Hysteresis and eddy-current losses of a transformer lamination viewed as an application of the Poynting theorem
Hysteresis and eddy current losses of transformer lamination as application of Poynting theorem
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Hysteresis and eddy current losses of transformer lamination as application of Poynting theorem
Digital computer method for determining eddy current and hysteresis losses in cylindrical rod of No. 1010 steel
A method of fabricating improved transformer cores from composites of thermoplastic matrices and iron-particles has been invented. Relative to commercially available laminated-iron-alloy transformer cores, the cores fabricated by this method weigh less and are less expensive. Relative to prior polymer-matrix/ iron-particle composite-material transformer cores, the cores fabricated by this method can be made mechanically stronger and more magnetically permeable. In addition, whereas some prior cores have exhibited significant eddy-current losses, the cores fabricated by this method exhibit very small eddy-current losses. The cores made by this method can be expected to be attractive for use in diverse applications, including high-signal-to-noise transformers, stepping motors, and high-frequency ignition coils. The present method is a product of an experimental study of the relationships among fabrication conditions, final densities of iron particles, and mechanical and electromagnetic properties of fabricated cores. Among the fabrication conditions investigated were molding pressures (83, 104, and 131 MPa), and molding temperatures (250, 300, and 350 C). Each block of core material was made by uniaxial-compression molding, at the applicable pressure/temperature combination, of a mixture of 2 weight percent of LaRC (or equivalent high-temperature soluble thermoplastic adhesive) with 98 weight percent of approximately spherical iron particles having diameters in the micron range. Each molded block was cut into square cross-section rods that were used as core specimens in mechanical and electromagnetic tests. Some of the core specimens were annealed at 900 C and cooled slowly before testing. For comparison, a low-carbon-steel core was also tested. The results of the tests showed that density, hardness, and rupture strength generally increased with molding pressure and temperature, though the correlation was rather weak. The weakness of the correlation was attributed to the pores in the specimens. The maximum relative permeabilities of cores made without annealing ranged from 30 to 110, while those of cores made with annealing ranged from 900 to 1,400. However, the greater permeabilities of the annealed specimens were not associated with noticeably greater densities. The major practical result of the investigation was the discovery of an optimum distribution of iron-particle sizes: It was found that eddy-current losses in the molded cores were minimized by using 100 mesh (corresponding to particles with diameters less than or equal to 100 m) iron particles. The effect of optimization of particle sizes on eddy-current losses is depicted in the figure.
Partially superconducting machines with cryocooler-cooled rotors are a potential near-term technology that can achieve the motor performance needed by future fixed wing electric aircraft. For this type of machine, minimizing cryogenic heat load is one of the keys for enabling high machine performance. Rotor eddy current loss is often the most difficult cryogenic heat load to mitigate due to current ripple from the motor drive. This paper presents the concept design for a 20 kW/kg, 99.5% efficient motor drive that has sufficiently low current ripple to enable high performance partially superconducting machines by minimizing eddy current loss in the rotor. The motor drive concept design uses a resonant, interleaved, and multilevel topology to achieve these high-performance metrics with little current ripple. Rotor magnetic loss analysis using NASA’s 1.4 MW High Efficiency Megawatt Motor (HEMM) is used in the design process to down select the motor drive topology and show that the final design generates less than 5 W of magnetic loss in the rotor.
Partially superconducting machines with cryocooler-cooled rotors are a potential near term technology that can achieve the motor performance needed by future fixed wing electric aircraft. For this type of machine, minimizing cryogenic heat load is one of the keys for enabling high machine performance. Rotor eddy current loss is often the most difficult cryogenic heat load to mitigate due to current ripple from the motor drive. This paper presents the concept design for a 20 kW/kg, 99.5 percent efficient motor drive that has sufficiently low current ripple to enable high performance partially superconducting machines by minimizing eddy current loss in the rotor. The motor drive concept design uses a resonant, interleaved, and multilevel topology to achieve these high-performance metrics with little current ripple. Rotor magnetic loss analysis using NASA’s 1.4 MW High Efficiency Megawatt Motor (HEMM) is used in the design process to down select the motor drive topology and show that the final design generates less than 5 W of magnetic loss in the rotor.
The availability of experimental data which characterize the performance of soft magnetic materials for the combined conditions of temperature and frequency over a wide flux density range for different types of excitation is almost nonexistent. An experimental investigation of an 80-20 Ni-Fe alloy (Supermalloy) was conducted over the temperature (T) range of 23 to 300 C, frequency (f) range of 1 to 50 kHz, and maximum flux densities (B(sub M)) from 0.1 T up to 0.7 T for both sine and square wave voltage excitation. The investigation focused on the effects of (B(sub M)), f, T, and excitation waveform on the specific core loss (SCL) and dynamic B-H loops. The results show that the ratio (R) of sine to square wave excitation specific core loss was always greater than unity for a given f and T and identical values of B(sub M). The values of R ranged from 1.07 to 1.34. The classical theory of core loss separation into a hysteresis and eddy current loss component was used to theoretically determine the lower and upper bounds on R, against which the experimental R-values were compared. The experimental R-values were also used to make a comparison of the core loss of a sine and square wave voltage driven transformer.
The design and fabrication of conventional and unconventionally processed Ti-Nb base and Al5-compound-base, respectively, composite superconductors is discussed in a nine section review. The first two sections introduce the general properties of alloy and compound superconductors, and the design and processing requirements for the production of long lengths of stable low loss conductor. All aspects of flux jump stability, and the general requirements of cryogenic stabilization are addressed. Conductor design from an a.c.-loss standpoint; some basic formulae describing hysteretic and eddy current losses and the influences on a.c. loss of filament diameter, strand (conductor) diameter, twist pitch, and matrix resistivity are discussed. The basic techniques used in the fabrication of conventional multifilamentary conductors are described.
The loss mechanisms associated with magnetic bearings have yet to be adequately characterized or modeled analytically and thus pose a problem for the designer of magnetic bearings. This problem is particularly important for aerospace applications where low power consumption of components is critical. Also, losses are expected to be large for high speed operation. The iron losses in magnetic bearings can be divided into eddy current losses and hysteresis losses. While theoretical models for these losses exist for transformer and electric motor applications, they have not been verified for magnetic bearings. This paper presents the results from a low speed experimental test rig and compares them to calculated values from existing theory. Experimental data was taken over a range of 90 to 2,800 rpm for several bias currents and two different pole configurations. With certain assumptions agreement between measured and calculated power losses was within 16 percent for a number of test configurations.
Spherical iron particles of three different size distributions, 6-10 micrometers in diameter, 100 mesh and 30-80 mesh, were mixed with 2.0 wt % of soluble imide and compression molded at 300 C under 131 MPa. Post-fabrication heat treatments were performed at 960 C for 6 h resulting in a significant enhancement of the permeability in low field region for all the specimens except for the one made of 30-80 mesh particles. The rate of core loss of these specimens at a magnetic induction of 5 kG measured up to 1 kHz shows a noticeable. increase after heat treatment which, along with the permeability enhancement, can be explained by the coalescence of particles forming a network of conductivity paths in the specimens. ne scanning electron micrographs taken for the 6-10 micrometer particle specimens show no evidence of heat treatment-induced grain growth. The untreated specimens show a very weak f(sup 2) -dependence of the core loss which clearly indicates a negligible contribution from the eddy current loss. In particular, an almost perfect linearity was found in the frequency dependence of the core loss of the untreated specimen made of 100 mesh iron particles.
Spherical iron particles of three different size distributions, 6-10 microns in diameter, 100 mesh and 30-80 mesh, were mixed with 2.0 wt. % of soluble imide and compression molded at 300 C under 131 MPa. Post fabrication heat treatments were performed at 960 C for 6 hours resulting in a significant enhancement of the permeability in low field region for all the specimens except for the one made of 30-80 mesh particles. The rate of core loss of these specimens at a magnetic induction of 5 kG measured up to 1 kHz shows a noticeable increase after heat treatment which, along with the permeability enhancement, can be explained by the coalescence of particles forming a network of conductivity paths in the specimens. The scanning electron micrographs taken for the 6-10 micron particle specimens show no evidence of heat treatment-induced grain growth. The untreated specimens show a very weak f(sup 2) dependence of the core loss which clearly indicates a negligible contribution from the eddy current loss. In particular, an almost perfect linearity was found in the frequency dependence of the core loss of the untreated specimen made of 100 mesh iron particles.
NASA’s High Efficiency Megawatt Motor (HEMM) is being developed to achieve the performance needed by single aisle class electrified aircraft. It is a 1.4 MW electric machine designed as a generator for NASA’s STARC-ABL concept vehicle. It has performance objectives of greater than 16 kW/kg electromagnetic specific power and efficiency of greater than 98%. A significant flaw in the preliminary electromagnetic design of HEMM was recently discovered. The stator teeth in the preliminary design cause the magnetic flux in the rotating components of HEMM to oscillate at a very high frequency (12,240 Hz). Two independent energy loss analyses are presented to show that the frequency is high enough to cause eddy current losses that significantly exceed the rotor’s loss limit (50 W), despite the very small magnitude of this flux oscillation (<0.01 T). To eliminate these rotor losses, while continuing to meet the target performance, it was determined that the stator teeth needed to be removed and the electromagnetic geometry of the motor needed to be revised. The revised, slotless HEMM motor design is summarized. Sensitivity of the new design to key unknown variables such as the temperature of and number of turns in the superconducting rotor coils and the stator winding’s average temperature.
Typically, fully active magnetically suspended systems require one axial and two radial magnetic bearings. Combining radial and axial functions into a single device allows for more compact and elegant packaging. Furthermore, in the case of high-speed devices such as energy storage flywheels, it is beneficial to minimize shaft length to keep rotor mode frequencies as high as possible. Attempts have been made to combine radial and axial functionality, but with certain drawbacks. One approach requires magnetic control flux to flow through a bias magnet reducing control effectiveness, thus resulting in increased resistive losses. This approach also requires axial force producing magnetic flux to flow in a direction into the rotor laminate that is undesirable for minimizing eddy-current losses resulting in rotational losses. Another approach applies a conical rotor shape to what otherwise would be a radial heteropolar magnetic bearing configuration. However, positional non-linear effects are introduced with this scheme and the same windings are used for bias, radial, and axial control adding complexity to the controller and electronics. For this approach, the amount of axial capability must be limited. It would be desirable for an integrated radial and axial magnetic bearing to have the following characteristics, separate inputs for radial and axial control for electronics and control simplicity, all magnetic control fluxes should only flow through their respective air gaps and should not flow through any bias magnets for minimal resistive losses, be of a homopolar design to minimize rotational losses, position related non-linear effects should be minimized, and dependent upon the design parameters, be able to achieve any radial/axial force or power ratio as desired. The integrated radial and axial magnetic bearing described in this paper exhibits all these characteristics. Magnetic circuit design, design equations, and analysis results will be presented.
Typically, fully active magnetically suspended systems require one axial and two radial magnetic bearings. Combining radial and axial functions into a single device allows for more compact and elegant packaging. Furthermore, in the case of high-speed devices such as energy storage flywheels, it is beneficial to minimize shaft length to keep rotor mode frequencies as high as possible. Attempts have been made to combine radial and axial functionality, but with certain drawbacks. One approach requires magnetic control flux to flow through a bias magnet reducing control effectiveness, thus resulting in increased resistive losses. This approach also requires axial force producing magnetic flux to flow in a direction into the rotor laminate that is undesirable for minimizing eddy-current losses resulting in rotational losses. Another approach applies a conical rotor shape to what otherwise would be a radial heteropolar magnetic bearing configuration. However, positional non-linear effects are introduced with this scheme and the same windings are used for bias, radial, and axial control adding complexity to the controller and electronics. For this approach, the amount of axial capability must be limited. It would be desirable for an integrated radial and axial magnetic bearing to have the following characteristics; separate inputs for radial and axial control for electronics and control simplicity, all magnetic control fluxes should only flow through their respective air gaps and should not flow through any bias magnets for minimal resistive losses, be of a homopolar design to minimize rotational losses, position related non-linear effects should be minimized, and dependent upon the design parameters, be able to achieve any radial/axial force or power ratio as desired. The integrated radial and axial magnetic bearing described in this paper exhibits all these characteristics. Magnetic circuit design, design equations, and magnetic field modeling results will be presented.
As the power density of electric machines and power electronics continues to increase to meet the demands of more electric aircraft, the thermal management of these devices becomes increasingly important. Ideally, the thermal management solution of the device should have high thermal conductivity and be electrically insulating so that it can be directly integrated with the device in question. Technical ceramics are a class of materials that meet these two requirements. Direct liquid cooling by submerging electric components in a dielectric fluid is an alternate option, but adds system complexity and may incur pumping loss. In this work, the thermal management solution for a high frequency inductor is presented. A conventional wicked heat pipe is designed that is made from a solid ceramic case with a sintered ceramic wick. This heat pipe can provide structural support for the core and windings and is electrically insulating, so it does not incur any additional eddy current losses from the high frequency magnetic fields. It does not require additional pumping power, because conventional wicked heat pipes are passive devices. In this paper, the manufacturing process of the ceramic heat pipe is also presented. It is shown that the sintering of large diameter spherical ceramic particles is difficult due to their high specific surface area and low surface free energy. To overcome this difficulty, a flux material was used to initiate liquid phase sintering. The results of the sintering trials show that for the 120 μm diameter α-Al2O3powder selected for the wick, the combination of 1650°C sintering temperature and the addition of 5 wt% talc sintered the porous matrix together sufficiently for use as a heat pipe wic
As the power density of electric machines and power electronics continues to increase to meet the demands of more electric aircraft, the thermal management of these devices becomes increasingly important. Ideally, the thermal management solution of the device should have high thermal conductivity and be electrically insulating so that it can be directly integrated with the device in question. Technical ceramics are a class of materials that meet these two requirements. Direct liquid cooling by submerging electric components in a dielectric fluid is an alternate option, but adds system complexity and may incur pumping loss. In this work, the thermal management solution for a high frequency inductor is presented. A conventional wicked heat pipe is designed that is made from a solid ceramic case with a sintered ceramic wick. This heat pipe can provide structural support for the core and windings and is electrically insulating, so it does not incur any additional eddy current losses from the high frequency magnetic fields. It does not require additional pumping power, because conventional wicked heat pipes are passive devices. In this paper, the manufacturing process of the ceramic heat pipe is also presented. It is shown that the sintering of large diameter spherical ceramic particles is difficult due to their high specific surface area and low surface free energy. To overcome this difficulty, a flux material was used to initiate liquid phase sintering. The results of the sintering trials show that for the 120 μm diameter α-Al2O3 powder selected for the wick, the combination of 1650°C sintering temperature and the addition of 5 wt% talc sintered the porous matrix together sufficiently for use as a heat pipe wick.
Thick film magnetic/insulating nanocomposite materials, with significantly reduced core loss, and their manufacture are described. The insulator coated magnetic nanocomposite comprises one or more magnetic components, and an insulating component. The magnetic component comprises nanometer scale particles (about 1 to about 100 nanometers) coated by a thin-layered insulating phase. While the intergrain interaction between the immediate neighboring magnetic nanoparticles separated by the insulating phase provides the desired soft magnetic properties, the insulating material provides high resistivity, which reduces eddy current loss.
A series of bulk-size magnetic/insulating nanostructured composite soft magnetic materials with significantly reduced core loss and its manufacturing technology. This insulator coated magnetic nanostructured composite is comprises a magnetic constituent, which contains one or more magnetic components, and an insulating constituent. The magnetic constituent is nanometer scale particles (1-100 nm) coated by a thin-layered insulating phase (continuous phase). While the intergrain interaction between the immediate neighboring magnetic nanoparticles separated by the insulating phase (or coupled nanoparticles) provide the desired soft magnetic properties, the insulating material provides the much demanded high resistivity which significantly reduces the eddy current loss. The resulting material is a high performance magnetic nanostructured composite with reduced core loss.
A magnetic suspension and balance system is designed to support models of aircraft or other objects in wind tunnels by means of magnetic forces. Major design improvements have been achieved, resulting in reductions of the system size, weight, and cost. These improvements are due to: (1) the use of holmium in the model core to increase its magnetic moment, (2) the use of a powerful new permanent magnet material in the model wings, (3) a new arrangement for the roll coils, and (4) the use of a nonmetallic structure to eliminate eddy current losses. The conceptual design of the holmium core superconductive solenoid and of the new permanent magnet wing assembly is described in detail. The discussion includes comparisons of the pole strengths for different model core magnets, the design of a superconducting solenoid and cryostat, and the analysis of model wing magnetic requirements.