I have a 03 F150 that is surging only when warm. When I have it in park or stopped with my foot on the brake, it will speed up and die down eventually killing the engine. It has a 4.6 liter Triton
Try the easiest and less expensive first. Remove the throttle body and IAC and clean completely with throttle body cleaner. Check for a vacuum lean. Check the PCV valve.
Sounds like an issue with phasers. 2003 came with phaser system which adjustes the timing as you accelerate or decelerate, if your oil pressure drops it will do that even though ur pressure gage doesn't detect it because there's enough pressure to keep the gage happy but not enough to actuvate your phaser system. Check oil pressure with an actual gage the the oil filter base. Try decelerating slowly when you get to a stop and you'll notice it'll won't miss as bad.
Update: I recently had the truck in the shop and they determined my idle control modual was bad! They also said the egr solenoid was also bad so I had them replaced but this morning it it started right up and ran down the highway fine but when I came to a stop in our parking lot and shifted into reverse the engine reved up to 800 rpms then back to 300 and died! It did this to me three times! Also the check engine light is on again so I dropped it off at the shop and told them to search further! It has to be another vacuum leak is what I'm thinking!
I still think it's the phasers. Only happens when it's warmed up and on deceleration. Ur loosing oil pressure and it can't adust the timing as it's supossed to. Let me know what they find. They'll probably tell it's the timing chains
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