About 7 years ago I bought an 89 Caprice 4 door. It had 53,000 original miles. I now have 72,000 miles on it and am having issues with what I found out was the rear axle.
On wet pavement when slowly turning away from my driveway I experience a severe shuddering which I figured was the front end. I rotated wheels and tires and checked the lugs for the proper torque. Made no difference. This has been happening for years and only on wet pavement.
I took it to what I believe is a reputable garage and was told the posi was not working right. He said something about the discs not meshing and the rear wheel which must be pushing hard as the other wheel wont break loose. Sounds feasible.
He said he would need to rebuild the center section if he could get parts and the cost would be between $1500 and $2000. I only paid $1000 for the car and really love it so I deferred for the moment. That shop called later and said they would need the car for 2 days. The first to break it done and the parts needed. The second was to reassemble. What I did not like was having them take it apart and tell me then how much it would cost. It could be more than the price quoted.
I told a good friend who has a private shop repairs and rebuilds older cars and he said in his experience if I put in limited slip modifier and new oil he was 90% certain it would solve the problem. He is about 55 years old and has been a mechanic all his life starting in his father's gas station.
I spoke to very knowledgeable parts guy who has an 86 Caprice which suffered the same symptoms and did the oil change, solving his problem. Two or three other persons have said the same thing and one so far as to tell me to run as fast as I can from the original mechanic.
I have the gear oil, LSD additive and gaskets and am all set to go.
I am easy on the car, don't really drive fast and do not do burnouts. Having driven it about 20,000 miles in 7 years shows that.
My final question was if I went through the oil procedure without success what would happen if I did nothing. The general consensus was that I would have no posi but all else would be fine. The car rides beautifully and there is no noise from the rear end at all. As to having the posi I don't really need it. It seldom snows here and when it does I don't drive. Why the car has a posi intrigues me as it was bought buy an older woman.
Appreciate any comments, thanks.

 

there's no point guessing. Everything is conjecture until somebody actually opens it up and looks at it.
Maybe it's just a friction issue that new fluid will fix, maybe not. Maybe the differential is about to puke its guts all over the road.
You're going to open it up anyway. My advice is to let a mechanic see inside and give your their assessment.
As you said, you did ignore the shudder and keep driving it for years instead of addressing it. That's never a good recipe.

 

Thanks for the reply. When I mentioned that this has been going on for a few years I should have clarified that I could probably count on both hands how many times I have encountered it. I am hoping that the differential does not "puke its guts out" but I do not know. There is no noise, no rattling or whining from the rear. It runs very smoothly. i also drove the car in tight figure 8's in a parking lot for about 30 minutes without any noises or clunks. Did make myself dizzy though!
I have access to a lift on October 5 and hopefully will find out what is wrong.

 

Sorry for the delayed update. But I got Covid finally and was not interested in crawling under my car. Anyway I bought the gaskets (there are at least 2 configurations for a 10 bolt), a couple of bottles of GM Limited Slip Modifier. At this point I could not find gear lube with the modifier in it but eventually found 80-90 weight Castrol for LSD.
Undid the cover bolts to drain the oil and it was black. Probably never changed before but it only had 72,000 miles on it. Cleaned the cover but checked the magnet for metal filings and such but it was clean. I used brake clean to clean the cover and the gasket surfaces. The original gasket was in perfect shape but I of course used a new one. Cover back on and torqued and then added just over 2 and a half litres of gear lube. Awkward place to get at.
As the problem was encountering only happened on rainy roads my timing was good as it has been raining since I changed the lube. Did a lot 360's and figure 8's and so far the the shuddering has gone. Fingers crossed it gets better by the mile,
My total cost was $11 for the gasket, $35 for the oil, one can of Brake Clean and I slipped the lift owner $50 for its use, his air wrench and used oil dump.