This topic has been discussed extensively but sure, lets beat the dead horse a little more. Here are some things to consider.
- Most of the time TJs work fine with 5.xx gears. Gearing extra low doesn't guarantee high speed vibrations but it does increase the probability of high speed vibrations.
- Nothing is perfectly balanced. The smallest weight we can get is 0.14 ounce. https://neapcoparts.com/dlw-1-driveshaft-weight/. Other factors contribute to the level of perfection that is achievable as well but for now lets just assume that we can only add weight in the increments of .14 ounces or more.
- The bigger the diameter a shaft is the faster the surface speed is and the greater the force of the balance weight will be. Critical speed is important to consider when ensuring that the shaft is not flexing at high speeds but generally speaking in a TJ critical speed is a non-issue. Which means that keeping the diameter small is actually advantageous as it minimizes the centrifugal force of any imbalances.
- The equation to calculate centrifugal force is F = m v² / r. I'm not smart enough to do it manually so I use the calculator linked above. However, I am smart enough to know that the little number 2 in that equation is important, it means squared. It tells us that as speed doubles the force quadruples. Just as 4² = 16 and 8² = 64, the base number doubles but the squared number quadruples. Same applies to the force of an imbalance. This is important to note because the effect of going from 3,500 rpm to 4,000 rpm, a 500 rpm increase is far greater of a change in force than going from 2,500 to 3,000 rpm even though it is also just a change of 500. The faster the shaft is spinning the more a couple hundred more rpm will affect the force of imbalances and thus vibrations.
- I've run the calculations for how much force this tiny weight creates, which is about the diameter of a nickel but not as thick, using the force calculator on this page https://www.omnicalculator.com/physics/centrifugal-force. Remember, it calls for radius so I'm halving the diameters.
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Now that I've demonstrated how much force the smallest balance weight can produce at different RPMs I'll explain some of the other factors that cannot be controlled by means of adding balance weight.
- Looseness/slop between drive shaft parts. Moving parts have to move, which means there has to be a tiny amount of clearance between them. Maybe it's only a couple thousandths of an inch. But image the entirety of the mass of the drive shaft shifting to one side and being .005" off-centered. How much of that shaft's weight is off center? As much as one of these small .14 ounce balance weights maybe? So if the moving parts of the drive shaft cause the mass of that drive shaft to shift to one side by a couple thousandths of an inch it can/will impact how smoothly that shaft runs at high speeds. Maybe next time you start up the Jeep the shaft shifts in the opposite direction by the same amount, moving the high side of the imbalance. This creates a moving target that is impossible to counter by adding balance weights.
- How many thousandths of an inch side to side play is there in your transfer case output bearing and your pinion bearing? This movement also causes the centerline of the mass of the drive shaft to shift around in the vehicle.
- Same thing with the centering of the x and y axis on the yokes that the shaft attach to in your vehicle. A $60-$75 transfer case yoke is not machined perfectly to the nearest .0001". Things might be off by a few thousandths of an inch, there are tolerances. Any little bit of off-centeredness in the yoke, where the joint sits, is going to make the drive shaft run a little bit off centered.
- Also, those yokes are cast before they are machined but much of the profile of the yoke is still a casting. Casting is literally pouring molten metal into sand so it stands to reason that the casting might be a half ounce, or more, thicker or heavier on one side than the other, adding to the aggregate mass of imbalance of the drive shaft as it is spinning at the same speed at the shaft and attached directly to the shaft. The transfer case and pinion yokes are not dynamically balanced parts.
The point I'm trying to make here is that there are so many nuanced little things that by themselves might not cause a noticeable vibration but as a whole can and sometimes do. Many of these things cannot be remedied by simply balancing the shaft better or changing the design of the shaft. Laws of physics have limitations. What is possible in manufacturing has limitations. At least unless you have a NASA budget but even then there are still limits, just less limited than what you're going to find available for your Jeep currently. Vibrations are inherent, they are present in anything that is in motion,
even in things that aren't in motion if you want to get real brainy. Gearing low (numerically high) increases the speed of the drive shaft, thus increasing the intensity of force of those rotating objects, and therefor the perceptibility of vibrations, in a quadratic (think exponential) manner and not in a linear manner. Every action has a reaction, every change you make to your Jeep affects something else.