Theoretical Taper due to tailstock height misalignment.

[Anonymous]

Posted by Howard Lewis on 07/06/2021 10:47:15:

If you take heavy cuts on material held between centres, especially if small diameter, the cutting forces will cause the workpiece to deflect in the middle, where it is not supported.

Quite so, but it's got nothing to do with the tailstock being vertically misaligned. So the question remains; why would vertical misalignment of the tailstock lead to a barrel shape? Personally I don't think it does.

Andrew

[duncan webster 1Participant @duncanwebster1]

Posted by Andrew Johnston on 07/06/2021 11:03:49:

Posted by Howard Lewis on 07/06/2021 10:47:15:

If you take heavy cuts on material held between centres, especially if small diameter, the cutting forces will cause the workpiece to deflect in the middle, where it is not supported.

Quite so, but it's got nothing to do with the tailstock being vertically misaligned. So the question remains; why would vertical misalignment of the tailstock lead to a barrel shape? Personally I don't think it does.

Andrew

It's tapered, big end at the tailstock, but not by a lot as the OP points out

[Howard LewisParticipant @howardlewis46836]

If the material is being turned between centres, being large at the Tailstock end, suggests to me that the tailstock is not on the same axis as the Headstock, , as first point of investigation.

Once is coaxial with the Headstock, then the Tailstock being high, and its lesser effect can be investigated.

My suspicion is that a vertical misalignment will have a far lesser effect than a horizontal one, since horizontal movement directly varies the distance between work and the cutting tool.

And the larger the diameter of the workpiece, the smaller will be the effect of any vertical misalignment.

A vertical misalignment of 0.001" on a 1" diameter bar would represent an angle of 0.11459 degrees

On a 1" diameter, this would increase the distance from tool to metal from 0.005" to 0.500001" A difference of 1/100,000 of an inch, (3.9370079 x 10 ^ – 8 mm . Approximately 4/100 of a micron by my calculation ).

If you hold the mic or calliper long enough to measure the discrepancy, the temperature effect will produce an error of that magnitude!

Howard

 

Edited By Howard Lewis on 07/06/2021 15:16:05

[david bennett 8Participant @davidbennett8]

Yes, conic sections do come into it. Imagine a perfect cylinder. Now picture cutting a section out of it as would be your travel i.e from half diameter at the headstock end (on centre) to below centre at the other end. When viewed from above, the section will be parabolic. That represents what you have cut.

Edited By david bennett 8 on 07/06/2021 17:32:10

Edited By david bennett 8 on 07/06/2021 17:54:55

[ZanParticipant @zan]

Tom Walshaw, or George Thomas did a study of this about turning morse tapers and the usual advice to get the tool exactly on centre. I seem to remember that even a 10 thou error made almost no difference , units on less than 10th of a thou difference, and the conclusion was that the top slide dovetails would have more error

[david bennett 8Participant @davidbennett8]

Yes, a 10 thou error would not matter much if it was constant along the length. In the case of a high tailstock the height of cut varies along the length, causing non-flat sides. I believe this would matter in a morse taper fitting, but the OP just wanted to visualise the problem.

[Frank GorseParticipant @frankgorse]

It was GHT He’s talking about tool height,which is constant along the length unlike tailstock height the effect of which increases but the result must be very similar.

Using a 2MT shank as an example,with the tool 10 thou high or low he calculates the error on diameter to be 0.000058” and the hollow in the middle 0.00000135”. which even he describes as ‘insignificant’ And,he tells us,always a hollow,never a barrel shape.

(Model Engineers Workshop Manual,p139 ,’the myth of tool height setting’

Edited By Frank Gorse on 07/06/2021 20:21:28

[david bennett 8Participant @davidbennett8]

Posted by Frank Gorse on 07/06/2021 20:18:41:

It was GHT He’s talking about tool height,which is constant along the length unlike tailstock height the effect of which increases but the result must be very similar.

Using a 2MT shank as an example,with the tool 10 thou high or low he calculates the error on diameter to be 0.000058” and the hollow in the middle 0.00000135”. which even he describes as ‘insignificant’ And,he tells us,always a hollow,never a barrel shape.

(Model Engineers Workshop Manual,p139 ,’the myth of tool height setting’

Edited By Frank Gorse on 07/06/2021 20:21:28

I should have clarified. Of course I meant the height of cut in relation to the centre of rotation of the work. The error is very small as the OP surmised,but the shape of the error is important. I think all of GHT's calculations were based on the centre height being the same at each end.

[david bennett 8Participant @davidbennett8]

Posted by Ian Johnson 1 on 04/06/2021 23:40:43:

Seems to me that it all depends on where the tool is held. If it is held vertically, 90 degrees to a normal toolpost, such as in a vertical milling attachment on the cross slide, and the tail stock is too high, it will produce a taper just like a tool held normally in the tool post would if the tail stock is skewed left or right.

IanJ

Ian, here is a version of what you are suggesting, which I posted on another site.**LINK** look towards the end for a post by dave-b (my alias there)

Edited By david bennett 8 on 19/07/2021 23:32:55

Edited By david bennett 8 on 19/07/2021 23:45:34

[John ViggersParticipant @johnviggers44499]

Robin, it has been many decades since I learned about quadratic equations, so I used Wolfram Alpha to derive the formula for radius difference induced at the tailstock by a height error of the tailstock centre. Using your diagram, but substituting r for the resulting radius increase, caused by height error h, on workpiece radius R, the formula is..

r =

which does approximate to your formula, and changes the results only slightly.

Apologies for being pedantic.

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Robin Graham on 07/06/2021 01:30:43:

Posted by John Reese on 06/06/2021 23:22:05:

When turning between centers vertical misalignment of the tailstock will result in a part that is fat in the middle.

Hmm. Can you explain that further John? If it's right I'm back to square one in trying to understand this. […]

.

Skimming back through this old thread prompted me to find this equally clear assertion:

”Vertical misalignment will result in a slight barrel shape to the bar, which needs several diameter checks along the length of the bar. This step is most often missed out and so vertical errors go undetected.”

Within a useful “Instructable” **LINK**

https://www.instructables.com/Aligning-a-Lathe-Tailstock-with-a-Difference/

… So is it fact, or is it dogma ?

MichaelG.

[DC31kParticipant @dc31k]

Posted by Michael Gilligan on 05/01/2023 08:24:45:

… So is it fact, or is it dogma ?

My immediate reaction to that is it is plausible but only under a special combination of circumstances.

Let us say the headstock is 'high', the cutting tool is 'in the middle' and the tailstock is 'low'. Then I think it could happen.

If you take the cutting tip as datum and have vertical misalignment at both ends in opposite directions I think the barrel would result.

I offer this for consideration rather than as mathematical fact.

[Martin ConnellyParticipant @martinconnelly55370]

Dogma.

Assuming cutting between centres:

With a perfectly set up lathe the tool will be on centre line and the distance of the tool tip from the rotational axis of the bar being cut will not change from one end to the other. The result, if there is no deflection and no wear on the tool tip, is a perfectly cylindrical bar.

If the tailstock centre is higher or lower than centre then the correct cutting height will only occur at one point along the rotating bar. As the tool moves away from this point the effective distance from the rotational axis to the tool tip will increase slightly. So where is the tool set up to the correct height?

If at the headstock there will be a taper that increases in diameter as the tailstock is approached.

If at the tailstock then it will increase in diameter as the headstock is approached.

If in the middle then the diameter will increase either side away from the centre.

The last case is the nearest to a barrel but in an inverse way as it is narrower in the centre than at the ends.

This tapering effect is only noticeable at small diameters and long parts, it decreases as the material diameter increases and for most people making a long thin part will probably require a travelling steady that will negate a lot of these issues. This is making a mountain out of a molehill that will make virtually no difference to the majority of work done on a lathe. The horizontal error on a tailstock can cause far more error and that is what needs to be concentrated on. With a suitable dumbbell setup bar you are setting the tailstock over to the point where the readings at both test points on the dumbbell are the same. This will negate any small height error in the tailstock as you would be moving the actual tailstock horizontal position to the point where the axis of rotation distance to the tool tip is the same at both ends which is not necessarily on the exact horizontal centreline of the axis of rotation. The height error is thus accounted for and so irrelevant.

Martin C

[Martin KyteParticipant @martinkyte99762]

If the tool is set to centre height half way along the work and tailstock is high traversing to to tailstock end will bring the tool to below centre. The radius of cut will be the hypotenuse of a triangle formed by the horizontal distance from the large centre and the vertical misalignment. At the centre of the work the radius of cut will be just the horizontal component. Clearly as the radius at the tailstock is larger than that at the centre the work will be narrower in the centre than at the end. A full cut would produce the very opposite of a barrel shape.
If as would be more normal the tool is set at centre height at the chuck end then the work would be a curve tapering out slightly to the tailstock.
As has been already stated even if the error in tailstock height is of the order of a few thou the variation from straight will be negligible, certainly less than the wear on the bed of your lathe.

regards Martin

[HopperParticipant @hopper]

Posted by Tony Pratt 1 on 04/06/2021 08:36:39:

Posted by DC31k on 04/06/2021 06:29:47:

Posted by duncan webster on 04/06/2021 00:16:17:

The bar will be bent upwards…

The OP says, "turning parallel between centres ".

You link to equations for a cantilever beam, which implies encastre at one end. How does a pointy centre do this?

Oh god here we go!

And still going 18 months later!

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.

[Michael GilliganParticipant @michaelgilligan61133]

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.

 

.

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

MichaelG.

.

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

[Martin KyteParticipant @martinkyte99762]

Why does it suggest it must matter? Surely it suggests that although there is an effect it doesn’t matter for small deviations in height. It’s just good engineering to design something to wear about the optimum within acceptable tolerances.

regards Martin

[JasonBModerator @jasonb]

I'd agree with martin, if head is high and tailstock low and tool at mid way then a concave part will be produced not a barrel

No need for anything more than holding a straight edge horizontally against something cylindrical which is at an angle and you will see the straight edge(toolpath) only contacts the cylinder in the middle so that is where material will be cut away

[JasonBModerator @jasonb]

Cad model for thos einterested

First create your workpiece with head end low and tailstock end high

Draw a rectangle to represent material removed by a cutting tool moving along the bed at mid height

Simulate what happens when the part rotating on its angled axis meets the horizontal tool path

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Martin Kyte on 05/01/2023 09:40:10:
.

Why does it suggest it must matter? […]

.

As per Hopper’s comment: “FWIW and just to keep it going a bit longer”

This is a forum, and the best outcome is when everyone has considered all the opinions, and we come to a collective understanding.

MichaelG.

[Michael GilliganParticipant @michaelgilligan61133]

It’s looking good from here, Jason

Which makes one wonder about the dogma

MichaelG.

[HopperParticipant @hopper]

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.

.

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

MichaelG.

.

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.

[noel shelleyParticipant @noelshelley55608]

To all of you ! I have spent my whole life learning, but never so much as after I joined this forum. Thank you Gentlemen. Noel.

[HopperParticipant @hopper]

Jason, shouldn't the simulation be head end on centre, tailstock end high, not head end low and tail end high?

[JasonBModerator @jasonb]

I suppose by the time the angle has been reduced to what it would actually be if there were only a thou or two height difference and an allowance made for the work flexing away from the tool which would go some way to counter act the concave cut it may simply be so small a difference that it is simply not worth getting excited about

Best not get into the effects of having one end in a chuck and the other supported with a ctr vs, turning between ctrs as that introduces bending into the part

[Author]

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