Hi and welcome to JA. What works the best is to put air to the fitting at the barrel end of the cylinder so the rod comes out all the way and the piston will push on the barrel gland and hold it or if it is still on the machine then use the hydraulics to hold it out and apply pressure to the gland.
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I have tried the air pressure with no luck, I could put the hydraulic lines back on and try the higher hydraulic pressure.
Is my read of the parts break-down correct that the big nut is threaded onto the gland and the gland is held in place with a snap ring? I see now that the online parts book is not page numbered the same as mine but I am looking at "Crowd Cylinder (818060-)" in John Deere parts online for the 310D backhoe.
Also, once opened, will the piston slide out of the barrel with ease past the snap ring groove?
Yes the piston will usually slide past the snap ring groove. but when you push the glad back to remove the snap ring verify that there is no rolled ridge in the barrel and if there is use a die grinder and grind it down to remove the ridge. and yes there is a internal snap ring
OK, got it apart; only problem that I ran into was that there was a cast iron ring that I didn't know about on the piston that wouldn't pass over the snap ring groove in the barrel; when using force to remove it the iron ring was broken but nothing else was damaged so all should be good with new parts. I guess that maybe it is possible to compress the iron ring in order to remove the piston in the propper maner.
Yes you can compress the ring with a piston ring compressor when you install it but the barrel should be tapered going back into the cylinder. and when you install it you should be fine