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Another thing to consider, especially on the smaller 9 x 20 lathes, is to check the pre-load on the spindle. The manual says something to the effect that it was done at manufactering.
I read that the best way to check for preload (providing the bearings are still good) is to 10 Remove the drive to the spindle, 2) give it a GOOD spin by hand, and 3) It should spin only 1 1/2 to 2 turns. If it spins more than that, It's worth trying to increase the load on the bearings. The spiral pattern only indicates that the cutting tool is cutting in a spiral. That's what it is supposed to do. Best of Luck.