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.

COMPENSATION CONTROL OF REAL-TIME UNBALANCE FORCE FOR ACTIVE MAGNETIC BEARING SYSTEM

Aiming at the stability and others properties of active magnetic bearing （AMB） system influenced by the periodic unbalance stimulation synchronous with rotor rotational speed, a new real-time adaptive feed-forward unbalance force compensation scheme is proposed based on variable step-size least mean square（LMS） algorithm as the feed-forward compensation controller. The controller can provide some suitable sinusoidal signals to com- pensate the feedback unbalance response signals synchronous with the rotary frequency, then reduce the fluctua- tion of the control currents and weaken the active control of AMB system. The variable step-size proportional to the rotational frequency is deduced by analyzing the principle of normal LMS algorithm and its deficiency in the application of real-time filtering of AMB system. Experimental results show that the new method can implement real-time unbalance force compensation in a wide frequency band, reduce the effect of unbalance stimulant force on the housing of AMB system, and provide convenience to improve rotational speed.

Unbalance Vibratory Displacement Compensation for Active Magnetic Bearings

As the dynamic stiffness of radial magnetic bearings is not big enough, when the rotor spins at high speed, unbalance displacement vibration phenomenon will be produced. The most effective way for reducing the displacement vibration is to enhance the radial magnetic bearing stiffness through increasing the control currents, but the suitable control currents are not easy to be provided, especially, to be provided in real time. To implement real time unbalance displacement vibration compensation, through analyzing active magnetic bearings （AMB） mathematical model, the existence of radial displacement runout is demonstrated. To restrain the runout, a new control scheme-adaptive iterative learning control （A1LC） is proposed in view of rotor frequency periodic uncertainties during the startup process. The previous error signal is added into AILC learning law to enhance the convergence speed, and an impacting factor/3 influenced by the rotor rotating frequency is introduced as learning output coefficient to improve the rotor control effects, As a feed-forward compensation controller, AILC can provide one tmknown and perfect compensatory signal to make the rotor rotate around its geometric axis through power amplifier and radial magnetic bearings. To improve AMB closed-loop control system robust stability, one kind of incomplete differential PID feedback controller is adopted. The correctness of the AILC algorithm is validated by the simulation of AMB mathematical model adding AILC compensation algorithm through MATLAB soft. And the compensation for fixed rotational frequency is implemented in the actual AMB system. The simulation and experiment results show that the compensation scheme based on AILC algorithm as feed-forward compensation and PID algorithm as close-loop control can realize AMB system displacement minimum compensation at one fixed frequency, and improve the stability of the control system. The proposed research provides a new adaptive iterative/earning control algorithm and control strategy for AMB displacement minimum compensation, and provides some references for time-varied displacement minimum compensation.

Model-Based Degree Estimation of Unbalance and Misalignment in Flexible Coupling-rotor System

The condition of rotor system must be assessed in order to develop condition-based maintenance for rotating machinery. It is determined by multiple variables such as unbalance degree, misalignment degree, the amount of bending deformation of the shaft, occurrence of shaft crack of rotor system and so on. The estimation of the degrees of unbalance and misalignment in flexible coupling-rotor system is discussed. The model-based approach is employed to solve this problem. The models of the equivalent external loads for unbalance and misalignment are derived and analyzed. Then, the degrees of unbalance and misalignment are estimated by analyzing the components of the equivalent external loads of which the frequencies are equal to the 1 and 2 times running frequency respectively. The equivalent external loads are calculated according to the dynamic equation of the original rotor system and the differences between the dynamical responses in normal case and the vibrations when the degree of unbalance or misalignment or both changes. The denoise method based on bandpass filter is used to decrease the effect of noise on the estimation accuracy. The numerical examples are given to show that the proposed approach can estimate the degrees of unbalance and misalignment of the flexible coupling-rotor system accurately.

A Review on Self-Recovery Regulation(SR)Technique for Unbalance Vibration of High-End Equipment

The high-end equipment represented by high-end machine tools and aero-engines is the core component of the national intelligent manufacturing plan,and the mass unbalance is the main reason for its excessive vibration,that seriously impacts the operation efficiency and running life of the equipment.In order to change the traditional way that the fault of equipment can only be repaired by human,the self-recovery mechanism of human and animal are given to the equipment in this paper,which forms the self-recovery regulation(SR)system for unbalance vibration of high-end equipment.The system can online generate the self-recovery force to restrain the unbalance vibration of the equipment in operation,which is an important direction for the development of the equipment to the advanced intelligent stage.Based on the basic principles of SR technique,the typical engineering application cases of this technique in the field of aeroengine and high-end machine tools are introduced,and four related studies promoting the development of this technique are summarized and analyzed in turn.It includes feature extraction,imbalance location,regulation method and balancing actuator.Self-recovery Regulation(SR)Technique is an important way to realize intelligent manufacturing and intelligent maintenance.Relevant research can lay a technical foundation for the development of high-end equipment with self-health function.

Science Letters:Multi-frequency proportional-resonant (MFPR) current controller for PWM VSC under unbalanced supply conditions

This letter presents a multi-frequency proportional-resonant （MFPR） current controller developed for PWM voltage source converter （VSC） under the unbalanced supply voltage conditions. The delta operator is used in place of the shift operator for the implementation of MFPR by using a low-cost fixed-point DSE The experimental results with an alternative control strategy validated the feasibility of the proposed MFPR current controller for the PWM VSC during voltage unbalance.

Effects of Unbalance Location on Dynamic Characteristics of High-speed Gasoline Engine Turbocharger with Floating Ring Bearings

For the high-speed gasoline engine turbocharger rotor, due to the heterogeneity of multiple parts material, manufacturing and assembly errors, running wear in impeller and uneven carbon of turbine, the random unbalance usually can be developed which will induce excessive rotor vibration, and even lead to nonlinear vibration accidents. However, the investigation of unbalance location on the nonlinear high-speed turbocharger rotordynamic characteristics is less. In order to discuss the rotor unbalance location effects of turbocharger with nonlinear floating ring bearings（FRBs）, the realistic turbocharger of gasoline engine is taken as a research object. The rotordynamic equations of motion under the condition of unbalance are derived by applied unbalance force and nonlinear oil film force of FRBs. The FE model of turbocharger rotor-bearing system is modeled which includes the unbalance excitation and nonlinear FRBs. Under the conditions of four different applied locations of unbalance, the nonlinear transient analyses are performed based on the rotor FEM. The differences of dynamic behavior are obvious to the turbocharger rotor systems for four conditions, and the bifurcation phenomena are different. From the results of waterfall and transient response analysis, the speed for the appearance of fractional frequency is not identical and the amplitude magnitude is different from the different unbalance locations, and the non-synchronous vibration does not occur in the turbocharger and the amplitude is relative stable and minimum under the condition 4. The turbocharger vibration and non-synchronous components could be reduced or suppressed by controlling the applied location of unbalance, which is helpful for the dynamic design, fault diagnosis and vibration control of the high-speed gasoline engine turbochargers.

Torsional vibration analysis of lathe spindle system with unbalanced workpiece

For the purpose of analyzing the torsional vibration caused by the gravitational unbalance torque arisen in a spindle system when it is machining heavy work piece,a 10-DOF lumped parameter model was made for the machine tool spindle system with geared transmission.By using the elementary method and Runge-Kutta method in Matlab,the eigenvalue problem was solved and the pure torsional vibration responses were obtained and examined.The results show that the spindle system cannot operate in the desired constant rotating speed as far as the gravitational unbalance torque is engaged,so it may cause bad effect on machining accuracy.And the torsional vibration increases infinitely near the resonant frequencies,so the spindle system cannot operate normally during these spindle speed ranges.

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.

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 e ects 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 di erent levels of induced unbalance magni?tude 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 e ects of induced unbalance in the turbine wheel is obvious stronger than the compressor wheel. As the unbalance magnitude increases from 0.05 gbration 1·mm to 0.2 g·mm, the vibration component changes from mainly 0.12× to synchronous vi×. 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.

A Practical Strategy of Unbalance Identification and Correction for 2-DOF Precision Centrifuges

Unbalance existing in the mechanical systems is one of the most common causes which leads to unexpected vibration,nonsmooth motions,uncertain dynamics and even instability. In this paper,the problem of unbalance identification and correction is investigated for the countershaft system of a precision centrifuge with two degrees of freedom. According to the characteristics of the load under test installed on the countershaft,a gradual subdivision algorithm is proposed to identify the phase of the unbalance,and its amplitude is calculated by using a space vector algorithm,where the vibration information of the mainshaft system is obtained by utilizing two axis-layout displacement transducers installed associated to the mainshaft.Based on ADAMS software,some numerical simulations are presented and compared,and further,the validity of the strategy is demonstrated by experimental examples.

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.

Voltage Unbalance Mitigation in Low Voltage Distribution Networks with Photovoltaic Systems

This paper proposes a technique to mitigate the voltage unbalance issue caused by the high penetration of photovoltaic （PV） systems into the low voltage distribution networks （LVDN） using a single phase energy storage system （ESS）. The ESS comprises a hi-directional power flow inverter and a battery bank. The system is capable of absorbing the excess power and delivering power to the network in order to keep the voltage unbalance factor （VUF） below the statutory limit of 1%. Investigations are carried out in the experimental small-scale energy zone （SSEZ）. The experimental results demonstrate that the ESS is capable of mitigating the VUF of the network.

Influence of dynamic unbalance of wheelsets on the dynamic performance of high-speed cars

With further increasing in running speed of newer high-speed EMUs（electric multiple units）,higher demand for wheelset dynamic balance is required.In order to study the influence of the dynamic unbalance of wheelset on the stability,ride quality,and curving performance for a high-speed car,a detailed dynamic model of a high-speed EMU car is established using the software SIMPACK.The analysis results indicate that the dynamic unbalance of the wheelset significantly influences the dynamic performance of the high-speed car.The increase in dynamic unbalance of the wheelset will decrease the hunting critical speed,worsen the vertical ride quality,and increase the wheelset lateral force,derailment coefficient,and wheel unloading ratio.Therefore,in order to improve the stability,ride quality,and running safety of high-speed car,the values of dynamic unbalance of wheelset should be strictly controlled in manufacturing,and periodically monitored in operation.

Identification of Rotor Unbalance as Inverse Problem of Measurement

In this paper, the problem of identification of the characteristics of the rotor unbalance on two supports is investigated as the inverse problem of measurement. The vibration of rotor supports in two mutually perpendicular directions used as the initial information. The inverse problem is considered, taking into account the error of the mathematical description of rotor-bearings system. To obtain estimates of real unbalance characteristics, the hypothesis as to the exact solutions is applied. The method of Tikhonov regularization is used to obtain stable results. Test calculations are given to illustrate the proposed approach.

Research of Three-Phase Unbalanced Treatment in Low-Voltage Distribution Network Based on New Commutation Switch

Low-voltage distribution systems in our country are mostly used in agricultural loads and household loads. The value and using time of these kinds of loads are uncontrollable, which lead to the three-phase imbalance in low-voltage distribution system, and seriously affect the quality of power supply. A new type of the commutation system and an improved quantum genetic algorithm (IQGA) are proposed in the paper. At last, the rationality and the efficiency of the method are verified by a practical example.

Three-Phase Unbalance Prediction of Electric Power Based on Hierarchical Temporal Memory

The difference in electricity and power usage time leads to an unbalanced current among the three phases in the power grid.The three-phase unbalanced is closely related to power planning and load distribution.When the unbalance occurs,the safe operation of the electrical equipment will be seriously jeopardized.This paper proposes a Hierarchical Temporal Memory(HTM)-based three-phase unbalance prediction model consisted by the encoder for binary coding,the spatial pooler for frequency pattern learning,the temporal pooler for pattern sequence learning,and the sparse distributed representations classifier for unbalance prediction.Following the feasibility of spatial-temporal streaming data analysis,we adopted this brain-liked neural network to a real-time prediction for power load.We applied the model in five cities(Tangshan,Langfang,Qinhuangdao,Chengde,Zhangjiakou)of north China.We experimented with the proposed model and Long Short-term Memory(LSTM)model and analyzed the predict results and real currents.The results show that the predictions conform to the reality;compared to LSTM,the HTM-based prediction model shows enhanced accuracy and stability.The prediction model could serve for the overload warning and the load planning to provide high-quality power grid operation.

Dynamic unbalance detection of cardan shaft in high-speed train based on EMD-SVD-NHT

Contrary to the aliasing defect between the adjacent intrinsic model functions(IMFs) existing in empirical model decomposition(EMD), a new method of detecting dynamic unbalance with cardan shaft in high-speed train was proposed by applying the combination between EMD, Hankel matrix, singular value decomposition(SVD) and normalized Hilbert transform(NHT). The vibration signals of gimbal installed base were decomposed through EMD to get different IMFs. The Hankel matrix constructed through the single IMF was orthogonally executed through SVD. The critical singular values were selected to reconstruct vibration signs on the basis of the key stack of singular values. Instantaneous frequencys(IFs) of reconstructed vibration signs were applied to detect dynamic unbalance with shaft and eliminated clutter spectrum caused by the aliasing defect between the adjacent IMFs, which highlighted the failure characteristics. The method was verified by test data in the unbalance condition of dynamic cardan shaft. The results show that the method effectively detects the fault vibration characteristics caused by cardan shaft dynamic unbalance and extracts the nature vibration features. With comparison to the traditional EMD-NHT, clarity and failure characterization force are significantly improved.

Influence of Operating Parameters on Unbalance in Rotating Machinery Using Response Surface Method

Wide range of rotating machinery contains an inherent amount of unbalance which leads to increase in the vibration level and related faults.In this work,the effect of different operating conditions viz.the unbalanced weight,radius,speed and position of the rotor disc on the unbalance in rotating machine are studied experimentally and analyzed by using Response Surface Methodology(RSM).RSM is a technique which consists of mathematical and statistical methods to develop the relationship between the inputs and outputs of a system by distinct functions.L27 Orthogonal Array(OA)was developed by using Design of Experiments(DOE)according to which experimentation has been carried out.Three accelerometer sensors were mounted to record the vibration responses(accelerations)in radially vertical,horizontal and axial directions.The responses recorded as root mean square values are then analysed using RSM.The relationship between response and operating factors has been established by developing a second order,non-linear mathematical model.Analysis of variance(ANOVA)has been performed for verification of the developed mathematical models.Results obtained from the analysis show that the unbalance weight and speed are most significant operating conditions that contribute the most to the effect the unbalance has on the rotating spindle.

A Sliding Mode Approach to Enhance the Power Quality of Wind Turbines Under Unbalanced Voltage Conditions

An integral terminal sliding mode-based control design is proposed in this paper to enhance the power quality of wind turbines under unbalanced voltage conditions. The design combines the robustness, fast response, and high quality transient characteristics of the integral terminal sliding mode control with the estimation properties of disturbance observers. The controller gains were auto-tuned using a fuzzy logic approach.The effectiveness of the proposed design was assessed under deep voltage sag conditions and parameter variations. Its dynamic response was also compared to that of a standard SMC approach.The performance analysis and simulation results confirmed the ability of the proposed approach to maintain the active power,currents, DC-link voltage and electromagnetic torque within their acceptable ranges even under the most severe unbalanced voltage conditions. It was also shown to be robust to uncertainties and parameter variations, while effectively mitigating chattering in comparison with the standard SMC.