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Although not a hard task, removing the pulley from the power steering pump on the TJ is something you will most likely have to do when you replace the power steering pump.
While attending the 5th Annual JeepsUnlimited Moab Run, my power steering pump started going out. It didn't leave me dead on the trail but I was doubting its ability to survive another day or two on the slickrock and then the 10 hour drive back to Phoenix. I had a Hi Performance TC pump shipped next day air to Moab from PSC. Because of my Hydroboost brake system, I could not use an off-the-shelf replacement pump from the local auto parts store. Before I mounted the pump, I picked up a pulley puller/installer (I rented one from the local AutoZone in Phoenix the previous time I installed a pump), some power steering fluid, and a new belt. The new belt was a 1/2" shorter (although I now realize that it could have been an inch shorter) due to the new pump using a 4.5" pulley (compared to the 5" stock pulley). The smaller pulley gives a little higher pump speed to help out at idle/low RPM situations where you need plenty of steering (like when rock crawling).
So....enough of why I installed a new pump, so on to using the pulley puller and installer.
The power steering pulley is held on the the pump shaft with friction, a simple press fit. To remove the pulley from the shaft, a puller is used. A conventional 3 or 4 jaw puller would not work as it would most likely distort/bend the pulley and cause a wobble which would result in belt wear.
The puller consists of three basic parts, a split collar (left), the threaded puller assembly (center), and the collar retaining ring (right). Depending on the manufacturer, the parts may vary slightly, but they are all pretty much the same.
Pulley remove starts by inserting the shaft of the threaded puller into the hole of the pump shaft. The shaft on my puller has a greased ball bearing at the end of it to allow easier turning of the puller.
After the threaded puller is in position, slide the two collars around the shoulder of the pulley shaft. The collars are sized for two different shaft diameters. Pick the one that most closely matches the pulley.
Slide the collar retaining ring over the two collar halves. This will keep them from separating under tension once you apply some muscle to the puller. Hold the lower part of the threaded assembly and screw the upper section into the pulley until you feel resistance. At this point, the puller's shaft is bottomed out in the hole in the pump shaft.
Place a wrench on the lower portion of the threaded puller assembly and a ratchet at the top of the threaded shaft. Screw the threaded puller assembly into the lower portion, tightening the nut/bolt parts so to speak. As you do, the puller will slowly slide the pulley off of the pump shaft.
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