I too had a similar problem. First I changed the steering stabilizer ( minor improvement). Next I changed the track bar ( one bushing was worn out, better improvement). Finally, I checked the ball joints. Driver side upper joint was bad. Replaced it. ( fixed it!).
Start with the cheapest fix and work your way up. Checking parts is free.
A speed-sensitive wobble, oscillation, steering wheel shimmy is 99.999% of the time nothing more than a wheel that isn't spinning true. Usually a tire that isn't perfectly balanced or perhaps a bent wheel which is far more common if you are running steel wheels. But usually it's nothing more than the tires just need a more carefully performed balancing. Many tire jocks only balance tires to what they consider "good enough" which for a TJ, isn't good enough unless it is perfect. And the bigger the tire, the more "perfect" becomes the operative word where tire balance is concerned.
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I had a death wobble for almost 2 years. I replaced TRE, shocks, obviously balanced and rotated many times, replaced the tires, track bar and front rotors. I took me so long to figure this out that my steering box started to leak and eventually leak to a point i would put an emtpy laundry container with kitty litter in it under it. As it turns out, i replaced my engine mounts and GONE no more death wobble. For me it occured around 60-65 mph. I write this to let you know the one thing i learned is that in a jeep MANY things can cause a death wobble.
Like Blackberry says "Start with the cheapest fix and work your way up. Checking parts is free."
I had a wobble on my old 77 Dodge power wagon with a 6" lift. Faster I went the worse it got. Had all four wheels balanced. No change. Thats when I learned I needed to clean the INSIDE of the wheels after spending time in the mud. (Why the guys balencing the tires didn't notice I don't know) It was about 2 inches think and like concrete on the wheels. Someone from Montana who was used to the problem tipped me off. My wife and I spent hours chiseling out the caked on mud from the back of the wheels. There was no more shimmy.
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Agree with Jerry, you have a tire problem.
Ours had what looked like nearly new Wranglers on it when we bought it.
Rotated/balanced the tires as I was seeing a little bit of chopping on the fronts.
Went from no problem to a terrible shimmy at 55. Could drive up to it and through it.
Started looking closer and first off saw the tires were built in 04, and I could see some dry rot between the treads. Jacked the jeep up and spun the tires to find the two now on the front were not round. 1/4" in difference as they spun.
So in trying to fix a problem I ended up creating one.
New BFG Mud Trackers took care of it.
97 Sahara, 74 Renegade, 72 CJ5, 55 Willy's (the Beast) Boss 302, 6:34 gearing, Bose 901 speakers.
God I miss that Jeep. Forgot the kinda Jeep, 80 SX4.
I have the same problem now, Jeep is fine untill about 50 to 55 mph before or after that it is fine but if the wobble catches before i can get through it i have to come to a compleat stop for it to quit and then its fine again. i replaced my stabilizer shock and that didnt realy help but it was shot. I just tightend up the steering box adjustment and that took most of it away but now the steering seems to tight, very sensitive. my tire on the driver side is starting to wear funny with the high and low tread spots, is it possable that this problem could be the steering box? Ive noticed this happens to alot of the 04 wranglers as mine is too.