Hysteretic Losses Research Articles

A three-phase multi-legged transformer model in ATP using the directly-formed inverse inductance matrix

A new transformer model based on core topology is developed. The model simulates the transformer as a set of coupled inductances. Winding flux linkages are chosen as state variables and currents are computed from the flux linkages using the directly-formed inverse inductance matrix, the /spl Gamma/-matrix. Due to the strong magnetic coupling among the windings, the inductance matrix of a transformer is ill-conditioned. Directly forming the /spl Gamma/-matrix will not only speed up the computation but also make it more stable. Transformer core saturation is represented by its anhysteretic magnetization curve. Eddy current and hysteretic losses of the core, and stray losses of the transformer are accounted for by a resistive load on the secondary. Winding capacitances are lumped to the terminals, the model is thus accurate up to 5 kHz. A supporting routine is written to generate /spl lambda/-i curve data for each segment of the core and the other input data for EMTP. The model has been incorporated into the Alternative Transients Program (ATP), the BPA EMTP, for evaluation, and has passed the benchmark test of the GPU line energization test of 1973.

Logarithmic AC Response in Rb3C60 Crystals

AC susceptibility measurements were performed on Rb3C60 crystals. Two peaks are observed in the imaginary part of the susceptibility χ′′(T) and the peak near the transition temperature T c is more pronounced. This is interpreted in terms of weak links in the fullerene superconductors. The temperature associated with the intragranular χ′′ maximum T m exhibits extremely weak dependence on ac frequency f; T m shifts to higher temperature with increasing f and the effect is enhanced by increasing dc magnetic-field amplitude H dc or ac amplitude h ac. The inverse temperature 1/T m is found to depend roughly linearly on logarithmic frequency. This result is consistent with the prediction of the thermally activated flux creep model. This implies that the ac power dissipation in the Rb3C60 superconductors is predominantly due to hysteretic losses and therefore that magnetic flux is in the irreversible regime of the magnetic phase diagram. The thermal activation energy for flux lines U0 is estimated to be ≈6.1 eV at H dc=1 kOe and h ac=1 Oe. Finally, (1-T m/T c)3/2 is found to depend linearly on ln f.

Dry friction losses in axially loaded cables

A model of a cable comprising interacting wires with dry friction forces at the interfaces is subjected to a quasi-static cyclic loading. The first cycle of this process, comprising of axial loading, unloading and reloading is investigated analytically. Explicit load-elongation relationships are obtained for all of the above phases of the cycle. An expression for the hysteretic losses is also obtained in an explicit form. It is shown that losses are proportional to the third power of the amplitude of the oscillating axial force, and are in inverse proportion to the interwire friction forces. The results obtained are used to introduce a model of a cable as a solid rod with an equivalent stiffness and damping properties of the rod material. It is shown that the stiffness of the equivalent rod is weakly nonlinear, whereas the viscous damping coefficient is proportional to the amplitude of the oscillation. Some numerical results illustrating the effect of cable parameters on the losses are given.

A Review of Adhesion Mechanisms Using the Peel Test in Air and Liquid Media

Abstract This paper deals with the analysis of peel energy of assemblies measured in different environments, i.e. in air and in the presence of liquids, and constitutes a brief review of the work of Professor Schultz' team in this domain. It is shown how such measurements can lead to a better knowledge of the nature as well as of the magnitude of fundamental interactions established at the interface between two solids. Earlier experiments have shown that peel energy can be expressed as a product of three terms corresponding, respectively, to the reversible energy of interfacial adhesion, the hysteretic losses of the bulk materials and the molecular dissipation near the crack front during peeling. This approach is well-verified when only physical interactions (van der Waals) are involved at the interface. However, more complex cases correspond to systems where specific interactions are also established between both materials, in particular acid-base interactions and creation of chemical bonds. In both case...

The influence of geometry on self-field AC losses of Ag sheathed PbBi2223 tapes

We measured axial fields along an Ag sheltered PbBi2223 superconducting tape 3 mm wide and 0.03 mm thick carrying 47 Hz alternating currents. Tte critical current of the tape at 77 K was 1 5 A corresponding to a critical current density of 16 000 A/cm 2. The axial electric field was measured by pairs of voltage leads brought out in a plane perpendicular to the tape axis, turned axially to meet and so led out to a voltmeter. The spatial variation and the current dependence of the electric field, obtained from several pairs of taps closed at different radial positions, were consistent with the prediction for a uniform superconducting thin rectangle with a critical current I c rather than a superconductor of elliptical cross-section. Our results also showed that the hysteretic losses at currents below I c can be measured with an accuracy of about 5% using a pair of taps closed at a radial distance about three times the tape half-width.

Stability and AC losses in HTSC/Ag multifilamentary strands

Large-scale applications of high-Tc superconductors (HTSCs) stem not only from their obviously high Tc values which offer the possibility of operation in liquid hydrogen, liquid helium as well as refrigerated gases, but also from their high Hc2 values when high operating temperature is not the primary consideration. The cryophysical properties central to dynamically and adiabatically stable conductor design are the temperature-dependent thermal conductivity and specific heat, respectively. Based on these data and the field and temperature dependence of Jc for melt-processed YBCO, calculations are presented of the limiting filament diameters for flux-jump-stable operation (at 4 and 77 K, and 0 and 5 T) of a hypothetical YBCO/Ag composite strand. A calculation is also presented of the field-amplitude dependence of 50 Hz hysteretic and eddy current losses of a model multifilamentary (MF) HTSC/Ag composite strand. It is demonstrated that the eddy current loss of a fully coupled MF strand is considerably larger than the hysteretic loss of the equivalent monocore. The roles of filamentarization and twisting in MF HTSC/Ag strands are discussed. The results of an experimental AC loss study of a series of MF Bi:2212/Ag strands are also presented. Various features of the AC loss are interpreted in terms of: (i) flux-creep enhanced field sweep rate dependence, (ii) bridging and “current-sausaging” enhanced effective filament diameter, deff; and (iii) bridging-induced sample-length dependence of the per-cycle AC loss and its modification by extreme current sausaging also referred to as ‘minor current loops’.

Forced Harmonic Response of a Continuous System Displaying Eigenvalue Veering Phenomena

Prior studies of self-adjoint linear vibratory systems have extensively explored the free vibration phenomena associated with veering of eigenvalue loci that depict the dependence of natural frequencies on a system parameter. The present work is an exploration of the effect of such phenomena on the response of a nearly-periodic continuum to harmonic excitation. The focus of the analysis is the prototypical system of a two-span beam with a strong torsional spring at the intermediate pin support. The results of an exact eigenvalue analysis, not previously disclosed, are used to perform a modal analysis of the steady-state response to a harmonic concentrated force applied to the middle of one span. The modal equations are used to identify situations in which the force response is localized to one span, as well as the degree to which the location and magnitude of the peak displacement display parameter sensitivity. The effect of hysteretic loss on forced localization is discussed.

Alternating current losses in Bi2Sr2Ca1Cu2O8+δ/Ag tapes at power frequencies

Measurements of transport alternating-current (ac) losses in Bi2Sr2CaCu2O8+x powder-in-tube Ag-sheathed tapes at 4.2 and 65 K and at 20, 60, 200, and 400 Hz were carried out and comparisons to the theoretically predicted hysteretic loss plus ohmic loss were made. The measured loss, albeit larger than predicted, was found to agree with Bean’s critical state model. The loss, having a linear dependence on the frequency of the alternating transport current and increasing with decreasing critical current density, confirms hysteresis as the dominant source of power dissipation at both 4.2 and 65 K. However, at 4.2 K, the loss varies as the square of the amplitude of the transport current, which is not consistent with the model.

Current, induction profiles and hysteretic losses in high-Tc superconducting tapes

Current, induction profiles and hysteretic losses have been calculated in the framework of numerical simulations for high Tc superconducting tapes in transverse magnetic field (self-field effects, anisotropic field dependence of the critical current density are taken into account). It appears that hysteretic losses are widely influenced by both the tape width and the field component perpendicular to the tape width, except for field nearly parallel to the tape.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Induced voltage, magnetization waveforms and the spectral response at the grain boundaries of YBCO superconductors and the critical state model

Critical state model for granular superconductors is applied to study the nonlinear a.c. response of YBaCuO superconductors at the grain boundaries. The measured induced voltage waveforms are studied and explained at different temperatures and the corresponding calculated waveforms are shown to match the data. The intergranular hysteretic magnetization losses and the first 10 spectral components of the a.c. harmonic response are also measured and calculated at different temperatures.

Effects of diffusion barrier on the magnetization cycles of Nb/sub 3/Sn strand for ITER conductor

High performance Nb/sub 3/Sn strands for the high field ITER (International Thermonuclear Experimental Reactor) magnets have been manufactured using diffusion barriers among the multifilamentary cores and the stabilizing copper. In the conductor development programme, billets using a single Ta or a double NbV barrier have been assembled. The barrier is shown to have an influence on magnetization characteristics. The measurements on samples from the two types of strands are shown and analyzed to correlate them with the magnetic behaviour of Nb at low field. The results show that at low field hysteretic losses are greatly increased by the pure Nb of the barrier. At high field, losses of samples with Ta barrier are larger, due to their higher J/sub c/.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Report on the second VAMAS AC loss round robin-magnetization measurement of low-frequency hysteretic loss

We report on the results of the 2/sup nd/ VAMAS (Versailles Project on Advanced Materials and Standards) intercomparison program on low-frequency (hysteretic) AC loss measurements. Two sets of multifilamentary NbTi strands were subjected to round-robin testing. In an initial series of tests, samples in various forms were measured mostly by vibrating-sample- and SQUID magnetometry. Considerable scatter was noted especially in the small-filament-diameter AC-loss data. In a study of measurement accuracy, a supplementary round-robin compared the results of VSM measurement of a given pair of copper-matrix samples. In the light of all the results, factors contributing to AC loss error are discussed and recommendations are made concerning the specification of future round-robin AC-loss testing.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

European development of high performance Nb/sub 3/Sn strand for the ITER model coils

The ITER model coils will use two types of strands, one with high Jc, HP I, one with low hysteretic losses, HP II. Main specifications for the two strands are: HP I: Jc (nonCu)>700 A/mm/sup 2/ at 12 T @ 4.2 K, hysteresis losses<600 mJ/cc (+-3 T); HP II: Jc (non Cu)>550 A/mm/sup 2/ at 12 T @ 4.2 K, hysteresis losses<200 mJ/cc (+-3 T). HP I strand performance is likely to be achieved by internal tin Nb/sub 3/Sn, HP II by a bronze route strand. About 25% of the 26 tonnes required by the model coils will be contributed by the European Community. The companies EM-LMI, Italy (for internal tin) and Vacuumschmelze, Germany (for bronze route) have been selected by ITER for the strand production. The achievement of HP II performance was already demonstrated by Vacuumschmelze on a 10 km strand manufactured for NET in the frame of a former contract. On the other hand, the HP I internal tin strand was to be developed. In view of this, a contract has been assigned to GEC Alsthom Intermagnetics, France, to have a back-up option for internal tin strand. EM-LMI (HP I strand) and Vacuumschmelze (HP II strand) have successfully manufactured Nb/sub 3/Sn multifilamentary wires complying with ITER specifications. Work is in progress at GEC Alsthom Intermagnetics to achieve HP I strand performances.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

MODELLING AC LOSSES IN HIGH‐TEMPERATURE SUPERCONDUCTORS AS A NONLINEAR DIFFUSION PROCESS

Ceramic superconductors experience losses when carrying alternating currents. A first step in an attempt to macroscopically model the loss mechanism is to consider the ac transport current in a ribbon that has a cross‐section of width much greater than thickness. To some extent high‐temperature superconductors behave in a way similar to type II superconductors in which the loss mechanism is described by the critical state model, where the current is assumed to flow with a constant critical density Jc and is independent of the magnetic flux density B and ∂B/∂t. The dominant mechanism is the irreversible motion of fluxoids due to their interaction with the pinning sites, resulting in a form of hysteretic loss that can be represented in macroscopic terms (in a system with only one component of magnetic field) as proportional to ∫HsdBa/T over a complete cycle of period T, where Hs is the surface magnetic field strength and Ba is the space average value of flux density. However, it is found that the high‐temperature materials exhibit strong flux creep effects, and so the critical state model may not provide a sufficient description. To find an alternative formulation it is necessary to consider the flux creep E‐J characteristic of the ceramic material. If a highly nonlinear expression for the resistivity ? can be found, it may be possible to model the flux and current behaviour as a diffusion process.

Influence of Ni additions on the low-temperature magnetic properties of a Cu–1% Mn alloy

dc susceptibility and magnetization measurements were made on three alloys with the nominal compositions Cu–1% Mn, Cu–15% Ni, and Cu–1% Mn–15% Ni. dc susceptibility [χdc=C/(T+θW)] measurements were made with a Curie-type balance from room temperature down to 77.2 K. Magnetization measurements consisted of M-H loops at 4.2 and 1.37 K, and initial magnetization runs from room temperature down to 1.37 K. The results were analyzed in terms of an addition of Ni to Cu-Mn. High-temperature χdc data were used to find θW, C, and μeff (from C and the concentration), and it is found that these properties are influenced only to a minor extent by the Ni addition. At low temperatures, however, a suppression of the freezing temperature and an enhancement in the superparamagnetic signal are noticed for Cu-Mn-Ni as compared to Cu-Mn. Finally, hysteretic loss and magnetization for the ternary at 4.2 K were compared to that of the Cu-Ni and Cu-Mn alloys in order to determine its suitability for use as matrix material in multifilamentary superconductive wire.

Fatigue of Cord-Rubber Composites

Abstract Fatigue failure mechanisms and their dependence on cyclic loading frequency were assessed in the case of a nylon fiber-reinforced elastomer matrix composite representing the actual carcass of bias aircraft tires. Under uniaxial tension, the angle-plied composite specimens were subjected to a considerably large interply shear strain before failure. The composite specimens exhibited infinite fatigue life when stress amplitude was below a threshold level, i.e., fatigue endurance limit. Under cyclic stresses exceeding the endurance limit, localized damage in the form of fiber-matrix debonding and matrix cracking was formed and developed into the delamination eventually leading to gross failure of the composite. The process of damage accumulation was accompanied by a continuous increase of cyclic strain as well as temperature. Fatigue lifetime and the resistance to damage accumulation of aircraft tire carcass composite were strongly influenced by cyclic frequency. The use of higher frequency resulted in shorter fatigue lifetimes at a given stress amplitude and lower endurance limit. The extent of xdynamic creep at gross failure, which is defined as the increase of cyclic strain beyond initial elastic deformation, was roughly independent of stress amplitude under the frequency of 1 Hz, but decreased with higher stress amplitude when the frequency was raised to 10 Hz. Obviously a critical level of dynamic creep exists for gross failure of the composite and this level appears to be independent of the stress amplitude at low frequency. When the frequency is sufficiently high, heat generation due to hysteretic loss is expected to degrade the materials. In this situation, the critical level of dynamic creep for gross failure seems to be reduced by the loss of matrix flexibility as well as fiber-matrix bonding strength, with the degree of reduction becoming greater under higher stress amplitude.

Hysteretic ac losses and susceptibility of thin superconducting disks.

We calculate hysteretic magnetization curves and ac-susceptibility components ${\mathrm{\ensuremath{\chi}}}_{\mathrm{n}}^{\ensuremath{'}}$ and ${\mathrm{\ensuremath{\chi}}}_{\mathrm{n}}^{\mathrm{\ensuremath{''}}}$ for n=1, 3, and 5 for a type-II superconducting thin circular disk subjected to a low-frequency oscillating applied field, extending previous approaches for calculating hysteretic current-density and magnetic flux-density profiles in the critical state. We also present limiting expressions for \ensuremath{\chi}\ensuremath{'}=${\mathrm{\ensuremath{\chi}}}_{1}^{\ensuremath{'}}$ and \ensuremath{\chi}\ensuremath{''}=${\mathrm{\ensuremath{\chi}}}_{1}^{\mathrm{\ensuremath{''}}}$ for both small and large values of the ac field amplitude, and we show how \ensuremath{\chi}\ensuremath{''} is simply related to the ac loss per cycle per unit volume. Finally, a comparison is made between our results and those obtained for slab and strip geometries.

Cumulative Damage of Fiber-Reinforced Elastomer Composites under Fatigue Loading

Fracture mechanisms under fatigue loading were assessed in the case of nylon fiber-reinforced elastomer matrix composite which represents the actual carcass of bias aircraft tires. Under uniaxial tension, the angle-plied carcass composite specimens were subjected to a considerably large interply shear strain before failure. The composite specimens exhibited semi-infinite fatigue life when stress amplitude was below a threshold level, i.e., fatigue endurance limit. Under cyclic stresses exceeding the endurance limit, localized damage in the form of fiber-matrix debonding and matrix cracking was formed and developed into delamination eventually leading to gross failure of the composite. The process of damage accumulation was accompanied by heat generation and a continuous increase of cyclic strain (dynamic creep). Fatigue lifetime and the resistance to damage accumulation of aircraft tire carcass composite were strongly influenced by cyclic frequency. The use of higher cyclic frequency resulted in shorter fatigue lifetime at a given stress amplitude and lower fatigue endurance limit. The extent of dynamic creep at gross failure, which is defined as the increase of cyclic strain beyond initial elastic deformation, was roughly independent of stress amplitude under the frequency of 1 Hz, but decreased with higher stress amplitude when the frequency was raised to 10 Hz. Obviously a critical level of dynamic creep exists for gross failure of the composite and this level appears to be independent of the stress amplitude at low frequency. When the frequency is high enough, heat generation due to hysteretic loss is expected to degrade the materials. In this situation, the critical level of dynamic creep for gross failure may be reduced by the loss of matrix flexibility as well as fiber-matrix bonding strength. The study also examined the effect of load sequence on the damage accumulation process of composite based on dual stress level fatigue testing. Palmgren-Miner's linear damage accumulation theory tended to overestimate the cumulative damage of angle-plied carcass composites. As an alternative to PalmgrenMiner's rule, a linear cumulative damage model based on dynamic creep was utilized. The sum of dynamic creep to gross failure was found to be unity indicating that the level of cumulative damage is independent of the load sequence.

2D vector Preisach models and rotational hysteretic losses

Depending on the physical nature of hysteresis, rotational hysteretic losses in isotropic materials may decrease to zero or even continuously increase with the increase in the magnitude of uniformly rotating magnetic fields. It is shown in the paper that recently developed 2D Preisach models of vector hysteresis accommodate this broad spectrum of behavior of rotational hysteretic losses.

Analysis of dry friction hysteresis in a cable under uniform bending

A cable is considered as a system of helical wires and a core with distributed dry friction forces at their interfaces. Deformations of the cable subjected to a uniform bending are analyzed. It is shown that there is a critical bending curvature when a slip at the wire-core interface occurs. It originates at the neutral axis of the cross section of the cable and then spreads symmetrically over the cross section with the increase of bending. The effect of slippage on the cable stiffness is investigated. This model is also used to analyze a cable under the quasi-static cyclic bending. Explicit expression for the hysteretic losses per cycle of bending is derived. Numerical examples are given to show the influence of dry friction and helix angle on the bending stiffness and hysteretic losses in the cable.