Normally a clothes dryer won't produce any sort of grinding noise when it operates. If your dryer starts making a grinding noise, pause it mid-cycle and don't reset it until you figure out what's producing the sound. Choosing to ignore it and continuing to use it only puts your dryer and the laundry inside at risk of damage.
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Metal Object in the Drum
One likely explanation for a grinding noise is that there is at least one metal object inside the drum that's hitting against the sides when it tumbles. Open the dryer's main access door, and empty the clothes inside. Look for a coin, key, belt buckle or screw that might have fallen from pant pockets or come loose from the dryer. Removing the item should eliminate the sound.
Rollers are a set of small, usually metal, wheels attached to the exterior side of the drum that help it spin inside the cabinet. If the rollers begin to wear, you might hear a grinding noise when the drum turns. Swapping out the bad rollers with new ones should quiet the dryer. Since they're often sold as a set, replace all of them at one time, which also ensures that they wear consistently and the grinding noise doesn't reoccur in the near future should another roller break.
On the drums outer rims are a pair of gliders that serve as a protective barrier so that the rim doesn't come in direct contact with the metal cabinet when the drum spins. Gliders are generally a thin seal made of either nylon or plastic, depending on your dryer model. Over time, they gradually wear down; when this happens, you might hear grinding or whining noises from the dryer. To stop the noise, you must replace them. Since they're typically sold as a pair, replace them both -- even if only one has deteriorated -- so they wear evenly.
A long, thick rubber belt encompasses the drum at its center. The belt supports the drum and allows it to rotate to dry clothes. If the belt slips from position, you might hear a grinding noise as the belt strains to maintain its position while the drum is spinning. Contact a dryer repair technician to replace the belt. After it has been replaced, the noise should end.
A clothes dryer's tensioner or idler pulley ensures that the belt is firmly positioned on the drum. The belt goes over the component's bracket, which is attached to a spring and wheel. If the wheel malfunctions, you're liable to hear a grinding noise as it struggles to turn and maintain the belt's tension. Contact a dryer repair technician to evaluate the tensioner's condition. If it needs replacing, you also should change out the belt. It might have incurred damage due to lack of enough tension.