A harmonic balance method combined with AFT and model reduction for parameter sensitivity analysis of shaft-hull-bearing systems

This paper presents a harmonic balance method integrated with the alternating frequency/time domain (AFT) method and model reduction to facilitate rapid parameter sensitivity analysis, which is subsequently applied to the optimization of structural and assembly parameters in the shaft-hull-bearing system. A dynamic model of the shaft-hull-bearing system, comprising 98 degrees of freedom (DOFs), is established using the finite element method. To obtain a semi-analytical solution with 8 DOFs, the proper orthogonal decomposition (POD) method and the harmonic balance alternating frequency/time domain (HB-AFT) method are employed. The results demonstrate that the reduced system effectively captures the major dynamic features of the original system, including its curve trends and amplitude variations. Building upon these methods, the sensitivities of the system parameters are rapidly analyzed, achieving a calculation time 5 times faster than that of the Runge–Kutta method. The analysis reveals that bearing stiffness and motor mass distribution significantly influence the shaft-hull-bearing system’s dynamic behavior. Changes in these parameters can have a substantial impact on dynamic characteristics, particularly concerning vibration modes and frequency response. Furthermore, to validate the accuracy of the theoretical methodology, a schematic diagram and an experimental platform for the shaft-hull-bearing system were designed and fabricated. The excellent computational efficiency and nonlinear processing capability underscore the potential of the model reduction combined with the HB-AFT method for rapid parameter sensitivity analysis for high-dimensional systems.