Electromagnetic Force Distribution Research Articles

Analytical Solution of Electromagnetic Force Lines in Rectangular Wave Guides for Transverse Electric Waves

The analytical solution of the electromagnetic field lines was derived, providing a foundation for generalizing conclusions and forming a coherent set of equations to describe the dynamics of electromagnetic waves. By applying Maxwell's equations, this paper analyzed the rectangular waveguide model, focusing on the guiding effect of the passive region on the propagation of electromagnetic waves. Additionally, the Helmholtz equation was used to describe the behavior of electromagnetic fields within the passive guided wave system. Through the analytical solution of the field lines, the distribution of electromagnetic forces could be determined through integration calculations. To enhance the understanding of these concepts, this paper utilized Python programming to simulate electromagnetic force lines, providing a visual representation of the discussed theories. This simulation not only deepened the understanding of electromagnetic principles but also demonstrated their importance in practical applications, contributing to the field of electromagnetism research. The results of the study emphasize the significance of analytical solutions in understanding electromagnetic phenomena and provide valuable insights for future research in related fields.

Experimental Investigation and Optimization of Electromagnetic Force Distribution of Magnet Based on Two Field Shaper Modules

Experimental Investigation and Optimization of Electromagnetic Force Distribution of Magnet Based on Two Field Shaper Modules

Mechanical properties and insulation damage of PMSG stator end windings with eccentricity considerations

The mechanical properties and insulation damage of stator end windings in permanent magnet synchronous generator (PMSG) are investigated by theoretical analysis, finite element analysis (FEA) and experiment verification. First, a theoretical model of the winding electromagnetic force (EF) and vibration response before and after eccentricity faults are established. Then, the stress/strain distribution of the end windings under different working conditions is analyzed. Finally, the insulation damage behavior of end windings with initial cracks is studied and characterized using the stress intensity factor (SIF). The results indicate that the winding EF and vibration responses vary under different faults. The stress/strain at the joint of the winding is the largest, and the insulation layer has the maximum stress/strain under the same section. Additionally, the SIF amplitude of the crack at the winding joint is the largest. And the SIF amplitude of the crack will increase with the increase of fault degree/crack depth/crack length. The contribution of this paper lies in the comprehensive analysis of the winding EF distribution, vibration response, stress and strain, and insulation damage before and after eccentricity. This analysis can provide valuable reference for the health monitoring of PMSG eccentricity faults and the prevention of winding insulation damage.

Research on Winding Dynamic Force and Displacement of Winding in Interturn Short Circuit of Stereo Roll Iron Core Transformer

Abstract The short circuit fault between the turns of the transformer winding accounts for 60% ∼ 70% of the whole winding fault, which seriously adversely impacts the regular functioning of the transformer. This study focuses on analysing the dynamic force and displacement characteristics of the winding in a stereo roll iron core transformer when an inter-turn short circuit occurs. First, a stereo roll iron core transformer finite element model in three dimensions is created. The electromagnetic-solid mechanics coupling method is used to figure out and study the transformer winding’s inter-turn short-circuiting current, leaking electromagnetic field, dynamic force, and displacement distributions. Furthermore, an experimental platform is built to simulate the inter-turn short-circuiting of a stereo roll iron core transformer. The displacement in the time domain and the acceleration in the frequency domain of the winding during the short circuit that occurs between turns will be recorded and analyzed. Finally, it is concluded that under normal working conditions, the winding vibration frequency is between 100 ∼ and 500 Hz. After 19 turns of the short circuit, the winding displacement increases by 32% ∼ 60%, and the high-order harmonic content of the winding vibration frequency increases significantly.

Research on the Relative Placement Angle of the Induction Heater and the Channel in a Four-Channel Induction-Heating Tundish.

In order to optimize the application effect of induction heating (IH) tundishes, a four-channel IH tundish is taken as the research object. Based on numerical simulation methods, the influence of different relative placement angles of induction heaters and channels on the electromagnetic field, flow field and temperature field of the tundish is investigated. We focus on comparing the magnetic flux density (B) and electromagnetic force (EMF) distribution of the channel. The results show that regardless of the relative placement angle between the heater and the channel, the distribution of B in the central circular cross-section of the channel is eccentric. When the heater rotates around channel 1 towards the bottom of the tundish, the distribution of B in the central circular cross-section of the channel changes from a horizontal eccentricity to a vertical one. Through the analysis of the B contour in the longitudinal section of the channel, the difference in effective magnetic flux density area (ΔAB) between the upper and lower parts of the channel can be obtained, thereby quantitatively analyzing the distribution of B in this section. The distribution pattern of ΔAB is consistent with the distribution pattern of the electromagnetic force in the vertical direction (FZ) of the channel centerline. The ΔAB and FZ of channel 1 gradually increase as the heater rotates downwards, while those of channel 2 reach their maximum value at a rotation angle of 60°. Compared to the conventional placement, when the heater rotation angle is 60°, the outlet flow velocities at channel 1 and channel 2 decrease by 15% and 12%, respectively. However, the outlet temperature at channel 2 increases by 1.96 K, and the molten steel flow at the outlet of channel 1 and channel 2 no longer exhibits significant downward flow. This shows that when the heater rotation angle is 60°, it has a dual advantage. On the one hand, it is helpful to reduce the erosion of the molten steel on the channel and the bottom of the discharging chamber, and on the other hand, it can more effectively exert the heating effect of the induction heater on the molten steel in the channel. This presents a new approach to enhance the application effectiveness of IH tundish.

Numerical simulation of the electromagnetic field in the secondary cooling zone of arc-shaped slabs

The magnetic field characteristics due to electromagnetic stirring in the secondary cooling zone of an extra-thick slab during continuous casting are numerically determined using Maxwell's equations, with particular emphasis on the distribution of magnetic induction intensity and electromagnetic force, as well as the influence of process parameters on the magnetic field. The orientation of the electromagnetic force is the same when the electromagnetic stirrers at the 30° and 60° posistions of the arc-shaped slab are powered in the same direction; otherwise, the orientation is opposite. The magnetic induction at the centre of the section of the stirrer's central axis at the 30° positio, as well as the current, frequency, and fitting formulae, are as follows: B = {0.075I(1/A)-0.3} mT and B = {-1.75f(1/Hz)+22} mT. The electromagnetic force and current fitting formula at the central point of the B-B section is F = {0.03168I2(1/A2)-03.762I(1/A)+326.7} N/m3, and the fitting formula of electromagnetic force and frequency at the centre point is divided into two segments. The first takes the form of a parabola: = {-21((f-4.3)-(1/Hz)2)+970} N/m3, and the second segment is negative linear: F = {-1.65f(1/Hz)+51.5} N/m3.

Calculation of electromagnetic force and temperature distribution of amorphous transformers in different operating modes by finite element method

The study used the Finite element method (FEM) by ANSYS 3D software to calculate the distribution of electromagnetic force (EMF) and temperature on the high voltage and low voltage windings (HLVWs) of the amorphous steel core 3 phase transformer (ASCT) which has a power of 1000kVA –22/0.4kV under different load cases: No load, full load and short circuit (SC). The obtained results show the exact temperature distribution and location where the highest temperature is found on the HLVWs of ASCT. From the analysis of the temperature distribution on the HLVWs, it is shown that when the transformer falls into an SC fault, it causes the greatest EMF and thermodynamic force, causing extremely heavy consequences for the transformers. The obtained results help designers, manufacturers, and operators have the most suitable options to improve strength of SC and increase the life of the transformer.

Analysis of electromagnetic vibration of submerged tubular linear motors based on wave propagation approach

This paper presents the properties of electromagnetic vibration in a submerged tubular linear induction motor through an analytical model. Firstly, the spatial and temporal characteristics of electromagnetic force acting in the stator are analyzed. Subsequently, based on the wave propagation approach, an analytical model is established to calculate the vibration response of the stator, which is simplified as a finite-length cylindrical shell. The accuracy of the proposed model is verified by comparing natural frequencies of axial breathing modes and frequency response with the finite element method. Finally, the effects of the position of electromagnetic force, the spatial distribution of electromagnetic force, radial static pressure and structure parameters on vibration response are investigated and discussed. Some conclusions are outlined, which is of great importance to reduce electromagnetic vibrations by optimizing the structure design of the motor.

Comparative the effect of distribution transformer coil shape on electromagnetic forces and their distribution using the FEM

Abstract During the normal life of the transformers, they are subjected to different electromagnetic stresses. One of these stresses is the electromagnetic forces resulting from the passage of short-circuit current in the transformer coils due to internal or external faults and may lead to the failure of the transformer when this electromagnetic force exceeds the threshold level. This work deals with the computation and analysis of leakage magnetic flux and electromagnetic forces when the worst-case fault (symmetrical short-circuit current) occurs in distribution transformer (DT) coils using the finite element method (FEM). The three types of DTs that were adopted in this work are similar in capacity and voltage transformation ratio (250 kVA and 11,000/416 V), but they are different in the shape of coils (oval, cylindrical, and rectangular coils). ANSYS software was used to build two-dimensional models of the three transformers, which were different in coil shapes and in the type of iron core. The objective of this work is to compare the effect of coil shape on the distribution of electromagnetic forces and their value, in order to find out which coil shape is the best to withstand electromagnetic forces when short-circuit current is passed in the coils. The results of the simulation of the finite element models were approximately equivalent to the results of the design calculations that depend on the classical method (the analytical method), but the FEM is more accurate, due to the accuracy of calculating the magnetic flux and its distribution, which cannot be calculated using the classical method. One of the most important contributions of this research is the analysis and calculation of electromagnetic forces for three types of DTs with different coils by applying the same design parameters to all the transformers. The research also contributed to determining the best coil shape by comparing simulation results, and it was found that transformers with cylindrical coils are the best to withstand electromagnetic forces due to the homogeneity of the cylindrical coil structure from all sides.

Fracture behavior of superconductor REBCO tapes with multiple edge cracks under electromagnetic force

It is often necessary to narrow wide tapes through a slitting process in applications of the second-generation high-temperature superconductor REBa2Cu3O7-x (REBCO, RE = rare earth) tapes. However, this results in some random length edge cracks appearing on the slit edge and extending at certain angles towards the center of the tape. In this paper, we proposed a randomly distributed multiple-edge crack model to investigate the fracture mechanism of the superconducting tape under electromagnetic force due to high magnetic fields and current density (∼10 T and ∼ 1010A/m2). The electromagnetic body force distributions within the superconducting tape, incorporating multiple edge cracks, are simulated based on the H-formulation. Then a fracture analysis is conducted under the combined loading of tensile and electromagnetic forces, with the numerical calculation of stress intensity factors (SIFs) using the J-integral method. To validate the model's accuracy, we compare the body force distribution caused by an edge crack and the SIFs of edge cracks under uniform tension with existing results. Detailed analyses are undertaken to explore the impacts of electromagnetic body force non-uniformity, interactions between neighboring cracks, and the stochastic nature of geometrical parameters (length, angle, and spacing) on the fracture behavior under an alternating magnetic field. Numerical results indicate that non-uniform electromagnetic body forces arising from defects are a critical factor in crack propagation. Furthermore, the randomness of the geometrical parameters amplifies the interactions between some of the neighboring cracks, causing the tendency of the tape containing random edge cracks to fracture. Therefore, it is advisable to avoid random cracks with substantial length, angle, and spacing during the mechanical slitting process.

Selection of Magnetic Pulse Crimping Process Conditions to Improve Crimped Terminal Quality

The crimping of copper terminals via hand-operated and hydraulic compressors is used to generate a compressive force between a terminal and a wire, generally on a worksite. However, this equipment often causes compression defects because non-uniform pressure is applied to the terminal surface in the radial direction during crimping. When the crimped terminal is connected to electrical parts such as the power transmission system, a low-quality crimped terminal can separate from the wire strands, increasing resistance to current flow through the terminal, energy loss, and the risk of fire due to overheating. For this reason, Magnetic Pulse Crimping (MPC), which can yield highly durable crimped terminals with uniform quality, has recently been developed. This process uses only the magnetic force generated by high electromagnetic interaction between the crimping coil part and the surface of the terminal, without physical contact. The objective of this research was to confirm the superiority of the MPC process over the conventional crimping process and then analyze the effects of the main process parameters, including the crimping length and the charge energy on the crimping part, so that this new process can be applied at worksites. To realize these goals, copper terminals and 35 mm2 copper wire strands were employed, and various types of crimping parts were manufactured under different crimping conditions. In particular, the distribution of electromagnetic force on the crimped parts were analyzed via numerical analysis. The crimping part performance was improved when the MPC process was applied to terminal crimping. In particular, decreasing the crimping length led to increased crimping quality, while increasing the charge energy caused increases in the compression ratio and pullout strength. However, excessively high charge energy caused the edge to break the wire strands; therefore, it is important to select the proper charge energy.

Use of DL Model to Capture Noise Variance of EV Motor by Eccentricity

In the era of mass-production of EVs, the expectations of performance and NVH performance required for power electric(PE) motors are gradually increasing. In order to satisfy the noise requirement and to prepare countermeasures, it is necessary not only to verify the nominal design value, but also to analyse the characteristics due to manufacturing variance. However, it was not easy to thoroughly examine the tilting and eccentricity issues that affect the noise characteristics of the axial type motor due to time and computational costs. To overcome this limitation, a machine learning model was developed to predict the electromagnetic(EM) excitation force of the motor eccentric condition. The training set of 2D EM FE results were generated with various eccentricity condition and RPMs. Using spatial-temporal frequency analysis and unbalanced magnetic pull analysis, the tendency of the excitation forces due to eccentricity was analysed. The distribution of electromagnetic force by time was predicted using random forest model. It showed R2 value of 0.999. The prediction model reduces the computational time within 5 minutes from 31 hours and enables the realistic analysis of tilting and eccentric condition. The 3D EM force distribution as Vibro-Acoustic FE model input could be predicted by putting the eccentricity value into the machine learning model.

Short‐circuit current difference of parallel strands in winding turns and its influence on the distribution of electromagnetic force

AbstractTransformer winding turns often consist of multiple parallel strands. The spatial position variation of each strand affects the leakage inductance of each branch, resulting in an uneven distribution of short‐circuit currents within the winding turns. And this unevenness persists even when transposition structures are implemented. Traditional methods in transformer analysis frequently overlooked the distribution characteristics of short‐circuit currents when calculating electromagnetic forces. A frequency‐domain calculation method for analysing the current distribution in winding turns was proposed, with a deviation of less than 3% compared to existing analysis methods. Two typical 110 kV transformer models were utilised to investigate the influence of uneven current distribution on the spatial distribution of electromagnetic forces. The spatial distribution of short‐circuit electromagnetic forces in low‐voltage (LV) windings exhibited significant changes, with maximum change rates of 10% and 61.2% for axial and radial electromagnetic force, respectively, in a LV winding with 4 parallel strands. The research also analysed how strand radial width and axial height affect current distribution unevenness and proposed specific design principles to mitigate these disparities in winding design. The findings offer valuable insights for selecting structural parameters and assessing short‐circuit stability during transformer design.

The Analysis of Permanent Magnet Vernier Synchronous Machine Vibration and Noise

The permanent magnet vernier synchronous machine (PMVSM) has the characteristics of high torque density and high power density and has advantages in the field of low-speed and high-torque applications. The PMVSM utilizes rich harmonics for torque enhancement, but it can also cause an increase in radial electromagnetic force and vibration noise. In this paper, we take a 12-slot 10-pole PMVSM as an example to analyze the source of radial electromagnetic force, vibration and noise. The electromagnetic finite-element model and structural finite-element model of the PMVSM are established for calculation. Through the analysis and calculation of two-dimensional electromagnetic fields, the radial electromagnetic force distribution of the PMVSM is obtained. We derive the radial electromagnetic force formula of the PMVSM and verify the correctness of the formula through harmonic analysis of the radial electromagnetic force. The sources of radial electromagnetic forces at various orders and frequencies within the PMVSM are analyzed and summarized by coupling the radial electromagnetic force obtained from the electromagnetic finite-element model to the structural finite-element model and conducting electromagnetic vibration harmonic response analysis on the PMVSM. The measured acceleration spectrum of the prototype is compared with the finite-element method (FEM) results, verifying the correctness of the finite-element simulation results for electromagnetic vibration.

Electromagnetic force behavior of high temperature superconducting coils coupled with multi-physics fields under different models

Rare earth barium copper oxide (REBCO) superconducting tape is the second generation of high temperature superconducting material with strong current carrying capacity and high mechanical strength, which has been studied most recently. In order to better investigate the electromagnetic force distribution characteristics of REBCO superconducting materials after electromagnetic excitation, firstly, the electromagnetic characteristics of superconducting tapes are numerically calculated by H method and T-A method on the basis of finite elements (FE) in this paper, and the effectiveness of T-A method is obtained. Based on this method, the influence of real size model (RS model) and homogenization equivalent model (HE model) on superconducting tape is further studied. The results show that the radial magnetic field reaches a peak of 1.01 T at the middle position of the upper surface of the pancake, while the axial magnetic field reaches a peak of 16.4 T at the inner side of the pancake, which indicates that the axial magnetic field contributes more to the total magnetic field. At the same time, the rationality of the equivalent method is obtained by comparing the calculation results of the RS and HE models. In addition, the mechanical changes of superconducting tapes are studied by T-A method under the HE model. It is found that the hoop stress and radial stress reach the peak values of 64.7 MPa and 6.84 MPa, respectively, and both are tensile stress, indicating that the hoop stress is more likely to cause damage to the superconducting tapes. Finally, the effect of different external tensile strains on the superconducting tape is discussed.

Accurate Electromagnetic Force Analysis of Offshore Wind Power Transformer Windings Based on Fractional Order Lumped Parameter Model

Accurate calculation of the electromagnetic force distribution of transformer windings under different loads and fault conditions is of great significance for transformer maintenance, condition evaluation and life prediction. Due to the influence of offshore wind power systems, offshore wind power transformers have high harmonic content and large changes in load rates, which can easily cause the coil destabilization, winding deformation or even damage because of the uneven distribution of the electromagnetic force. To improve the accuracy of electromagnetic force calculation, this paper proposes a fractional order numerical method. First, a three-dimensional axisymmetric transformer model and a symmetrical lumped parameter equivalent circuit model are established, respectively, based on field-circuit coupling. Second, the fractional order approximation of circuit components is realized by using the improved Oustaloup filter. In the fractional order model, the transformer is replaced by the lumped parameter equivalent circuit model. Third, as in the calculation process for integer order electromagnetic force, the integer order current has a large error, and the current waveform does not match the actual power frequency. The fractional order current and electromagnetic force at the 0.9 order are closer to the rated value. Finally, the effects of different load rates, three-phase short circuits and harmonic conditions are studied with the fractional order model. Compared with the traditional integer order finite element electromagnetic model, the fractional order equivalent circuit model established in this paper is more accurate and suitable for electromagnetic force calculation. The proposed method is significant for the structural design and state detection of transformers and also could be applied in the analysis of other dry-type transformers.

A Distributed Equivalent-Permeability Model for the 3-D Design Optimization of Bulk Superconducting Electromechanical Systems

This paper deals with accelerating 3D optimization scenarios for bulk superconductor-based electromechanical systems. For this objective, distributed equivalent-permeability models for High-Temperature-Superconducting bulks are first developed. These are stationary models capable of replicating the distribution of electromagnetic forces in bulks when subjected to external magnetic fields, minimizing the need for time-dependent simulations using the E-J power law. After introducing these models, their initialization phases are proposed to minimize their computational time requirements while still providing good accuracy. Optimization of a 3D Zero-Field-Cooled levitation system is presented to demonstrate the models' applicability. To validate the equivalent-permeability model, experimental tests are carried out. The measured experimental levitation forces resulting close to the ones obtained using the proposed equivalent-permeability model and the time-dependent <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H-$</tex-math></inline-formula> formulation with the E-J power law. After validation, a multi-objective optimization using the NSGA-II tool is performed to maximize levitation force while minimizing the HTS bulk volume. Hence, using the equivalent-permeability models, stationary and linear FEM simulations provide highly accurate results and significantly reduce computational time, mainly in 3D optimization scenarios.

ТРИСТУПЕНЕВА ЕЛЕКТРИЧНА МАШИНА З ВНУТРІШНІМ ТА ЗОВНІШНІМ РОТОРОМ: ПОРІВНЯЛЬНИЙ АНАЛІЗ ПОКАЗНИКІВ КЕРОВАНОСТІ

Two structures of electric machines with three degrees of freedom of the rotational movement of the rotor are considered - with an external and an internal rotor held on an internal cardan suspension. A three-plane symmetric magnetic system was chosen for the comparative analysis and such a choice was justified. Limitations are formulated that allow considering the rotor as a conservative mechanical system, as well as considering the magnetic field in the electric machine as magnetostatic. Mathematical models of the rotational motion of a body with a fixed center of mass, as well as the force interaction of the magnetic field of a permanent magnet located on the rotor and the control winding located on the stator, are given. The peculiarities of the distribution of electromagnetic forces in both structures are analyzed and the greater efficiency of the formation of these forces in the structure with an internal rotor is shown. Expressions for the components of the electromagnetic moment for use in the "COMSOL Multiphysics" interface are obtained. Forced precession movement for both structures was analyzed in the case of equal radii of the control windings and in the case of the same dimensions of the magnetic systems. It was determined that the structure with an external magnetic circuit is able to provide an order of magnitude smaller angular velocity of precessional movement and, at the same time, an equally smaller range of nutation. References 14, figures 10.

Modelling and analysis of electromagnetic vibration in long sheet secondary tubular linear induction motors

AbstractThis paper aims to clarify the behaviour and mechanism of electromagnetic vibration in long sheet secondary tubular linear induction motors (LSS‐TLIMs). Firstly, the spatial and temporal characteristics of electromagnetic force acting in the stator are analysed. Secondly, based on the wave propagation method, an analytical model is established to calculate the vibration response of the stator, which is simplified as a finite cylindrical shell. The accuracy of the proposed model, as well as the rationality of the simplification, are verified by 3D FEM simulation. It is indicated that the electromagnetic vibration response of LSS‐TLIMs mainly depends on the “axial breathing mode” (ABM) and corresponding “modal participation factor”. Moreover, the influences of the spatial distribution of electromagnetic force and the structural dimensions on the vibration are investigated. Finally, the “static vibration test” is performed to validate the above analysis. It is concluded that, compared with a rotary motor, the low‐frequency vibration of LSS‐TLIMs can be easily controlled since the natural frequency of ABMs tends to be much higher than that of the circumferential mode.

Imbalanced Force Suppression Due to Static Eccentricity by using Triple Three-phase Winding Motor

Permanent magnet synchronous machines (PMSMs) are widely used in a variety of applications. The static eccentricity of the rotor is a common fault in the fabrication process. These faults cause imbalanced electromagnetic force and exert unexpected vibration and acoustic noise during the design process. In the worst case, it causes bearing or motor failure. This research investigates the impact of this fault on the temporal and spatial harmonic distribution of gap flux density and electromagnetic force. Moreover, a compensation method has been proposed to suppress imbalanced force due to static eccentricity by using a triple three-phase winding motor. By controlling the three inverters independently, the winding current of each group can be controlled. Therefore, the gap flux density and electromagnetic force in each group can be brought into a desired state. Therefore, the imbalanced electromagnetic force can be restored using this system. In this paper, the effectiveness of the proposed method is verified by Finite Element Analysis (FEA) and experiment.