V-belt alternator slips through…

Hi, new day, new problems No, little fun… Since our “big” repetition I have the following problem: The belt of the alternator slips through for about a second at the start of the engine. No thing I thought about, tightened the straps a little bit and it’s all ok again^^ But that doesn’t work so well, because: As soon as I really just tighten the straps the Lima starts the permanent “jauling”…That’s not because I’m rough motor, and net knows how to fix it I am aware that the bearings of Lima are the best after the mileage net more, but I don’t really want to replace them or repair them because they are still doing their job properly. Can it also be that the V-belt disc has worn out over time and therefore less grip is available? According to Etos, this part costs only 15 euros, which is not enough to be used by the user. I am very sympathetic to. Well, I am open to further suggestions Greeting