As I recall, not all spindals lock on with a set screw. The brass spindals on my Balfour motor in the QuattroPro system are a press fit brass, with no set screws.
If yours has set screws, gently tighten them on the flat of the shaft, and check to make sure they run true, if they do not, re-adjust the spndal until it is, then tighten the set screw(s).
If no set screw:
Try tapping on the “pointy end” gently with a soft mallet, turn on the machine, and make sure that the spinal is running true, if not true it up, then when you are certain that the spinal is running true, strike the pointed tip harder with your mallet, to really set the spindal in place on the shaft.
It is also possible that the spindal may be worn, and should be replaced.