An AC shop says I have a bad compressor clutch and that I need to replace the entire compressor. I don't have the money to pay such a high bill. I asked about just replacing the clutch and they don't recommend it because apparently removing the old one often takes a piece of metal from the compressor housing with it, thus causing the compressor to fail a few months later. Is this correct?

Relay maybe , or the PCM - engine computer isn't energizing the relay , or the compressor clutch is bad . Video's on youtube showing how to diagnose .
https://www.youtube.com/watch?v=2NVGB-LulKg

to convert from r12 to r 134 a the entire system has to be changed
that is condensor, compressor, evaporator, hoses ,the lot because r134a runs at much higher pressures than r12 ( nearly 3 times higher in psi)
it needs different gauges and has different fill connections so that the gasses cannot be mixed
to make it worse the oil used in the compressor is different because of the different gas and is not compatible with the r12
there was nothing wrong with r12 gas but companies and customers were "hoodwinked" into believing that the r12 was bad for the atmosphere and r134a was the answer
just as you have been " hoodwinked" by the person into getting a gas change over without being fully informed of what was involved and why
with r134a gas there has to be a fan in front of the condenser that works immediately the ac is switched on as the temp of the gas being converted back to liquid is much higher because of the higher pressure need to convert it back from gas to liquid
without that fan the system starts to circulate gas and so the evaporation of the liquid at the evaporator in the car is lost and no heat from the car is transferred back outside
what it means is this --- if you can get r12 gas , change the compressor back to an r12 compressor, have the system completely flushed, vacuumed down for at least 1/2 hour and then refill with r12
If on the other hand you have to use r134a because that is the only compatible compressor available then the evaporator , hoses and condenser have to be changed as well and that means a new ac kit basically
find yourself an accredited ac specialist shops and get quotes

sometimes depending on how bad the bearings are its not worth repairing replacing is best. If you want to repair most major auto parts store have that loan a tool program where you pay the price of the tool you bring it back and you get all your money back

If you are talking about the part behind the pulley on the compressor, its part of the clutch assembly.
You get the pulley and coil as a kit which bolts to the shaft.
Check the online auto parts stores for ac clutch.

i dont know of any domestic cars that dont have rebuildable/replaceable clutches on the compressor. best way to find out is to call a parts store and see if you can get the part.

Sounds like it is clicking in and out which meens its eather low on freon or maybe a bad low pressure switch ? Expansion valve maybe clogged (could be more but too hard to get into?) you do not have orifis tube...hope this helped you?

Buy a whole new clutch for about $200. You need a special puller to remove the old one if you intend to refurbish it. It's not worth the effort. Just remove the clips and knock the old one off with a hammer. Chuck it away and replace with a brand new clutch assembly.

check to make sure the a/c system is fully charged, if it is not the system will not turn on, if you need more help get back to me. please rate my fix as i strive to be the best

Get a rebuilt compressor or waste you money gambling on a clutch. It will have to come out anyway if you want to replace the bearing that is pressed in.

ok if the clutch is vivrating then the clutch assembly is not good you need to replace it, unfortunatelly the clucth might cost you
almost as much as a new or rebuilt compressor except to you if
you want to replace either or, but if you want to save some money go to a place where they specialize in a/c and ask to buy a used clutch, but if you don't know how to replace it then have some one do it for you, but if you know little be about mechanic you should be hable to do it your self, just se the gap between the front side of clutch to the compressor pulley and try to leave about the same gap when you installed the way todjust the gap is very simple just add ar remove washers between cluch and shaft