Taper turning with Boring Head in lathe

[Metal Butcher]

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]

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]

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]

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]

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]

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