What might cause a grinding noise when the AC clutch is engaged on a 1993 Chevy PU you have replaced the compressor with three new ones and still have the problem?

You may have burned it up. AC compressors need oil initially.

Usually the compressors require additional lubrication during the installation. The warranty on compressors usually require the replacement of the dryer (Accumulator), orfice tube, and flushing the system. This will eliminate debrie and contaminates from damaged compressor in which was replaced. The compressor may be checked for the grinding noise by the following procedure. Disconnect the battery ground. Remove drive belt from clutch. Place wrench on nut in center of clutch and rotate slowly clockwise. If the shaft doesn't rotate smoothly there is likely damage inside the compressor cylinders and pistons. If the compressor checks OK, check other components while the drive belt is disconnected. For example, The pulley on the alternator, idler pulley, and water pump should not have any end play. The AC compressor puts a heavier load on the drive belt and may cause other components to make noise. The only other possibility that comes to mind is that the compressor clutch bearing is bad or the clutch is slipping. ! Good luck!