"When we initially remove the support under the bucket the weight of the bucket is applied to the rod trying to pull it out of the cylinder. Oil is incompressible so if the seals are tight the oil pressure on the rod end side of the piston simply goes up offsetting the added force and the rod is held in place by the increase in oil pressure. In fact that trapped oil pressure will hold much much more than the weight of the bucket as long as the seals are tight."
True.
"But when the seals are leaking that elevated pressure is transmitted through the leaking seal to the oil on the lower pressure side of the piston. That causes an increase in the pressure on the base end, the piston moves and the rod extends."
No, that can't happen. If the rod extends and the piston tries to move toward that end, The volume of oil displaced by the movement of the piston that goes past the piston seal is less than the volume of oil needed to fill the space created behind the piston. There's no rod on the back side of the piston so that space is larger. Air would have to be introduced to allow the piston to move.
"Once the oil pressure on both sides is once again equal the piston and rod stop moving. The pressure will never be equal on both sides until the bucket has dropped to the mechanical limit of it's travel and something other than oil pressure is supporting its weight."
It has nothing to do with pressure. It's volume. Take a double acting cylinder. Take the piston out and throw it away. Insert the rod halfway into the cylinder. Fill the cylinder completely with oil and cap both ports. There's no piston at all, so that's a big seal leak. Try to move the rod. You can't. You can't move it in or out. You cannot cap both ports to test for a piston seal leak.
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Today's Featured Article - Oil Bath Air Filters - by Chris Pratt. Some of us grew up thinking that an air filter was a paper thing that allowed air to pass while trapping dirt particles of a particles of a certain size. What a surprise to open up your first old tractor's air filter case and find a can that appears to be filled with the scrap metal swept from around a machine shop metal lathe. To top that off, you have a cup with oil in it ("why would you want to lubricate your carburetor?"). On closer examination (and some reading in a AC D-14 service manual), I found out that this is a pretty ingenious method of cleaning the air in the tractor's intake tract.
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