Unbalanced Magnetic Pull Research Articles

Study of Unsymmetrical Magnetic Pulling Force and Magnetic Moment in 1000 MW Hydrogenerator Based on Finite Element Analysis

The large dimensions of the 1000 MW hydroelectric generator sets require high mounting accuracy. Small deviations can lead to asymmetry, which in turn triggers unbalanced magnetic pulls and moments. Therefore, symmetry is a central challenge in the installation and operation of giant hydroelectric generators. In this paper, the effects of radial eccentricity, axial offset, and rotor shaft deflection on the unbalanced magnetic pull and moment are investigated by transient finite element analysis of the asymmetric magnetic field. The results of the time-domain and frequency-domain analyses show that asymmetric operation generates unbalanced magnetic forces and moments. These forces and moments increase linearly with increasing offset or deflection rate. When the eccentricity meets the installation criteria, the unbalanced magnetic pull forces are small and within acceptable limits. This study helps to understand the relationship between asymmetry and unbalanced magnetic pulling forces in large hydroelectric generators, and provides a theoretical basis for standardizing installation deviation control.

A comprehensive study on electromagnetic torque and rotor UMP based on an improved 3D static air-gap eccentricity model

Static air-gap eccentricity (SAGE) is a common fault in generators. Current researches primarily focus on the parallel SAGE types, while the inclined static air-gap eccentricity (ISAGE) has been rarely investigated. This paper proposes an improved air-gap eccentricity model and presents a study on the electromagnetic-mechanical properties in synchronous generators under typical ISAGE running conditions. Such electromagnetic-mechanical properties include not only the magnetic flux density (MFD) variations, but also the mechanical responses of the electromagnetic torque (EMT) and rotor unbalanced magnetic pulls (UMP). The typical ISAGE factors include: 1) a varied rotor inclined angle θ, and 2) different values of axial inclined distance z (indicates the offset combination case of the two rotor ends). This work is based on the MFD analysis calculation. Theoretical analysis, finite element analysis, and experimental study are carried out, respectively, by taking a 5 kVA two-pole prototype generator as the study object. It is shown that the electromagnetic-mechanical properties of the generator will change when the inclined eccentricity occurs. The EMT, and the rotor UMP as well as the vibrations will increase as the rotor inclined θ and z increase. Specifically, the 2nd harmonic has the most significant variation.

Research on unbalanced characteristics of axial-varying eccentric rotor based on signal demodulation

In the presence of non-uniform loads, rotor misalignment emerges as a prevalent fault in permanent magnet synchronous motors (PMSMs), leading to the manifestation of an axial-varying eccentric air–gap. Considering the three-dimensional (3D) nature of magnetic flux under axial-varying eccentric fault, 3D finite element (FE) analysis method was used in this paper. Then, the electromagnetism simulations were conducted to calculate the magnetic flux density and unbalanced magnetic pull (UMP). With the signal demodulation algorithm based on principal component analysis (DPCA), the frequency modulation of various signals from simulation and experiment was extracted. Furthermore, based on the modulation features, the relevance among magnetic flux density, UMP, and vibration acceleration was established with shaft frequency as the link. The coupling of magnetic field and vibration level shown in results was analysis, which provide important theoretical and engineering references for the safe operation of PMSM system and the exact identification of rotor tilting faults.

Torsional and lateral vibration analysis of wind turbine generator bearing outer ring fault considering unbalanced magnetic pull

Rolling bearings play a critical role in wind turbine generators, operating continuously in an electromagnetic excitation environment. Their fault vibration characteristics are affected by unbalanced magnetic pull (UMP), which has received little attention in previous studies. Moreover, torsional vibration can provide advantages in bearing fault diagnosis, since it has a good signal-to-noise ratio (SNR) and it can be easily measured by the encoder. However, torsional vibration is rarely considered in the existing model of wind turbine generator. Accordingly, this paper proposes a dynamic model with 8 degrees of freedom to analyze the bearing outer ring fault characteristics of wind turbine generator under the influence of UMP, while also taking into account the torsional vibration in the model. The validity of the model is verified through experiments conducted on a test rig. The results displays modulation of the ball pass frequency outer (BPFO) harmonics with both UMP frequency and rotation frequency in lateral vibration, and this phenomenon can also be observed in instantaneous angular speed (IAS) and instantaneous angular acceleration (IAA) signals that represent torsional vibration. Besides, the lateral vibration spectrum reveals two distinct resonance bands, and simulation analysis suggested that the rotor and bearings give rise to low-frequency and high-frequency resonance, respectively. This study provides a reference for bearing faults diagnosis in wind turbine generator.

Nonlinear response of hydraulic turbine generator set caused by unbalanced magnetic pull and oil film force

Hydraulic turbine generator sets are crucial for harnessing water energy. However, the nonlinear phenomena resulting from the combination of unbalanced magnetic pull (UMP) and oil film forces remain unclear. A mathematical model of the rotor-bearing system is introduced to investigate the effects of UMP and the nonlinear oil film force on system. The UMP and nonlinear oil film force are derived from the air-gap magnetic energy and short bearing theory, respectively. The proposed model is verified by the stability experiments of hydraulic turbine generator set in the idling, no-load, and load conditions. The results show that, firstly, the system turns unstable for oil whip and oil swirl, and which experiences bifurcation and undergoes dynamical motions such as period-1 to period-5, quasi-periodic, and chaotic motions. Then, at moderate speeds, the rotor eccentricity has the greatest effect on the bifurcation at idle. While the nonlinear characteristics of the system are most sensitive to the rotor eccentricity at loaded condition. Finally, the existence of UMP reduces the instability caused by oil film forces.

Analysis on Rotor Vibration Characteristics under Dynamic Rotor Interturn Short Circuit Fault in Synchronous Generators

A dynamic rotor interturn short circuit fault may occur during synchronous generator operation. However, there is no method to analyze the generator’s characteristics under the dynamic rotor interturn short circuit fault and identify the fault. In order to solve this problem, a new dynamic rotor interturn short circuit fault analysis model is creatively proposed through mathematical derivation. Firstly, the rotor vibration characteristics and the mechanical response under magnetic pull excitation are theoretically analyzed. In addition, a finite element modeling method for the dynamic rotor interturn short circuit fault is proposed, and an experimental device is designed. The model of a synchronous generator under the dynamic rotor interturn short circuit fault is established to obtain the rotor’s unbalanced magnetic pulls and mechanical responses by finite element calculation. Finally, the rotor vibrations are tested on a CS-5 prototype generator. The validity of the model is verified by finite element calculation and an experiment. This paper provides theoretical support for the diagnosis of a synchronous generator’s dynamic rotor interturn short circuit fault.

Study on unbalanced magnetic pull of permanent magnet toroidal motor with planet rotor eccentricity

Permanent magnet toroidal motor (PMTM) is a novel spatial motor that integrates toroidal drive system and permanent magnet synchronous motor. The unbalanced magnetic pull (UMP) with planet rotor eccentricity is the main cause of vibration in PMTM. In this paper, the analytical model of magnetic field with planet rotor eccentricity is established with the consideration of magnetic flux leakage. The calculation results of eccentric magnetic fields are compared with simulation results of finite element model. Based on the Maxwell tensor method, the analytical model of UMP with planet rotor eccentricity is established. The changes of UMP with initial eccentricity are obtained. The UMP is analyzed with the effects of eccentric distance and angle. The transient variations of UMP are discussed with different eccentric situations respectively. In addition, both simulation and calculation results for UMP have a good agreement, which verifies the validity of analytical model.

Unbalanced Magnetic Pull Disturbance Compensation of Magnetic Bearing Systems in MSCCs

Unbalanced magnetic pull (UMP) disturbance seriously affects the stable operation of the magnetically suspended rotor (MSR) system. This article proposes an UMP disturbance suppression method based on a linear extended state observer (LESO) and adaptive peak filter (APF). The cascade structure of LESO and APF can accurately estimate the UMP disturbance in the whole speed range. First, the dynamic model of the active magnetic bearing rotor systems is established and the UMP caused by the dynamic eccentricity in the MSR system is analyzed. Second, a third-order LESO and an APF are designed. The performance evaluation of the LESO indicates that estimation error of disturbance decreases with the increase of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\omega _{o}$</tex-math></inline-formula> , and the addition of APF can make UMP disturbance estimation unaffected by the high-frequency noise. After adding this method, the closed-loop system remains stable within the working rotation speed range. Finally, simulation results show that the UMP disturbance can be estimated and compensated. Experimental results validate the proposed method can well suppress the large vibration of the UMP on the rotor.

Dynamic Characteristics Analysis of Magnetic Levitation Rotor Considering Unbalanced Magnetic Pull

The working principle of the motor can cause unbalanced magnetic pull (UMP) between stator and rotor unavoidably. Previous research about nonlinear vibration excited by UMP was focused on the rotor supported by traditional mechanical bearings or gas bearings. However, the magnetic levitation rotor is particular due to the low rigidity provided by the active magnetic bearing (AMB). UMP amplifies rotor vibration in the resonant zone and further excites the nonlinear electromagnetic force, thus producing different vibration phenomena. The paper calculates rotor orbit, spectra analysis, and time-history plot with numerical methods and studies the influence of the rotation speed, eccentricity, key control parameters, and UMP on rotor dynamics in detail. Results illustrate displacement response spectra of the magnetic levitation rotor are quite different from previous research results. The appearing frequency components are inducted by universal formulas in this paper. Furthermore, research shows a slight adjustment of the control parameters affect significantly harmonic components and vibration characteristics. The research results have practical reference significance for fault diagnosis, feature recognition, and controller optimization of the AMB-rotor system.

Dynamic analysis of grinding electric spindle bearing-rotor system under eccentric action

To study the influence of eccentricity on the dynamic characteristics of grinding electric spindle, firstly, the nonlinear oil film force (NOFF) expression of sliding bearing is established based on the boundary condition of adhesion pressure. Then, the expression of the unbalanced magnetic pull (UMP) under the eccentricity of the air gap is derived. Finally, the bearing-rotor dynamics equation of the grinding electric spindle considering the NOFF and UMP is established, and the dimensionless processing is carried out. The nonlinear dynamics study of the bearing-rotor system under the influence of geometric eccentricity and mass eccentricity is carried out through the shaft center trajectory and the shaft center vibration spectrum. The research results can provide reference for the optimal design of grinding electric spindle.

Design and Optimization of a Radial Magnetic Bearing Considering Unbalanced Magnetic Pull Effects for Magnetically Suspended Compressor

In magnetic suspended centrifugal compressors, the unbalanced magnetic pull (UMP) may cause saturation on power amplifier currents driving the coils of the active magnetic bearing (AMB), eventually affecting the stability of the rotor. This article addresses the issue on the stable operation of the AMB-rotor system subject to the UMP. A mathematical model of the UMP with uneven magnetization of permanent magnet (PM) and eccentricity is proposed for a surface-mounted PM synchronous motor supported by magnetic bearings. Based on this model, an improved radial magnetic bearing (RMB) with control and bias separated coil structure is designed and optimized to decrease the compensation current used to balance the UMP. First, a mathematical model containing the unevenness of the magnetization and eccentricity is established to estimate the UMP. Next, the compensation current for the UMP is analyzed based on the UMP model. Then, with the aim of minimizing the compensation current, the proposed RMB is optimized under the constraints of the starting current, the magnetic bearing volume, and the coil current density. The compensation current of the optimized RMB is reduced by 25%, compared with that of the original RMB. Finally, the experimental results on a 132-kW magnetic suspended centrifugal compressor, equipped with the optimized RMB, show the effectiveness of the modeling and optimization design.

Modeling and analysis of unbalanced magnetic pull in synchronous motorized spindle considering magneto-thermal coupling

The unbalanced magnetic pull (UMP) is one of the main vibration sources of the motorized spindle. A calculation model of UMP in a synchronous motorized spindle considering the magneto-thermal coupling is proposed in this paper. The finite element analysis models of the electromagnetic field and the temperature field of a motorized spindle are first established. Then a two-way coupling analysis method considering the effect of temperature variations on electromagnetic material properties of the motor is proposed. An experiment is conducted to verify the efficiency of this method. The thermal deformations of the spindle are calculated and used to analyze the air-gap variations between rotor and stator of the built-in motor. The 3D finite element electromagnetic model is adopted to calculate the UMP in the motorized spindle. The analysis results show that the eccentricity caused by thermal deformation can generate large UMP in the motorized spindle.

Effect of the unbalanced magnetic pull force and oil-film force on nonlinearity of a dual-rotor bearing system

Turbogenerator sets, the indispensible rotating machinery in thermal power plants, can be simplified into a dual-rotor bearing system. In this case, its nonlinear phenomenon largely results from the unbalanced magnetic pull (UMP) and the nonlinear oil film forces, which, however, are not well understood. In this study, a mathematical model for a dual-rotor bearing system is established, the effects of the UMP and the oil-film forces on its nonlinear phenomenon are investigated creatively. Of which, the UMP force is initially calculated by the integration of the air-magnetic energy, and the short journal bearing assumption is employed to derive the oil-film force. The fitness of the developed model is validated through the stability experiments of a 660 MW turbogenerator set. Results indicate that in the idling condition, nonlinear phenomenon of the system can be described as the period-1 and quasi-periodic motions as the rotational speed rises. At low speeds, the amplitude of oil whirl appears. With the rising rotational speed, the oil whirl turns into oil whip in the second quasi-periodic. Interestingly, the electromagnetic force can greatly alleviate the system amplitude and enhance its stability considering the UMP force. The nonlinear effect of air-gap distance of the system under load conditions is also investigated. The system is still in the quasi-periodic state with the increasing air-gap distance at low/high speed. But the system is still unstable owing to oil whirl/whip and UMP force, causing the system experiences multiple states and becomes more stable at the intermediate speed.

Dynamic characteristics analysis of asynchronous motorized spindle considering combined unbalanced magnetic pull and nonlinear bearing restoring force effects

The built-in motor of the motorized spindle is the key to realizing its movement. However, the unbalanced magnetic pull (UMP) generated in the built-in motor seriously affects its dynamic stability. In this work, a generalized time-varying dynamic model of the motorized spindle is proposed to evaluate the effect of dynamic loads on the spindle system. The external dynamic loads on the spindle mainly include the UMP generated by the built-in motor, the nonlinear restoring force of the bearing, and the eccentric excitation of the system mass. Considering the change of magnetic path caused by the dynamic displacement of the rotor, the radial and axial projection model and additional torque model of UMP are proposed. Numerical simulations are employed to handle the dynamical equation containing the time-varying UMP function. Based on the simulation results, the effects of built-in motor parameters, bearing parameters, rotor static eccentricity, and other factors on the dynamic characteristics of the spindle system are analyzed. The numerical results of the vibrations are verified experimentally.

Nonlinear dynamic characteristics of full-ceramic motorized spindle considering axial transfer of unbalanced magnetic pull

Full-ceramic motorized spindle is suitable for high-grade CNC machine tool due to its high stiffness and wear resistance, while axial transfer of unbalanced magnetic pull (UMP) caused by reverse magnetic characteristic leads to random vibration at the shaft end. In order to investigate the nonlinear dynamics of full-ceramic motorized spindles under the influence of reverse magnetic, a five-degree-of-freedom dynamic model of bearing-rotor system considering the axial transfer of UMP is constructed. The improved transfer matrix method is proposed to establish the axial transfer model of UMP and the vibration mode of the shaft is obtained. The dynamic characteristics of the bearing-rotor system are analyzed considering the effect of UMP. The magnetic field density and vibration characteristics of the motorized spindle system is studied, and the full-ceramic motorized spindle shaft influence of UMP axial transfer, the vibration of the rotor tends to decrease from inward to outward, while the shaft end vibration also tends to increase gradually with the increase of rotation speed and eccentricity value. The results show that the vibration of ceramic shaft end is 55.4% weaker than that of metal shaft end. It can be seen that under the action of the diamagnetic property, UMP transfer occurs on the ceramic shaft, which reduces the vibration. The experiments show that the average error between the calculated value and the experimental result is 8.5% at the operating speed, which verifies the accuracy of the model developed in this paper.

Permanent Magnet Synchronous Machines With Nonuniformly Distributed Teeth

An increasing interest for permanent magnet synchronous machines with low torque ripple and low vibration is observed. The purpose of this paper is to investigate the topology of non-uniformly distributed teeth and its influence of on cogging torque, tooth ripple harmonics and torque ripple of permanent magnet synchronous machines. The topologies with different number of non-uniformly distributed teeth are investigated. Analytical procedure is developed to illustrate the impacts of non-uniformly distributed teeth on cogging torque and unbalanced magnetic pull (UMP), and then identify the appropriate non-uniformly distributed teeth. A commercial 10kW 8-pole 48-slot V-shaped IPM machine is taken as the reference base machine. The machines with 2- and 6 non-uniformly distributed teeth are chosen to make an overall comparison to that with the well-known skewing slots. The machine with 2 non-uniformly distributed teeth is finally chosen to be fabricated. Intensive experiments including cogging torque, back-EMF, load current, efficiency and instantaneous torque are done.

A comprehensive study on stator vibrations in synchronous generators considering both single and combined SAGE cases

This paper presents a comprehensive study on the stator vibration properties in synchronous generators under varied static air–gap eccentricity (SAGE) conditions. Current studies mainly focus on the electromechanical and thermal properties such as stator/rotor vibration, electromagnetic torque, phase current, stator temperature, etc., in single and combined faults composed of SAGE and winding interturn short circuit, while the dangerous position of the stator core due to the over stator vibrations caused by 3D SAGE is rarely investigated. Differently from the other researches, this work concentrates on the radial magnetic pull per unit area (MPPUA) and the axial unbalanced magnetic pull (UMP) on the stator to investigate the radial and the axial vibrations, taking into account not only the conventional radial SAGE, but also the axial SAGE and the combined SAGE (mixture of radial SAGE and axial SAGE). A 5kVA two-pole prototype synchronous generator, which is designed and manufactured by the authors, is employed as the study object of the finite element analysis (FEA) and the experiment for a validation. The proposed study as well as the 3D eccentricity simulating structure scheme of the prototype generator can be used as a reference for the further/similar investigations. It is shown that the most dangerous position of the stator core is close to the minimum air gap length point. Such conclusion can be employed to detect the detailed 3D eccentricity location and specifically prevent the insulation damage of the stator core.

Control mechanism of unbalanced magnetic pull in doubly fed induction generator using extra pole‐specific stator windings

The doubly fed induction generator is commonly used in commercial wind turbines because of its simplicity and robustness; it is a wound rotor induction machine. It has a relatively small airgap which makes it more vulnerable to unbalanced magnetic pull. This paper presents a simulation model to investigate the ability of extra stator windings with pm ± 1 pole-pairs to control the unbalanced magnetic pull (UMP). These auxiliary windings are inserted in the stator slots and they are used to produce counteracting flux that reduces the UMP. In the theory section, an UMP control matrix is fully developed that involves additional winding currents for obtaining active UMP control. The algorithm for controlling the UMP is then introduced. This uses vector control with stator flux orientation. Several simulations are carried out using MATLAB and Altair Flux 2D finite element analysis. These show a good reduction of UMP under open circuit and locked rotor tests. These models allow the study of the combined effects of radial forces with changes in the machine design. It was found that the average power absorbed by the auxiliary windings equals 13% of the total power losses in normal operation conditions.

Study on Static Characteristics of Ultra-Precision Aerostatic Motorized Spindle under Gas–Magnetic Field Coupling

In the working process of ultra-precision aerostatic motorized spindles, the journal and the rotor must have a certain eccentricity to have a certain bearing capacity and stiffness, which will induce the unbalanced magnetic pull (UMP). The intercoupling of the UMP and the gas film force will affect the motion state of the rotor and the accuracy of spindles. In order to deeply study the influence of the UMP caused by the rotor eccentricity on the equilibrium position of aerostatic spindles, a physical model of an aerostatic spindle based on slit throttling gas bearing is established and the coupling effect between the rotor and the motor rotor is studied and analyzed as a whole. The equilibrium position of the rotor under the combined action of gravity, the gas film force and the UMP is deduced, and a gas–magnetic field coupling calculation program based on the finite difference method is proposed. The calculation results show that with the increase in rotational speed, the equilibrium position of the rotor will move to the center of the journal in the micron scale, and the moving amplitude will gradually slow down. The UMP caused by rotor eccentricity can offset the rotor equilibrium position in nanometer scale, and the influence degree decreases sharply as the rotor moves to the journal center. With the increase in rotational speed, the direct stiffness and the cross stiffness will increase, and the amplitude of the cross stiffness is greater than the direct stiffness. This study is of great significance for further studying the influence of the rotor eccentricity on the equilibrium position and the accuracy of the rotor.

Analysis of rotor winding interturn short circuits affected by the initial dynamic eccentricity in large synchronous condensers

To investigate the effect of initial dynamic eccentricity on the rotor winding turn-to-turn short circuit (RWISC) in a large synchronous condenser, this paper uses the study object of a 300 MVar dual water intercooler condenser. Firstly, the air gap flux density characteristics, unbalanced magnetic pull (UMP) and stator circulating current of the condenser under single and compound faults are derived theoretically. Then, a phase-modulated field-circuit coupling model is constructed using Anosoft software. It is used to simulate and analyse the condenser. Finally, the operation of the condenser was simulated with the SDF-9 experimental setup, and the correctness of the theoretical derivation and simulation analysis was verified. The results show that the initial dynamic eccentricity of the condenser has a cutting effect on the fault characteristics generated by the RWISC. The 2nd harmonic of air gap flux density and stator circulating current and the fundamental wave of UMP decrease and increase with eccentricity. This study can provide theoretical guidance to eliminate disturbing factors to improve the accuracy of RWISC diagnosis in large synchronous condensers.