How to: Replace John Deere 44 inch snow thrower belt on 300 series tractor
How to: Replace John Deere 44 inch snow thrower belt on 3 series tractor - YouTube
If this is the same snow thrower you have, replacing the belt is really difficult. JD did a horrible job on putting that thrower together. Those belt guides on the pulleys should be welded in place and the bolt that holds the pulley should be a stud, not a loose bolt,
And as you can see in the video, he can not get the one guide back in place with the belt on the pulley.
Also I have to assume that one of the pulleys is spring loaded. That's a long belt from the engine to the thrower. Engine power pulses will cause the belt to flop around. The spring loaded pulley can not stop it. As a matter of fact, at certain engine RPM, there will be a resonance with the pulley and belt that will greatly increase the belt flop.
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The belt flopping around is most likely what is causing your belt to come off the pulley. From watching the video, it appears that there is no belt guide on the main engine pulley. When the belt is flopping around, it will get very loose as the spring load idler is bouncing back and forth. This will cause the belt to come off of the engine pulley or the spring laded idler.
The simplest cure for this is a rubber stop positioned just behind the spring loaded idler. It has to be positioned so that the idler can not bounce away from the belt. In the past, on my own snow thrower with a long belt, I used an old shock absorber top mount. In addition to that, I also used a belt flopping pulley about half way between the two pulleys. It had just enough tension on the belt to be in contact with it at all times. I put it on the slack side of the belt between the two pulleys.
Richard