A CESSNA AT 2000 FT ON A TRAINING MISSION EXPERIENCES A NEAR MISS AND DURING EVASIVE ACTION INSTRUCTOR NOTES LACK OF L TURN CAPABILITY CAUSED BY FROZEN L INBOARD AILERON PULLEY BEARING.

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I WAS THE FLT INSTRUCTOR ABOARD C172. I HAD JUST COMPLETED SLOW FLT WITH MY STUDENT. I ASKED THE STUDENT FOR A R CLRING TURN. AS HE RAISED THE R WING; ANOTHER HIGH WING CESSNA WAS COMING IN HEAD-ON. I TOOK THE FLT CTLS AND IMMEDIATELY ROLLED THE PLANE HARD TO THE L. MY ACFT BARELY TURNED. THE OTHER ACFT TURNED AND WE MISSED BY LESS THAN 100 FT. I NOTICED IN THE L TURN MY RATE ON MY PLANE WAS INCORRECT. I FLEW TO X47 TO INSPECT. I NOTICED NOTHING WRONG ON THE GND. WE TOOK OFF FROM X47 AND OPTED TO TEST IT IN THE AIR. THE L TURN WAS BARELY THERE AND THE YOKE WAS VERY TIGHT. I RETURNED TO MY HOME ARPT OF DAB. MAINT INSPECTED AND FOUND A BAD BEARING ON THE PULLEY. MY CHIEF FLT INSTRUCTOR AGREED THIS WAS FLT CTL FAILURE. THE NTSB WAS NOTIFIED. I CONTACTED FAA SAFETY INSPECTOR AT THE MIAMI FIELD OFFICE. MR ABC AGREED THIS WAS A FLT CTL FAILURE SINCE THE ACFT WOULD NOT PROPERLY TURN. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATED IN EXECUTING MANEUVER DURING THE NEAR MISS EVENT IT WAS NOTED THE L AILERON WAS TIGHT AND INEFFECTIVE AND A VERY SLOW RATE OF TURN WAS ACCOMPLISHED. THE RPTR SAID A LNDG WAS MADE AND THE ACFT WAS GND CHKED BY THE RPTR AND STUDENT AND A DECISION WAS MADE TO FLY THE ACFT TO THE HOME STATION. THE RPTR SAID MAINT FOUND THE L AILERON INBOARD PULLEY BEARING FROZEN FROM LACK OF LUBRICANT.