Been plagued with this for a bit. Horrible noise, I turn my AC off when coming into the work parking lot out of embarrassment.
Warning:
​​​ long story incoming.

What I've replaced so far...
Water pump
Main drive belt and AC belt
Pullleys and tensioners for drive and AC belts
AC compressor

Background: had a bad screeching marbley sound for a bit. Much worse when AC was on. Figured it was pulley/tensioners and with 150k decided to replace all of them. Didn't help, replaced belts because they looked warn and probably needed it. Didn't really help. Decided to just drive it until something broke, which one day the water pump decided to puke itself. Replaced that and the old one definitely made a grindy sound when out of the car.
Summer comes and I'm using the AC more, it makes a terrible screeching almost grindy noise when first driving the car, mostly gets better on the way to work but after sitting it always makes that noise. I figured bad AC compressor/clutch and changed it. Noise still remains. NOTE- noise only happens when AC compressor is engaged.
Any ideas? Noises have evolved for sure. Before the water pump went out it was a more constant noise. AC on still added extra noise though.
Harmonic balancer looks fine visually, car is stock. 99 FRC manual.
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bad screeching marbley sound that describes a real bd bearing noise. there are 2 or 3 idlers and the tension er with the same bearings and one of them is frozen

 

Assuming a new A/C clutch assembly was installed on the new compressor? You kinda said a new clutch was installed. I agree with above post that one of the two A/C tensioners probably has a bad bearing. If not that, are you 100% certain the correct length A/C belt was installed? If you installed yourself, you know the right length belt can be tough to install. One thing you could try for diagnostic purposes is belt dressing. It might be a bit messy, but if the squeal stops, then changes to a "shhhhhhhhhh" sound, then the belt is either too long, or a bit of oil is leaking on it, causing the squeal. Hope this helps........

 

I'll give the dressing a try. Clutch on compressor is new. pulley and tensioner are new too.

I'll have to see what belt I ordered. It's odd that only when the AC is on the noise happens

 

Not really odd, because the A/C belt tensioners and belt drive are a totally separate system from the Serpentine water pump/alternator/power steering pump belt and tensioners. The fact that the noise only happens when the A/C is engaged tells you that it is an isolated problem within the A/C drive system, or compressor. Either your belt is slightly too long, and is slipping, the belt is correct and one, or both tensioners have a bad bearing, or the new compressor has a bad bearing. There is one other possibility that I hate to even bring up, but here goes-Was the system purged/flushed before the new compressor was installed? WHY was the new compressor installed? Because if the new one was installed due to the old compressor seizing up, or totally failing within the system, the lines and condenser should've been completely flushed. Because there could be metallic particles and other junk in the condenser and lines. If the system wasn't flushed, and there was/is junk floating around in there, there's a good chance the crap has ruined the new compressor. I'm again assuming you did get a NEW compressor, NOT a reman unit, correct? It could even be a bad new tensioner, or a bad, new compressor. Sometimes new stuff is bad from the get go. It happens. Please keep us informed as to what you find. Hope this helps, and best of luck to you....

 

You might try using an Automotive stethoscope to listen to the bearings

 

I had bad experience with belt dressing years ago - it was inconsistent and sticky and my belt chugged intermittently around pulley erratically. It was scary - I had to wipe off with Alcohol solvent. I thought someone said here spray mist water on the belt instead to help diagnose pulley issues 🤷🏻‍♂️

 

This^^
I just dropped a pile for an entire A/C system overhaul after my compressor seized on the highway which caused a slight fire as the clutch and belt burned up trying to turn it. As it turned out my dad (the PO) had the same thing happen 2 years ago, replaced the compressor and nothing else against the advice of the tech at the dealer. The tech who just fixed it again is sure the system was contaminated from the previous compressor failure.