Theoretical Taper due to tailstock height misalignment.

You should check if there is movement when clamping, and if it is measurable then use the clamped setting, as you would when using centres. Drilling is not so exacting, so that doesn't matter so much.

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. Assuming the tool is dead centre at the headstock end and travels parallel to the spindle's rotational axis I can't see how it gets closer to the rotational axis at the vertically displaced tailstock end than it was at the middle of its travel.

Robin.

Edited By Robin Graham on 07/06/2021 01:31:17

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.

This will result in a barrel shaped piece.

To avoid this, a travelling steady needs to be used (Or a "Running Down tool" which supports the work close to the point where the tool is cutting. )

On Capstan and Turret lathes, a Roller Box performs this task.

Turning slender work, without support at the outer end will produce a similar result with the outer end larger in diameter than at the chuck which prevents deflection.

Howard

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

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

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

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

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.

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.

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

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.

.

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.

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.

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

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

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.

.

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