DEPARTING VFR ON A VECTOR FROM PWK; IL; A COLLISION AVOIDANCE MANEUVER DIRECTED BY A COLLISION AVOIDANCE SYS RESULTS IN UNAUTH ENTRY INTO OVERLYING CLASS B AIRSPACE.

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DEPARTED FROM PWK (VFR) TO PICK UP AN IFR FLT PLAN OVER GRR. THE ASSIGNED RWY WAS RWY 16. I DEPARTED UNDER PWK TWR CTL AND WAS ASSIGNED AN APPROX 90 DEG HDG; DIRECT GRR. KNOWING THAT THIS RWY FACED CHICAGO'S O'HARE AIRSPACE; I ATTEMPTED TO CONTACT CHICAGO DEP CTL IMMEDIATELY AFTER DEP ON THE CORRECT FREQ. CHICAGO RESPONDED THAT IF I WAS VFR THEY WERE TOO BUSY TO TALK TO ME. SHORTLY THEREAFTER; I RECEIVED A COLLISION AVOIDANCE WARNING FROM MY SYS. I RESPONDED WITH EVASIVE ACTION THAT ENTAILED A CLB. I DECIDED TO CLB SINCE I HAD JUST DEPARTED AND WAS RELATIVELY CLOSE TO THE GND OBSTRUCTIONS (APPROX 1000 FT AGL). THIS CLB INADVERTENTLY PLACED ME INTO CHICAGO'S CLASS B AIRSPACE. SHORTLY AFTER THE FIRST COLLISION AVOIDANCE WARNING; I RECEIVED ANOTHER AND YET ANOTHER. I RESPONDED BY CLBING AND THEN A CLBING TURN AWAY FROM THE TFC. BOTH SUBSEQUENT CLBS PUT ME FURTHER INTO CHICAGO'S CLASS B AIRSPACE. IN MY 9 YRS OF FLYING I HAVE NEVER PENETRATED ANY AIRSPACE WITHOUT PROPER CLRNC. MY HOME BASE; HAS KENNEDY'S CLASS B DIRECTLY ABOVE IT. THEREFORE; I AM KEENLY AWARE OF OPS IN AND AROUND CLASS B AIRSPACES. FURTHERMORE; I HAVE FLOWN INTO PWK DOZENS OF TIMES WITHOUT INCIDENT. I FEEL I WAS FORCED INTO PENETRATING CLASS B AIRSPACE BY A SEQUENCE OF CIRCUMSTANCES BEYOND MY CTL. THE CONCLUSION I HAVE COME TO IS THIS: IF DEPARTING VFR FROM A RWY THAT WILL FACE ME INTO AN AIRSPACE; REQUEST A DOWNWIND DEP THAT WILL ALLOW A 180 DEG TURN AWAY FROM THAT UPCOMING AIRSPACE. I WOULD RECOMMEND THIS AS AN ESTABLISHED PROC AT PWK.