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Improving the bearing design helps in reducing the negative consequences related to errors in installation, manufacturing, deflections under severe loading conditions, progressive wear of machine elements, and many other aspects. One of the methods of such a design improvement effort is changing the bearing profile along the bearing width to compensate for the reduction in the geometrical gap between the shaft and the bearing inner surface due to the aforementioned causes. Since in all rotating machinery, unbalance usually exists at some level, this paper deals with the response of this modified bearing to unbalanced excitation to evaluate the effectiveness of such geometrical design on the dynamic characteristics of the rotor-bearing system. The numerical solution is performed using the finite difference method by assuming Reynolds boundary conditions to determine the cavitation limits, and the 4th-order Range-Kutta method is used to determine the time responses resulting from the unbalance excitation. The time responses to this type of excitation show that the rotor-bearing with the improved geometrical design is more stable, particularly at high speeds. In addition, this modification leads to an improvement in the lubricant layer thickness and the reduction in the levels of the generated pressure between the surfaces despite the presence of large deviations from the perfectly aligned bearing system. Furthermore, the suggested geometrical design overcomes the problem of asymmetricity in the pressure field resulting from the shaft deviation to a large extent. The results of this work (the enhancement in the level of the film thickness and the improvement in the dynamic response of the system as well as the reduction of the maximum pressure value) extend the range of misalignment in which the rotor bearing systems can operate safely which represents a significant step in designing the rotor-bearing system. [ABSTRACT FROM AUTHOR]

This paper considers the discontinuous characteristics of a real aero-engine rotor system, that is, the existence of bolted connection characteristics, and establishes a new bolted connection rotor system model. Taking into account the bending stiffness and the nonlinear Hertzian contact force of the rolling bearing, the Newmark- β numerical method is used to solve the system response, and the influence of the bending stiffness on the system is studied. Moreover, the effects of bending stiffness and eccentricity on the system dynamics are analyzed. The results show that the nonlinear phenomena of the system are more abundant and the critical speed of the system is higher when the bending stiffness is involved. With the increase of bending stiffness, the critical speed of the system increases, and the frequency component of the system becomes more complex. Then, the influence of eccentricity on the system is studied based on the bending stiffness. It is found that the greater the eccentricity, the greater the critical speed of the rotor and the greater the amplitude of the main frequency. In the case of the same eccentricity, the main frequency increases as the rotational speed increases, and the frequency doubling component appears in the 2-period motion. This paper provides a basis for predicting the nonlinear response of bolted rotor-bearing system. [ABSTRACT FROM AUTHOR]

In this paper, the rotor system with nonlinear bearing force and base excitation load was modeled based on finite element method, and its response characteristic under the excitation of base load was studied. The results show that the response of the rotor is the superposition of the basic impulse response and the unbalanced response. The pulse excitation energy can be dispersed while the rotation speed and pulse frequency are close to each other. When the phase difference of unbalanced excitation is 180°, the response amplitude of rotor bearing system was the smallest. The correctness of the rotor bearing system model was verified by experiments. [ABSTRACT FROM AUTHOR]

Abstract A technique for estimation of unbalance parameters of rotor-bearing systems has been presented and verified by numerical simulations and experimental measurements. The method uses system model and response measurements for unbalance identification. A rigid rotor model is considered in the present work. Unbalance force estimation using a joint-input state estimation technique is followed by unbalance parameter identification using least-squares fitting. Results are presented for different shaft speeds and measurement noise levels. Unbalance parameters are identified accurately with noisy measurements, which verifies the robustness of the proposed technique. The proposed technique is verified on a rotor-bearing test rig for different unbalance configurations. Sensitivity analysis is also performed by varying the values of system parameters. Highlights • A model-based approach for unbalance parameter estimation is proposed. • Unbalance force is estimated using a joint-input state estimation technique. • Numerical and experimental results are presented for the verification. • Effect of measurement noise is shown. • Sensitivity analysis is performed by varying system parameters. [ABSTRACT FROM AUTHOR]

Highlights • A dynamic model is built for diagnosing REBs' pseudo-fault of rotor-REBs system. • The spectral DCS method is proposed for pseudo-fault feature extraction of REBs. • The experiment is set up for verifying the spectral DCS method based on the MFS. Abstract The pseudo-fault is a common phenomenon in a system, which is defined as the faulty feature of a healthy component caused by a defective component. Pseudo-fault signals, coupled with signals of both faulty component and healthy component, may lead to false diagnosis for healthy component. It is a challenging task to decouple pseudo-fault feature based on the single-channel pseudo-fault signal of rotating machinery. An issue is presented for feature extraction of the pseudo-fault signal of a rolling element bearing (REB) in a rotor-bearing system. To address the matter, a method is proposed for feature extraction of a REB pseudo-fault in a rotor-bearing system based on spectral degree of cyclostationarity (DCS). Firstly, a dynamic model of the rotor-bearing system is established to produce pseudo-fault signals, considering different deflection exponents and slippage of bearings caused by both outer race and inner race defects. The dynamic and time-frequency characteristics are then analyzed to show the amplitude modulation of pseudo-fault signals. The cyclostationary analysis is implemented for pseudo-fault extraction and verified by numerical simulation. The spectral DCS method is proposed to capture the cyclostationarity of filtered signals ordered by kurtosis, evaluated by the crest factor upon the spectral kurtosis gradient. An experimental system, under four assembly modes and three rotating speeds, is constructed based on a machinery fault simulator (MFS) to verify effectiveness of the proposed spectral DCS method. Experiment results show that quasi-cyclostationarity distribution with respect to kurtosis remains almost constant in the spectral kurtosis and degree of cyclostationary (SK-DCS) spectrogram and that the crest factor upon the spectral kurtosis gradient is closer to zero. Thus, the proposed spectral DCS method can be used as a tool of feature extraction for pseudo-fault in REBs by single-channel signal to avoid false diagnosis. [ABSTRACT FROM AUTHOR]

In twin-screw refrigeration compressor for high pressure applications, journal bearing has been a preferred option to bear larger and larger radial force. Hence, the stability of rotor-journal bearing system is worth investigating to ensure the reliability of a twin-screw refrigeration compressor, which can be reflected on axis orbit. This paper presents a homogeneous two-phase flow model to calculate the axis orbit of journal bearing used in a twin-screw compressor, considering gas-induced force, unbalanced force and gravitational force. In order to compute gas-induced force acting on bearings by FEM, the p - V indicator diagram is measured experimentally. In addition, axial orbit under different evaporating temperature and different built-in volume ratio was investigated experimentally. Meanwhile it verifies that the proposed two-phase flow model has a good agreement in terms of orbit shape with the experimental result. Moreover, the effects of refrigerant mass fraction at supply groove and structural parameters are analyzed theoretically. [ABSTRACT FROM AUTHOR]

Shaft cracks in a rotor system may lead to destructive failure, if not detected at right time. The transient vibrations of a rotor system with a transverse breathing crack during rotor shut-down has been analyzed using Finite Element Method (FEM) for flexural vibrations. Since the vibration signals during shut-down are non-stationary, continuous wavelet transform (CWT) has been used to extract the crack feature when the rotor is decelerating through critical speed during shut-down. A parametric study for different crack depths has been studied for different decelerations and it is found that CWT can be effectively used to detect the crack during rotor shut-down. [ABSTRACT FROM AUTHOR]

This paper presents a technique for modelling the nonlinear behavior of a rotor-bearing system with Hertzian contact, clearance, and rotating unbalance. The rotor-bearing system is separated into linear and nonlinear components, and the nonlinear bearing force is replaced with an equivalent describing function gain. The describing function captures the relationship between the amplitude of the fundamental input to the nonlinearity and the fundamental output. The frequency response is constructed for various values of the clearance parameter, and the results show the presence of a jump resonance in bearings with both clearance and preload. Nonlinear hardening type behavior is observed in the case with clearance and softening behavior is observed for the case with preload. Numerical integration is also carried out on the nonlinear equations of motion showing strong agreement with the approximate solution. This work could easily be extended to include additional nonlinearities that arise from defects, providing a powerful diagnostic tool. [ABSTRACT FROM AUTHOR]

The proper orthogonal decomposition (POD) method is a main and efficient tool for order reduction of high-dimensional complex systems in many research fields. However, the robustness problem of this method is always unsolved, although there are some modified POD methods which were proposed to solve this problem. In this paper, a new adaptive POD method called the interpolation Grassmann manifold (IGM) method is proposed to address the weakness of local property of the interpolation tangent-space of Grassmann manifold (ITGM) method in a wider parametric region. This method is demonstrated here by a nonlinear rotor system of 33-degrees of freedom (DOFs) with a pair of liquid-film bearings and a pedestal looseness fault. The motion region of the rotor system is divided into two parts: simple motion region and complex motion region. The adaptive POD method is compared with the ITGM method for the large and small spans of parameter in the two parametric regions to present the advantage of this method and disadvantage of the ITGM method. The comparisons of the responses are applied to verify the accuracy and robustness of the adaptive POD method, as well as the computational efficiency is also analyzed. As a result, the new adaptive POD method has a strong robustness and high computational efficiency and accuracy in a wide scope of parameter. [ABSTRACT FROM AUTHOR]

Bearing dynamic parameters are important factors governing the vibration characteristics of rotating machinery; however, they are difficult to determine due to limited experimentation, and inaccurate in modelling. In this paper, a parameter identification method is presented to identify the bearing dynamic parameters of a flexible rotor-bearing system. In this method, the parameter identification problem is formulated as an inverse problem. The bearing dynamic parameters have been characterized through minimizing the error squared of the rotor-bearing system unbalance response between the experiment results and the computational ones. The intergeneration projection genetic algorithm is used to minimize the error squared. As an efficient method for analysing the dynamic behaviour of a rotor-bearing system, an improved transfer matrix method has been employed to calculate the unbalance response. This approach has been applied to identify the bearing dynamic parameters of a test rig supported by two anisotropic bearings, according to the unbalance response experimental data. Results indicated that this method could identify the bearing dynamic parameters. It is also robust to the noise effects. [ABSTRACT FROM PUBLISHER]

Parametric instability of flexible rotor-bearing system under time-periodic base angular motions is analyzed in this paper. The accurate finite element model for the flexible rotor-bearing system under time-varying base angular motions is derived based upon the energy theorem and Lagrange’s principle. Three base angular motions, including the rolling, pitching and yawing motions, are assumed to be sinusoidal perturbations superimposed upon constant terms. Considering the time-varying base movements, the second order differential equations of the system will have time-periodic gyroscopic and stiffness coefficients. The discrete state transition matrix (DSTM) method is introduced for numerically acquiring the instability regions. Based upon these, instability computations for a rotor-bearing system with one base motion alone and two base motions together are conducted, respectively. The effects of rotating speed, amplitudes of base motion and phases between two base motions on both the primary and combination instability regions are discussed in detail. [ABSTRACT FROM AUTHOR]

An effective method for identifying and diagnosing the concurrent fault combined by two or more single faults is yet to be further developed because most existing approaches focus on single faults. On the other hand, rotor-bearing system is an important part of rotating machinery. Therefore a new fault identification and diagnosis method based on wavelet packet transform (WPT) and zero space classifiers is presented in this paper. Firstly, the vibration signals collected from the rotor-bearing system are decomposed into several time-frequency compositions by WPT. Then the appropriate composition characterizing fault signatures is selected to extract features for constructing zero space classifiers. Finally, the effectiveness of the proposed method is demonstrated by an experiment carried out on a machinery fault simulator. The experimental results show that the proposed approach is feasible and effective to identify and diagnose the concurrent faults in a rotor-bearing system. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the cross-coupled bending vibrations of a rotating shaft, with a breathing crack, mounted in resilient bearings are investigated. The equations of motion of the continuum and isotropic rotating model of the shaft follow the theory of Rayleigh. The governing equations are coupled in the two main directions, and the partial solution is obtained by solving a linear system of equations, for each time step, taking into account the non-linearity due to the breathing crack. The coupling is introduced in three different ways: the equations of motion, the resilient bearings and the crack. A main focus is made in the coupling introduction due to crack compliance variance while rotation with the cross-coupling terms of the local compliance matrix due to the crack to be calculated analytically as functions of the rotational angle. The three causes of coupling between the vertical and horizontal vibrations should be distinguished with regard to the effects that each one of them has on the dynamic response of the rotor. Inversely, the existence of each type of coupling in the frequency response could be used to identify the respective cause. [Copyright &y& Elsevier]

Abstract: The nonlinear dynamic analysis of the rotor–bearing system is studied in this paper and is supported by oil-film short bearings with nonlinear suspension. An observation of a nonlinearly supported model and the rub–impact between rotor and stator is needed. Therefore for more precise analysis of rotor-bearing systems, the rub–impact between rotor and stator is also proposed in this paper. The displacements in the horizontal and the vertical directions charactering the theoretical model of the system are considered with non-dimensional speed ratio. Inclusive of the analysis methods of the dynamic trajectory, the power spectrum, the Poincaré maps and the bifurcation diagrams are used to analyze the behavior of the rotor centre and bearing centre in the horizontal and vertical directions under different operating conditions. The maximum Lyapunov exponent analysis is also used in this study to identify the chaotic motion. It is concluded that the trajectory of rotor centre and bearing centre have undesirable vibrations. Especially at s=5.6, the rotor centre is at chaotic motion but the bearing centre is still at quasi-periodic motion. With the analysis of the dynamic behavior of these operating conditions, the theoretical and practical idea for controlling rotor–bearing systems and optimizing their operation can be more precise. [Copyright &y& Elsevier]

The current article deals with the non-linear dynamic behaviours of a flexible rotor system with multi-span bearing supports. The shaft is modelled by using the finite-element method that can take the effects of inertia and shear into consideration. A modified modal synthesis technique with free interface is proposed to reduce the degrees of freedom of the model of a flexible rotor system. In order to keep the accuracy of non-linear analysis and save computational cost, a truncated modal transformation is used to reduce the linear degrees of freedom of the system, whereas non-linear oil-film forces and non-linear degrees of freedom of the system are retained in the physical space. Thus, the non-linear excitation and unbalance force can be easily added to the system equation and the reduced system keeps the non-linearity. In accordance with the physical character of oil film, a variational constraint approach is proposed to revise continuously the variational form of the Reynolds equation at every step of the dynamic iterative procedure. Non-linear oil film forces and their Jacobians are calculated simultaneously without an increase in computing costs and compatible accuracy is obtained. The numerical example shows that the proposed methods not only save computing costs but also have good precision. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the damage detection from non-stationary mechanical vibration signals collected during acceleration and deceleration was performed. A laboratory grinding spindle-typed rotor-bearing system was equipped, and modal testing was carried out to identify system characteristics and operating range. Time–frequency analysis method such as Fast Fourier Transform (FFT), Short-Time Fourier Transform (STFT), Wigner–Ville Distribution (WVD), and Discrete Wavelet Transform (DWT) was applied to vibration data of normal rotor and shaft-cracked rotor in speed-varying process and the results of feature extraction from shaft-cracked condition were also compared with those in normal condition. [Copyright &y& Elsevier]

Abstract: The dynamic analysis of the rotor-bearing system is studied in this paper and is supported by oil film journal bearings. An observation of a nonlinearly supported model and the rub-impact between rotor and stator is needed for more precise analysis of rotor-bearing systems. Inclusive of the analysis methods of the dynamic trajectory, the power spectra, the Poincaré maps, the bifurcation diagrams and the Lyapunov exponent are used to analyze the behavior of the rotor centre and bearing centre in the horizontal and vertical directions under different operating conditions. The periodic, quasi-periodic, sub-harmonic and chaotic motion are demonstrated in this study. A special phenomenon is occurring at s =2.27, the motions of the bearing centre and the rotor centre in the horizontal direction are still at chaotic motions but the motions of the bearing centre and the rotor centre in the vertical direction are at 3T-periodic motions. It is concluded that the trajectory of rotor centre and bearing centre have undesirable vibrations. With the analysis of the dynamic behavior of these operating conditions, the theoretical and practical idea for controlling rotor-bearing systems with rub-impact condition can be more precise. [Copyright &y& Elsevier]

Abstract: This paper shows that the steady state and the dynamic characteristics of a rotor-bearing system with turbulent effects can be conveniently evaluated by applying the Hopf bifurcation theory to the equations of motion of a rigid rotor symmetrically supported by two identical fluid-film journal bearings. Results are presented for stiffness and damping coefficients and stability characteristics of a journal bearing, which take turbulence into consideration. [Copyright &y& Elsevier]

Based on the mechanized mathematics and WU Wen-tsun elimination method, using oil film forces of short-bearing model and Muszynska’s dynamic model, the dynamical behavior of rotor-bearing system and its stability of motion are investigated. As example, the concept of Wu characteristic set and Maple software, whirl parameters of short-bearing model, which is usually solved by the numerical method, are analyzed. At the same time, stability of zero solution of Jeffcott rotor whirl equation and stability of self-excited vibration are studied. The conditions of stable motion are obtained by using theory of nonlinear vibration. [ABSTRACT FROM AUTHOR]