Fatigue stress estimation of metro bogie frame through frequency response functions by using limited sensors

In this paper, the fatigue state estimation of the metro bogie frame is discussed based on limited sensors through frequency domain methods. The middle-frequency and high-frequency vibration fatigue damage cases of one metro bogie frame is discussed. The main excitations come from the wheel/rail interactions including wheel out-of-roundness and rail irregularities. The most common modal vibration of the bogie frame, where the transom bending deformation is dominant, is taken as the research object to study the possibilities of fatigue failure monitoring on concerned points of the bogie frame transom focusing on specific transfer paths. To eliminate unnecessary input signals which are not closely related to the occurrence of large stress amplitudes, the coherence analysis of different loads including the transmission load, carbody load and wheel-rail impact load is conducted through various methods including the short-time Fourier transform spectrum analysis, the magnitude-squared coherence analysis and the partial directed coherence analysis. Then the power spectral densities (PSDs) of the measured accelerations and cross power spectral densities (CPSDs) are calculated to obtain the transfer functions, whose output is the Y-axis stress at the concerned point. The stress PSDs are obtained using the instantly measured input accelerations and the prepared transfer function. Then the spectral moments and the stress amplitudes distribution functions are calculated through the frequency domain method to overcome the computational burden. The stress reconstructions based on inverse fast Fourier transform are analyzed and the fatigue damage results show good consistency with the experimental ones.