Ariens Model # 924028 Serial # 006182 Auger Drive Sheave Slipping

My oldy but goody snowblower is ailing. The drive sheave for the auger/rake slips along its' shaft, toward the auger. The 2 set screws are not holding it in place. When it slips, it comes off the woodruff key, which promptly disappears, and the sheave no longer spins, hence the snowblower no longer blows snow. Is this due to a misalignment with the drive shaft pulley off the engine? Or was there some sort of stop on the sheave that prevented it from sliding along the shaft as it now does. There's  not one now and I cannot find a close enough image of the sheave to ascertain if there's supposed to be one, like a lip that catches the end of of the auger shaft or something that's worn away with time and service. Hard to see whats not there. I've spot welded a washer onto the tractor side of the sheave to provide  a stop lip as described. The sheave with the stop against the end of the shaft, aligns well with the wear marks on the idling brake shoe next to it.  I've yet to re-assmble the thing and started thinking I should maybe ask around before employing the solution of a thousand headaches to this venerable old workhorse. Thoughts? Don't dally too long, I'm drifted in.

Wow, thanks Kshansen. Coffeed up or no, your on the ball. The link is helpful. I have downloaded the literature and will see what I can see. The parts are not showing significant undo wear, no excessive wobble, and the shaft is hardened steel of course. I did try new set screws (a fart in the wind). As I've studied the issue, it seems to me that the drive pulley from the engine may be mis-aligned to the auger sheave slightly towards the auger. This may be enough for the belt to pull the sheave along the shaft and off the key as described. I'll inspect that portion of the assembly, make sure the engine pulley isn't loose, and see what I see. Again, I appreciate the quick response. If you really need some snow, I've got some to spare.

In appreciation for the support received on this forum I thought I should post some information that may be of use to others who experience the issue being discussed. As it turned out when I slowed down a bit and examined the problem, looking at the bigger picture, I saw that the nylon flange bushings on the idler arm were worn nearly to the point of non existence, causing the arm to tilt severely toward the snow thrower (auger) assembly, which caused the belt to drag the sheave along the shaft and off its woodruff key. I replaced the bushings with brass bushings as they were all I could find locally. (they're very proud of them at the hardware store). They righted the arm so it now aligns with the drive pulley and the auger sheave.
I should note that in the process the sheave, apparently in retribution for delayed maintenance, sheared the pin that carries the idler brake arm. On my machine, this is welded to the auger housing so I have removed the brake for now until I can address this consequential damage. Not a safe situation but I had to get the driveway dug out, Mama said so. 

Hi and thank you all!