This problem could be due to the engine pulley, but it's not something we see very often. Because of that I'm going to have you check some other stuff. Also, to check for the engine pulley it's a process of elimination unless you happen to have a brand new one sitting there (I'll assume you do not).
First: Have the engine off and lower the mower deck down to where you can get your hands to the pulleys. Now take the belt off of the engine pulley. Now
HAVE THE ENGINE OFF
and engage the lever for the blades.
Once you have that in order reach on top of the mower deck and spin each pulley by hand. You should be able to turn all of them with minimal effort. If there is one you cannot spin, we need to look at why that is.
Now, disengage the lever for the blades and notice if the small flat idler on the right hand side of the deck moves several inches when you do. You may need someone to work the lever while you watch the pulley. If the pulley does not move, that could very well be the problem. The reason for that is if the pulley does not move all the way in each direction then the blades could
A: Not fully engage and cause the belt to smoke
B: Not fully disengage and cause the belt to smoke.
If all of those things are in order then have a very close look at the belt. If it's old or stretched out a bit you can have some smoking, but it's usually not going to do that.
If you go over all that and everything appears to be in good working order then I would say it is most likely going to be a bad engine pulley. Again, it does happen but it's extremely rare.
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