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I had this happen on my 2 w/d f250 7.3 and mine seems to have been caused by bad tires and I had a large bracket that was cracked and separated that attaches to the frame. Had both replaced and it never happened again. Good luck Hope you find your problem.
 

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Ford dealership used an aftermarket part (drag link?) that did not work out too well so they got the original Ford part in there and problem mostly solved. I am installing a new red head gear box that will correct for the loose steering and then the fix will be in. Thanks, y'all have helped a lot.
 

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OK, I haven't answered this question in a long time. I will once more for those that are interested in understanding "cause" not treatment of symptoms. So far everyone is wrong and claiming that treating this or that symptom solved the problem, it did not it just moved it from a diagnostic perspective.
The issue is lack of stiffness, low mass, low energy degradation system and a phenomenon called resonance. Given enough source force impact any assembly can be made to resonate energy at its natural frequency or the net natural frequency of multiple assemblies mated together, system natural frequency. An object being impact resonated will act as a force multiplier of 10 to 50 x the source force. Given enough force some assemblies will maintain this system of vibration energy with a very low continuing source force after the starting impact. In the vibration diagnostic business that is called locked resonance. Once a vibrating system is created very little energy is needed to keep it going like swinging a child on a swing, the major energy required is starting the system to vibrate, then just a small cyclic push will keep it swinging. That is why some report that they hit a pot hole, a RR track, a curb or ran it with severely unbalanced tires and had to come to a complete stop to eliminate the shaking. The follow on source force didn't have to be as severe as the big starting impact to support the vibrating system.
Some things make it make likely, mechanical looseness, front end mods like bigger tires, bad steering dampers, and unbalanced tires. That's the cause, but its a problem that has to be managed by symptoms or peripheral parts. You cant change the "cause" physics, it is induced resonance amplitude. Think of a bell, impact it and it acts as a resonating force multiplier. Sure , you can dampen in but given enough source force it WILL resonate. Oneof6
 

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Does this mean inside every Powerstroke there is a “Death Wobble” lying in wait for the opportune moment to strike?
 

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The potential for impact induced vibration is not limited to Fords, Power PSD or any particular vehicle. Some front end assemblies damp, resist acceleration forces, more than others. Others like old Jeep front ends and trucks with leaf spring loaded steering assemblies. Sometimes one can move the point of resonant frequency to a frequency it is less likely to be resonated by adding mass, which lowers the frequency, or stiffening which raises the frequency. The target should be having the system natural frequency 25 to 40 % higher than the expected excitation frequency for units running below first critical. So the answer to your question is yes but no more than any object impacted in its operation. One can't remove the potential for natural frequency excitation one can only build a machine where the natural frequencies of individual parts and net assemblies are unlikely to be resonated during normal operation. Much preventative Engineering goes into rotors and assemblies like turbines, power plant fans, fluid drives and heavy equipment. Testing called "Bump Testing" is even done on large foundations when there is a suspected resonant condition that will coincide with the machines rotational frequency. That is cause, what owners are calling here "Death Wobble" is the effect and the solution is to not shade tree Engineer mechanism mods with man years of Engineering in them and expect no negative resultant. Front ends are not maintenance free, they can't have points of mechanical looseness, keep the tires balanced, preferably with a Hunter Force Balancer, a good steering damper and stick with stock tire sizes, that's what the assembly was Engineered for. Oneof6
 
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