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Oil analysis on the differential lube to rule out limited slip differential clutches wearing prematurely. There have been some LS clutch problems with the Serling rear ends.
Have the service manager or mechanic ride with you when you've got the trailer hooked up.
Have someone observe the axle wrap-up when you start out from a loaded stop. This measurement could be critical to the first best guess for the shim packs. I suspect that your pinion angle under load is moving too much. There are "traction bars" for trucks that will allow full suspension movement, yet limit the wrap-up from a torquey start.
Get the dealer service department to work with you on shimming the axle.
Four wheel alignment.
Remove the shims from the driveline carrier bearing.
If you have opportunity to tow a trailer other than yours, I'd do that too. Your trailer could need an axle alignment in relation to the tongue. Double and triple axle trailers that crab walk are harder to start out from a stop.
I appreciate the kudo's guys. I may not know Diesel engines to the fullest extent yet, but I have had experience with 4x4's and other off road vehicles for the last 25 years. (And I'm only 42) That said, I've trouble shot, been frustraighted with my own vibrations in lifted rigs, friends lifted rigs, and lowered rigs for much of that time. I've also worked with steam turbines with driven shafts up to 25,000 rpm. A vibration there, and things come apart in a hurry. I've also worked with military aircraft generators that spin up to 15,000 rpm. Clearances between windings don't allow for much shaft vibration. I'm just trying to lend a hand here.
There isn't much i haven't done to the drive train of a 4x4. Both Ford, Dodge and GM. Any time you change components from factory design, there's bound to be issues. This is only one example. One of my most favorite rigs I sold several years ago can be read about here:
I have a 05 F350 with 2,500 miles that sounds like it is having a similar problem. From a dead stop under heavy acceleration I get a brief vibration (a second or so) from the rear end. If I accelerate normally I feel nothing so it hasn't bothered me much. I will be pulling a 8,500lb travel trailer this summer and wonder if it will be worse, I guess it's time to get it looked at. Just a thought, I wonder if it is a problem with my LS diff? Maybee someone forgot to add the friction modifier at the factory. What's the chances it would be that easy of a fix?...not with my luck.
I ran into this while looking for some other information.
Driveline Vibration, F-250/350 137" or 142" Wheelbase: This may be due to improperly installed rear axle spring spacer blocks (installed on wrong side). The blocks should be taller at the front than the rear when installed correctly. Broadcast Message 1572
Were the problems solved? If so, what was the solution?
I just bought an '05 350 KR with 3.73's and am having the same problem. There is very little vibration when not towing, but a lot as soon as I hook up the trailer. Obviously it is much worse when I really get on it, but it is always there. It is from approximately 1800 RPM's through 2200 RPM's and from a dead stop. There is nothing when accelarating while in motion.
Well Ford wanted to adjust my pinion and I did not want to do that. After going through the grapevine I found out it is VERY easy to overload an F350. My truck is almost bottomed out with my gooseneck attached to the truck. Now I have decided to get the airbags for my F350 which will bump it up another 5,000 pounds in the rear which of course will fix that. Its a shame though b/c my 99 truck handled it 50 times better and Ford advertises that the 05 have more payload. I do not want a F450 or 550 just because of the fact it will be a bumpy ride with the airbad system I can turn them off when not in use. If you get a 450 or 550 it will ride like crap and the gear is a 4.88 instead of my current 4.10 which I love. I guess the extra 1,000 dollars will be worth for i have to drive this truck about everyday. This is my story and I'm sticking to it.