Electromagnetic Force Density Research Articles

Transformable 3D curved high-density liquid metal coils – an integrated unit for general soft actuation, sensing and communication

Rigid solenoid coils have long been indispensable in modern intelligent devices. However, their sparse structure and challenging preparation of flexible coils for soft robots impose limitations. Here, a transformable 3D curved high-density liquid metal coil (HD-LMC) is introduced that surpasses the structural density level of enameled wire. The fabrication technique employed for high-density channels in elastomers is universally applicable. Such HD-LMCs demonstrated excellent performance in pressure, temperature, non-contact distance sensors, and near-field communication. Soft electromagnetic actuators thus achieved significantly improved the electromagnetic force and power density. Moreover, precise control of swinging tail motion enables a bionic pufferfish to swim. Finally, HD-LMC is further utilized to successfully implement a soft rotary robot with integrated sensing and actuation capabilities. This groundbreaking research provides a theoretical and experimental basis for expanding the applications of liquid metal-based multi-dimensional complex flexible electronics and is expected to be widely used in liquid metal-integrated robotic systems.

The influence of ITSF on vibration of high voltage Line-Start permanent magnet synchronous motor

PurposeThe purpose of this paper is to present the influence of inter-turn short circuit faults (ITSF) on electromagnetic vibration in high-voltage line-starting permanent magnet synchronous motor (HVLSPMSMS).Design/methodology/approachIn this paper, the ampere–conductor wave model of HVLSPMSM after ITSF is established. Second, a mathematical model of the magnetic field after ITSF is established, and the influence law of the ITSF on the air-gap magnetic field is analyzed. Further, the mathematical expression of the electromagnetic force density is established based on the Maxwell tensor method. The impact of HVLSPMSM torque ripple frequency, radial electromagnetic force spatial–temporal distribution and rotor unbalanced magnetic tension force by ITSF is revealed. Finally, the electromagnetic–mechanical coupling model of HVLSPMSM is established, and the vibration spectra of the motor with different degrees of ITSF are solved by numerical calculation.FindingsIn this study, it is found that the 2np order flux density harmonics and (2 N + 1) p order electromagnetic forces are not generated when ITSF occurs in HVLSPMSM.Originality/valueBy analyzing the multi-harmonics of HVLSPMSM after ITSF, this paper provides a reliable method for troubleshooting from the perspective of vibration and torque fluctuation and rotor unbalanced electromagnetic force.

Nonlinear motion characteristics of the high-temperature superconducting levitation system with boundary crack

High-temperature superconducting levitation systems have nonlinear behaviors, such as the period-doubling bifurcation and chaotic vibration under external excitation, in connection with the nonlinear hysteresis interaction between the high-temperature superconductors (HTSC) and permanent magnet. The HTSC is a non-ideal type II superconductor in which the fracture is generated internally during manufacturing, and the material properties are brittle. The HTSC tends to crack under a strong magnetic field and electromagnetic force, and its internal defects are likely to cause structural damage with the variable Lorentz force. The fracture performance of the superconducting magnetic levitation system will affect the temperature variation of HTSC, in which the temperature is coupled with the internal electromagnetic force. In this paper, we analyze the fracture characteristics of the HTSC in nonlinear vibration with thermal effect. A superconducting magnetic levitation system model with boundary cracks is applied to study the coupling of multiple physical fields in dynamic processes. The Maxwell equation and superconducting electromagnetic constitutive equation are used to obtain the superconductor’s current density, and the temperature is calculated through the heat conduction equation. The superconducting magnetic flux flow and creep model is applied to analyze the magnetic flux motion inside the superconductors. We compare the superconducting levitation system’s electromagnetic force, temperature, and current density with four critical current densities. The numerical results show that the critical current density of superconductors significantly impacts bifurcation motion, and the temperature of the crack tip of the superconductors varies greatly during vibration, causing the superconductor to lose its superconductivity.

Analytical Solution for Electromagnetic Performance Analysis of Permanent Magnet Synchronous Motor with a Parallel Magnetized Cylindrical Permanent Magnet

High-speed direct-drive permanent magnet synchronous motors (PMSMs), supported by elastic foil gas bearings, have broad applications, such as in microcompressors. However, some problems remain to be solved for the electrical performance analysis of PMSMs. For example, there is presently no related analytical model that can be used in rotor dynamics expression for this type of PMSM. This study aimed to establish theoretical models for electromagnetic force density and torque. The process involved both theoretical and experimental research. The analytic models of air gap magnetic density, electromagnetic force density, and electromagnetic performance were established for a PMSM with a parallel magnetized cylindrical permanent magnet. The analytic calculation was conducted, and the results of the analytic model were obtained. The analytical model of the electromagnetic torque and force can be applied in theoretical research on rotor dynamics. The model provides a theoretical basis and method for studying the influence of the electromagnetic load on rotor dynamics. A finite element simulation analysis of the electrical performance of the PMSM was carried out. An electrical performance experiment was conducted. The deviation between the experimental result and the theoretical value was less than 4%. This result indicated that the analytic models could be used in a dynamics analysis of compressors that are directly driven by a PMSM for application in engineering and industrial contexts.

Fast Calculation of Electromagnetic Vibration of Surface-Mounted PMSM Considering Teeth Saturation and Tangential Electromagnetic Force

In view of the shortcomings of the existing calculation methods of electromagnetic forces, this paper proposes an analytical method (AM) combining the magnetomotive force (MMF)-permeance method and the improved subdomain method. The amplitude of each force density component considering stator teeth saturation and current harmonics is calculated, and the specific order and frequency components in the radial and tangential electromagnetic force densities are analyzed and sorted out. In modal analysis, the stator core and the casing are regarded as cylindrical shells with axial ribs, the natural frequencies of the stator are obtained based on the energy method, and the accuracy is well verified by the modal test. Finally, the frequency response functions of low-order modes of the stator only related to the stator structure parameters are determined, and the vibration accelerations under different working conditions are obtained based on the linear superposition principle by only updating the electromagnetic forces. Compared with the multi-physical coupling finite element analysis, the total calculation time of the proposed AM is reduced by more than 92%, which facilitates the fast prediction and effective reduction of electromagnetic vibrations in the motor design stage.

The microscopic Ampère formulation for the electromagnetic force density in linear dielectrics

We present a detailed derivation of the electromagnetic force density and pressure in linear dielectric media according to the so-called microscopic Ampère formulation, which considers the classical dipolar sources in matter along with the hidden momentum contribution. It is seen that, among the other formulations existing in the literature, our proposal is the only one universally compatible with the experimental works reported to date. A new radiation pressure equation for non-magnetic dielectrics under oblique illumination from p-polarized beams is also derived.

Electromagnetic Performance Investigation of Rectangular-Structured Linear Actuator with End Ferromagnetic Poles

Saving energy from domestic appliances is a focus in the effort to combat energy challenges. Linear compressors are a more efficient alternative to the traditional compressors used in refrigerators, which account for 20–40% of all residential electricity use. This article investigates the new topology of the moving magnet (MM), dual-stator single-mover linear oscillating actuator (DSSM-LOA) for linear compressor application. Both the stators were C-shaped, with coils looped across their end sides. Two permanent magnets (PMs) that were axially magnetized were housed on the mover. The PM structural shape significantly affected its fabrication cost and magnitude of magnetic flux density (B). The DSSM-LOA makes use of axially magnetized rectangular-shaped PMs because they are inexpensive and generate high electromagnetic (EM) force density. End ferromagnetic core materials were used to improve the magnetic flux, linking from the stator to the mover. All the design parameters were optimized through parametric analysis using the finite parametric sweep method. Parameters present within the three primary parameters (length, height, and depth) that were assumed constants were optimized, and the optimal dimensions were selected based on the EM force. The investigated DSSM-LOA was contrasted with traditional LOA designs, and they showed significant improvement in EM force per ampere, generally named motor constant (MC), MC per PM mass, MC density, cogging force, and stroke. Additionally, the proposed DSSM-LOA had a simple structure and low cost, and it operated in a feasible range of strokes for linear compressor application.

Research on Electromagnetic Vibration Characteristics of a Permanent Magnet Synchronous Motor Based on Multi-Physical Field Coupling

Background and Purpose: The stator vibration characteristics are comprehensively mastered by considering the influence of winding and the housing structure on the stator modes. This effect is neglected in the research field of electromagnetic vibration of permanent magnet synchronous motors (PMSMs). Methods: The radial air-gap flux density equations and PMSM’s electromagnetic force density are derived, and then the harmonic characteristics of electromagnetic force density are studied. An equivalent finite element model of the stator is proposed that investigates the impacts of the winding and stator housing rules on the stator modal frequency. Finally, the harmonic response and acoustic analyses of electromagnetic vibration are carried out based on multi-physics field coupling. Results: The equivalent radiated power distribution laws and acoustic field of motor electromagnetic vibration under transient operating conditions are obtained. The theoretical analysis results are consistent with the experimental results. Conclusion: The obtained results show that the spatial order of the radial electromagnetic force is not equal to the order of the radial mode of the motor stator. The reason for this is that structural resonance is induced when the frequency components of the spatial radial electromagnetic force are coupled with the intrinsic frequency of the stator.

FE Modeling of Superconducting EDS System Employing Mixed Formulations and Field-Circuit Coupling Method

Superconducting (SC) electrodynamic suspension (EDS) technology utilizes the electromagnetic force generated by the interaction between the onboard SC magnets and ground figure-8-shaped coils. In this article, a transient 3-D finite-element (FE) model using a suspension unit with cross-connected null-flux coils is established. First, mixed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$A$ </tex-math></inline-formula> – <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V$ </tex-math></inline-formula> formulations are adopted to solve different domains. The field-circuit coupling method is introduced to connect the 8-shaped coils on two sides of the track and realize the simulation of the operation of lateral offset. Second, the periodic linear extrusion operator solves the continuity of electromagnetic quantities across the common boundaries of the moving and fixed domains and avoids mesh reconstruction and distortion. The computational efficiency of the model is significantly improved. The custom boundary conditions are demonstrated in detail. The dynamic circuit analytical model is used to verify the correctness of the model. Finally, high-speed operations of a vertical or lateral offset of the EDS system are simulated. The transient electromagnetic force and force density acting on the figure-8-shaped coils are analyzed. This article provides a more efficient and general analysis approach for the long-term operation of EDS trains with cross-connected figure-8-shaped null-flux coils, especially with lateral offset.

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.

An Engineering Model of Magnetic Flux Density and Electromagnetic Force Density at the Structural Discontinuity within Transformer Cores.

The structural discontinuities in the form of air gaps in transformer cores cause the concentration of electromagnetic force, which is an important source of transformer vibration and noise. In this paper, an engineering model of magnetic flux density and electromagnetic force density on transformer core discontinuities is analytically developed. Based on a reasonable structural simplification and assumptions, magnetic flux density and electromagnetic force density are deduced as explicit functions of the geometric, material, and electrical excitation characteristics of the gap region and the transformer core. The accuracy of the established model is validated by the finite element method (FEM) combined with a magnetic measurement experiment. According to this engineering model, the electromagnetic force density can be reduced by decreasing the gap ratio and increasing the gap thickness to a reasonable level. The outcome of this paper can help to understand the physical mechanism of the electromagnetic force generated by core air gap discontinuities, which is meaningful for noise control and the condition monitoring of transformers.

Design and experimental analysis of high electromagnetic force density moving magnet linear actuator with end ferromagnetic poles

A Linear Oscillating Actuator (LOA) generates bi-directional electromagnetic (EM) force between two extreme points. A new topology of moving magnet LOA with axial magnetised PMs and a C-shaped stator core is proposed. On each side of the mover, two chamfered tubular-shaped core material parts are attached. All the design parameters, such as mover mass and EM force of the LOA, are optimised using parametric analysis via parametric sweep, and the optimum values of the parameters are chosen based on design and performance parameters. The LOA's performance is examined for various input loading values and at different oscillation region positions. For various values of time-dependent supply, the EM force's oscillating nature is analysed. The effect of resonance analysis on input current, stroke to current ratio, and efficiency are discussed. The proposed LOA is compared to current LOA topologies in terms of design structure and performance parameters. The FEM results are validated using a special experimental setup. The proposed LOA produces feasible results for the compressor in a refrigeration system.

The Mechanical Analysis of ELM Joint under Coupling Field

The Edge Localized Mode coil is the key component to prohibit the phenomena of disruptive instability occur-ring in the edge of Tokamak plasma. And the coil is made of Stainless Steel Jacketed Mineral Insulated Con-ductors. The different pieces of conductor are connected by joints. During the normal operation of Tokamak device, the joint will be shocked by electromagnetic and thermal loads. Thus, it is necessary to perform the mechanical analysis to verify whether or not the ELM joint has sufficient safety margin to resist the impact of coupling field. In order to obtain the load boundary condition for mechanical analysis, the electromagnetic and thermal analysis are launched first. Then the temperature and electromagnetic force density are inserted into the mechanical analysis model. And the equivalent stress is calculated. The analysis results indicate there is stress intensity at the component of supporting rail. To mitigate the stress intensity, the local structural optimi-zation design is employed. Finally, the stress evaluation is carried out based on analytical design. The assess-ment results demonstrate the optimized model has sufficient safety margin to withstand the combined action of multiple loads.

Analysis of Characteristics of the Magnetic Field in Demagnetization Fault for Permanent Magnet Synchronous Motor

To demagnetization fault for permanent magnet synchronous motor, referring to the 96-slot 32-pole permanent magnet synchronous motor, set up motor model using finite element software, and the demagnetization fault of single magnetic steel and double magnetic steel in the motor were simulated and analyzed. The motor flux-density waveforms on different kinds of demagnetization fault were analyzed for the flux-density wave-form periodic trends and volatility in different numbers of magnets or different demagnetization rates. The motor flux-density component path diagram on different kinds of demagnetization fault were analyzed to get radial-tangential flux-density path diagram to analyze regular of path diagram distribution. The air gap flux-density waveform is analyzed by finite element software on different kinds of demagnetization fault, which fourier analysis is used to analyze each harmonic frequency and its weight, and the rule of change of harmonic between the normal condition and under the condition of demagnetization fault is compared. The simulation of tooth electromagnetic force density waveform curves and harmonics for different demagnetization faults is used to analyze its effect on the vibration. The results concerning permanent magnet motor of demagnetization fault lays the foundation of motor fault tolerance analysis and characteristic analysis.

Numerical Simulation of Arc and Droplet Behaviors in TIG-MIG Hybrid Welding.

Tungsten inert gas-metal inert gas hybrid welding (TIG-MIG) combines the advantages of tungsten and metal inert gas welding. It can efficiently produce high-quality weld joints that meet modern manufacturing quality and efficiency requirements. Based on heat transfer, fluid dynamics, and electromagnetic theory, a three-dimensional coupled transient model of arc-droplet interactions in TIG-MIG hybrid welding was established. In this study, the temperature field, flow field, electromagnetic force, pressure, and current density parameters were analyzed in the arc space. The results show that introducing TIG welding has a significant impact on MIG welding.

Balazs thought experiment and its implications for the electromagnetic force density in continuous media. Relativistic analysis

We analyze the Balazs thought experiment under minimal assumptions and show that the two expressions for the force density that have been recently discussed in the literature (the conventional Lorentz force density and the generalized or Einstein–Laub force density) are fully consistent with conservation of energy, conservation of momentum and the center-of-energy theorem. This conclusion contradicts some of the previously published claims that the conventional Lorentz force density is inconsistent with the center-of-energy theorem. We identify the sources of errors in these claims. We conclude that the conventional Lorentz force density captures all experimentally-observable effects of interaction of electromagnetic fields with matter and no other law or postulate (such as a resolution of the so-called Abraham–Minkowski dilemma) is necessary.

A Self-Adaptive Control for Phase-Controlled Electromagnetic Contactor Using Weighted Moving Average Filter

This article proposes a self-adaptive control strategy for controlling the holding current of a novel phase-controlled contactor. The closing moment of contact can be captured by calculating the drop slope of current and the pulsewidth modulation is then applied to decrease the holding current. The weighted moving average filter is employed to filter the current and voltage signals. A novel approach using a quintic B-spline curve-fitting algorithm is proposed to determine the number of sampling values and their weights. Numerous theoretical analyses of electromagnetic force and magnetic flux density distributions are developed. A cosimulation coupling magnetic field, machinery, and circuit are carried out with the Maxwell and circuit editor software. A prototype is manufactured and the experimental results validate the effectiveness of the proposed self-adaptive control strategy for minimizing the holding current.

Electromagnetic-thermal behaviors of bulk superconductor with cuboid slot under moving magnetic field

We established a 3D coupled model to study the electromagnetic-thermal behaviors of a levitation system containing a bulk high-temperature superconductor (HTS) with a cuboid slot under the nonuniform magnetic field due to the movement of a permanent magnet (PM), analysing the influences of the geometrical parameters of the slot and inclination angle on the electromagnetic-thermal behaviors, giving the dynamic distribution of the global electromagnetic force density in the HTS. The results show that the longer the length of the slot, the smaller the levitation force, and the greater the loss. As its length takes up 7/10 of the HTS diameter, the loss is 4 times that of the HTS without damage. Due to the homodromous induced current appearing near the slot, the maximum guidance force increases with the length. The levitation force decreases with the increase of the slot depth. Its curve near the maximum becomes blunt and the loss increases significantly. As the depth is 3/5-4/5 of the HTS height, the loss is 300–400 times of that without damage. The guidance force and loss increase with the depth. As the inclination angle rises, the levitation and guidance force both drop. At 30 °, their maximums decrease by 70 % and 90 %, respectively. The lateral stability of the system thus becomes poorer, indicating the inclination angle is one of the important factors for instability. As the PM moves vertically, the guidance force density symmetrically distributes near the both wide sides of the slot. Its side faces with the wide sides will bear the shear force, resulting in that the slot has the tendency to tear along these faces. As the PM reciprocates laterally, the slot is subjected to the lateral shear force, proportional to the displacement.

The Mechanical Analyses of CFETR CSMC Local Components Under the Steady-Operating Condition

The R&D of the central solenoid model coil (CSMC) is preparatory toward the final fabrication of the Chinese fusion engineering test reactor central solenoid coil. CSMC is being designed and partly fabricated in the Institute of Plasma Physics, Chinese Academy of Sciences (ASIPP). During the process, new manufacturing technologies are developed and some design optimization is proposed. Based on the latest design update, a mechanical analysis is launched to verify whether or not the local components can withstand the shock of the complex loads at the CSMC's steady operation stage. The local components here referred to are the current lead joint and joggle. The current lead joint is the key component to transfer the current into coil modules. The joggle is designed to achieve the smooth transition between the different layers during the conductor winding process. The representative current lead joint and joggle are chosen for the mechanical analysis. The electromagnetic analysis is carried out first to calculate the magnetic field and electromagnetic force density by using the software ANSYS. Then, a one-fifth structural analysis model is built to analyze the stress state of the local components under the combination loads. Finally, the local components are evaluated based on the analytical design.

Research on weakening measure of radial electromagnetic force waves in permanent magnet synchronous motors by inserting auxiliary slots

The accurate calculation and analysis of electromagnetic force waves are especially crucial for comprehensively predicting and weakening the electromagnetic vibration of electrical machines. In this study, a fast and accurate calculation method of radial electromagnetic force density of surface-mounted permanent magnet synchronous motor (PMSM) is presented, the radial electromagnetic force density including amplitude, frequency and order is obtained and the accuracy is verified. Comprehensively considering that the effects of the auxiliary slots on cogging torque and torque ripple, the weakening measure of radial electromagnetic force waves by inserting auxiliary slots is research, and the optimal determinations of the number and the structural parameters of auxiliary slots in PMSMs with different slot–pole combinations are summarised, and six PMSMs with 6-pole/36-slot (6p36s), 4p36s, 6p9s, 8p9s, 8p12s and 10p12s are analysed to verify the universality of the conclusions.