Magnetic Equivalent Circuit Research Articles

Design of Hybrid Magnetic Stage for a Magnetic–Pneumatic Levitation System

This article presents a magnetic–pneumatic levitation system for gravity offload system of large deployable mechanisms, which combines the attractive force of magnetic stage and thrust force of air-bearing and is characterized by inner stability. The article focuses on the design of the hybrid magnetic stage. The equivalent magnetic circuit network method is used to analyze the electromagnetic (EM)-permanent hybrid magnetic field, the distribution of magnetic flux density of the air gap is solved, and then the magnetic force is obtained. To improve the design efficiency, the two-step design is adopted. First, the air gap is determined by sweeping the reluctance ratio to reduce the influence of parameter deviation of cast iron on the magnetic force. Then, the other parameters of the hybrid magnetic stage are optimized based on the multi-objective particle swarm optimization (MOPSO) algorithm. Through the comparison between the results of finite-element simulation and prototype experiments, the accuracy of the model is verified, and the expected design goal is achieved.

Vector-Based Magnetic Circuit Modelling of Induction Motors

Electro-mechanical devices incorporating rotating magnetic fields can be modelled using a wide range of analytical techniques. Choosing a modelling technique usually requires a trade off between computational efficiency and accuracy. Magnetic flux-based models aim to achieve an optimum balance between computational intensity and accuracy, as required for real time control applications. This paper demonstrates how vector-based magnetic circuit equations can be used to describe the operational characteristics of an induction motor at a more fundamental level than commonly used magnetic flux models. Doing so allows for closed form equations to be derived directly from device-specific geometry. The resultant model has advantages of numerical method-based analytical techniques while retaining the computational efficiency of closed form equations.

Unified magnetic equivalent circuit-based model of two-core Sen transformer for low-frequency electromagnetic transients and its numerical calculation

This paper proposes a low-frequency electromagnetic transient model of two-core Sen transformer (TCST) based on unified magnetic equivalent circuit (UMEC) and also presents its numerical calculation procedure for revealing the internal electromagnetic characteristics of TCST. Firstly, the magnetic equivalent circuits of the two parts of TCST including series unit and exciting unit are established according to their associated iron-core structures. Secondly, the electromagnetic transient models about the two parts are deduced by the electromagnetic coupling relationship. Finally, the electromagnetic transient model of TCST can be obtained through the combination of the series unit and the exciting unit on the basis of the internal electrical connections between them. The saturation and hysteresis characteristics of the iron core are represented by the J-A model, and a cascaded R-L lumped circuit is used to depict the eddy current effect. The case studies have been carried out in the environment of MATLAB and PSCAD/EMTDC. The comparisons between the results from the numerical calculation and the time-domain simulation reveal the effectiveness of the proposed model. Furthermore, it is found that the current flowing through the tap-changer in TCST is about 50% of the corresponding current in single-core ST (SCST), which implies the former may have lower cost and higher reliability. Moreover, the actual step length of TCST is about 0.5 times smaller than that of SCST, which may lead to more accurate control performance for TCST.

A New Hybrid Analytical Model Based on Winding Function Theory for Analysis of Unbalanced Two-Phase Induction Motors

The purpose of this paper is to present a new hybrid analytical model (HAM) based on winding function theory (WFT) for electromagnetic analysis of performance of one typical unbalanced two-phase induction motor (UTPIM). Different indexes of electromagnetic modeling such as winding distribution, slotting effect, and magnetic saturation can be accurately considered by using the proposed HAM. For obtaining this new hybrid technique, the winding function theory is reformulated for considering the magnetic saturation in addition to the influence of slotting and winding distribution. The conformal mappings (CMs) are used to accurately calculate the slotted air-gap length. The magnetic equivalent circuit (MEC) model is used to consider the magneto-motive force (MMF) drop in iron parts of stator and rotor due to the excitation of one phase-winding. The obtained results of CMs and MEC are then utilized in reformulated WFT to calculate the inductances of respective phase-winding. Transient analysis is then done to calculate the indexes of performance such as air-gap magnetic field, phase currents, electromagnetic torque, and rotor speed by using the lookup table of inductances while considering different capacitors in auxiliary phase. In each step, the accuracy of analytical results is verified by comparing with corresponding results obtained through FEM.

Flux-Barrier Design and Torque Performance Analysis of Synchronous Reluctance Motor with Low Torque Ripple

In this paper, an improved rotor structure with cross-shaped flux-barriers was proposed to improve the torque output capacity and reduce the torque ripple of the synchronous reluctance motor (SynRM). Firstly, an improved rotor structure of synchronous reluctance motor with cross-shaped flux-barriers, which can be described by two main parameters, is presented. Second, the improved motor is qualitatively analyzed by using magnetic equivalent circuit (MEC), and then the effects of the main parameters of the improved flux-barriers on the distribution of air-gap flux density, average torque, and torque ripple were analyzed by using the finite element method. Based on the above analysis, the rotor structure parameters of the proposed cross-shaped flux-barriers were obtained, and the performance was compared with that of the initial motor. The results show that the proposed rotor structure with cross-shaped flux-barriers can significantly reduce the torque ripple and increase the average torque.

Development of a Dual-Input Magnetic Gear Train for the Transmission System of Small-Scale Wind Turbines

Magnetic gear mechanisms have advanced to have a promising future in transmission technology. Previous research indicates that magnetic gear mechanisms might replace mechanical gear mechanisms in some applications. Small-scale wind turbines (SWT) with counter-rotating rotors that were initially fitted by bevel gears are proposed to be replaced by a coaxial magnetic gear train (CMGT). The CMGT is intended for use as a speed multiplier in order to obtain maximum power at low wind speeds, due to its beneficial transmission of power without physical contact. The primary objective of this study is to build a dual-input CMGT that will be employed in the transmission system of small-scale counter-rotating wind turbines. A dual-input CMGT is built through the analytical modeling of an equivalent magnetic circuit (EMC), which aims to predict the magnetic flux density in the air-gaps of CMGT. Several models within design constraints were compared to obtain the optimum design parameters of the preliminary CMGT design resulting from an EMC analysis. The optimized critical design parameters were then selected and analyzed using finite-element analysis (FEA) to depict the performance of the proposed SWT design. According to the findings, the developed design can generate an inner air-gap flux density of 0.8314 T and an outer air-gap flux density of 1.0200 T. The model likewise produces promising simulation results with an output transmitted torque in the inner rotor (output link) of 8.7 Nm, 56.9 Nm in the outer rotor, and 48.0 Nm in the carrier with pole-pieces. Thus, this design can generate higher torque than a bevel-geared wind turbine. The speed characteristics are also compromised in order to raise the generator’s rotating speed to generate more power. Finally, this study demonstrates the performance and embodiment design of the proposed SWT using CMGT.

Analysis of Linear Machine by Parameter Study using Equivalent Magnetic Circuit and FEA

This study proposes an analytical approach by optimum process that is generalized by number of phases, magnet, and pole-pair of linear machines based on a physical magnetic circuit model. The linear machine increases the force output of the machine due to generation of the magnetic field created by the armature winding. There is a strong attractive force between the iron-core armature and the permanent magnet. Therefore, this paper deals not only with one-phase systems by the number of magnet and pole pairs but also two-phase machines in linear machines. All this is carried out for optimum process using geometric parameters based on analytical electromagnetic field research. The best structure for optimum design is selected by a parameter study and it is accomplished with 2-D finite element analysis. The object function and design variables for this parameter study by constraints are chosen for practical and effective design of the machine. Eventually, it suggests new design rules based on optimal design through parameter study. The proposed methods allow us to draw a very important design rule, as a result it can be provided to less time of the machine design and analysis.

Analytical Modeling of Open-Circuit Magnetic Field in Permanent Magnet Assisted Synchronous Reluctance Motors Considering Iron Bridge Saturation Effects

<div class="section abstract"><div class="htmlview paragraph">Calculating accurately iron bridge saturation effects of the magnetic field, for Permanent Magnet Assisted Synchronous Reluctance Motors (PMASynRMs), remains to be a knotty problem. This paper presents an analytical modeling method to predict open-circuit magnetic field distributions and electromagnetic performances of PMASynRMs, considering iron bridge saturation effects. This analytical modeling method combines the magnetic equivalent circuit method, superposition principle, the solution of the governing Maxwell’s field equations and a complex relative permeance function. A quadruple-layer PMASynRM are remodeled into four surface-inserted permanent magnet synchronous motors (SPMSMs) which have different surface-inserted permanent magnets. Each layer of the interior permanent magnets of the PMASynRM is transformed into a new equivalent surface-inserted permanent magnet whose equivalent thickness needs to be defined by the magnetic equivalent circuit method due to iron bridge saturation effects. Based on superposition principle and the solution of the Laplace’s or Poisson’s field equation, the distribution characteristics of the radial and tangential magnetic flux density are obtained for PMASynRMs. The slotting effect is considered by a complex relative permeance function. To confirm the accuracy of the proposed analytical modeling method, the analytical solutions of magnetic flux density and cogging torque have been compared with Finite Element Method (FEM) simulation results. The root mean square errors of radial and tangential magnetic flux density between analytical and FEM results are 0.000553 and 0.0000916 respectively. The results indicate that the proposed analytical modeling method can consider iron bridge saturation effects effectively, which is suitable for performance predictions and parametric studies of PMASynRMs.</div></div>

Gimbal effect of magnetically suspended flywheel with active deflection of Lorentz-force magnetic bearing

The magnetically suspended flywheel (MSFW) could output gyroscopic moment for attitude control. The conical magnetic bearing (MB) with cone-shape airgap is designed to stably suspend the rotor on three translational degrees of freedom (DOFs), and the Lorentz-force MB with long torque-arm could actively deflect the rotor around radial axes on two DOFs. Firstly, the force models of the conical MB are developed on the basis of the equivalent magnetic circuit, and then the force characteristics of the Lorentz-force MB are analyzed. With the stable position control of rotor, the gimbal effect of the Lorentz-force MB is investigated, and then the gimbal moment generated by rapid deflection via the Lorentz-force MB is quantitatively analyzed. Finally, the experimental results prove that the maximum deflection angle approaches to 1.7°, and the outputted gyroscopic moment reaches to 10Nm with 3.14°/s deflection velocity. Therefore, the gimbal effect of MSFW with the conical MB and the Lorentz-force MB is demonstrated by actively deflecting the rotor.

Research on Vibration Characteristic Analysis of Magnetic Suspended Dual-Rotor System with Fixed-Point Rubbing

Due to the elimination of wear and lubrication system and effective solution to the vibration control issue, magnetic suspended dual-rotor system (MSDS) offers the possibility to significantly enhance the performance of aero-engines. However, research on MSDS vibration characteristics under fixed-point rubbing with the consideration of nonlinear support characteristics of active magnetic bearing (AMB) has rarely been addressed. In this research, an improved EF model of AMB is proposed by equivalent magnetic circuit method and verified by finite element model. Then, the Lankarani-Nikravesh model is employed to describe the impact force during rubbing process. On this basis, the rubbing dynamic model is established by finite element method and verified by comparing with the experimental results in literature. Finally, the MSDS vibration characteristics are explored, and some interesting phenomena are found. Fixed-point rubbing will cause abundant frequency components equally spaced around the combined frequency components of rotor rotational speeds at different frequency intervals. Due to the stimulation of the AMB nonlinear EF, the fractional frequency component of MSDS second-order critical speed emerges in a certain speed range and implies potential instability of the system, and the rotational speed corresponding to the initial appearance of this frequency component will decrease when fixed-point rubbing occurs. With the decrease of proportional coefficient and the increase of differential coefficient, the maximum normal impact force in the rubbing process decreases.

Comparison and analysis of different rotor structures of double‐stator permanent magnet synchronous motor

Compared with the single-stator permanent magnet synchronous motor(SS-PMSM), the double-stator permanent magnet synchronous motor(DS-PMSM) can make full use of the space in the motor cavity to make it have higher torque density, so it is more suitable for direct-drive occasions with low-speed and high-torque. This paper aims to design and compare the parameters and performances of DS-PMSMs with four different rotor structures: 1)Series magnetic circuit of radial magnetised single-layer permanent magnet(type Ⅰ), 2)Series magnetic circuit of radial magnetised double-layer permanent magnet(type Ⅱ), 3)Parallel magnetic circuit of radial magnetised double-layer permanent magnet(type Ⅲ), 4)Parallel magnetic circuit of tangential magnetised permanent magnet(type Ⅳ). Firstly, the equivalent magnetic circuit method is used to analyse the magnetic circuits of the four DS-PMSMs. Next, the finite element analysis tool is used to compare the performances of the four DS-PMSMs with the same volume. Their air-gap flux density, no-load back-EMF, cogging torque, torque characteristics, moment of inertia, rotor loss and efficiency are quantitatively analysed and compared. Finally, this paper provides guidance and suggestions for the selection of the rotor structure of DS-PMSM.

Parameter Sensitivity Analysis and Robust Design Approach for Flux-Switching Permanent Magnet Machines

Parameter sensitivity analysis is usually required to select the key parameters with high sensitivity to the optimal goal before the optimization is carried out, especially for flux-switching permanent magnet (FSPM) machines where lot of design parameters should be considered. Unlike the traditional studies on parameter sensitivity, which are generally experience- or statistics-based, and are time-consuming, this paper proposes a parameter sensitivity analysis method of a FSPM machine based on a magnetic equivalent circuit (MEC), which enables the parameters’ sensitivities to be evaluated by their exponential in the nondimensionalized equations, thus providing a fast and accurate way to obtain the parameter sensitivities. Thereafter, the influences of modular manufacturing methods on magnetic performances are discussed, and the robust design approach for the FSPM machine is introduced, which aims to achieve the best machine stability and robustness by setting boundaries on design dimensions when taking into account the manufacturing tolerances. Experimental validations are also presented.

Design, modelling and analysis of a hybrid-magnet variable-flux PMSM with variable series-parallel magnetic circuit

Variable-flux permanent magnet synchronous machines (PMSMs) which use low-coercive-force permanent magnets have gained a lot of attention as a perspective alternative in the variable-speed driving application for their advantages of operating with improved efficiency in higher speed through adjusting the variable-flux PMSMs’ magnetization states. A hybrid-magnet variable-flux machine which has the variable series-parallel magnetic circuit is investigated. Magnetization state and magnetic circuit type of this variable-flux PMSM are adjustable. This machine’s equivalent magnetic circuit (EMC) model at different magnetization states is established and evaluated. This model can precisely represent the complicated and changeable magnetic circuit in variable-flux PMSMs and provide an effective way for the operating principle and performance analysis. The electromagnetic performances are investigated in detail. The magnetization state variation’s range is wide. Magnetizing/demagnetizing current is small. By fully using reluctance torque, variable-flux PMSM’s torque ability improves greatly. The ratio of high efficiency area in total torque-speed operating area increases obviously. The efficiency during high speed operation also increases. This machine has advantages and overcomes limitations of variable-flux machine which has series magnetic circuit or parallel magnetic circuit.

Open-circuit field prediction of IPM machine using multiple flux source network model

Accurate modeling of motor magnetic fields facilitates all aspects of motor analysis, design, and optimization. Existing methods are difficult to balance the speed and accuracy of modeling, among which the widely popular finite element method is relatively time-consuming and the accuracy of magnetic circuit modeling is difficult to guarantee. In this regard, this paper presents a magnetic equivalent circuit model based on the multiple flux source network for interior permanent magnet (IPM) machines. The model considers the magnetic saturation effect through a non-linear iterative process. The accuracy improvement of the proposed model has been verified by comparison with the traditional single-flux-source model. Furthermore, the proposed model greatly saves the calculation time while bringing fairly good accuracy compared to the finite-element method, which is beneficial for the design optimization of the IPM machines.

No-Load Electromagnetic Performance Analysis of a Mechanically Modulated Permanent Magnet Homopolar Inductor Machine

Conventionally, the nonadjustable air-gap flux density generated by the permanent magnet (PM) of PM machine would cause large core loss during the standby operation state of flywheel energy storage system (FESS), which would reduce the energy conversion ratio of system. To suppress the no-load core loss, a mechanically modulated PM homopolar inductor machine (MM-PMHIM) is proposed. However, the MM-PMHIM has intrinsic three-dimensional (3-D) flux density distribution, which would be time-consuming to analyze the no-load electromagnetic performance by the finite element method, especially in the initial design stage. Addressing this issue, an analytical method based on magnetic equivalent circuit (MEC) considering the different flux weakening states of the MM-PMHIM is proposed in this article. First, the special topology and operation principle of the MM-PMHIM are analyzed. Second, the MECs of this machine under different flux weakening states are established, and the detailed building processes are presented. Third, several main electromagnetic performance indexes, including flux density distribution, flux linkage, back-electromotive force (back-EMF), etc., are fully analyzed. Finally, the no-load electromagnetic performance of the proposed MM-PMHIM under different flux weakening states is evaluated and the effectiveness of the MEC models are proved by finite-element method (FEM) and prototype test. The result shows that the proposed analytical method can quickly and accurately analyze the no-load performance of the MM-PMHIM.

Iron Loss Analysis in Axial Flux Permanent Magnet Synchronous Motors With Soft Magnetic Composite Core Material

Accurate calculation of iron losses in electric machines are essential for optimal machine design. This is especially important for axial flux permanent magnet motors with solid stator and rotor cores. This paper investigates iron losses in axial flux motor with soft magnetic composite material for the stator and the rotor. First, an analytical model is proposed to estimate iron losses under different operating conditions. The model is based on combining the Quasi 3-D computation approach and the magnetic equivalent circuit. The proposed model can be modified to account for different motor topologies and different stator and magnet designs. Then, The effect of torque ripple, on iron losses, is studied by comparing two motors: an optimized motor, with dummy pocket added to the stator tooth, and a non-optimized motor. Finally, the effect of the motor control scheme and the inverter switching frequency is studied by implementing two controllers: the Field Oriented Control and the Trapezoidal control. Simulations using 3-D finite element analysis and experimental tests are conducted, under different operating conditions, on two <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{12}\,V$</tex-math></inline-formula> , 6 slots, 8 poles single stator single rotor fractional horsepower axial flux permanent magnet synchronous motor prototypes. Test results shows that motor optimization, the choice of the motor control scheme, and the selected switching frequency can significantly affect iron losses in the motor. Using an optimized motor with a smooth control scheme, such as Field Oriented Control, and a high switching frequency, can cause a variation in iron losses by around 14% compared to a non optimized motor with the Trapezoidal control and a low switching frequency.

Modeling and Analysis of Dual-Winding Bearingless Flux-Switching Permanent Magnet Motor Considering Magnetic Saturation Based on Subdomain Model

Dual-winding bearingless flux-switching permanent magnet machine (BFSPMM) is composed of power winding and suspension winding. The permanent magnet and the power winding provide a biased air gap magnetic field, and the suspension winding generates an air gap modulation magnetic field. The structure of stator and rotor are double salient poles. This paper proposes a subdomain model for the on-load field prediction in dual-winding BFSPMM. In the developed model, the field domain is divided into seven types of subdomains, viz. rotor slot, internal air gap, stator slot, permanent magnet slot upper layer, permanent magnet slot lower layer, permanent magnet, and external air gap. The electromagnetic parameters of the motor are analyzed, including air gap flux density, flux linkage, back-EMF, suspension forces, and electromagnetic torque. Based on the principle of conservation of magnetomotive force, a distributed equivalent magnetic circuit model is proposed to compensate for the magnetic saturation. Finally, the analytical predictions are verified by finite-element analysis and prototype experiments.

Research on Influence of Motor Parameters on the Negative-Salient Permanent Magnet Synchronous Motor

The d-axis inductance <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(L_{d})$</tex> of the negative-salient permanent magnet synchronous motor (NSPMSM) is larger than the q-axis inductance <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(L_{q})$</tex> . Compared with the traditional motor, the NSPMSM has the characteristics of a high overload capacity, wide speed range, and preventing permanent magnet demagnetization. Positive d-axis current <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(i_{d})$</tex> is applied to control positive reluctance torque when running at base speed. When the motor is running at high speed, a relatively small <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$i_{d}$</tex> can achieve speed expansion and effectively expand the motor flux-weakening range. The use of a magnetic bridge to increase the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L_{d}$</tex> and a W-type permanent magnet to reduce the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$L_{q}$</tex> is proposed in this article as a novel NSPMSM rotor structure. Firstly, the working principle of the NSPMSM was determined according to the equivalent magnetic circuit. Secondly, using the finite element method, the influence of motor structure on torque and speed performance of NSPMSM was analyzed, and the motor structure was optimized. Thirdly, the effect of the internal power factor angle on the performance of the two motors is analyzed. Finally, the short circuit simulation and analysis verified that the NSPMSM has a stronger short circuit current suppression ability without sacrificing overload ability.

Comparative Study of High Torque Density Spoke-Type PM In-Wheel Motors for Special Vehicle Traction Applications

With the development of the transportation electrification, the demand for high-performance motor is growing rapidly. High torque density and wide constant power operating range are two key requirements of the electric vehicle (EV) traction applications. Considering the limited voltage and current, a successful EV traction machine should realize good linearity of torque–current characteristic and a proper characteristic current. In order to meet these strict demands, an optimized Fractional-Slot Concentrated-Winding(FSCW) permanent magnet (PM) machine with different rotor structures is proposed in this article based on the traditional spoke-type PM machine topology. The machine structures are introduced and optimized in the design procedure, and a magnetic equivalent circuit model is applied to illustrate its principle. The electromagnetic performances, including back electromotive force, output torque, and efficiency map, are compared between the original and optimized design to highlight the performance improvement of the optimized topology. Finally, a prototype machine has been built for the experimental validation. The experimental results, which agree well with the Finite Element (FE)-predicted results, confirm the validity of the analysis method used in predictions and the advantages of the optimized design.

An efficient multidisciplinary design research for the integrated low speed permanent magnet motor system based on analytical and numerical hybrid analysis

This paper proposed an efficient high-accuracy multidisciplinary design process for the integrated system of low speed permanent magnet synchronous motor (PMSM). The method combined the analytical models and numerical models together to get an efficient way to design the integrated motor. In the proposed method, a magnetic equivalent circuit (MEC) model of the motor is established first based on one modular structure of the motor, and the finite element analysis (FEA) numerical model is used to correct the results of the analytical model next. Then the iron loss, copper loss, and switching loss from the results of the electromagnetic model are loaded to a proposed simplified lumped parameter fluid-thermal model. This fluid-thermal coupled analytical model cuts the fluid flow into several parts depends on the parameters of the cooling path, each parts act as a current controlled voltage source coupled with these parameters. And because this coupled model has controlled sources, the conventional node voltage method is not suitable anymore, so a more universal list parameter calculation method is proposed for this coupled model. Finally, the computational fluid dynamics (CFD) model is used to correct the results of the analytical model as well. The aim of the above analytical models is to quickly get the suitable multidisciplinary pre-design or design trends, and this pre-work or trends will reduce the design process time of the high-accuracy numerical models.