It's also common if you have a tiny piece of the wire left in there after welding. Here of this problem commonly where someone just does a poor or sloppy weld and a tiny little particle breaks and will make a "whirling" sound. I've welded a few of these myself too. But as stated above, it could be due to bad bearings, but you would also probably notice that while driving the car before welding it (if this diff that was welded was the same as the one that was in your car before welding).
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