If there is runout on the unsupported section of the shaft, often that is caused by runout on the coupling flange relative to the shaft center. This "kicks" the shaft off center, and the runout gets worse the further from the coupling, until shaft is supported by a bearing which brings it back to center.
Often this probem shows up when the flanges are separated for some work and put back together in a different orientation. It can be as simple as a thin layer of rust on the flange faces!!! I have cured several of these by simply breaking the flanges and cleaning the mating faces. Clean clean clean!! Put back together and runout is gone.
If you are using a solid coupling, these can be difficult to get a smooth running shaft. They come either too tight or too loose. And flange faces can have just a few thou of runout and that is enough to kick shaft off center down the line.
For that reason I like using split couplings. Better grip on the shaft, too.
One trick (besides cleaning flanges) is to loosen bolts on coupling flange and then roll shaft- If runout is gone, there is a runout problem on the flanges.
If the only problem is shaft wobble, I would try to fix that first before going to AD. AD is a nice rig, but that is a lot of work and expense to fix a problem that may be easily done another way.
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