Air-gap Magnetic Field Distribution Research Articles

Analytical Modeling of 3-D Magnetic Field and Performance in Magnetic Lead Screws Accounting for Magnetization Pattern

Mounted with helical magnets, the magnetic lead screw (MLS) could realize contactless conversion between rotation and linear motion. Since the magnetic field in the MLS is essentially three dimensional (3-D), previous 2-D analytical magnetic field calculation methods fail to behave well in the accuracy, while 3-D numerical methods suffer from poorer efficiency in computation time. In this article, an analytical model is developed to predict the 3-D magnetic field distribution and the electromagnetic performance of the MLS. Both radial and parallel magnetizations of the helical magnets are considered. It is shown that the air-gap magnetic field distribution is closely dependent on the magnetization pattern of helical magnets. Both 3-D finite-element (FE) simulation and prototype experiment are performed to validate the accuracy of the proposed analytical model. The analytical results are in good agreement with those by FE analysis and experiment, respectively. And it is highlighted that the magnets magnetized in parallel result in the deformation of thrust force and torque characteristics. Finally, the impact of the number of parallel magnetized magnets on the distortion of MLS performance is discussed. The work can be served as a valuable tool for precise and fast optimization design of the MLS.

A New Hybrid Method for Magnetic Field Calculation in IPMSM Accounting for Any Rotor Configuration

In this paper, a new hybrid model is proposed for the prediction of air gap magnetic field distribution (MFD) in interior permanent magnet machines with any rotor configuration. The slotless magnetic field is first predicted by finite-element method (FEM) with automatic scripting in MATLAB to consider saturation in the rotor iron. Afterward, the conformal mapping viz., Schwarz–Christoffel mapping is introduced to take the slotting effect into account. Consequently, the MFD could be calculated. The back electromagnetic forces, cogging torque, and output torque are obtained accordingly. Then a subdomain model is developed to consider the armature reaction. The results show that the proposed hybrid approach agrees well with the FEM. The model is further verified by experiments. The main contribution of this paper is to reduce the computation time remarkably while maintaining the calculation accuracy.

General Analytical Modeling for Magnet Demagnetization in Surface Mounted Permanent Magnet Machines

This paper proposes an analytical model for the prediction of airgap magnetic field distribution for axial flux permanent magnet (AFPM) machine with partial magnet demagnetization. The AFPM machine geometry is first converted to a polar representation. Consequently, the subdomain model based on current sheet technique is developed. Then current sheet representation of PM is derived to consider the partial demagnetization using superposition principle. The back electromagnetic forces and cogging torque are obtained accordingly based on Maxwell's equations. The results show that the results of proposed approach agrees with that of finite-element method. The model is further validated by experiments under both healthy and demagnetized conditions, which can validate the proposed approach. Main contribution of the work is to consider the partial irreversible demagnetization. Moreover, the proposed method is applicable for both AFPM and radial flux permanent magnet machine.

Analytical calculation of magnetic field in surface-mounted permanent-magnet machines with air-gap eccentricity

PurposeThis paper aims to present an analytical method, which combines the complex permeance (CP) and the superposition concept, to predict the air-gap magnetic field distribution in surface-mounted permanent-magnet (SMPM) machines with eccentric air-gap.Design/methodology/approachThe superposition concept is used twice; first, to predict the magnetic field distribution in slot-less machine with eccentric air-gap, the machine is divided into a number of sections. Then, for each section, an equivalent air-gap length is determined, and the magnetic field distribution is predicted as a concentric machine model. The air-gap field in the slot-less machine with eccentricity can be combined from these concentric models. Second, the superposition concept is used to find the CP under eccentricity fault. At this end, the original machine is divided into a number of sections which may be different from the one for slot-less magnetic field prediction, and for each section, the CP is obtained by equivalent air-gap length of that section. Finally, the air-gap magnetic field distribution is predicted by multiplying the slot-less magnetic field distribution and the obtained CP.FindingsThe radial and tangential components of the air-gap magnetic flux density are obtained using the proposed method analytically. The finite element analysis is used to validate the proposed method results, showing good agreements with the analytical results.Originality/valueThis paper addresses the eccentricity fault impact upon the air-gap magnetic field distribution of SMPM machines. This is done by a combined analysis of the complex permeance (CP) method and the superposition concept. This contrasts to previous studies which have instead focused on the subdomain method.

Tilting Torque Calculation of a Novel Tiered Type Permanent Magnet Spherical Motor

This paper proposes a novel tiered type permanent magnet spherical motor (T-PMSPM) of which the output torque is relatively higher than that of the most existing spherical motors. The proposed T-PMSPM has three stators along axial direction; each of the stator is consisted of an iron core and a three-phase winding. An analytical method is developed in order to calculate the tilting torque based on the air gap magnetic field distribution generated with the specific pole–slot combinations. For performance verification and accurate calculation, three-dimensional finite-element analysis (FEA) is adopted. Two typical rotor configurations are compared and analyzed, focusing on the ability of large torque production, especially for the tilting torque. Finally, a prototype motor as well as the auxiliary apparatus used for experimental measurements has been manufactured. Considering that the friction torque is nonnegligible, a test procedure of torque measurement and separation is designed and performed. The tilting torque obtained from the experiments is compared with the FEA results after friction compensation.

Analytical Prediction of No-Load Stator Iron Losses in Spoke-Type Permanent-Magnet Synchronous Machines

This paper presents an analytical approach for the prediction of no-load stator iron losses in spoke-type permanent-magnet synchronous machines. The influence of bridge saturation is considered. According to the permeability distribution, the bridge is equivalent to fan-shaped saturation region with constant permeability. The magnetic equivalent circuit and iterative method are used to calculate the permeability. The motor is divided into six regions, i.e., shaft, inner saturation region, magnet, outer saturation region, air-gap, and slot. The air-gap magnetic field distribution is first calculated on the basis of Poisson's and Laplace's equations. Then, according to the flux paths, the stator core is divided into tooth and yoke. The magnetic densities of the tooth and yoke are obtained on the basis of the continuity of magnetic flux. Finally, the Bertotti model is employed to calculate the stator iron losses. The validity of the proposed method is verified by the finite element method.

Exact analytical modeling of magnetic vector potential in surface inset permanent magnet DC machines considering magnet segmentation

Abstract Surface inset permanent magnet DC machine can be used as an alternative in automation systems due to their high efficiency and robustness. Magnet segmentation is a common technique in order to mitigate pulsating torque components in permanent magnet machines. An accurate computation of air-gap magnetic field distribution is necessary in order to calculate machine performance. An exact analytical method for magnetic vector potential calculation in surface inset permanent magnet machines considering magnet segmentation has been proposed in this paper. The analytical method is based on the resolution of Laplace and Poisson equations as well as Maxwell equation in polar coordinate by using sub-domain method. One of the main contributions of the paper is to derive an expression for the magnetic vector potential in the segmented PM region by using hyperbolic functions. The developed method is applied on the performance computation of two prototype surface inset magnet segmented motors with open circuit and on load conditions. The results of these models are validated through FEM method.

Electromagnetic properties of cylinder permanent magnet eddy current coupling

This paper focuses on the electromagnetic properties of new cylinder type twelve-pole permanent magnet eddy current coupling. By combining conventional equivalent magnetic charge method and superposition principle, the analytical calculation model of air gap magnetic field distribution for the cyli nder type permanent magnet eddy current coupling is established; by considering the skin effect, the analytical model of eddy current density is set; the analytical model of electromagnetic-transfer torque is given with the demagnetization effect taken into consideration. Based on the established analytical calculation model, the variation law of air-gap magnetic induction intensity, eddy current density distribution and magnetic torque characteristic curve are analyzed and plotted in detail. At the same time, finite element simulations of the air gap magnetic field, eddy current density and electromagnetic-transfer torque are carried out based on multi-physics, and the results are compared with analytical calculations. Moreover, the paper analyzed the thickness of magnet conductive plate impacts on eddy current and explored relations between torque and coupling distance under different pole pairs. Finally, in order to verify the simulations, the prototype test of torque transfer characteristics is carried out. This paper compares the experimental results with the theoretical analysis and simulation results, and finds out the error is within the allowable range.

Influence of curvature on air-gap magnetic field distribution and rotor losses in PM electric machines

PurposeThe purpose of this paper is to study the effect of curvature on the magnetic field distribution and no-load rotor eddy current losses in electric machines, particularly in high-speed permanent magnet (PM) machines.Design/methodology/approachThe magnetic field distribution is obtained using conformal mapping, and the eddy current losses are obtained using a cylindrical multilayer model. The analytical results are validated using a two-dimensional finite element analysis. The analytical method is based on a proportional-logarithmic conformal transformation that maps the cylindrical geometry of a rotating electric machine into a rectangular configuration without modifying the length scale. In addition, the appropriate transformation of PM cylindrical domains into the rectangular domain is deduced. Based on this conformal transformation, a coefficient to quantify the effect of curvature is proposed.FindingsNeglecting the effect of curvature can produce significant errors in the calculation of no-load rotor losses when the ratio between the air-gap length and the rotor diameter is large.Originality/valueThe appropriate transformation of PM cylindrical domains into the rectangular domain is deduced. The proportional-logarithmic transformation proposed provides an insight into the effect of curvature on the magnetic field distribution in the air-gap and no-load rotor losses. Furthermore, the proposed curvature coefficient gives a notion of the effect of curvature for any particular geometry without the necessity of any complicated calculation. The case study shows that neglecting the effect of curvature underestimates the rotor eddy-current losses significantly in machines with large gap-to-rotor diameter ratios.

Analytical model of magnetic field distribution in the air-gap of quartz flexible accelerometer

As common high precision inertial sensors, quartz flexible accelerometers have wide application prospect in many circumstances such as low cost inertial navigation systems. In order to quickly evaluate magnetic field distribution in air-gap of these accelerometers and provide an insightful knowledge for design optimization, we introduced an analytical method based on scalar magnetic potential to describe their magnetic behaviour. Some related Laplace and Poison equations are solved by separating variables and the parameters of the solutions are calculated by a set of linear vector equations considering boundary conditions. Magnetic field computed with the proposed analytical method is proved effective through finite element method and some preliminary experiments, additionally, the scale factor estimated can be validated by the gravitational field roll-over test.

Analysis of Air-Gap Magnetic Field in Homopolar Inductor Alternator by Analytical Method and FEM

This paper investigates the air-gap magnetic field characteristics of homopolar inductor alternator (HIA), including theoretical analysis, numerical calculation, and experiment. First, the structure and magnetic circuit characteristics of HIA are analyzed. Second, a linear model of distributed magnetic circuit of HIA is established. An analytical formula for calculating the main air-gap magnetic field at different axial positions is deduced and obtained. Third, finite element method (FEM) is used to compute the magnetic field of HIA. The results from FEM are nearly consistent with those from analytical method. Finally, a prototype is constructed to verify the theoretical analysis and numerical computation. The research shows that the distribution of the main air-gap magnetic field of HIA is uneven along the axial direction. The proposed analytical formula contributes to calculate the main air-gap magnetic flux density of HIA.

Research on Electromagnetic and Dynamic Properties of LPMBLDCM for Electromagnetic Launch

In order to improve the thrust characteristics of moving-magnet type linear permanent magnet brushless DC motor (LPMBLDCM), the structural characteristics and magnetic field are analyzed. The influence of electrical parameters and structural parameters on the electromagnetic properties and thrust performance are researched by finite element analysis (FEA). The cogging force, back electromotive force (back-EMF), air-gap magnetic field distribution, mover velocity as well as thrust output are studied by taking some practical parameters into account, including pole/arc coefficient, air-gap width, voltage and current. The LPMBLDCM system is established, and some relevant tests are taken to verify the simulation results. Simulation and experimental results show that the thrust and mover velocity are mainly affected by some key parameters. The results will surely provide the reference and guidance for the optimization of electromagnetic and thrust characteristics of LPMBLDCM.

Air-Gap Magnetic Field Analysis of Wind Generator With PM Embedded Salient Poles by Analytical and Finite Element Combination Technique

A combined analytical and FEM technique is proposed for predicting the air-gap magnetic field distribution of a PM embedded salient pole wind generator. The influence of slotting on both radial and circumferential components of air-gap flux density is taken into account. By employing the proposed combination technique, the magnetic field distributions when the stator and rotor are at different relative positions can be calculated much faster than that by FEM. Based on the magnetic field distributions, the cogging torques are predicted and verified by the FEM, while the relationship between cogging torque and design parameters are further investigated. The proposed combination technique provides an efficient and accurate prediction method for the air-gap magnetic field distribution of large electrical machines with a complex PM pole structure.

Research of Air-Gap Magnetic Field Distribution of Segment-Powered Linear Induction Motor

For segment-powered linear induction motor (LIM), there is major asymmetry among the mutual inductance of stator windings. Based on magnetic motive force theory, this paper derived the magnetic motive force distribution of single-phase winding of the segment-powered linear induction motor, and confirmed the characteristics of magnetic motive force distribution of the segment-powered linear induction motor. Based on the magnetic motive force distribution of single-phase winding, the analytic expressions of air-gap field distribution of the segment-powered linear motor were derived, and the finite element simulation results verified the analytic results.

Analytical Method for Open-Circuit Air Gap Magnetic Field Calculation in Surface-Mounted Permanent Magnet Motors with Rotor Eccentricity

Analytical method with vector magnetic potential is proposed to calculate the open-circuit air gap magnetic field distribution in surface-mounted permanent magnet motors with rotor eccentricity, and the method is applicable to both internal and external rotor eccentric structure. The Laplace’s or Poisson’s equations and associated boundary conditions are formulated. The analytical expressions of eccentric air gap flux density are deduced by a perturbation method; and the perturbation quantity  is dimensionless. The analytical results are compared with the finite element method analysis results which verify the correctness and the effectiveness of the perturbation method.

Static Airgap Magnetic Field of Axial Flux Permanent Magnet Disk Motor

Abstract Due to flat structure of the axial flux permanent magnet disc motor (AFPMDM), the airgap magnetic field distribution is more complex. To study the static airgap magnetic field of AFPMDM, the conventional magnetic circuit method and the method of taking slice in finite element software Magnet are used respectively. Then axial airgap flux density distribution characteristics along circumferential direction and radial direction are analyzed. The accurate three-dimensional airgap magnetic field distribution can be gotten with the above methods. At last, analytical method, finite element method and average radius method are used to calculate the airgap magnetic flux of per pole respectively. Three results are approximate and can reflect per pole magnetic flux of AFPMDM generally. The research for airgap magnetic field of AFPMDM provides theoretical basis for its wide application.

Design of the Reaction Flywheel System Based on Axial-flux Motor

To satisfy the requirements of miniaturization for attitude control unit in distributed small satellite system(DSSS),a reaction flywheel system based on axial-flux motor is presented.The three-dimensional distribution of air-gap magnetic field is analyzed by using the finite element method(FEM).A computational model for back-EMF of the motor is established based on the printed circuit board(PCB) winding.The multidisciplinary design optimization method is applied to optimize the main structure size of the flywheel rotor to minimize the weight of the flywheel system while meeting the requirements of strength,stiffness and the air-gap flux density under the premise of using sequential quadratic programming(NLPQL).The total mass of the flywheel rotor is decreased from 0.899 kg to 0.741 kg(namely reduced by 17.6%) after optimization.A flywheel prototype is designed based on the optimal results and the no-load performance is tested.The results show that the maximum error between the calculated and measured values of back-EMF is 9.7%,which verifies the correctness of the design method and provides an important reference in the miniaturization design of reaction flywheel system.

Calculation of 3D Airgap Magnetic Field Distribution of an Axial Flux Permanent Magnet Motor

With the slice tool in finite element software Magnet, 3D magnetic field distribution in airgap of an axial flux permanent magnet motor (AFPMM) is studied. Then analytical method, finite element method and average radius method are used to calculate the airgap magnetic flux of per pole respectively. The results which are gotten through these methods are approximate and can reflect per pole magnetic flux of AFPMM generally. The above research has achieved anticipated effect and provided a basis for the calculation of AFPMM airgap magnetic field.

A new method to reduce end effect of linear induction motor

A new method to compensate the end effect of a linear induction motor (LIM) in low-speed maglev vehicles is proposed. With this method, the motors are close to each other so that the front motor’s exit-end magnetic field extends into the next motor’s entry zone. As a result, the motor’s magnetic field traveling wave become continuous and the end effect of short primary LIMs is greatly weakened. In the analysis of the air-gap magnetic field distribution, the LIM is assumedly divided into two identical motors with the distances of 20, 40, 60, and 80 mm. The results show that the air-gap magnetic field is still continuous within these distances due to LIM’s end effect. As the distance between two motors increases, the distortion of the air-gap magnetic field becomes more severe. Then, we investigate the relationship between the secondary speed and the thrust in three cases, i.e., a single LIM, two motors divided with 72 mm with pole pitch corrected, and two motors divided with 60 mm without the pole pitch being corrected. We find that the thrust has a small decrease when the speed increases, which means that the magnetic field is already continuous and its amplitude is approximately a constant. Furthermore, the thrust loss of case 3 is more than that of case 2, which indicates that the pole pitch correction is effective.

Magnetic force enhancement in a linear actuator by air-gap magnetic field distribution optimization and design

The focus of this paper is to show that the magnetic force generated by a linear actuator may be enhanced through the optimization and design of the devices air-gap magnetic field distribution. Specifically, the use of a periodic ladder structure is proposed for magnetic field manipulation, and a simplified finite element analysis is adopted in lieu of a higher cost computational model. The optimal magnetic field distribution that maximizes the actuator force is then found via structural topology optimization. This force enhancement is explained using a Maxwell stress tensor analysis and validated through experimental studies. Finally, a periodic-ladder structure is designed for an equivalent optimal magnetic field distribution, and the linear actuator force enhancement is confirmed.