3406e stutter

Check your fuel tank vents, check the lines for kinks, and check the bottoms of the tanks for junk, as well if you have a screen on the in tank pickup, it is possible that it is clogged.

 

Sounds like someone put some sugar in your tank or something along those lines, you will probably have to change your filters several times. Also investing in locking caps would be a good idea.

 

It's hard to say, but if you found junk in your filter, you probably found the culprit.

You will know after changing the filters a couple more times.

 

That's getting about to the age where I would start to suspect a collapsing line, however that should be black chunks not papery stuff.

 

Cam sensor. Mine did the same thing. Almost like the engine shuts off for a split second during acceleration. I thought it was fuel related too, but it was just the sensor. I am willing to bet this is your issue. Common on E models.

 

I had a similar problem on a 99 W900L with a 98 3406E, the cam sensor was original so i changed it, didn't help.
Next step i used a piece of lath to hold the throttle open as i checked the wiring and sure enough the harness on the drivers side that goes into the top plug of the ECM midway down the motor as i pulled on it the engine would sputter, when i changed it out i noticed some worn through areas where it goes over the motor to the passenger side, called the local Peterbilt dealer that had it in stock, installed it, though the problem was solved.
Next day went to move a machine, started to sputter again, started to re-check wiring and noticed a plug "future pto wiring" touching the braided stainless steel air line from the air compressor as i pulled on it, wires were chaffed and causing the motor to sputter when it hit the ss line, problem solved.