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View Full Version : who can solve for X on this math problem

tattoomike68
01-24-2008, 08:52 PM
http://i44.photobucket.com/albums/f24/snoopdog6502/problem1.jpg

Carld
01-24-2008, 09:04 PM
You would have to know what the standard milling machine taper is or the diameter of the small end of the taper to get an answer. At least I would.

tattoomike68
01-24-2008, 09:09 PM
Nope this is not that tough.

Errol Groff
01-24-2008, 09:16 PM
The taper is probably 3 1/2" per foot but that is just an assumption and we all know what happens when we assume.

But, if you are going to solicit help for a problem like this the least you could do is to post a decent picture or drawing of the problem. I, for one, can't read most of the dimensions on your picture so I can't, or maybe won't, help you out.

Errol Groff

tony ennis
01-24-2008, 09:19 PM

tony ennis
01-24-2008, 09:20 PM
solicit help for a problem

He's quizzing us. That diagram is from '98

DocZ
01-24-2008, 09:30 PM
If I read the dimensions correctly the solution is

4.5-(1.843+(2X1.237))=X
4.5-(1.843+2.474)=X
4.5-4.317=X
0.183=X

Cheers
Z

01-24-2008, 09:33 PM
Solving for X would be a piece of cake if the figures were clear but I couldn't read them. Zoom in a little and use more light. Better yet, run the drawing through a scanner, crop, adjust contrast, and post that..

Scatterplot
01-24-2008, 09:47 PM
If I read the dimensions correctly the solution is

4.5-(1.843+(2X1.237))=X
4.5-(1.843+2.474)=X
4.5-4.317=X
0.183=X

Cheers
Z

X should be a little less than 4.5. Look at the drawing. .183 is too small.

The big problem here is that the system is unconstrained, unless one thing- are we to assume the two diagonal lines touching the circle are parallel to the two lines describing the top left and bottom left edges?

tattoomike68
01-24-2008, 09:51 PM
If I read the dimensions correctly the solution is

4.5-(1.843+(2X1.237))=X
4.5-(1.843+2.474)=X
4.5-4.317=X
0.183=X

Cheers
Z
Oh yea. you know whats up...

thanks...

Carld
01-24-2008, 09:53 PM
I still don't see how you can arrive at an answer without knowing the taper the ball sits in or the diameter of the small end.

DocZ
01-24-2008, 10:06 PM
If I read the dimensions correctly the solution is

4.5-(1.843+(2X1.237))=X
4.5-(1.843+2.474)=X
4.5-4.317=X
0.183=X

Cheers
Z

Sorry I wasn't quite complete I should have used

4.5-(1.843+(2X1.237))=Y
4.5-(1.843+2.474)=Y
4.5-4.317=Y
0.183=Y

Then X=4.5-Y
X=4.5-0.183

X=4.317

Sorry for the confusion

tony ennis
01-24-2008, 10:11 PM
I think you're drawing an invalid conclusion about the left side of the circle. The mark you're using is measure the location of that bevel.

dan s
01-24-2008, 10:42 PM
I think you're drawing an invalid conclusion about the left side of the circle. The mark you're using is measure the location of that bevel.

not to mention when you go back and calculate the taper it comes out odd.

this can't be solved.

It seams like a typo type of deal, because w is easy to find.

Paul Alciatore
01-24-2008, 10:53 PM
"Standard milling machine taper". What does that mean? R8? Or one of many other "standard" tapers? Which one. The answer depends on what the taper is. It can not be calculated from the information on the print.

torker
01-24-2008, 11:00 PM
Sorry, I don't see what the taper has to do with X. They show the distance of the circle from the rear...add the diameter...subtract from the toal length...no? Or did I get up waay to early :D

lazlo
01-24-2008, 11:09 PM
He's quizzing us. That diagram is from '98

The title of the drawing is "Trig 2" -- it looks like an old Vo-Ed dimensioning quiz.

"Standard milling machine taper". What does that mean? R8?

The big end is 2.767 inches, which is pretty close to a 50 taper (2.75") -- much bigger than an R8 taper (which is 1.25" across the opening).
Like Tony says, it looks like a quiz, and the milling machine taper is hypothetical.

jacampb2
01-24-2008, 11:11 PM
I got 4.314

andy_b
01-24-2008, 11:15 PM
Sorry I wasn't quite complete I should have used

4.5-(1.843+(2X1.237))=Y
4.5-(1.843+2.474)=Y
4.5-4.317=Y
0.183=Y

Then X=4.5-Y
X=4.5-0.183

X=4.317

Sorry for the confusion

i agree with Doc Z.

andy b.

dan s
01-24-2008, 11:19 PM
I don't think you can assume the left side of the circle is 1.84" from the left side.

that seams like a massive assumption.

JoeFin
01-24-2008, 11:27 PM
Standard milling machine taper - 3.5” per ft

lazlo
01-24-2008, 11:29 PM
Right, but it's not exactly a 50 taper (which is 2.75" at the big end), so it may not have the standard 3.5" per foot taper ;)

J Tiers
01-24-2008, 11:36 PM
If this IS really the 3.5" taper that is assumed from the "standard taper".

The mouth of the taper is given as 2.767, which is at 4" from small end of taper, since the cylindrical portion is 0.5" back from the 4.5" dimension.

To get contact point you need the diameter, which can be found from the angle of the taper.

arctan((taper/2)/12)) = half angle of taper = 8.297 deg

then hypotenuse is the radius, and so

half diameter is radius * cos(half angle) =1.224

So diameter at contact is 2.448, difference of mouth vs contact is 0.319, and distance from mouth is (.319/3.5) * 12 = 1.094

Now the distance of center from contact is required.

sin 8.297 * radius = that distance, which is therefore 0.179

If I didn't fat-finger any numbers, that ought to be

X = 4 - 1.094 + 1.237 + 0.179 = 4.322

This is rounding to 3 places, which gives a net precision actually less than the 3 places. In fact it says on the print that the accuracy is only 0.003 for three place numbers.

Since every number on there is 3 place, the actual values might vary fairly widely from the above.

Rich Carlstedt
01-24-2008, 11:56 PM
Very poor quiz.
It is more about what the "standard Milling taper is" than the question on Dimensions.

The Proper term would be
"American Standard Steep Machine Taper"
That would define it....
It may as well be like asking " how many flutes are needed
on a tap for a 1/4-20 hole ?"

Rich
Source
Tool Engineers Handbook by SME

skeeter
01-25-2008, 12:01 AM
Hey I am not a math person. The answer as I see it is: 3.077"

LES A W HARRIS
01-25-2008, 12:41 AM
I concur with J Tiers.

http://i37.photobucket.com/albums/e97/CURVIC9/2008%20GENERAL/0180824012008_222536.jpg

dan s
01-25-2008, 12:46 AM
Les i think you're wrong about W. I think you need to calculate the angle not the distance.

tony ennis
01-25-2008, 12:53 AM
I figured there was a reason the problem was called "trig 2" or whatever.

They should have just asked what the standard taper was. :rolleyes:

ErnieD
01-25-2008, 01:01 AM
Hi,

Being rusty in math I went to my trusty CAD program and made a drawing of the part shown. I used 3.5 inches per foot for the machine taper. I find that distance x=4.3218 and distance w=.253. This was a nice practice piece.

ErnieD

Oops, 3.806-3.000=.806/2=.403 not .253. I mis read the 3.806 as 3.506 at first.

LES A W HARRIS
01-25-2008, 01:02 AM
Les i think you're wrong about W. I think you need to calculate the angle not the distance.
3.806"-3.000" = .806/2 = "W" ?

dan s
01-25-2008, 01:33 AM
think
Pythagorean theorem (http://en.wikipedia.org/wiki/Pythagorean_theorem) & Law of sines (http://en.wikipedia.org/wiki/Law_of_sines)

c=(1.84^2+0.403^2)^(1/2)
c=1.884

a/Sin(A)=c/Sin(90)

a/Sin(A)=c

a/c= Sin(A)

.403/1.884=sin(A) A=W

W=12.35 degrees

lazlo
01-25-2008, 01:33 AM
If this IS really the 3.5" taper that is assumed from the "standard taper".

The mouth of the taper is given as 2.767,

Why would they imply the National Machine Tool Association taper of 3.5" per foot, but use a non-standard gauge line? A "real" 50 taper would have a 2.75" gauge line.

Is it a Harbor Freight 50 taper, where the spindle opening is .017" too big, so a standard 50 taper adapter will fall out? ;)

JoeFin
01-25-2008, 07:35 AM
I think you guys are assuming too much information.

There is nothing on that drawing that indicates to me the angles are the same. The outside angle is dimensioned but not the inside.

So as the drawing stands, I would have to kick it back along with an RFI for correction

John Stevenson
01-25-2008, 08:14 AM
http://homepage.ntlworld.com/stevenson.engineers/lsteve/files/0180824012008_222536.jpg

The ringed dimensions are invalid as they are not given on the original drawing.
It doesn't define 'Standard taper' so it can't be used.

Only the given dimensions can be used.

Given what is there it can't be solved.
The ball touches the taper at a tangent point and none of this is dimensioned so where the tangent point is in relation to the taper staring from it's given point of 2.767 determines the angle and hence X

It's backfired on them as they have not given all the information needed.
There is no such thing as a standard machine taper : period There are standard machine tapers 7/24, R8, Morse etc

.

aboard_epsilon
01-25-2008, 09:34 AM
bet there was originally a set time limit to answer that question ..
and looks like you all went over ...so failed

BTW what was the time limit

i cant be bothered ...unless it was a personnel problem i had to solve for myself.

for the others who think its a real problem it ain't ...its a maths exam question.

All the best.markj

lazlo
01-25-2008, 09:51 AM
bet there was originally a set time limit to answer that question ..
and looks like you all went over ...so failed

I think what TattooMike left out is the description of the problem from the quiz. It probably had the details in the text that you would need to fully constrain X.

deltaenterprizes
01-25-2008, 09:58 AM
Assuming that 1.84 is to the edge of the circle,the solution is 2R + 1.84 =
(2 x 1.237)+ 1.84 = 2.474 =1.84 = 4.314

X = 4.314

Without the actual drawing to confirm this Sir John may be more accurate.

x

Carld
01-25-2008, 10:56 AM
I've said it twice before and I'll say it again. The problem is not solveable because not enough info is given, namely the angle of the taper or the dia. of the small end of the taper.

Without knowing the taper one can't determine the tangent contact point on the circle to determine the distance from the tangent contact point to the OD of the circle to determine X.

Every solution that has been posted has ASSUMED an angle. There is no angle given and there is no standard machine taper. There are numerous machine tapers so tell me which one is considered standard and why?

If this was a test question I suspect it was to trap those that ASSUME and nothing more, which it has done here as well.

tattoomike68
01-25-2008, 06:47 PM
This is a 1st quarter math problem for a community college machine shop class. The teacher is a real hard ass. It is solvable if you look things up.

He likes to make students look things up in the machinerys handbook.

Optics Curmudgeon
01-25-2008, 07:17 PM
Nothing hard about that guy, he's just a plain ass. Now if he specified what taper...

Joe

John Stevenson
01-25-2008, 07:21 PM
Mike,
He might be a hard ass but he's an opinionated one.

He hasn't given enough information unless some is included with the question.

The drawings says Standard Milling machine taper but doesn't specify what standard.

The whole purpose of a drawing is so the manufacturer can make the part given the drawing. In this case he's trying to be too clever.
Morse tapers are also standard in some machines and these can go up to 3" in diameter so who's or what standard.

.

01-25-2008, 07:25 PM
All that said I've solved nastier problems than that out in the rain in the bottom of a drydock when setting the splay and drift angles of the bore of a ship's strut bearing from plan data adjusting for droop and temperature. The problem shown seems to be a classroom exercise of the type I did hundreds of out of Wolf and Phelps (Vols I and II) to prepare me for the real thing in the drydock in the rain. Now nothing in shop math scares me.

I hated those problems when I had to do them for apprentice math homework instead of watching "Maverick" (Yes, that long ago when James Garner was young and handsome) on TV. Later on in my career I blessed my harsh training when time, material, and money was at stake. My faculty with shop math and bonehead physics has over the years saved my employers thousands and earned me any number of awards with some nice (\$\$\$) checks attached.

Bless that teacher as you curse him. He's giving you hell now to save your job later. The best steel is forged from a hot furnace.

tattoomike68
01-25-2008, 07:42 PM
My friend is taking the class, he is having a good time just like I did in 1990-1991

At that class the students punch a time clock and work it just like a job.

If a student runs a machine he will stop and quiz them about the set up, speeds and feeds, tool geometry. If you dont have all the answers he will send you to the classroom to do machinerys handbook lessons.

All his prints for projects have missing dimentions to make the students think and solve problems.

The teacher there is wonderful. I would like to go back and get my AAAS degree there.

bob_s
01-25-2008, 07:59 PM
And the winner is DELTAENTERPRISES

Importing the image provided into PHOTOSHOP, blowing it up greatly, it is possible to draw a line from one corner of the holder to the opposite side, which just touches the inscribed circle. No assumption required. The answer is 4.314"

aboard_epsilon
01-25-2008, 08:08 PM
ah i see
the students are not meant to do trig

they are supposed to look up the missing dimensions in the machineries handbook .

all the best....mark

LES A W HARRIS
01-25-2008, 10:59 PM
Les i think you're wrong about W. I think you need to calculate the angle not the distance.
Dan, senior moment, yes "W" is an angle, lousey drawing or not.

By TI-30XA guessing box:
W = arctan 0.403/1.840, = 0.219022, = 12.353945 deg.

DocZ
01-25-2008, 11:18 PM
err read the earlier posts ;)
And the winner is DELTAENTERPRISES

Importing the image provided into PHOTOSHOP, blowing it up greatly, it is possible to draw a line from one corner of the holder to the opposite side, which just touches the inscribed circle. No assumption required. The answer is 4.314"

J Tiers
01-25-2008, 11:30 PM
One thing nobody has mentioned (I did, though) is that all your answers are wrong................ because the precision of the various measurements is so abysmal.

The error of each measurement is 0.003 max. This adds up to quite a nice total error.

The large end diameter is probably the worst one, since a variation there of diameter will move the contact point in or out. The total amount of that possible difference is related to the slope of the taper, or 12/3.4, which gives a multiplier of 3.4x.

So am error of +0.003 directly changes "X" by 0.01". Ditto for an error of -0.003, for a total error from that source of about 0.02". Then errors in the 0.5" or 4.5" dimensions add in directly 1:1.

So far, we are at a total uncertainty of about 0.046" in the value of "X".

I think all the answers so far fall within that limit..... and they are all apparently based on nominal values of all dimensions.

So the nominal value of the "X" dimension is one thing, but the QC limits that would be derived from reading all the information given on the face of the drawing would be something else entirely.

As far as the objection that my value is based on an assumption, so what? I stated it to be derived from that assumption up front.

Paul Alciatore
01-26-2008, 01:21 AM
This is a 1st quarter math problem for a community college machine shop class. The teacher is a real hard ass. It is solvable if you look things up.

He likes to make students look things up in the machinerys handbook.

Just because it comes from a "teacher" in a community college, does not mean it makes sense. I have seen PhDs in physics make simple mistakes. Most of them are sensible enough to admit the error when it is pointed out.

Now, perhaps in his class, this "teacher" has taught some value for a "standard milling machine taper" and if so, he has a right to assume the students should remember it and use it. But we do not have that information here. I do not know where to look it up. Perhaps there was a standard in the 1850s or the 1920s but in today's world it simply does not exist. There are many different tapers used in milling machine spindles and each one of them will give a different answer.

So, in the form it is presented here, the question can not be properly answered. There is simply insufficient information given.

tattoomike68
01-26-2008, 02:54 AM
Just because it comes from a "teacher" in a community college, does not mean it makes sense. I have seen PhDs in physics make simple mistakes. Most of them are sensible enough to admit the error when it is pointed out.

Now, perhaps in his class, this "teacher" has taught some value for a "standard milling machine taper" and if so, he has a right to assume the students should remember it and use it. But we do not have that information here. I do not know where to look it up. Perhaps there was a standard in the 1850s or the 1920s but in today's world it simply does not exist. There are many different tapers used in milling machine spindles and each one of them will give a different answer.

So, in the form it is presented here, the question can not be properly answered. There is simply insufficient information given.

Knowing teacher hardass I bet he wants an answer for all common milling machine tapers that fit the size range. he really is a good teacher and yes all the info is there. I could make the part and have it pass. you could too.

He is the RTFB type ( read the freakin book) if you dont read the machinist handbook and have the answers he will punish you with some long winded machinist handbook lessons that will make you wish you had done the homework.

aboard_epsilon nailed it when he said what he said.

John Stevenson
01-26-2008, 05:51 AM
Knowing teacher hardass I bet he wants an answer for all common milling machine tapers that fit the size range. he really is a good teacher and yes all the info is there. I could make the part and have it pass. you could too.

I have the NMTB [ National Machine Tool Builders ] design book in front of me and also the Russian equivilant which is far better.

There is NO taper that fits that design range.
INT 50 is closest but is out by 17 thou so if he's OK with working to plus or minus 17 thou then the answer is somwhere between a zip code in Arizona and one in Nevada.

I think we all know what he means but he's missed the last piece of information on the drawing defining the taper as 7/24 or 3-1/2" per foot.
If he wants to be pedantic and make you think then I can be pedantic and tell him to do his job correctly.

BTW there is another taper that's also close. A 6-1/2 Morse which is a standard in some spindle noses is also close.
However because of the shallow taper of the morse X will be totally different.

So using 6-1/2 Morse or INT 50 will give you 2 answers, which one is correct ?

.

oldtiffie
01-26-2008, 07:58 AM
Knowing teacher hardass I bet he wants an answer for all common milling machine tapers that fit the size range. he really is a good teacher and yes all the info is there. I could make the part and have it pass. you could too.

I've thought it was OK from the start - and I still do.

If I've got it right, the teacher has not nominated any of what may well be any one of a number of "standard tapers" in common use at the time.

This is a trigonometry problem - not a math or CAD drawing problem.

This being the case it is up to the student to find out what tapers are in use, select any one of them, use (say) "Machinerys hand-book" for the data (large and small end diameters and taper per foot) to suit.

The answer will be correct for any taper that is chosen.

I suspect that the teacher is interested in the process rather than the size/s.

So, if say 6 of us each chose a different standard taper and the process was correct in each case, the answer in each case would be correct but each and every answer would be different but correct none-the-less.

Once the taper is defined (the large diameter is already defined) the tangent point on the ball and the arctan can be resolved.

Think first and don't just charge in at all.

See the outcome required and then look for the solution.

Hasten slowly.

As TM says, all that you need to know is there. Just choose your "standard" taper - any "standard" taper - and get the details from a reference chart/book - and away ya go!!

DR
01-26-2008, 01:01 PM
This is a trigonometry problem - not a math or CAD drawing problem.

I guess you could trig it out. It's trivial to do in CAD.

NickH
01-26-2008, 01:25 PM
So we have to assume data to get AN answer so there is no SET answer, and Mr "I can Make it" will end up with one of half a dozen possible parts?
What's the point of that then? :p
Nick

Carld
01-26-2008, 01:56 PM
I went to the shop and looked in:

American Machinists' Handbook, second edition, third printing, Octobr, 1915. There is no standard machine taper but there are numerous tapers listed. There is a taper called Standard Tool Compainies Tapers by The Standard Tool Co. for their machines. Perhaps that is the one of which he indicates :rolleyes: .

Machinery's Handbook, sixth edition, 1914. There are several machine tapers none of which are called standard.

Machinery's Handbook, Twenty-second Edition, Third Printing, July, 1985. It lists no standard machine taper while it also lists many tapers used in machines.

I am with oldtiffle, pick a taper and even though the large end matches none of the tapers use math to determine the angle or the small end and solve the problem. As he said, with the information given any taper will work.

You can read the Machinery Hanbook all day long and you will not find a Standard Machine Taper in it anywhere.

However, it is not the machinist's job to find a missing measurement on a drawing and if he does so he is assuming the job of the engineer/designer and would be wrote up or fired for doing so. When a drawing has a missing dimention you had best turn it over to the boss and let him solve it. While the teachers intentions may be good he is setting his students up for trouble.

To teach them to assume is a faulty teaching method. As to using CAD to solve the problem, how many shops have CAD in the machine shop for the machinists to use? Maybe the CNC shops but are the operators supposed to solve for missing dimentions? I bet not.

Paul Alciatore
01-26-2008, 05:43 PM
I went to the shop and looked in:

American Machinists' Handbook, .......

To teach them to assume is a faulty teaching method. ......

Thanks Carld. My points exactly. There really is no standard taper for milling machines. To assume a number that is not given is a sure invitation to disaster. I really hope you guys that keep insisting on such assumptions are not making bridges or airplane parts, or any of a number of items that may cause loss of life (perhaps mine).

Weather you use trig, or CAD, or whatever, there is insufficient information given in the problem to find an answer and that statement is the only correct answer. If this "teacher" insists otherwise, he is a very poor instructor indeed. None of us should place blind trust in a person just because he/she is a teacher or an engineer or whatever. Everyone can make mistakes.

BobWarfield
01-26-2008, 06:34 PM
Ya'll would obvious not enjoy going back to school!

Chuckle,

BW

oldtiffie
01-26-2008, 07:24 PM
That teacher is one very smart guy.

He can nominate any taper he likes.

He can make each student go to a particular machine in the machine shop with that ball, find a taper that it fits into, measure that taper or check the machine manual/specs for it and then use THAT taper on THAT (students) work-sheet.

He may even require the students to use a micrometer/digital guage/caliper to measure the amount the ball is below or projects above the end of the taper. They will then have a reference to check their work ("trig", geometry, logic, math, logic). If there is an error they might have to find and rectify it.

The sizes of the ball and taper will be correct to a very high order.

The tolerances on the drawing for anything else are irrelevant and are a "smoke screen" or "red herring".

This is all typical "shop stuff".

You don't have to use all of the data/dimensions/sizes given - just those that you need.

In this way, there is less likelihood of students cheating from each other.

Further, I'd guess that the teacher would have answers for every taper in the shop.

This is pure practical application of trigonometry as it might apply in the shop if say the taper were left off the drawing in error - can happen.

It will also teach the student the importance of critical dimensioning etc. etc.

I would also guess that the student would still get most marks if the process/logic he used was "structured" and "sound" even if the math were a bit out due to a minor error.

This is a good exercise in using geometry with trigonometry instead of using them in isolation.

This is basic stuff that should be in the tool-chest of any machinist.

It can be solved just using the printed logarithm and "trig" tables in most printed references - even without a pocket calculator, a CAD system or a computer.

Its too easy to blame the boss or the Engineer or the drafter. I hear a lot about how "the shop" could/would do it" if THEY were "in charge".

Well here's your chance to show us just how good and creative you are.

I'd imagine that your Boss/Foreman etc. would not be too pleased if you couldn't make phone call and then having got the requirements, "sorted it out".

I'd also reckon that you'd get a few "brownie" points (and "bragging rights?) if YOU sorted it out.

I still agree with the OP in that all the info is there - perhaps all you needed to do was ask or find a taper that suited and get on with the job.

The OP alluded to but actually refrained from saying that this is "Kids stuff" - which I agree with.

It CAN happen in your HSM shop - with no one else to blame or throw the job back to other than yourself.

I suspect that there are a few (more than?) slightly bruised egos "out there".

John Stevenson
01-26-2008, 07:43 PM
That teacher is one very smart guy.

He can nominate any taper he likes.

I suspect that there are a few (more than?) slightly bruised egos "out there".

OK playin by these rules I make X= 89.65475432987 but I'm not sharing what taper it is.

I have double checked my figures with calculator, spread sheet and CAD so I know it's right. :D

.

oldtiffie
01-26-2008, 07:55 PM
That teacher is one very smart guy.

He can nominate any taper he likes.

I suspect that there are a few (more than?) slightly bruised egos "out there".

OK playin by these rules I make X= 89.65475432987 but I'm not sharing what taper it is.

I have double checked my figures with calculator, spread sheet and CAD so I know it's right. :D

.

Good onya John.

I knew I could depend on you to take it the right way (err not that sort of "right way" - even if I am ex-Navy!!).

You might wind up being "teacher" (again or still?).

John Stevenson
01-27-2008, 05:54 AM
Anyway that teacher is being far too smart.

Why make something that is useless anyway ? Is this the way to train people ? get them to work out all the maths, make it and then chuck it in the bin ?

Because he asks you to assume a taper we must do the same so we'll assume INT50 as it fit the bill the closest.

Now look at the part, what is it ? It looks to be an insert to convert two tapers.

Now look at the internal taper information we are given. Large diameter is 2.769 and the taper starts 0.5" in.

Now a taper sit on the largest OD on what is called the gauge line [ missing from drawing ] which for a INT50 is 2.750" The flange of the holder is always 1/8" further up the taper so you have daylight to prove it's on the taper.

Now in this drawing with the OD being larger than the gauge line and the start of the taper being 0.500" down the hole what will happen is that the flange will fit the insert well before the taper comes anywhere near making contact.

In fact it will never make contact and finish up rattling around inside like a prick in a shirt sleeve.

.

lazlo
01-27-2008, 10:04 AM
Anyway that teacher is being far too smart.

I think Mike's friend left off the description from the quiz.

Since this was a Vo-Ed trig quiz, like I conjectured on the first page ;), the description (that Mike's friend didn't include) was probably something like:

"Johnny the machinist is given an assignment by his boss, Bob the Builder. Bob needs a spindle with a Standard Machine Taper of X.YYYY cubits per furlong. Complete the dimensions on the attached sheet to deliver to the machine floor. You have 10 minutes."

dhansen
01-27-2008, 10:31 AM
On page 933 of the Machinery's Handbook (large print 27th edition), table 6 defines Standard Steep Machine Tapers which are ANSI #5 thru #60 milling machine spindle tapers. All of these tapers have a taper per foot of 3.5".

lazlo
01-27-2008, 10:54 AM
Right, that's the 50 Taper I mentioned on page 2. But a 50 taper has a gage line (diameter of the big end) of 2.75", and but the drawing doesn't.

So it's an imaginary taper, and only the quiz description would have the remaining detail necessary to solve for X.

Carld
01-27-2008, 11:29 AM
As a quiz to do math it may have some merit but if the teacher is instructing his students to take it on themselves to assume a missing dimension and make the part there will be hell to pay when they do so at work.

I don't think any boss, engineer, designer or draftsman would give anyone an attaboy for assuming they know what was supposed to be on a drawing.

It's true we don't know the content of the question in the quiz and while that may help to solve the problem it don't resolve the fact that if the instructor is in fact teaching the students to take it on them selves to correct or add to a drawing they will be doing good work is faulty teaching.

I think if you went into any shop or factory and asked the bosses or management if they would want a worker to assume a dimention on the drawing you would get a resounding, hell no, we may fire him/her for that.

Gentlemen, each and everyone that says they can solve the problem are ASSUMING they know what taper the engineer wants.

The old saying is, to assume makes an ASS out of U and ME. You can't assume anything and to teach to do so is not in the best interest of the students.

Now, if the teacher tells the students to never add to or change a drawing on the job without consulting the management then he is ok.

Lew Hartswick
01-27-2008, 11:43 AM
I certainly HOPE that the instructor in question has been pointed to
this discussion. It can't help but make him a lot better instructor IF
...lew...

dhansen
01-27-2008, 01:32 PM
Using 3.5" per foot as the taper, I came up with 4.3222 (rounded) for dimension X. Don't know if my math is correct, but I double checked it.

dp
01-27-2008, 02:20 PM
I haven't tried to solve this yet but it appears to me that it doesn't matter what the taper is that you assume. Provided you describe the taper you choose in your solution, it will solve. X being different for different tapers, of course. The quiz then, is to describe a method to solve for X, not to nail a value to X. Then again I'm still working on my first cup of coffee this am so may have missed something.

oldtiffie
01-28-2008, 05:45 AM
I thought that this had gone on long enough.

It was time for an answer.

First of all - the original problem.

There was nothing wrong with the question paper.

It was not a shop drawing for manufacture - at all.

It was an exercise in trigonometry and logic.

It was also a "general/generic case" project.

There was no specific numerical answer - at all.

This was made clear enough by the "standard milling taper" notation.

I went for the generic case construction in which figures or values could be substituted for letters and symbols.

There is a lot of information on the drawing that is irrelevant.

I decided to do a basic construction of the items that would affect the answer.

http://i200.photobucket.com/albums/aa294/oldtiffie/SolutionforX_1A.jpg

I selected an arbitrary (ie any) taper and applied it to the end of the parallel bore and extended it to intersect the job and ball centre-line.

Next, I "off-set" a line from that (previous) line by the radius of the ball.

The centre of the ball was at the intersection of that line and the centre-line of the work and the ball.

In the second sketch, I worked out the trigonometry for the solution for a generic "X".

So, assuming I am correct, the solution will work for any combination of bore diameter and length, taper, overall length of work and ball diameter.

I am just about sure that is what the teacher/instructor required.

The "standard machine tapers" are given in unit rise/offset per unit length ie x/y which = tan theta (half the included angle of the bored taper).

So, again if I am correct, you can insert the dimensions of the bore, the taper and the ball into the generic equations and you should get the answer "X" for that specific case.

I will admit that there was a bit of "head-scratching" going on and I did have several goes at it. I was mostly correct the first time and just needed to refine or "fine tune" it - and there it was.

I did not need any tables or Machinerys Hand-Book, nor did I need a calculator, computer or CAD system.

I must say though that a CAD system would have made it faster.

It could easily be set up for the general/generic case in a spread-sheet.

Please do check my logic and equations.

I hope this helps.

NickH
01-28-2008, 07:34 AM
I can't see it helping those who imagined they could make this part to spec from the drawing and "get it passed", they need professional help :D
Nick

J Tiers
01-28-2008, 07:59 AM
Forgive me for this observation.............. I don't want to be mean........

But you seem to have stated the obvious as your "general case solution".

Your equation using "X=W-H" is obtainable by inspection of the original problem, and might almost be said to be contained in the statement of the problem as it was presented on the face of the sheet and the auxiliary instructions. It also is not sufficient to solve the problem.

You have given a cloud of variables, and a number of additional equations, which may or may not (I have not detail checked them) contain the information needed to solve for the distance required.

However, as a minimum, the next step for the "general case" would be to "expand" the single variables "W" and "H" in your "general case" to show explicitly the other equations defining them, and then collect terms so that you have "X" on one side and all the other known or directly derivable parameters NOT including "X" on the other, hopefully in their "minimum representation" (least complex form) .

A couple other people have "shown their work", and shown how the problem can be solved for ANY value of the taper, so it isn't at all correct to say or imply that everyone has simply given the answer for this case.

As for being "time for an answer", I'll leave that as an exercise for the student................

tattoomike68
01-28-2008, 01:47 PM
I thought that this had gone on long enough.

It was time for an answer.

First of all - the original problem.

There was nothing wrong with the question paper.

It was not a shop drawing for manufacture - at all.

It was an exercise in trigonometry and logic.

It was also a "general/generic case" project.

There was no specific numerical answer - at all.

This was made clear enough by the "standard milling taper" notation.

I went for the generic case construction in which figures or values could be substituted for letters and symbols.

There is a lot of information on the drawing that is irrelevant.

I decided to do a basic construction of the items that would affect the answer.

http://i200.photobucket.com/albums/aa294/oldtiffie/SolutionforX_1A.jpg

I selected an arbitrary (ie any) taper and applied it to the end of the parallel bore and extended it to intersect the job and ball centre-line.

Next, I "off-set" a line from that (previous) line by the radius of the ball.

The centre of the ball was at the intersection of that line and the centre-line of the work and the ball.

In the second sketch, I worked out the trigonometry for the solution for a generic "X".

So, assuming I am correct, the solution will work for any combination of bore diameter and length, taper, overall length of work and ball diameter.

I am just about sure that is what the teacher/instructor required.

The "standard machine tapers" are given in unit rise/offset per unit length ie x/y which = tan theta (half the included angle of the bored taper).

So, again if I am correct, you can insert the dimensions of the bore, the taper and the ball into the generic equations and you should get the answer "X" for that specific case.

I will admit that there was a bit of "head-scratching" going on and I did have several goes at it. I was mostly correct the first time and just needed to refine or "fine tune" it - and there it was.

I did not need any tables or Machinerys Hand-Book, nor did I need a calculator, computer or CAD system.

I must say though that a CAD system would have made it faster.

It could easily be set up for the general/generic case in a spread-sheet.

Please do check my logic and equations.

I hope this helps.

That would work. You would pass the math test easy.

And yes the part could be made to the print. I have made parts to the print only to find out the print was wrong due to no fault of my own.

I am amazed that a 1st quarter math problem has so many people stumped.

lazlo
01-28-2008, 02:37 PM
Why would they imply the National Machine Tool Association taper of 3.5" per foot, but use a non-standard gauge line? A "real" 50 taper would have a 2.75" gauge line.

Is it a Harbor Freight 50 taper, where the spindle opening is .017" too big, so a standard 50 taper adapter will fall out? ;)

And yes the part could be made to the print.

I am amazed that a 1st quarter math problem has so many people stumped.

Really Mike? You could make part to that print?

So what Standard Machine Taper would you use? National Taper, Jarno, Morse, Brown & Sharpe ...?
You do realize that none of those "Standard Machine Tapers" have a gauge line of 2.676"?

tattoomike68
01-28-2008, 03:55 PM
yes I would use the taper angle of the NMTB Shank
Also called Quick Change, NMTB, MM, National Standard, American Standard Machine Taper, ISOxx, and QCxx...etc.

http://www.tools-n-gizmos.com/specs/Tapers.html

With the taper known all sizes could be known.

The fact it may not be to spec of any machine tool holder or spindle is Irrelevant. it just has the same taper, thats all.

It may be a part for a dairy farmers manure spreader. ;)

aboard_epsilon
01-28-2008, 03:57 PM
well mike you told them how it was

still they keep trying to solve it

reminds me of rainman ...
and his whose on first base :)

all the best.mark

Carld
01-28-2008, 04:38 PM
If you worked for me and you assumed a dimention on a print and made the part I would fire you on the spot. Any teacher that teaches the student to assume should be fired as well.

He is using faulty teaching and is setting the students up for failure.

Where does this teacher teach at?

tattoomike68
01-28-2008, 04:38 PM
In fairness to all I will post the returned graded paper when my friend gets it back from the instructor.

lazlo
01-28-2008, 04:42 PM
yes I would use the taper angle of the NMTB Shank
...
The fact it may not be to spec of any machine tool holder or spindle is Irrelevant.

So you'd cut the taper, knowing that they got the taper dimensions wrong, and that the part wouldn't fit any machine ever made?

In this instructor's quiz, did he also have a standard acme leadscrew, except the it used a 36.9 degree included angle? ;)

tattoomike68
01-28-2008, 05:06 PM
So you'd cut the taper, knowing that they got the taper dimensions wrong, and that the part wouldn't fit any machine ever made?

It may not go to a milling machine at all.

J Tiers
01-28-2008, 10:41 PM
OK, so there is No standard milling machine taper................ right?

Apparently none of you work for the Morse Twist Drill & Machine Tool Co.

This is out of my "Machinists Practical Guide"...........

Note the words at the top of the sub-section........... And the reference to the "NMTB" having set the standard as has bee alluded to.

Whether the mouth of the taper is correct for one of the standard taper sizes is not relevant when the "taper" is referenced "as a taper" and not as a particular size socket.

Would I make it like that without a call to the customer? No.

So you'd cut the taper, knowing that they got the taper dimensions wrong, and that the part wouldn't fit any machine ever made?

If the print had the actual taper explicitly called out I sure would.

But the reference for the purpose of setting the problem is quite clear, and caviling about "standard" etc seems very "legalistic" within the terms of the problem.

http://img.photobucket.com/albums/0803/jstanley/MMT.jpg

oldtiffie
01-28-2008, 10:45 PM
Thanks tatoomike.

Those taper tables are a big help and very instructive.

There are some people getting quite "hung up" on how bad the Teacher/Instructor is and how he is so wrong and incorrect as they don't agree with (or like?) him.

Tough.

I think he is an excellent Teacher and is doing a great job in his instructional vocational training role.

This stuff is "101" machine shop stuff.

Any trainee who passes this should do very well in a machine shop - perhaps as a machinist but hopefully as Leading Hand, Foreman etc.

He will have the math and logic back-ground, thanks in no small part to the teacher who set this assignment.

The fact that some think its wrong because they don't like the assignment or the Teacher without detailing what is wrong with the Teacher or the assignment reflects no credit on them nor does it reduce the stature of the Teacher in my estimation - at all.

There has been a lot of criticism of missing dimensions (wrong) and/or re-interpreting drawings (wrong - but many of the critics have done just that themselves while wrongly admonishing the student/teacher of it).

There is nothing wrong with the drawing.

If some here can't read nor understand nor accept what is written and set in the drawing instead of putting their own interpretation of either or both what the drawing actually says or should say, then I am quite disappointed.

Just about the last thing I'd do is sack some-one for finding a fault in a drawing or making the part to the drawing if the drawing was wrong. The Foreman or Estimator etc. who gave him the drawing as correct is at fault here - not the machinist. Further, this is the "jam on the bread and butter" if the job was quoted and and the client had warranted the drawing/s. In this case your boss is in the "box seat" as he can claim "extras" and "variations" at his "charge out rate" which, more often than not is above his "quote rate" for an as yet indeterminate number of hours etc.

The text on the drawing clearly said "Standard milling taper". Check it for yourselves.

http://i44.photobucket.com/albums/f24/snoopdog6502/problem1.jpg

It did not say to use any particular standard taper nor any milling tool/item with any particular adaptor to fit that taper.

For example:
a.
the NST taper is 3 1/2" per foot - 3 1/2 /12 = 7/24.
There is no length or diameters specified.

The most commonly used adaptors using the NST taper are the No. 30, No. 40 and No. 50

b.
the morse taper varies from 1:19212 (MT0) to 1:20020 (MT2) to 1:19180 (MT6).

Diameter and lengths of each MT are therefore specified.

c.
the Brown & Sharp taper is approximately/2" per foot except 10 which is 0.5161" per foot.

Diameter and lengths of each MT are therefore specified.

d.
The Jarno taper numbers (2 to 20 inclusive) are specified in terms of the length of the taper, and the diameters at each and of the taper in terms of a fraction of the number of the taper.

I have attached links to pics of the tapers as described.

The links are at the end of this post.

I stand by my use of "first principles" to develop a general/generic case as a solution for "X".

To make it a solution for a specific case, put in the specific dimension and the taper you require - just substitute the numbers in place of the letters.

All of the equations are required.

If someone were really clever, they would put the generic case into a spread-sheet and have it use the parametric facility in a CAD package (eg AutoCAD) to import those figures from spread-sheet and automatically produce the drawing for you/them.

The angles do not need to be determined/found. Just use similar triangles and proportionality:
if the taper is give as being: x/y

and the job "X" is required for the "Y" on the job

therefore X/Y = x/y

and X = (xY)/y

If I am wrong, please do tell me - I will appreciate it. But I won't appreciate it if you "don't like it", "don't think its right", "the Teacher is terrible", "the drawing is wrong", "what I'd do about or with it", "what I think it says/means" etc.

If there are a few bruised egos or noses either bent or out of joint because they don't like or understand it, or want to "take charge" - tough.

Don't pick on the teacher - he is not here to explain or defend himself. In my opinion, he doesn't have to.

In case you missed it, I do not like to see people wrongly pilloried nor have their professional integrity challenged, vilified or shredded without a chance to either defend or explain themselves or be defended.

But in the event that some who have been so critical of the teacher were to contact him, I'd suggest that your ego and self-esteem will not be enhanced by the discussion.

Nor should it/they be.

Thanks to those who either supported or who did not "rubbish" the Teacher.

I am a big fan of Vocational Training. Schools, Colleges, Teaching and support staff as well as and particularly the students, trainees and graduates. They are - in the vast majority - very talented and dedicated people - staff and students alike.

If someone needs a bit of help to understand my approach to solving for "X", please PM me if you prefer and I will genuinely try my best to assist.

Now, for the links to the pics re tapers etc.

http://i200.photobucket.com/albums/aa294/oldtiffie/machine_tapers/Machine-taper1.jpg

http://i200.photobucket.com/albums/aa294/oldtiffie/machine_tapers/Machine-taper2.jpg

http://i200.photobucket.com/albums/aa294/oldtiffie/machine_tapers/Machine-taper3.jpg

http://i200.photobucket.com/albums/aa294/oldtiffie/machine_tapers/Machine-taper4.jpg

http://i200.photobucket.com/albums/aa294/oldtiffie/machine_tapers/Machine-taper5.jpg

lazlo
01-28-2008, 11:06 PM
From the first page:

The taper is probably 3 1/2" per foot but that is just an assumption and we all know what happens when we assume.

OK, so there is No standard milling machine taper................ right?

Right, Errol established that the instructor most likely meant the National Taper on page 1 of the thread Jerry, and I, Tony, Sir John, and several others pointed out then that if the instructor meant to specify the National Taper, he got the taper dimensions wrong.

Note the words at the top of the sub-section........... And the reference to the "NMTB" having set the standard.

Yep, everyone in this thread knows about the National Taper, except for Mike's Vo-Ed instructor ;)

Now, notice in the document you posted, that each row in the "Standard Taper" lists the 'A' dimension and the 'B' dimension. Now notice on the last line, for NT 50, it lists the A dimension as 2.75", and the B dimension as 1 9/16".

So, tell me which which one of the Standard Machine Tapers in your spec is the one with the 2.767" A dimension? :D

lazlo
01-28-2008, 11:09 PM
Thanks tatoomike.

Those taper tables are a big help and very instructive.

Mike didn't post the taper tables, JTiers did.

There are some people getting quite "hung up" on how bad the Teacher/Instructor is and how he is so wrong and incorrect as they don't agree with (or like?) him.

We're not hung up over it Tiffie. The instructor botched the quiz, and typed 2.767" instead of 2.75" That happens, no big deal.

The part that's amusing is you and Mike trying to make up reasons for why you'd still want to make that drawing, when the taper dimensions are clearly wrong, as everyone else in this thread has pointed out.

J Tiers
01-28-2008, 11:13 PM
Tiffie.......

I don't know if you are complaining about me or not as far as "not understanding or accepting" your math.

I certainly hope not, since I "showed my work" way back on page 1 of this thread, and it is essentially the same I believe as yours.

I did use specific numbers, after stating clearly that I assumed the NMTB taper for purposes of the calculation, as opposed to retaining variable names.

I believe at least one other person also "showed their work" as well.

However, I don't believe that anyone can say that Morse, B&S, or, (gaaack) Jarno tapers have any claim to be called "standard milling machine tapers". I am unaware of any "agreement" to use one of those.

There is really only exactly ONE contestant for that title, and it is the NMTB taper of 3.5" per foot. There IS an actual "agreement" on that as a standard taper, whether or not the problem actually uses the "socket size" of a standard spindle nose.

lazlo
01-28-2008, 11:26 PM
Here, this is for Mikey's instructor :D

http://i164.photobucket.com/albums/u15/rtgeorge_album/MMT.gif

J Tiers
01-28-2008, 11:46 PM
Eh....... For some reason, posts don't always show up in correct order........ a couple snuck in that seem not to have been there when I posted

The rest of the post I made MENTIONED the issue of the mouth size,

NOTE THAT THE "TAPER" VALUE IS A COMPLETELY DIFFERENT AND SEPARATE THING FROM THE "TAPER SOCKET" DIMENSIONS

Look over to the left, where the "taper" is stated as 3.5" per foot, and the mouth size is listed as "A".

"TAPER" refers to a 'slope" or rate

Wiki:

"In geometry, or in the casual description of a shaper or object, a gradual thinning or narrowing towards one end"

Wiki again, re NMTB:

"The taper is variously referred to as NMTB, NMT or NT. Essentially this defines a taper of 3.500 inches per foot, or 16.2602047... degrees. All NMTB Tooling has this taper but the tooling comes in different sizes."

So the "taper" is the rate.

It really is incorrect to extend the meaning of "taper" to include the whole socket dimensions.........

Yep, everyone in this thread knows about the National Taper, except for Mike's Vo-Ed instructor

And those others who said there is no "standard milling machine taper" ............in this very thread..... ;)

lazlo
01-28-2008, 11:50 PM
It showed up the correct order JT, you're just posting on PM at the same time you're posting here :)

It really is incorrect to extend the meaning of "taper" to include the whole socket dimensions.........

I disagree, so does Machinery's Handbook, and so does the Morse specification you posted.

The National Machine Tool Builder's Association/ANSI B5.18 specification defines a machine tool shank, and not just a taper. So the NMTB/ANSI spec includes the taper per foot, the big end, the small end, the draw-bolt, the collar, ...

This is from Mike's link. Same dimensions are specified in MH:

http://www.tools-n-gizmos.com/specs/Tapers_NMTB_1.jpg

This is not just being pedantic -- like I said earlier in the thread, if you tried to fit a 50 taper shank into the Vo-Ed quiz spindle, which is 17 thou too large, the shank would just fall out.

A lot of grinding wheel arbors are 3 1/2" per foot, but people don't call them National Taper ;)

lazlo
01-28-2008, 11:53 PM
And those others who said there is no "standard milling machine taper" ............in this very thread..... ;)

I agree with John, Carld, and the others who have said there is not a single standard milling machine taper. National Taper, or National Machine Tool Association Taper, etc is one of several standard milling machine tapers.

Errol Groff summed it up perfectly, on the third post in this thread:

The taper is probably 3 1/2" per foot but that is just an assumption and we all know what happens when we assume.

J Tiers
01-28-2008, 11:56 PM
A lot of grinding wheel arbors are 3 1/2" per foot, but people don't call them National Taper ;)

Ignoring the fact that that is a male taper on the spindle, of course............. ;)

Mostly I see it listed as "taper socket dimensions" in tables, but whatever.

In any case, with the mouth dim clearly stated, and a leader to the 'sloped line" stating "XXX taper", the print clearly indicates what is intended, IMO.

And, I'd still call the customer.

Reversing your logic, if an NMTB SOCKET were intended, it would be correct to state "NMTB 40 socket" and let the standard rule the dimensions. So why wouldn't that be stated directly if it were intended?

lazlo
01-29-2008, 12:02 AM
Ignoring the fact that that is a male taper on the spindle, of course............. ;)

Sure, but I'm just pointing out that 3 1/2" per foot is a common taper used all over machine tools, and in most places it's not a National Taper ;)

Reversing your logic, if an NMTB SOCKET were intended, it would be correct to state "NMTB 40 socket" and let the standard rule the dimensions.

50 Taper is closest (off by 17 thou), but yes -- I would have happily solved for X and made the part if the drawing called out NMTB 50 and left off the FUBAR'd gauge line. I think many here would agree that it would even be safe to assume 50 Taper, even if NTMB wasn't specifically called out, if the gauge line was correctly dimensioned as 2.75".

In any event, like you say, the safest thing would be to call the customer to clarify, but since this was a poorly composed Trig quiz, as many have pointed out...

oldtiffie
01-29-2008, 01:47 AM
This is a very good trig exercise.

It is not, was not and clearly was never intended to be a manufacturing or shop drawing.

I would agree that it is pretty well certainly a 7/24 taper.

The requirement was for a standard milling machine taper - which 7/24 clearly is.

The diameter of the larger end of the taper was given.

The are not nor was there any requirement that the taper diameter/s be "adjusted" to suit any of the NST spindle tapers which have a specific larger diameter as well as the taper itself.

That is an assumption/presumption by some here.

It is both incorrect and quite unjustified.

I would not be surprised if the larger bore size was set so close to the 50 taper to "trap" those who assumed that the NST 50 taper was what was required and that the drawing should be assumed to be incorrect.

If that were the case, it certainly succeeded!!

It was or would be the general taper that was specified - not a specific instance of the taper - ie 30, 40, 50 etc.

The drawing could have been say 20 or 30 thou either way and still be correct.

The arbor and spindle tapers are specific instances of the use of the 7/24 taper.

The 7/24 taper can be projected to infinity - both ways - and is still correct through-out its infinite length.

Even a cursory look at the job will show that if the job were a 50 taper that because of the parallel bore "ahead" of the taper bore/socket that the "mating" arbor/plug would not and could not fit because of the flange on the arbor taper.

The details of the spindle/socket and arbor/plug tapers are shown (again) in the link at the end of this post.

The drawing at the link is metric as Australia is metric as is the inch (which is now derived from the metre) and the standards are "hard converted" from "inch" (USA) to "metric" (ISO/International) at ISO-297.

I still support my "general case" solution.

It is no different to, say, Ohm's Law where E=IR as the general case. A specific case is made when suitable quantities are inserted in place of any 2 of E, I or R so as to solve (for) the unknown quantity.

http://i200.photobucket.com/albums/aa294/oldtiffie/machine_tapers/Machine-taper5.jpg

tattoomike68
01-29-2008, 02:35 AM
The requirement was for a standard milling machine taper - which 7/24 clearly is.

The diameter of the larger end of the taper was given.

The are not nor was there any requirement that the taper diameter/s be "adjusted" to suit any of the NST spindle tapers which have a specific larger diameter as well as the taper itself.

That is an assumption/presumption by some here.

It is both incorrect and quite unjustified.

I would not be surprised if the larger bore size was set so close to the 50 taper to "trap" those who assumed that the NST 50 taper was what was required and that the drawing should be assumed to be incorrect.

If that were the case, it certainly succeeded!!

It was a perfect math quiz

He puts traps in all his prints, It forces a machinst to look things over a bit farther before he starts cutting.

Yep, like I said before, it could be a part for a manure spreader and was never meant to mate to any machine tool.

Some guys would have gone nuts all day about while others would have made the darn thing in 30+/- minutes and been done with it. :D

LMAO!

lazlo
01-29-2008, 08:31 AM
This is a very good trig exercise.

It is not, was not and clearly was never intended to be a manufacturing or shop drawing.

Yet, the quiz was presented as a shop drawing. Hmmm....

I would agree that it is pretty well certainly a 7/24 taper.

Great, then you agree that the big end of the 7/24 taper specification is 69.85 mm (in your drawing) == 2.75", right? :D

http://i164.photobucket.com/albums/u15/rtgeorge_album/Machine-taper5.gif

The drawing could have been say 20 or 30 thou either way and still be correct.

The drawing could have specified any dimension for the big end except 2.75", and it would still be wrong.

Or, more accurately, the drawing could have specified the 5/8" large end as specified for NT 10, 7/8" large end for NT 20, 1 1/4" for NT 30, 1 3/4" for NT 40, or 2 3/4" for NT 50.

oldtiffie
01-29-2008, 08:06 PM
The heading - and the task - in the original post by tattoomike68 , was and and only is:

who can solve for X on this math problem

All that was and is in the original post is:

http://i44.photobucket.com/albums/f24/snoopdog6502/problem1.jpg

So, to re-quote the heading of the OP:

who can solve for X on this math problem

That is all that the OP required - solve a math problem. This problem required the use of 2 branches/components of "math" - ie geometry and trigonometry - to solve for "X".

Nothing more - nothing less.

That some "senior" members "ran away" with it and "did their thing" and decided and/or saw it as a manufacturing/turning/lathe drawing for a 50 taper is something that was not and is not justified - at all.

And even more importantly and of concern was the way the Teacher/Instructor was "trashed" for no reason at all that I could see. That includes all those that "jumped on-board" for the "kill" and seemed to be somewhere between Lemmings and carrion-eaters.
http://en.wikipedia.org/wiki/Lemming
http://en.wikipedia.org/wiki/Carrion

It was not a pretty sight - anything but and far from it!

The title of the drawing is "Trig 2".

There are no units - at all. Inches was assumed, but it could be any units at all - millimeter, meter, foot, furlong etc.

There is nothing to say that any dimension is a diameter.

There is no tolerance for angles.

There is no indication that the radius is other than all or part (ie arc) of a circle. It certainly does not say it refers to a ball or sphere.

There is nothing to say that the sketch is a half-section of any cylindrical object/s at all either. The fact that the drawing is symmetrical about the apparent centre-line is no justification for considering it to be cylindrical.

Given that there is no indication or elevation there is nothing to say and no reason to assume that the sketch relates to anything that has "depth/length" in the "Z" plane. (The drawing is defined as being in the "X-Y" plane).

There is no material given - so why assume that it is any metal.

who can solve for X on this math problem 50 taper was not specified - so why assume it?

And if it was in fact cylindrical, why only assume that the taper was to be manufactured and not the ball?

The "radius" was the clue and confirmation I needed as I'd expect a circle or a ball to be defined by its diameter.

This is a bog-standard geometry/trigonometry sketch - straight out of any text-book on these two subjects.

We were asked to insert the gradient of a "standard milling machine taper".

There a quite few milling machine tapers of which the 7/24 taper is but one. Note that this defined as being mono-planar - it is neither round, circular nor multi-planar.

It is only when a specific length of line at a slope of say 7/24 is off-set from a centre-line that a "standard" (ie 30, 40, 50) spindle taper is defined. It is only a spindle taper when the off-sets (radii) of the ends of that taper are defined as radii that a conic section or section of a cone is defined - ie it is revolved around the centre. It only becomes a drawing of a 30, 40, or 50 milling spindle or arbor taper when the rest of the machining/dimensions are defined.

This is not defined nor required in this drawing.

For the purpose of the exercise we can assume that the taper is "X" units "rise" per "Y" units "run". Thus in this particular case if we assume that the taper is 3 1/2" per foot = (3 1/2)/12 = 7/24 which equates to 0.2917 which is the tangent value of the angle of taper/gradient/slope.

Arc tan 7/24 = 16.2602 arc degree = 16 deg 15 min 36.7369 min

OK - now that defines the 7/24 taper - which happens to be used on most heavy milling machines. Many lighter mills and mill-drills use Morse tapers (MT) in their milling spindle bores.

Now take a look at and read the top left paragraph in the pic that follows.

[Open quote]
National Standard Taper.

This taper, designed by the National Machine Tool Builders Association, and accepted by machine tool builders world-wide, is now universally used in all machines where a non-stick taper is required. It has been written up by the International Standards Organisation in 10 different sizes in ISO-297. The taper is 3 1/2 in. per 12 in. and is commonly termed the 7/24 taper.

The three tapers No. 30, 40 and 50 are the most commonly used.[End quote]

http://i200.photobucket.com/albums/aa294/oldtiffie/machine_tapers/Machine-taper5.jpg

So, in as much as the drawing did not call up a "non-stick taper", then any taper in current use that would accommodate the radius as drawn would meet the requirement of the drawing in terms to drawing or defining the taper.

So, my justification for going back to "first principles" and developing the "general" case seems to be justified.

Just insert the required values into the sketch and the equations and all should be OK with "X" solved (for).

For "tattomike68":

Thanks for the challenge. I enjoyed it. It certainly pointed up/out some gaps in my logic, problem-solving and "math".

(It obviously didn't do much to improve my "social skills" though!!).

lazlo
01-29-2008, 08:28 PM
That some "senior" members "ran away" with it and "did their thing" and decided and/or saw it as a manufacturing/turning/lathe drawing for a 50 taper is something that was not and is not justified - at all.

OK, so you're disagreeing with Mike: he says that the diagram was a 50 NMTB, and that not only is it a manufacturing/turning/lathe drawing for a 50 taper, but that he can build this part:

And yes the part could be made to the print.

I would use the taper angle of the NMTB Shank

oldtiffie
01-29-2008, 10:38 PM
That some "senior" members "ran away" with it and "did their thing" and decided and/or saw it as a manufacturing/turning/lathe drawing for a 50 taper is something that was not and is not justified - at all.

OK, so you're disagreeing with Mike: he says that the diagram was a 50 NMTB, and that not only is it a manufacturing/turning/lathe drawing for a 50 taper, but that he can build this part.

And yes the part could be made to the print.

I would use the taper angle of the NMTB Shank

First of all, you are taking an awful lot of licence and being more than just a bit disingenuous in the way you have either mis-used or mis-interpreted and certainly mis-quoted Mike.

He categorically did NOT say

............. diagram was a 50 NMTB, and that not only is it a manufacturing/turning/lathe drawing for a 50 taper, ......

What he DID say was

I would use the taper angle of the NMTB Shank

So, as I understand it, all Mike said was that he would use the NMTB taper ie 7/24.

He did NOT say that the job was circular, nor did he say that it was of a 50 NMTB spindle collectively or its bore specifically.

So, all he is saying that the job can be made with a 7/24 reducing taper commencing at the left end of the horizontal line.

So.

OK, so you're disagreeing with Mike: he says that the diagram was a 50 NMTB, and that not only is it a manufacturing/turning/lathe drawing for a 50 taper, but that he can build this part:

I am NOT disagreeing with Mike - at all. I agree with what he said.

Sure - no doubt about it - once the right end of the right hand taper is defined.

But even that is not necessary.

As there are no units defined, I could could draw/make that item to any scale or size that I liked provided that all details were in their correct proportion.

I could even cut the drawing up and drop it on the desk - job done (providing that I used the taper required - presumably 7/24).

I might just draw it to scale on paper and cut it out. I may cut the circle out or not - I've got both options, both of which will comply with the drawing.

I might even make it out of rectangular stock and imagine that the drawing was an end elevation of some unknown depth.

And yes, I could use a NST taper - 7/24 with a larger end size of 2.767 units.

I could make it out of wire, flat plate, any material that I could find that would suffice.

I might even make it out of round stock and cut it in half (half section) and either cross-bore/drill the hole or fit on a hollow or solid cylinder of indefinite length either onto the job (projecting upwards) or a very thin tube pushed all or part way through the drilled/bored hole. This too would comply with the drawing.

I could do the same with paper or flat plate.

The centre part (parallel and tapered lines and the circle) could be "planted on" or "let in" and the circle "planted on" or "let in" to that as well. If on paper or plate the centre could be cut out and the circle remain or vice-versa.

I could "make" it in a CAD/graphics software where it would reside as a "virtual" job.

The list goes on and on ..............................

All of them will meet the drawing requirements.

So.

I also think you "read in" something/s that was/were not there.

It was only a "Trig" exercise.

You were a bit "creative" in how you interpreted what Mike said.

You even mis-quoted him to the extent that you said he said something he clearly did not. I hope that was an honest error.

So far as I can see, I think you did not comply with the requirements of the OP - ie solve for "X".

I agree with Mike.

So, if that seems to be (my words) from a silly old f*ck-wit and an ex-sailor from way down here in Orstray-lee-yah who can't tell crap from clay - well that's the best I can do - almost.

Rich Carlstedt
01-30-2008, 01:46 AM
You guys are getting your knickers in a twist....
This is not a tool holding collet, spindle, work piece.
You guys have said you can make this part, but I tell you, a 50 taper tool will not fit it !
First, a machine spindle taper cannot be bigger than spec, or the tool will
wallow in the hole.
Second the .50 depth prevents the tool from even entering the taper !
So there are two reasons it is not a spindle tool holder or standard taper!
A TOOL SPINDLE TAPER has TWO parts....diameter, and taper.
Either without the other is worthless !
Try reaming your tailstock out another 17 thou and see what happens !

The drawing shown, means it is some part, with a taper bore , and the drawing does not spec out what the taper is..
Again (see pg 3 ) a 24/7 taper used on machine tool spindles is the "American Standard STEEP Taper"
there are many tapers guys, if you want to hang your hat on the term "standard taper" you have a long issue...and don;t dare forget the "diameter" part !

Define tap drill size if you think you have all the answers.
Rich

J Tiers
01-30-2008, 07:57 AM
there are many tapers guys, if you want to hang your hat on the term "standard taper" you have a long issue...and don;t dare forget the "diameter" part !

Define tap drill size if you think you have all the answers.
Rich

Anything with an ISO standards document defining it can be legitimately defined as a "standard", and it would be very difficult to argue against it.

For those who are whining and sobbing that it isn't the ONLY standard, where did it say "the one and only special standard" on the drawing?

It said "standard".

So anything that can be said to be "standard" (i.e. has a defining document from a standards organization) fills the bill.

Then again, it does not say the "socket" will fit anything. In fact it does bot refer to the item AS a "socket".

It merely refers to the taper rate, or angle between two lines on the drawing.

So quit the whining and sobbing about the "wrong" standard, or the "wrong" this or that.......

IF YOU CAN FIND THE VALUE FOR ONE TAPER YOU CAN FIND IT FOR ANOTHER ONE.

I happen to think the NMTB is the primary "standard" for a milling machine.

If it had said "dividing head taper", I'd have immediately thought of the B&S, probably a #9..........

However, that doesn't "exclude" any other one absolutely.

oldtiffie
01-30-2008, 09:03 AM
OK.

First of all - thanks J Tiers (Jerry) for seeing the problems.

Now.

The task was to solve for "X" using a standard milling machine taper.

Nothing more, nothing less.

So as previously, I resolved it for the general case.

I went through that in detail again and found that 2 equations were incorrect and revised/amended them.

They are the equations for "K" and "S" - in the lower right of the revised/amended "General Case Solution" (following):

http://i200.photobucket.com/albums/aa294/oldtiffie/SolutionforX_1B.jpg

I inserted the standard NST 7/24 taper as I said I would.

This made this solution a specific case.

My solution for "X" is as follows:

http://i200.photobucket.com/albums/aa294/oldtiffie/SolutionforX_2.jpg

This came a quite surprise as I expected the arc to remain within the envelope of the taper and parallel lines (as on the drawing provided by the OP). But the arc projected beyond the envelope.

I went and checked my logic and it seemed OK.

As I haven't yet installed a CAD system on this computer ("XP - my "W2K" with the CAD system on it is "down" and awaiting repair). So I "out-line" sketched it with what few drawing aids I had on graph paper as follows:

http://i200.photobucket.com/albums/aa294/oldtiffie/SolutionforX_3.jpg

This pretty well confirmed that the arc protruded as per the calculations.

I should not have been too surprised as there was no statement on the OP drawing that said it was to any scale.

I did suspect it though when I realised how close the diameter formed by the arc was to the distance between the 0.500 long parallel lines. But on the other hand I also suspected that my calculations were wrong - again - but that was not the case - I think.

So, I can confidently say that I have completed 2 tasks in that I have:
- solved for "X" in the general case as required by the OP; and
- solved for X" with a standard milling machine taper of 7/24 as I said I would during the course of the posts on this thread. I just substituted the figures in the drawing in the OP and the 7/24 taper.

Please do check my work for validity and errors.

I really would like to know if there are any errors in logic or process/es.

I do not claim that my solution is the only solution.

There may well be others. I didn't look any further once I was satisfied that the approach I was taking seemed to be valid.

I would appreciate knowing if there are any other solutions.

lazlo
01-30-2008, 09:06 AM
Anything with an ISO standards document defining it can be legitimately defined as a "standard", and it would be very difficult to argue against it.

The National Machine Tool Builder's Association specification defines a machine tool shank that is most definitely a standard: it's ANSI B5.18, ISO-297. No one is arguing that Jerry. But the instructor didn't call out NTMB, or NT, or 7/24. He indicated "standard milling machine taper." There is no such thing, and since he botched the dimensions of the big end, you can only assume that he really meant NTMB. That was his first mistake.

More importantly, the National Machine Tool Builder's Association specification doesn't just specify a taper. You don't get to call any 3 1/2" taper per foot NTMB, NT, 7/24, or ANSI B5.18, ISO-297. The specification clearly mandates the big end and small end of the taper, otherwise, the adapters wouldn't be interchangeable.

You can't pick and chose from the spec, and use the taper from the NTMB specification, and pick your own big and and little end. Like I said on the second page of this thread, if you assume the instructor meant NTMB taper, with the 2.767" big end, the NTMB shank will just fall out.

That was the instructor's second mistake.

2.75", it's not just a good idea, it's the law :p

http://i164.photobucket.com/albums/u15/rtgeorge_album/Machine-taper5.gif