A CANADAIR CL-65 IN CRUISE AT FL310 DECLARED AND EMER AND DIVERTED DUE TO AILERON TRIM RUNNING CONTINUOUSLY L AND R WING DOWN; CAUSE UNKNOWN.

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FLT FROM XXX TO ZZZ. WE PUSHED OUT OF XXX; ON PUSHBACK WE NOTICED THE ACFT TRIM WAS OUT OF NORMAL RANGE FOR TKOF. I TRIED TO PUT IT BACK IN LIMITS IT WOULD NOT CHANGE. SO WE CONTINUED WITH PUSHBACK NOT TO ALTER OUR ROUTINE. AFTER PUSHBACK WAS COMPLETE AND ENGINES WERE STARTED. WE TRIED TO CHANGE THE TRIM SETTING IT HAD NOT MOVED; IT HAD RUN TO FULL R WING DOWN SETTING DURING THE PUSHBACK. WE HAD NO MESSAGES ON THE EICAS OR ON FLT CONTROL PAGE. NOTHING IN THE QRH; WE CHECKED THE CIRCUIT BREAKERS. ALL OF THEM WERE IN. WE PULLED BACK INTO THE GATE; WHEN MAINT ARRIVED THEY NOTICED THE AILERON TRIM CB WAS OUT. (BUT IT WASN'T OUT WHEN WE STARTED TO PULL BACK INTO THE GATE.) HE RESET THE BREAKER. HE CONTACTED MX IN ZZZ. THEY INSTRUCTED US TO DEPOWER THE PLANE; WAIT 2 MINS AND TRY IT AGAIN. WE COMPLETED THIS TASK AND IT OPERATED NORMALLY. MX COMPLETED THE APPROPRIATE PAPER WORK AND WE DEPARTED. WE WERE KEEPING TRACK OF THE AILERON TRIM. IT SEEMED TO BE WORKING NORMALLY UNTIL ABOUT 80 NM DME OF AAA IT STATED TO RUN TO R WING DOWN FULL DEFLECTION. I DISCONNECTED THE AUTO PLT AND TRIED TO CONTROL IT WITH AILERON TRIM SWITCH. THE SWITCH WAS INEFFECTIVE (UNABLE TO CONTROL IT.) THE FO HAND FLEW THE ACFT. I CONTACTED MX WHO PROVIDED LITTLE ASSISTANCE; THEY WANTED US TO CONTINUE TO ZZZ. (THE CIRCUIT BREAKER WAS STILL IN.) I DECIDED TO CONTACT DISPATCH AND GET AN ALTN TO DIVERT TO WITH RWY'S FAVORABLE TO THE WINDS. THEY GAVE BBB AS THE CLOSEST. WE NOTIFIED DISP OF THE SIT; DECLARED AN EMER; AND PROCEEDED TO BBB WITHOUT FURTHER INCIDENT. THE FA AND PAX WERE NOTIFIED. UPON ENTERING THE TERMINAL AREA THE AILERON TRIM RAN FROM FULL R WING DOWN TO FULL L WING DOWN. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED THE CAUSE OF THE AILERON TRIM MALFUNCTION IS NOT KNOWN AS MAINT DID NOT ADVISE THE FIX. THE RPTR SAID BEFORE THE CREW LEFT THE AIRPLANE A PEDESTAL BOX WITH THE TRIM SWITCH WAS REPLACED AND IT TRIPPED THE CIRCUIT BREAKER. THE RPTR STATED THE AIRPLANE WAS THEN TAKEN OTS.