CD Spindle Wobble -- How Do I Check It?

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I've been working on cleaning up my Sony XE-500 with the CDM14-5BD20/C loader. From time to time it does not like CD-Rs so I've taken a peek under the hood. One thing I noticed was when playing a CD the disc wobbles a bit.

Looking from the side and using a the top of the tray as a reference there is a slight amount of vertical movement at the edge of the disc. Looking from the top there is a slight side to side motion at the edge.

Looking at the center of the magnetic clamp the center of the clamp tends to wobble slightly side to side as well. At first I figured the CD was a bit warped or then hole was not perfectly centered so I tried another disc, and then another. Some were better than others but there was always more motion than I would expect.

With the disc installed and the motor stopped it appears that the clamp has some play with respect to the spindle support -- it is not a perfect match. This suggests looking at the clamp motion might not be an accurate indicator.

Also, the Sony loader has quite soft rubber isolators so any unbalance in the disc tends to make the whole laser-sled- spindle assembly move a bit with each rotation with respect to the frame.

In short, I can't seem to figure a way to observe the spindle wobble independent of the motion of everything else.

The spindle "feels" tight -- more so than observations would suggest so the problem might merely be the way the loader's soft suspension responds to normal disc unbalance.

Any suggestions on how to check this out further?