DIAGNOSIS: That's a worn or obstructed paper feed roller gear or a foreign object in the paper path. The right side houses the main paper feed mechanism.
FIX: Inspect and clean the paper feed rollers. Power off the printer. Open the rear cover and the document feeder tray. Look for torn paper bits, paper clips, or staples. Use a flashlight to check. Manually rotate the rollers to feel for grit. Clean the rollers with a damp lint-free cloth.
IF THAT DIDN'T WORK: The gear assembly itself may be worn. Try switching to a different paper type setting (e.g., from Plain Paper to Thick Paper) which changes the feed pressure. If the noise persists, the mechanism is likely failing and needs professional service.
HEADS UP: Continuing to use it with this noise can cause a catastrophic paper jam or strip the gears. Stop using it if the grinding is metallic or severe until you've cleared the obstruction.