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Sökning: L773:0018 9464 OR L773:1941 0069 > (2005-2009)

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1.
  • Abeywickrama, K. G. Nilanga B., et al. (författare)
  • Determination of complex permeability of silicon steel for use in high-frequency modeling of power transformers
  • 2008
  • Ingår i: IEEE transactions on magnetics. - : IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC. - 0018-9464 .- 1941-0069. ; 44:4, s. 438-444
  • Tidskriftsartikel (refereegranskat)abstract
    • Information about frequency dependence of complex permeability of silicon steel is a vital input parameter in calculations of transformer winding inductance used for modeling. high-frequency behavior (100 Hz-1 MHz). We present two ways of determining small signal complex permeability spectra in frequency domain and compare and discuss the results. The first method is based on an optimization procedure, in which inductance of a winding is measured and calculated by analytical formulas and finite-element modeling. The second method makes use of a single sheet tester. We show that the magnitude of effective permeability of the silicon steel laminations remains significant up to about 100 kHz. We also report on the effect of magnetic viscosity on complex permeability.
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2.
  • Danielsson, Oskar, et al. (författare)
  • Flux Distribution in Linear Permanent-Magnet Synchronous Machines Including Longitudinal End Effects
  • 2007
  • Ingår i: IEEE transactions on magnetics. - 0018-9464 .- 1941-0069. ; 43:7, s. 3197-3201
  • Tidskriftsartikel (refereegranskat)abstract
    • We investigated the longitudinal ends' influence on the flux distribution in a permanent-magnet linear synchronous machine with an analytic model and with numeric finite-element methods. We derived a general analytic expression, on closed form, from a linear reluctance model. The model reveals that the flux in a linear machine differs from that in a rotating machine in several aspects. The longitudinal ends introduce a pairwise coupled flux pattern, which will behave differently in circuits with odd or even numbers of magnets. In linear machines with an even number of magnets the pairwise coupled flux will spread throughout the whole machine, whereas in linear machines with an odd number of magnets it will be transformed into an equally distributed flux in the middle. The latter case will give rise to a nonsymmetric air gap flux distribution, where every second pole has larger flux. We confirmed the pairwise coupled flux and the nonsymmetric air gap distribution predicted by the analytic model by finite-element simulations. We noted additional effects when nonlinear behavior of the steel is taken into account. We conclude that saturation counteracts the pairwise coupled flux pattern at the longitudinal ends. Again, a nonsymmetric air gap flux distribution occurs as the pairwise coupled flux is transformed into an equally coupled flux. The pairwise coupling of the flux and the nonsymmetric air gap flux distribution give rise to a number of secondary effects, which we discuss.
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3.
  • Dave, Renu W., et al. (författare)
  • MgO-based tunnel junction material for high-speed toggle magnetic random access memory
  • 2006
  • Ingår i: IEEE transactions on magnetics. - 0018-9464 .- 1941-0069. ; 42:8, s. 1935-1939
  • Tidskriftsartikel (refereegranskat)abstract
    • We report the first demonstration of a magnetoresistive random access memory (MRAM) circuit incorporating MgO-based magnetic tunnel junction (MTJ) material for higher performance. We compare our results to those of AlOx-based devices, and we discuss the MTJ process optimization and material changes that made the demonstration possible. We present data on key MTJ material attributes for different oxidation processes and free-layer alloys, including resistance distributions, bias dependence, free-layer magnetic properties, interlayer coupling, breakdown voltage, and thermal endurance. A tunneling magnetoresistance (TMR) greater than 230% was achieved with CoFeB free layers and greater than 85% with NiFe free layers. Although the TMR with NiFe is at the low end of our MgO comparison, even this MTJ material enables faster access times, since its TMR is almost double that of a similar structure with an AlOx barrier. Bit-to-bit resistance distributions are somewhat wider for MgO barriers, with sigma about 1.5% compared to about 0.9% for AlOx. The read access time of our 4 Mb toggle MRAM circuit was reduced from 21 ns with AlOx to a circuit-limited 17 ns with MgO.
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4.
  • Durr, Hermann A., et al. (författare)
  • A Closer Look Into Magnetism : Opportunities With Synchrotron Radiation
  • 2009
  • Ingår i: IEEE transactions on magnetics. - 0018-9464 .- 1941-0069. ; 45:1, s. 15-57
  • Forskningsöversikt (refereegranskat)abstract
    • The unique properties of synchrotron radiation, such as broad energy spectrum, variable light polarization, and flexible time structure, have made it an enormously powerful tool in the study of magnetic phenomena and materials. The refinement of experimental techniques has led to many new research opportunities, keeping up with the challenges put up by modern magnetism research. In this contribution, we review some of the recent developments in the application of synchrotron radiation and particularly soft X-rays to current problems in magnetism, and we discuss future perspectives.
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5.
  • Engel, B. N., et al. (författare)
  • A 4-mb toggle MRAM based on a novel bit and switching method
  • 2005
  • Ingår i: IEEE transactions on magnetics. - 0018-9464 .- 1941-0069. ; 41:1, s. 132-136
  • Tidskriftsartikel (refereegranskat)abstract
    • 4-Mb magnetoresistive random access memory (MRAM) with a novel magnetic bit cell and toggle switching mode is presented. The circuit was designed in a five level metal, 0.18-mum complementary metal-oxide-semiconductor process with a bit cell size of 1.55 mum(2). The new bit cell uses a balanced synthetic antiferromagnetic free layer and a phased write pulse sequence to provide robust switching performance with immunity from half-select disturbs. This switching mode greatly improves the operational performance of the MRAM as compared to conventional MRAM. A detailed description of this 4-Mb toggle MRAM is presented.
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6.
  • Huang, Xinghui, et al. (författare)
  • A comparison of multirate robust track-following control synthesis techniques for dual-stage and multisensing servo systems in hard disk drives
  • 2006
  • Ingår i: IEEE transactions on magnetics. - 0018-9464 .- 1941-0069. ; 42:7, s. 1896-1904
  • Tidskriftsartikel (refereegranskat)abstract
    • This paper presents the system modeling, design, and analysis of multirate robust track-following controllers for a dual-stage servo system with a microelectromechanical systems (MEMS) microactuator (MA) and an instrumented suspension. A generalized model is constructed which includes a nominal plant, disturbances, uncertainties, and multirate sensing and control. Two major categories of controller design methodologies are considered. The first includes synthesis methodologies that are based on single-input single-output (SISO) design techniques, and includes the sensitivity decoupling (SD) and the PQ methods. In this case, a high sampling-rate inner loop damping control is first implemented using the auxiliary sensor signals. Subsequently, a low-rate outer loop controller is designed for the damped plant using either the SD or PQ design methods. The second category of design methodologies includes those based on multirate, multi-input multi-output (MIMO) design techniques, including mixed H-2/H-infinity, mixed H-2/mu, and robust H-2 synthesis. In this case, a set of controllers, which is periodically time-varying due to multirateness, is designed by explicitly considering plant uncertainty and hence robust stability. Comparisons are made between all the design techniques in terms of nominal H-2 performance, robust stability, and robust performance between these controllers, When the feedback controller is closed around the full order, perturbed plant. The advantages and disadvantages of each of these methods are discussed, as well as guidelines for their practical implementation.
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7.
  • Iovan, Adrian, et al. (författare)
  • Tunneling spectroscopy of magnetic double barrier junctions
  • 2007
  • Ingår i: IEEE transactions on magnetics. - 0018-9464 .- 1941-0069. ; 43:6, s. 2818-2820
  • Tidskriftsartikel (refereegranskat)abstract
    • Scanning tunneling microscopy (STM) is used to study transport in magnetic double tunnel junctions (DTJs) formed using a fixed transparency barrier of a patterned tunnel junction (TJ), and a variable tunnel barrier between the top electrode of the patterned junction and the STM tip. A sufficiently thin top electrode has been predicted to result in a rectification of charge current through a DTJ when the two barriers have different transparency. Our measurements indeed show a high current rectification ratio for 3-nm-thick, continuous film top electrodes, which is observed for junctions with asymmetric tunnel barriers.
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8.
  • Krah, Julius Hartwig (författare)
  • Optimum discretization of a physical Cauer circuit
  • 2005
  • Ingår i: IEEE transactions on magnetics. - 0018-9464 .- 1941-0069. ; 41:5, s. 1444-1447
  • Tidskriftsartikel (refereegranskat)abstract
    • physical Cauer circuit is used to model skin effect in a conductor or eddy currents in a magnetic lamination. A physical lumped element model was chosen, because equivalent circuits are inconvenient for nonlinear materials such as magnetic materials. Approaches to discretize the used circuit are presented and compared. An iterative fitting technique is suggested that requires fewer elements and yields higher accuracy than an exponential discretization.
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9.
  • Lundin, Urban, 1972-, et al. (författare)
  • Method for modeling time-dependent nonuniform rotor/stator configurations in electrical machines
  • 2009
  • Ingår i: IEEE transactions on magnetics. - USA : IEEE. - 0018-9464 .- 1941-0069. ; 45:7, s. 2976-2980
  • Tidskriftsartikel (refereegranskat)abstract
    • Nonuniform air gaps in electrical machines cause problems with forces and noise. There are a number of analytical and numerical methods to calculate the response due to nonuniform air gaps. In this paper, we present an efficient method based on an effective air gap permeability. Our unified method enables all nonuniform rotor-stator configurations to be simulated. We provide some results from simulations of static and dynamic eccentricity as well as irregularity.
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10.
  • Lundin, Urban, et al. (författare)
  • Poynting Vector Analysis of Synchronous Generators Using Field Simulations
  • 2007
  • Ingår i: IEEE transactions on magnetics. - 0018-9464 .- 1941-0069. ; 43:9, s. 3601-3606
  • Tidskriftsartikel (refereegranskat)abstract
    • The Poynting vector has been used to gain an understanding of energy flow in rotating electrical machines. Previous studies of energy flow in rotating electrical machines have used the Poynting vector in crude formulas to obtain a qualitative picture. In this paper, we present a study based on numerically calculated fields and quantities entering the Poynting vector. We obtained a detailed understanding of how energy flows in the air gap and into the winding of a synchronous generator. In particular, we found that, at no-load, energy is flowing both to and from the stator as a result of cogging, while for normal load cases the energy flow is unidirectional.
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11.
  • Meessen, K. J., et al. (författare)
  • Inductance calculations of permanent-magnet synchronous machines including flux change and self- and cross-saturations
  • 2008
  • Ingår i: IEEE transactions on magnetics. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9464 .- 1941-0069. ; 44:10, s. 2324-2331
  • Tidskriftsartikel (refereegranskat)abstract
    • Accurate inductance calculation of permanent-magnet synchronous machines is a relevant topic, since the inductances determine a large part of the electrical machine behavior. However, the inductance calculation, as well as the inductance measurement, is never a completely straightforward task when saturation occurs. In this paper, the total flux in the d and q axes are obtained from finite-element method or measurements and therefore include saturation and cross-couplings. The inductances are obtained from analytical post-processing based on an equivalent magnetic circuit. The originality of this method is that it accommodates the changes in the magnet flux and the inductances with the level of saturation. The resulting inductance values are the ones seen by the converter or the grid, as found by a more accurate approach.
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12.
  • Müsing, Andreas, et al. (författare)
  • Efficient calculation of non-orthogonal partial elements for the PEEC method
  • 2009
  • Ingår i: IEEE Transactions on Magnetics. - 0018-9464 .- 1941-0069. ; 45:3, s. 1140-1143
  • Tidskriftsartikel (refereegranskat)abstract
    • For various electrical interconnect and EMC problems, the partial element equivalent circuit (PEEC) method has proven to be a valid and fast solution method of the electrical field integral equation in the time as well as the frequency domain. Therefore, PEEC has become a multipurpose full-wave method, especially suited for the solution of combined circuit and EM problems, as found, for instance, on printed circuit board layouts, power electronics devices or EMC filters. Recent research introduced various extensions to the basic PEEC approach, for example a non-orthogonal cell geometry formulation. This paper presents a fast, flexible and accurate computational method for determining the matrix entries of partial inductances and the coefficients of potential for general non-orthogonal PEEC cell geometries. The presented computation method utilizes analytical filament formulas to reduce the integration order and therefore to reduce computation time. The validity, accuracy, and speed of the proposed method is compared with a standard integration routine on example cell geometries where the numeric results of the new method show improved accuracy, coming along with reduced computation time.
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13.
  • Owens, Frank J., et al. (författare)
  • Unusual room temperature ferromagnetism in bulk sintered GaP doped with copper
  • 2007
  • Ingår i: IEEE transactions on magnetics. - 0018-9464 .- 1941-0069. ; 43:6, s. 3043-3045
  • Tidskriftsartikel (refereegranskat)abstract
    • Robust room temperature ferromagnetism is obtained in single phase Gallium Phosphide doped with Cu2+ prepared by simple solid state reaction route. The saturation magnetization at 300 K is 1.5 x 10(-2) emu/g and the coercivity was found to be 125 Oe. A strong ferromagnetic resonance signal confirms the long range magnetic order which persists to temperatures as high as 739 K. X-ray absorption spectroscopy (XAS) indicate that Cu is in a +2 state. Ab initio calculations also show that the ferromagnetic ordering is energetically favorable in Cu doped GaP. When the spin-orbit coupling is included we get an enhanced total magnetic moment of 0.31 mu(B) with a local moment on Cu 0.082 and on P 0.204 mu(B). per atom.
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14.
  • Perers, Richard, et al. (författare)
  • Saturation Effects on Unbalanced Magnetic Pull in a Hydroelectric Generator With an Eccentric Rotor
  • 2007
  • Ingår i: IEEE transactions on magnetics. - 0018-9464 .- 1941-0069. ; 43:10, s. 3884-3890
  • Tidskriftsartikel (refereegranskat)abstract
    • We report an investigation of saturation effects on the unbalanced magnetic pull in a hydroelectric generator with 20% static eccen-tricity. We determine the magnetic pull force by the finite-element method in parallel with a simple analytical model for various no-loadvoltages and loads. Saturation significantly affects the magnitude of the unbalanced magnetic pull for high voltages and large loads.
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15.
  • Ranlöf, Martin, et al. (författare)
  • Core Loss Prediction in Large Hydropower Generators : Influence of Rotational Fields
  • 2009
  • Ingår i: IEEE transactions on magnetics. - USA : IEEE. - 0018-9464 .- 1941-0069. ; 45:8, s. 3200-3206
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper, we discuss the accuracy of several core loss models as compared to experimental data obtained from measurements on commercial hydropower generators. Our aim in this paper is twofold. First, we emphasize the problem of total core loss prediction by comparing the core loss figures obtained by different loss prediction schemes with measured no-load losses. Second, we examine the predicted net effect of bidirectional flux, i.e., the rotational loss. We show that the average degree of rotation in the stator core, and hence the rotational loss, is closely related to the stator slot geometry.
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16.
  • Ribbenfjärd, David, et al. (författare)
  • Hysteresis modeling including asymmetric domain rotation
  • 2007
  • Ingår i: IEEE transactions on magnetics. - 0018-9464 .- 1941-0069. ; 43:4, s. 1385-1388
  • Tidskriftsartikel (refereegranskat)abstract
    • This paper presents a technique for modeling of asymmetric domain rotation in magnetic materials. The technique uses a variable pinning strength, instead of a constant, to model the asymmetry. This allows modeling of quasi-static hysteresis effects, which show very good agreement with measurements for different magnetic materials.
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17.
  • Ribbenfjärd, David, et al. (författare)
  • Novel method for modelling of dynamic hysteresis
  • 2008
  • Ingår i: IEEE transactions on magnetics. - 0018-9464 .- 1941-0069. ; 44:6, s. 854-857
  • Tidskriftsartikel (refereegranskat)abstract
    • The dynamic hysteresis model for magnetic materials presented by Bertotti [1] uses the classical eddy current expression, where the applied field is assumed to penetrate the material homogenously. However, for this to be valid for a material exposed to a field varying with a frequency in the kilohertz range or higher, the material has to be very thin, e.g., a thin laminate, typically thinner than 0.1 mm. In this paper a novel method is presented. The idea is to combine Bertotti's model with a Cauer circuit and divide the material into a number of sections, each exhibiting different magnitude of magnetic field caused by the eddy current shielding. Furthermore, the eddy currents are modeled by "magnetic inductances" instead of the classical eddy current expression. This modelling technique yields simulation results that agree very well with measurements.
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18.
  • Shin, D. Y., et al. (författare)
  • Precise investigation of domain pinning energy in GaMnAs using planar hall effect and magnetoresistance measurements
  • 2007
  • Ingår i: IEEE transactions on magnetics. - 0018-9464 .- 1941-0069. ; 43:6, s. 3025-3027
  • Tidskriftsartikel (refereegranskat)abstract
    • The planar Hall effect (PHE) and magnetoresistance (MR) measurements have been carried out on a GaMnAs ferromagnetic semiconductor. The PHE and MR spectra exhibit interesting two-step magnetization switching behavior arising from the magnetic anisotropy properties of the system. By fitting the angle-dependent planar Hall resistance (PHR) data taken at 5 kG with the Stoner-Wohlfarth model, the cubic and uniaxial anisotropy constants were independently obtained. The anisotropy constants lead to the precise determination of easy axis direction, which turns out to be in good agreement with the easy axis determined from the angular plot of the switching field. The domain pinning energies were further obtained by fitting the angle dependence of the switching field, including the effect of uniaxial anisotropy. © 2007 IEEE.
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19.
  • Wass, Torbjörn, et al. (författare)
  • The magnetic circuit of a controllable reactor
  • 2006
  • Ingår i: IEEE transactions on magnetics. - 0018-9464 .- 1941-0069. ; 42:9, s. 2196-2200
  • Tidskriftsartikel (refereegranskat)abstract
    • Reactive power compensation is vital for obtaining efficient operation of long transmission power lines or cables. A controllable shunt reactor that controls the transmission of power by continuous reactive power compensation will reduce the transmission losses and increase the transmission capacity of active power. We show that the saturation phenomena of iron and the high current density of a high-temperature superconductor can be utilized to design controllable reactors with large dynamic range, low losses, and limited harmonic distortion. We have designed and constructed a small-scale prototype of a controllable shunt reactor with a high-temperature superconductor control winding. We present a simple model of the magnetic circuit of the controllable reactor and we compare alculations from the model to experimental measurements on the controllable reactor.
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20.
  • Wolfbrandt, Anna (författare)
  • Automated Design of a Linear Generator for Wave Energy Converters - A Simplified Model
  • 2006
  • Ingår i: IEEE transactions on magnetics. - 0018-9464 .- 1941-0069. ; 42:7, s. 1812-1819
  • Tidskriftsartikel (refereegranskat)abstract
    • An encouraging way to convert ocean wave energy into electricity through direct drive is by using a linear, synchronous, longitudinal-flux permanent-magnet machine (LFM), where the piston is driven by a buoy. In this paper, the speed of the piston is assumed to be constant or sinusoidal. The paper presents an automated method for optimizing the design variables of an LFM with a rectifier, using time-stepping finite-element analysis. The method yields feasible LFM designs tailored to a given ocean wave climate, assuming constant or sinusoidal piston speed. The method will help to avoid a large amount of field calculations to obtain an optimal LFM driven by a buoy. The systematic approach results in a transparent investigation, giving the engineer an easy way to determine the best design. The paper presents LFM designs for a calm site in the Baltic Sea as examples.
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21.
  • Zha, Chaolin, et al. (författare)
  • Dependence of Ordering Kinetics of FePt Thin Films on Different Substrates
  • 2008
  • Ingår i: IEEE transactions on magnetics. - 0018-9464 .- 1941-0069. ; 44:11, s. 3539-3542
  • Tidskriftsartikel (refereegranskat)abstract
    • FePt thin films are deposited on SMO3, MgO, and a 2 nm-FeOx underlayer on an Si substrate at room temperature and then annealed at elevated temperatures. Studies of the L1(0) ordering process in each case show that the ordering temperature for the FePt film on the nonepitaxial Si/FeOx substrate is similar to 150 degrees C lower than the epitaxial FePt films deposited on MgO and SrTiO3 substrates. We argue that internal stresses arising from lattice defects and a recrystallizing process as well as thermal strain from differences in thermal expansion between substrate and film are responsible for the differences in ordering kinetics from the A1 to L1(0) phase of FePt on the various substrates.
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22.
  • Zha, Chaolin, et al. (författare)
  • Exchange Bias in L1(0) (111)-Oriented FePt-Based Pseudo Spin Valves
  • 2009
  • Ingår i: IEEE transactions on magnetics. - 0018-9464 .- 1941-0069. ; 45:10, s. 3881-3884
  • Tidskriftsartikel (refereegranskat)abstract
    • The coupling between hard FePt and soft NiFe layers through a Cu interlayer has been studied in L1(0) (111) FePt(20)/CoFe(1.5)/Cu(3.5 or 4.5)/CoFe(2)/NiFe(3) (in nanometers) pseudo spin valves. The soft-layer hysteresis loops exhibit clear shifts in the field axis (exchange-bias-like) and a marked coercivity enhancement. It is found that several parameters such as the thickness of the Cu layer or the interface roughness influence the exchange bias properties of the systems, while others (e. g., temperature) are less important. This interlayer coupling arises from the competition between dipolar and Ruderman-Kittel-Kasuya-Yoshida (RKKY) interactions between the layers.
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23.
  • Zha, Chaolin, et al. (författare)
  • Study of Pseudo Spin Valves Based on L1(0) (111)-Oriented FePt and FePtCu Fixed Layer With Tilted Magnetocrystalline Anisotropy
  • 2009
  • Ingår i: IEEE transactions on magnetics. - 0018-9464 .- 1941-0069. ; 45:10, s. 3491-3494
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper, we demonstrate a series of pseudo-spin-valve structures based on L1(0) (111)-oriented FePt and FePtCu with titled magnetocrystalline anisotropy. Highly ordered (111)-oriented L1(0) FePtCu with large anisotropy is achieved by optimizing the Cu content. Magnetoresistance (MR) up to 5% has been obtained by 1) optimizing the FePtCu growth using different underlayers, 2) enhancing the interface spin polarization using thin CoFe at the Cu interfaces, and 3) adjusting the Cu spacer thickness. The substantial MR realized with tilted fixed layer magnetization is an important prerequisite for the realization of tilted polarizer spin torque oscillators (STOs) or spin-transfer torque magnetoresistive random access memories (STT-MRAMs).
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24.
  • Zheng, P, et al. (författare)
  • Influence of saturation and saliency on the inductance of a four-quadrant transducer prototype machine
  • 2006
  • Ingår i: IEEE transactions on magnetics. - 0018-9464 .- 1941-0069. ; 42:4, s. 1319-1322
  • Tidskriftsartikel (refereegranskat)abstract
    • An inductance determination method that can be based on both experiments and calculations is discussed in this paper. The inductances of a four-quadrant transducer (4QT) prototype machine were measured and calculated with the two-dimensional time-stepping finite-element method (FEM), and the measured and calculated results are in good agreement. It is found that the d- and q-axis inductances are different, and the inductances obtained from the phase and line voltage are also different for both the two machines of the 4QT prototype machine. Analysis shows that the differences are caused by the saliency and d-axis saturation. Although there is little saliency for the double rotor machine (DRM), the two kinds of the inductance differences of the DRM are more serious than that of the stator machine (SM). This is because of the higher level of the d-axis saturation of the DRM. The inductances obtained from the phase voltage at very low frequency are recommended as final results for both experiments and calculations.
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25.
  • Zheng, P., et al. (författare)
  • Investigation of the winding current distribution in a 4-quadrant-transducer prototype machine
  • 2005
  • Ingår i: IEEE transactions on magnetics. - 0018-9464 .- 1941-0069. ; 41:5, s. 1972-1975
  • Tidskriftsartikel (refereegranskat)abstract
    • The 4-quadrant energy transducer (4QT) is a solution to realize both the torque and speed control of the internal combustion engine (ICE) for hybrid electric vehicles. Since the base frequency of the prototype 4QT is much higher than the industrial one, the effect of eddy current on winding current distribution is considered in this paper. A two-dimensional (2-D) eddy-current FEM model is established and used for analysis. Current density and strand current distribution are given. It is pointed out that owing to the effect of eddy current, the conductor currents are unevenly distributed within the strands of the same turn. According to the 2-D FEM analysis, when the uneven current distribution is considered, the average rms turn current is increased by 1.05 times for the stator and 1.65 times for the inner rotor, and the copper loss is increased by 1.1 times for the stator and 3.16 times for the inner rotor. Since the inner rotor slots are much deeper than the stator slots, the inner rotor current distribution is more uneven than the stator. It means that for high-frequency deep slot machine the eddy current effect should be considered seriously. Because of the increased current and copper loss, more ventilation will be needed for the 4QT, especially for the inner rotor. The average torques of stator machine and double rotor machine meet the requirements, and the torque ripples are small owing to the skewed slots.
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