Theoretical Taper due to tailstock height misalignment.

[Robin GrahamParticipant @robingraham42208]

This doesn't seem to be a problem for me, but I came across discussions of the influence of lathe tailstock height misalignment on turning parallel between centres whilst looking for other related info. The discussions were initiated by people who had bought a lathe and, by one method or another, had found the tailstock centre to be high with respect to the headstock. The advice from seasoned hands was not to worry – provided the tailstock is OK in the horizontal plane, vertical alignment (unless grossly out) would be insignificant, but no explanation was given. I wanted to understand this better and tried to work it out.

I'm very bad at 3-D visualisation so tried to approximate the problem by imagining that the tool was cutting dead on centre at the headstock and low by delta_h at the tailstock:

After a bit of algebra it came out that the radius at the tailstock end would be the radius at the headstock plus the square of the distance of the tool under centre at the tailstock divided by the diameter of the work at the headstock.

If this is so, it would explain to me why vertical alignment is relatively unimportant – on a nominal 10mm diameter workpiece, even if the tailstock were 0.1mm high it would lead to a discrepancy of 0.1×0.1/10 = 0.001mm on radius.

I'm not sure that I've set the problem up correctly though – I've a sneaky feeling that I've over simplified, and conic sections or something come into it. The intersection of a plane with a cylinder can be an ellipse, so maybe turning with the tailstock off-height gives a barrel shape – I just can't visualise it!

I realise that this may have little practical importance at home workshop levels of accuracy, but I'd like to understand it better.

Robin

[Robin GrahamParticipant @robingraham42208]

[duncan webster 1Participant @duncanwebster1]

The bar will be bent upwards, but not by a kink at the chuck, the gradient will increase towards the tailstock. The offset (dh) can be worked out fairly readily from the top equation in beam bend. Your expression for dR is correct for small dh/R (less than say 0.1).

I suspect it is some kind of peculiar section, it certainly isn't a simple taper.

[DC31kParticipant @dc31k]

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?

[Tony Pratt 1Participant @tonypratt1]

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!

[duncan webster 1Participant @duncanwebster1]

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?

Easy, by not reading what the OP says.

[Bo’sunParticipant @bosun58570]

I'm not sure I understand why vertical misalignment (up or down) should be any different to horizontal misalignment. Off-centre is surely off-centre, irrespective of what plane it's in, or have I missed something obvious.

[Alan JacksonParticipant @alanjackson47790]

Vertical misalignment will make a small error, but horizontal misalignment will make much more error simply because the cutting tool moves in a horizontal plane.

[EmgeeParticipant @emgee]

Posted by Alan Jackson on 04/06/2021 09:40:07:

Vertical misalignment will make a small error, but horizontal misalignment will make much more error simply because the cutting tool moves in a horizontal plane.

Does this mean if the tool is made to work in a vertical plane horizontal misalignment won't create a taper ?

Emgee

[Anonymous]

Posted by Bo'sun on 04/06/2021 09:27:56:

……….have I missed something obvious.

Yep, 'fraid so.

If the tailstock is offset horizontally the distance from the tool tip (at the tailstock) to the work axis changes by the offset value. However, if the work is offset vertically the distance from the tool tip to the work axis is the hypotenuse of the triangle where the other two sides are the radius of the work and the vertical offset, as in the OPs diagram. The increase in distance from tool tip to work axis is much smaller in the latter case.

Andrew

[Alan DonovanParticipant @alandonovan54394]

Hello All.

My experience is that having a 'high' tailstock is not unusual for a conventional lathe.

I served my engineering apprenticeship (late 60s/early 70s) at a machine tool company, where it was accepted that tailstocks could be a little 'high'. My memory is vague on this but I think 0.001 inches was the maximum allowable compared to the headstock.

The logic behind this was that as the tailstock would be moved around with use, the tailstock base would wear (headstocks being fixed), so the tailstock would gradually drop to be on dead centre height with the headstock before becoming 'low'. This therefore extended the time the vertical relationship between headstone and tailstock remained accurate.

Alan.

[old martParticipant @oldmart]

Robins take on the height of the tailstock is correct, fortunately, as the same applies to worn lathe beds where the tool height varies as the saddle is moved. The error would be relatively greater the smaller the workpiece diameter is, and would also be subject to the distance between the spindle and the tailstock.

It is best to have the tailstock at or less than 0.002", 0.050mm high, as it can make centre drilling easier.

Edited By old mart on 04/06/2021 11:57:37

[Neil WyattModerator @neilwyatt]

Posted by duncan webster on 04/06/2021 09:17:57:

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?

Easy, by not reading what the OP says.

🤣

[Neil WyattModerator @neilwyatt]

Incidentally, this is why 'laser ultrasonic tape measures' give pretty consistent results even if you don't aim them particularly well.

Neil

[old martParticipant @oldmart]

Posted by Neil Wyatt on 04/06/2021 13:47:18:

Incidentally, this is why 'laser ultrasonic tape measures' give pretty consistent results even if you don't aim them particularly well.

Neil

I tried out an online trigonometry calculator with a set of common measurements where those laser or ultrasonic measuring devices might be used for and the results surprised me.

Measuring a 16 foot room and pointing 6" off of dead square would have an error of plus 0.093"

[Robin GrahamParticipant @robingraham42208]

Thanks for replies – it seems that my analysis is right. I confess that, like Bo'sun, I thought off-centre was off-centre whatever the direction until I put pen to paper and tried to work it out.

I think that if the formula I derived [I arrived there by discarding terms O(delta_h^4/R^2) and above] is correct I have the answer to my question about the profile of the taper which results from vertical misalignment. The deviation delta_h of the tool path from the rotational axis of the work is linear in Z, the distance the tool has traveled, so delta_R is quadratic in Z, ie the taper is parabolic, in contrast to the linear taper from horizontal misalignment. I think!

Thanks again, Robin

[old martParticipant @oldmart]

The tailstock of the Smart & Brown model A at the museum is the common type made from 2 parts to allow offsetting for taper turning between centres. To get it pointing along the axis, we had to shim the joint, with the shims tapering fore and aft to get the quill horizontal. Fortunately, the quill was in line viewed from above, so the adjustment for that was straightforward. The quill axis is 0.002" high and everything is locked because the offset is never used. With a taper turning attachment, the need to offset the quill is not likely to ever be needed. I have toyed with milling the faces of the joint and then using a thick shim, but have never had the nerve, as the tailstock is better than most as it is.

[Ian Johnson 1Participant @ianjohnson1]

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

[Michael GilliganParticipant @michaelgilligan61133]

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

.

That seems a very reasonable interpretation, Ian

[Assuming that the effects of gravity are trival in the matter] : The ‘concept’ of Vertical is meaningless, and we should be thinking about XYZ axes … where Z is the axis of the lathe spindle.

X and Y are perpendicular, and both are perpendicular to Z, but are free to rotate as a pair around it.

MichaelG.

.

Sorry if that’s clumsily worded … I need some Coffee !

[Howard LewisParticipant @howardlewis46836]

One question.

When checking the vertical alignment, is the tailstock barrel clamped?

There might well be a difference between any figures obtained clamped and unclamped, not to mention any difference depending on the amount of barrel extension.

Howard

[Pete RimmerParticipant @peterimmer30576]

There for sure will be measurable differences between clamped and un-clamped. Only the quality of fit / extent of wear will dictate the degree of difference. My old Monarch has a bit of wear in the tailstock and I can adjust the taper with the tailstock clamp, it's one of the jobs I have to tackle in the near future.

[old martParticipant @oldmart]

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.

[John ReeseParticipant @johnreese12848]

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

[Robin GrahamParticipant @robingraham42208]

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. 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

[Howard LewisParticipant @howardlewis46836]

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

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