Hi, could not find a similiar situation to mine but could be wrong, sorry in advance.

My mini has about 155 000km on the clock.
It currently has belt slippage, my supercharger pulley keeps being pulled into the casing and i have a high scratchy noise sometimes on start up for about 5 seconds.
We have already replaced the tensioner, idler pulley along with the alternator with a new belt.
We noticed that the SC Pulley was being pulled into the casing and it was making a steel on steel contact noise.
We stripped the car recently to take off and inspect the supercharger pulley, cleaned it good, seems to be in good condition just a bit of wear on where it connected with the casing and the shaft looks undamaged.
When the pulley was put back there was a space of about 2mm between the pulley and the sc.
Been driving it for two days and the pulley is snug against the casing again and belt is slipping, no noise so far but every time i drive i move the belt back in to place it moves about 1 to 2 grooves out every time i drive but i have been driving it very carefully (economcally).
Read a few articles where it can be numerous things. Need help just to narrow it down. Any advice?

 

Is your crank pulley in good condition? The original rubber pulley tends to crack and allows it to wobble while running. For me, it resulted in a shredded belt.

No offense but if a car has a problem after it was recently serviced, I always suspect that work. Since you just replaced the alternator, are you certain that it is properly aligned and all the bolts tight? Tensioner bolts all installed and tight? The pin in the tensioner removed?

I just replaced my tensioner and forgot to remove the pin. It was as I was watching it idle that I noticed I left it in. Oops!

 

Also doublecheck/replace the idler pulley

 

So it sounds like the supercharger pulley is slipping on the shaft. This is not normal and not good.
The easiest (and cheapest) solution is to install an aftermarket pulley. This has the added benefit of giving you more power too because it is smaller and makes the supercharger run faster.
You will need to install a smaller belt too.

 

This. Pull off the OEM pulley, and install a 15% or 17% pulley, and be done with it. The longer you run your slipping oem pulley, the more it's going to wear on the shaft. I

 

If the supercharger pulley has moved on the shaft in or out you will likely need to rebuild the supercharger and replace the pulley as once they slip it's damaged.

 

I replaced the supercharge pulley for a 15%, sounds different but its working, thanks for the advice.