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The rotor misalignment fault, which occurs only second to imbalance, easily occurs in the practical rotating machinery system. Rotor misalignment can be further divided into coupling misalignment and bearing misalignment. However, most of the existing references only analyze the effect of coupling misalignment on the dynamic characteristics of the rotor system and ignore the change of bearing excitation caused by misalignment. Based on the above limitations, a five degrees of freedom nonlinear restoring force mathematical model is proposed, considering misalignment of bearing rings and clearance of cage pockets. The finite element model of the rotor is established based on the Timoshenko beam element theory. The coupling misalignment excitation force and rotor imbalance force are introduced. Finally, the dynamic model of the ball bearing-coupling-rotor system is established. The radial and axial vibration responses of the system under misalignment fault are analyzed by simulation. The results show that the bearing misalignment significantly influences the dynamic characteristics of the system in the low-speed range, so bearing misalignment should not be ignored in modeling. With the increase of rotating speed, rotor imbalance and coupling misalignment have a greater impact. Misalignment causes periodic changes in bearing contact angle, radial clearance, and ball rotational speed. It also leads to reciprocating impact and collision between the ball and cage. In addition, misalignment increases the critical speed and the axial vibration of the system. The results can provide a basis for health monitoring and misalignment fault diagnosis of the rolling bearing-rotor system.

This paper proposes a barrier function adaptive non-singular terminal sliding mode controller for a six-degrees-of-freedom (6DoF) quad-rotor in the existence of matched disturbances. For this reason, a linear sliding surface according to the tracking error dynamics is proposed for the convergence of tracking errors to origin. Afterward, a novel non-singular terminal sliding surface is suggested to guarantee the finite-time reachability of the linear sliding surface to origin. Moreover, for the rejection of the matched disturbances that enter into the quad-rotor system, an adaptive control law based on barrier function is recommended to approximate the matched disturbances at any moment. The barrier function-based control technique has two valuable properties. First, this function forces the error dynamics to converge on a region near the origin in a finite time. Secondly, it can remove the increase in the adaptive gain because of the matched disturbances. Lastly, simulation results are given to demonstrate the validation of this technique.

In the research on rolling bearing misalignment, the influence of bearing misalignment on the vibration characteristics of the rotor system is rarely considered, especially for the dynamic bearing misalignment. Based on the limitations of the existing research, a five-degree of freedom (5-DOF) nonlinear force model considering bearing misalignment is proposed firstly. The model comprehensively considers the parallel and angular misalignment, static and dynamic misalignment, inner ring and outer ring misalignment. Secondly, the effects of misalignment on the dynamic contact characteristics of bearing and the vibration characteristics of the rotor system are analyzed. Then, based on the dynamic response, the evaluation indexes of bearing misalignment are given. Finally, the similarities and differences between parallel and angular misalignment, static and dynamic misalignment are compared. The results show that the bearing misalignment increases the resonance speed of the rotor, and the amplitude jumping phenomenon appears in the resonance region, showing the characteristics of hardening-type nonlinearity. In terms of frequency characteristics, dynamic parallel misalignment and dynamic angular misalignment increase the amplitude of frequency components f r and 2 f r , respectively. The research can be used as a theoretical basis and valuable reference for fault identification of the rotor-bearing system.

Multi-rotor system (MRS) wind turbines can be a competitive alternative to large-scale wind turbines. In order to address the structural behavior of the turbine tower, an in-house aeroelastic tool has been developed to study the dynamic responses of a 2xNREL 5MW twin-rotor configuration wind turbine. The developed tool has been verified by comparing the results of a single-rotor configuration to a FAST analysis for the same simulation conditions. Steady flow and turbulent load cases were investigated for the twin-rotor configuration. Results of the simulations have shown that elasticity of the tower should be considered for studying tower dynamic responses. The tower loads, and deformations are not straightforward with the number of rotors added. For an equivalent tower, an additional rotor will increase the tower-top deflection, and the tower-base bending moment both in the fore-aft direction will be more than doubled. The tower torsional stiffness becomes a crucial factor in the case of a twin-rotor tower to avoid a severe torsional deflection. Tower natural frequencies are dominant over the flow conditions in regards to the loads and deflections.

This paper proposes a novel cylindrical conformal contact model for the large-diameter bearing with small clearance to its housing in aero-engines. Since the clearance between them is usually below one-thousandth of the bearing nominal diameter, Hertz’s law is not feasible in this case. The proposed contact model accounts for the surface contact condition and more geometric parameters of the bearing-housing component to obtain more accurate prediction results, which are validated by the finite element method (FEM) results. Based on this novel contact model, the vibration response of a single-disk rotor introduced by Ishida et al. is investigated. Numerical results are in good agreement with experimental results by Ishida et al. Influences of several critical parameters on the vibration responses are also studied. Furthermore, a complex dual-rotor system whose front bearing has a clearance stop between the outer ring and housing is analyzed with the proposed model. Good agreement is shown in the comparison between numerical and experimental results, which shows the feasibility of the proposed model in the contact simulation of large-diameter bearings with a small clearance. The results show that periodic collision between the bearing and housing could lead to self-excited vibrations. A natural frequency component in frequency-domain responses is an important indicator for the occurrence of self-excited vibration. This work provides a reference for the fault diagnosis of practical rotor-bearing systems with bearing clearance.

Three-point contact ball bearings (TPCBBs) belong to the main bearings of aeroengines. Their contact state will change significantly with external forces, which will affect the nonlinear vibration responses of rotor systems. This paper presents a quasi-static model for a 5-DOF TPCBB, taking into account various external conditions. Using the structure of a certain aeroengine as a reference, both the TPCBB’s quasi-static model and a cylindrical roller bearing model are introduced into the dynamic model of the TPCBB-rotor system. An innovative solving method, which combines the Newton–Raphson method and the Newmark-HHT method, is proposed. The solving method is used to analyze the acceleration responses, displacement responses, and contact forces of the TPCBB-rotor system with varying axial and radial forces. Furthermore, the validity of the proposed model is verified by a comparison of simulation and experimental results. The results indicate that the three-point contact state and the two-point contact state of the TPCBB will switch with the change of axial and radial forces. Compared with the three-point contact state, the acceleration amplitude and displacement amplitude of the system in the two-point contact state are smaller. And the contact forces between the balls and one of the inner rings will become 0 N.

The bearing-rotor system of a multi-shaft air separation centrifugal compressor becomes complex due to gear coupling interactions, necessitating the establishment of a dynamic characteristic analysis model that meets engineering practicality. This study focuses on an actual multi-shaft unit in an air separation system, constructing a bending vibration characteristics model for a complex multi-stage gear-bearing-rotor system. The model incorporates the effects of time-varying meshing stiffness, bearing stiffness, and unbalanced masses. Unbalanced response analyses of the rotor system were conducted under two conditions: with and without consideration of gear meshing stiffness. The actual unit’s vibration characteristics test bench was developed, and vibration and critical speed tests were performed. The results indicate the minimal influence of meshing stiffness on the rotor’s unbalanced response for the multi-shaft air separation system with a double-overhung gear-coupled rotor configuration. This is attributed to the fact that the gear meshing interface corresponds to the first-order bending mode, whose modal frequency lies outside the operational speed range. Critical speed test data closely align with numerical simulations, demonstrating that the proposed modeling methodology effectively characterizes the bending vibration behavior of the double-overhung multi-shaft gear-rotor system. These findings provide critical data support for the design and safe operation of complex multi-shaft units.

This paper focuses on the nonlinear response characteristics of an aero engine dual-rotor system coupled by the cylindrical roller inter-shaft bearing. The motion equations of the system are formulated considering the unbalance excitations of the two rotors, vertical constant forces acting on the rotor system and the gravities. By using numerical calculation method, the motion equations are solved to obtain the nonlinear responses of the dual-rotor system. Accordingly, complex nonlinearities affected by the bearing radical clearance, the vertical constant force and the rotating speed ratio are discussed in detail. The jump phenomenon, hard resonant hysteresis characteristics are shown for a relatively large bearing clearance, and the soft resonant hysteresis characteristics can be observed for a relatively large vertical constant force. Moreover, the super-harmonic frequency components and the combined frequency components caused by the inter-shaft bearing are observed for both rotors. But the corresponding frequency components for the low-pressure rotor are more complex than that for the high-pressure rotor in same condition. These results would be helpful to recognize the nonlinear dynamic characteristics of dual-rotor bearing system.

In order to study the dual-rotor system’s rubbing fault, a new dynamic model is established. The unbalance and the rubbing faults are modeled, respectively. Considering the softening characteristics of casing, the Lankarani–Nikravesh model is utilized to describe the impact force between the disk and fixed limiter. The numerical integral method is applied to obtain system’s dynamic behavior, and the characteristics of the rubbing faults are analyzed by time-domain waveform, 3D waterfall plot and spectrum cascades. The influences of rotational speed ratio, initial clearance, mass eccentricity and inter-shaft bearing stiffness on the dynamic characteristics are investigated. The vibration displacement of the low-pressure rotor is collected from the impact experiment performed on a dual-rotor test rig. The analysis result of simulation is identical with the experiment result. Consequently, this method can be used to study characteristics of rubbing faults of dual-rotor bearing system efficiently.

Multi-fault rotor system is a hot spot in the study of rotor dynamics and fault diagnosis. The present study is aimed to deal with the vibration response and nonlinear behavior of a cracked rotor system with rub-impact supported by sliding bearings. A dedicated experiment is designed to verify the interaction between the several faults for a rotor system. These faults are crack, rub-impact and oil-film instability. The time domain plot, frequency spectrum and cascade spectra are employed to extract the response features of the rotor system. The numerical investigation is given to compare with the experiment results, which concentrates on the effect of crack depth and stator stiffness on the vibration response and system instability of the multi-fault rotor system. The bifurcation diagrams, frequency spectra, Poincare maps, and cascade spectra are used to analyze the nonlinear coupled behaviors of the multi-fault rotor system. The results from experiment and simulation indicate that the coupling effect exists in the faults of crack, rub-impact and oil-film instability. The crack interferes with the formation of oil whirl, that is, the oil whirl is delayed to appear. Moreover, enhancing the stator stiffness can restrain the appearance of the oil whirl and simplify the dynamic motion of the system. The study discloses the coupling phenomenon of multi-fault rotor system and presents the response characteristics and nonlinear dynamical behaviors of the interaction between multiple faults for such a rotor-bearing system.