The dryer will make a loud scretching noise like metal rubbing on metal and then after about 10 minutes the dryer will shut off and when you try to restart pushing the timer/start button, it just make a buzzing noise?

I had a problem similar to this on my Frigidaire dryer. I found that there is a felt ring that goes around the drum inside. This acts like a washer to prevent the drum from rubbing on the housing. On mine, the felt somehow got pushed in some and the drum was squeeking as it rotated. I had to order a whole new drum and replace it since on my model it was part of the drum.

Well, sir, it is metal on metal, and you did well to stop it. Someone will be needing to take the whole thing apart and find the problem. It may be easy because the metal should show where it was rubbing because it will be shiny bright.
Be blessed.

could be the drum wheels

get it checked for an air lock should sort that out

A drum support wheel bearing could need lubrication or be replaced. Also some drum support wheels have a rubber coating that wears off causing misalignment and noise. Possibly drum gasket (sometimes felt material) where drum meets rear panel is worn allowing metal-to-metal contact--should be replaced. See the following for info about dryer repair: http://home.howstuffworks.com/how-to-repair-a-dryer.htm

Your drum may be out of round. The drum belt on the outside of the drum may be rubbing against the cabinet. When the cabinet heats up, the side walls of the cabinet may be bowing inward, thus making contact with the belt on the drum. This would explain why it is intermittant. When the heater turns off, the cabinet cools and the sides bow back out.

Can you push the drum up and down. If so then the main bearing has gone bad and needs to be replaced. This is the only metal on metal rubbing you will get unless the machine is off balanced. This is caused usually by doing to heavy of loads and wearing out the bearing

It might be metal on metal. It is possible that something worked it's way from inside the drum it between the drum and the rest of the dryer. There's just a couple of srcews that holds the back and top on to the dryer. Take them out after un-plugging the dryer, and consider plugging it back in and running it to see if you can here where the squeek is coming from.

there are 2 drum rollers at the back of the dryer. shut off power, pull drum and you will see 2 rubber wheels. there is a little plastis triangle that keeps the roller in place. try spinning the rollers . they probably will not spin too freely. remove triangles ,inspect inside of roller the stainless steel bearing may have gunk on it try to clean off . also check shaft roller rides likewise remove any debri use a little rubbing alcohol to remove gunk. also check the idler roller that routes the belt for the same things. good luck

Hello, sounds like the rear drum rollers are in need of replacement which is causing the motor to get hot and cut out on the thermal cut out. It can be tricky to service if you not handy. Good Luck