Dynamics in large generators due to oval rotor and triangular stator shape

Earlier measurements in large synchronous generators indicate the existence of complex whirling motion, and also deviations of shape in both the rotor and the stator. These non-symmetric geometries produce an attraction force between the rotor and the stator,called unbalanced magnetic pull（UMP）.The target of this paper is to analyse responses due to certain deviations of shape in the rotor and the stator.In particular,the perturbation on the rotor is considered to be of oval character,and the perturbations of the stator are considered triangular.By numerical and analytical methods it is concluded for which generator parameters harmful conditions,such as complicated whirling motion and high amplitudes,will occur.During maintenance of hydro power generators the shapes of the rotor and stator are frequently measured.The results from this paper can be used to evaluate such measurements and to explain the existence of complex whirling motion.

Analysis on Dynamic Performance for Active Magnetic Bearing-Rotor System

In the application of active magnetic bearings (AMB), one of the key problems to be solved is the safety and stability in the sense of rotor dynamics. The project related to the present paper deals with the method for analyzing bearing rotor systems with high rotation speed and specially supported by active magnetic bearings, and studies its rotor dynamics performance, including calculation of the natural frequencies with their distribution characteristics, and the critical speeds of the system. One of the targets of this project is to formulate a theory and method valid for the analysis of the dynamic performance of the active magnetic bearing rotor system by combining the traditional theory and method of rotor dynamics with the analytical theory and design method based on modern control theory of the AMB system.

Effectof Film Force Nonlinearity on Unbalance Responseof a Jeffcot RotorJournal Bearing System

The effect of oil film force nonlinearity on unbalance response of Jeffcot rotor elliptical bearing system is studied. Linear analysis is done by linearizing the bearing oil film dynamic forces and expressing them with stiffness and damping constants. Nonlinear dynamic simulation is done by taking the nonlinearity of bearing oil film dynamic force into full consideration, with the latter being expressed by a special database which is generated beforehand, and based on non stationary Reynolds equation and Reynolds boundary condition of film rupture. The linear and nonlinear unbalance responses of a Jeffcot rotor supported on a pair of elliptical bearings is studied. The resulting dynamic characteristics and rotor and journal whirling orbits are compared. While good consistancy between nonlinear and linear predictions is found under very small unbalance, significant or even drastic differences are found whenever the unbalance is not small, indicating the necessity of including the nonlinearity of oil film dynamic forces, especially when response to large unbalance is to be predicted.

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.

Bearing loads of dual rotor-bearing system under stationary and transient conditions

Aimed at aeroengine vibration failure, bearing loads of dual rotor-bearing system caused by unbalance are calculated under stationary and transient conditions. The three-dimensional （3-D） finite element method （FEM） model of dual rotor-bearing system was established. Applying the ro- tor dynamics function of Ansys 12.0, bearing loads were calculated under various unbalance force in stationary condition, and the transient vibration characteristics and the effect of acceleration on bearing loads were discussed. On the basis of simulation results, the influence disciplines of unbal- ance on bearing loads and theoretic reference for reducing bearing loads during start-up were ob- tained.

Variable Parameters PD Control and Stability of a High Rate Rigid Rotor-Journal Active Magnetic Bearing System

Stability is a key problem that means whether a high rate rotor-active magnetic bearings system works reliably or not. Aiming at a bearings system described with nonlinear equations, this paper built a linear model according to the system behavior. Considering realization of the control system and behavior of a high rate rotor system (magnetic force is far smaller than input force produced by mass eccentricity) this paper proposes a design method of variable parameters PD control algorithm that can be used universally. The control system was simplified and a mass of adjusting work of control parameters was reduced. Analysis and simulation indicated that the bearings system could get a wider stable region of harmonic motion, and proved that the algorithm is robust and advanced. The control system can be realized because the winding electric currents are positive. The method is convenient for operation and can easily be used for engineering practice.

Hot deformation characteristics of as-cast high-Cr ultra-super-critical rotor steel with columnar grains

Isothermal hot compression tests of as-cast high-Cr ultra-super-critical（USC） rotor steel with columnar grains perpendicular to the compression direction were carried out in the temperature range from 950 to 1250°C at strain rates ranging from 0.001 to 1 s^（-1）. The softening mechanism was dynamic recovery（DRV） at 950°C and the strain rate of 1 s^（-1）, whereas it was dynamic recrystallization（DRX） under the other conditions. A modified constitutive equation based on the Arrhenius model with strain compensation reasonably predicted the flow stress under various deformation conditions, and the activation energy was calculated to be 643.92 kJ ×mol^（-1）. The critical stresses of dynamic recrystallization under different conditions were determined from the work-hardening rate（θ）–flow stress（σ） and-θ/σ–σ curves. The optimum processing parameters via analysis of the processing map and the softening mechanism were determined to be a deformation temperature range from 1100 to 1200°C and a strain-rate range from 0.001 to 0.08 s^（-1）, with a power dissipation efficiency η greater than 31%.

Combined resonance of low pressure cylinder-generator rotor system with bending-torsion coupling

A nonlinear model of a low pressure cylinder-generator rotor system is presented to study sub-synchronous resonance and combined resonance. Analytical results are obtained by an averaging method. Transition sets and bifurcation diagrams are obtained based on the singularity theory for the two-state variable system. The bifurcation characteristics are analyzed to provide a basis for the optimal design and fault diagnosis of the rotor system. Finally, the theoretical results are verified with the numerical results.

Dynamic Behavior of a Brushless in Runner Motor

In this article, a model of a rotor with an asymmetric disk is presented in order to represent Campbell’s diagrams and instability maps as a function of the rotations of the support which can significantly change the dynamic behavior of the rotor. Critical rotating speeds can also lead to unacceptable levels of vibration. Indeed, the critical speeds are a function of the dynamic rigidity of the rotating systems and the presence of the gyroscopic forces creates a dependence between the rotating speed of rotation and the natural frequencies to such structures (the CAMPBELL diagrams): this implies that the correct determination of the critical speeds is one of the essential elements when sizing such dynamic systems.

THE ANALYSIS FOR THE AIRFLOW EXCITING-VIBRATION FORCE OF CONTROL STAGE OF STEAM TURBINE

Based on the hydrodynamics, the airflow exciting-vibration force of control stage of steam turbine is studied by using the momentum theorem. A formulation for calculating the air exciting-vibration force of the control stage of steam turbine is deduced first by using theoretical analysis method and taking all the design factors of vane and nozzles into consideration. Moreover, the exciting-vibration forces in different load cases are discussed respectively.

Application of the Non-Stationary Oil Film Force Database

The technique of non stationary oil film force database for hydrodynamic bearing is introduced and its potential applications in nonlinear rotor dynamics are demonstrated. Through simulations of the locus of the shaft center aided by the database technique, nonlinear stability analysis can be performed and the natural frequency can be obtained as well. The easiness of 'assembling' the individual bush forces from the database to form the bearing force, makes it very convenient to evaluate the stability of various types of journal bearings. Examples are demonstrated to show how the database technique makes it possible to get technically abundant simulation results at the expense of very short calculation time.

SOLUTION FOR PRESSURE DISTRIBUTION IN SQUEEZE FILM DAMPER WITH ELECTROHYDRAULIC ACTIVE CONTROL

Aiming at the problems existed in the squeeze film damper of the rotating machinery utilizing traditional passive dynamic pressure film bearing, a project of dynamic pressure and static pressure hybrid oil film bearing with piezoelectric crystal electrohydraulic active control supply orifice hole is proposed. For this kind of hybrid film bearing, the π film assumption can not hold true. In order to solve the pressure distribution, a new kind of solving method is proposed.

Identification method for helicopter flight dynamics modeling with rotor degrees of freedom

A comprehensive method based on system identification theory for helicopter flight dynamics modeling with rotor degrees of freedom is developed. A fully parameterized rotor flapping equation for identification purpose is derived without using any theoretical model, so the confidence of the identified model is increased, and then the 6 degrees of freedom rigid body model is extended to 9 degrees of freedom high-order model. Bode sensitivity function is derived to increase the accuracy of frequency spectra calculation which influences the accuracy of model parameter identification. Then a frequency domain identification algorithm is established. Acceleration technique is developed furthermore to increase calculation efficiency, and the total identification time is reduced by more than 50% using this technique. A comprehensive two-step method is established for helicopter high-order flight dynamics model identification which increases the numerical stability of model identification compared with single step algorithm. Application of the developed method to identify the flight dynamics model of BO 105 helicopter based on flight test data is implemented. A comparative study between the high-order model and rigid body model is performed at last. The results show that the developed method can be used for helicopter high-order flight dynamics model identification with high accuracy as well as efficiency, and the advantage of identified high-order model is very obvious compared with low-order model.

Interval analysis of rotor dynamic response based on Chebyshev polynomials

Uncertainty is extensively involved in the rotor systems of rotating machinery, which may cause an unstable vibrational response. To take the uncertainty into consideration for the uncertain rotor-bearing system, an improved unified interval analysis method based on the Chebyshev expansion is established in this paper. Firstly, the Chebyshev Interval Method(CIM) to calculate not only the critical speeds but also the dynamic response of rotor with uncertain parameters is introduced. Then, the numerical investigation is carried out based on the developed double disk rotor model and computation procedure, and the results demonstrate the validity. But when the uncertainty is sufficiently large to influence critical speeds, the upper and lower bounds are far from the actual bounds. In order to overcome the defects, a Bound Correction Interval analysis Method(BCIM) is proposed based on the Chebyshev expansion and the modal superposition. In use of the improved method, the bounds of the interval responses, especially the upper bound,are corrected, and the comparison with other methods demonstrates that the higher accuracy and a wider application range.

Rapid solution for analysis of nonlinear fluid film force and dynamic behavior of a tilting-pad journal bearing-rotor system with turbulent and thermal effects

To analyze the nonlinear dynamics of a tilting-pad journal bearing(TPJB)-rotor system with high accuracy and speed,the database method(DM)is modified to rapidly determine the nonlinear fluid film force(NFFF)of a TPJB while considering turbulent and thermal effects.A high-accuracy,large-capacity NFFF database for a single pad is constructed by numerically solving the turbulent adiabatic hydrodynamic model for five equivalent state variables of the journal,which are discretized in the pad coordinates.The remaining variables are not discretized in the DM.A combined linear and parabolic interpolation polynomial based on the database is established to accurately calculate the NFFF of the tilting pads;thus,the NFFF of a four-pad TPJB is obtained in the bearing coordinates.The DM is applied to analyze and compare the nonlinear dynamic behavior of a water-lubricated TPJB-Jeffcott rotor system with and without turbulent and thermal effects.The present DM solution without these effects and the previous DM solution are shown to be consistent.The results demonstrate the importance of the flow regime and the negligibility of temperature increases in the nonlinear dynamics of a water-lubricated TPJB.This work contributes to the accurate and efficient analysis of the nonlinear dynamics of high-speed TPJBs and low-viscosity-fluid-lubricated TPJBs.

Dynamic behavior of aero-engine rotor with fusing design suffering blade off

Fan blade off（FBO） from a running turbofan rotor will introduce sudden unbalance into the dynamical system,which will lead to the rub-impact,the asymmetry of rotor and a series of interesting dynamic behavior.The paper first presents a theoretical study on the response excited by sudden unbalance.The results reveal that the reaction force of the bearing located near the fan could always reach a very high value which may lead to the crush of ball,journal sticking,high stress on the other components and some other failures to endanger the safety of engine in FBO event.Therefore,the dynamic influence of a safety design named ‘‘fusing＂ is investigated by mechanism analysis.Meantime,an explicit FBO model is established to simulate the FBO event,and evaluate the effectiveness and potential dynamic influence of fusing design.The results show that the fusing design could reduce the vibration amplitude of rotor,the reaction force on most bearings and loads on mounts,but the sudden change of support stiffness induced by fusing could produce an impact effect which will couple with the influence of sudden unbalance.Therefore,the implementation of the design should be considered carefully with optimized parameters in actual aero-engine.

Innovated Inertia Control of DFIG with Dynamic Rotor Speed Recovery

High wind power penetration(WPP)is challenging system frequency stability.As a countermeasure,virtual inertia controls are introduced,utilizing kinetic energy(KE)stored in wind turbine generators(WTGs)for frequency regulation.Without restoration,generation efficiency of WTGs will be degraded after inertia contribution.To counter this issue,we propose an inertia control scheme of a doubly fed induction generator(DFIG),aiming at achieving dynamic inertia recovery regarding both KE and DC link energy.An asymmetrical droop control,referred to as the rate of change of frequency(RoCoF),is proposed for KE management.The upper boundary of droop gain is extended to give full play to converters and is revised,considering the system frequency state,to counter positive feedback issues induced by reversible gain regulation,which is restricted by KE to ensure stable operations as well.The inertial DC energy needed to cooperate with KE control regarding countering small fluctuations,is improved with an orderly recovery behavior.Case studies are conducted under dynamic wind conditions and the results indicate that with our proposed scheme,the ability of dynamic inertia recovery can be obtained,bringing DFIG higher generation efficiency and more adequate operation margin for sustained regulation.Essentially,the inertial frequency response and fluctuation suppression ability is well maintained.

Study on dynamic stiffness of supporting structure and its influence on vibration of rotors

The dynamic response of the rotor depends on not only itself but also the dynamical characteristics of the structures that support it. In this paper, the coupling vibration characteristics of the rotor and supporting structure are studied using one simple rotor-supports model firstly, and then the dynamic stiffness of the typical supporting structure of an aero-engine is investigated in use of both numerical and experimental methods. While, one simulation strategy is developed to include dynamic stiffness of realistic supports in the dynamical analysis of the rotor system. The simulated and tested results show that the dynamic stiffness of the supporting structure not only depends on the structural parameters but also is related to the frequency of the excitation force. The dynamic stiffness is affected by the damping and inertia effect when the excitation frequency is high and closed to the resonance frequency of the support, which may decrease the dynamic stiffness sharply.More resonance frequencies may be induced and the critical speed could be reduced or increased.While higher vibration response peak and overload of the bearing may also be caused by the varied dynamic stiffness, which needs to be avoided in the design of the rotor-supports system.

Solar-PV inverter for the overall stability of power systems with intelligent MPPT control of DC-link capacitor voltage

This paper demonstrates the controlling abilities of a large PV-farm as a Solar-PV inverter for mitigating the chaotic electrical,electromechanical,and torsional oscillations including Subsynchronous resonance in a turbogenerator-based power system.The oscillations include deviations in the machine speed,rotor angle,voltage fluctuations(lead-ing to voltage collapse),and torsional modes.During the night with no solar power generation,the PV-plant switches to PV-STATCOM mode and works as a Solar-PV inverter at its full capacity to attenuate the oscillations.During full sun in the daytime,on any fault detection,the PV-plant responds instantly and stops generating power to work as a Solar-PV inverter.The PV-farm operates in the same mode until the oscillations are fully alleviated.This paper mani-fests the control of the DC-link capacitor voltage of the Solar-PV inverter with a bacterial foraging optimization-based intelligent maximum power point tracking controller for the optimal control of active and reactive power.Kundur’s multi-machine model aggregated with PV-plant is modeled in the Matlab/Simulink environment to examine the rotor swing deviations with associated shaft segments.The results for different test cases of interest demonstrate the posi-tive outcomes of deploying large PV-farms as a smart PV-STATCOM for controlling power system oscillations.

Constitutive analysis and optimization on hot working parameters of as-cast high Cr ultra-super-critical rotor steel with columnar grains

Isothermal hot compression tests on the as-cast high-Cr ultra-super-critical rotor steel with columnar grains were carried out in the temperature range from 1223 to 1523Kand at strain rates from 0.001 to 1s^（-1）.The compression direction was parallel to the longitudinal direction of columnar grains.The constitutive equation based on Arrhenius model was presented,and the processing maps based on the dynamic material model were developed,correlating with microstructure observation.The main softening mechanism was dynamic recovery at 1223 Kunder strain rates from 0.1to 1s^（-1）,whereas it was dynamic recrystallization under other deformation conditions.The constitutive equation modified by strain compensation reasonably predicted the flow stresses.The processing maps and microstructure evolution mechanism schematic indicated that the optimum hot working parameters lay in the zone defined by the temperature range from 1423 to 1473Kand the strain rate range from 0.001 to 1s^（-1）.