John, if I recall correctly the arbor came from a Jacobs box but the chuck was 'chucked' in a plastic bin with a lot of others newly arrived from China. They were shop man "gifts" given because I gave the shop man a box of beers for helping me move the lathe home and get it set up in my garage.
I could almost swear there is a subtle difference in the taper as there is a distinct impression that the small end of the arbor is smaller than the hole in the chuck and there were clear bright marks on the arbor indicating the most pressure had been at the other end. So I dont think it is a case of the arbor being too long as that would surely give the wobble at the other end.
It is stuck on right now, I will be checking for centreing this afternoon (it is Saturday and of course it is pouring with rain in sunny Wellington). If it is out I will be pondering the next step.
I am wondering at this process:
1: put a bar in the main chuck, 1/2", 12mm or whu.
2: skim bar to be accurately concentric with spindle;
3: place the small chuck on the bar with jaws towards main chuch, tighten firmly.
4: put arbor in tailstock
5: put 'something' on arbor
6: bring up tailstock and clamp down
7: use tailstock ram to advance arbor gently into the chuck just until contact is made while turning the lathe by hand
8: withdraw arbor and look for marks.
Question is, what stuff should be used in 5? I dont have engineer's blue though I guess I could get some, maybe I will try with a felt pen marker.
If the tapers are subtly different can I lap the two pieces together in this rig up?
[Thinks, why dont lathes have a hand grip on the spindle? Using the chuck key as a tommy bar seems so uncouth and I am sure is not good practice]