Even with stock components if everything is tight you should be able to run a 37" D rated tire with no issues, seen it done. Totally agree E rated tires are a better option especially for heavy loads but the blank statement of "What is the tire rating? E's only, if you have D rated tires you are just wasting your time " is a poor statement and immediately saying blame the tires with no diagnosing is a good way to wast money.
I don't disagree you can run a 37" D rated tire on an empty truck successfully. However, that is not a 31-33" D rated tire. Few of those tires will meet the quality the 37 has to meet to NOT be a total piece of junk. The run of the mill D rated tires are just not suited to a vehicle with the load ratings these trucks have, not to mention what they are subject to. I will clarify that as it is a bit broad, a D rated tire on a truck hauling a 12k trailer is not a good idea. SOME type of problem is going to rear its ugly head in that scenario.
You are not going to run a 37" tire with stock components, it won't work. At a minimum there is a lift, control arms, and wheels to make them fit correctly. If the lift, control arms, and wheels are done correctly with high quality parts, even with the change in the attack angle on the ground, it has drastically changed the behavior of the suspension. It can make it worse or it can make it better depending on choices. Still not a fair comparison to the stock system though.
Granted doesnt seem to be near the issue of the earlier trucks but thats also largely due to the increase in the diameter of the Track bar, Drag Link and Tie Rod.
The new system is far from perfect but it is a step in the right direction. The shape and angles of the track bar and tie rod have changed enough it eliminates a lot of the earlier issues across a broader range of suspension travel. Not going to stop the DW you are talking about with loose steering components and loose track bar mounts that will let it go into a horizontal shimmy. However, a lot of that can be eliminated with a much solider track bar mount and\or dampers. The reason that horizontal shimmy happens is the track bar mounts themselves, NVH has dictated the track bar isolates the front axle as much as possible. Those rubber mounts are soft enough to allow more horizontal movement than is really good in extreme situations. In normal usage it is fine but it does not take much with large tires and heavy weight to get excess sideways movement. The angles just enhance the process when it happens. It is the same concept as the vertical bounce with tires and shocks, rapid sharp force start a process that is just accelerated and compounded beyond the ability of components to control. The typical fix is replace one end with a heim and the other with poly bushings. That helps to a degree but there is still movement there with the poly bushings on the frame end. Replace them with a hard rubber or solid mount and you could likely run without a steering damper, given everything else is good.
So your saying that a truck can hit a bump, compress the suspension on both sides, then individual sides just fine but if a shock is bad then suddenly the track bar and draglink are somehow no longer parallel????
No, it is when the suspension cycles differently side to side that induces problems. Almost never going to see these sharp forces equally applied to tires at road speed. It almost always one side or the other changes position rapidly. When the suspension cycles unevenly you get pry on the steering or bump steer. Depending on the condition of ALL the parts it could induce either a horizontal shimmy or a vertical oscillation. It is never all one way or another and it is never the same, end sup being a very specific set of circumstances that cause the issues.
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I am confused by your second paragraph as it contradicts your previous statement that shocks cause DW , of course it will be more prevalent on a lifted truck then a stock height as the track bar and drag link are at a steeper angle and have increased leverage on them.
The lift kits not only change the suspension geometry, they change the spring response. You can't JUST lift it with springs, the rates and travel MUST change to compensate for the height. More compression up and down and the energy released goes up. If the shocks cannot handle the increased energy the rebound gets out of hand, same as the tires. It is all about how much energy is stored and how it is released to manage the suspension movement. With the stock system it will hit coil bind and bump stops at the extreme. With a 4" lift to get to that point requires exponentially more energy and it has to be managed. If not, the whole system goes into uncontrolled movement, the pivot point on the track bar transfers to the other side and it responds the same way.
Shocks wear out, that is why the high end ones are re-buildable. A worn King shock in the right conditions is not going to handle the energy like a new one.