Theoretical Taper due to tailstock height misalignment.

[Martin KyteParticipant @martinkyte99762]

Posted by Michael Gilligan on 05/01/2023 21:59:23:

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.

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

[Michael GilliganParticipant @michaelgilligan61133]

.

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

MichaelG.

[Martin KyteParticipant @martinkyte99762]

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

[Robin GrahamParticipant @robingraham42208]

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.

[david bennett 8Participant @davidbennett8]

Posted by duncan webster on 05/01/2023 13:11:35:

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

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

[duncan webster 1Participant @duncanwebster1]

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

[david bennett 8Participant @davidbennett8]

Posted by duncan webster on 06/01/2023 00:19:34:

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

Sorry to pursue this, but if the tool is at centre height at the headstock, have you allowed for the constantly changing tool height in relation to the centre of rotation?

dave8

[HopperParticipant @hopper]

Posted by duncan webster on 05/01/2023 13:11:35:

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

Which raises its own question:Why is it so? Why are power station cooling towers that circular hyperboloid shape?

Having worked in and on a few powerstations and always admired the graceful shape of the cooling towers, I always was told they were that shape because of a venturi effect that would draw more air up through the tower and increase cooling efficiency.

But more recently I have seen several things on the net saying the venturi effect is not a factor and that cooling towers are that shape because they are easier to build, without expensive formwork and specialised scaffolding because the single layer of thin concrete blocks is self-supporting as they go upwards in construction. Also it is a cost saving as the shape allows the use of thin blocks in a single layer, not massive thick concrete walls like the smoke stacks. (You could drive a small car around the top rim of a stack, it is that thick.)

Having never seen a cooling tower under construction (We always arrived to do the mechanicals after all the "sand and gravel" work was finished.) I have no idea if this is correct or not but it sounds plausible.

 

Edited By Hopper on 06/01/2023 03:24:07

[JasonBModerator @jasonb]

Posted by david bennett 8 on 06/01/2023 00:05:13:

s 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

Dave did you miss my practical demonstration as well as the CAD simulation, here it is again, looks a lot like Duncan's link to me. It is that constantly changing relationship between tool an angled workpiece axis that produces the curve. adjusting where the two axis meet simply moves the deepest part of the waist.

I won't come out barrel shaped as the tool does not go anywhere near the tailstock end when set on headstock ctr height.

Edited By JasonB on 06/01/2023 07:05:02

[Michael GilliganParticipant @michaelgilligan61133]

Posted by david bennett 8 on 06/01/2023 00:05:13:

[…]

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

.

The animated gif on the Wikipedia page is the picture that speaks a thousand words :

Can’t work-out how to insert the gif here, but this is a direct link: **LINK**

https://en.wikipedia.org/wiki/File:Cylinder_-_hyperboloid_-_cone.gif

MichaelG.

.

Edit: hopefully it is obvious, but, I will just emphasise …

all those lines that are interconnecting the circles are, and remain, straight

… and in reality, the number of those lines is infinite !

Edited By Michael Gilligan on 06/01/2023 08:28:40

[HopperParticipant @hopper]

Interesting video, Jason. The definitive answer. How much higher than the headstock did you make the tailstock to get that pronounced result? Just curious as to the relationship between diameter and offset to achieve such a result.

[Michael GilliganParticipant @michaelgilligan61133]

In support of Robin’s bid for the ‘drift’ award …

This is the iconic pedestrian link, in Manchester, between the Arndale Centre and M&S

… built after the I.R.A. bombing:

**LINK**

https://i2-prod.manchestereveningnews.co.uk/incoming/article610061.ece/ALTERNATES/s810/C_71_article_1409799_image_list_image_list_item_0_image.jpg

.

MichaelG.

[SillyOldDufferModerator @sillyoldduffer]

Posted by Hopper on 06/01/2023 03:22:42:

Posted by duncan webster on 05/01/2023 13:11:35:

…

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

Which raises its own question:Why is it so? Why are power station cooling towers that circular hyperboloid shape?

Having worked in and on a few powerstations and always admired the graceful shape of the cooling towers, I always was told they were that shape because of a venturi effect that would draw more air up through the tower and increase cooling efficiency.

But more recently I have seen several things on the net saying the venturi effect is not a factor and that cooling towers are that shape because they are easier to build, without expensive formwork and specialised scaffolding because the single layer of thin concrete blocks is self-supporting as they go upwards in construction. Also it is a cost saving as the shape allows the use of thin blocks in a single layer, not massive thick concrete walls like the smoke stacks. (You could drive a small car around the top rim of a stack, it is that thick.)

…

How annoying! I own a proper engineering book with a chapter on cooling towers and can't find it. From memory, which I admit is unreliable:

• As structures go cooling towers are short and squat compared with tall thin chimneys. Wind pressure on a tall thin structure like a chimney has much more leverage, so the structure has to be made strong enough to resist snapping and toppling. Thick walls and guy wires if there's room. The leverage on a cooling tower is smaller, and the tower has a much larger base. As snapping and toppling are much less likely, the structure of a cooling tower is comparatively lightly built because it only has to resist moderate sideways forces.
• The input to a chimney is a relatively low volume of hot gas, well above 100°C, that accelerates up the chimney helped by the pressure difference between top and bottom. Two useful effects:
  • a chimney attached to a furnace pulls air into the fire, causing it to burn more fiercely. More heat faster is often useful, and blasting exhaust steam up the chimney of a steam locomotive is a good way of improving it's performance.
  • the chimney lifts pollution away from people at ground level and then dilutes it by ejecting it into a large volume of the air. Wind and weather disperse it further, hopefully to the point that it doesn't cause any bother.
• The input to a cooling tower is a high volume of relatively cool water vapour, mostly water below boiling point. Chimney effect is mild because the temperature is low and the vapour doesn't accelerate anything like as fast as hot gas up a chimney. However, acceleration is improved by venturi effect. A large volume of vapour pushes into a narrowing orifice, causing its velocity to increase, and then speed is maintained by gently opening the exit. At the bottom of the tower, large holes allow plenty of cold air in to maximise flow, so it's important to keep the weight of the tower low. The curves, diameters and heights are all calculated to maximise flow, and a shaped tower cools more efficiently than a straight one.

Cooling towers are a good example of form following function. Physics and maths determine the shape, not that particular shape being easy to build. A straight tower doing the same job would be easier to erect, but to remove the same amount of heat it would have to be physically bigger, hence more expensive.

Dave

[JasonBModerator @jasonb]

Hopper, height difference is about 20mm, the holes on the boring head are 3/4" apart and I'm a little offset upwards. length approx 150mm

I mentioned this morning that with tool on ctr height at headstock end there is little chance of it cutting a barrel as the work is furthest from the cutting tool at the tailstock end, you can see how far in my exajerated example.

Though if one was turning a bit of bar with the intention to measure for taper the tool would be feed in at the tailstock end and the cut started from there and the resulting full length cut would be a concave surface along the bar being largest at the headstock end. Most people would just measure each end and assume a straight taper and for all intents and purposes that's what it practically measures. But certainly not going to be fat in the middle

[JasonBModerator @jasonb]

You can see in this image how the CAD revolves the "cut" around the axis of rotation which is just like the series of straight lines in Duncan's link sowing how the shape is made up.

The way the blue lines representing the cuts can be seen to flair out even more beyond the arear they can further confirms that you won't get a barrel shape.

Edited By JasonB on 06/01/2023 10:11:44

[Michael GilliganParticipant @michaelgilligan61133]

Great illustration, Jason

Physically producing those lines, with a pen held in a sliding block, was exactly what I had in mind when I suggested using the Dividing Head set-up.

MichaelG.

[duncan webster 1Participant @duncanwebster1]

Posted by david bennett 8 on 06/01/2023 00:52:08:

Posted by duncan webster on 06/01/2023 00:19:34:

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

Sorry to pursue this, but if the tool is at centre height at the headstock, have you allowed for the constantly changing tool height in relation to the centre of rotation?

dave8

Yes, if the tool is on centre at the tailstock end you get half of the shape, bigger at the chuck, but still not barrel shaped.

[Michael GilliganParticipant @michaelgilligan61133]

I’ve just returned from a good long walk in the [very] fresh air … so please permit me one more observation

Taking the very helpful animated gif from Wikipedia: It should be abundantly clear that the only way a barrel shape can be produced is to start with all the rods running axially, and then compress the structure.

One of the many ways it could then shorten is to form a barrel shape

… I will leave the interested reader to estimate the improbability !

MichaelG.

[JasonBModerator @jasonb]

Probability could be that the gorilla handed user is a bit heavy handed with the tailstock handwheel and compresses the test bar before taking a cut. Upon removing the bar from the lathe and allowing it to return to it's uncompressed length you will again end up with a waist not a barrel

[duncan webster 1Participant @duncanwebster1]

I'm sure someone has mentioned this before, but if the work is between centres and no travelling steady even with everything perfectly aligned there is a tendency to produce a barrel shape as the job will deflect in the middle of travel

[david bennett 8Participant @davidbennett8]

I had to prove it to myself by doing it . I was proved totally wrong, and apologise to all involved. (edit there was supposed to be a pic  of negative barrel shape here – it should be in my albums)

dave8

Edited By david bennett 8 on 06/01/2023 19:32:03

Edited By david bennett 8 on 06/01/2023 19:35:18

[Michael GilliganParticipant @michaelgilligan61133]

Good man, Dave

MichaelG.

[John ViggersParticipant @johnviggers44499]

Robin, The formula which reignited this conversation, for some reason did not appear on the post. It appeared initially, but later disappeared.

It assumes that tool is centered at the headstock centre, that the error in tailstock height is h, that the radius of the workpiece turned at the headstock is R, and the additional radius turned at the tailstock is r. The same error r would occur whether the tailstock height error is high or low.

So, using basic right angle triangle geometry a^2 + b^2 = c^2 (apologies for the notation. I cannot see how to use superscripts and other mathematical symbols on this forum. Maybe someone can inform me?)…….

R^2 + h^2 = (R+r)^2

Solving for r

r = SQRT(h^2 + R^2) – R (thanks to Wolfram Alpha for solving this)

r = 

 

 

 

Edited By John Viggers on 06/01/2023 21:56:48

Edited By John Viggers on 06/01/2023 21:58:07

[Robin GrahamParticipant @robingraham42208]

Posted by John Viggers on 06/01/2023 21:37:41:

Robin, The formula which reignited this conversation, for some reason did not appear on the post. It appeared initially, but later disappeared.

It assumes that tool is centered at the headstock centre, that the error in tailstock height is h, that the radius of the workpiece turned at the headstock is R, and the additional radius turned at the tailstock is r. The same error r would occur whether the tailstock height error is high or low.

So, using basic right angle triangle geometry a^2 + b^2 = c^2 (apologies for the notation. I cannot see how to use superscripts and other mathematical symbols on this forum. Maybe someone can inform me?)…….

R^2 + h^2 = (R+r)^2

Solving for r

r = SQRT(h^2 + R^2) – R (thanks to Wolfram Alpha for solving this)

r =

Edited By John Viggers on 06/01/2023 21:56:48

Edited By John Viggers on 06/01/2023 21:58:07

Sorry John, image of Wolfram calculation still not visible (to me at least). But no matter, in the formula I gave in my OP I indicated that that my result was approximate and in a later post gave the order of the approximation. I can't remember, but probably a Taylor expansion on the back of an envelope or summat – sadly I don't have Wolfram or anything like these days.

Anyhow, I think it's sorted (for me at least) – but thanks again for contributing.

Robin.

[Martin ConnellyParticipant @martinconnelly55370]

John, if you are using a full sized 102 key keyboard then (with windows at least) some available sub and superscripts and symbols are easy to do. For example if you hold down the Alt key, press 0176 on the numeric keypad, then release the Alt key you produce °

Alt 0216 gives Ø

Alt 0176 gives °

Alt 0177 gives ±

Alt 0178 gives ²

Alt 0179 gives ³

0185 ¹

0188 ¼

0189 ½

0190 ¾

I never found anything for a negative to precede a superscript number or a square root symbol by typing.

So some of your equations are doable, R²+h²=(R+r)²

Martin C

[Author]

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