Midshaft rating for turbomachine engines

A method of operating a turbomachine engine including a fan assembly, a high-pressure compressor, a high-pressure turbine, a high-speed shaft that couples the high-pressure compressor and the high-pressure turbine, and a combustion chamber that is in flow communication with the high-pressure compressor and the high-pressure turbine, a power turbine that is in flow communication with the high-pressure turbine, and a low-speed shaft that is coupled to the power turbine and the fan assembly, the method comprising:

• combusting fuel and air in the combustion chamber to generate combustion gases;
• driving the high-pressure turbine with the combustion gases;
• driving the high-pressure compressor with the high-pressure turbine via the high-speed driving the power turbine with the combustion gases;
• shaft;
• driving the fan assembly with the power turbine via the low-speed shaft;
• driving the low-speed shaft, wherein the low-speed shaft is characterized by a midshaft rating (MSR) between two hundred (ft/sec)1/2 and three hundred (ft/sec)1/2;
• and
• operating the turbomachine engine up to a redline speed without passing through a critical speed associated with a first-order bending mode of the low-speed shaft.