Ron Hoff posted about this several years ago. The Cummins 5.9 engines with the Bosch VP44 fuel injection pumps have what Ron called the doldroums, or a low a low frequency vibration according to Google. There is a speed up, and slow down every rotation of the engine crankshaft. This is the drive line rattle. This is most prevalent at slow engine idle. The driveline will destroy itself if ignored. Ron said this has been a problem for all the Cummins equipped TS14Gs. He set up the low idle to 900 rpm and it helped somewhat. It's not nearly as much trouble on the Detroit/Navistar engines.
So to reduce your problems, once the engine is started(most ECMs don't like to see increased throttle at startup-safety measure for startup wear), make a shim to fit under the bottom end of the throttle pedal to keep the low rpm at 900-1000(get creative and make a flip around metal stop, only needed for the front engine).
Also, if you can stick a screwdriver in the driveshaft and rotate it more than 1/4" with the engine off, you have too much wear in the driveline. The splines are worn and/or the torsional damper needs replaced. Also check the yoke going into the transmission torque converter. That yoke likes to wear the torque converter input shaft(those two parts come from John Deere).
The torsional dampers were one part that Terex sorely missed on a needed redesign. If you get more than 3000 hours on one, it's shot and needs replaced.
I've found an economical source for OEM dampers. Private message me(which I don't check as often as I should), or call nine3seven-five7zero-2sixtwonine. I'm in SW Ohio.
The top damper is the worn one. See the gap between the side of the spring coils and metal. The picture doesn't give justice to the wear on the metal at the end of each spring.
