Lathe (re)Setup Question

For making a arbor your best chances of making a good one are gonna be between centers.
A quick lathe dog can be made with a piece of pipe larger than your work. Drill two holes 180* apart. One hole put a set screw for securing your part, other hole take a bolt long enough to bend a 90 on it which will engage the drive plate and thread in other hole of the dog.
 
Just curious, Brockwood. Does the part need to be that long? The reason I ask is that turning between centers is indeed the most accurate way to turn a piece but you are going to find that turning a long piece is not that simple. Deflection is going to be an issue so a follow rest might be needed. This is especially true if the material is hard, like a tool steel. You will find that chatter will be an issue, especially on the tailstock end of the work, and the harder the material the worse it gets. Tooling will also make a difference and a good HSS tool might work better than carbide as it will deflect less.

I'm not clear why you would need to repeatedly remove the work piece from the lathe if you are cutting a taper. Normally you would cut it in one go, measure it to make sure your dimensions are accurate and then remove it or part it off. Why are you planning to repeatedly remove the work? The reason I ask is because doing that is going to make accurately repositioning the work a challenge, and taper turning tends to require a bit of careful work if you want to maintain decent accuracy of the taper.

It might help to give us some idea of the size/dimensions of the part, material, tolerances and so on. Perhaps there is another option for work holding?
 
It's cold rolled 1 1/2 diameter. The plan was to cut it in 1 go & be done - but the lathe broke. I have it so long because the plan was to make 2 parts end to end - all in 1 go. I've managed 0.035 cuts without chatter or deflection. This lathe doesn't have enough oomph to deflect this bar.

Anyway, my current plan is to remove the bar, set up a rotary table to make a few repair parts for the lathe repair & get back to finishing out this bar on my newly repaired & improved lathe. The bar will be 1 long & 1 short indexing center.289510
 
When I am turning between centers using a chuck, I first chuck up a piece of steel and cut a 60 degree point on it. Accuracy of the chuck, spindle, and whatever then no longer matters. I will then make or adapt a dog to fit the work and be able to be pushed by the chuck jaw, just ONE chuck jaw that is marked with a Sharpie for being able to remount the work in the same clock position. Then, go to town. I agree with Mikey on the length of the work. It will cause inaccuracies.
 
I may be off base here but if I was making that part from nominal mild steel stock (cold rolled comes in many alloys so not sure what you mean), I would throw it in a 3 jaw chuck and face one end and center drill it, then extend it only enough to cut the 6" long straight part. I would bring that to size, screw cut the thread and cut the keyway. Then I would remove it from the chuck, cut off the length I need to finish the part and dial in the part in a 4 jaw chuck, holding it with the just turned part, of course. I would then support the work with a dialed in steady rest and face the end and center drill it.

Given that the taper is 5-3/16" long, I assume you either have a taper attachment for your lathe or you plan to use the offset tailstock method (or use a modified boring head or a Royal taper attachment). I also assume that your compound does not have enough travel to use that to cut the taper. If you use the offset tailstock method then you can mount the work between centers and try to cut it that way. Once you have the taper, I would personally mount a Morse Taper adapter in my spindle bore and insert the one you just cut into it before cutting the tip of the work piece for the 60 degree tip. Hopefully it will be concentric enough to be accurate enough.

Then I would make the second part separately.

Pretty sure that's how I would make these parts, although this is just off the top of my head right now and I haven't studied it carefully. I would definitely not try to make two parts with two tapers, a screw cut thread on one end and accurate 60 degree tapers on each end out of one single work piece in one go. There is just no way that I could personally keep such a monster accurate enough to be used as centers. My opinion, of course, so don't let me discourage you from trying.

I also think I would make centers from tool steel instead of mild steel for longevity.

EDIT: Deflection is a function of radial cutting forces and on a work piece as long as you were planning to use, I guarantee you that deflection will occur. Given that you're cutting tapers and cannot use a follow rest then I suspect an accurate taper on a really long part is going to be particularly challenging. I'm not trying to discourage you; just trying to point out that doing it in one go on a part this long and complicated is maybe not the best approach. I really want you to succeed and maybe the other guys can figure out how to help you do this.
 
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Mikey! I appreciate your post. Often the read is more difficult than the write. So, having taken your suggested steps & process into account, I am able to learn how to approach these projects & hopefully find a greater chance for success! As is, I just want to get the lathe up & running again. At the end of the day, it's a Chinesium lathe & all my tolerances seem to only come spot on with sandpaper after the lathe gets close. I now have HSS cutters that I hope will give a better finish. Perhaps this will put me in the realm of real machining.

Still haven't removed the part (as I forge ahead on my lathe repairs), but realigning it in the 4 jaw is good practice right!
 
For what its worth, Brockwood, that is a hell of a part to make in two pieces, let alone one. It might be an idea of maybe think it through and then ask the forum for step by step help as you make it. This stuff is just turning but it does matter how you hold the part and the order of operations you use. Hope I didn't confuse or discourage you, and if I can help just let me know.
 
From your first photo you want to cut the part in one piece. It looks to me like cutting he taper is the crux.
If you use the offset tail centre approach, the amount of offset in the tail centre might be impossible or unworkable. I would certainly do the calculations carefully beforehand.
If you use the compound set at the right angle approach you will probably need two steps to cut the full length of the taper. This would be the better way to cut an B+S taper in my books.
Do you have a steady rest?
 
This lathe did not come with a steady rest. 2 step taper cut to get the full length is all I have in my arsenal at this point. A learning experience if nothing more.
 
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