FLT CREW OF B737-300 NEED TO RETURN TO DEICE PAD TO BE DEICED A SECOND TIME AFTER ENG VIBRATION INDICATORS REVEAL PRESENCE OF ICE ON THE FAN BLADES.

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AFTER A LONG DELAY AFTER PUSHBACK DUE TO WAITING FOR DEICE; WE RETURNED TO GATE TO DEICE THE ENGS AFTER ENG #2 HAD HIGH VIBRATION INDICATION DURING ENG RUN-UP PRIOR TO TKOF. I FAILED TO REALIZE THAT ICING CONDITIONS EXISTED AS VISIBILITY WAS 1.5 MI AND NO PRECIP WAS VISIBLE TO US IN THE COCKPIT. I WAS VERY CONSCIOUS OF WHAT HAPPENED LAST OCTOBER AND BELIEVE THE DAMAGED ENGS WERE DUE TO ICE ON BACK OF BLADES PICKED UP ON APCH THAT WAS NOT REMOVED BEFORE DEP. WITH THIS IN MIND; I SPOKE WITH GATE DEICE PERSON AND ALSO WENT OUT TO CHK BOTH ENGS TO MAKE SURE ICE WAS GONE BEFORE WE PUSHED. AT THE TIME I WENT OUTSIDE I FELT NO PRECIP BUT WE HAD TO BE DEICED AT THE PAD DUE TO STRUCTURAL ICE PICKED UP INBOUND. THERE WERE 8 OR SO PLANES AHEAD OF US AS WE GOT IN LINE. 2 OTHER AIRPLANES ON RAMP FREQ DECLINED DEICING AND THIS REINFORCED THE IDEA THAT ANY SIGNIFICANT FREEZING DRIZZLE/DRIZZLE HAD STOPPED. STILL NOT SEEING ANY DRIZZLE I DID THINK ABOUT DOING ENG RUN-UP ANYWAY; BUT I WAS CONCERNED ABOUT JETBLAST. INSTEAD I SNUCK THE ENG UP TO 50-55% PERIODICALLY AS THE LINE MOVED WHICH I SHOULD HAVE KNOWN WAS NO HELP AT ALL. WE HAD ONLY ENG #2 RUNNING FOR THE TAXI OUT. WE HEARD NO OTHER ACFT IN LINE ASKING TO CLR FOR RUN-UP WHICH ALSO MADE ME THINK WE WERE OK. AFTER ABOUT 45-50 MINS WE ARRIVED AT DEICE PAD. WE STARTED #1 ENG BEFORE PULLING INTO PAD. DEICE TOOK 20-25 MINS AND WE TAXIED TO RWY 25. DURING RUN-UP BEFORE TKOF; ENG #2 VIBRATION SLOWLY ROSE UP TO 4.0 OR MORE SO WE CLRED RWY AND CALLED DISPATCH AND MAINT CTL. THE FO ADVOCATED TRYING ANOTHER LONGER RUN-UP TO CLR THE ICE. HOWEVER; I WAS NOW CONCERNED ABOUT POSSIBLE ENG DAMAGE SHEDDING THE ICE. ALTHOUGH OUR CONNECTION WITH MAINT WAS NOT CLR; I DID GET THE IDEA HE ALSO PREFERRED A RETURN FOR DEICING. OUR RETURN RAISED MUCH CONCERN WITH THE DEICE PEOPLE. I DID ADMIT WE DID NO REAL ENG RUN-UPS BEFORE THE RWY AND DID TRY TO CONVINCE THEM IT WAS MY ERROR AND CONDITIONS WEREN'T THAT BAD. ENG #1 ALSO HAD ICE ON SPINNER EVEN THOUGH IT WASN'T STARTED UNTIL WE WERE ENTERING DEICE PAD. THEY NOTED NO DAMAGE TO EITHER ENG. AFTER SOME TIME WE WERE ALLOWED TO PUSH AGAIN. THIS TIME WE DID 2 RUN-UPS BEFORE DEICE AND 1 AFTER. I WAS SURPRISED TO SEE THAT ONLY 13 MINS AFTER ENG START WE DID SEE VIBRATION RISE TOWARD 3.0 ON BOTH ENGS AND FINALLY DROP BACK AFTER 20+ SECONDS ABOVE 70%. DURING THE SECOND RUN-UP IT TOOK 73-74% TO SHED ICE. I ALSO CLOSELY LOOKED AT BOTH ENGS AFTER ARR AND SAW NO DAMAGE. I'M SORRY I RELIED TOO MUCH ON WHAT I SAW OUT THE WINDOW; WHAT I FELT ON MY FACE; AND MY PAST EXPERIENCE; INSTEAD OF WHAT WAS ON PAPER AND WHAT IS EXPECTED OF ME. I ALSO SHOULDN'T HAVE BEEN TOO TIMID TO MAKE WAVES TO DO MY JOB.