Why not just turn one? I love turning knitting needles, all 14" of them. To do that, I turn a mandrel to hold the stock as I feed it through. You could do something similar, but run a bolt through the mandrel to hold your buff on.
You might find using a reverse thread worm with a straight shank gripped in a chuck is your safest way of using a buffing wheel/brush or polishing mop . a mandrel will flex slightly when pressure is put on it making it untrue for any future work and a morse taper has the likelihood of working free an d damaging your work.
I was reading some of the comments on your mandrel requirements, exactly wh at are you trying to do with them/it?
As for the wood for the knitting needles, I have used African Blackwood, As h, Jatoba and some others. Basically, any hardwood with a straight grain w ill work. There are two requirements for turning knitting needles:
You need a set of mandrels:
One fitted to the stock you will be using for the knitting needle. This on e goes in the head stock and is a tight fit, as all Morse Tapers should be, but cut like a collet to squeeze the stock so you can just bump the end of the stock to move it through the collet.
The other mandrel needs to be fitted to the Morse Taper on your tailstock b ut have the center drilled out just over the size of the needle you are tur ning. This mandrel keeps the piece from whipping around.
The other thing you will need is a micrometer, or a fixed gauge. DO NOT tr y to use calipers, they simply will not remain true- regardless of how tigh tly you lock them down.
Position the tailstock about six inches, or so, from the headstock and slow ly feed your stock through, turning it to the rough size and then sanding t o final size, for each section of the needle.
For a 14" needle, you will need a starting piece of stock around 20" long, and 24" would not hurt.
What I do is find a set of needles that is the size desired and just mike t hat set. BTW, speaking of crochet needles, avoid the kit PennState has. T here is no way anyone can use that (while nice looking) bulbous handle whil e trying to make their stitches.
The nice thing about the mike is that the measuring surface is larger than most calipers.
The length seems to be rather standardized, but since you are the "creator" you can make them any length the user desires.
Not only that off the main drive spindle but have used a flex shaft coming off and used off to the side.
I also cut my own through spindle bolt that comes to a nut in the morse 2 then having a threaded amount and using two more nuts and washers I've mounted face plates and work.
One just has to remember - speed kills. A 8" disk has a very high surface speed when the spindle it cranking on high speed.
The forces can really control you. Be careful before, during and after.
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