The rubber "grip" around the spindle will collect dust and link over time. This will cause the spindle to lose grip of the disc during quick rpm changes. That noise the rubber "grip" spinning on the disc.
The only way to get to that spindle is to take the top off the drive. Then you can clean the rubber off with a q tip and alcohol. While you're doing that, you might as well clean the laser lense, too. Also use a q tip and alcohol for that. You don't need the q tip soaked for the laser; just a little damp. Gently spin the q tip on the lense. Don't push down too hard.