What was found
ON THE AFTERNOON OF 6-4-2021, DEPARTING OUT OF KMDQ AND HEADING TO KBJC, THE CREW FELT A SLIGHT VIBRATION THROUGHOUT THE AIRPLANE PROGRESSIVELY GETTING WORSE. NO ABNORMAL INDICATIONS WITH ANY OF THE AIRCRAFT SYSTEMS WAS NOTED. THEY DECIDED TO DIVERT INTO KMEM WHERE THEY LANDED SAFELY. THE VIBRATION WAS STILL PRESENT ON THE GROUND WITH ENGINES RUNNING. ON THE GROUND THE CREW COMPLETED THEIR "WALKAROUND" AND NOTICED THE RH ENGINE COWLING HAD BLACK SOOT EXITING FROM THE STARTER/GENERATOR COOLING DUCT EXIT. MAINTENANCE WAS DISPATCHED FROM EL PASO WITH A NEW STARTER/GENERATOR AND INSTALLED IT ONTO THE AIRCRAFT. ENGINE RUNS COMPLETED, NO VIBRATIONS NOTED. THE CREW CONTINUE THEIR FLIGHT INTO KBJC WITH NO OTHER ISSUES/VIBRATIONS NOTED.