A PA34 INSTRUCTOR PLT AND STUDENT EXPERIENCE A NOSE GEAR COLLAPSE DURING THEIR 4TH TOUCH-AND-GO AT AZO; MI.

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WE WERE ON OUR 4TH TOUCH-AND-GO. I WAS THE STUDENT IN THE L SEAT AND MY INSTRUCTOR WAS IN THE R. WE WERE LNDG ON RWY 17. ON DOWNWIND; MY INSTRUCTOR FAILED THE R ENG. THEN WE WENT THROUGH THE NORMAL ENG SHUTDOWN PROC; BUT DID NOT FEATHER THE R ENG. MY INSTRUCTOR PUT THE ENG IN SIMULATED FEATHER. WE TURNED BASE; PUT IN 25 DEGS OF FLAPS. TURNED FINAL; PUT THE LNDG GEAR DOWN AND GOT 3 GREEN LIGHTS AND THE NOSE GEAR IN THE MIRROR. THEN I DID A GUMPS CHK. GAS -- ON; UNDERCARRIAGE -- 3 GREEN 1 IN THE MIRROR; MIXTURE FULL FORWARD; PROPS FULL FORWARD. WE THEN TOUCHED DOWN ON RWY 17. WE WERE ROLLING OUT AND MY INSTRUCTOR BROUGHT UP THE FLAPS. THROTTLES WERE STILL AT IDLE. THEN WE SAW THE NOSE START DROPPING. THEN WE VEERED OFF TO THE L; THEN STARTED SLIDING ON THE BELLY OF THE ACFT. WE STARTED SLIDING SIDEWAYS AND THEN CAME TO A STOP AT THE INTXN OF RWY 17 AND RWY 27. WE TOLD TWR WE HAD A PROB. THEN MY INSTRUCTOR SHUT DOWN ALL OF THE ELECTRICAL. I SHUT DOWN ALL OF THE MAGNETOS AND WE GOT OUT OF THE ACFT. I THINK THIS WAS A SYS FAILURE. WE VERIFIED WE HAD 3 GREEN AND 1 IN THE MIRROR TWICE BEFORE WE LANDED. SUPPLEMENTAL INFO FROM ACN 468184: WHAT CAUSED THE NOSE TO COLLAPSE ON THE ROLLOUT IS UNKNOWN AT THIS TIME. ALL PRECAUTIONS TO VERIFY GEAR DOWN AND LOCKED WERE TAKEN.