Extraction of features of a specific signal in fluid-structure interaction is among the hottest problems in the field of mechanics. Yet, a comprehensive study of such problems remains a challenge due to their high nonlinearity and multidisciplinary nature. The study presented in this article is focused on a particular engineering application of fluid-structure interaction. The governing equation of a spinning rotor submerged in an incompressible viscous fluid is modelled by means of well-established dissipative energy principle, yielding a highly coupled 3-degree-of-freedom system with strong nonlinear terms. A two-dimensional model of the Navier-Stokes equations for the incompressible flow is developed for the viscous fluid motion around the spinning rotor under high fluctuations induced by unbalance, rotor-stator rub and a crack. The extracted features through frequency spectrum, orbit patterns and rotor-coupled deflection revealed that the performances of rotor systems are highly impacted by the hydrodynamic terms which are the sources of multiple frequency response. The results showed that the complex fluid-rotor model yields good analysis of fault diagnosis, and responses at more than one parametric resonance appear and reach a point of complex feature extractions when more than one fault coexists in the system. Furthermore, a nonlinear denoising by thresholding the wavelet coefficients is performed to overcome the complexity of discretization and for effective multiple fault diagnoses.

This paper presents a theoretical and experimental analysis of a coupled lateral and torsional vibrations of two identical rotors interconnected by a flexible Hooke's joint and modelled as a multibody system with a small misalignment angle. Using energy principle and a Lagrangian transformation, the governing equation of the propeller shaft system is established by considering a nonlinear elastic shaft time-dependent perturbation. To study the sensitivity of the crack for a rotating shaft, the model is enriched by considering the periodical feature of the time-varying stiffness deriving from the crack breathing model. The nonstationary response of a cracked rotor system in the presence of unbalance has been evaluated using orbit patterns and Fast Fourier Transform. The highly oscillated feature of the rotors system is theoretically obtained and experimentally analysed. The analysis demonstrated that the crack parameters in the input shaft tend to inhibit the occurrence of unstable oscillations in lateral deflection, orbit and frequency spectrum of the secondary response. It is also found that the passage of the cracked primary shaft near to an integral multiple of the critical speed leads to the phenomenon of sup-harmonic resonance. Subsequently, the experimental analysis conducted equally indicated that the quantitative relation between the faults and the performance of the transmission is impacted by the time-varying stiffness and is the main cause of the frequency-modulated feature in the Cardan shaft system. Finally, the experimental results were informative for the transient response exploration and comparable to the theoretical findings for validating the proposed twin-rotor model.

The vibrational behaviour of misaligned rotating machinery is described and analysed in this paper. The model, constructed based on the equations of vehicle dynamics, considered the dynamic excitation of a single Hooke’s joint. The system adopted the breathing functions from a recent publication to approximate the actual breathing mechanism of a cracked driveshaft. The study aimed to understand the transmission of a nonlinear signal from the unbalanced and cracked driveshaft to an unbalanced driven shaft via a Hooke’s joint. The governing equation of the system was established based on the energy principle and the Lagrangian approach. The instantaneous frequency (IF) identification of the cracked driveshaft was extracted based on the synchrosqueezing wavelet technique. To correlate the results, the nonlinear synchrosqueezing wavelet transforms combined with the classical waves techniques were experimentally used in various scenarios for dynamic analysis of the Cardan shaft system. The variations in the dynamic response in the form of a rising trend of higher harmonics of rotational frequency and increased level of sub-harmonic peaks in both shafts were presented as significant crack indicators. The synchrosqueezing response showed breathing crack excitation played a crucial role in the mixed faults response and caused divergence of the vibration amplitudes in the rotor’s deflections. The simulation and test results demonstrated that the driveshaft damage features impacted the transfer motion to the driven shaft and the Hooke’s joint coupling was the principal source of instability in the system. The proposed model offers new perspectives on vibration monitoring and enhancement analysis to cover complex Cardan shaft systems.

Dynamic analysis of a combination of misaligned rotors, the disturbance of the Cardan joint and the rotor–stator rubbing within a restricted clearance space in a viscous fluid is complex and can result in persistent vibration anomalies that are often misunderstood. It becomes increasingly important to gain some insights into how the transmission of coupled motion responds dynamically under a variety of conditions. This paper introduces an efficient simulation of the misaligned multi-degree-of-freedom rotor’s model, which was developed to predict the transient dynamic behaviours of a driveshaft deflection. The model accounts for tight clearance as a function of contact deformation according to nonlinear Hertzian contact theory. The paper also examines recent research by considering the influence of parameters such as eccentric masses, applied torques and flexible coupling joint perturbation introduced in the proposed rotor system. The simulation results indicated that the viscous fluid surrounding the driveshaft had sufficient torsional flexibility to dampen the rubbing impact to the driven shaft displacement. In addition, the torsional fluctuations of the flexible coupling abruptly increased, and then significantly impacted the vibration of the submerged driveshaft. Parametric studies involving the interconnected rotor models indicated that the effects of fluid on a close-bounds contact area can create partial disturbance reduction. The high rubbing contact is shown to be lost through the Hooke’s joints during power transmission. The speed-frequency spectrum maps provide valuable information on all the modelled excitations over the frequency of the twice-running speed resonance in a viscous medium. Further, nonlinear characteristics are reconstructed through orbit shapes and can be adopted in the condition monitoring of rotors in engineering practice.

This paper presents the recent application of the scalogram of Continuous Wavelet Transform (CWT) as a vibration monitoring and signal processing tool for a rotor dynamic response under parametric excitation. The experimental test data of coupled lateral-torsional vibrations of a rotor-stator system with transverse crack was obtained through a data acquisition setup interfaced with Rotor-Kit-4 (RK-4). Analysis was executed on rotor deflection, orbit, frequency and time-frequency spectrum of the RK-4 experimental data. The scalograms of CWT were used experimentally to represent the aperiodic occurrence of rub between the rotor-stator and crack features. Variation in 3-D scalogram peaks in the presence of rub and crack were unique and were used to distinguish quasi-periodic motion from other types of motion. An unbalanced cracked rotor gave a higher frequency amplitude response compared to an unbalanced rotor with rub under the same conditions. Irregularities in orbit orientation near sub-harmonic resonances were observed in the test data. Multiple rebounds inside the orbit loop were unique rub indicators. Conspicuous horizontal components of the higher harmonics were observed near the critical speed when a crack existed. CWT established inherent feature patterns that discriminated unbalance, rub and a crack.