You said it is a friction drive - that is, a right-angle drive where the edge of one wheel presses against the flat side of the other, and the drive ratio is varied by moving the edge-on wheel radially across the flat-on wheel. You also said it is a cork friction material. That sounds a bit odd. Cork is inherently a rather soft, low contact pressure material, used for flat plate clutches. Friction drives generally require high pressure contact. Are you sure you have used the right material?
If the friction drive slips (and it obviously is slipping if it squeals) it will not last long.