Localization of breathing cracks in stepped rotors using super‐harmonic characteristic deflection shapes based on singular value decomposition in frequency domain

Abstract

An output‐only multiple‐crack localization method is proposed in this paper to detect and localize breathing cracks in a stepped rotor, which utilizes the crack‐induced local shape distortions in super‐harmonic characteristic deflection shapes (SCDSs). To minimize the noise effects on SCDSs and improve the accuracy of SCDS‐based crack localization, singular value decomposition is adopted to estimate the SCDS as the dominant singular vector of output power spectral density matrix at a super‐harmonic frequency. Then, in order to better reveal shape distortions in the SCDSs, an after‐treatment technique called gapped smoothing method is applied to derive a damage index. Numerical experiments are carried out to investigate the performance of the proposed method based on a two‐disc stepped rotor‐bearing system with breathing cracks established by the finite element method. Results show that the method is effective for single and multiple crack localization in stepped rotors and interference of steps can be excluded. Furthermore, the method is robust to noise. Influences of crack depths and rotating speeds are also investigated, and how to choose the rotating speed for better crack localization is discussed.

Crack localization in stepped rotors based on Bayesian fusion of multiscale superharmonic characteristic deflection shapes

“…The concept of SCDSs was defined in a previous work 34 of the authors, but for the convenience of understanding this current paper, the concept will be briefly introduced first. Let y i be the response from sensor i , then the system response matrix Y can be constructed by the simultaneously measured responses from the n distributed sensors along the shaft: where m is the length of each response.…”

“…With SCDS obtained by frequency domain decomposition, the crack localization can be accomplished by amplifying the distortions via evaluating the curvature of SCDS or the after‐treatment methods such as gapped smoothing method (GSM), which is proposed for crack localization in rotating rotors with steps in the authors' previous work 34 . However, robustness of this method is still an unsolved issue to be addressed.…”

“…The cracked element is shown in Figure 1B, and its stiffness matrix is derived from linear fracture mechanics with crack closure line position (CCLP) method 36 . By assembling the matrices of the cracked elements and uncracked elements, the motion equation of the rotor in the stationary coordinate system can be constructed as where M is the system mass matrix, D = a M + b K is the system Rayleigh damping matrix, Ω is the rotating frequency, D g is the system gyroscopic matrix, K ( t ) is the system stiffness matrix which is time varying with the crack breathing, F u is the unbalance excitation force vector, F g is the gravitational excitation force vector, F ex is the external excitation force vector and q is the displacement vector of n nodes which can be expressed as Here, q i is the displacement vector of node i : The detailed expressions of the variables were presented in the authors' previous paper 34 …”

A Super-Harmonic Feature Based Updating Method for Crack Identification in Rotors Using a Kriging Surrogate Model

“…In order to analyze the characteristics of a two-disc rotor with a breathing crack, the finite element method is adopted to establish the model, in which the breathing crack is simulated by the CCLP (crack closure line position) breathing model proposed by Darpe et al [55]. Since the method has been elaborated in the previous work by the authors [56], here, for the conciseness of the paper, the modelling procedure will just be briefly introduced. Further, validation of the established model is carried out by modal experiment and comparison with previous published work.…”

“…Figure 1 shows the two-disc cracked circular rotor-bearing system, the cracked shaft element, and the finite beam element model. To establish the model of the cracked rotor, the key point is to model the crack appropriately and calculate the stiffness matrix of the crack element that can be calculated by the strain energy release rate approach [56]. After that, through assembling the cracked and un-cracked elements, the finite element model of the rotor can be obtained.…”