Theoretical Taper due to tailstock height misalignment.

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

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.

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 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

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.

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

.

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.

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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.

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

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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:

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Do please check the scale-bar

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MichaelG.

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

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

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

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

regards Martin

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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.

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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.

I meant that in no way as a dig Michael, just thought you would be interested. Google ATP synthase animation, there are several on YouTube. It sits in the mitochondrial membrane and provides all of us with the energy to live. Amazes me to think that my life is powered by a tiny molecular turbine driven by Hydrogen nuclei.

regards Martin

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Sorry, Martin … I wrongly assumed that you were turning it into some sort of competition.

MichaelG.

Not at all Michael, merely reinforcing your point that mechanical structures go right down in dimension even to molecular scales. There are molecules called Dyneins that act as cellular postmen carrying protein cargo and walking along the cytoskeleton within cells to deliver their protein cargo to the area it’s needed literally putting one molecular foot in front of another. Far from just chemistry there is an awesome amount of mechanical systems at work down at the scale of 10nm . However I am probably guilty of running off at a tangent so I’ll leave it at that.

Best wishes Martin

Edited By Martin Kyte on 05/01/2023 23:02:45

I got back to my computer tonight to see a barrage of MEW forum notifications - thought I must have sleepwalked and posted something controversial! Phew, just an old thread which I started.

I think (like many of the questions I have posed on this forum) my opening post was answered in the first few replies, but it's always good to discuss stuff.

Unfortunately I couldn't see John Vigger's Wolfram calculation (which reignited the thread), perhaps because it it's John's first post. I'd be interested though. Anyhow, thanks for your contribution John and welcome to the forum.

I think JasonB's simulations are pretty much definitive and rather more accessible than the raw algebra. In my opening post I did say that that I suspected that conical sections might be involved and the link that Duncan gives tells us that 'A modern view of the unification of the sphere and hyperboloid uses the idea of a conic section as a slice of a quadratic form. ' , which I'm sure clarifies things.

I propose that there should be a prize for the thread that wanders most off topic - if adopted, I'll throw my hat in the ring - from misaligned lathe parts to ATP synthase animations. I love it, the way one thing leads to another.

Robin.

Circular hyperboloids are a new one on me, but I don't see how a simple lathe could turn any of the 3 illustrations you linked. Perhaps you mean one half of each illustration ? In which case it could be either barrel shaped or narrow in the midle ?

dave8

If the tool is set so that it is on centre half way along the workpiece it will turn the shape on the left of the link. If it's on centre at some other point the shape will be distorted, but there is no way it can be fat in the middle, so barrel shaped is wrong. I still think it's just loose terminology, but Michael's negative barrel has a certain charm