Magnetic Circuit Model Research Articles

Multiobjective optimization of 3-DOF magnetic bearing considering eddy current effects and saturation

The multiobjective optimization method of three-degrees-of-freedom hybrid magnetic bearings (3-DOF HMBs) is crucial compared to time-consuming finite element calculation due to their three dimensional magnetic field. Solid rotors are the first choice for high-speed applications because the yield strength of laminated rotors is lower. However, solid materials may induce eddy current effects and saturation problems. In addition, a 3-DOF HMB has solid and laminated materials and permanent magnet materials, and the material price presents a risk for the structure. In view of the above mentioned problems, a dynamic magnetic circuit model of the 3-DOF HMB with eddy current and saturation effects is initial given. Subsequently, a multiobjective optimization design method for maximum axial and radial bearing capacity and the lowest cost is proposed. Finally, the optimized parameters are given, and a prototype is manufactured. The range of all optimal solutions considering saturation is less than that without saturation, and the maximum reduction is 99%. The experimental results demonstrate the effectiveness of the optimized design results.

Wireless power transfer tuning model of electric vehicles with pavement materials as transmission media for energy conservation

Wireless power transfer (WPT) is one of the ways to alleviate the charging difficulties of electric vehicles, accelerating the growth of ownership of electric vehicles to replace petrol vehicles towards carbon net zero in transportation. In order to ensure the durability of the primary circuits of WPT and prevent the circuits to become obstacles for driving, the primary circuits need to be buried in the pavement structure. However, pavement materials can adversely affect the resonant induction coupling process of WPT, reducing the power and efficiency of charging. In order to explore the influence of the type and thickness of pavement materials on the WPT, vibrating sample magnetometer was used to test the magnetization performance of raw materials of pavement. The effective relative permeability of the three most commonly used pavement materials, including AC-13, SMA-13 and PCC, was calculated according to the magnetic circuit model. The simulation models of primary coil, secondary coil and pavement materials were established in Ansys Maxwell software. The self-inductance and mutual inductance of the coils after inserting pavement materials were obtained. The output power and transmission efficiency of WPT were calculated according to the theoretical calculation formulae. The results showed that inserting pavement materials between the primary and secondary coil as transmission media enhanced the primary self-inductance, secondary self-inductance and mutual inductance, leading to the detuning of resonant circuit and the reduction of output power. After adjusting the frequency of the high-frequency voltage to the resonant frequency, the output power of WPT was improved. Among the three materials, the output power was the highest when AC-13 was used. In addition, the calculation formulae of resonance frequency, output power and efficiency after introducing pavement materials were given, providing calculation basis for the design of WPT pavement.

Analytical modelling of one cage rotor induction motor for electric submersible pumps

A new hybrid analytical model (HAM) based on conformal mapping (CM) method and magnetic equivalent circuit (MEC) model is presented in this paper for electromagnetic modelling of cage rotor induction motors (CRIMs) used in electric submersible pumps (ESPs). For every operating point, the iron parts are modelled with a non-linear MEC model to calculate the equivalent virtual currents, which represent the influence of magneto motive force (MMF) drops and MMF sources in stator and rotor cores. The effects of the equivalent virtual currents on the air-gap magnetic field are then considered using the CM method and Hague's solution. This approach for calculating the air-gap field is also used to prepare a 3-D lookup table (3-D LUT) for each element of inductance matrix and derivative of inductance matrix in terms of rotor position. These LUTs are then used for transient modelling and analysis of CRIM under no-load and loading conditions. The accuracy of proposed HAM is validated by comparing the results obtained through HAM with corresponding results obtained from finite element method and experiment set-up.

Reluctance Mesh-Based Magnetic Equivalent Circuit Modeling of Switched Reluctance Motors for Static and Dynamic Analysis

Designing a switched reluctance machine (SRM) is an iterative process. Sizing of the motor is one of the fundamental steps where the main geometry parameters are determined to achieve the performance requirements. Usually, finite element method (FEM) is employed in all design stages, which might require extensive computational burden. The magnetic equivalent circuit (MEC) method is an alternative for typical FEM. There are two approaches for the MEC method: conventional MEC method and reluctance mesh-based MEC method. The conventional MEC method can be challenging when modifying the motor geometry while conducting dynamic analysis with current control. This article presents a reluctance mesh-based MEC model for SRMs that can overcome those challenges. Reluctance mesh-based MEC models are developed for three-phase 6/4, 6/16, 12/8 SRMs and four-phase 8/6, 8/10, and 16/12 SRMs. The models calculate the static and dynamic characteristics of the considered SRMs. The static and dynamic characteristics are compared with the results obtained from FEM and experimental tests.

Analytical Model of Electromagnetic Performance for Permanent-Magnet Vernier Machines Using Nonlinear Exact Conformal Model

This paper investigates the air-gap field distribution of the permanent-magnet vernier machine (PMVM) using nonlinear exact conformal model (NECM) to account for slotting effect, flux modulation effect and iron nonlinearity. The exact conformal model based on the region of one-slot and one-flux-modulation-pole (OSECM) are introduced to show the effectiveness of linear analytical model for PMVM. It can keep high calculation accuracy and significantly reduce the computational burden. Then, the NECM is developed from OSECM by introducing the equivalent saturation current into the air region and coil region. The lumped parameter magnetic circuit model (LPMCM) model is used to obtain the magnetic potential of iron region and therefore calculate the equivalent saturation current. The NECM which combines LPMCM and OSECM can essentially improve the accuracy of linear analytical model. The harmonic analysis of air-gap field is performed to theoretically explain the component of electromagnetic torque. Both finite element model (FEM) simulation and test results are presented to validate the NECM.

Improved Open-Circuit Airgap Field Model for FSCW-STPM Machines Considering PM-MMF Fluctuation

In this article, we propose an improved analytical model for the fractional-slot concentrated-winding spoke-type permanent-magnet (PM) machines, where the impact of slotting on magnetomotive force (MMF) is elaborately considered. First, the deficiency of the existing MMF-permeance model using Carter's coefficient is discussed. It is found that adopting Carter's coefficient will cause considerable prediction errors in flux density, especially for machines with a small equivalent airgap and considerable PM-MMF fluctuation. Second, an improved analytical model is proposed based on the relative permeance function and a simplified magnetic circuit model. The proposed model enables to predict common electromagnetic performance, such as PM flux density and back electromotive force with higher accuracy. Moreover, the radial forces exerted on the stator teeth can be predicted precisely as well, which is conducive to further vibration analysis. Both the experimental and finite-element analysis results indicate that the proposed model can enhance the characterization capability of the slotting effect and improve the performance prediction accuracy.

A new hybrid analytical model for electromagnetic analysis of wound rotor induction motors

AbstractAccurate modeling of slotting and magnetic saturation effects has been two main challenges for analytical modeling of electric machines. In this article, first, different techniques such as sub‐domain (S‐D) model, winding function theory, magnetic equivalent circuit (MEC) model, and conformal mapping (CM) method are introduced to analytical model and analysis of electric machines. These techniques are also compared in terms of their accuracy, and computational complexity. Second, with respect to the comparison results, a new hybrid analytical model is presented for electromagnetic modeling of wound rotor induction motors, which consider the modeling accuracy of slotting and magnetic saturation effect, simultaneously. In this way, the air‐gap region is modeled by using S‐D model, and the iron parts are considered by using MEC model assisted by CMs. In final, the analytical results are verified by comparing with corresponding results obtained through finite element method and experiment set‐up.

Modeling and Design of Resonant Magnetic Field Sensors in the Scheme of Differential Magnetostrictive Actuation With Compact Bias Magnetic Circuit

A type of differential resonant magnetic field sensor is developed by employing the composite elements of FeGa plates, piezoelectric quartz crystal double-ended tuning forks (DETFs) and bias permanent magnets. The model and analysis show that the differential design brings the benefits of doubled sensitivity, increased linearity and low temperature drift. Importantly, a small and compact magnetic circuit containing a pair of permanent magnets and dual FeGa plates ensures the generation of differential actuation, which not only reduces the leakage flux but also improve the field-sensitivity and resolution. The magnetic circuit model based on the “lumped parameters” method is established. As an important aid, the distribution of magnetic flux density along the longitudinal direction of the FeGa alloy is simulated by finite element analysis software. In order to avoid the prediction error caused by parameter errors, simulations in different conditions are carried out for comparative analysis. This method ensures the magnetic circuit provides qualified magnetic field. The experimental results show that the differential resonant magnetic field sensor with frequency readout has the characteristics of high sensitivity of 4.4 Hz/Oe, high resolution of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${&lt; }3.04\times 10^{-4}$ </tex-math></inline-formula> Oe, low temperature drift and excellent linear (non-linearity error of 1.3%FS) and low hysteresis (1.5%FS) over its measurement full scale (FS) of ±100Oe.

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.

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.

On Unintentional Demagnetization Effect of Switched Flux Hybrid Magnet Memory Machine

This paper investigates the unintentional demagnetization (UD) characteristics of low-coercive-force (LCF) permanent magnets (PMs), in switched flux hybrid magnet memory machines (SF-HMMMs). Although the LCF PM field is magnetically in parallel to the magnetic fields produced by the NdFeB PM, as well as the armature reaction in the investigated machines, the UD phenomenon of LCF PMs still possibly occurs, particularly, under on-load operation due to the magnetic saturation effect. First, the UD effect is revealed by the frozen permeability method (FPM), and analytically explained via a magnetic circuit model. Various UD types are then identified with the finite-element (FE) method, coupled with a virtual linear hysteresis curve (VLHC) of LCF PM and FPM. In addition, the dimension and grade of the LCF PM are designed with the aid of VLHC, in order to prevent the UD effect. Finally, a fabricated SF-HMMM prototype is tested to verify the theoretical analyses.

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.

Dynamic Hysteresis Modeling Taking Skin Effect Into Account for Magnetic Circuit Analysis and Validation for Various Core Materials

This article presents a novel magnetic circuit model which can represent the dynamic hysteresis characteristics considering the skin effect. The proposed model is mathematically equivalent to the previously proposed magnetic circuit model incorporating the play model and Cauer circuit. However, the previous one has a problem in practical use that the magnetic circuit analysis must be performed by coupling with the external electric equivalent circuit to take the skin effect into account. Thus, it is difficult to apply the previous method to the analyses of devices with complicated shapes such as electric motors due to model complexity and convergence deterioration. On the contrary, the proposed model is more practical since it is composed of only the magnetic circuit elements. The calculation accuracy of the proposed model and its versatility for various kinds of core materials are experimentally proved by using ring cores made of grain-oriented (GO) and non-oriented (NO) silicon steels, an amorphous alloy, and a soft magnetic composite (SMC).

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.

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.

Study on the Peripheral Magnetic Leakage and Shielding Measures of Surface-mounted Permanent Magnet Motor

Permanent magnet (PM) motors are widely used in our daily lives. Taking a surface-mounted PM motor as an example, a magnetic circuit model considering the peripheral magnetic flux leakage is established. Maxwell software is used to simulate different loads and thicknesses and the materials of the shielding layers. The magnetic flux leakage around the motor has a sinusoidal distribution in the space. The value of the magnetic flux leakage is inversely proportional to the power of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$P+1$</tex> from the surface of the core. The thicker the shielding layer, the smaller the magnetic leakage. The greater the relative permeability of the shielding layer, the better the shielding effect. The results provide ideas and recommendations for the magnetic flux leakage analysis and the design of non-magnetic or low magnetic motors.

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.

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.

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.