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.

Oh god here we go!

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.

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

Emgee

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.

🤣

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"

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.

.

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 !

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.

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

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