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I have an 02 Z06. The crank pulley seems to be off balance. You can see it wobbling pretty drastically. Is it possible that it's just not aligned properly? Can I just take the bolt off, adjust it, and re-tighten? Or am I going to have to buy a new pulley?
Search in the C5 Tech forum using keywords "wobbling crank pulley". There's plenty of past discussions to read.
Look for the red banner near the top of that forum where it says "search this forum" and enter those keywords there...
Yes, LSX stock pulleys have a history of failure beyond 60K miles, yes you need to replace it ASAP (waiting could cause you to lose your motor).
Some folks (including myself) use this as an opportunity to do a cam upgrade, since the effort to do so is only slightly more than the pulley repair. Also, some of us (including myself) go for a higher-quality under drive (worth about 5HP) aftermarket replacement vs. putting another stock pulley on.