Axial Electromagnetic Force Research Articles

Research on Magnetic-Thermal-Force Multi-Physical Field Coupling of a High-Frequency Transformer with Different Winding Arrangements

In order to clarify the magnetic-thermal-force changing rule of high-frequency transformers under different winding arrangements, this paper tests the magnetization and loss characteristics of nanocrystalline materials at different temperatures, and based on the magnetization and loss data, establishes a magnetic-thermal-force coupling calculation model of 15 kVA, 5 kHz nanocrystalline high-frequency transformers, and calculates and analyzes the magnetic flux density, loss and temperature rise distributions of high-frequency transformers with three different winding arrangements under no-load and short-circuit conditions, respectively. Through comparative analysis, it was found that under no-load conditions, the cross-transposition of winding has less influence on the magnetic flux of the high-frequency transformer core, but it can reduce the iron-core loss and transformer temperature rise. The cross-transposition of winding under short-circuit conditions can significantly reduce the leakage magnetic field strength of high-frequency transformers; complete cross-transposition weakens the high-frequency transformer losses and temperature rise better than partial cross-transposition. According to the winding current density and core leakage field distribution under short-circuit conditions, we calculated and analyzed the distribution of its the axial and radial electromagnetic forces. The results show that the axial electromagnetic force causes the winding to be squeezed from both ends to the middle, the radial electromagnetic force causes the primary winding to shrink inward and the secondary winding to expand outward, so cross-transposition can greatly reduce electromagnetic force and weakening the deformation of the winding. Therefore, high-frequency transformers of winding cross-transposed should be used in actual projects to reduce transformer temperature rise and improve efficiency and security. This research has theoretical significance for the multi-physical field coupling of high-frequency transformers and its structural design.

Calculation of Forces to the High Granularity Calorimeter Stainless Steel Absorber Plates in the CMS Magnetic Field

The general-purpose Compact Muon Solenoid (CMS) detector at the Large Hadron Collider (LHC) at CERN incorporates a hadronic calorimeter to register the energies of the charged and neutral hadrons produced in proton–proton collisions at the LHC at a center-of-mass energy of 13.6 TeV. This calorimeter is located inside a superconducting solenoid that is 6 m in diameter and 12.5 m in length, generating a central magnetic flux density of 3.8 T. For operating optimally in the high pileup and high radiation environment of the High-Luminosity LHC, the existing CMS endcap calorimeters will be replaced with a new high granularity calorimeter (HGCal) with an electromagnetic section and a hadronic section in each of the two endcaps. The hadronic section of the HGCal will include 44 stainless-steel absorber plates with a relative permeability value well below 1.05. The volume occupied by 22 plates in each endcap is about 21 m3. The calculation of the axial electromagnetic forces acting on the absorber plates is a crucial element in designing the mechanical construction of the device. With a three-dimensional computer model of the CMS magnet, the axial forces on each absorber plate were calculated, and the dependence of forces on the central magnetic flux density value is presented. The method of calculation and the obtained results are discussed.

Analytical Calculation and Low-Order Component Optimization of Axial Electromagnetic Force for an Axial Flux Motor

The low-order high-amplitude component of axial electromagnetic force is the leading cause of electromagnetic vibration and noise of axial flux permanent magnet (AFPM) motors. In this paper, based on the analytical calculation of the axial electromagnetic force for a 20-pole 24-slot AFPM motor, the low-order axial electromagnetic force component is weakened by optimizing the motor’s electromagnetic structure. First, the three-dimensional (3-D) structural model of the motor is equated to a two-dimensional (2-D) analytical model, which is used to calculate the magnetic field generated by each of the armature winding and permanent magnet. Then, combined with the Maxwell tensor method, the axial electromagnetic force waveform is further obtained, and the target low-order high-amplitude component is extracted by 2-D Fourier analysis. Finally, taking this axial electromagnetic force component minimization as the target function of optimization, considering the output torque and ripple as constraints, the genetic algorithm is used to search for the optimal point by varying the structural parameters of the motor. The results show that the target low-order high-amplitude component of the axial electromagnetic force of the optimized motor is effectively suppressed, and the output torque ripple decreases with slightly increased torque amplitude, which provides a practical method for vibration and noise reduction of AFPM motors.

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.

A peak time shifting phenomenon in transformer axial short‐circuit electromagnetic force due to the coupling of electromagnetic‐axial vibration

AbstractAccurately calculating axial electromagnetic force is essential to analyse transformer winding axial stability. Prior research has mainly focused on the effect of winding structure on static axial electromagnetic force and studying vibration by substituting the static force in a time‐varying function. However, the coupling effect between axial electromagnetic force and winding vibration has not been addressed, and no calculation method for the axial electromagnetic force that considers both winding meso‐structures and vibration coupling effects has been proposed. Previously the authors presented an electromagnetic force calculation model that considers winding structure characteristics, and an iterative algorithm for magnetic‐structure coupling calculation. Currently, the winding vibration model was first proposed and the dynamic calculation method was formulated. By applying the method to a typical 110kV transformer, the spatial‐temporal distribution of winding axial short‐circuit electromagnetic force was obtained. It was found that the peak value of the axial short‐circuit electromagnetic force of some windings appears at the second or third peak moment of the short‐circuit current, which is called as peak time shift phenomenon. Further stress analysis indicates that existing evaluation methods may overestimate the short‐circuit resistance of windings by only considering short‐circuit electromagnetic force under maximum peak of short‐circuit current.

Numerical Investigations for Vibration and Deformation of Power Transformer Windings under Short-Circuit Condition

The analysis of the dynamic process of winding destabilization under sudden short-circuit conditions is of great importance to accurately assess the short-circuit resistance of power transformers. Based on magneto-solid coupling, an axisymmetric model of the transformer and a 3D multilayer model of the transformer considering the support components are established, respectively, and the short-circuit electromagnetic force (EF) is simulated by using the finite element method. It is concluded that the middle layer of the winding is subjected to the larger radial EF, while the axial EF has a greater effect on the layers at both ends. Moreover, the impression of the preload force, aging temperatures, and the area share of spacers on the vibration and deformation of windings are studied under short-circuit conditions. The overall distribution of plastic strain and residual stress in the winding is symmetrical, and the maximum values occur in the lower region of the middle of the winding. Finally, considering the material properties of disks and insulating components, the cumulative effect of plastic deformation under multiple successive short-circuit shocks is calculated. Compared with the traditional axisymmetric model of transformer, the three-dimensional multilayer model of the transformer established in this paper is more suitable for the actual winding structure and the obtained results are more accurate.

Research on the influence of trapezoidal magnetization of bonded magnetic ring on cogging torque

Abstract In this article, the influence of trapezoidal magnetization method on cogging torque of permanent magnet motor is studied. First, the structure is analyzed by analytical method to explain its mechanism of reducing cogging torque. Then, in order to verify the effectiveness of the formula, a six-slot four-pole motor is introduced for finite element analysis. Through comparison of the original structure motor, the magnet skew structure motor, and the trapezoidal magnetic pole structure motor, it demonstrates that the trapezoidal magnetic pole structure motor can effectively reduce the Cogging torque and does not produce additional axial electromagnetic force. Finally, a magnetizing fixture with a trapezoidal magnetic pole structure is made to magnetize the magnetic ring. The magnetized magnetic ring is installed on the motor, and the Cogging torque, Back EMF, etc., are tested. The test results are in good agreement with the simulation results. This method can be used to optimize the cogging torque of the permanent magnet motor.

Three-Dimensional Analytical Modeling of Axial-Flux Permanent Magnet Drivers

In this paper, the axial-flux permanent magnet driver is modeled and analyzed in a simple and novel way under three-dimensional cylindrical coordinates. The inherent three-dimensional characteristics of the device are comprehensively considered, and the governing equations are solved by simplifying the boundary conditions. The axial magnetization of the sector-shaped permanent magnets is accurately described in an algebraic form by the parameters, which makes the physical meaning more explicit than the purely mathematical expression in general series forms. The parameters of the Bessel function are determined simply and the magnetic field distribution of permanent magnets and the air-gap is solved. Furthermore, the field solutions are completely analytical, which provides convenience and satisfactory accuracy for modeling a series of electromagnetic performance parameters, such as the axial electromagnetic force density, axial electromagnetic force, and electromagnetic torque. The correctness and accuracy of the analytical models are fully verified by three-dimensional finite element simulations and a 15 kW prototype and the results of calculations, simulations, and experiments under three methods are highly consistent. The influence of several design parameters on magnetic field distribution and performance is studied and discussed. The results indicate that the modeling method proposed in this paper can calculate the magnetic field distribution and performance accurately and rapidly, which affords an important reference for the design and optimization of axial-flux permanent magnet drivers.

Research on electromagnetic noise of submersible motors with a radial skewed slots rotor

Skewed slots are widely used in many industrial applications because they can effectively reduce electromagnetic vibration and noise. In order to eliminate axial electromagnetic force in ordinary skewed slots rotor, a double skewed slot was proposed, which can useful reduce axial electromagnetic force and is superior to traditional skewed slots on reducing the electromagnetic vibration and noise. However, it still suffers from the problem of the difficult manufacturing process in large-sized submersible motors. In this paper, a radial skewed slot to reduce the electromagnetic vibration and noise is proposed, which has the advantages of a simple manufacturing process and obvious effect about reducing noise. Large-sized submersible motors are noisier than ordinary motors but lack effective means to reduce electromagnetic vibration and noise. So this paper adopts 2-D FFT and multi-physics coupling analysis method to analyze and compare the performances of the straight slot and the radial skewed slot in large-sized submersible motors.

Research Into Controlling the Material Flow for Electrohydraulic Forming Alloy Tubes by a Pulsed Magnet

Electrohydraulic forming is a kind of high-velocity forming process that can improve the formability of materials compared with quasi-static forming. Due to the lack of adequate material supplementation of the forming area, this method always faces problems such as uneven thinning and bursting when bulging tubes to required radial depths. To solve the above shortcomings and promote the material flow for the electrohydraulic forming process, this paper introduces an additional push coil to generate an axial electromagnetic force at the end of the tube. First, a finite element model was established to design the parameters of the push coil and the developed forming system. Then, a series of experiments using aluminum alloy tubes (AA6061-O) were conducted to verify the effectiveness of the proposed system. The results show that the limitation of the tube bulging depth can be increased by approximately 21.5%, and the thickness reduction can be reduced by more than 44% compared with conventional electrohydraulic forming. In addition, the forming morphology for tubes can be adjusted by the use of different combinations of discharge voltages for the push coil and exploding wire. The developed method and obtained results are of great value for improving the forming ability of electrohydraulic forming.

Coupled Magnetic-Structural Modeling of Power Transformer for Axial Vibration Analysis Under Short-Circuit Condition

When an external short circuit occurs, the axial electromagnetic force increases dozens of times. Under the effect of the axial short-circuit electromagnetic force, the transformer windings vibrate violently. The spatial distribution of the disks is constantly changing during vibration, which can change the temporal and spatial distributions of the leakage magnetic field and the axial electromagnetic force. This process is called the strong coupling phenomenon of the structural field and the leakage magnetic field. In this article, a strong coupled magnetic-structural model is proposed by using the analysis method. The strong coupling equations, where the independent variables are the axial position of the disks, are obtained. The vibration process with strong coupling phenomenon considered can be obtained. The accuracy of the strong coupling model is verified by the iterative method. By comparing the results calculated by the strong coupling model with those calculated by the weak coupling model, the influence of the strong coupling phenomenon <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on</b> the vibration process is obtained. Due to the influence of the strong coupling phenomenon, the winding vibration intensity increases and the maximum displacement of the disks can be doubled, which implied that the strong coupling phenomenon cannot be ignored when investigating the short-circuit strength of power transformers.

Target Force Curve Searching Method for Axial Electromagnetic Dynamic Balance of Scroll Compressor

In order to explore the axial electromagnetic dynamic balance force curve of a scroll compressor under the action of thermal energy, radial clearance, mechanism friction, and other factors in actual working conditions, an axial force exploration method that can automatically approach sections is proposed in this paper. Considering the dynamic response ability of the electromagnetic balance system, an automatic optimization algorithm of the partition number was proposed to find the optimal partition number in order to achieve the optimal tracking effect. An experimental platform was built to test the effect of the segmented tracking method on calibrating the deviation between the theoretical axial force curve and the real curve. The results show that the curve construction method proposed in this paper has convergence. This method can automatically and accurately construct the axial balance force curve required by the electromagnetic dynamic balance. Through the automatic optimization algorithm, the standard error (RMSE) between the target curve and the theoretical curve was reduced from 290 to 22.6, and the number of partitions with the lowest standard error was 20. The results provide a useful reference for the accurate, automatic, and efficient exploration of the actual axial sealing force of the scroll compressor.

Research on Electromagnetic Force of Transformer in Different Short-circuit Modes

When a short-circuit fault occurs on a power transformer, the windings of the transformer under the combined action of the short-circuit current and the leakage magnetic field, which is easy to deform the winding or damage the insulation of the transformer. Therefore, it is necessary to research on the force of the transformer under short-circuit situation, analyze and calculate the size and distribution characteristics of the electromagnetic force in different short-circuit modes. Based on the structural parameters of a transformer with a rated capacity of 200kVA, a three-dimensional model of a three-phase transformer is established by finite element simulation software. The axial and radial electromagnetic forces of windings in different short-circuit modes are analyzed by this model, comparing and analyzing the experimental results. In the simulation model, It can be known that the electromagnetic force of voltage zero-crossing closing phase when three-phase short-circuit occurs on low-voltage winding is basically the same as that of short-circuit phase electromagnetic force when single-phase short-circuit occurs. The analysis results have a certain reference value for improving transformer short-circuit withstand ability.

Electromagnetic Force and Mechanical Response of Turbo-Generator End Winding under Electromechanical Faults

This paper comparatively studies the electromagnetic force and mechanical response of the end winding before and after 3 kinds of typical electromechanical faults in turbo-generator. The analytical expression of electromagnetic force of end winding is derived under the composite fault of static eccentricity and rotor interturn short circuit. Meanwhile, the three-dimensional transient finite element simulation is carried on, and the frequency composition and amplitude variation characteristics of the radial, axial, and tangential electromagnetic force are analyzed for the end windings under static eccentricity, rotor interturn short circuit, and composite fault. Therefore, it provides a reference for the vibration wear detection and electromagnetic force control of the end winding. Moreover, the maximum stress and deformation of different positions on the end involute are obtained. And the three-directional vibration acceleration characteristics of the end winding are further analyzed. Finally, the distribution law of winding fatigue failure and vibration wear is acquired, which lays a foundation for the reverse suppression of end winding fatigue failure and insulation wear.

Effect of Pole Number on Generator End Winding Electromagnetic Force and Mechanical Response before and after RISC

This paper comparatively studies on the end winding electromagnetic force and mechanical response for generators with different numbers of poles. The analytical expression of the end winding electromagnetic force is derived under the rotor winding interturn short circuit (RISC) considering the pole number. Meanwhile, the three-dimensional transient finite element simulation is carried on two generators with one-pair poles and three-pair poles. Then, the frequency composition and amplitude variation characteristics of the radial, axial, and tangential electromagnetic forces are analyzed. Further, the maximum stress and deformation on the end winding are calculated and the similarity and difference of the coil failure law are obtained for two kinds of generators. It is found that RISC will bring odd harmonics to electromagnetic force for one-pair pole generators but it will bring odd and fraction harmonics for multipair pole generators. Moreover, the max mechanical response under RISC will decrease for one-pair pole generators but it will increase for multipair pole generators.

Mechanical Faults in Oil‐Immersed Power Transformers with Disc‐Type Windings Due to External Short Circuit

This study investigated mechanical faults in oil‐immersed power transformers with disc‐type windings. Short‐circuit tests were conducted on eight aged removed transformers. Before the short‐circuit tests, accelerated aging tests were conducted on all the transformers to discuss the life limit of transformers. Six out of eight transformers experienced the internal ground faults. Although the radial electromagnetic force and the tolerance of the insulation paper against it have been mainly focused in discussing the life of the power transformers, the ground faults were triggered by the crush of the pressboard by the axial electromagnetic force. The axial compressive stress applied to the pressboards varies from the transformer to the transformer, depending on the design of the windings. The transformer, whose axial compressive stress was relatively lower, passed the short‐circuit test. However, even for the similar deterioration degree of the pressboard, the transformer, whose axial compressive stress was relatively higher, experienced the ground fault. These results indicate that the axial compressive stress during an external short circuit and deterioration of the pressboard are critical factors that determine the life of transformers with disc‐type windings. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Behaviors of Axial and Radial Electromagnetic Force for Cryogenic Disk Motor

There are axial and radial electromagnetic forces between the stator and rotor of axial flux disk motor besides the useful torque. The electromagnetic forces act on the rotor and are crucial to the stable operation in magnetic levitation applications driven by disk motor. This article concerns the behaviors of axial and radial electromagnetic forces of disk motor using for cryogenic submersible pump. It is measured experimentally that the electromagnetic properties of motor materials, including the electrical conductor and magnetic conductor materials, in room temperature (RT) and liquid nitrogen (LN2) environment. Then, the 3D finite element model (FEM) of the three-phase asynchronous disk motor in RT environment is built which is also validated by the RT experimental tests. Finally, the behaviors of axial and radial electromagnetic forces in LN2 environment are investigated using the modified FEM taking account of the effect of cryogenic environment on the motor material. It is concluded that the axial electromagnetic force decreases monotonously with the increasing air-gap thickness or the decreasing rotating speed. When the rotor exhibits radial eccentricity, there is a restoring radial electromagnetic force, trying to pull the rotor back to the central position. The radial electromagnetic force increases with the increasing rotational speed and radial eccentric displacement.

Structural Analysis of Single-Sided Axial-Flux Permanent Magnet Machines With Different Magnetic Materials

Structural analysis of single-sided axial-flux permanent magnet (AFPM) machines for automotive cooling applications is presented in this article. First, the machine configuration and various magnetic materials for this machine, namely, electrical steel (ES) and soft magnetic composite (SMC), are introduced. Second, analytical modeling of the axial electromagnetic force is established to identify the components having a significant influence on the machine vibration and noise. Third, the electromagnetic forces for AFPM machines with different magnetic materials and machine eigenmodes are studied based on finite-element analysis. By using 2-D fast Fourier transform (2-D-FFT), the spatial and temporal orders of the electromagnetic force are obtained to verify the analytical modeling. Finally, by coupling the results from electromagnetic analysis and modal analysis, the vibration and noise for AFPM machines with different magnetic materials are investigated. The results show that the application of different magnetic materials greatly affects the vibration and noise characteristics of single-sided AFPM machines.

Analysis and Optimization of the Axial Electromagnetic Force for an Axial-Flux Permanent Magnet Vernier Machine

The axial-flux permanent magnet vernier machine (PMVM) is a competitive machine applied in the field of direct-drive which features on low speed and high torque. The rotor of axial-flux PMVM has a tendency to deflect to stator under the effect of the large and unbalanced axial electromagnetic force, which probably results in the collision between rotor and stator. Therefore, this article presents an analysis and optimization of the axial electromagnetic force of the axial-flux PMVM. First, the three-dimensional finite-element model (3-D FEM) is converted to equivalent two dimensional finite-element model (2-D FEM) for further axial electromagnetic force derivation and optimization. Subsequently, four design parameters that are sensitive to the axial electromagnetic force are selected and analyzed for further optimization, which aims to obtain an equal output torque, and reduce the axial electromagnetic force of entire rotor and peak force density of axial electromagnetic force as much as possible. Finally, a Kriging model between the objective functions and design parameters is constructed based on considerable simulation results, and genetic algorithm is applied to search for the proposed optimized result which is ultimately validated by simulation.

Electromagnetic Force Distribution and Forming Performance in Electromagnetic Tube Expansion with Axial Compression

Electromagnetic tube expansion has been given much attention due to its superior cold forming properties. The traditional electromagnetic coil is of single structure, which results in substantial tube wall thinning and mechanical strength reduction. This shortcoming restricts further development of the electromagnetic tube expansion technology in various industrial applications. This paper proposes an axial-radial electromagnetic force bidirectional loading method to increase the axial fluidity of the material and eliminate the wall thinning issue that currently exists in the traditional method. Furthermore, the performances of three proposed structures for the axial compression electromagnetic tube expansion using three-coil, two-coil and one-coil are analyzed and compared. In this context, the electromagnetic force distribution and the wall thinning of the tube during the expansion process are analyzed based on finite element modelling. Results show that with the proposed modified structure of the traditional single coil, the axial electromagnetic force can be substantially increased which results in reducing the tube wall thinning significantly. The proposed technique in this paper paves the way for further development and more industrial applications of the electromagnetic expansion technology.