gplief:
Thanks for posting the photos. Confucius got it right (1 picture is worth 1000 words).
Here is what I suss out from your photos:
1. The pump has (3) plungers, one of which has its strap (the part which goes around the eccentric) and eccentric rod removed. Whether this was done to slow the speed of travel of the ram, or due to damage to the plunger/cylinder would have to be determined by taking apart that cylinder. I believe I see the eccentric rod laying in the oil sup.
2. The "doorknobs" appear to be handles for lifting the pump suctions on each cylinder. Each pump cylinder has an independent suction. The doorknob rods have a wedged detent on them and from what I get from the photo, the suction strainers ? look to be pivotted. IOW, lift up on a doorknob, the wedged detent engages in the guide just below the doorknob, and that cylinder is out of service. This was a way of controlling the rate at which the ram moved.
If you remember your basic physics and hydraulics (at least when I was an undergrad, we took a Civil Engineering course in basic hydraulics, as in the flow of water or incompressible fluids), Pascal's law is still in effect, not abrogated nor otherwise changed. "Pressure on a confined fluid is transmitted undiminished thruout". So, whether one piston or all three of them are working, the force on the ram is going to be the same.
3. The "capstan" type handle below the gauge is a valve for controlling flow of oil to the ram. My guess is this is a needle valve with a bypass port. Start the pump with the needle seated hard (capstan probably turned clockwise), and the oil flow bypasses thru the valve body and back to the sump. Open the valve (counter clockwise would seem likely) and a piston or set of lands on the valve stem covers the bypass port in the valve body while oil flows thru the needle valve to the ram cylinder.
4. The weighted levers below each pump cylinder may be pressure relief valves. If you use one, two, or three pump cylinders, each is setup to run independently of the others (as per the "doorknobs" I wrote about, above).
5. The ram is single acting. There are two sheaves or pulleys with grooves at the butt-end of the ram body (the closed end of the ram cylinder, which is a hemispherical portion of the body casting). These sheaves may have had smaller diameter wire rope running over them which was connected to the yoke on the ram (horizontal runs of wire rope) and to a heavy weight (vertical runs of the wire rope). The weight and wire rope are not shown in your photos, but seeing the sheaves and the fact the ram is single acting, it seems the most likely way to get the ram retracted.
6. I am not sure what the fitting is in the piping connected to the ram, making a 90 degree turn in the piping. If a simple 90 degree turn were all that was wanted, a 90 degree elbow would have been used. You may be seeing an in-line high pressure strainer. Someone was into the piping at some point, given the wrench marks on the piping.
7. The guard on the gearing looks to be a later addition, shop made. Similarly, the extra 'axle support' or guide also looks to be shop made, hogged out of heavy steel rather than cast.
8. Each pump cylinder does have a simple "packing gland" and "stuffing box". Square braided packing is used. This is cut into rings that just girdle each plunger or piston. The rings are stacked with the butt joints staggered. Old packing can get fossilized and not make a seal around the pistons. Taking up on the nuts on the packing gland studs may not improve matters, and hard/fossilized packing can cut into (known as scoring) the piston rods, really making problems. If you have to remove the packing, you use "packing extractors" or "packing pullers". These are corkscrews which are attached to flexible cable (like auto speedometer cable, used in older cars and motorcycles). Each piece of flex cable has a tee handle. You remove the packing gland, or suspend it on baling wire or twine to access the packing material. You then turn in the corkscrews 180 degrees from each other, and start pulling a little at a time. The packing may break, not unexpected with old dried/fossilized packing that's been compressed for ages. You work out all the packing, keeping count of the number of rings. I doubt there will be a 'lantern ring' (soft brass spacer ring with holes thru it to allow oil to lube the packing rings as it works along the piston rod).
You will then be able to pull the piston (or plunger) on the cylinder which is disconnected. That will give you an idea of what kind of packing or sealing arrangement is on the pistons. As old as that press is, I would make a sizeable wager that you will find cup leathers.
When you re-pack the piston rods, you stagger the joints on the packing. You do not wind the packing around the rod and then cut the rings from the spiral you made. That gives rings that are too large in diameter. Oldtimers would turn a piece of scrap stock or hardwood to the diameter of the piston rod and use it to roll the packing around and then cut each ring and make sure it fit, trimming as needed. A single-edge razor blade or drywall knife works well for this, or, if you carry a pocketknife and keep it well stoned (I've carried a jacknife since I was a kid, 60 years, and keep mine reasonably well stoned for this sort of thing as well as other uses such as cutting open a roll or baguette to make a sandwich...), you can use your pocket knife. No need to use a large pig sticker or anything specialized.
Square braid packing comes in regular sizes based on the width. Measure the inner diameter of the counterbored area where the packing was removed from, then measure the piston rod. Subtract the piston rod diameter from the counterbore inner diameter and divide by 2, and you have the packing size. Packing is sold by the pound, not the inch nor foot. A square braid pump packing for oil service is all that is needed, nothing too fancy nor high temperature rated.
The press has been drained of oil and appears to have been dry for ages. The sump will need a good cleaning before either oil or kerosene (for flushing) is put into it.
The pump will not need to be primed, since the suctions for each cylinder will be submerged in the sump.
It is an interesting old wheel press, and while it might look a bit complex or perhaps a bit of a mystery, it does follow the "K.I.S.S." rule of engineering: "Keep it simple, Stupid !". Instead of dinking around with a variable displacement pump or variable speed drive to the pump, Niles simple made a pump which had individually connectable cylinders. Given the era this press was designed and built, there were little or no "off the shelf" industrial hydraulic components. No variable displacement pumps, no spool type control valves, no micrometer metering valves, no hydraulic hose nor spin on filters for the oil return line... I'd take the guard off the gearing (after making sure the power to the motor was disconnected either by opening a breaker or opening a disconnect switch and locking/tagging it out). Once you have made the motor safe to work on, remove the guard and try pulling over the bull gear by hand, or turning the motor pinion by hand if you can't initially move the bull gear. You may find things are "set up" from disuse and lack of oil in the pump cylinders, but you need to make sure nothing is frozen, seized, or locked solidly before you try starting the motor.
The pump is probably bi-directional, not caring which way the eccentric shaft turns in order to deliver oil pressure to the press. Ordinarily, when a motor on a piece of equipment is being installed or has been un-wired, we do a "bump test" to determine rotation. A "bump test" is best done with the motor uncoupled from whatever it is going to be driving. A brief "bump" of the switch (or contactor) is done to see which way the motor shaft is turning. If it is OK, the wiring stays as-is. If opposite to the desired rotation, as the old saying goes, "lift two phases and swap the wires". I would not imagine motor rotation matters with this oldtimer's pump.
That's about all I can suss out from your photos.