John:
Thank you for being a gentleman and understanding the 'prohibition' against 'hobby' machinery.
Before the thread is locked, I hope to offer some general advice. If you are going to check things like bearing play or runout, unless it is large enough to be seen/felt, a dial indicator is needed. In your video clip (or whatever it is called) of your lathe running, I believe I saw the belt guard on the headstock vibrating. I'd suggest you get a dial indicator and check bearing play in the headstock/spindle bearings. If the lathe uses 'antifriction' bearings (such as ball or roller bearings), and those bearings are badly worn, the spindle will describe an orbit as it turns. Belt pull on the headstock cone pulley as well as tool load will turn this orbit into something other than circular.
To check bearing play:
-remove any chuck or faceplate from the spindle.
-slack the drive belt to the headstock cone pulley
-put the quadrant gears (which select direction of carriage travel) in neutral position.
-back gear must be disengaged.
-setup a dial indicator so it is rigidly mounted and its tip contacts the spindle where the threads end and an unthreaded portion (known as the 'register') or a larger
diameter collar is located. This will be immediately to the right of the front spindle bearing.\
-zero the dial indicator.
-put a bar into the spindle, a hardwood hammer handle works well for a smaller lathe like yours. Press the bar down as hard as you can. Note any movement of the
dial indicator.
-with the spindle bottomed out in the bearing, re-zero the indicator and pull up had on the bar. Note the reading on the indicator.
-this reading gotten by pulling upwards is the bearing play top-to-bottom.
-setup the indicator so its axis is horizontal, tip contacting the spindle nose at 9:00 when facing the spindle nose. Repeat the above steps.
-the two sets of readings will give you an idea of bearing play in two axis.
To check spindle runout, simply turn the spindle by hand with the indicator setup as per above, either position being OK.
-to check tail bearing play (the small end of the spindle where the drive to the quadrant gears is located), you will need to slack any thrust adjustment on the spindle
(if used, though not likely if roller or ball bearings used for the spindle journals).
-setup the dial indicator as per above, and take the same readings top-to-bottom and side-to-side
I would also check the fit of the cone pulley on the spindle. The cone pulley is free to turn on the spindle when the back gears are engaged. The cone pulley is fixed to the spindle by a pin when running 'direct'. If the cone pulley hub were run without proper lubrication with the lathe running in back gear, there may be some excessive wear in the pulley hub. I am unfamiliar with your lathe. lathes I have worked on with cone pulleys and back gearing had a bronze bushing in the cone pulley. This provided a bearing for the pulley to turn relative to the spindle. If this fit is worn on your lathe, the cone pulley will float on the spindle, probably running eccentric to the centerline of the spindle. It will wind upcreating an imbalance when the lathe is running and cause vibration.
Your lathe's issues are more likely due to badly worn spindle bearings. Again: get a dial indicator and take some readings. Try turning the spindle by hand and see if you feel any roughness as you rotate the spindle. Worn ball or roller bearings often produce a roughness as they run and it can be felt.
