Inspect Inside the Drum
The drum tumbles clothes as heat is pumped in through a vent, usually in the back of your Kenmore dryer. The drum's air temperature is regulated by a thermostat that's attached to the wall by screws. It's possible for the thermostat or other parts of the dryer to break off while it's spinning and end up in the bottom of the drum. As the drum rotates, you might hear a banging noise from the loose object hitting against the walls. Stop the dryer and empty its contents. Feel around the drum's interior for loose or broken components. Contact a dryer repair technician to identify and repair the damaged part if you find one.
Check the Condition of the Rollers
Certain Kenmore dryer models have drums equipped with rollers. Rollers are small wheels on the outside of the drum that support it as it turns. Over time, the weight of the drum puts pressure on the rollers, which can cause them to fail. If one or more rollers becomes damaged, the remaining good rollers might not be able to properly hold the drum in position, so it bangs on the cabinet when it rotates. Open the dryer's main access panel to inspect the rollers. If they appear worn, replace them.
Confirm that the Gliders Aren't Faulty
Around the outside of your Kenmore dryer's drum is a pair of gliders. They're basically nylon or plastic seals that support the drum and prevent it from scraping the cabinet as it tumbles. Gliders can wear down with excessive dryer use. When this occurs, the drum can bang against the cabinet sides and create an annoying sound. Locate the gliders by removing the dryer's main access panel so that you can access them easily. If they appear cracked or split, swap out the pair for a new set to stop the banging noise.
Clean the Blower Wheel
Your Kenmore dryer has a blower wheel that circulates air inside the dryer. The wheel can become congested with lint, which can hamper its blowing abilities and also restrict airflow in the dryer. If the blower wheel becomes blocked, you might hear a banging or rattling sound when the dryer runs. Refer to the user's manual for your Kenmore dryer to help locate the blower then note the directions for how to clean it. If the banging noise continues after you've cleaned it, the lint clog might have permanently damaged the wheel, requiring its replacement.