Air-gap Magnetic Field Research Articles

Effect of Eccentricity Factors on End Winding Electromagnetic Force in Turbo-generator

Static eccentricity will cause the abnormal distribution of air gap magnetic field and further affect the electromechanical characteristics of the generator. This paper comparatively studies on the end winding electromagnetic force of turbo generator under different eccentricity ratio and eccentricity angle. The analytical expression of end winding electromagnetic force is derived after eccentricity. Meanwhile, the three-dimensional transient finite element simulation is carried on under several eccentricity cases. Then the amplitude variation characteristics with eccentricity ratio and angle are analyzed. Further, the force characteristics are verified by experimental vibration acceleration of CS-5 simulating generator. It is found that the static eccentricity will not change the frequency components of the end winding force. However, it will change the amplitude of the electromagnetic force, and the increase or decrease tendency depends on the winding position, eccentricity ratio and eccentricity angle. The number of force amplitude increasing coils is close to half of the total number, and it changes slightly with the eccentricity ratio and eccentricity angle. The force increment of coil near the minimum air gap will be larger with the increase of eccentricity ratio, but it is not affected greatly by eccentricity angle. Moreover the coil with the most obvious force increase is located in the interphases position near the minimum air gap.

Field Reconstruction for Modeling Multiple Faults in Permanent Magnet Synchronous Motors in Transient States

Conventional field reconstruction model (FRM) for electrical machines has proved its main strength in efficient computations of magnetic fields and forces in healthy permanent magnet synchronous machines (PMSM) or faulty machines in steady states. This study aims to develop a magnet library of different magnet defects and include inter-turn short-circuit (ITSC) in the FRM for PMSM. The developed FRM can model a combination fault between ITSC, and magnet defect in a PMSM in transient states. Within the framework, an 8-turn ITSC was modelled in both finite element analysis (FEA) and FRM, and then identified by the extended Park’s vector approach. The air-gap magnetic field reproduced by the FRM shows a good agreement with the result from time-stepping FEA. The computation speed is over 1000 times faster than an equivalent time-stepping FEA. The suggested FRM allows for quickly understanding effect of faults in the rotor and stator on the air-gap magnetic flux density and identifying unique signatures for such defects.

STATIC ECCENTRICITY FAULT DETECTION METHOD FOR ELECTRICAL ROTATING MACHINES BASED ON THE MAGNETIC FIELD ANALYSIS IN THE AIR GAP BY MEASURING COILS

Electrical rotating machines have a great economic significance as they enable conversion of energy between mechanical and electrical state. Reliability and operation safety of these machines can be greatly improved by implementation of continuous condition monitoring and supervisory systems. Especially important feature of such systems is the ability of early fault detection. For this reason, several methods for detection and diagnosis of the machine faults have been developed and designed. As fault detection methods can largely differ in the types of detectable faults, machine adoptability and price of the system, a novel method was developed that can be used for cost-effective detection of various faults of electrical machine. Machine fault detection technique presented in this paper is based on the measurement of magnetic field in the air gap. Numerous studies have proven that crucial information about the machine condition can be determined based on measurement and analysis of the magnetic field in the air gap. It has also been confirmed that analysis of the air gap magnetic field can be used to detect, diagnose and recognize various electrical faults in their very early stage. Proposed method of positioning and installation of the measuring coils on ferromagnetic core parts within the air gap region of the machine enables differentiation of various faults. Furthermore, different faults can be detected if measuring coils are placed on the stator teeth then when placed on the rotor side. The paper presents method on how to analyse and process the measured voltages acquired from measuring coils placed within the machine, especially in the case of rotor static eccentricity detection. The methodology is explained by means of finite element method (FEM) calculations and verified by measurements that were performed on the induction machine. FEM calculation model was used to predict measurement coil output of the induction motor for healthy and various faulty states (at different amounts of static eccentricity). These results were then confirmed by measurements performed in the laboratory on the induction traction motor that was specially modified to enable measurements of faulty operation states of the machine. Measurements comprised of several machine fault conditions broken one rotor bar, broken multiple rotor bars, broken rotor end ring and various levels of rotor static eccentricity.
 Other methods used for faults detection are primarily based on the monitoring of quantities such as current and vibration and their harmonic analysis. This new system is based on the tracing the changes of induced voltage of the measuring coils installed on the stator teeth. Faults can be detected and differentiated based on RMS value of these voltages and the number of voltage spikes of voltage waveform i.e. without the need of harmonic analyses. If these coils are installed on the rotor it is possible to detect the stator winding faults in a similar manner.

Optimization of Rotor Salient Pole Reluctance for Typical Field Modulated Electric Machines

The objective of this article is to investigate the possibility to improve the torque characters of electric machines featuring rotor salient pole reluctance from the perspective of the general airgap field modulation theory. The torque production mechanisms of two typical field modulated machines, namely, the magnetically geared machine (MGM) and the flux-reversal permanent magnet (FRPM) machine, are discussed based on the Maxwell stress tensor (MST) method, where the mono-harmonic mechanism of rotor PM machine like the MGM is revealed. Several common theoretical salient rotor pole configurations, like the upright/inverted trapezoidal configuration, are introduced in detail, based on which general and modified rotor configuration advices for the two electric machines are proposed to provide initial design and future optimization guidance. It is proven that there is a possible opportunity to make the torque characters better via reasonable selection of rotor configuration and topological parameters. Electromagnetic performances validation based on 2-D finite-element analysis, such as improved airgap magnetic field harmonic distributions, load flux linkage/electromotive force (EMF), and general torque performances of two field modulated machines is provided to demonstrate the effectiveness of theoretical analysis. It is also verified by experimental measurements on the FRPM machines with different pole pair combination.

Analytical Calculation of Complex Relative Permeance Function and Magnetic Field in Slotted Permanent Magnet Synchronous Machines

In order to analyze accurately the airgap magnetic field of the slotted permanent magnet synchronous machine (PMSM) taking into account the influence of slotting effects, this article proposes an analytical method for calculating the complex relative permeance function. Based on one tooth pitch of the machine as the solution model, the governing Laplace field equation of the airgap region is solved analytically in the polar coordinate system. According to the boundary conditions between the slot and airgap region, the analytical expressions of the radial and tangential components of the complex relative permeance function are derived. With this complex permeance, the no-load radial and tangential airgap magnetic fields of the internal and external slotted PMSM with different slot/pole combinations are obtained. The accuracy of the analytical model is validated by the results of finite element analysis. With good simplicity and generality, this model can be an effective means for further study of motor performance.

Triple resonances involving two frequencies in the motor frequency conversion start phase

A rigid body model of torsional vibration of stator and rotor coupling system excited by electromagnetic force of motor is established in this paper. Energy method is introduced to solve the nonlinear vibration of the coupling system. Based on the linear part of the kinetic energy, potential energy and air gap magnetic field energy, the Lagrange function is obtained. And then, the Lagrange-Maxwell equation is used to solve natural characteristics. The nonlinear part is used to derive the nonlinear vibration equations of coupling system in torsional vibration modes. With numerical calculation, considering the triple resonances involving two natural frequencies, the influences of tuning parameters, damping coefficient and magnetic flux-density on resonance characteristics are illustrated and analyzed by the frequency-response curves. The results provide a theoretical basis for the subsequent calculation.

Vibration noise suppression approach based on random switching frequency control for permanent magnet motor

The vibration noise of the distributed drive autonomous ground vehicle (AGV) is mainly produced by the inverter-fed brushless DC permanent magnet in-wheel motor (PMIWM). It is necessary to reduce the vibration noise level of the PMIWM driven by pulse width modulation (PWM). A suppression approach of electromagnetic vibration noise for the PMIWM is investigated. First, the air gap magnetic field of the inverter-fed PMIWM was analyzed. The electric current harmonics and the unbalanced magnetic force (UMF) were investigated. The natural frequency and noise of the PMIWM were presented. Then, a flux-weaken approach was employed to maintain the robustness of the PMIWM when a sudden drop of DC bus voltage. The random switching frequency (RSF) PWM control method based on a two-state Markov chain is proposed to decrease the amplitude of the harmonics caused by the switching frequency and the multiple switching frequencies. The experimental results show that the RSFPWM can not only effectively reduce the vibration noise and the inverter losses, but also improve the robustness of the PMIWM control system under unpredictable uncertainties.

Multi-Objective Optimization of the Halbach Array Permanent Magnet Spherical Motor Based on Support Vector Machine

The fundamental harmonic amplitude and waveform distortion rate of the air-gap flux density directly affect the performance of a permanent magnet spherical motor (PMSM). Therefore, in the paper, the axial air-gap magnetic field including the end leakage of the Halbach array PMSM is analyzed and optimized. In order to reduce the calculation time of the objective function, the air gap magnetic field model adopts a non-linear regression model based on support vector machine (SVM). At the same time, the improved grid search (GS) algorithm is used to optimize the parameters of SVM model, which improves the efficiency and accuracy of parameter optimization. Considering the influence of moment of inertia on the dynamic response of the motor, the moment of inertia of the PMSM is calculated. This paper takes the air gap magnetic density fundamental wave amplitude, waveform distortion rate and rotor moment of inertia as the optimization objectives. The particle swarm optimization (PSO) algorithm is used to optimize the motor structure with multiple objectives. The optimal structure design of the PMSM is selected from all of non-dominated solutions by the technique for order preference by similarity to an ideal solution (TOPSIS). The performance of the motor before and after the optimization is analyzed by the method of finite element (FEM) and experimental verification. The results verify the effectiveness and efficiency of the optimization method for the optimal structure designing of the complex PMSM.

편심 자석 로터의 내·외측 자기장 변조를 이용한 마그네틱 하모닉 기어

In a magnetic harmonic gear, the magnetic field on the high-speed side is modulated by the air-gap movement according to the rotation of the eccentric body. Owing to the modulated magnetic field, the permanent magnet layer outside the high-speed rotor rotates in synchronization with the stator composed of another permanent magnet. Therefore, transferring only the synchronous rotational motion outside the eccentric body to the output side requires a complicated conversion mechanism. In this study, we propose a magnetic harmonic gear that utilizes both the inner and outer magnetic fields of an eccentric permanent magnet layer. The outer magnetic field is utilized for the deceleration function as in the existing harmonic gear, whereas the additional inner magnetic field is utilized to extract the rotational motion. The topology of the system is verified by the harmonic analysis of the air-gap magnetic field and with experimental set-up.

Harmonic current suppression method with adaptive filter for permanent magnet synchronous motor

ABSTRACT Due to the distortion of air gap magnetic field and the inherent non-linear characteristics of the inverter, the stator current of permanent magnet synchronous motor (PMSM) contains a large number of high order harmonic components, which distorts the current waveform and generates torque ripple, limiting the application of the PMSM in high speed and precision situations. To solve this problem, a harmonic current suppression method is proposed based on synchronous rotating coordinate transformation theory and adaptive filtering algorithm. The PMSM harmonic mathematical model is established and the coordinate transformation method is used to extract the 5th and 7th harmonic currents. On the basis of the original double closed-loop control system, the harmonic current loop is added, and the harmonic components are suppressed by injecting harmonic voltages. In order to improve the filtering effect and reduce the harmonic content, an adaptive filter is designed to replace the conventional low pass filter in the process of harmonic current extraction. According to the results of coordinate transformation, the adaptive filter continuously adjusts the parameters online through the least mean square (LMS) algorithm to extract the harmonic current. The simulation and experimental results proved the correctness and effectiveness of the proposed method.

Investigation of the Torque Transmission Characteristics in Dual-Flux-Modulated Magnetic Gear

Due to the field-modulation effect, the coaxial magnetic gear (CMG) can achieve a low-speed high-torque transmission. To further improve the torque capability, a dual-flux-modulated CMG (DFM-CMG) derived from conventional CMGs is presented. The DFM-CMG has two rotors, two modulators, and three air gaps. The operation principle and torque transmission are revealed. The air-gap magnetic fields are modulated by the two modulators. The output torque of DFM-CMG can be adjusted by the relative angular displacement between the two modulators. The optimal shift angle of the inner modulator is 0. The DFM-CMG is a combination of CMGs I and II. The CMG I component makes a major contribution to the output capability. The measured pull-out torque of the DFM-CMG prototype is 6.08 $\text{N}\cdot \text{m}$ . It shows a 28.3% growth over CMG I.

A Novel 2-DOF Lorentz Force Actuator for the Modular Magnetic Suspension Platform.

The modular magnetic suspension platform depends on multi degree of freedom of Lorentz force actuators for large bearing capacity, high precision positioning and structure miniaturization. To achieve the integration of vertical driving force and horizontal driving force, a novel 2- (two degrees-of-freedom) DOF Lorentz force actuator is developed by designing the pose of the windings and permanent magnets (PMs). The structure and the working principle are introduced. The electromagnetic force mathematical model is established by the equivalent magnetic circuit method to analyze the coupling of magnetic flux. The distribution characteristics of magnetic flux density are analyzed by the finite-element method (FEM). It is found that the coupling of the magnetic flux and the large magnetic field gradient severely reduce the uniformity of the air-gap magnetic field. The electromagnetic force characteristic is investigated by FEM and measurement experiments. The difference between FEM and experiment results is within 10%. The reasons of driving force fluctuation are explained based on the distribution of air-gap magnetic field. The actuator performance are compared under the sliding mode control algorithm and PID control algorithm and the positioning accuracy is 20 μm and 15 μm respectively. Compared with the similar configuration, the motion range and force coefficient of the Lorentz force actuator in this paper are larger. It has a certain guiding significance on the structure design of the multi degree of freed Lorentz force actuator.

Characteristic analysis and direct measurement for air gap magnetic field of external rotor permanent magnet synchronous motors in electric vehicles

In this study, the air gap magnetic field characteristics of external rotor permanent magnet synchronous motors (PMSMs) under both the stator and rotor coordinate systems considering low-order current harmonics and high-order sideband current harmonics are analysed. A direct measurement technique (DMT) for air-gap magnetic field is proposed. First, an analytical model of air gap magnetic field of external rotor PMSMs is established. The spatial order and frequency characteristics of stator/rotor air gap magnetic field are revealed. Then, a 24-pole 27-slot external rotor PMSM is taken as an example. The analytical and finite element (FE) results are compared and analysed. The difference of the spatial order and frequency characteristics between the stator and rotor air gap magnetic field are verified. Next, a new DMT is proposed, which can detect the precise distribution and local microscopic characteristics on the order of 10−1 mm with high resolution. The accuracy of analytical and FE model are verified by the DMT and an indirect experimental test of no-load back electromotive force. Finally, the mechanical challenges of in-wheel motors and the practicablility of DMT for eccentricity detection are further discussed.

Analytical modelling of air‐gap magnetic field of interior permanent magnet synchronous motors

A general analytical model, which is applied to pre-estimate the air-gap magnetic field of interior permanent magnet synchronous motors (IPMSM) under the no-load and load conditions, is proposed in this study. First, the analytical formulas of both the slotless permanent magnetic field and the armature reaction magnetic field are derived, respectively, by virtue of solving the Laplace field equation in polar coordinates. Then, the complex relative permeance is employed to account for the slotting effect. Subsequently, the proposed analytical model, which can reflect the spatial and temporal distribution characteristics of the air-gap magnetic field, has been applied in a 4-pole-24-slot IPMSM as an example. Finally, the analytical air-gap magnetic field with the spatial order and frequency characteristics is validated by the finite-element result. Additionally, the consistency between the analytical and finite-element results further indicates that the proposed analytical model is effective.

Effect of magnetic slot wedge on the performance of bulb tubular turbine generator

Purpose Owing to the salient pole structure and stator slots of hydro-generator, the air gap magnetic field in the generator is unevenly distributed. High-frequency harmonic components contained in the inhomogeneous air gap magnetic field will have a negative impact on the generator performance. The purpose of this paper, therefore, is to improve the distribution of air gap magnetic field by using appropriate magnetic slot wedge, thereby improving the generator performance. Design/methodology/approach Taking a 24 MW, 10.5 kV bulb tubular turbine generator as an example, the 2 D electromagnetic field model of the generator is established by finite element method. The correctness of the model is verified by comparing the finite element calculation data with the experimental data. The influences of the permeability and thickness of the magnetic slot wedge on the generator performance are studied. Findings It is found that the intensity and harmonic content of the air gap magnetic field will change with the permeability of slot wedge and then the performance parameters of the generator will also change nonlinearly. The relationship between the eddy current loss, torque ripple, output voltage and other parameters of the generator and the permeability of slot wedge is confirmed. In addition, the variation of losses and torque with wedge thickness is also obtained. Originality/value The influence mechanism of magnetic slot wedge on the performance of hydro-generator is revealed. The presented results give guidelines to selecting suitable magnetic slot wedge to improve generator performance.

Vibration Reduction by Magnetic Slot Wedge for Rotating Armature Permanent Magnet Motors

There is only slot frequency electromagnetic vibration and no pole frequency vibration in rotating armature permanent magnet motor (RAPMM), which is the advantage of this motor. The open of slot makes the air-gap magnetic field distorted and causes the harmonic of electromagnetic excitation force. In order to reduce the slot frequency vibration of the RAPMM, the method of placing magnetic slot wedge (MSW) at the slot opening is put forward accordingly. Through the finite-element simulation, it is finally shown that the MSW is capable of weakening the harmonic of the air-gap flux density, as well as decreasing the high-frequency component of the electromagnetic excitation force. Therefore, it is acknowledged that MSW can suppress the cogging torque and the vibration of corresponding frequency on the stator significantly. Finally, it is confirmed by the experiments that the built-in MSW is an effective measure for reducing the vibration of the RAPMM.

Influence of hybrid laminated remanufactured stator core on no‐load air‐gap magnetic density

Considering the cost and performance of the remanufactured motor, a motor remanufacturing method with a hybrid stator core structure was proposed, a prototype of the remanufacturing motor was made and the experiment was carried out. The modified magnetic circuit model of the hybrid stator motor was established by fitting the B–H curves of the two materials to consider the influence of the stator material. The errors for silicon steel and amorphous alloy were approximately 4.9 and 4.3%, respectively. The variation in no-load air-gap magnetic density along the axial direction was studied via simulation, and the air-gap flux density decreases gradually from the centre of silicon steel segment to the centre of amorphous alloy segment. A deflection occurs in the distribution of the air-gap magnetic field, which is in connection with the saturation degree of the materials. The method for calculating the air-gap magnetic density of the hybrid laminated stator from the magnetic density of the two materials was proposed. Compared with the stator composed of only one material, the calculation result obtained by the proposed method is in good agreement with the simulation result, with an error of <5%.

A Simple Analytical Model of Static Eccentricity for PM Brushless Motors and Validation through FEM Analysis

The paper firstly summarizes a simple analytical model of the air gap flux-density distribution for isotropic permanent magnet (PM) synchronous machines, in the presence of static eccentricity. The model was proposed by the authors in a previous paper and is based on an efficacious analytical expression of the variable length of air gap magnetic field lines which occur in eccentric brushless machines with surface-mounted permanent magnets. The approximate expression of the air gap field makes it possible to achieve a mathematical model with concentrated parameters close to that of a PM machine without eccentricity. The expression of the armature voltages and electromagnetic torque are found, also with reference to steady-state operating conditions at fixed rotor speed and impressed currents. The differences introduced by the considered type of eccentricity are evaluated and highlighted especially with reference to the air gap inductance and to waveforms and frequency spectra of voltages and shaft torque. Numerical results in a case-study of an 8-pole, 110 kW PM motor are compared to those obtained by using finite element analysis.

Tilting Torque Analysis of an Iron-Cored Tiered-Type Permanent Magnet Spherical Motor

This article mainly studies the tilting torque characteristic of a novel iron-cored tiered-type permanent magnet spherical motor (T-PMSpM), which has the merit of large torque ability benefitted from the use of iron cores in both rotor and stator. However, the use of ferromagnetic materials also makes the iron-cored T-PMSpM much different from other air-cored spherical motors. Thus, the influence on the tilting torque characteristic is investigated theoretically and numerically. First of all, the active tilting torque is obtained based on a simplified model of air-gap magnetic field distribution. According to this model, the influence of the magnetic field distortion caused by the tilting motion is evaluated. Then, the characteristic of the restoring torque, which obviously exists in the iron-cored T-PMSpM and hinders the tilting motion, is analyzed under different working conditions. The three-dimensional finite-element analysis (FEA) is adopted to calculate the accurate output tilting torque. Finally, an experimental procedure is designed to measure the output tilting torque of the prototype motor for verification. The measured results are compared with the FEA results.

Improved EL Model of Long Stator Linear Synchronous Motor Via Analytical Magnetic Coenergy Reconstruction Method

Electromagnetic-suspension (EMS)-type maglev, based on long stator linear synchronous motor (LSLSM), suffers from the flux linkage and thrust ripple. This is due to the non-sinusoidal airgap magnetic field distribution caused by the slot effect and end effect. In this article, it is intended to address this issue by establishing a nonlinear mathematical model of LSLSM for real-time simulation and controller design, considering the spatial harmonics and core saturation. The Euler-Lagrange (EL) model is improved by means of coenergy and then applied to obtain the general equations of LSLSM. At first, the variation in coenergy in LSLSM regarding the mover position and stator current are analyzed, in the presence of spatial harmonics and core saturation. Afterward, an analytical model of coenergy is constructed by two Fourier basis vectors of mover position and torque angle, and a coefficient matrix polynomial of stator current magnitude. Then, a new model of LSLSM is derived based on the coenergy model and EL method. The parameters of the model can be obtained from the numerical data of coenergy in all operation ranges via finite-element analysis (FEA). Finally, the new model of LSLSM and its propulsion system are integrated in MATLAB/Simulink setup. The simulation results show that the improved EL model can achieve satisfactory accuracy compared with the FEA results well, whereas the computational efficiency is improved largely.