Showing papers on "Magnetic circuit published in 2015"

Design of a Resonant Reactive Shield With Double Coils and a Phase Shifter for Wireless Charging of Electric Vehicles

Abstract: In this paper, a novel resonant reactive shield using a double-shield coil and phase-shift circuit is proposed to reduce magnetic field leakage in electric vehicle wireless charging applications. The double-reactive shield with a four-capacitor phase shifter generates a canceling magnetic field, the phase of which is perfectly opposite to that of the incident magnetic field, effectively reducing the leakage magnetic field as a result. The concept and structure, and an equivalent-circuit model analysis of the double-reactive shield are explained and discussed. The shielding effectiveness of the double-reactive shield is compared with that of a conventional reactive shield with a single-shield coil by a simulation and is verified by experiments.

Loss and Efficiency Analysis of Switched Reluctance Machines Using a New Calculation Method

Abstract: In this paper, a fast and accurate analytical method is proposed to analyze the loss and efficiency of switched reluctance machines (SRMs) under various operating conditions. The analyses are applied on a four-phase 16/12 SRM with high power density and wide speed range, which was designed for traction application. A direct method is proposed to calculate hysteresis and eddy current loss without empirical equations. The machine is discretized into a limited number of elements according to the magnetic flux density distribution using an analytical magnetic circuit method. Variable loss coefficients are used for each element to improve the accuracy. The developed method has been validated with simulation and experimental results.

Magnetic Equivalent Circuit Modeling of the AC Homopolar Machine for Flywheel Energy Storage

Abstract: This paper develops a magnetic equivalent circuit model suitable to the design and optimization of the synchronous ac homopolar machine. The ac homopolar machine is of particular interest in the application of grid-based flywheel energy storage, where it has the potential to significantly reduce self-discharge associated with magnetic losses. The ac homopolar machine features both axial and radial magnetizing flux paths, which requires finite element analysis to be conducted in 3-D. The computation time associated with 3-D finite element modeling is highly prohibitive in the design process. The magnetic equivalent circuit model developed in this paper is shown to be a viable alternative for calculating several design performance parameters and has a computation time which is orders of magnitude less than that of 3-D finite element analysis. Results obtained from the developed model are shown to be in good agreement with finite element and experimental results for varying levels of saturation.

Torque, Power, Losses, and Heat Calculation of a Transverse Flux Reluctance Machine With Soft Magnetic Composite Materials and Disk-Shaped Rotor

Abstract: In this paper, the authors introduce a type of transverse flux reluctance machines. These machines work without permanent magnets or electric rotor excitation and hold several advantages, including a high power density, high torque, and compact design. Disadvantages are a high fundamental frequency and a high torque ripple that complicates the control of the motor. The device uses soft magnetic composites (SMCs) for the magnetic circuit, which allows complex stator geometries with 3-D magnetic flux paths. The winding is made from hollow copper tubes, which also form the main heat sink of the machine by using water as a direct copper coolant. Models concerning the design and computation of the magnetic circuit, torque, and the power output are described. A crucial point in this paper is the determination of hysteresis and eddy-current losses in the SMC and the calculation of power losses and current displacement in the copper winding. These are calculated with models utilizing a combination of analytic approaches and finite-element method simulations. Finally, a thermal model based on lumped parameters is introduced, and calculated temperature rises are presented.

Inductance Calculation of Flux Concentrating Permanent Magnet Motor through Nonlinear Magnetic Equivalent Circuit

Abstract: In order to design a permanent magnet synchronous motor (PMSM), the inductance must be computed. In this paper, the flux concentrating PMSM (FCPMSM) is introduced. Calculating the inductance is difficult because of the complex structure of the rotor. Because the rib and the bridge consist of an iron core, they have nonlinear characteristics. In order to obtain the effective value of the inductance, nonlinear characteristics must be considered in a magnetic equivalent circuit (MEC). In this paper, to calculate the inductance of an FCPMSM, the relative permeance of the rotor was analyzed. Then, the dq -axis MEC, including the nonlinear magnetic reluctance, was created using the flux line. Finally, we verified the validity of the proposed inductance calculation method by comparing the results between the finite-element method and the proposed method.

Linear Flux Pump Device Applied to High Temperature Superconducting (HTS) Magnets

Abstract: This paper presents a novel linear flux pump which could be used to magnetize 2G HTS tapes and coils. The design is based on an iron magnetic circuit together with copper solenoids and is powered by a current source driver circuit. Several applied waveforms were tested including a symmetric sine wave and an asymmetric trapezoidal wave. Both standing and travelling waves were applied. The measurements focused on the effects of frequency and magnitude of the applied field and their effect on the system pumping efficiency. It was found that a trapezoidal wave was more effective than a sine wave, producing a greater final current at the same applied frequency and field strength. The maximum induced current in the superconducting coil was 19 A which was achieved using an applied field of 50 mT, applied as a travelling trapezoidal wave. The driving current to the copper coils was 5 A in amplitude with a frequency of 10 Hz. It was found that when the applied field magnitude was less than 16 mT pumping did not occur. It proved possible to pump the system with a standing wave as well as a travelling wave. This effect needs to be investigated further as it is possible that the standing wave had travelling components.

Development of a Magnetless Flux Switching Machine for Rooftop Wind Power Generation

Abstract: This paper proposes and implements a new single-phase magnetless flux switching machine (FSM) for rooftop wind power generation. The key is to integrate an outer-rotor FSM and an inner-rotor FSM with shared stator yoke and stator drum windings. In such a way, this proposed machine can not only realize flux switching function to regulate magnetic flux effectively, but also incorporate the field and armature windings within one stator to reduce the copper losses and improve the overall machine efficiency. Meanwhile, the structure is compact and rotors can be directly driven by blades to capture the wind power. The machine design guidelines from both magnetic and electric aspects are illustrated, the machine characteristics are analyzed by using time-stepping finite-element method, and the system performances are evaluated based on mathematical modeling. Both simulation and prototyping test are conducted to verify the validity of the proposed machine and system.

Open Circuit Performance Analysis of a Permanent Magnet Linear Machine Using a New Hybrid Analytical Model

Abstract: This paper presents the analysis of open circuit performance of a permanent magnet linear machine using a new hybrid analytical model (HAM). The goal is to show the capabilities offered by this new modeling approach. The new HAM is based on a strong coupling of magnetic equivalent circuits method and analytical models. The analytical model, based on the formal solution of Maxwell’s equations, is established because of the separation of variables method. The open circuit performance are: 1) cogging force; 2) electromotive force; and 3) open circuit iron loss, obtained from the HAM are compared with corresponding results obtained from a finite-element analysis. A very good agreement has been obtained.

MEC-Based Modeling and Sizing of a Tubular Linear PM Synchronous Machine

Abstract: Linear machines are currently considered as viable candidates for direct-drive wave and free-piston energy converters. This paper is devoted to an approach based on a magnetic equivalent circuit (MEC), which is also called lumped circuit, dedicated to the modeling and sizing of a tubular linear permanent-magnet synchronous machine (T-LPMSM). The proposed approach considers, in a first step, the cancelation of the end-effect phenomenon. To do so, a dedicated design procedure, consisting in 1) achieving a $2\pi/3$ -shift between the armature phase flux linkages by selecting a fractional ratio of the stator pole pitch to the mover one and 2) balancing the amplitudes of the phase flux linkages by extending the stator magnetic circuit with teeth of appropriate dimensions, is firmly applied on two basic T-LPMSM topologies using a dedicated MEC. Then, an investigation of the influent sizing parameters on the force production capability of the initial concept is carried out. The MEC-based prediction of the force requires the incorporation of the mover displacement, yielding the so-called “position varying MEC” on one hand and the armature magnetic reaction on the other hand. The finite-element analysis of the armature phase flux linkages and the developed force enable the validation of the results yielded by the established MECs.

Design Methodology for Variable Leakage Flux IPM for Automobile Traction Drives

Abstract: This paper presents a novel methodology for the variable leakage flux interior permanent-magnet (VLF-IPM) motor taking advantage of the variable leakage flux property in the rotor core controlled by the $q$ -axis current, without any additional components. The fundamental phenomenon is explained with finite-element analysis results; then, the theoretical equations expressing the variable flux linkage controlled by the $q$ -axis current have been conducted. The proof-of-principle model was designed, and the fundamental properties, such as torque–speed envelope and efficiency map, were evaluated. It was shown that the proposed motor can reduce energy consumption on duty-cycle driving.

High bit-rate magnetic communcation

Abstract: A magnetic communications transmitter includes a magnetic field generator and a controller. The magnetic field generator is configured to generate a magnetic field. The controller is configured to control the magnetic field generator by controlling an electrical current supplied to the magnetic field generator, and causing the magnetic field generator to generate an optimized variable amplitude triangular waveform.

A novel partitioned stator flux reversal permanent magnet linear machine

Abstract: A novel partitioned stator flux reversal permanent magnet (PS-FRPM) linear machine with segmented iron mover is introduced. The operation principle of the PS-FRPM linear machine is described, and the optimisation of the machine leading design parameters for maximum thrust force using genetic algorithm has been carried out. Moreover, in order to investigate the longitudinal end effect on the machine performance a periodic model has been employed to compare with the real model. It is found that the end effect has a significant impact on the machine performance, particularly in terms of unbalanced magnetic circuit and cogging force. Additionally, the influence of the mover iron pole numbers on the electromagnetic performance of PS-FRPM linear machines has been examined, i.e. 6/4, 6/5, 6/7, 6/8, 6/10 and 6/11 stator/mover pole combinations are designed and compared. It is concluded that the machine with a mover pole pitch which is closer to the stator slot pitch exhibits the best performance among the others.

Design and Realization of a Novel Compact Fluxgate Current Sensor

Abstract: A new closed-loop magnetic current sensor is presented in this paper. The sensor consists of two toroidal magnetic cores. One core works in fluxgate principle for the measurement of dc and low-frequency ac, and the other one is used as a current transformer for higher frequency application. Based on the simulation results, a prototype was designed, and the test results have a good agreement with the simulation results. The closed-loop configuration with a magnetic core and a feedback winding in the sensor improved the sensitivity of the sensor, eliminated the offset and drift related to temperature, and greatly reduced the error caused by magnetic hysteresis phenomenon. It can measure currents up to 20 A, with an accuracy of 0.5%, and a 50 kHz small signal bandwidth.

MEC-Based Sizing of a Hybrid-Excited Claw Pole Alternator

Abstract: The paper is aimed at a magnetic equivalent circuit (MEC)-based sizing of a novel hybrid-excited claw pole alternator. It consists in a claw pole concept with a NdFeB permanent magnet (PM) excitation in the rotor and a dc one in the stator, with the homopolar flux eradicated owing to a magnetic barrier inserted between the stator yoke and lamination. The proposed MEC considers both linear and saturated magnetic circuit, with a focus on the modeling of the leakage fluxes. The developed model is applied for the prediction of the no-load characteristic which is validated by 3-D finite-element analysis (FEA). Then, a dual FEA-experimental validation is carried out considering the case of a dc excitation. Moreover, the proposed MEC makes the investigation of the influent sizing parameters on the machine back-electromotive force (EMF) production capability easy. This latter is enhanced owing to the integration of two ring ferrite PMs linked to the stator, along with a reduction of the volume of the NdFeB PM in the rotor. It has been found that the gained improvement is better than the benefit yielded by as many pole number ferrite PMs inserted between the claws.

Optimization of Magnetic Circuit for Brushless Doubly Fed Machines

Abstract: This paper presents an optimized design method for the magnetic circuit of brushless doubly fed machines (BDFMs). The BDFM is an attractive electrical machine, particularly for wind power applications, as a replacement for doubly fed slip-ring generators. This study shows that the conventional design methods for the BDFM stator and rotor back iron can be modified, leading to a lighter and smaller machine. The proposed design concepts are supported by analytical methods, and their practicality is verified using two-dimensional finite-element modeling and analysis. Two BDFMs with frame sizes D180 and D400 are considered in this study.

Characteristics Optimization of the Maglev Train Hybrid Suspension System Using Genetic Algorithm

Abstract: This paper focuses on the optimal structural design of a hybrid permanent-magnet-electro-magnetic suspension system (PEMS) for a magnetic levitation (Maglev) transportation system in order to decrease the suspension power loss. First, the nonlinear magnetic force expression of a PEMS system is obtained by developing the magnetic equivalent circuit of the hybrid structure. The proposed analytical framework accounts for leakage fluxes and material properties such as iron reluctances. A number of design considerations are also presented to attain more practical results. Genetic algorithm is then employed to optimize the lifting force while reducing the system power loss. Moreover, 3-D finite element method (FEM) is utilized in the analyses and it is shown that the results calculated from the proposed model match well with those obtained from FEM. In addition, superiorities of the implemented model over the existing approaches are demonstrated. The outcomes show that the proposed method has increased the magnetic force, while significantly reducing the suspension power loss compared with those in the conventional pure electromagnet structure and in a previously proposed hybrid structure.

An overview of analytical methods for magnetic field computation

Abstract: In this paper, several of analytical methods for modelling the magnetic field are described These models are used in design routines of the rotating machines, linear motors as well as actuators Thanks to their high accuracy and low requirements for computation power, they are successfully implemented in designing high precision machines In order to enlarge the applicability of the methods it is a common practise to combine two or more model such as Magnetic Equivalent Circuit (MEC) and Harmonic Method (HM), Schwartz Christoffel (SC) mapping and Tooth Contour Method (TCM), those combinations turns into so called Hybrid Methods which are also intended to increase the computation speed and results precision

A New Coupled-Inductor Structure for Interleaving Bidirectional DC-DC Converters

Abstract: A new EƗƎ-shape coupled inductor structure and its magnetic circuit models are presented. The proposed EƗƎ-shape coupled inductor structure retains the advantages of high power density and tackles the drawback of high air-gap fringing flux losses in conventional EƎ-shape coupled inductor structure. Besides, the proposed EƗƎ-shape structure gives the advantages of shorter winding length and more uniform thermal distribution compared with the conventional EƎ-shape structure. The proposed EƗƎ-shape structure and its magnetic models are successfully simulated by ANSYS and Maxwell 2-D, and implemented to apply to interleaving bidirectional dc/dc converters. The simulated and experimental results show that the proposed EƗƎ-shape structure of coupled inductors is superior to the same volume EƎ-shape structure of coupled inductors in terms of temperature, inductance, losses, inductor ripple currents, and efficiencies. The theoretical prediction and experimental results are in good agreement.

Electrothermal Combined Optimization on Notch in Air-Cooled High-Speed Permanent-Magnet Generator

Abstract: A 30kVA, 96000rpm, air cooled high-speed permanent magnetic generator (HSPMG) is investigated in this paper. Considering effects on both the magnetic circuit and heat transfer paths comprehensively, the stator slot notch in this HSPMG is optimized. First, by using the time-stepping finite element method, the transient electromagnetic fields of HSPMG is numerically calculated, and the electromagnetic losses in different components are obtained. Then, after the determination of other mechanical losses in such a machine, a three-dimensional fluid-thermal coupling calculation model is established, and the working temperature distribution in the HSPMG is studied. Thus, the electromagnetic-fluid-thermal coupling analysis method on the HSPMG is proposed, by using which the influences of machine notch height on machine magnetic circuit and cooling air flowing path are investigated. Meanwhile, both the electromagnetic performance and the temperature distribution in HSPMG with different stator notch height are studied, and a series of analytical equations are deduced to describe the variations of machine performances with stator notch. By using the proposed unbalance relative weighting method, the notch height is optimized to enhance the performance of HSPMG. The obtained conclusions could provide reference for HSPMG electromagnetic calculation, cooling system design, and optimization design.

Novel linear impact-resonant actuator for mobile applications

Abstract: In this study, a novel linear impact-resonant actuator was proposed for mobile device applications. The most significant issue in mobile haptic actuators is the ability to provide various vibrotactile and alert functions despite their size and power consumption limitations. This study aimed to achieve fast and strong impact vibrations over a wide frequency range, including the resonant frequency, which decoupled the intensity and frequency of the vibration to achieve both fruitful vibrotactile feedback and strong alarming vibration. To accomplish this, a new mechanism was proposed that can amplify the impact force at the end of the stroke and increase the speed of the response. The magnetic flux path was optimized using an equivalent magnetic circuit model to maximize the electromagnetic force. The performance of a prototype actuator (11 mm × 9 mm × 3.2 mm) was evaluated in terms of the response time and vibration acceleration amplitude under an input power of 0.3 W. The experimental results clearly showed that the proposed actuator could create a vibration acceleration that was greater than 2 g over a frequency range of 1–210 Hz with a fast response of 4 ms and extremely short residual vibration. In addition, a stronger impact force of around 3 g could be generated near the resonant frequency of 190 Hz.

Electromagnetic Transient Analysis of the Saturated Iron-Core Superconductor Fault Current Limiter

Abstract: Superconducting fault current limiters offer superior technical performance in comparison with conventional methods to limit fault currents. Due to prominent advantages and practical demand, the saturated iron-core superconductive fault current limiter (SISFCL) has been applied on transmission lines and distribution system. Considering the actual structure, the sophisticated equivalent magnetic circuit of the SISFCL was proposed first in the paper. Based on those above, the electromagnetic transient simulation model of the SISFCL was built in Matlab/Simulink. To realize accurate electromagnetic transient simulation, Newton iteration method and fundamental magnetic magnetization curve are introduced into the calculation of the current-limiting inductance during simulation. The transient behavior of the SISFCL in simulation tests illustrated that the proposed method is valid and correct.

On the proprieties of the differential cross-saturation inductance in synchronous machines

Abstract: The cross-saturation inductance is a mutual inductance due to the saturation of portions of the magnetic circuit of one axis caused by the current of the other axis. In the sensorless drives, the differential cross-saturation inductance causes an error in the estimation of the rotor position when performed by means of the high frequency signal injection methods. The knowledge of the properties of cross-saturation inductance is therefore essential to minimize any distortion effect on the machine control. This paper aims to describe the properties of the cross-saturation inductance for different synchronous machine types, such as reluctance, interior PM and surface PM machine. Information are also given to predict the error in the estimated position for any stator currents useful for implementing an error compensation technique. The analysis is supported by finite element simulations and experimental measurements.

High-Frequency Low-Power Magnetic Full-Adder Based on Magnetic Tunnel Junction With Spin-Hall Assistance

Abstract: Perpendicular-anisotropy magnetic tunnel junction (MTJ) is one of the most promising candidates to build hybrid logic-in-memory architecture, because of its nonvolatility, infinite endurance, and 3-D integration with a CMOS technology. A novel magnetic full-adder (MFA) based on this architecture is proposed, with MTJs switched by spin-Hall-assisted spin-transfer torque (STT). Owing to the assistance of spin-Hall effect (SHE), MTJ switching time can significantly be reduced, and high operation frequency can be achieved. Moreover, the endurance of oxide barrier is largely enhanced as the requirement of lower write voltage. Using an industrial CMOS 28 nm design kit and a physics-based three-terminal spin-Hall-assisted STT-MTJ model, functionality and performance of the proposed MFA have been simulated and validated. A 1 ns STT current pulse assisted by 0.35 ns SHE current pulse is sufficient to switch the MTJ configuration. When compared with the previous MFAs based on STT-MTJ, the proposed MFA achieves 38% less operation time and 31% less power consumption to perform read and write operations.

Analysis and Optimization of a Novel Tubular Staggered-Tooth Transverse-Flux PM Linear Machine

Abstract: A novel tubular staggered-tooth transverse-flux permanent magnet linear synchronous machine is proposed. The machine is characterized by simple structure and low flux leakage. First, the structure and the operational principle are introduced. Second, the 3-D equivalent magnetic circuit model of the machine is built, and the analytical expression of the electromagnetic force is derived. Last, the force density and the force ripple are optimized with respect to three key dimensional ratios by the 3-D finite-element method. An optimized scheme with the high force density of $2.697 \times 10^{5}$ N/ $\text{m}^{3}$ and the low force ripple of 2.78% is achieved. In addition, the characteristics of the proposed machine are compared with other topologies of linear machines.

A novel transverse flux machine for vehicle traction aplications

Abstract: A novel transverse flux machine topology for electric vehicle traction application using ferrite magnets is presented in this paper The proposed transverse flux topology utilizes novel magnet arrangements in the rotor that are similar to Halbacharray to boost flux linkage; on the stator side, cores are alternately arranged around a pair of ring windings in each phase to make use of the entire rotor flux that eliminates end windings Analytical design considerations and finite element methods are used for an optimized design of a scooter in-wheel motor Simulation results from Finite Element Analysis (FEA) show the motor achieved comparable torque density to conventional rare-earth permanent magnet machines This machine is a viable candidate for direct drive applications with low cost and high torque density

A system for controllable magnetic measurements of hysteresis and Barkhausen noise

Abstract: A specially developed setup for precise measurement of the magnetic hysteresis and Barkhausen noise is presented in this work. A novelty of the setup consists in a unique combination of two main features: an accurate local determination of the magnetic field and an improved feedback control of the magnetization process. Firstly, the magnetic field is measured by two Hall sensors at different distances above the sample. Linear extrapolation of this measured profile of the tangential fields to the sample surface gives the true local values of the magnetic field. Secondly, a digital feedback loop for precise control of the ac magnetization process is proposed. The system combines two known methods of magnetizing signal adjustment: linear corrections of the magnetizing voltage amplitude and phase. The presented system is able to adjust the waveform of the magnetic induction or field to the prescribed sinusoidal or triangular shape. This provides stable and physically accurate results, which are independent of a specific experimental configuration.

A Distributed Magnetic Circuit Approach to Analysis of Multiphase Induction Machines With Nonsinusoidal Supply

Abstract: A 15-phase induction machine supplied by voltages with third-order harmonic injection has nonsinusoidal magnetomotive forces distribution. This paper introduces a distributed magnetic circuit approach to perform magnetic circuit calculations in order to determine the magnetizing inductance for both the fundamental and third-harmonic component. The proposed approach divides the half-pole or one-pole machine model into a large number of fan-shaped sectors. The air-gap flux densities for all sectors are then solved iteratively. The fundamental and third-harmonic inductances are extracted via Fourier analysis of air-gap flux density distribution. Calculated fundamental and third-order harmonic inductances are compared with those obtained from no-load tests of a 15-phase prototype induction machine. The good agreement between calculated and experimental results verifies the accuracy of the presented method.

Multiphase Inductive Power Transfer Box Based on a Rotating Magnetic Field

Abstract: The industrial use of inductive power transfer (IPT) systems is becoming widespread, ranging from monorail systems, motors, people movers, and battery charging applications. This paper proposes a 3-D IPT system driven by a multiple-phase power converter. This is aided by spice circuitry simulation of the power converter, finite-element-assisted software magnetic frequency analysis, and via implementation of the proposed system. The proposed system consists of a cubic power transfer primary window generated by a rotating magnetic flux flow path. This rotating field is loosely coupled via magnetomotive force (MMF) induction into a secondary power pick-up. The system has been demonstrated as a low-power battery charging system.

Distributed Multilevel Current Models for Design Analysis of Electromagnetic Actuators

Abstract: This paper presents a generalized source modeling method, referred here as distributed multilevel current (DMC) models, utilizing equivalent magnetizing currents as local point sources to describe material effects of commonly used magnetic components. Unlike existing numerical methods, which solve for the magnetic fields from Maxwell's equations and boundary conditions, the DMC-based method develops closed-form solutions to the magnetic field and force problems, while allowing tradeoffs between computational speed and accuracy using a multilevel structure to discretize geometry and minimize modeling errors in the neighborhood around the point sources. Typical DMC models for volume and surface current elements, permanent magnets, electromagnets, iron plate, and induced eddy currents are derived and validated by comparing their magnetic fields and forces with known (analytical, numerical, and/or experimental) solutions. Results of benchmark comparison demonstrate that the DMC methods reduce the computation time of magnetic fields and forces by several orders as compared to exact solutions numerically integrated from the Biot–Savart law and Lorentz force equation and finite-element analysis. The DMC models were experimentally applied to identify the EM coil position and PM magnetization of a commercial PM linear synchronous motor validating their effects on its torque ripple.

Toward Accurate Design of a Transverse Flux Machine Using an Analytical 3-D Magnetic Charge Model

Abstract: Low-speed high-torque applications, e.g., wind energy generation, favor high number of pole solutions. This usually results in a dominating leakage flux in traditionally radial or axial field machines, while the output power remains constant. Within transverse flux machines (TFMs), an increase in output power proportional to the number of poles is achieved by traversing the flux direction. However, TFMs still suffer from a relatively large leakage, reducing their application in present industries. In order to research this leakage, fast and relatively accurate 3-D models are essential. To date, finite-element models (FEMs) have been dominantly used to calculate these 3-D magnetic fields. However, the FEM requires a large number of elements, hence it is very time consuming (hours for a single solution). A fast and more accurate parameterized model is essential to maximize the power factor while maintaining a high torque density. In this paper, the validity of a 3-D analytical magnetic charge model is used to investigate its applicability to model TFM topologies. As such, an automated parametric search has been undertaken to minimize machine volume, i.e., without considering power factor although with fixed constraints on magnetic flux density and slot leakage. Although this does not provide a global optimized minimum, it is surely interesting for the experienced machine designer who wants to further understand the physics of this machine. To illustrate the accuracy of the magnetic charge model, the error of the final result of such a parametric search is compared with a 3-D FEM, which shows an error in force prediction of only 8.9%.