When I turn the dryer on there is a loud humming sound, Then after it runs for about 10 minutes and as soon as it heats up it will just shut off. Then if you let it cool down it will come back on and do the same thing. What can be the problem?
Here are your parts
http://www.appliancepartspros.com/partsearch/modelsearch.aspx?model=LE8317W2
It sounds like your motor is getting hot and tripping it’s internal thermal cutout.
Open the door and rotate the drum, it should turn fairly easily.
Not a bad idea to try a couple other dryers just to see what is normal.
If OK this will eliminate a mechanical overload as the reason for the motor overheating.
Other possible causes are:
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Low voltage - check the voltage L1 to Neutral and L2 to Neutral, both should be close to 120 volts AC. This assumes it is an electric dryer. This is a possibility but not very likely
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Motor is so full of lint that it cannot cool.
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Motor’s centrifugal switch is welded shut so the start winding gets power all the time. Only way to fix is replace the motor.
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Motor is just at the end of it’s life time, this is the most likely.