Unplug the machine and remove the collar, pulley, gear, and key.
Loosen the rear locking ring and snug the front ring up until play is eliminated at the front bearing – the bearings should not be under load and the spindle should rotate smoothly.
A bar in the spindle/chuck to act as a lever will enable you to check more easily for sideways movement.
Having achieved this, hold the front ring still with the spanner and tighten the rear ring to lock it – it may take a few goes to get it feeling just right – patience is the key!
Replace the key, gear, pulley etc. and test run the machine – it should run smoothly and freely at 2000 rpm, and without getting hot at the bearings (warm after prolonged running is okay).
If it feels stiff, "notchy," or labouring to reach maximum speed, you will have to go back, loosen the rings, and release the bearing load by tapping the back of the spindle towards the tailstock with something soft, such as a piece of wood. Repeat adjustment until satisfied – it sounds laborious, but doesn't take long and is worth doing carefully because the improvement in the feel of the cutting action and the finish on the work are marked on this small machine.
The photo's provided by Nick include the section regarding adjustment of the spindle bearings, such as they are..