Turning a taper, which is the prefered method?

I've been thinking about this some more.

Here's some sketches showing a conventional 60-deg center drilled part. I just used #4 center drill geometry but they are generically similar through size progression. The turned part itself is angled at arbitrary 5-degrees in top view, just to show exaggeration in offset tailstock taper turning mode. And then showing 2 styles of tailstock support centers - a typical 69-deg cone and a ball ended profile. The dimensions aren't important, more just a visual thing. Here are my eyeballing observations, see if you agree.

It seems to me that the 60-deg support can only have one point of contact. Either on the lip end of the part or possibly the inside corner where the smaller pre-drill transition. And I think 'point' is the right term (viewed in mid plane horizontal section view). It cant be a line if there is any offset. That can only occur when axis are coincident. There may be one unique setting where the center is supported by both corners mentioned, but that doesn't help us much & probably isn't desirable.

The ball end support superimposed inside the 60-deg center drill cone has a resultant 'circle' as a tangential ring constantly in contact. I drew it up in 2D just to confirm the geometry satisfies this & it does. The tangent contact occurs in slightly different positions (red arrows). I was having trouble 'mating' the parts in 3D but that was probably just me. Actually the ball would work for any angle like 45-deg chamfer, just showing 60-deg for similar comparison.

So now add tool cutting pressure to one side of the parts arrangement & a bit of wear on whatever makes contact. Seems to me the ball has to be better. Its spreading that side imposed load on at least half the tangent arc. The 60 cone within a cone is concentrating all that pressure on one teeny point area. What do you think? Am I barking up the wrong tree?

Some other points to ponder

- re the special curved profiled center drills. I don't know what kind of curve they have so cant really draw them up. But I could visualize where they might have similar connected ?circular? contact similar to the ball. At least they would prevent potential interference with the pilot drill. But this presumes you can actually drill your part. In the case of gun barrel this might not me an option, or not without a secondary lopping off operation.

- a 60-deg live center in a 60 deg hole. What's happening here? Its kind of teh same point contact thing but maybe better? The part would drive the center even though not on the same axis, kind of like bevel gears in principle? If so, that might be an improvement over 60-deg dead center. (But more work to integrate a live center bearing assembly into a boring head used for offset.

- and thus far we have been talking about the tailstock end. But seems to me the exact same geometry issue is happening at the headstock side if its got a typical dead center & drive dog arrangement. The relative part-to-dead center doesn't care that the displacement is higher at the TS end, its the same angular difference the 2 axis on either end, no?

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I am pretty sure that the offset angled 60 degree setup will give two points of contact. The ball center will indeed have a full ring of contact. Yes, it is the same issue at both ends of the work.
 
It seems to me that the 60-deg support can only have one point of contact. ...Seems to me the ball has to be better. Its spreading that side imposed load on at least half the tangent arc.... seems to me the exact same geometry issue is happening at the headstock side if its got a typical dead center...

The 'dead' center might be tilted to make the 60 degree work better (you're already
offsetting it, adding a tilt knuckle is relatively benign). The beauty of the ball center is
that it tolerates any tilt (but at the headstock, the driven ball swings against the work
according to the spindle rotation, it'd have to be a LUBRICATED ball for
a ball center there).
 
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Peter, those drawing are very helpful, each worth 1000 words.
As whitmore mentioned above, there is a slight difference at the headstock in that the barrel will rock slightly on the ball so lubrication is required there too.
At the tailstock end the location of the contact ring on the ball, although it is tilted, is constant.
Thinking about all this helps me appreciate why 60 deg. is chosen for centers as opposed to any other angle.
 
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I just used a hand ground vertical shear yesterday to take the finish pass on a 10" long 416 tapered shaft. It works ok, but I found slow rpm, slow feed, small depth of cut. Just a couple thousandths. Its really only good in my opinion for finish cuts.

Its not hard to grind. Just give it a little relief angle behind the edge. Stone the edge to make it as sharp as its possible to make.

A vertical shear will even make the finish on low C steel "better." Better being a relative term.

Bob, I just did some testing with a shear bit and concur with your comments.
On a 416SS, 1.125'' dia. test piece at 235 rpm, feed of .003''/rev and .010'' doc, using cutting oil, it cut very freely. Chips were wispy. No smoking of the cutting oil and the HSS tool stayed sharp the whole time. The tool has 5 deg relief on the nose and the cutting edge is slanted to roughly 20 deg. with zero rake.Finish was just what I need. Interesting!
It remains to be seen how this technique would work on a longer work piece but I am optimistic.

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Just got done cutting a long taper between centers. A tangential tool holder worked best. Am very happy with the results. Did the job with an MT3 boring head offset by .158'', a conventional center in the headstock and a ball center in the boring head. No intermediate support was used and once I found the right DOC, speed and feed it cut very smoothly with the chips carrying the heat away.

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Just an update on my second barrel. This time I wanted to try offsetting the TS. A live centre was tried first in the TS but it was too bulky. Finally an MT3 end mill holder was used with a DIY ball centre. The ball bearing floats in the centre and a grease fitting is provided so the ball can turn either in the barrel or in the centre.
A very sharp HSS-Co bit was used in a tangential holder. A follow rest was cobbled up using a auto lug bolt and nut. A spring loaded 520 motorcycle chain was used to put constant pressure on the barrel.
The first 5 inches of the cut was done without the follow rest. After the first 5 inches the lathe is stopped and the rest installed.
It is very important to add some extra drag on the barrel to prevent chatter and patterning. Cutting fluid was brushed on heavy.
Care needs to be taken to adjust the centres when heat builds up in the work and to keep chips out of the follow rest but all things considered I would do it again this way.
 

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