Theoretical Taper due to tailstock height misalignment.

[JasonBModerator @jasonb]

Hopper I was commenting on DC31K's post and Martin's subsequent comments

 

EDIT

Effect of setting the tool height (blue arrows) to height of axis at headstock end  just moves the deepest part of the convex cut to the point where the two axis cross (red arrow) So if one was to only measure an actual workpiece at each end you could be forgiven for thinking you have a constant taper particularly as any taper is likely to be very shallow the concave will not be visible to the eye

Edited By JasonB on 05/01/2023 10:18:50

Edited By JasonB on 05/01/2023 10:21:18

[Martin KyteParticipant @martinkyte99762]

Posted by Hopper on 05/01/2023 10:04:17:

Posted by Michael Gilligan on 05/01/2023 09:21:19:

Posted by Hopper on 05/01/2023 09:16:23:

[…]

FWIW and just to keep it going a bit longer, good quality lathe manufacturers deliberately set their tailstock centres to be a few thou higher than the headstock spindle centre so that as the base of the tailstock wears, it comes down into perfect alignment before starting its gradual journey towards the centre of the earth.

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Which suggests, that [in some as-yet-undepicted way] it must matter

MichaelG.

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Edit: __ If some kind soul with nothing better to do has a Dividing Head with an elevating Tailstock, it would be a relatively simple matter to demonstrate the effect on a suitably exaggerated scale.

Reductio ad absurdum

Edited By Michael Gilligan on 05/01/2023 09:32:06

Or if someone with a lathe stuck some strips of 10 thou shim under their tailstock before clamping it down and then took a cut along some bar, all would be revealed.

I suspect if they did then the only result would be a thread asking how to measure deviations of millionths of an inch from a true cone. (and it’s always going to be a cone because I defy anyone to parallel turn to those limits.)

regards Martin

[Dave HalfordParticipant @davehalford22513]

Rather we would have a thread concerning 'why can't I drill a half inch hole with a half inch drill in my tailstock'.

[HopperParticipant @hopper]

Thanks Jason. I have caught up, finally!

Just checked Connolly's bible Machine Tool Reconditioning and he allows 0 to .001" high for vertical alignment of tailstock.

Edited By Hopper on 05/01/2023 11:20:49

[Howard LewisParticipant @howardlewis46836]

Being a simple minded soul, and thinking in terms of a 1 inch bar in a lathe with the Tailstock set 0.002" high I visualised a right angled triangle.

The hypotenuse is 0.5, and the perpendicular is 0.002.

Applying Pythagoras,

0.5^2 = 0.25

0.002^2 = 4 x 10^ – 6

So 0.25 – (4 x 10^- 6 ) = 0..249996 (The Base ^ 2 )

The square root of that is 0.499996

So we seem to be looking at a difference of 4 x 10^ – 6 on a piece of material an inch in diameter.

This is the sort of dimension common in temperature and humidity controlled Calibration Rooms, when checking gauge blocks, rather than our workshops.

The local temperature generated by cutting will probably cause a much greater expansion than that, not to mention effects of the necessary clearances between Centre and Centre Drilling, Saddle and Lathe bed, and any deflection of cutting tool and workpiece.

Consequently, ignoring such errors seems to be acceptable to me.

Howard

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[Martin KyteParticipant @martinkyte99762]

Posted by Hopper on 05/01/2023 11:19:00:

Thanks Jason. I have caught up, finally!

Just checked Connolly's bible Machine Tool Reconditioning and he allows 0 to .001" high for vertical alignment of tailstock.

Edited By Hopper on 05/01/2023 11:20:49

Yes, and that limit will be constrained by the effect it has on drilling from the tailstock rather than turning as has been alluded to.

regards Martin

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Martin Kyte on 05/01/2023 10:22:42:

Posted by Hopper on 05/01/2023 10:04:17:

[…]

Or if someone with a lathe stuck some strips of 10 thou shim under their tailstock before clamping it down and then took a cut along some bar, all would be revealed.

I suspect if they did then the only result would be a thread asking how to measure deviations of millionths of an inch from a true cone. (and it’s always going to be a cone because I defy anyone to parallel turn to those limits.)

regards Martin

.

That’s why I suggested the use of a Dividing Head with Elevating Tailstock

One could then easily demonstrate the effect [whatever it might be] by doing things on an enlarged scale.

In less-blinkered places than here, that would perhaps be called a Model …

MichaelG.
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P.S. __ Jason’s use of 3D CAD probably obviates the need for a physical model.

[Martin KyteParticipant @martinkyte99762]

Posted by Howard Lewis on 05/01/2023 11:44:38:

Being a simple minded soul, and thinking in terms of a 1 inch bar in a lathe with the Tailstock set 0.002" high I visualised a right angled triangle.

The hypotenuse is 0.5, and the perpendicular is 0.002.

Applying Pythagoras,

0.5^2 = 0.25

0.002^2 = 4 x 10^ – 6

So 0.25 – (4 x 10^- 6 ) = 0..249996 (The Base ^ 2 )

The square root of that is 0.499996

So we seem to be looking at a difference of 4 x 10^ – 6 on a piece of material an inch in diameter.

This is the sort of dimension common in temperature and humidity controlled Calibration Rooms, when checking gauge blocks, rather than our workshops.

The local temperature generated by cutting will probably cause a much greater expansion than that, not to mention effects of the necessary clearances between Centre and Centre Drilling, Saddle and Lathe bed, and any deflection of cutting tool and workpiece.

Consequently, ignoring such errors seems to be acceptable to me.

Howard

.

 

No the hypotenuse is what you need to calculate. The long side is 0.5 and the short side is 0.002 for your example. The hypotenuse (the radial distance from the centre of the workpiece is root 0.5^2 + 0.002^2

what ever that is (don’t have a calculator handy) but it’s a tad bigger than 0.5” not smaller.

regards Martin

all that said I agree that the effect is not worth bothering about.

Edited By Martin Kyte on 05/01/2023 12:02:39

[Howard LewisParticipant @howardlewis46836]

So we're worrying about a tenth of a micron on a 25 mm workpiece?

Don't even breathe on it. Even your radiated body heat might produce an error!

Howard

[Martin KyteParticipant @martinkyte99762]

I don’t know if the moderators can edit the thread title maybe by adding the word(s) insignificant, theoretical, or minuscule. It may make it a little less misleading.

regards Martin

[JasonBModerator @jasonb]

Well for those that doubt the new fangled CAD I thought something more practical may be of interest. Not fancying cranking my rotary table round and round to use Michaels adjustable tailstock suggestion I came up with teh idea of offsetting the tailstock ctr, not horizontally but vertically using a boring head.

First cut shows the effect of having the tool height mid way between the headstock and tailstock heights which as the CAD showed produces a concave waist. Second is with tool on headstock ctr height which just shifts the position of the narrowest part of the waist. Did get so tool rubbing on teh first setup as the tool was way too high and I think diameter plays a part a sthe second option is not quite so curved but dia is smaller

[duncan webster 1Participant @duncanwebster1]

This topic has generated more than its fair share of theorems. It's quite simple, if the tailstock is offset vertically you generate a circular hyperboloid

No need for physical tests, the maths is well proven. This is the shape of cooling towers amongst other things

[Andrew TinsleyParticipant @andrewtinsley63637]

This reminds me of the law passed down from above, that it is VITAL to get the tool dead centre if turning a taper. This has been repeated down the ages. If you don't get it centre height you will get barrel or pincushion type distortion that will ruin the job.

GHT debunked that theory and showed that you could be quite a way off below centre height before problems occurred (see A "Workshop Manual" by GHT.). It only took a very simple calculation to show that the claim did not hold up.

Andrew.

[Michael GilliganParticipant @michaelgilligan61133]

Seems very reasonable, Duncan

Now … Do you have any idea where the ‘Barrel-Shape’ Dogma originated ?

[ a mis-placed minus sign, perchance ? ]

MichaelG.

Edited By Michael Gilligan on 05/01/2023 15:27:26

[Howard LewisParticipant @howardlewis46836]

I fear that theory is causing us to lose sight of reality.

Whether the radius is used as the Hypotenuse, or not, 0.002" error on a 1",diameter, represents an angle of the third place of decimals of a degree, (At 10 minutes of a degree, the values of Sine and Tangent are virtually the same, and in the third place of decimals, so that the discrepancy is still a fraction of a micron, over 25 mm, )

Consequently, the horizontal displacement of the work relative to the cutting tool is of minimal importance for practical ,purposes..

Let us not suffer from delusions of ability to measure the effect of such miniscule dimensions, unless anyone has a woirkshop which is temperature and humidity controlled with instruments certified to a traceable suitable standard. (AKA Calibration Room )

.Surely the reason for placing the cutting edge of the tool on centre height is to optimise cutting conditions, rather than having a too high tool that rubs, rather than cuts.

Howard

[old martParticipant @oldmart]

Height errors get bigger as the diameter of the work, and the length are reduced. An error of 0.001" at 1" diameter in a 10" length would be tiny, but the same error with a 1/10" diameter and 1/2" long would be relatively much greater. Same with taper turning, try turning the end of a 1" bar at 45 degrees, to a point, if the tool is not on centre.

[duncan webster 1Participant @duncanwebster1]

Posted by Michael Gilligan on 05/01/2023 15:26:33:

Seems very reasonable, Duncan

Now … Do you have any idea where the ‘Barrel-Shape’ Dogma originated ?

[ a mis-placed minus sign, perchance ? ]

MichaelG.

Edited By Michael Gilligan on 05/01/2023 15:27:26

I think someone mis-spoke. By the way if you google Hyperboloid structures you get loads of intersting stuff, but that would be thread drift, so we don't want to go there

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Howard Lewis on 05/01/2023 16:46:28:

I fear that theory is causing us to lose sight of reality.

[…]

.

Have no fear, Howard … reality is always in my direct line of sight

[ and I hope & trust that goes for most of us ]

… But I do find that taking a peripheral glance at the ‘inconsequential’ assists comprehension.

It’s not trivial unless and until you have decided to call it so.

I have quite old microscopes that have usefully large knobs graduated in microns, and modern labs have mechanical stages that step by nanometres …

So … Whether such theory is classed as fantasy or reality depends where you are standing, and why [if at all] you are interested.

MichaelG.

[Michael GilliganParticipant @michaelgilligan61133]

Posted by duncan webster on 05/01/2023 17:58:59:

[…]

By the way if you google Hyperboloid structures you get loads of intersting stuff, but that would be thread drift, so we don't want to go there

.

Funny, that … I was tempted to mention that Dave’s famous pendulum-support structure is prone to adopting that shape, as a vibration mode.

But I had better not mention that here, because the deflections would be tiny in the context of ‘reality’

Oops … I’ve gone and done it now

MichaelG.

[Martin KyteParticipant @martinkyte99762]

Posted by Howard Lewis on 05/01/2023 16:46:28:

I fear that theory is causing us to lose sight of reality.

Whether the radius is used as the Hypotenuse, or not, 0.002" error on a 1",diameter, represents an angle of the third place of decimals of a degree, (At 10 minutes of a degree, the values of Sine and Tangent are virtually the same, and in the third place of decimals, so that the discrepancy is still a fraction of a micron, over 25 mm, )

Consequently, the horizontal displacement of the work relative to the cutting tool is of minimal importance for practical ,purposes..

Let us not suffer from delusions of ability to measure the effect of such miniscule dimensions, unless anyone has a woirkshop which is temperature and humidity controlled with instruments certified to a traceable suitable standard. (AKA Calibration Room )

.Surely the reason for placing the cutting edge of the tool on centre height is to optimise cutting conditions, rather than having a too high tool that rubs, rather than cuts.

Howard

Totally agree Howard, the only reason I mentioned your maths is I didn’t want us going back down the barrel shape track.

regards Martin

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Michael Gilligan on 05/01/2023 19:21:51:

.

… But I do find that taking a peripheral glance at the ‘inconsequential’ assists comprehension.

.

This is clearly ‘inconsequential’ … because we are not attempting to make one in our shed

But I offer it as an example of the reality to which we are largely oblivious:

.

.

Do please check the scale-bar

.

MichaelG.

.

Credit: https://naturalhistory.museumwales.ac.uk/diatoms/glossary.php

 

Edited By Michael Gilligan on 05/01/2023 21:40:07

[david bennett 8Participant @davidbennett8]

Posted by Michael Gilligan on 05/01/2023 15:26:33:

Seems very reasonable, Duncan

Now … Do you have any idea where the ‘Barrel-Shape’ Dogma originated ?

[ a mis-placed minus sign, perchance ? ]

MichaelG.

Edited By Michael Gilligan on 05/01/2023 15:27:26

Perhaps my posts of 7/6/21 had something to do with it?

 

dave

 

 

 

 

 

 

 

 

 

 

 

 

Edited By david bennett 8 on 05/01/2023 22:11:11

[Martin KyteParticipant @martinkyte99762]

Posted by Michael Gilligan on 05/01/2023 21:37:47:

Posted by Michael Gilligan on 05/01/2023 19:21:51:

.

… But I do find that taking a peripheral glance at the ‘inconsequential’ assists comprehension.

.

This is clearly ‘inconsequential’ … because we are not attempting to make one in our shed

But I offer it as an example of the reality to which we are largely oblivious:

.

.

Do please check the scale-bar

.

MichaelG.

.

Credit: **LINK**

Edited By Michael Gilligan on 05/01/2023 21:40:07

ATP synthase has a molecular motor a lot smaller than that, essentially it is a protein turbine driven by protons.

regards Martin

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Martin Kyte on 05/01/2023 21:49:18:

[…]

ATP synthase has a molecular motor a lot smaller than that, essentially it is a protein turbine driven by protons.

regards Martin

.

I give up

… I was only trying to demonstrate my point, by showing something that is visually comprehensible as ‘engineering’ but falls outside Howard’s and your current working-definition of ‘reality’

MichaelG.

[Michael GilliganParticipant @michaelgilligan61133]

Posted by david bennett 8 on 05/01/2023 21:46:10:

Perhaps my posts of 7/6/21 had something to do with it?

.

Perhaps they did

[now that I realise you are not claiming to explain the origin of the erroneous Dogma]

… credit where it’s due.

MichaelG.

[Author]

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