Replace the steering stabilizer. It looks like a shock absorber and is bolted to the frame on one end and the steering linkage on the other end. It works exactly like a shock absorber except it has high resistance in both directions. Regular shock absorbers pull apart real hard to prevent tires from dropping into potholes, and push together real easy to prevent bumps from pushing the vehicle up.
As bad as you described the problem being, I suspect the oil has all leaked out of the unit, and it's dry now so your mechanic overlooked it.
There are two other problems that cause steering wander that you should be aware of, but the symptoms won't be nearly as severe as you're describing. One very common one is a worn track bar. It's attached to the passenger side of the front axle with a rubber bushing. The other end has a big curve in it to go over the differential, and is attached to the frame with a ball and socket. That ball and socket will develop looseness allowing the axle to move left and right just a little, but since the steering linkage is not moving at the same time, the relationship between them changes resulting in the front wheels turning a little. The result is you are constantly correcting the steering wheel as you drive. Chrysler allows.080" of movement in this joint, but it will never get that bad because you won't be able to control it. You'll be complaining of the handling before it has.020" of movement.
To check the track bar, watch the ball and socket very closely while someone rapidly turns the steering wheel back and forth about 4 inches either side of center. You will see the track bar move up and down a little, possibly only 1/16". When you turn the steering wheel, the axle moves sideways a little first, THEN the tires start to turn. The parts stores have a replacement track bar that costs less than the dealer's, and many have a lifetime warranty.
The second problem is slop in the pitman shaft of the steering gear box. Have your helper do the same thing with the steering wheel, but a little slower, while you watch where the shaft comes out the bottom of the gear box. If you see the shaft move sideways a very small amount, bottom out, and THEN start to turn, the bushing inside is worn. This will also cause steering wander, and when it gets bad enough, there will be a power steering fluid leak caused by the shaft moving away from the seal. A new seal will not solve the leak for more than possibly a few days. Repair requires a rebuilt gear box. I've never yet autopsied one, and I've never looked into finding repair parts.
The second problem isn't real common. The track bar is; but both of these problems won't cause what you're describing. The main thing to look for is that steering damper. Be aware too that it can be mispositioned in such a way as to allow it to rub against, ... Uhm, ... Something, and a hole will be rubbed through causing it to leak all the oil out. I messed one up once after performing an alignment, and it came back a few weeks later with the problem you're describing. It's been too long; I can't remember exactly what it rubbed against, but it might not be real obvious at first. If you replace it yourself, be sure to mount the clamps in the same location as where the old ones were. If not positioned correctly, it will reach the end of its travel too soon in one direction and prevent you from turning fully in that one direction.
One more thing to mention. Caster is one alignment angle that affects directional stability and steering wheel return after turning a corner. (Think of the fork on a bicycle or motorcycle, and how it is angled forward on the bottom. With your weight on the bike, that angle is what allows you to ride no-handed). On older cars, caster was adjusted individually on each wheel, and the difference side-to-side could cause or reduce a pull to one side. The difference side-to-side on your truck can not be changed because it has a solid axle, but he entire axle can be rotated with a pair of cam bolts on the front of the two lower control arms. Increasing caster, (tipping the top of the axle rearward), increases the effort required to turn the steering wheel, but it increases the stability, or tendency to want to travel straight ahead. The disadvantage to higher caster is that after you turn a corner, then let go of the steering wheel, it returns to center so violently that it overshoots and goes in the other direction. This is the problem you're experiencing. Hitting even small bumps sets up the same reaction since there's too little friction in the steering linkage to stop the bouncing back and forth. It's the job of the steering damper to stop that over-traveling.
Thursday, December 3rd, 2009 AT 3:10 AM