A/C clutch rubber blew out on my last a/c compressor so I replaced the compressor and had the system recharged. Now the clutch will start spinning when a/c is turned on but wont engage the compressor. I don't hear the click sound when an a/c usually engages. no leaks in system and had recharged by shop. Clutch does not spin by hand when vehicle is off.
You may be seeing some rotation of the compressor clutch that may be due to loss of refrigerant. Less refrigerant allows the compresor to turn easily. Virtually all vehicle ac compressors have a clutch plate configured with metal straps and large rivets - a flexure assembly with hub bolted to the compressor shaft allowing the clutch plate to flex a few thousandths of an inch to magnetically cling to the idler pulley when the clutch coil is powered up. Ac off, the clutch plate/compressor shaft doesn't turn. The compressor's idler pulley is always rotating since the serpentine belt is turning to power water pump, power steering pump, and alternator. With ac off (engine running) the drive belt still turns the compressor idler pulley. With ac on, the large center clutch should turn with the belt.
98% of all ac problems are loss of refrigerant, the leak few diyers are knowledgeable enough to find and repair. The lack of the distinctive metallic 'click' (clutch plate engaging the idler pulley face) usually indicates one of several possibilities; loss of refrigerant from a leak, blown ac fuse, damaged ac relay, shorted ac diode blowing the ac fuse. A combination low/high pressure sensor detects excessively high or lower than normal operating pressures and sends a signal to the engine computer to disable power to the compressor clutch. This sensor protects against compressor damage if loss of refrigerant occurs. Refrigerant moves lubricating oil throughout a system, eventually returning to the suction side to continue lubricating the compressor. Oil misting occurs so returning refrigerant gas is mixed with oil droplets. Loss of refrigerant means loss of lubrication. If allowed to run without refrigerant, the compressor simply self destructs from lack of lubrication.