Rotating machines are commonly used in the industry e.g., gas turbines, and centrifugal machines in the process industry and clinical laboratories. The undesired or self-excited vibrations are usually caused by mass imbalance, misalignment, and variations of manufacturing tolerances in these machines which can cause fatigue or failure of the system. Therefore vibration suppression and fault detection are vital tasks that require non parametric, or parametric system models such as a state-space representation.

In this study, we utilize the Observer/Kalman Filter Identification (OKID) and the Eigensystem Realization Algorithm (ERA) to identify the modal parameters of a high-speed, centrifugal machine. The modal parameters include frequencies, damping, and mode shapes of the machine. The Observer/Kalman Filter Identification (OKID) is formulated entirely in the time domain and is able to handle general response data. The Eigensystem Realization Algorithm (ERA) was developed for modal parameter and model reduction of dynamic systems using test data. The combined OKID/ERA techniques have been successfully applied to the identification of flexible space structures such as the Space Shuttle remote manipulator and Hubble space telescope but to the best of authors' knowledge, not on high-speed, centrifugal machines. To this end, we use an experimental setup to generate random input-output measurements that are corrupted by noise. Then we utilize OKID to determine the system Markov parameters. The obtained Markov parameters are validated by finding the inverse Fast Fourier Transform (IFFT) of the frequency response functions (FRFs). The Hankel matrix of the system is determined based on the Markov parameters. The order of the system can be determined by examining the singular values of this matrix. After that, we construct a minimum-order realization using a shifted block Hankel matrix. Then we determine the eigensolution of the realized state matrix and we transform the realized model to modal coordinates where the system damping and natural frequencies are calculated. The modal amplitude coherence and mode singular values are evaluated to quantify the system and noise modes.

The derived model describes the lateral vibration of a vertical-shaft, high-speed centrifugal laboratory machine. We validate the model by comparing it with a standard identification method such as the subspace state-space system identification (N4SID). Furthermore, we compare the critical speeds predicted by the developed model with the frequency response functions of the system. The results confirm that OKID/ERA is a reliable time-domain method for identifying the modal parameters of this type of centrifuge machines. The identified state-space realization can be used for designing active or passive vibration control systems as well as fault detection in a centrifuge machine.


An Eigensystem Realization Algorithm for Modal Parameter Identification of a Vertical-Shaft High-Speed Centrifugal Machine

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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