E4OD shifting twice with each gear
What you describe is not the "part of the design of transmission", however it should unlock/lock the torque converter clutch when shifting briefly but that would only happen above 35mph or so when the TCC functions. Below that speed it does not lock up, and will unlock even if you do not let off the gas once you drop under that speed.
Its locking and unlocking during shifts should not be noticeable, happens fast, right as the tranny shifts.
When the tranny was rebuilt, do you know if the MLPS (Manual lever position sensor) was replaced or not?
I'd start with a quick visual inspection of the wires in the wiring harness from the solenoid pack at the trans itself, following them back up under the hood looking for pinched, snagged, burnt or a otherwise damaged section of the wires in it. Pay close attention to where it passes very near the front drive shaft.
Anyway, my truck was doing the same thing. I believe that it is in the torque converter, but as long as it doesn't get any worse than it is, I'll just live with it.
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Had I continued to listen to everyone I would have had the tranny replaced agian, as nothing else could be found wrong with it. Pay 28 hundred again? only to find it has the same problems once it was in?
Nope, no way was I accepting it needed a tranny again so soon, so I looked into it myself, basically doing what I paid those before me top dollar to do.
I always felt it was a electrical problem, made the motor run funny as well. Dogged it down slammed gears. Sifted up and down, shifted up into OD in a matter of a 100 feet and so on.
I bought a service manual for the tranny to go with the manual for the truck, then doing what I asked those before me to do I looked over the wiring harness and connections.
Found where the wire had been damaged near the front drive shaft. Repaired that damage and it has been fine since. Plowed snow again this winter with it, shifts fine, never misses a beat, never once puked fluid out the front seal (A new fan clutch corrected that issue).
Anyway that is why the first thing I suggest doing is checking the harness on these trucks. The use these trucks see, driving through fields and over brush and icy snow banks. Through the deeper water and mud, things a car doesn't do can and does subject the wiring to damage. From what I've read and seen first hand these trucks are kinda notorious for electrical problems to start with. Everything they do depends on good solid connections, something as simple as one bad wire can bring it to its knee's in a hurry.
Now I'm not suggesting the OP get under there and peal open and inspect every inch of every wire in the harness, just to look at the harness for signs of obvious damage. Then if needed, as needed test those wires for continuity. And no, not a cure all and it may not be the problem but it is certainly worth a quick look.
Replacing parts at random with no real proof they need replaced is not the answer, been there, done that......
My only saving grace was I had extra parts and another "working" truck to try parts off of for testing. I did have to buy a computer, luckily the bone yard gave me in store credit for its cost when I returned it when I found real quick it was not the problem.
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