Look at the part number of the coils in their catalog. If they are the same, the part numbers will be the same. Not likely between a Size 5 and a Size 6 in my opinion.
What exactly is the "solid state motor control"? Have a part number? It may be a Solid State Overload Relay and if that's the case, you may have killed it by applying 480V to it (if you did, not sure of what the circuit looks like from your description).
Causes of coil chatter (others will likely add to the list):
1) Low control circuit voltage. This can be the result of a voltage drop on the entire system from starting a 400HP motor X-Line. it could also be a bad or under sized control power transformer or a high resistance somewhere in the control circuit causing a voltage drop (distance, bad contact etc.) Being that you used a 480V coil and it didn't fix the problem, that would eliminate the bad CPT, but still could be something else, especially overall system voltage drop from X-Line starting. Coils on NEMA contactors typically have a drop-out voltage of 70% but as you approach it, they will sometimes chatter before dropping out completely.
2) Rapid cycling of a control circuit element. For instance, if you have something like a float switch or pressure switch in the circuit, usually you must have either a hysteresis in the device (difference between on and off state) or you need a "de-bounce" timer in there. Without something to prevent fluttering of the control element, you will toast the coil rapidly.
3) A mechanical jam or separation of the pole faces of the armature in the contactor. one that prevents the yoke from making full clean contact with the magnet face. Rust, debris, drill filings, insect carcasses, any little thing that prevents full mating of the faces can cause that.
4) Previous damage. It could be that you had a low voltage problem, that caused the initial coil fire, but that has now cause a slight alignment problem in those pole faces. The Sq. D 8536 starters use what is called a "Bell Crank" mechanism in the mechanical movement, that is why you feel it being difficult to push in only at the last part of the stroke. But any damage to any of those levers and fulcrums in that system may leave you with an incomplete close. In that case, toss the entire contactor and start over.
If it were me, I would junk the thing and replace it with a solid state soft starter. 400HP is too big a motor to be starting X-Line in my opinion.
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