NTC 444 BCIV hesitation during acceleration

I would put a restriction gauge on the front side of filter housing or between filter and pump.
0-2 is sucking air
3-7 is normal
Above 8 is a restriction

Cummins put their filters on the suction side so start there. Make sure the drain on bottom is sealing properly but they are usually hard to start if that’s issue. There is a wide funny looking plug on top of the pump takes a big flat head, under it is a washable screen check it for sure odds are that’s at least part of the issue with that trucks age. I would lean toward fuel supply because it seems power related. You also didn’t mention any smoke timing issues almost always have smoke with them. Just for giggles turn the manual screw on the pump all the way in see what that does.

The 444 was an STC engine. The timing was changed or controlled by oil pressure. That could be an issue not trying to step on anyone’s toes but the 444 was good when right but seldom right and few could get one right. Many were converted to big cam 3’s. Thing there is we’re they marked with the CPL they were converted to. So parts may be a shot in the dark. Finding someone to work on a 444 that’s actually seen one is a shot in the dark. They are not a simple big cam. Not that they are complicated but education is expensive. There is a way to check the STC with regulated air psi but I rather not type all that if I don’t have too.

 

Only thing Id add is to try a new filter first. I know we wanna believe we are getting high quality fuel for the current price. But I have seen some of my davco filters needing replaced as low as 5k miles. Even tried different fuel stops.

 

Process of elimination really bud, my first thought was when was the fuel filter last changed? Could be the injectors, fuel pump, how does it run when you sit still and try and rev it up? Air cleaner also when was that last changed, you'd be amazed at how much dust is in the air specially if your running in drier states. If it rained all the time I'd worry less about the air cleaner as the rain keeps the dust out of the air but how often does that happen?

 

JMO... but @wore out was pretty well spot on in his post
I sure don't claim to be a vast wealth of knowledge about Cummins 444 but I know the timming advance is more temperamental than a bi-polar hooker and theres not very many mechanics that know how to fondal those fuel pumps to make them perform as they were designed
I do know that they seem to demand constent attention

 

My dad was a Cummins guy through and through. If you ever wanted to hear some of the most creative colorful language. You just mentioned a 444. He bought a new 88 FL cabover with one. Loved the power. But Cummins couldn't make it run right. Low milage, high fuel dilution and dirty oil. Couldn't stay together or out of the shop. He named it "The Hanger Queen". I know years later they finally got them right. But he was so impressed he ordered a 1990 with a Detroit.

 

My .02, I knew someone with a 444, he loved it, only problem he had a hesitation that would come and go, would drive him crazy. He took it to countless shops(Cummins guru’s) including Cummins itself. They could never fine the problem. They had it under dyno several times, they would see the hesitation but could never pin point it. Cost him lots of $$$$$$ and it was never fixed. Eventually due to Commiefornia(CARB), he dump that engine and dropped a 6NZ from a wreck truck. This was way back.
Edit;
They replaced just about every part in that 444, still had the hesitation.

 

Air filters should make black smoke, anytime one gets off start with a fuel filter. I have seen bad one which is why I said start, check air filters, and listen to see if ones lazy or if it’s slow etc.

One more thought is a 444 is jacket cooled not CAC so antifreeze in a cylinder is a possibility but again should smoke

 

I worked at a Cummins dealer when the NTC444 came out. They were quite
problematic all right. Your problem sure sounds like a fuel restriction to me.
Is there a place to plumb in a vacuum gauge at the inlet of the fuel pump? If
I remember correct 8 inches of vacuum was the maximum Have a
good look at all the fuel lines for kinking. Debris in the tank.
Had a new machine once doing something similar, it was because of a
welding glove in the fuel tank.