Nonlinear Magnetic Model Research Articles

Nonlinear Magnetic Model of IPMSM Based on the Frozen Permeability Technique Utilized in Improved MTPA Control

In this paper, the enhanced nonlinear magnetic model of the low voltage interior permanent magnet synchronous machine (IPMSM) is developed using the frozen permeability (FP) technique in finite element analysis (FEA) FEMM 4.2 software. The magnetic model is derived by obtaining flux saturation maps for a wide range of dq stator currents. Furthermore, the FEA FP technique accounts for the corresponding offset in the flux maps due to the excitation of the permanent magnets, and well as for fitting the coefficients for the curve-fitting procedure. In order to demonstrate the usefulness of the proposed magnetic model, a nonlinear control strategy based on the maximum torque per ampere (MTPA) optimal algorithm for IPMSM is employed. The magnetic model and the MTPA control strategy are validated through a variety of computer simulations based on FEMM 4.2 and MATLAB R2023a software, as well as on a real IPMSM electric vehicle (EV) traction drive experimental setup.

Structure optimization design and magneto-mechanical characteristics analysis of amorphous alloy with oriented silicon steel composite wound core

Three-dimensional wound cores are widely used in three-phase distribution transformer due to the symmetrical magnetic circuit structure. Amorphous alloy and oriented silicon steel are two kinds of ferromagnetic materials commonly used to make distribution transformer cores, each has own advantages and disadvantages in magnetic and mechanical characteristics. The amorphous alloy and oriented silicon steel composite core can synthesize the advantages of both. In this paper, a double-layer composite wound core (DCWC) structure is proposed and the corresponding dual nonlinear electric circuit and magnetic circuit coupling model is established. A structure optimization design method for the DCWC based on the free parameter scanning method is proposed by taking the percentage of oriented silicon steel in the composite core and the structure parameters as free variables. Based on the proposed optimization design method, a DCWC is designed and the experimental prototypes are manufactured. Further, the flux density distribution, core loss and mechanical vibration displacement of the DCWC are analyzed, and the effectiveness of the proposed method is verified by comparing with the measured results.

Direct Observation of Rising‐Tone Chorus Triggered by Enhanced Solar Wind Pressure

AbstractChorus waves play a significant role in both electron precipitation and acceleration in Earth's radiation belts. Their generation includes the initial linear process and subsequent nonlinear process. After the amplitude of whistler‐mode waves reaches a sufficient value in the linear phase, the nonlinear process takes effect and results in the frequency chirping of chorus waves. Here we present the first report on the generation and intensification of rising‐tone chorus driven by two sudden increases of solar wind dynamic pressure observed by Van Allen Probes on 20 December 2015. First, whistler‐mode waves are excited by the anisotropic thermal electrons (∼10s keV), which is quite consistent with the linear theoretical expectation. Then, rising‐tone chorus waves are nonlinearly generated from the existing whistler‐mode waves, triggered by the first increase of solar wind dynamic pressure. Subsequently, the second increase of solar wind pressure further intensifies the rising‐tone chorus. Based on the nonlinear theoretical model and Ts04 magnetic field model, we demonstrate that the decreasing inhomogeneity of the background magnetic field due to the increasing solar wind dynamic pressure is the major cause to trigger rising tones, which essentially reduces the wave amplitude threshold of the nonlinear process. Our study emphasizes the significance of solar wind dynamic pressure in the Earth's radiation belts from a micro perspective.

An improved equivalent magnetic network model of IPM motor in electric vehicles for dynamic simulation of transient effects

The existing electric motor model for electric vehicles cannot address the simulation of transient conditions. Moreover, it is difficult to balance the computation time and simulation accuracy. To address these shortcomings, an improved internal permanent magnet motor model containing nonlinear magnetic field factors was proposed based on the equivalent magnetic circuit theory. The effects of the magnetic circuit saturation, cogging torque, and magnetic field harmonics on the electromagnetic torque could be reflected. Furthermore, the electromagnetic vibration and rotor eccentricity could be considered. To improve the computational efficiency of the equivalent magnetic network method, lumped parameter or mesh-based methods were used for flux paths with different complexities. Second, the single-layer mesh-based method with local variable permeability parameters improved the efficiency of the air-gap dynamic analysis and computational efficiency while simulating 2D flux paths. The radial and tangential electromagnetic forces were calculated using the Maxwell tensor method and the action on the rotor. The accuracy of the nonlinear magnetic field modeling was verified by finite element analysis and experimental. In addition, the motion modeling method and dynamic characteristics of the model were studied. A reference was provided for dynamic simulations of electric vehicles and other using permanent magnet motors.

Non-Contacting Two-Dimensional Position Estimation Using an External Magnet and Monocular Computer Vision

Abstract This paper develops a position estimation system for a robot moving over a two-dimensional plane with three degrees-of-freedom. The position estimation system is based on an external rotating platform containing a permanent magnet and a monocular camera. The robot is equipped with a two-axes magnetic sensor. The rotation of the external platform is controlled using the monocular camera so as to always point at the robot as it moves over the 2D plane. The radial distance to the robot can then be obtained using a one-degree-of-freedom nonlinear magnetic field model and a nonlinear observer. Extensive experimental results are presented on the performance of the developed system. Results show that the position of the robot can be estimated with sub-mm accuracy over a radial distance range of +/−60 cm from the magnet.

Unconditional superconvergence analysis of an energy-stable C–N fully discrete scheme for the nonlinear magnetic diffusion model with memory

The unconditional superconvergence behavior of an energy-stable Crank–Nicolson (C–N) fully discrete scheme with nonconforming EQ1rot finite element method (FEM) is investigated for the nonlinear integro-differential system associated with the diffusion of the magnetic field. The stability of the numerical solution in the broken H1-norm is proved by the Gagliardo–Nirenberg (G–N) inequality, and the unique solvability is demonstrated by the Brouwer fixed point theorem. In which the boundness of the L∞-norm and the inverse inequality are eliminated. The combination of the Green formula and two special properties of EQ1rot element leads to the unconditional superconvergence estimate without any restriction between the time step and space partition size. Finally, the validity of the theoretical findings is supported by some numerical results.

Piecewise Affine Modeling of Wound-Rotor Synchronous Machines for Real-Time Motor Control

High-performance control of Wound Rotor Synchronous Machines (WRSM) motor drives requires a nonlinear magnetic model that captures magnetic saturation and cross saturation. This research proposes a generalized Piece-wise Affine (PWA) magnetic and state-space model that divides the current and flux space into simplices. PWA functions are obtained from experimental or Finite Element Analysis (FEA) data leveraging the Delaunay triangulation. Error margins and memory requirements can be optimized for given applications by varying the number of PWA functions. The PWA domains can be irregular and an algorithm to optimize accuracy for a given number of PWA domains is proposed. The PWA performance is compared with a high-fidelity magnetic model. Irregular PWA functions have lower error than regularly gridded tables at reduced size: average error is improved from 15% to 1%; peak error is improved from 20% to 9%. Finally, the PWA state-space model is validated on an experimental testbench with a real-time Micro-Controller Unit (MCU). The state space equations are verified using steady-state and dynamic tests.

Design and modeling of a novel triple-magnet magnetic dynamic vibration absorber

A novel Triple-magnet Magnetic Dynamic Vibration Absorber (TMDVA) with Eddy Current Damping (ECD) and Coulomb damping is proposed in this paper. A multi-storey structure is selected as the vibration reduction object. First, the equivalent dynamics model of the TMDVA multi-storey structure vibration reduction system is established. Then the nonlinear magnetic force model is built according to the magnetizing current theory. Next, an ECD accurate calculation model is developed and derived based on Faraday’s law of electromagnetic induction. Because of the model, the ECD coefficient can be designed and adjusted arbitrarily. The full text indicates that adjusting the ECD coefficient properly can not only improve the vibration reduction effect of the TMDVA, but also reduce the sensitivity of the vibration reduction effect to the excitation amplitude as well as enhance the broadband vibration reduction performance and the robustness of the TMDVA. With its simple structure, the TMDVA is easy to be implemented and miniaturized. And the low frequency vibration reduction effect of the TMDVA is better than other existing magnetic dynamic vibration absorbers. Taken together, the TMDVA has potential application value in passive vibration reduction of engineering structures.

Dynamically synergistic transition mechanism and modified nonlinear magnetic force modeling for multistable rotation energy harvester

Multistable energy harvesters with magnetic interaction have received increasing attention. However, the synergistic transition mechanism of the different oscillation states for rotation harvesters remains uninvestigated, and there is lack of precise magnetic force model for investigating the effect of the external magnetic force on dynamic characteristics and harvesting performance. This study proposes a synergistic transition and regulation mechanism for rotation energy harvesting and a modified model of the magnetic force is derived by taking the relative displacement and rotational angle into consideration. The transition mechanism of different oscillation states for the rotation system is studied under the guidance of static bifurcation, potential diagram, and dynamic behaviors, respectively. Based on the extended Hamilton’s principle, the theoretical model is established and the complexity dynamic characteristics are simulated. A prototype of multistable energy harvesters with magnetic interaction was fabricated and the effectiveness of the theoretical model was validated by experiments. The experimental results exhibit good agreement with the numerical results. The proposed harvester can harvest energy effectively in a wide rotation speed range of 280–500 rpm, and the output voltage and power can reach 6.4 V and 4 mW.

Vibration Characteristics and Experimental Research of an Improved Bistable Piezoelectric Energy Harvester

Bistable piezoelectric energy harvester (BPEH) can remove mechanical energy waste, which is expected to realize the self-power supply of wireless sensors. To further improve the energy harvesting efficiency, we designed an improved bistable piezoelectric energy harvester (IBPEH). The restoring force model of the composing beam is acquired based on fitting experimental data, and the nonlinear magnetic model is obtained by using the magnetic dipole method. The electromechanical coupling dynamics model of the system is established based on Newton’s second law and Kirchhoff’s law. Based on the control variable method, the influences of excitation frequency and excitation amplitude on the vibration characteristics of IBPEH and BPEH are compared in simulation analysis. Moreover, the correctness of the theoretical analyses is verified by experiments. The results show that variations in the number of magnets and appropriate adjustments in their positions can broaden the operating frequency bandwidth of the bistable piezoelectric energy harvester, and realize large-amplitude periodic motion at lower excitation amplitudes. IBPEH can yield a higher voltage than BPEH under the same excitation conditions. This paper provides a theoretical basis for optimizing the potential well and further improving the electric energy harvest efficiency of the bistable piezoelectric energy harvester device.

Vibration Characteristics and Experimental Research of Combined Beam Tri-Stable Piezoelectric Energy Harvester.

Vibration energy harvesting technology is expected to solve the power supply and endurance problems of wireless sensor systems, realize the self-power supply of wireless sensor systems in coal mines, and promote the intelligent development of coal mine equipment. A combined beam tri-stable piezoelectric energy harvester (CTPEH) is designed by introducing magnetic force into the combined beam structure. In order to explore the vibration characteristics of CTPEH, a nonlinear magnetic model is obtained based on the magnetic dipole theory, and the dynamic equation of the system is established using the Lagrange theorem and Rayleigh–Ritz theory. The influence of the different magnet distances and excitation conditions on the static bifurcation characteristics and dynamic response characteristics of the system are analyzed by numerical simulation, and the simulation results are validated by the experiments. The research results show that the motion state of the CTPEH system has four transition forms from mono-stable to tri-stable with the change in magnet distance. The tri-stable system has three potential energy curves with different characteristic shapes. The appropriate starting excitation position and excitation frequency can make it easier for the system to realize a large-amplitude response state, thereby improving the output performance of the system. This research provides new ideas and methods for optimizing the performance of the combined beam piezoelectric energy harvester.

A Novel Mesh‐Based Equivalent Magnetic Network for Deep Saturation Region of Permanent Magnet Machine

AbstractPartial deep saturation of magnetic circuit is common in short‐term working permanent magnet (PM) machines in aviation, aerospace, new energy power generation and other fields. In order to accurately calculate the electromagnetic characteristics of the short‐term working machine, a novel mesh‐based equivalent magnetic network for the deep saturation region is proposed. Firstly, the deep saturation mechanism of the magnetic circuit of short‐term working motor is analyzed, and the deep saturation region is determined; Secondly, a Pointy topped hexagonal segmentation approach (PT‐HSA) grid generation method is proposed to effectively simulate complex magnetic flux paths. The PT‐HSA grid division and node compilation rules were analyzed in detail. In addition, a nonlinear magnetic network model based on reluctance grid model and equivalent magnetic circuit model is established. Compared with the quadrilateral segmentation approach (QSA) model, the calculation results of PT‐HSA model are closer to the finite element simulation results in the loading and instantaneous compensation conditions. Finally, an experimental platform is built, and the accuracy of the PT‐HSA magnetic network model is verified by the experimental results. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.

Development of New Phenomenological Models for Predicting Magnetic Permeability of Isotropic and Anisotropic Magneto-Rheological Elastomers

Designing smart devices based on magneto-rheological elastomers (MREs) is a quite challenging task due to the inherent nonlinear behavior of MREs in the presence of an applied magnetic field. In the early stage of the design process, the magnetic circuit parameters need to be optimized either via analytical approaches or FE simulations. These require a precise nonlinear magnetic permeability model (B-H curve formulation) of MREs. The model should consider the effect of essential design factors (particle volume fraction and anisotropy) and loading conditions (magnetic field and pre-strain). The main contribution of the present study is to formulate a field-dependent novel and reliable nonlinear B-H relation for MREs as functions of the basic design and loading factors. Three batches of isotropic and anisotropic MRE samples were fabricated with different particle volume fractions (15%, 30%, and 45%). Subsequently, a simple methodology was presented to determine the magnetic permeability and then the nonlinear B-H curves of the MREs considering wide variations in pre-strain (0, 12.5%, 25%, 37.5%, and 50%) as well as coil current, ranging from 0.2 A to 8 A. Experimental results showed that the relative magnetic permeability of both types of MREs increased with increasing pre-strain. Phenomenological-based models were consequently developed to estimate the nonlinear B-H curves of the isotropic and anisotropic MREs accurately and efficiently over the entire design and loading conditions considered. The proposed model can be effectively utilized for modeling and design optimization of MRE-based smart devices.

Coronal Magnetic Field Measurements along a Partially Erupting Filament in a Solar Flare

Abstract Magnetic flux ropes are the centerpiece of solar eruptions. Direct measurements for the magnetic field of flux ropes are crucial for understanding the triggering and energy release processes, yet they remain heretofore elusive. Here we report microwave imaging spectroscopy observations of an M1.4-class solar flare that occurred on 2017 September 6, using data obtained by the Expanded Owens Valley Solar Array. This flare event is associated with a partial eruption of a twisted filament observed in Hα by the Goode Solar Telescope at the Big Bear Solar Observatory. The extreme ultraviolet (EUV) and X-ray signatures of the event are generally consistent with the standard scenario of eruptive flares, with the presence of double flare ribbons connected by a bright flare arcade. Intriguingly, this partial eruption event features a microwave counterpart, whose spatial and temporal evolution closely follow the filament seen in Hα and EUV. The spectral properties of the microwave source are consistent with nonthermal gyrosynchrotron radiation. Using spatially resolved microwave spectral analysis, we derive the magnetic field strength along the filament spine, which ranges from 600 to 1400 Gauss from its apex to the legs. The results agree well with the nonlinear force-free magnetic model extrapolated from the preflare photospheric magnetogram. We conclude that the microwave counterpart of the erupting filament is likely due to flare-accelerated electrons injected into the filament-hosting magnetic flux rope cavity following the newly reconnected magnetic field lines.

A Curve-Shaped Beam Bistable Piezoelectric Energy Harvester with Variable Potential Well: Modeling and Numerical Simulation.

To improve the energy harvesting performance of an energy harvester, a novel bistable piezoelectric energy harvester with variable potential well (BPEH-V) is proposed by introducing a spring to the external magnet from a curve-shaped beam bistable harvester (CBH-C). First, finite element simulation was performed in COMSOL software to validate that the curved beam configuration was superior to the straight beam in power generation performance, which benefits energy harvesting. Moreover, the nonlinear magnetic model was obtained by using the magnetic dipoles method, and the nonlinear restoring force model of the curve-shaped beam was acquired based on fitting the experimental data. The corresponding coupled governing equations were derived by using generalized Hamilton’s principle, the dynamic responses were obtained by solving the coupling equations with the ode45 method. Finally, the numerical simulations showed that the proposed harvester can make interwell oscillations easier due to the spring being efficiently introduced to pull down the potential barrier compared with the conventional bistable harvester. Spring stiffness has a great impact on characteristics of the system, and a suitable stiffness contributes to realize large-amplitude interwell oscillations over a wide range of excitation, especially in the low excitation condition.

An arch-linear composed beam piezoelectric energy harvester with magnetic coupling: Design, modeling and dynamic analysis

A novel bistable piezoelectric energy harvester (BPEHC) is constructed by introducing a nonlinear magnetic force on an arch-linear composed beam. The nonlinear magnetic model is obtained by using equivalent magnetizing current method, and the nonlinear restoring force model of the arch-linear composed beam is acquired based on fitting experimental data. The corresponding coupled governing equations are derived by using generalized Hamilton principle. The dynamic responses are obtained by solving the coupling equations with the ode45 method, and the effect mechanism of the excitation frequency and amplitude on large-amplitude periodic response is discussed and analyzed via the bifurcation diagram, the maximum Lyapunov exponent diagram, and the Poincaré map. Moreover, the correctness of the theoretical analyses is qualitatively verified by experiments. The results reveal that the threshold excitation amplitude for the system to realize large-amplitude interwell oscillation is increased with the increasing of the excitation frequency, if the system starts with appropriate excitation level, it can do large-amplitude interwell oscillations at low excitation frequency. Compared with the non-magnet energy harvester, the BPEHC has much better energy harvesting performance owing to the nonlinear magnetic force being efficiently introduced to broaden bandwidth. The arch-linear composed beam is superior to the conventional straight beam in enhancing output voltage and power. Overall, introducing the arch-linear composed beam into the bistable piezoelectric energy harvesting system contributes to enhance power output, improve energy harvesting performance of the piezoelectric energy harvester.

A new magnetic core model for magnetorheological fluid-based applications considering fringing effect of gap and magnetic nonlinearity of fluids

This research aims to introduce a new magnetic core model for magnetorheological (MR) applications requiring high and wide controllable force. In general, the existing models linearize the magnetic behavior of magnetic cores for computational convenience. However, when MR applications such as MR damper require both high actuating force and relatively wide controllable force range, the nonlinearity of the magnetic properties becomes significant, which makes a big difference between the model and actual result. For this reason, the finite element method (FEM) is frequently adopted for modeling the magnetic cores, but it requires a lot of cost and time. To compensate for these disadvantages, a new nonlinear magnetic core model considering both the nonlinearity of the B–H curve of MR fluid and the fringing effect of the gap is proposed in this work. The approach is an extension of Kirchhoff’s law, which performs conformal mapping and backward calculation techniques. After formulating the analytical model, a magnetic core with specific parameters is designed as an illustrative example to validate the proposed model. It is shown through comparative investigations on the proposed model, linearization model, and FEM model that the proposed model is very effective to predict the high controllable force of MR applications.

Smart Collaborative Performance-Induced Parameter Identification Algorithms for Synchronous Reluctance Machine Magnetic Model

In rail transit traction, due to the remarkable energy-saving and low-cost characteristics, synchronous reluctance motors (SynRM) may be a potential substitute for traditional AC motors. However, in the parameter extraction of SynRM nonlinear magnetic model, the accuracy and robustness of the metaheuristic algorithm is restricted by the excessive dependence on fitness evaluation. In this paper, a novel probability-driven smart collaborative performance (SCP) is defined to quantify the comprehensive contribution of candidate solution in current population. With the quantitative results of SCP as feedback in-formation, an algorithm updating mechanism with improved evolutionary quality is established. The allocation of computing resources induced by SCP achieves a good balance between exploration and exploitation. Comprehensive experiment results demonstrate better effectiveness of SCP-induced algorithms to the proposed synchronous reluctance machine magnetic model. Accuracy and robustness of the proposed algorithms are ranked first in the comparison result statistics with other well-known algorithms.

Self-Adaptive Synergistic Optimization for Parameters Extraction of Synchronous Reluctance Machine Nonlinear Magnetic Model

For mechanism analysis and high-performance control of synchronous reluctance machine (SynRM), accurate and reliable parameter identification of nonlinear magnetic model is always required. However, the accuracy and robustness of traditional heuristic algorithms are restricted by incomplete individual performance evaluation and single population evolution mechanism. In this paper, we propose a self-adaptive synergistic optimization (SSO) algorithm for extracting the parameters of the model. A novel synergistic-performance evaluation is first established to classify candidates automatically. Then, a self-organized mechanism is proposed to select optimal evolution strategies designed for classified candidate solutions. Around the current best candidate, the exploration is guaranteed in priority. Meanwhile, a self-adaptive mechanism is introduced to select other candidates to construct more promising evolutionary direction. Thus, achieving a good balance between exploration and exploitation. The parameter estimation performance of SSO algorithm is evaluated through standard datasets of SynRM magnetic model obtained by the finite element analysis. Comprehensive experiment results demonstrate the competitiveness and effectiveness of the proposed SSO algorithm compared with other algorithms, especially in terms of the accuracy and robustness. According to these superiorities, it can be concluded that the proposed algorithms are promising parameter identification methods for SynRM nonlinear magnetic model.

Dynamic Equivalent Magnetic Network Analysis of an Axial PM Bearingless Flywheel Machine

A nonlinear dynamic equivalent magnetic network model for an axial permanent magnet bearingless flywheel machine (APM-BFM) is proposed in this paper. The model focuses on analyzing the magnetic field changes at the air gap of the machine. According to the relative position of the stator and rotor, the magnetic circuit between the rotor and the suspension pole (the torque pole) is divided into 7 stages (8 stages), and dynamic equivalent magnetic network models are established. The local saturation coefficient is introduced to characterize the local magnetic saturation phenomenon of the rotor yoke during the rotation of the rotor. Using the proposed model and based on the obtained winding flux, the opposing electromotive forces and inductances of the suspension and torque windings of the APM-BFM are all analyzed and calculated. Finally, the validity of the proposed model is verified by finite element analysis (FEA).