GAS TURBINE ENGINE WITH A DUAL TOWERSHAFT ACCESSORY GEARBOX AND METHOD OF OPERATION

A gas turbine engine assembly (20) includes a first spool (32) having a first turbine (54) operatively mounted to a first turbine shaft (50), and a second spool (30) having a second turbine (46) operatively mounted to a second turbine shaft (40). The first and second turbines (54, 46) are mounted for rotation about a common rotational axis (A) within an engine static structure (36). The first and second turbine shafts (50, 40) are coaxial with one another. First and second towershafts (64, 66) are respectively coupled to the first and second turbine shafts (50, 40). An accessory drive gearbox (62) has a set of gears. A compressor (80) is driven by the first towershaft (64). The engine assembly (20) further includes a starter generator assembly (76), and a transmission (92) coupling the starter generator assembly (76) to the first set of gears. The transmission (92) is transitionable between a first mode where the starter generator assembly (76) is driven at a first speed relative to the second towershaft (66), and a second mode where the starter generator assembly (76) is driven at a different, second speed relative to the second towershaft (66).