbooks still include trig tables. MH could use all that paper to finally publish standards for the R8 taper.



Bwahahahaaaa! Good one.


----------



## Tin Falcon

Marv MH dropped the trig tables some time ago 
MB was referring to the 15th edition IIRC published sometime in the 1950s
My 25th edition does not have them. 
Tin


----------



## mklotz

It's about time.

My 23rd edition, published in 1989, still has them - 44 pages of eye-glazing boredom.


----------



## Metal Butcher

mklotz  said:
			
		

> It's about time.
> 
> My 23rd edition, published in 1989, still has them - 44 pages of eye-glazing boredom.



LOL, "eye glazing boredom", that,s funny Marv! And yet you didn't find counting the 44 pages to be boring! :big:

My other slightly older MH is the 13th edition published in 1946. Never found a use for either one until now. ;D

-MB


----------



## 1hand

This is all very interresting to me. 

So I guess the next step is to make a "stub" dead center for my boring head.

Do I chuck a piece of stock in the lathe, and turn it to 1/2" to fit the boring head? Then set the compound at 30deg. and taper the end? And would 12L14 or 1018 be the best suited material for this?

I haven't done any taper turning what so ever, other than chanfering with the width of the tool bit.

Will also have to get a MT2 for the tail stock, for my boring head has the R8 for my mill.

Also I would imagine that with this new found talent, one could turn their own Morse taper? What is the tangent for a MT2?


----------



## Brian Rupnow

BLATANTLY COPIED FROM THAT "OTHER" FORUM I POST ON---

I did up one of the tailstock boring head rigs a while back (can't find the thread now) and it works well. The boring head came in a bunch of stuff I got cheap and had a non-removable 3/4" straight arbor. I had another one with R-8 arbor to fit my mill so I decided to dedicate this one for tailstock use and turned a 2MT taper to fit the tailstock.

Only problem I had was getting the centers to fit and work smoothly. I bumped into the following info about using a single ball bearing at each end of the work somewhere on the web (apologies to the creator) and found it to work very well. I keep it safely in my "Lathestuff" folder for occasional use. Never can remember it for some reason.

Quote:

"When offsetting the tailstock for taper turning, or using a special 
tailstock fixture for the same purpose, the 60 degree center points don't 
fit well in the centerholes of the work being taper turned.

This method needs custom-made lathe centers for both headstock and tailstock. 
The sharp point is turned off for a short distance, and centerdrilled just 
as is done for the work being turned.

Hardened steel balls are captured in the centerholes between the lathe 
centers and the work, at each end.

The correct centerhole size is important in relation to the bearing ball diameter.

For a standard 60 degree centerdrill, the opening of the hole at the ends 
should ideally be between 88% and 90% of the diameter of the ball. (.389 for my .4325 ball)

If larger, there may not be enough clearance between the lathe center 
and work to allow any offset.
If the hole's opening is smaller than 87% of the ball's diameter, only 
the corner of the hole's opening will contact the ball and the whole 
thing may come loose under heavy cutting pressure.

In practical experience, I've had very good results with this technique 
while turning morse taper shanks.

For the purpose of accurately setting the tailstock setover, the effective 
length of the workpiece is measured between the centers of each ball. 

Just mike the workpiece with the balls in place, and subtract the total of 
one half the diameter of each ball.

Be sure to use your favorite tailstock center lube on that end 
(I use white lithium grease)." End Quote

Here's the last setup used with a .4375" ball. (I have an endless supply of those from a certain unnamed imported luxury car sealed double row front wheel bearing.


----------



## Blogwitch

Matt,

It is a bit of a catch 22 situation.

Unless you have a topslide long enough to cut the MT taper, you will have to use your offset taper turning attachment (which you don't have) to make your offset taper turning attachment. :big: :big: :big:

As I explained, you really need to make an attachment to clamp around the tailstock nose. It would be a lot more secure than an MT taper, which is liable to rotate inside the tailstock ram under cutting pressure. See C-o-C for the idea I have in mind, and hope to make soon.

With refernce to the ball bearing centres, which I think John Stevenson uses to good effect. There is another way, and is the normal way for offset taper turning. That is to use a curved centre drill on your workpiece. It works in the same way as the ball bearing centre, but you can use normal centres in the holes. See piccy below.
Because they are used so infrequently, they will last for many years. I think I have had mine for about 15 to 20 years and they are still like new.

Blogs


----------



## 1hand

Thanks blogs. As usual I jump the gun and went and bid on a MT2 boring head "1 piece of course" that will be useless to me, doing the addapter mentioned. Oh well maybe I'll get out bid. Then I'll be able to use the head I have for that's a 2 piece.

I guess for now I need to know how to fix up this sort of ball dead center, or taught how to turn the regular dead center stub.

Thanks Matt.


----------



## tel

> Unless you have a topslide long enough to cut the MT taper, you will have to use your offset taper turning attachment (which you don't have) to make your offset taper turning attachment. big laugh big laugh big laugh



With care you can do it with two bites with a shorter topslide


----------



## Deanofid

Rick, and all other folks who would like a math book geared to normal people, (machinists), check out this google book:

Mathematics for Machinists
http://tinyurl.com/yjdn6bs

Lindsay's Books used to have it in print. Maybe still does. Well worth buying a copy if
you can get one.
Has all kinds of math pertaining specifically to the machine shop. I keep a copy on the 
tool chest.

Dean


----------



## Metal Butcher

Thanks Dean. I book marked it as future reference material.

My teacher's a slacker and doesn't know any shop math. What little he does know is done with paper and pencil (cyfrin), and on occasion I catch him using his fingers as a sort of quick calculator. He's taught me to do presentable, but basic work. On complicated parts he shrugs his shoulders and says, "make it look good and work good, use the machining techniques you know." I usually go with that to get the build finished up, for presentation to the viewing audience.

I'm working to change his ways, but its hard to learn from a guy with that attitude! ;D

-MB


----------



## Twmaster

Guys, 

I don't know if ya' all noticed but you can download it as a PDF.... See the link in the upper right corner....

Dean, thank you. That's getting printed tonight.


----------



## websterz

1hand  said:
			
		

> Thanks blogs. As usual I jump the gun and went and bid on a MT2 boring head "1 piece of course" that will be useless to me, doing the addapter mentioned. Oh well maybe I'll get out bid. Then I'll be able to use the head I have for that's a 2 piece.
> 
> I guess for now I need to know how to fix up this sort of ball dead center, or taught how to turn the regular dead center stub.
> 
> Thanks Matt.



If ya' get stuck with it Matt I'm sure you can resell it and get your money back.


----------



## Metal Butcher

Twmaster  said:
			
		

> Guys,
> 
> I don't know if ya' all noticed but you can download it as a PDF.... See the link in the upper right corner....
> 
> Dean, thank you. That's getting printed tonight.



I tried that and it said that an error was encountered and adobe 9.1 had to close? 

I don't know what that means, or how to deal with it.

I don't know much of any thing about computers.

-MB


----------



## Twmaster

MB, try this:

Go to the link Dean provided. 

Right click on the PDF link. 

Chose 'save as' then download.

It downloaded just fine for me. I just read a handful of pages. Great stuff.


----------



## 1hand

Websterz,

Thanks not too worried. Nothing else it will get me started. I'll just watch my depth cuts. I could cut off the taper, and make the attachment blogs was referring to just make the end that goes towards the boring head sorta like the way it mounts to the tail stock spindle. Clamped around the outside, instead of threaded on. It may look a bit goofy, but it won't feel alone, there will be two of us in the shop then. *bang*

Matt


----------



## Metal Butcher

Twmaster  said:
			
		

> MB, try this:
> 
> Go to the link Dean provided.
> 
> Right click on the PDF link.
> 
> Chose 'save as' then download.
> 
> It downloaded just fine for me. I just read a handful of pages. Great stuff.



Thanks for trying to help. I saved the file three times but it won't open. A window pops up over the fist page and when I click to send the error report the file closes on me. If I click on don't send the same thing happens. My computer guy will be around tomorrow to help me out. I did see a listing of the page amount and its in the hundreds! Or does that mean something else?

-MB


----------



## Twmaster

MB, yes the page count is ~250.

It sounds like your copy of Acrobat Reader is b0rken. Let your comp-geek tame it.


----------



## 1hand

FYI................I went to Deans site and now I think I got an idea of how to turn my own dead center stub.


Thanks Dean

Matt


----------



## Deanofid

Rick, if you would like to buy one, Amazon has them. About 10 of them showing right now. Some brand new ones for $17.95. Less than the ink cartridge it would take you to print it out.

It's great to have books and manuals on your computer. I really like having certain printed references in the form of real books in my shop, though. Much more convenient than running back and forth looking stuff up on my magic box thingy.

Dean


Matt, just caught your post. Glad you found something you could use!

DW


----------



## 1hand

The Machinery's Handbook Guide also has practical examples, solutions, questions to make sense of using the big Handbook.


----------



## Captain Jerry

Marv

I read this thread before I went to bed last night and all was clear. When I woke up this morning, before I even got out of bed, a thought popped into my head. It said "The workpiece is the hypotenuse. Isn't that a sine function?"

What a strange thing, the sleeping mind!

I had to check it out. At small angles, the values are verrrry close. Even so, an 8" workpiece with a 5 degree half angle, the offset difference is about .002".  I don't have a boring head but isn't that within the capability of a boring head to resolve?

Jerry


----------



## Metal Butcher

Thanks for the idea Dean. The printing paper and cartridge is a big factor. I would be "borrowing" it, and that's been a no-no- in the past. Binding the whole pile of papers together is a project I wouldn't want to tackle. I would need a book to teach me how to bind, or bandages for the blisters on my hand after punching at least 750 holes!

So, I order a 'good used' one to be used in the shop environment as reference material. I will try to get a working PDF copy on the computor for casual reading and easy access to the information. I might need it for posting replies to questions posted on the forum.

-MB


----------



## Maryak

CJ,

The result is the hypotenuse, but to get there you use the vertical side of a right triangle as the centre line of the job and hence the horizontal side of this triangle is the offset, derived from the tangent of the top angle; which in turn equals half the included angle of the taper.

Hope this helps

Best Regards
Bob


----------



## 1hand

1hand  said:
			
		

> Thanks blogs. As usual I jump the gun and went and bid on a MT2 boring head "1 piece of course" that will be useless to me, doing the addapter mentioned. Oh well maybe I'll get out bid. Then I'll be able to use the head I have for that's a 2 piece.
> 
> I guess for now I need to know how to fix up this sort of ball dead center, or taught how to turn the regular dead center stub.
> 
> Thanks Matt.


Somebody really wanted that boring head today.......Thank you! Now I'll get a chance to try my hand at 1 1/2 -18 treads on the lathe.

Matt


----------



## Deanofid

1hand  said:
			
		

> Now I'll get a chance to try my hand at 1 1/2 -18 treads on the lathe.
> Matt



1 1/2-18? Is that a typo, Matt, or do you really have something with that thread?
Just curious.

Dean


----------



## Blogwitch

Dean,

Depending on the size of the boring head, for the 2" ones I have made before, they are about that size. It is always better to check first though.


John


----------



## 1hand

You know what Dean, I've never taken the boring head off the R8 shank before. I've just been going off the ads of CDCO, and shars. They say their heads and shanks are 1 1/2 x 18. Well after reading your post I took mine apart, and low and behold...........It's not 1 1/2 x 18. I got out my gage, and it appears to be 20 tpi, and an OD of .867, so like a 7/8 x 20 sound right? 

Good call Dean.

Matt


----------



## 1hand

I went back through my receipts from last year to find where I got it. 

http://www.littlemachineshop.com/products/product_view.php?ProductID=1266&category=1963256902

There it is in black and white 7/8 x 20


----------



## Blogwitch

I think it is all to do with who the manufacturer is Matt, they all seem to have their own ways of making things, just so that you have to buy their arbors. I definitely know mine is of the larger size.

Once I get this burner build out of the way, the first job will be making one of those clamp fittings, as it should only be a couple of hours work. Getting the slot in the clamp deep enough will be the main problem, but it should work with only a partial slot if the fitting for the nose is close enough.

Another item that I need to make is a floating reamer head for the tailstock, but I am having trouble finding free plans for that one. Anyone any ideas?


Blogs


----------



## steamer

The 1 1/2 -18 sounds right for the 3"......seems oddball, but that is what I needed for my 3" boring head......turning the thread is no worries either 1hand.  7/8-20 too.

Dave


----------



## Captain Jerry

Maryak  said:
			
		

> CJ,
> 
> The result is the hypotenuse, but to get there you use the vertical side of a right triangle as the centre line of the job and hence the horizontal side of this triangle is the offset, derived from the tangent of the top angle; which in turn equals half the included angle of the taper.
> 
> Hope this helps
> 
> Best Regards
> Bob



Bob

I agree, almost. The problem is that all you know is the angle and "L", the length of the workpiece. The offset is at right angle to the lathe centerline, not to the length of the workpiece. Once the offset is made, L is the hypotenuse, not the adjacent side of the resulting triangle. 

See the attachment. I know its splitting hairs, but that's what we do.

Jerry 

View attachment tailstock offset.cad


----------



## Captain Jerry

Sorry, I attached a proprietary file type above. Here is a PDF file 

View attachment tailstock offset.pdf


----------



## chipswarf

I agree with Captain Jerry's analysis. The distance between the lathe centers decreases as the offset is increased, the constant is workpiece length, which is the hypotenuse, with center distance being the cosine side and the offset being the sine side.

With this in mind, the algebra looks like:

Let L = workpiece length and t = taper per foot or t/12 inches per inch.
The taper for the half angle is half that (taper per 'side' rather than taper per diameter), so that the half angle of the taper = arctan t/24
If we agree that this is the angle that the workpiece must make with the lathe centerline, then,

Offset = L sin (arctan t/24)

We can make this even easier by dispensing with the trig altogether. For small angles (the half angles of Morse and B&S self-holding tapers are all less than 1.5 degrees - small enough), sin angle ~ tan angle, or, equivalently, arctan number ~ arcsin number. So,

Offset = L sin (arctan t/24) ~ L sin (arcsin t/24) = Lt/24

Example:

t = 0.6 inches per foot
L = 5 inches

Using the trig explicitly, Offset = 0.12496
The simplified way has Offset = 0.12500, an 'error' of 4 one hundred thousandths of an inch.

I'm trained in math and thus can make spectacular errors. What do y'all think?

Mark

Jeez, first post. Hi, Guys!


----------



## Maryak

CJ,

I follow your analysis and it looks correct to me. :bow: :bow: 

All I can say is that using tan rather than sin to calculate the angle has not let me down over a good few years, don't ask me how cause I don't know.

On the other hand matching tapers M to F I use bearing blue and adjust for the final cuts.

Best Regards
Bob


----------



## chipswarf

Maryak, your technique of using tan instead of sin is right on for small angles. Recall that tan = sin/cos. For small angles, cos angle is nearly one.

Mark


----------



## kvom

Often a taper is defined not by the angle but by the different diameters at each end of the taper. If the drawing shows these, then it's just a matter of moving the boring head by the difference in the radii at each end (which is what the calculation is determining).

It's probably safe to say that most tapered parts on model engines are decorative, so the angle isn't critical but more an esthetic choice.


----------



## black85vette

Being a former US Marine, while in SE Asia I got a good Tan and learned to Sin along with the best of them. :big:

Sorry, lame humor. I'll try to make up for it:

Here is a handy triangle calculator that I use on-line. I am sure there are many more. I do have a basic understanding of Trig but don't trust my memory to recall every function. With this you can put in your known variables and it will spit out every thing else. I find it useful. Many problems can be reduced to a simple right triangle function anyway.

http://www.carbidedepot.com/formulas-trigright.asp

Here is another good link sent to me by a co-worker that has all sorts of tutorials on math and science. You can go as far as you want on this web site;

http://www.khanacademy.org/


----------



## mklotz

I think you folks have gotten a bit off track here. You're worrying about how to calculate the offset rather than worrying about how to cut a taper.

The real advantage of using the BH (boring head) is the fact that it's a quick and dirty way to offset the TS center without disturbing the TS itself. The fact that the BH offset is calibrated is nice but not key to the utility of the technique.

If you were turning a non-critical taper (e.g., the column on a beam engine) where a fraction of a degree or so didn't matter then, yes, you could do the setup using the BH calibration. You mount the workpiece, its length determining one side of the triangle, then crank in the offset on the BH, said offset determining the other side of the triangle. What really matters though is the distance between the two pivot points of the workpiece and that changes minutely when you introduce the offset. Thus you'll never turn *exactly* the taper you calculated.

However, if you're turning a critical taper (e.g., a Morse taper to fit a machine socket), you would never use the technique described above. It's just not accurate enough.

Mount a true cylindrical piece of stock between centers. Mount a straightedge of some sort on the compound. By pushing the straightedge against the stock, get it aligned parallel to the lathe centerline and clamp it in place.

Now, mount the BH and set up the workpiece in the lathe. With a sinebar set to the correct angle against the straightedge, twiddle the adjustment on the BH to bring the workpiece parallel to the sinebar, thus establishing the correct angle.

Aside: A precision angle block can sometimes be used in lieu of the sinebar.

If fiddling with a sinebar and such is too much for you, there is another less accurate way. Rough adjust the BH using the calculated offset. Now, with a DI mounted in the toolholder, measure the offset of the workpiece over an accurately measured (use another DI) interval of saddle motion. If that saddle motion is 'L' then the DI-measured offset should be:

os = L * tan(phi)  (phi = taper half angle)

Continue fine tuning the BH offset until you get the calculated value for 'os'.


----------



## Captain Jerry

Marv

I think yoy are right about the sine bar being the only way to get an accurate taper. I think the real problem of using a calculated offset is knowing the effective length of the workpiece after center drilling and setting ball centers.

Goofy question: Why not use a tan bar? *club* 

Jerry


----------



## kvom

> Goofy question: Why not use a tan bar?



Sine bars have a precision length hypotenuse that doesn't change as the angle is changed. So when you set it with precision gauge blocks you need the sine of the angle.


----------



## mklotz

Some very interesting tangent bar designs have been proposed, e.g....

http://www.freepatentsonline.com/2669027.pdf

However, with all the moving parts in that design, I fail to see how it could be as accurate as a sine bar. Still, it rates a 10 on the coolness scale.

I've never seen a tan bar offered for sale. Does anyone market one?


----------



## DavesWimshurst

Marv,
Perhaps a sine bar made out of wood? :big:
Dave


----------



## mklotz

DavesWimshurst  said:
			
		

> Marv,
> Perhaps a sine bar made out of wood? :big:
> Dave



Reminds me of an article I saw in _Fine Woodworking_.

Some woodbutcher had "invented" this super accurate way of setting up miter cuts on his table saw. Basically, he had built a 12" sine bar out of wood replete with wooden rollers.
He had even made up a set of wooden "gage blocks" with which to set the angle.

I should have clipped the article and put it in my "highly polished turds" file.


----------



## websterz

mklotz  said:
			
		

> Some very interesting tangent bar designs have been proposed, e.g....
> 
> http://www.freepatentsonline.com/2669027.pdf
> 
> However, with all the moving parts in that design, I fail to see how it could be as accurate as a sine bar. Still, it rates a 10 on the coolness scale.
> 
> I've never seen a tan bar offered for sale. Does anyone market one?



Found this one Marv...

http://cgi.ebay.com/NEW-6PC-TANGENT...emQQptZLH_DefaultDomain_0?hash=item48392dfa8c


----------



## Captain Jerry

Marv, Bob, Websterz, Kvom, and others that I may have offended, 

I was really being facetious when I asked about a tan bar. I had no idea such things existed. Of course the sine is the proper function to use when the hypotenuse is known and constant. Thats the point I was trying to make.

I live on a horse farm and occasionally horses die of natural causes. Not from being beaten. And we certainly don't beat them after they are dead. But once in a while I ........  Please forgive me.

Jerry


----------



## chipswarf

Captain Jerry  said:
			
		

> Marv
> 
> I think you are right about the sine bar being the only way to get an accurate taper. I think the real problem of using a calculated offset is knowing the effective length of the workpiece after center drilling and setting ball centers.
> 
> Jerry



CJ, the effective length of a center-drilled workpiece can be measured as follows. Seat a pair of balls in the drilled centers, ones that match the diameters of the lathe center balls. Measure length over these balls and subtract the radius of each ball. This is the workpiece length (hypotenuse) to use for the offset calculation. It remains constant as offset is cranked in. Offset (short leg of the triangle) increase results in a decrease in the longitudinal separation between the lathe centers (long leg of the triangle) - you have to feed the tailstock in a bit when offsetting the center, to keep the balls seated in the holes. We don't care about this long leg, as long as the centers are well seated. 

One advantage of using ball centers is that we can so easily measure this length, and it remains unchanged, unless the balls brinell into the center holes (you could give each a little rap with a hammer). Two of the corners, or vertices, those at the ends of the workpiece, are always at the centers of the balls, which removes head scratching about what happens with an offset on conical centers. This workpiece length is analogous to the length of a sine bar, but not known to the same accuracy. The offset replaces the gage blocks. Same calculation. Measurement errors would make this less accurate than the sine bar for setting an angle, but much faster in roughing in a taper, and you still have to cut and try to get it nailed. Note that my other post uses taper per foot directly in the formula - no calculation of an angle, no sine tables, no more intermediate steps.

I don't yet have ball centers (propose to use tooling balls, see McMaster), so I can't try this yet. I'm sure curious to see what real accuracy is inherent in these calculations. Fun stuff.

Mark


----------



## Maryak

Jerry,

I for one am not offended in any way. I can only say thank you for thinking out and pointing out something I have taken as read for many years. :bow: :bow:

Now it's time to get out of the bar, go get a tan and find a cosine(r) whilst I'm still young enough to remember what I should do. :

Best Regards
Bob


----------



## websterz

Offended? Pish...you haven't enough time in the day to find a way to offend me. :big:


----------



## Metal Butcher

fgleich  said:
			
		

> Metal Butcher:
> See this link for tips.
> 
> http://books.google.com/books?id=vd...Q6AEwBQ#v=onepage&q=tailstock setover&f=false
> 
> for a morse 3, the taper is 1/20 per inch or 0.050. If you have a workpiece 9 inches long, then you'd set over 9 x 0.50 or .45 inch.



Thanks for the link. 

I started to read it and it looks like a lot of good info.

-MB


----------



## fgleich

I think I had the setover wrong   . It shows in the article what it should be, .025 for a total of .05. So for 9 inches, it would be 1/2 of what I figured or 0.45/2. Duh........lol ;D


----------



## chipswarf

Well, fui, or good for me, depending. I started thinking this Lt/24 thing must have been familiar to the old shop hands and just found it on page 481 of the 4th edition, 1991, of "Machine Tool Practices" by Kibbe, Neely, Meyer and White. Probably in every comprehensive shop text since 1871. So much for my sniffing about how I value my library. Gots to read the stuff, chippy.

They didn't derive it though, the buggers, just laid it out. So, I can still feel good about myself.  :

Mark

ps - note that the 'setover factors' in the chart shown in the above link are all t/24, where t = taper per foot. So, Offset = L x setover factor = Lt/24

As Basil Fawlty might have said - "Here we have Mr Chipswarf, special subject, the bleeding obvious."


----------



## fgleich

Here's a link with a picture of one set up, with a level setting jig attached. Cool !

http://home.iprimus.com.au/stevor/BoringHead.htm


----------



## Blogwitch

That really is an easy way of getting the boring head level.

Thanks for the link


Blogs


----------



## Metal Butcher

Deanofid  said:
			
		

> Rick, and all other folks who would like a math book geared to normal people, (machinists), check out this google book:
> 
> Mathematics for Machinists
> http://tinyurl.com/yjdn6bs
> 
> Lindsay's Books used to have it in print. Maybe still does. Well worth buying a copy if
> you can get one.
> Has all kinds of math pertaining specifically to the machine shop. I keep a copy on the
> tool chest.
> 
> Dean



My book arrived today, yipee!!! Thanks for the good advise, Dean! I saw new ones advertised, and also a listing of 5 used ones starting at (are you ready for this) forty nine cents! Soo... of course I bought the one for 49 cents. ;D

They overcharged me on the $3.98 shipping. The postage tag shows $2.38, and the most the bubble bag could have cost is 75 cents. Should I complain about the $1 they overcharged me on the price of the shipping??? "Honey" says the book looks like it was never opened or read, based on the lack of a single crease on the spline. The seller called its condition only "good". I was expecting a tattered and stained book, or one with a few holes in it made by someone trying out their pellet gun.

I just love buying on the internet! 8)

-MB


----------



## mklotz

> a math book geared to normal people (machinists)



So, does this imply that mathematicians are not "normal"?

And machinists *are* normal?


----------



## Deanofid

mklotz  said:
			
		

> And machinists *are* normal?



You better believe it, chief.

Dean


p.s. You're welcome, Rick! That's the same copy I have.

DW


----------

