Vibration mechanism of an integrated underwater propulsion system based on an electromechanical rigid-flexible coupling model

Low-vibration design remains a critical challenge in underwater vehicle propulsion systems. Motor-gearbox integrated architectures improve power density but introduce strong electromechanical coupling due to motor excitation, gear meshing forces, and structural flexibility. This study proposes a novel bidirectionally coupled electromechanical rigid-flexible modeling framework for underwater propulsion systems. The model explicitly captures two-way interaction between electrical and mechanical domains, overcoming the limitation of conventional one-way or decoupled methods. Structural flexibility of the motor stator, gears, and motor-gearbox housing is incorporated using beam elements and substructure condensation. Experimental validation demonstrates that the proposed model achieves a vibration acceleration root mean square error of 8.9%, showing improved accuracy over conventional approaches. Results reveal that the 5th and 7th stator current harmonics and propeller excitation are the dominant coupled components. Furthermore, structural flexibility is found to weaken electromechanical coupling and reduce the transmission of inverter switching frequency into the mechanical system.