Two-speed epicyclic gearbox with clutch for aircraft propulsion system

A method of operating an aircraft propulsion system that includes a thermal engine, the method comprising:

• providing a gearbox that includes an input shaft, an output shaft, an epicyclic gear arrangement, a drive gear, and a first layshaft assembly, wherein the input shaft is driven by the thermal engine, wherein the epicyclic gear arrangement includes a sun gear, a plurality of planet gears, and a ring gear, wherein the sun gear is connected with the drive gear;
• operating a hydraulically actuated clutch system in a first mode or a second mode, wherein the hydraulically actuated clutch system includes a hydraulic coupling device engaged with the first layshaft assembly;
• wherein the first layshaft assembly extends along a first layshaft rotational axis and includes a first layshaft, a first layshaft input gear, and a first layshaft ring engagement gear, wherein the first layshaft ring engagement gear is engaged with the ring gear, and the first layshaft input gear is engaged with the drive gear and the input shaft;
• operating the hydraulically actuated clutch system in a first mode during a first flight segment by disposing the hydraulically actuated clutch system in an disengaged configuration wherein the first layshaft ring engagement gear is uncoupled with the first layshaft input gear;
• and
• operating the hydraulically actuated clutch system in a second mode during a second flight segment by disposing the hydraulically actuated clutch system in an engaged configuration wherein the first layshaft ring engagement gear is coupled with the first layshaft input gear.