A Modified Iterative Learning Control Approach for the Active Suppression of Rotor Vibration Induced by Coupled Unbalance and Misalignment

This paper proposes a modified iterative learning control(MILC)periodical feedback-feedforward algorithm to reduce the vibration of a rotor caused by coupled unbalance and parallel misalignment.The control of the vibration of the rotor is provided by an active magnetic actuator(AMA).The iterative gain of the MILC algorithm here presented has a self-adjustment based on the magnitude of the vibration.Notch filters are adopted to extract the synchronous(1×Ω)and twice rotational frequency(2×Ω)components of the rotor vibration.Both the notch frequency of the filter and the size of feedforward storage used during the experiment have a real-time adaptation to the rotational speed.The method proposed in this work can provide effective suppression of the vibration of the rotor in case of sudden changes or fluctuations of the rotor speed.Simulations and experiments using the MILC algorithm proposed here are carried out and give evidence to the feasibility and robustness of the technique proposed.

A Comprehensive 3-Steps Methodology for Vibration-Based Fault Detection,Diagnosis and Localization in Rotating Machines

In any industry,it is the requirement to know whether the machine is healthy or not to operate machine further.If the machine is not healthy then what is the fault in the machine and then finally its location.The paper is proposing a 3-Steps methodology for the machine fault diagnosis to meet the industrial requirements to aid the maintenance activity.The Step-1 identifies whether machine is healthy or faulty,then Step-2 detect the type of defect and finally its location in Step-3.This method is extended further from the earlier study on the 2-Steps method for the rotor defects only to the 3-Steps methodology to both rotor and bearing defects.The method uses the optimised vibration parameters and a simple Artificial Neural Network(ANN)-based Machine Learning(ML)model from the earlier studies.The model is initially developed,tested and validated on an experimental rotating rig operating at a speed above 1st critical speed.The proposed method and model are then further validated at 2 different operating speeds,one below 1st critical speed and other above 2nd critical speed.The machine dynamics are expected to be significantly different at these speeds.This highlights the robustness of the proposed 3-Steps method.

VIBRATION CHARACTERISTIC INVESTIGATION OF COUNTER-ROTATING DUAL-ROTOR IN AERO-ENGINE

Two methods for vibration characteristic investigation of the counter-rotating dual-rotors in an aero-en- gine are put forward. The two methods use DAMP tool on the MSC. NASTRAN platform and develope the re- solving sequence. Vibration characteristics of a turbofan engine are analyzed by using the two methods. Com- pared with results calculated using transfer matrix method and test results, the two methods are valuable and have great potential in practical applications for vibration characteristic investigation of aero-engines with high thrust-weight ratio.

REDUCING VIBRATION WITH FRICTION-DAMPING IN HIGH-SPEED ROTOR SYSTEM

To reduce the excessive vibration of a high-speed rotor system at the critical speed, a friction damper with a flexible support structure is introduced. The mechanism of vibration reduction and support characteristics are analyzed and a friction damper is designed. The effect on an unbalanced response is studied. Results show that the stiffness factor and the friction-damping factor of the damper are related to the cone angle and the friction factor of the inner-ring when adopting a proper structure. By changing these parameters and the Z-directional stiffness of the outer-ring, the stiffness and the damping characteristic of the damper can be varied. Introducing a friction damper into the support can reduce the stiffness and increase the damping of the support, thus decreasing the critical speed to avoid the operating speed, suppress the resonant response of a rotor system, and attenuate vibration forces to the outside.

Nonlinear dynamic behavior of rubbing rotor under interaction between bending and torsional vibrations

The nonlinear dynamic behavior of a rubbing rotor system was studied with a mathematical model established with the eccentricity and interaction between bending and torsional vibrations taken into consideration. The nonlinear vibrational response of a rubbing rotor was analyzed using numerical integral, spectroscopic analysis and Poince mapping method, which made it possible to have better understanding of the vibrational characteristics of partial rubbing and complete circular rubbing rotors. The numerical results reveal the response of torsional vibration mainly takes a form of superchronous motion, and its frequency decreases as the rotational speed increases when partial rubbing occurs, and the response of torsional vibration is synchronous when complete circular rubbing occurs. The comparison of the dynamics of rubbing rotors with and without the interaction between bending and torsional vibrations shows the interaction between bending and torsional vibrations advances the rotational speed, at which the response of bending vibration changes from a synchronous motion into a quasi periodic motion, and the interaction between bending and torsional vibrations reduces stability of the rubbing rotor.

DESCRIPTION AND PREDICTION OF CATASTROPHE OF VIBRATION STATE FOR FAULTY ROTORS

A sudden increase of vibration amplitude with no foreboding often results in an abrupt breakdown of a mechanical system.The catastrophe of vibration state of a faulty rotor is a typical nonlinear phenomenon,and very difficult to be described and predicted with linear vibration theory.On the basis of nonlinear vibration and catastrophe theory,fhe eatastrophe of the vibration amplitude of the faulty rotor is described;a way to predict its emergence is developed.

Experimental study on vibration suppression in a rotor system under base excitation using an integral squeeze film damper

Base excitation is one of common excitations in rotor system.In order to study the dynamic characteristics of rotor systems under base excitation and the effect of integral squeeze film dampers(ISFDs)on their dynamic characteristics,a single-disk rotor test rig,where mass imbalance and base excitation could be applied,is developed.Experimental research on the rotor system response under sinusoidal base excitation conditions with different frequencies and excitation forces is performed and the effect of ISFD on the dynamic characteristics of the rotor is investigated.The experimental results demonstrate that when the sinusoidal base excitation frequency approaches the first critical speed of the rotor system or the natural frequency of the rotor system base,strong vibration occurs in the rotor,indicating that the base excitation of the two frequencies has a greater impact on rotor system response.In addition,with the increase of the base excitation force,the vibration of the rotor will be increased.ISFDs can significantly inhibit the vibration due to unbalanced forces and sinusoidal base excitation in rotor systems.To a certain extent,ISFDs can improve the effect of sinusoidal base excitation with most frequencies on rotor system response,and they have a good vibration reduction effect for sinusoidal base excitation with different excitation forces.

Nonlinear Vibration Induced by the Water-film Whirl and Whip in a Sliding Bearing Rotor System

Many industrial applications and experiments have shown that sliding bearings often experience fluid film whip due to nonlinear fluid film forces which can cause rotor-stator rub-impact failures. The oil-film whips have attracted many studies while the water-film whips in the water lubricated sliding bearing have been little researched with the mechanism still an open problem. The dynamic fluid film forces in a water sliding bearing are investigated numerically with rotational, whirling and squeezing motions of the journal using a nonlinear model to identify the relationships between the three motions. Rotor speed-up and slow-down experiments are then conducted with the rotor system supported by a water lubricated sliding bearing to induce the water-film whirl/whip and verify the relationship. The experimental results show that the vibrations of the journal alternated between increasing and decreasing rather than continuously increasing as the rotational speed increased to twice the first critical speed, which can be explained well by the nonlinear model. The radial growth rate of the whirl motion greatly affects the whirl frequency of the journal and is responsible for the frequency lock in the water-film whip. Further analysis shows that increasing the lubricating water flow rate changes the water-film whirl/whip characteristics, reduces the first critical speed, advances the time when significant water-film whirling motion occurs, and also increases the vibration amplitude at the bearing center which may lead to the rotor-stator rub-impact. The study gives the insight into the water-film whirl and whip in the water lubricated sliding bearing.

Research on suppress vibration of rotor misalignment with shear viscous damper

A new type of shear viscous damper for rotating machinery is designed. The new damper with good stability and reliability can inhibit all kinds of frequency multiplication vibration caused by misalignment in the condition of nonstop machine. It analyzes and discusses the use of the shear viscous damper for misalignment vibration response inhibition with a finite element method, and experi ments are extensively carried out with a laboratory test rig. Both the simulation and experimental re suits basically agree well in that, the damper can effectively control the misalignment vibration of the rotor system and improves the stability of the plitude of one time running speed component bration has been basically eliminated. entire rotor system. Experimental results show the am decreases by 30% , and the two time running speed vibration has been basically eliminated.

Experimental Investigation on Vibration Control of Rotor-bearing System with Active Magnetic Exciter

Vibration control is an efficient way to minimize a rotating machine’s vibration level so that its vibration fault-free can be realized.While,several factors,such as unbalance,misalignment and instability,contribute to the serious vibration of rotating machines.It is necessary that one apparatus can depress vibration caused by two or more reasons.The fault self-recovery(FSR) mechanism is introduced and investigated.Strategies of vibration control are investigated theoretically using numerical method firstly.Active magneticelectric exciter(AME) are selected as the actuator of a FSR device because it can provide suitable force by varying the control current in the exciters depending upon a proportional and derivative control law.By numerical study,it is indicate that only a small control force is needed to improve stability margins of the compressor and prevent subsynchronous vibration fault efficiently.About synchronous vibration,three control strategies,searching in whole circle,fast optimizing control(FOC),and none mistaking control,are investigated to show which of the control strategy can realize the fault self-recovery in the shortest time.Experimental study is conducted on a test rig with variable rotating speed.Results of the test indicate that the non-mistake control strategy can minimize synchronous vibration in less than three seconds.The proposed research can provide a new insight for subsynchronous and synchronous vibration restraining about centrifugal compressor.

GENERATOR VIBRATION FAULT DIAGNOSIS METHOD BASED ON ROTOR VIBRATION AND STATOR WINDING PARALLEL BRANCHES CIRCULATING CURRENT CHARACTERISTICS

Rotor vibration characteristics are first analyzed, which are that the rotor vibration of fundamental frequency will increase due to rotor winding inter-turn short circuit fault, air-gap dynamic eccentricity fault, or imbalance fault, and the vibration of the second frequency will increase when the air-gap static eccentricity fault occurs. Next, the characteristics of the stator winding parallel branches circulating current are analyzed, which are that the second harmonics circulating current will increase when the rotor winding inter-turn short circuit fault occurs, and the fundamental circulating current will increase when the air-gap eccentricity fault occurs, neither being strongly affected by the imbalance fault. Considering the differences of the rotor vibration and circulating current characteristics caused by different rotor faults, a method of generator vibration fault diagnosis, based on rotor vibration and circulating current characteristics, is developed. Finally, the rotor vibration and circulating current of a type SDF-9 generator is measured in the laboratory to verify the theoretical analysis presented above.

Experimental study of suppressing the unbalanced response vibration of rotor system with a G-type integral squeeze film damper

Conventional squeeze film dampers have numerous challenges including lock up,bistable response and incoordinate precession.In order to resolve these nonlinear problems,a novel G-type integral squeeze film damper(GISFD)is proposed in this research.The experimental test rig is provided to investigate the rotor system with an unbalanced single disk.Numerical simulation results show that the structural design of GISFD is reasonable,which can ensure its safe and stable operation.The influence of different support stiffnesses on the first-order speed of the rotor system is analyzed.Experimental results show that GISFD can effectively suppress the unbalanced response vibration of the rotor.In a certain range,it is found that the suppression effect of GISFD increases with the increase in the kinematic viscosity of the damping fluid.When the silicone oil with kinematic viscosity coefficients v=30.0 cm^(2)/s is employed,the vibration reduction of GISFD is approximately 71.51%.Furthermore,the experimental results show that with the increase of the unbalance,there is a linear relationship between the unbalance and the corresponding amplitude of the unbalanced response.It is concluded that GISFD has excellent linear damping characteristics and reduces the sensitivity of the rotor system to the unbalanced mass.

Coupled lateral-torsional-axial vibrations of a helical gear-rotor-bearing system

Considering the axial and radial loads, a math- ematical model of angular contact ball bearing is deduced with Hertz contact theory. With the coupling effects of lateral, torsional and axial vibrations taken into account, a lumped-parameter nonlinear dynamic model of helical gearrotor-bearing system （HGRBS） is established to obtain the transmission system dynamic response to the changes of dif- ferent parameters. The vibration differential equations of the drive system are derived through the Lagrange equation, which considers the kinetic and potential energies, the dis- sipative function and the internal/external excitation. Based on the Runge-Kutta numerical method, the dynamics of the HGRBS is investigated, which describes vibration properties of HGRBS more comprehensively. The results show that the vibration amplitudes have obvious fluctuation, and the frequency multiplication and random frequency components become increasingly obvious with changing rotational speed and eccentricity at gear and bearing positions. Axial vibration of the HGRBS also has some fluctuations. The bearing has self-variable stiffness frequency, which should be avoided in engineering design. In addition, the bearing clearance needs little attention due to its slightly discernible effect on vibration response. It is suggested that a careful examination should be made in modelling the nonlinear dynamic behavior of a helical gear-rotor-bearing system.

INFLUENCE OF UNBALANCE ON LOW-FREQUENCY VIBRATION OF ROTOR-BEARING SYSTEM

The influence of unbalance on low-frequency vibration exists whenthere are nonlinear factors in oil film force. Based on the Muszpeka oil film mod-el , a theoretical proof is presented. Some new results are obtained based on the im-proved simulation meth

STUDY ON ROTOR HEAD VIBRATION ABSORBER OF HELICOPTER

Rotor Head Vibration Absorber (RHVA) is a new kind of vibration reduc-tion device for helicoper, which provides some advantages in applications. The mechan-ical model for analysing and designing such kind of device is presented, two analyticalmethods (in frequency domain and time domain) and its adaptabihty are studied. At thesame time the charactenstics of RHVA are analysed. The deduced rotor receptancesproved by model test are presented. At last the effectiveness of mechanical model andanalytical methods presented in this paper and of RHVA are illustrated in the calculation example.

Magnetic field effects on the nonlinear vibration of a rotor

The nonlinear vibration of a rotor operated in a magnetic field with geometric and inertia nonlinearity is investigated. An asymmetric magnetic flux density is generated,resulting in the production of a load on the rotor since the air-gap distribution between the rotor and the stator is not uniform. This electromagnetic load is a nonlinear function of the distance between the geometric centers of the rotor and the stator. The nonlinear equation of motion is obtained by the inclusion of the nonlinearity in the inertia, the curvature, and the electromagnetic load. After discretization of the governing partial differential equations by the Galerkin method, the multiple-scale perturbation method is used to derive the approximate solutions to the equations. In the numerical results, the effects of the electromagnetic parameter load, the damping coefficient, the amplitude of the initial displacement, the mass moment of inertia, and the rotation speed on the linear and nonlinear backward and forward frequencies are investigated. The results show that the magnetic field has significant effects on the nonlinear frequency of oscillation.

Vibration Characteristics of Rotor System with Loose Disc Caused by the Insufficient Interference Force

The rotating parts looseness is one of the common failures in rotating machinery.The current researches of looseness fault mainly focus on non-rotating components.However,the looseness fault of disc-shaft system,which is the main work part in the rotor system,is almost ignored.Here,a dynamic model of the rotor system with loose disc caused by the insufficient interference force is proposed based on the contact model of disc-shaft system with the microscopic surface topography,the vibration characteristics of the system are analyzed and discussed by the number simulation,and verified by the experiment.The results show that the speed of the shaft,the contact stiffness,the clearance between the disc and shaft,the damping of the disc and the rotational damping have an influence on the rotation state of the disc.When the rotation speed of the disc and the shaft are same,the collision frequency is mainly composed of one frequency multiplication component and very weak high frequency multiplication components.When the rotation speed of the disc and the shaft is close,the vibration of the disc occurs a beat vibration phenomenon in the horizontal direction.Simultaneously,a periodical similar beat vibration phenomenon also occurs in the waveform of the disc-shaft displacement difference.The collision frequency is mainly composed of a low frequency and a weak high frequency component.When the rotation speed of the disc and the shaft has great difference,the collision frequency is mainly composed of one frequency multiplication,a few weak high frequency multiplication components and a few low frequency multiplication component.With the reduction of the relative speed of the disc,the trajectory of the disc changes from circle-shape to inner eight-shape,and then to circle-shape.In the inner eight-shape,the inner ring first gradually becomes smaller and then gradually becomes larger,and the outer ring is still getting smaller.The obtained research results in this paper has important theoretical value for the diagnosis of the rotor system with the loose disc.

Study on online elimination of sudden unbalance-induced vibration using active balancing technology

An active balancing technology has been applied to solve the severe vibration caused by sudden unbalance in rotating machineries during their working process. First, based on the generation principle of sudden unbalance, a simulation test stand with a sudden unbalance generation device was set up. Then, the balancing planes were optimized by using the finite element method （FEM） to determine the position for balancing device installation. Finally, the active balancing experiments were carried out on the test stand. The experimental results indicate that the vibration response caused by sudden unbalance can be decreased from 77μm to 8μm by using the active balancing device, and the vibration amplitude reduction was up to 89.6%. From this example, it can be concluded that the active balancing device, which is installed on a proper position of the rotor, can effectively control the random transient synchronous vibration, demonstrating its high value in engineering practice.

ZERO MODE NATURAL FREQUENCY AND NONLINEAR VIBRATION OF COUPLED LATERAL AND TORSION OF A LARGE TURBINE GENERATOR

Zero mode natural frequency (ZMNF) is found during experiments. The ZMNF andvibrations resulted by it are studied. First, calculating method of the ZMNF excited byelectromagnetic in vibrational system of coupled mechanics and electrics are given from the view ofmagnetic energy. Laws that the ZMNF varies with active power and exciting current are obtained andare verified by experiments. Then, coupled lateral and torsional vibration of rotor shaft system isstudied by considering rest eccentricity, rotating eccentricity and swing eccentricity. UsingLargrange-Maxwell equation when three phases are asymmetric derives differential equation of thecoupled vibration. With energy method of nonlinear vibration, amplitude-frequency characteristics ofresonance are studied when rotating speed of rotor equals to ZMNF. The results show that ZMNF willoccur in turbine generators by the action of electromagnetic. Because ZMNF varies withelectromagnetic parameters, resonance can occur when exciting frequency of the rotor speed is fixedwhereas exciting current change. And also find that a generator is in the state of large amplitudein rated exciting current.

SUPPRESSION OF TRANSIENT RESPONSE OF A ROTOR IN ACTIVE VIBRATlON CONTROL

Transient response and its influence factors are investigated and a methodfor attenuating the transient response is developed by means of a time varying model.The system gain matrix is obtained by choosing weighting matrices and solving the timevarying Riccati equation. Control forces are applied to the system via a feed back loop.Comparisons of responses with and without control are made. The results show that thetransienl and steady state responses are significantly suppressed in the close loop systemand control forces are very small.