Like many others on this thread, my vibrations pulse. In fact, I’ve noted that if I go into 4WD at freeway speeds, I can pause the vibrations at any point in their cycle. I can pause them at the loudest and at the quietest by simply timing my 4WD shift.
This gives me the impression that the vibrations are an interaction between the front and rear driveshafts. As we drive in 2WD, the rear tires actually rotate slightly faster than the front tires due to slip. All tires slip to some degree when a force is applied. Since there is significantly more torque (and thus thrust force) on the rear tires, they slip faster than the front. And since the front tires are merely coasting, they slip in the opposite direction. The result is that the two driveshafts are not spinning at the same speed.
My thought behind the pulsing effect is that we are hearing the effects of the vibrations of each shaft going in phase versus out of phase with each other. In music, this is called a “beat” when two instruments are played simultaneously with one instrument slightly out of tune. You are hearing alternating constructive and destructive interference. The more out of tune one instrument is with the other, the faster the beats are.
There is also the question of what is actually vibrating in each driveline. This is probably the hardest question to answer. Pretty much all things vibrate. The questions we actually have to ask, are does it matter? Will anything excite a vibration by approaching a natural frequency or harmonic? Can we change the frequency or harmonic? It’s less of a matter in preventing every vibration, but more isolating problem vibrations and figuring out ways to make them non-problem vibrations or reduce/eliminate those specific ones.
I have recently suspected the source of many TJ vibrations to be the Double Cardan joint. The Double Cardan joint is not a true CV joint. While the in and out speeds are always the same, the intermediate carrier speed fluctuates with each rotation. As the driveshaft spins with a DC joint at an angle, the DC intermediate carrier must accelerate and decelerate slightly twice with every rotation. With Newton’s laws in effect, that torsional acceleration has to come from an applied moment. That applied moment can only come from one or both ends of the DC joint. Thus, the DC intermediate carrier introduces a fully reversed moment twice per each rotation of the driveshaft against either end of the driveshaft.
As to why we generally only feel it with one driveshaft installed, I suspect it’s because the vibrations induced by one shaft alone are below the threshold of being noticeable. Perhaps there is enough damping or compliance in the system to accommodate one shaft worth of vibrations. But when we add in a second shaft, we get the effects of constructive and destructive interference. And at least the constructive peaks of the combined vibrations are of a high enough amplitude to be significantly noticeable.
As to how these torsional vibrations become vibrations in the linear sense, I am less able to guess. I think that the point of transmission of the torsional vibrations to linear is likely in the transfer case. The two vibrating shafts are not collinear - they are offset from one another. In particular, the front shaft is offset from the rest of the engine/transmission/transfer case. So in order for that moment to be transferred through the transfer case, there must be a moment or force applied to the case itself, transmitting vibrations to the mounts and thus to the body. How this would work I am really not quite sure. A possibility I suspect is that the shaft is applying an oscillating force on the output bearings as the moment in the shaft oscillates, because since the shaft operates at an angle, the reaction moments on the axle pinion and the transfer case output pinion are not in the same plane, and thus require one or more out of plane reaction moments to balance it. These moments would have to be provided by the output bearing, the pinion bearing, or both. And at that point, the vibrations have become linear, and can be felt in the skid, the frame, and the body.
As to why the vibrations might be worse in a gear other than the 1:1 drive gear for some people, I suspect that the gear reduction in the transmission provides an extra means for torsional vibrations to become linear, as the difference in torque between the transmission input shaft and output shaft must be made up by torque on the case itself. Thus if the moment on the output shaft at any instant changes, so does the moment on the transmission case. If the transmission is in the 1:1 gear, there is no effective torque applied to the transmission case.
(This is all speculation and should not be taken as fact.)
