Vibration Response Of Rotor Research Articles

Effect of wear on the dynamic characteristics of a rigid rotor supported by journal bearings

The purpose of this work is to examine the effects of wear severity on the static and dynamic characteristics of journal bearings, and on the vibration response of a rigid rotor supported by journal bearings. Numerical simulations using MATLAB was conducted for three different operating regimes, namely low loaded operating regime (ϵ0=0.15\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon _0 = 0.15$$\\end{document}), moderately loaded operating regime (ϵ0=0.45\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon _0 = 0.45$$\\end{document}) and highly loaded operating regime (ϵ0=0.75\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\epsilon _0 = 0.75$$\\end{document}) with wear depth parameter ratio (δ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta$$\\end{document}) varied from 0 to 0.5 at increments of 0.1. Numerical results showed that the vibration response of the rotor generally increases with the increase of the wear depth for all cases of low, moderately and highly loaded operating regimes of the bearings. For the values of parameters considered in this work, it was shown that the vibration response amplitude of the rotor in worn journal bearings may be six times larger compared to the response amplitude of the rotor in non-worn bearings.

A data driven method applied on nonlinear vibration of flexible rotor supported on centralized squeeze film damper

This paper discusses the application of Dynamic Mode Decomposition (DMD) on vibration response of flexible rotor supported by a Centralized Squeeze Film Damper (CSFD). The mathematics behind DMD and its applications to rotor vibration data such as linearization, reconstruction has been established. Vibration data from the flexible rotor system supported on CSFD exhibits both linear and nonlinear behavior. Further, DMD has been applied on periodic and quasi-periodic vibration data of CSFD for prediction and forecasting. DMD is observed to have successfully linearized a nonlinear system with the linear Henkel Matrix. The reconstruction and forecasting of time series data from rotor has been achieved with a maximum error of 0.2% even for nonlinear vibration data. Further, White Gaussian Noise has been intermixed with CSFD data to demonstrate the noise reduction capability of DMD method for nonlinear systems. Lastly, the application of DMD algorithm on experimental data from Jeffcott rotor based test setup has been shown.

Self-excited vibration suppression of a spline-shafting system using a nonlinear energy sink

The rotating instability and corresponding non-synchronous vibrations seriously affect the long-term operations of modern high-speed rotating machinery. However, there is still a lack of effective control methods to prevent the unstable vibration of the rotor system. This study focuses on the effective suppression of large-amplitude self-excited vibrations in spline-shafting systems using a nonlinear energy sink (NES). A nonlinear dynamic model for a spline-shafting system incorporating the non-smooth friction interface is developed. The corresponding friction-induced vibration and the instability mechanism are explored through the time-frequency analysis. The NES is then employed for the self-excited vibration suppression and the optimum parameters of the NES are obtained through the rotor vibration response surface. Several numerical analyses are conducted to investigate the suppression performance of the NES under the condition of different load torque. Lastly, the mitigation of the rotor self-excited vibration is realized and the mechanism of NES suppressing self-excited vibration by strong modulated response is elucidated. The obtained results show that the NES can not only effectively reduce the vibration of the rotor system in the vicinity of resonance, but also alleviate the large amplitude of self-excited vibration simultaneously, which may provide helpful guidance for the dynamic design of complex rotor systems.

Damage Detection in a Rotor Dynamic System by Monitoring Nonlinear Vibrations and Antiresonances of Higher Orders

Since rotor systems are very sensitive and vulnerable to transverse crack, early detection of damage is of paramount importance and essential for rotating machinery. Therefore, one of the main issues is to identify robust characteristics of the rotor vibration response that can be directly attributed to the presence of a transverse crack in a rotating shaft, preferably when the crack is small enough, in order to avoid catastrophic failures of rotating machines. This study investigates the potential links between the nonlinear vibrations and the locations of higher-order antiresonances and structural modifications due to the presence of a breathing crack in rotor systems. Using the proposed numerical results on the evolution of the nonlinear responses of a cracked rotor system, it was observed that a robust diagnostic of the presence of slight damage can be conducted by tracking nonlinear vibrational measurements, with particular attention to the antiresonance behavior of higher orders. These observations can easily serve as target observations for the monitoring system and for identifying the positions of damage at an early stage.

A partial similitude method for vibration responses of rotor systems: Numerical and experimental verification

Similitude theory provides the necessary conditions to predict the structural responses of the full-scale prototype through the scaled model, and is widely used in full-scale experiments of large structures. However, the prediction accuracy is insufficient in partial similitude. Aiming at this issue, this paper proposes the frequency adjustment laws to predict vibration responses of full-scale rotor in non-resonant state, since the rotating machinery usually works in non-resonant state. On this basis, a partial similitude method is presented by combining the frequency adjustment laws with the current method. The proposed method provides several scaling laws in the whole range of rotating speed, while only one scaling factor is used to predict the vibration responses in existing methods. The accuracy of the proposed method is verified by the numerical and experimental case studies, where the geometrical distortion is considered. In the numerical case study, the scaling laws of a rotor system are obtained by the proposed method and existing methods. The predicted results of the proposed method are compared with those of the existing methods. It is found the proposed method accurately predicts the displacements and accelerations of prototypes through those of scaled model. Moreover, the proposed method achieves a higher accuracy. The experimental study carries out the testing for the prototype and model test rigs. The experimental results show that the proposed method provides better results in predicting the displacement and acceleration compared with the existing methods. The proposed method allows designers to design a scaled model and to reproduce the vibratory behavior of the full-size prototype, which reduces the difficulty, costs and time of experimental test. Moreover, the proposed partial similitude method has a better performance than the existing methods.

Structural Damage Identification of Composite Rotors Based on Fully Connected Neural Networks and Convolutional Neural Networks.

Damage identification of composite structures is a major ongoing challenge for a secure operational life-cycle due to the complex, gradual damage behaviour of composite materials. Especially for composite rotors in aero-engines and wind-turbines, a cost-intensive maintenance service has to be performed in order to avoid critical failure. A major advantage of composite structures is that they are able to safely operate after damage initiation and under ongoing damage propagation. Therefore, a robust, efficient diagnostic damage identification method would allow monitoring the damage process with intervention occurring only when necessary. This study investigates the structural vibration response of composite rotors by applying machine learning methods and the ability to identify, localise and quantify the present damage. To this end, multiple fully connected neural networks and convolutional neural networks were trained on vibration response spectra from damaged composite rotors with barely visible damage, mostly matrix cracks and local delaminations using dimensionality reduction and data augmentation. A databank containing 720 simulated test cases with different damage states is used as a basis for the generation of multiple data sets. The trained models are tested using k-fold cross validation and they are evaluated based on the sensitivity, specificity and accuracy. Convolutional neural networks perform slightly better providing a performance accuracy of up to 99.3% for the damage localisation and quantification.

Effect of Uncertainty in the Balancing Weights on the Vibration Response of a High-Speed Rotor

Abstract This work investigates how uncertainties in the balancing weights are propagating into the vibration response of a high-speed rotor. Balancing data are obtained from a 166-MW gas turbine rotor in a vacuum balancing tunnel. The influence coefficient method is then implemented to characterize the rotor system by a deterministic multi-speed and multi-plane matrix. To model the uncertainties, a non-sampling probabilistic method based on the generalized polynomial chaos expansion (gPCE) is employed. The uncertain parameters including the mass and angular positions of the balancing weights are then expressed by gPCE with deterministic coefficients. Assuming predefined probability distributions of the uncertain parameters, the stochastic Galerkin projection is applied to calculate the coefficients for the input parameters. Furthermore, the vibration amplitudes of the rotor response are represented by appropriate gPCE with unknown deterministic coefficients. These unknown coefficients are determined using the stochastic collocation method by evaluating the gPCE for the system response at a set of collocation points. The effects of individual and combined uncertain parameters from a single and multiple balancing planes on the rotor vibration response are examined. Results are compared with the Monte Carlo simulations, showing excellent agreement.

Unbalance Vibration Characteristics and Sensitivity Analysis of the Dual-Rotor System in Aeroengines

The unbalance of the rotor system is the main factor causing the vibration of aeroengines. Research on unbalancing vibration coupling, vibration transmission, and vibration sensitivity of inner and outer dual rotors is the key link of the whole machine vibration and dynamic balance research. In this paper, the motion differential equation and dynamic model of the inner-outer dual-rotor system are established, and the unbalanced vibration of the dual-rotor system considering the coupling effect of the intermediate bearing is studied by combining theoretical analysis and simulation methods. The influence of unbalanced position, the magnitude and phase of unbalance, and the stiffness of the intermediate bearing on the vibration response of dual rotors are obtained. Aiming at the randomness of the unbalance vector distribution in the rotor system, the unbalance vector is extracted based on the Monte Carlo sampling principle. The multidisk and multiplane unbalanced vibration response law of the dual-rotor system is obtained, and the vibration transmission law and vibration sensitivity of the rotor under an unbalanced state caused by the coupling action of the inner-outer rotors are revealed. Finally, an experiment is carried out based on a self-designed test bed; the measured results are consistent with the analytical and simulation results.

Transverse nonlinear vibration modeling and response of eccentric rotor in a switched reluctance motor

In order to investigate the transverse vibration of eccentric rotor in a 12/8 switched reluctance motor (SRM), a whole nonlinear coupled vibration equation of eccentric rotor is built with finite element method (FEM). Based on single tooth radial force and the key parameters variation with rotor position, an analytical formula of magnetic resultant taking into account of the rotor’s vibration displacement is deduced in detail, which is applied onto the intermediate node of eccentric rotor in form of concentrated force. Once the windings currents obtained either by experiments or numerical simulations is input, the vibration response can be solved numerically by Newmark-[Formula: see text] method. Six phase windings currents under angle position control (APC) strategy are chosen as an example and the vibration response are discussed to reflect intrinsic vibration characteristics. From radical resultant vector and its amplitude spectrum, it is proved that the magnetic resultant vector presents multi-petals star shape. The frequency components in magnetic resultant are [Formula: see text], [Formula: see text], and [Formula: see text], [Formula: see text], related to rotational speed, current waveform and minimum common multiple of stator and rotor teeth. However, from displacement locus and its amplitude spectrum, the frequency component of the rotor vibration displacement is also related to the critical whirl speed of the rotor. Transverse superharmonic resonance of eccentric rotor appears at some particular rotational speed and result in a larger rotor vibration. If the rotor runs at the superharmonic speed of 1/19 of first-order critical whirl speed, the maximum vibration displacement radius of the eccentric rotor reaches almost four times that of the rated speed. The vibration locus at these particular speed show rich diversity.

Investigating Nonlinear Vibration Behavior of Rotors with Asymmetry Shaft Considering Misalignment

In this paper, the nonlinear vibration behavior of a rotor with asymmetric shaft considering misalignment is studied. The system consists of a rectangular shaft and a disk which is connected to a motor through a flexible coupling. In order to consider higher order deformations, nonlinear Bernoulli beam is used for modeling the shaft. Gibbons’ equations are utilized to apply misaligned coupling forces. The equations of motion of the system are derived using the Lagrangian method and then discretized by the Rayleigh-Ritz method. In order to solve nonlinear equations and hence obtaining nonlinear responses, multiple scales method is used. The vibration behavior of the system near the resonance frequencies is studied by taking into account various parameters including unbalance forces and the effect of the asymmetry of cross section of the shaft. The analytical results are consistent with those of numerical method with a good accuracy. In addition, the effects of variations of the system parameters on the rotor vibration behavior have been shown graphically. In the end, the changes in the various parameters of the system and their effects on the rotor vibration response are discussed.

Study on vibration response and orbits of misaligned rigid rotors connected by hexangular flexible coupling

This paper analyzes the deformation of a hexangular flexible coupling connecting two rigid rotors which have angular and parallel misalignment and calculates the dynamic reaction force varying with rotational angle. A 6 degree-of-freedom (DOF) dynamic model including the two rigid rotors connected by the hexangular flexible coupling is established by using Lagrange method. The high order Runge-Kutta algorithm is applied to solve the differential equations and to calculate vibration response of the coupled rotors with parallel or angular misalignment or combined misalignment. The rotor vibration amplitude and frequency information are acquired by Fast Fourier Transform (FFT) analysis. The relationship between vibration responses of first, second and third order components and moving orbits of the coupled rotors with or without misalignment at different rotational speed are numerically simulated. The results provide a theoretical support for fault diagnosis and detection of rotating machinery connected by hexangular flexible coupling.

Vibration characteristic analysis of rotor in excitation winding inter‐turn short circuit state of turbo generator

The distribution characteristics of fault electromagnetic field and temperature field and the unbalanced stresses on the rotor could be obtained through establishing a three‐dimensional model of the rotor and two‐dimensional models of the stator and rotor, and respectively solving the electromagnetic field and the temperature field of excitation winding inter‐turn short circuit fault by using the finite element analysis method. Two kinds of unbalanced stresses can be respectively equivalent to the unbalanced masses on the rotor surface. The equivalent centrifugal forces as excitation are added into the rotor dynamic equation, and solving the dynamic equation of the rotor by means of Newmark can finally obtain the rotor vibration response. The results show that the fault will cause the changes of amplitude and phase of rotor fundamental frequency vibration. So the amplitude and phase difference of the rotor fundamental frequency vibration can be used as the fault criterion in order to make an accurate diagnosis of excitation winding inter‐turn short circuit fault. © 2019 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Investigation of Induced Unbalance Magnitude on Dynamic Characteristics of High-speed Turbocharger with Floating Ring Bearings

Due to operational wear and uneven carbon absorption in compressor and turbine wheels, the unbalance (me) vibration is induced and could lead to sub-synchronous vibration accidents for high-speed turbocharger (TC). There are very few research works that focus on the magnitude effects on such induced unbalance vibration. In this paper, a finite element model (FEM) is developed to characterize a realistic automotive TC rotor with floating ring bearings (FRBs). The nonlinear dynamic responses of the TC rotor system with different levels of induced unbalance magnitude in compressor and turbine wheels are calculated. From the results of waterfall and response spectral intensity plots, the bifurcation and instability phenomena depend on unbalance magnitude during the startup of TC. The sub-synchronous component 0.12× caused rotor unstable is the dominant frequency for small induced unbalance. The nonlinear effects of induced unbalance in the turbine wheel is obvious stronger than the compressor wheel. As the unbalance magnitude increases from 0.05 g·mm to 0.2 g·mm, the vibration component changes from mainly 0.12× to synchronous vibration 1×. When unbalance increases continuously, the rotor vibration response amplitude is rapidly growing and the 1× caused by the large unbalance excitation becomes the dominant frequency. A suitable un-balance magnitude of turbine wheel and compressor wheel for the high-speed TC rotor with FRBs is proposed: the value of induced un-balance magnitude should be kept around 0.2 g·mm.

Analysis of stator vibration response for the diagnosis of rub in a coupled rotor-stator system

The present day rotors are more susceptible to rub due to reduced clearance that adversely affects the performance of the machines. In most of the theoretical investigations on rub, the structural connectivity between rotor and the stator casing is ignored and the dynamics of the rotor are studied with stator interaction as external to the system. Thus, in the present study, a coupled rotor-stator system is modelled where the vibrating rotor transmits the force to the stator structure through the bearing support and during the direct contact. The rub interaction is defined using contact mechanics based Lagrange multiplier method. The model ensures dynamic rotor-stator contact boundary and more realistic contact constraints in contrast to most of the earlier approaches. The stator thus responds through its own vibratory motion and the instantaneous clearance decides the nature of interaction between them. The stator vibration data at the casing location is explored to provide conclusive indication of the rub phenomenon. The intermittent rub interactions that are non-synchronous to rotational frequency cause the system to exhibit quasi-periodic response and the transient excitation due to impacting rotor generates natural frequencies in the system response. In the stator vibration spectrum, the presence of sub harmonic frequency components and stronger presence of harmonics of rotational frequency near the natural frequencies of the system indicate the occurrence of rub. Only low amplitude rotational frequency component is observed otherwise. Strongly correlated with rotor vibration response, the stator vibration response and its rub specific features are proposed for the rub diagnosis.

Analysis of Rotor Thermal Bow and Vibration Response in Gas Turbine

Analysis of Rotor Thermal Bow and Vibration Response in Gas Turbine

Dynamic Characteristics and Experimental Research of Dual-Rotor System with Rub-Impact Fault

Rub-impact fault model for dual-rotor system was further developed, in which rubbing board is regarded as elastic sheet. Sheet elastic deformation, contact penetration, and elastic damping support during rubbing of sheet and wheel disk were considered. Collision force and friction were calculated by utilizing Hertz contact theory and Coulomb model and introducing nonlinear spring damping model and friction coefficient. Then kinetic differential equations of rub-impact under dry rubbing condition were established. Based on one-dimensional finite element model of dual-rotor system, dynamic transient response of overall structure under rub-impact existing between rotor wheel and sheet was obtained. Meanwhile, fault dynamic characteristics and impact of rubbing clearance on rotor vibration were analyzed. The results show that, during the process of rub-impact, the spectrums of rotor vibration are complicated and multiple combined frequency components of inner and outer rotor fundamental frequencies are typical characteristic of rub-impact fault for dual-rotor system. It also can be seen from rotor vibration response that the rubbing rotor’s fundamental frequency is modulated by normal rotor double frequency.

Ultrasonic Measurement of Cylindrical Roller Bearing Lubrication Using High Pulse Repletion Rates

This paper describes a measurement of lubricant-film thickness in a roller bearing using a new ultrasonic pulser-receiver, which has a maximum pulse repetition rate (PRR) of 100 kHz. The experimental results show that a higher PRR can help to get more measurement points and more details of the oil-film thickness distribution. Furthermore, the influence of rotor vibration response for the oil-film thickness is discussed, which is in keeping with the simulation result. Finally, the limits of the PRR are discussed in detail and the effect of the transducer focal zone size is also observed.

Experimental determination of stiffness and damping in rotating systems using metaheuristic hybrid optimization and state observers

Recently, more research have been conducted on the analysis of the vibration response of rotors, so that new techniques, which are used to characterize the dynamic response of rotating machines, have been developed to aid and predict the lifespan of such systems. One of the vibration management techniques in rotating systems is the monitoring of stiffness and damping parameters of the bearings and system excitation forces. In this context, this paper aims to estimate the stiffness and damping of the bearings through a hybrid metaheuristic method. This uses a population-based search method as a starting point for direct search method, genetic algorithms and quasi-Newton method, respectively, in this work. The function to be minimized contains experimental bearing data. Moreover, the state observer is used to reconstruct all states of the system from the experimental data from the sensors. Thus, it is proposed to identify the excitation forces using orthogonal functions, Chebyshev polynomials specifically, and then, to verify the effectiveness of the method when compared to the calculated force excitation of the system.

Model assessment of a composite mock-up bladed rotor based on its vibration response and radial expansion

Composite materials provide high strength and stiffness-to-weight ratios and adjustable directional material properties. As a result, a growing application of composite materials in weight-relevant and complex-loaded structures is noticeable, especially, for the production of high-speed rotors. However, their material complexity, their parameter scatter and unpredictable impact events contribute to the prediction uncertainty of the operational capability.The in situ measurement of damage-sensitive features can provide information for reliable simulation models. Such models are a prerequisite for the analysis of the damage behaviour in practice-relevant loading scenarios.For this purpose, a novel optical measurement system is introduced measuring the rotor deformation. The system offers a measurement rate of 1.6kHz with an 7μm error independent on the rotational speed. Furthermore, the rotor vibration response was identified using a combined excitement-measurement system for different rotational speeds. Both measurement systems were successfully applied on a glass fibre-reinforced composite rotor.Based on the experimental results, a simulation model was adjusted using an advanced mixed numerical–experimental technique. A good compliance between experimental and simulation results was identified for rotor-typical stress states. In addition, the rotor temperature is shown to have a significant influence on the model accuracy and has to be incorporated in future models.

New Finite Element Modeling Approach of a Propagating Shaft Crack

Transverse shaft cracks are one of the most dangerous malfunctions of the rotating machines, including turbo- and hydrogenerators, high-speed machine tool spindles, etc. The undetected crack may grow slowly and not disturb normal machine operation. However, if it extends to a critical depth, the immediate shaft fracture may completely damage the machine, resulting in a catastrophic accident. Therefore, in-depth knowledge of the crack propagation process is essential to ensure reliable and safe operation of rotating machinery. The article introduces a new model of the propagating shaft crack. The approach is based on the rigid finite element (RFE) method, which has previously proven its effectiveness in the dynamical analysis of numerous complicated machines and structures. The crack is modeled using several dozen spring-damping elements (SDEs), connecting the faces of the cracked section of the shaft. By controlling the exact behavior of individual SDEs, not only the breathing mechanism, but also the crack propagation process can be simply introduced. In order to accomplish this, the stress intensity factors (SIFs) along the crack edge are calculated using the novel approach based on the modified virtual crack closure technique (VCCT). Based on the SIF values, the crack propagation rate is calculated from the Paris law. If the number of load cycles is greater than the constantly updated threshold number, then the crack edge is shifted by a small increment. This way, starting from the first initially cracked SDE, the crack is extended little by little, continuously changing its shape. The approach is illustrated with numerical results, demonstrating the changes in the rotor vibration response and in the crack shape and also explaining some issues about the breathing mechanism due to the propagating shaft crack. The increasing amplitude of the 2X harmonic component is recognized as an evident propagating crack signature. The numerical results correspond well with the data reported in the literature. The RFE model of the rotor is validated by comparing the vibration responses obtained experimentally and numerically. A good agreement between these data confirms the correctness and accuracy of the proposed model. The suggested approach may be utilized for a more reliable dynamic analysis of the rotating shafts, having the potential to experience propagating transverse cracks.