12.99 for a magnetic base and 16.99 for a dial indicator at harbor freight will give you a great idea where things are. No, it wont be accurate to tenths (tenth of a thousandth - .0001") but will be good enough to help you find out where your issue is. I have one I would lend you - but between shipping back and forth, youll be a couple dollars away from owning your own.
Eyeballing run out wont do much good. Id say the top end of acceptable is .003" (the appx width of a human hair). But the farther out you go, the more amplified it is... half a thou run out at the chuck is a WHOLE LOT more at 3" out from the chuck.
Start with nothing, check the taper socket of the spindle (ID)... add the chuck, no nut (dont know what the adapter bushing looks like so cant say if you can check the run out on that without the chuck on), check the run out on the ID taper, insert the collet in the nut, assemble the chuck making sure the collet does not come out of the nut, slide the mandrel in, check that.
Where you say 3/4-10 threads... you may not have a MT socket, so look for a machined diameter as close to the end of the spindle as you can find.
Odds are, the collet is not seated in the nut first and is giving you run out due to the collet not seating properly, or having not done that initially, it damaged the collet and wont run true until you find and stone off the bur it created - and may still not if it tweaked the collet. Or, there are burs on the spindle or adapter mating faces, not allowing the chuck to seat properly (true). If the run out comes in only when the mandrel is installed (measured as close to the collet as you can get) - grab something else that should be straight and verify (like the shank - non-fluted portion of a 5/8 drill bit. If the run out is the same, the problem is back at the spindle or chuck. If it goes away with the drill bit, its likely the mandrel - assuming the drill isnt bent, which isnt very likey on the short portion that doesnt have flutes.
If the needle wiggles much at all at any point, Id be keeping both eyes open for issues - - it will likely bounce a round a little due to surface finish where the probe rides - rougher will bounce more, smoother, less so - so you may have to sort of average out the bouncing. But anything more than .003" would really have me looking closely at things. I havent run an indicator on any of mine recently, but can if you want to compare the run out on a beat up 10 year old harbor freight lathe, or a fairly new HF clone of the Jet/Delta Mini/Midi.
If its the mandrel, I cover the shipping both ways for a replacement (bad one back to me, new one out to you). If you want me to check the mandrel, like I mentioned in my email, feel free to send er my way. If she is bad, Ill owe you for shipping to me - if its good, youll owe me shipping to ship er back. Id expect runout on the EA5858 mandrels to be the same as the runout of the chuck - which would likely be tenths depending on the bearings in the lathe and spindle condition.
Being methodical and attention to detail is key... Your hands can sense the tiniest of burs, so feeling edges and surfaces can often give clues when looking at mating faces.
Wade
