TRANSMISSION AND METHOD FOR CONTROL OF BOOST SPOOL

A gas turbine engine (10) includes a first spool (16) associated with a primary combustor (70), a second spool (12) associated with a secondary combustor (84), and a third spool (14), each spool (12) including a compressor (24, 74, 18) and a turbine (26, 82, 20) mounted to a shaft (28, 76, 22). A transmission (400) and accessory gearing (402) are enclosed within a housing (420) of an accessory gearbox (422). The transmission (400) rotationally couples the third spool (14) to the second spool (12) and accessory gearing (402). A method of operating the gas turbine engine (10) includes supplying a first fuel flow rate to the primary combustor (70) and supplying a second fuel flow rate to the secondary combustor (84) within an intermediate speed range of the gas turbine engine (10).