Hysteretic Losses Research Articles

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.

Magnetic properties of Fe/sub 73.5/Cu/sub 1/Nb/sub 3/Si/sub 16.5/B/sub 6/ coated with sputtered SiO/sub 2/

In this work the influence of nanocrystalline structure on magnetic losses is pointed out. Annealed samples, with and without SiO/sub 2/ coating, show mainly hysteretic losses. Eddy current losses are more important in the as cast state than in the other cases. These measurements suggest that the occurrence of the nanocrystalline structure modifies the wall kinetics and so the contribution of eddy current losses in comparison with the amorphous state. >

Influence of direct and alternating transport current on the diamagnetic response of Bi-based ceramics

AC susceptibility measurements performed on single-phase ceramic Bi2Sr2Ca2Cu3Oy slab carrying direct Idc or alternating Iac transport current are presented. A strong suppression of intra- and intergranular superconducting properties by transport current was observed. It is displayed as a sharp shift of real χ′ and imaginary χ″ components of ac susceptibility to lower temperatures with increasing I. The hysteretic losses peak shifts to low temperatures as transport current density j increases at the rate Δtδj ≈ 4 K/(A/cm2). The increase of I, in the contrary to increase of exciting magnetic field Hac, does not broaden the χ′(T) and χ″(T) curves. The influence of ac transport current is quite different from that of dc current. With increasing Iac the value of both the in-phase and quadrature components of diamagnetic response increases, while increase of Idc does not effect the value of χ′(T) and χ″(t).

Role of Crack‐Bridging Ligaments in the Cyclic Fatigue Behavior of Alumina

The cyclic fatigue crack growth behavior in two aluminas with different grain sizes and purities has been investigated using tapered cantilever beam specimens. The curves of load–crack opening displacement revealed a hysteretic loss behavior, in both aluminas, produced by frictional forces generated in the crack wake. From measurements of the specimen complinces it is concluded that the fatigue cracks in these materials were strongly bridged by both “frictional” and “elastic” load‐bearing ligaments. It is shown that the “elastic” contribution to the total crack‐bridging force is far greater than that produced by fristional sliding ligaments. The results support the view that cyclic loads produce degradation of the strength of the bridging ligaments. The effect of grain size and compressive loads on the magnitude of the bridging forces is discussed.

Suppression of intra- and intergranular properties by transport current in Bi-based ceramic superconductors

The influence of a direct transport current I/sub dc/ on the diamagnetic response of Bi/sub 2/Sr/sub 2/Ca/sub 2/Cu/sub 3/O/sub y/ ceramics as a function of temperature T has been investigated experimentally. The real chi '(T) and imaginary chi "(T) parts of AC susceptibility shift toward lower temperatures, and the hysteretic loss values decrease as I/sub dc/ increases. In contrast to what is observed with increasing exciting magnetic field H/sub ac/, increase of I/sub dc/ does not broaden the transition regimes in chi '(T) and chi "(T).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Similarity laws of the internal damping of stranded cables in transverse vibrations

Similarity laws governing the internal damping of stranded cables in transverse vibrations are based on the assumption of hysteretic loss factor associated with the flexural rigidity of the cable and the assumption that this loss factor is the same for all cables of the same construction. These laws are derived from the basic cable differential equation. The proportionality factors, the exponents of the various parameters in the laws, are obtained from the experimental results of a typical member of a family of similar cables. The same set of laws has been found to apply very well to ACSR (aluminum conductor steel reinforced) conductors having the same number of strands and fairly well to all ACSR conductors. Other families of cables, such as ACAR (aluminum conductors aluminum reinforced), steel cables, etc., could each have their own set of similarity laws, which would all look alike. >

Numerical analysis of bifurcations in Duffing's equation with hysteretic functions

AbstractThis paper analyzes numerically the bifurcation phenomenon in Duffing's equation containing a hysteretic function and reports on the result of investigation of the effect of the hysteretic characteristics on the bifurcation.First, a large number of steady hysteresis loops is derived by numerically integrating the state equation of the system with various initial conditions, and the sets of the steady periodic solutions are observed. Then, using the method already proposed by the authors, the bifurcation of the steady solution is analyzed while varying the parameters of the system. The effects of the hysteretic loss and the ohmic loss on the bifurcation of the system are compared, and the difference is discussed. An example of the generation of chaos caused by increasing the hysteretic loss is shown.

Fatigue fracture behaviour of PEEK: 2. Effects of thickness and temperature

Experimental results on the effects of specimen thickness and environmental temperatures on fatigue fracture behaviour of poly(ether ether ketone) (PEEK) are reported. Low cycle fatigue experiments are conducted on injection moulded single-edge notched specimens of 1.57, 2.70 and 5.42 mm in thickness at ambient temperatures, and on specimens 2.70 mm thick at environmental temperatures of 39, 50, 63, 75 and 100°C. In all the thickness experiments and in the experiments with temperatures of 39 and 50°C, the crack tip profile is initially round. At long crack lengths the crack tip profile changes to a triangular shape. When the test temperature is 63, 75 and 100°C, the crack tip remains round throughout the fracture process. The crack tip angle is primarily dependent upon the test temperature. Examinations of the fracture surfaces and transverse sections indicate that in the thickest specimen, relatively rough fracture surfaces are observed and a few discontinuities (crazes or cracks) underneath the main crack path. Thus, crack propagates in a ‘brittle’ manner. In all other experiments both ‘brittle’ and ‘ductile’ modes of fracture are observed. The point of transition from ‘brittle’ to ‘ductile’ fracture is dependent upon the specimen thickness and test temperature. Fatigue striations are seen throughout the fracture surfaces. Correlation of the striations and the number of cycles indicates a one-cycle crack growth mode. Hysteretic losses during fatigue crack growth are negligible until a few cycles prior to unstable fracture. Crack opening displacements are independent of the specimen thickness and increase with rise in temperature. When crack growth rates are correlated with the elastic energy release rate, they are independent of specimen thickness and increase with increase in temperature.

Hysteretic method of lower critical field determination in high-Tc superconductors

The per unit volume per cycle AC hysteretic loss of samples with different radii, R0 (filament radii, in the case of multifilamentary materials), can be meaningfully compared as function of field-sweep amplitude, Hm, by normalizing the loss to some reference radius, Rref.. The R0-normalized Qh can then be used to compare the Jcs of different samples in both the low- and high-field regimes. A new function, Qh=(10/3 pi 2JcR0)((3/2)Hc1(Hm-Hc1)2+(Hm-Hc1)3), has been developed for describing the low-field hysteretic loss in transverse-field cylindrical samples. Two methods are outlined for using this equation to extract Hc1 from thick high-Jc samples-samples which defy the conventional deviation-from-linearity approach. Applications of these procedures to samples of melt-processed YBCO and multifilamentary NbTi are presented.

Three dimensional solution of critical state models: AC hysteresis losses

The alternating field, hysteretic power losses in strongly pinned superconducting spheres and spheroids are studied within the Bean-London Model. Analytic solutions for small flux penetration and numerical determination for arbitrary applied field are presented. By changing the eccentricity, geometries from needles to flat discs may be analyzed.

Thermomechanical Coupling in Inelastic Solids

Coupling between mechanical and thermodynamic processes can be significant in solid media when material inelasticity occurs. Significant mechanical energy may be converted into heat via hysteretic loss, and this coupling may be significant even under quasi-static conditions. Important advances have been made since the second world war in modeling this thermomechanical coupling. This paper reviews many of the major achievements on this subject. The paper opens with a short review of historical milestones on the subject. A theoretical model is then reviewed, including both conservation laws and constitutive models for certain classes of solids. The paper concludes with a discussion of recent attempts to solve the inelastic coupled thermomechanical field problem.

Influence of composition and long term annealing on the weak link behaviour of the high-Tc superconductor (Bi, Pb)2+xSr2−yCa2+yCu3+zO10+δ

Abstract A comparative study of the low field AC susceptibility of the superconducting compound (Bi, Pb) 2+ x Sr 2− y Ca 2+ y Cu 3+ z O 10+ δ with x =0(0.1), y =0(0.4, 0.2, 0.1, 0), and z =0.5(0.6, 0.3, 0.15, 0) is presented. The samples were prepared by the conventional solid state reaction in air. X-ray diffraction patterns reveal the virtually single phase nature of the pellets. Resistively measured critical temperatures T c0 up to 113 K could be obtained. The AC susceptibility data show onset temperatures in the temperature range 108–112.9 K. Convincing agreement between theory and experimental data was obtained by assuming a critical state model with field dependent critical transport current density j c for the intergranular component of the shielding behaviour according to the Anderson-Kim model. As a rule, the intragranular part of the AC susceptibility reveals no sign of hysteretic losses (χ″) for field amplitudes up to 150 A/m. The field dependent shift of the imaginary part χ″ of the complex AC susceptibility χ can be used to infer the transport critical current density of the weak link network.

Field and frequency dependences of the susceptibility of granular YBCO films as a result of pinning and thermally assisted flux flow

The frequency and field dependences of the ac diamagnetic response of HTS films were investigated in fields of amplitudes H ac=0.1−120 mOe and frequency ω/2 π=0.7−15 kHz. It is found that the temperature T m corresponding to the hysteretic loss maximum changes by the law T m=T c[1−(H ac/H ∗) 2 3 In(ω ∗/ω)] . This regularity is described quantitatively in the model uniting the critical state and flux creep concepts.

Input-dependent Preisach model and hysteretic energy losses

Expressions for hysteretic energy losses are derived by using the ‘‘input-dependent’’ Preisach model of hysteresis. These expressions are valid for arbitrary (not only periodic) variations of magnetic field.

Magnetization and critical current density of ultra-fine multifilamentary superconducting wires

Multifilamentary superconducting wires with a greatly reduced level of losses have been produced with lengths of several tens of kilometers. In spite of the reduction of the filament diameter, proximity effects are avoided, and the best possible use of the reversible motion of the flux lines is made, so that the hysteretic losses are reduced. The concepts lead to a realization of conductors comprising filaments of Nb-Ti (0.1-0.2- mu m diameter) embedded in a highly resistive CuNi matrix. In order to characterize the possible application to industrial power systems, it is necessary to investigate the losses in submicrometric filaments. It is possible to determine the correct value of the critical current density with critical current measurements and magnetization curves on such wires.

Coils performances of superconducting cables for 50/60 Hz applications

Multifilamentary superconducting wires with a greatly reduced level of losses have been produced with unit lengths of several tens of kilometers. With the reduction of the filament diameter, proximity effects are avoided and maximum advantage is taken of the reversible motion of flux lines, so that the hysteretic and matrix losses are lower. These concepts have led to the manufacture on an industrial scale of three wires comprising 377982, 597102 and 920304 filaments of NbTi with a diameter of 0.14 mu m and a 0.13- mu m spacing between the filaments. The matrix material is 30%-Ni-content copper-nickel. Cables made from six such insulated wires have been made with more than 1-km kilometer unit lengths. Numerous impregnated and nonimpregnated coils have been wound with single strands and 6+1 cables. A report is presented on 50-Hz and DC quench currents, 50-Hz AC losses, and 50-Hz electromagnetic stability results. These results are analyzed taking into account proximity effects, reversible motion of flux lines, current sharing, and the thermal behavior of the coil.

Dissipative Processes Due to Fluxoid Motion in Superconductive YBCO Specimens

AbstractComparative measurements are made on the dissipative effects due to dc current flow and ac magnetization processes on the same YBCO superconducting specimen at 77.3 K. The material is brought into the Abrikosov mixed phase by a dc magnetic field H0. Different sets of data are reported concerning: (a) the dependence of the dc resistivity ϱ on H0 and on the current density J, (b) the dependence of H(t) on the frequency and on the value of H0 of the magnetic power loss generated by a very small (0.34 A/m) sinusoidal magnetic field H(t) superimposed to H0. By a numerical calculation it is shown that at high frequencies the magnetic power loss is very closely equal to the one expected for eddy current dissipation in a conducting material whose resistivity depends on the current density and has a value rather closely equal to the one measured on the YBCO specimen with a conventional four‐terminal technique. A second component of the magnetization power loss, which is closely proportional to the magnetization frequency and corresponds to the hysteretic loss, is also seen.

Magnetization and critical currents of tin-core multifilamentary Nb/sub 3/Sn conductors

Critical current and magnetization data are presented for some multifilamentary Nb/sub 3/Sn wires that have been produced by the internal-tin method. A comparison of magnetization and transport critical current measurements shows that filament bridging during heat treatment is a common occurrence leading to effective filament diameters that are sometimes an order of magnitude larger than the geometrical filament size. At present J/sub c/'s (in the noncopper region) greater than 1300 A/mm/sup 2/ at 10 T have been achieved in some conductors, which also exhibit high losses. Low losses have only been seen in conductors with a high local ratio of copper to niobium. The use of (Nb-1%Ti) alloy instead of pure Nb helps to reduce low-field loss and increase high-field J/sub c./ Measurements of the temperature dependence of hysteretic loss to 5 T indicate that loss decreases linearly with increasing temperature.

Critical currents and AC losses on subsize cables of the NET-EM/LMI 40-kA Nb/sub 3/Sn cable-in-conduit conductor prototype

Critical currents have been measured on subsize cables, up to the 27-strand level, of the 40-kA NET-EM/LMI Nb/sub 3/Sn prototype conductor for the OH solenoid of NET (Next European Torus). Energy losses in basic strands were determined by magnetization cycles. Copper and stainless steel were used as conduit materials to produce CIC (cable-in-conduit) conductors with a 0.35 void fraction, which is lower than that of the full-size conductor. The experimental results have shown that, compared to the single-strand current, practically no degradation is observed in cables with a Cu conduit, while the cables with a stainless steel conduit have a critical current lowered by cool-down strain to 0.57 of the expected current in a 27-strand cable at zero intrinsic strain. The measurements of AC losses have indicated high hysteretic losses (effective diameter of =70 mu m). Coupling losses are expected to be negligible.

Fatigue fracture behaviour of PEEK: 1. Effects of load level

Results of experimental studies on fatigue fracture behaviour of PEEK are reported. Experiments are conducted on injection moulded single edge notched specimens of 2.68 mm in thickness. At low crack speeds the crack tip is relatively round. At relatively higher crack speeds, the crack tip geometry changes to a triangular shape with an angle of 90° which remains constant until close to unstable fracture. Optical microscopy observations of fracture surfaces and of transverse sections show that at relatively short crack lengths growth occurs in a ‘brittle’ manner. Subsequently necking or lateral contraction of the specimen around the crack tip is observed and is associated with a ‘ductile’ mode of growth. The point of transition from ‘brittle’ to ‘ductile’ fracture is dependent upon the level of the stress. Fatigue striations are observed throughout the fracture surface. Correlation of the striations and the number of cycles indicates a one cycle crack growth mode. The critical crack length is assumed to correspond to the point of minimum thinning which is shortly after the last striation. Hysteretic losses during fatigue crack growth are negligible until a few cycles prior to unstable fracture. Energy release rates evaluated from load displacement curves are practically equal to J 1 = δσ y ( σ y is the yield stress of the material and σ is the crack opening displacement). The ‘brittle’ phase of crack propagation is well described by linear elastic fracture mechanics parameters. For the entire phase of propagation and for the same level of J 1 (= δσ y), the crack speed is practically independent of the stress level.