C650 CREW RPTS UNCOMMANDED ENG SHUTDOWN DURING DSCNT AT HIGH ALT. THEY ALSO RECEIVED AN 'UNSAFE GEAR' WARNING ON LNDG.

Narrative

ACFT WAS HANGARED PRIOR TO FLT. WX WAS CLR AND COLD WITH NO PRECIP. 9.1 HRS ON HOBBS METER. WALKAROUND AND ROTARY TEST WAS NORMAL. R-HAND ENG WAS STARTED FIRST; BUT EXPERIENCED CLASSIC NO LIGHT OFF CONDITION (A KNOWN ISSUE). ROTATION; BUT NO IGNITION; ITT OR FUEL FLOW. START WAS ABORTED. WE TURNED OFF PWR AND CHKED CIRCUIT BREAKERS IN THE COCKPIT AND AFT J-BOX. NO ECS LIGHTS. PWR WAS TURNED BACK ON AND L-HAND ENG WAS STARTED NORMALLY FOLLOWED BY THE R-HAND ENG STARTING WITH NORMAL INDICATIONS. WE TOOK OFF AND CRUISED AT FL430. FLT TIME WAS 3 HRS 18 MINS. ON APCH TO ZZZ; WE DSNDED THROUGH CLOUDS WITH ANTI-ICE ON. BROKE OUT OF CLOUDS AT 2000 FT AND ANTI-ICE WAS TURNED OFF. NORMAL LNDG. WE SHUT DOWN THE ACFT AND THEN FOUND OUT THEY WERE GIVEN THE WRONG FBO LOCATION. WE STARTED BOTH ENGS NORMALLY AND PROCEEDED TO THE CORRECT FBO. WE WERE ON THE GND FOR 2 HRS AT TEMPS JUST BELOW FREEZING WITH NO PRECIP. DEPARTING FOR ZZZ2 WE HAD 2 NORMAL STARTS AND ON TKOF WERE ABLE TO CLB THROUGH A THIN CLOUD LAYER THROUGH A HOLE AND DID NOT HAVE TO TURN ON ANTI-ICE. FLT TIME FOR LEG WAS 2 HRS 11 MINS WITH A CRUISE ALT OF FL430. APCHING ZZZ2; CTR HAD US DSND FROM FL430 TO FL410. WE SELECTED VERT SPD MODE OF DSCNT WITH A 500 FPM RATE AND SLOWLY ADJUSTED THROTTLES FOR SPD. WITHIN 2 MINS ATC CTR CLRED US FL370. WE THEN SELECTED VNAV MODE OF DSCNT WITH APPROX 2100 FPM AND ADJUSTED THROTTLES WITH A SLOW PULL BACK TO SET SPD. I PULLED THE THROTTLES BACK BUT NOT QUITE TO FLT IDLE. 10-20 SECONDS LATER THE 'R-HAND GENERATOR' ANNUNCIATOR LIGHTS UP WITH THE MASTER CAUTION AND AS I TURNED TO LOOK AT THE GENERATOR SWITCH AND AMP OUTPUT THE 'R-HAND LOW OIL PRESSURE' LIGHT COMES ON WITH THE MASTER WARNING. WE THEN LOOKED AT THE ENG GAUGES AND DETERMINED WE HAD LOST THE R-HAND ENG. MY COPLT RADIOS ATC CTR AND DECLARES AN EMER. WE ARE THEN CLRED TO FIX POINT AND 24K FT. WE PERFORM THE ENG FAILURE PRECAUTIONARY SHUTDOWN PROC TO SECURE THE ENG. WE THEN ASSESSED THE ENG PARAMETERS AND DETERMINED WE SHOULD TRY AN INFLT START. WE SLOWED THE ACFT TO 200 KTS AT 23K FT AND THEN PERFORMED A STARTED ASSIST INFLT ENG START PROC. THE START WAS SUCCESSFUL. MY COPLT THEN CALLED ATC CTR AND CANCELED THE EMER. THE APCH TO ZZZ2 WAS NORMAL WHICH MEANS THEY HAD MULTIPLE SPD AND PWR ADJUSTMENT BTWN FLT IDLE AND CRUISE SETTING. THE ENG PERFORMED NORMALLY. ADDITIONALLY; ON LNDG; WE HEARD 'LNDG GEAR' VOICE ANNUNCIATION MEANING WE HAD AN UNSAFE LNDG GEAR CONDITION. WE HEARD THAT WARNING AGAIN DURING THE TAXI IN AND OBSERVED A RED GEAR UNLOCKED ANNUNCIATOR AT THAT TIME. THE REST OF THE TAXI TO THE RAMP WAS UNEVENTFUL AND SHUTDOWN WAS NORMAL. THERE IS A RECENT HISTORY OF LNDG GEAR ACTUATORS UNLOCKING DURING TAXI DUE TO LOADS ON THE NOSE GEAR AND AT LEAST 1 INCIDENT OF A GEAR COLLAPSE IN SOUTH AFRICA. AFTER THE GEAR WARNING; I SHOULD HAVE STOPPED AND DEPLANED THE AIRPLANE AND ASKED TO HAVE THE ACFT TOWED TO PARKING. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE RPTR STATES THAT THIS WAS A NEW ACFT WITH LESS THAN 10 HRS. THE ENG MANUFACTURER IS SERIOUSLY INVOLVED IN TRYING TO FIND OUT THE REASON FOR THE ENG PROBS. THE START FAILURES AND INFLT SHUTDOWNS ARE PROBABLY RELATED. THE NOSE GEAR ACTUATOR AND R ENG FUEL CTL WERE CHANGED PRIOR TO A FERRY FLT BACK TO HOME BASE; WHICH WAS UNEVENTFUL.