So I recently bought a Jeep Wrangler 2004 sport has 140,000 miles with some 35" mud terrains and a 4" lift and its a automatic. So the problem is whenever im driving and i reach about 55 mph it begins to shake and vibrate and you can feel it like if you have something in the passenger seat it will vibrate so after you give it gas and make the RPMS go above 2 and half and get around 65 and above it stops and drives smoothly no shaking but when you get back down to around 55 mph it begins doing it again and when the RPMs get about to 2 and above and its going 55 mph it doesnt shake as much as when the RPMS are below 2, the tires are a bit wore down i have had alignment done along with a rotation, and it has fixed the problem a bit but not completely i have checked my U-joint and whenever i shake them they have no play the rear ones have a bit of play but not alot the only thing i noticed that was weird was the SWAY BAR LINKS are not broke but cracked right in the middle it seems as if they were dipped into some type of outer casing and the outer casing has cracked but the inside of the SWAY BAR LINK its fine you see shiny metal but when you push on the bumper you can see the sway bar link crack move up and down, so idk if that could cause it to shake? also the shaking is not as bad as some of the people who have death wobble it just kinda vibrates and shakes a little bit but not a whole lot....does anyone know what it could be?
Try getting the tyres balanced, then if that hasn't worked start checking the steering components. There's many threads on the so called "death wobble" but until you get your tyres balanced you won't know if this is what you have or not.
Also when i dont give it any gas and i just cruise at 55mph the shaking stops and it cruises fine its only when i give it gas that it begins to shake but after i pass 60 it runs smooth as a cadillac so even tho it doesnt always shake could it still be the tires? im thinking it maybe the steering damper or the u-joints since im assuming there stock and it has been lifted.
A speed sensitive shimmy is nearly always caused by a bad or imperfectly balanced tire, or a bent wheel. I'd assume your tires just need to be carefully balanced by a shop that isn't happy with just getting the tires balanced to the point of "good enough"... on a TJ, "good enough" is never good enough where tire balance is concerned.
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A good knock by a pothole, rock or kerb will throw your tyre balance out anywhere up to 50grams. 5 grams will cause a descent shimmy at between 80-100 (45-60 mph) However you said it happens when you accelerate. I'm now thinking it could be an unbalanced prop shaft. Get your tyres done 1st then go from there.
Mine had the same issue. I replaced all ujoints and it helped a little. Then a new stearing stabilizer and they helped a lot. Then new shocks and that was a wash. Even thought the drag link bushing seemed fine, I replaced it and that really did the trick. I would do the bushing and stabilizer first. 15$ and 30$. Easy to replace with rental ujoint press from the parts store and 2 hours work. Front axle ujoints are easy if the hub has ever been removed. It is hell when it hasn't.