The leaking oil might be a problem if it bothers you enough to try fixing it. Mine was doing the same thing, leaking oil and slowly lowering the boom. There were no numbers stamped on the jack but the label had a model number to work with.
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A google search told me it was a Torin jack so I called and told them what I needed. Turns out they carry rebuild kits for their 8T rams but not the 3T. I decided to see if I could source the parts locally so I took it apart.
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Not much to it. Only three rubber parts, two o-rings and a wedge-shaped piece on the piston. I knew the wedge bit would have to be reused but figured I could get the other two. Wrong. The larger o-ring has a flat inner edge which nobody had and the smaller o-ring is a metric size, nobody had that either.
I tried the ghetto fix by flipping the o-rings over and reassembling it. It sort of worked, it stopped leaking oil, but started lifting the ram erratically. It was obvious there was air in the system and I tried bleeding it out, but after 15 minutes of pumping/bleeding with no improvement it was apparent one of the worn parts was pumping air into the system. Game over.
I had a 20% HF coupon in my wallet so I went and got a whole new jack. There was only a few dollars difference between their regularly priced 8T manual and the 8T w/air assist which was on sale. I got the air/hydraulic model and some jack oil for around $75.00.
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I rattle-canned over the orange so it matches the hoist. I'm going to replace the 4-foot rubber hose with a longer neoprene piece so I can guide the engine better and lift at the same time. I'm not one of those fortunate people that has friends that will help pull an engine. That's how you find out who your friends are, tell 'em your moving next weekend or pulling an engine then watch them scatter.
I found a pdf file with a parts list that might match your Blubird, but finding someone that actually carries the rebuild kits might be a challenge. The phone number listed for Bluebird is still active but answered by a recording that says "Thank you for calling Husqvarna..." I dunno what that's about.
http://weborder.bluebirdintl.com/order_static/doc/RIPL/RIPL2006/RIPL2006-8277R01.pdf