An efficient approach for predicting resonant response with the utilization of the time transformation method and the harmonic forced response method

Resonant response of turbomachinery blades can lead to high cycle fatigue (HCF) if the vibration amplitudes are significant. Therefore, the dangerousness assessment of the resonance crossing is important. It requires accurate predictions of the aerodynamic excitation, damping, and response, which will consume immense computational costs. The novel aspect of this study is the development of an efficient approach, which incorporates the time transformation (TT) method to predict the aerodynamic excitations and the harmonic forced response method to obtain the response levels. The efficiency and accuracy of this method were evaluated by comparing with traditional methods for the resonance crossing excited by upstream wake in a 1.5 multistage compressor. For the aerodynamic excitation, discrepancies of ±2% at the mean pressure and ±25% at the harmonic pressure in most areas expect for the blade root were observed, but the calculation time required by the TT method was only 5% of that by the time-marching method. Moreover, response levels with the same aerodynamic forces were compared between the harmonic forced-response and transient dynamic methods. Small differences in the displacement and stress variables were observed; the relative deviation was smaller than 2% with only 1% computing time compared with the transient method, indicating the high accuracy and efficiency of the efficient approach.