Hysteresis Energy Loss Research Articles

Effect of substitution of titanium by zirconium in TiFe on hydrogenation properties

The influence of partial substitution of titanium by zirconium in the intermetallic compound TiFe on the hydrogenation characteristics was investigated. The compositions of the alloys correspond to the formula Ti 1− x Zr x Fe with x = 0, 0.01, 0.04, 0.07, 0.1 and 0.2. X-ray analysis showed that the lattice parameters of the alloys increased with an increase in zirconium content. Activation properties were largely enhanced with an increase in zirconium content. It was found that the absorption of hydrogen by the zirconium-containing compounds reached saturation earlier than in the case of pure TiFe as the absorption-desorption cycle for activation was continued. The pressure-composition isotherms revealed that the thermodynamic properties of the alloys were different. The hydrogen storage capacity was drastically reduced and the γ phase disappeared. The plateau was inclined and the plateau pressure of the zirconium-containing compounds was lower than that of pure TiFe. The ΔH, ΔS, ΔG values were obtained from the plot of In P versus 1 T by the van't Hoff relation. The hysteresis energy loss was nearly constant with varying zirconium content.

The effects of aluminium substitution in TiFe on its hydrogen absorption properties

The influence of the partial substitution of iron by aluminium in TiFe on the hydrogen absorption properties was systematically investigated. The pressure-composition isotherms were determined to establish differences in the thermodynamic properties. When aluminium was added to the TiFe compound, the hydrogen storage capacity decreased markedly and the γ phase was not formed. The plateau pressure was sloping and was higher for TiFe 0.98Al 0.02 and TiFe 0.96Al 0.04 and lower for TiFe 0.94Al 0.06 and TiFe 0.90Al 0.10 than for pure TiFe. These results are explained by the difference between the number of valence electrons present in aluminium and iron. The ΔH o , ΔS o and ΔG o values were obtained from plots of In P versus 1 T using the van't Hoff relation. The hysteresis energy loss decreased with increasing aluminium content.

Anomalous eddy current loss and amorphous magnetic materials with low core loss (invited)

Heat-treatment methods for obtaining low core loss in Fe rich amorphous alloys with high magnetic induction and the physical mechanism concerned will be discussed. Field annealing is necessary to avoid inducing local magnetic anisotropies or magnetic domain wall fixing, and then to make stress relieving effective. Consequently, field annealing can reduce hysteresis energy loss. However, core loss at high frequencies involves a fairly large anomalous eddy current loss. This is due to a large size of 180° magnetic domains resulting from field annealing. Oblique field annealing is, on the other hand, effective to reduce anomalous eddy current loss, because of increase in the number of 180° domain walls. The experimental relation between core loss and domain structure obtained on Fe(72)Co(8)Si(5)B(15) has satisfactorily been explained by the simple model on the basis of bar-like 180° wall motion. Magnetic properties of Fe(81)-(B, C, Si) (19) amorphous alloys suitable for transformer materials will also be reported. In Fe(81)B(13)C(2)Si(4), for example, core loss at 50 Hz is 1.3 mw⋅sec/kg at 15 KG and 25°C (2.2 mw⋅sec/kg at 15 KG and 80°C).

Analysis of Fatigue Process of Rubber Vulcanizates

Abstract The relationship between energy-input and hysteresis energy-loss during repeated deformation was analyzed, with gum and filled-rubber vuloanizates. It was recognized that the hysteresis energy-loss decreases more quickly with repeated deformation than the energy-input does. After a number of cycles both the energy-input and the energy-loss approach constant values. When these values are plotted against strain, curves similar in shape are obtained, regardless of the type of rubber. This is because the network chain is well relaxed. A group of the linear relationships between log W and log H was found with respect to N and λ. Examining the parameters, g1, g2, f1 and f2 as functions of N and λ, simple expressions, (4) and (5), were obtained for both the first deformation and after many cycles. At the latter state the hysteresis ratio tends to be constant in the wide range of λ. Finally, the relation between W and H at fatigue break is expressed with the same form of equation proposed by Grosch for the tensile break at the first extension.

Suppression of AC Hysteresis Energy Loss in Nonideal Type-II Superconductor with the Application of Longitudinal Magnetic Field

Suppression of AC Hysteresis Energy Loss in Nonideal Type-II Superconductor with the Application of Longitudinal Magnetic Field

銅-鉄合金の高温時効に伴なう内部摩擦の変化について

The changes in internal friction, hardness, electrical resistivity, magnetic properties and microscopic structure of 2.3, 5.4 and 9.6 wt% iron-copper alloys by aging at the temperatures from 600° to 750°C, were studied. During the aging process, the hardness change shows a single peak, while the electrical resistivity decreases in the stage of age-hardening and reaches an equilibrium state before the hardness reaches a maximum. In 2.3 wt% iron-copper alloys, there is no change of internal friction in the stage of age-hardening, but in the stage of over-aging, the internal friction increases remarkably. At the same time, the amplitude dependence appears and the break-away point shifts to the lower amplitude side with aging time. In the 5.4 and 9.6 wt% iron-copper alloys, the internal friction decreases in the stage of age-hardening and the change of internal friction in the stage of over-ageing is similar to that of the 2.3 wt% iron-copper alloys. The above change of internal friction in the stage of over-ageing begins at a shorter aging time with rising aging temperature and increasing iron concentration. This change of internal friction is related to the growth of the precipitate particles. Internal friction of copper-iron alloys in this study is neither a relaxation-type of energy loss nor a magnetomechanical hysteresis energy loss due to the precipitate, but it is a hysteresis energy loss of vibrating dislocation. On the basis of these results, the change of coherency between the matrix and the precipitate and hardening mechanism in these alloys have been discussed.

Hysteresis losses in rolling and sliding friction

Previous work on the mechanism of rolling friction has shown that it is mainly due to elastic hysteresis losses in the rolling elements. Under conditions of uniform tension or torsion it is generally assumed that the energy dissipated by hysteresis is a constant fraction (the hysteresis loss factor) of the elastic energy introduced during the cycle. This elastic input energy has been calculated for a hard cylinder or sphere rolling on rubber, and with the above assumption expressions have been obtained for the rolling friction. These expressions predict correctly the dependence of rolling friction on load, ball or cylinder diameter and elastic constants of the rubber. However, the absolute values of the frictional force are too small. The experimental values are two to three times the theoretical estimates. This suggests that it is invalid to use the hysteresis loss factor, as measured in a simple deforma­tion cycle, for more complex cycles such as those involved in rolling. For a thin-walled rubber tube to which tensional and torsional stresses could be applied, the hysteresis energy losses for complex stress cycles were measured. In such a system there are two relevant shear stresses which contribute to hysteresis losses; if these are plotted graphically, a deformation cycle can be expressed by a stress diagram which, in general, will form a closed loop. A hypothesis is put forward which suggests that the losses in the cycle are proportional to the square of the length of this loop. An investigation of different types of stress cycle show that this hypothesis may be used fairly reliably to estimate energy losses in complex stress cycles. In particular it may be shown that if the rubber is deformed in such a way that its elastic strain energy is constant throughout the cycle, marked hysteresis losses occur. The earlier concept would predict no energy loss. This result is of general importance and explains the earlier discrepancies between theoretical and experimental values for the friction of rolling cylinders and spheres. Although this hypothesis has limitations (these and alternative hypotheses are discussed) it is applicable to the deformation of material by a hard roller and an analysis is given for a long cylinder rolling on rubber. It is shown that the losses are over three times as great as those deduced from the earlier concept and for a spherical roller the loss is about twice as great as earlier estimates. This is in good agreement with experiment. The analysis is extended to the case of rolling over short distances and it is shown that the resistance increases linearly from zero as a cylinder, starting from rest, commences to roll. An experimental study indicates that this is approximately true. Only when each element has passed under the roller and out of the contact region does the hysteresis loss reach its maximum steady-state value. For minute displacements of a roller, there is evidence that adhesion may not be entirely destroyed, and though, in general, rolling friction is dominated by hysteresis losses, it is suggested that under these limiting conditions the effect of adhesion may not be negligible.

THEORETICAL INVESTIGATION INTO THE PHYSICAL PROPERTIES OF TEXTILE MATERIALS (IB) ELASTIC BEHVIOUR AND BINDING MECHANISMS OF THE FIBRE SYSTEM

For quatitative information as to the elastic behaviour of fibre bundles, for example card sliver, top and roving, the present study was undertaken to establish an elastic model for a fibre system built from an elementary unit such as bar-like fibre which may be in itself deformable and mutually slippery. The treatments for a bundle (length L, bulk density ρ, linear density k) of parallel units (elementary fibres of length l, diameter b, density ρ, Young's modulus e_??_, Poisson's ratio σ_??_ and coefficient of friction f, in the sense of all “effective”) are developed on assumptions that, -(1) When stress S in a stretched bundle is elastic equilibrium to the external force P, the apparent extension of bundle γ would occur in such a fashion that γ becomes linear combination of the elongation of bar-like unit e as the strain of a line element in the elastic medium of constants e, σ subject to stress S, and the mutual slippage of the centre of each unit, e as the displacement of a point in elastic medium of constants e, σ subject to the same stress S, (2) Distribution of the position of elementary units is uniform over the full range, and digstribution of their direction θ is symmetrical about the long axis of bundle.Then from assumption (1) we obtaine the following relations: where e, e are Young's moduli, σ, σ are Poissonn's ratios in two sets of assumed elastic medie respectively. Here, specific length of bar-like unit to gauge length of bundle λ, fullness of units in the cross-section ω and frictional factor of inter-units α are defined by assumption (2):Then, according to the Hooke's law appropriate for this bundle with two sets of assumed elastic constants, the observed Young's modulus E and Poisson's ratio ∑ may be expressed as:Now, when we expand E and ∑ in terms of power of extension γ by means of above relations in which e, α and λ are the functions of γ, we may derive the analytical formulae of stressstrain curve S(γ), lateral contraction curve β(γ), change of sectional area A(γ), and change of bulk density ρ(γ) by the definitions of eqs. (12.12) to (12.15) respectively. We therefore obtain load-elongation curve from expression P(γ)=A(γ)S(γ), and find the breaking strength PM, . breaking elongatiou γM as the maximum values of P(γ) curve. These computed analytical formulae mainly depend upon the particular values of λ and α to which their numerical values of bundle's charactor correspond. Several examples given are by the eqs. (12.19) to (12.38) for the typical region of values of λ and α.Comparisons of the computed and experimental values as to the nature of unit fibre, for various viscose staple slivers with charactors given in Table II, are made in Table I and III. A slight disagreement of theoretical and experimental values of unit fibre properties is introduced by regarding the elementary bar-like unit as coressponding to only one fibre in bundle. Therefore we see that by the interpretation in term of an elementary unit as a group of fibres, the assumptions upon which the computations were based are essentially correct to the elastic model of fibre bundle.Other interesting expressions deduced from this model are those of hysteresis energy loss H(γr) and elastic resilience φ(γr) which appeared with cyclic elongation γr. In the range of small values of γr, H(γr) and φ(γr) are given by eqs, (12.43) to (12.46)

THEORETICAL INVESTIGATION INTO PHYSICAL PROPERTIES OF TEXTILE MATERIALS (IB) ELASTIC BEHAVIOUR AND BINDING MECHANISMS OF THE FIBER SYSTEM

For quatitative information as to the elastic behaviour of fibre bundles, for example card sliver, top and roving, the present study was undertaken to establish an elastic model for a fibre system built from an elementary unit such as bar-like fibre which may be in itself deformable and mutually slippery. The treatments for a bundle (length L, bulk density ρ, linear density k) of parallel units (elementary fibres of length l, diameter b, density ρ, Young's modulus ε_??_, Poisson's ratio σ_??_ and coefficient of friction f, in the sense of all “effective”) are developed on assumptions that, -(1) When stress S in a stretched bundle is elastic equilibrium to the external force P, the apparent extension of bundle γ would occur in such a fashion that γ becomes linear combination of the elongation of bar-like unit e as the strain of a line element in the elastic medium of constants ε, σ subject to stress S, and the mutual slippage of the centre of each unit, e as the displacement of a point in elastic medium of constants ε, σ subject to the same stress S, (2) Distribution of the position of elementary units is uniform over the full range, and digstribution of their direction θ is symmetrical about the long axis of bundle.Then from assumption (1) we obtaine the following relations: where ε, ε are Young's moduli, σ, σ are Poissonn's ratios in two sets of assumed elastic medie respectively. Here, specific length of bar-like unit to gauge length of bundle λ, fullness of units in the cross-section ω and frictional factor of inter-units α are defined by assumption (2):Then, according to the Hooke's law appropriate for this bundle with two sets of assumed elastic constants, the observed Young's modulus E and Poisson's ratio ∑ may be expressed as:Now, when we expand E and ∑ in terms of power of extension γ by means of above relations in which ε, α and λ are the functions of γ, we may derive the analytical formulae of stressstrain curve S(γ), lateral contraction curve β(γ), change of sectional area A(γ), and change of bulk density ρ(γ) by the definitions of eqs. (12.12) to (12.15) respectively. We therefore obtain load-elongation curve from expression P(γ)=A(γ)S(γ), and find the breaking strength PM, . breaking elongatiou γM as the maximum values of P(γ) curve. These computed analytical formulae mainly depend upon the particular values of λ and α to which their numerical values of bundle's charactor correspond. Several examples given are by the eqs. (12.19) to (12.38) for the typical region of values of λ and α.Comparisons of the computed and experimental values as to the nature of unit fibre, for various viscose staple slivers with charactors given in Table II, are made in Table I and III. A slight disagreement of theoretical and experimental values of unit fibre properties is introduced by regarding the elementary bar-like unit as coressponding to only one fibre in bundle. Therefore we see that by the interpretation in term of an elementary unit as a group of fibres, the assumptions upon which the computations were based are essentially correct to the elastic model of fibre bundle.Other interesting expressions deduced from this model are those of hysteresis energy loss H(γr) and elastic resilience φ(γr) which appeared with cyclic elongation γr. In the range of small values of γr, H(γr) and φ(γr) are given by eqs, (12.43) to (12.46)

Mechanical Hysteresis Properties of Single Fibers and Cords

An apparatus for stretching and relaxing single fibers for the purpose of determining mechanical hysteresis losses is described. Results obtained on cotton, viscose rayon, and nylon fibers are compared with similar data previously obtained on cords from which the fibers were taken. Such comparison indicates that interfiber friction is probably the major cause of hysteresis energy losses in cotton and rayon tire cords under cyclic loads at low frequencies.

Characteristics of Iron in High Frequency Rotating Magnetic Fields

Characteristics of electrolytic iron in rotating magnetic fields of high frequency, 52,000 to 172,000 and of strength 0.7 to 5 gauss, have been determined by measurements on a disk, ${10}^{\ensuremath{-}3}$ cm thick shellacked to a half inch cover glass. Equations are derived by which $H$ and $I$ can be computed from measurements of the impressed field, the fluxes through a coil with and without the disk in it, and the torque exerted on the disk by the rotating field. This field is produced by means of two Helmholtz coils with axes at right angles, each in series with a separate oscillating circuit, coupled to the main oscillating circuit. The results agree with previous work and show that (1) the susceptibility decreases with increasing frequency; (2) the hysteresis angle tends to increase with frequency and for a given frequency reaches a maximum for $I$ at about 500; (3) the hysteresis energy loss per cycle ${E}_{h}$ increases with frequency for constant magnetic intensity and decreases for constant field, the exponent $\ensuremath{\alpha}$ in the equation ${E}_{h}=A{H}^{\ensuremath{\alpha}}$ increasing from 2.9 to 3.37 as frequency is increased from 52 to 172 kilocycles.

Magnetization and Hysteresis in Hematite Crystals

Magnetization and Hysteresis in Hematite Crystals; Experimental Procedure.---In a previous paper, the author has given the results of an investigation of the magnetic properties of crystallized hematite, the measurements being of the force exerted upon a sphere when it is placed in a non-uniform magnetic field. The present paper contains some results obtained by measuring the couple exerted when a hematite sphere is suspended in a uniform magnetic field. The couple in a uniform field measures the component of magnetization perpendicular to the field; the force measures the component parallel to the field.Experimental Data.---The paper contains (1) magnetization curves (Fig. 4) for two specimens of hematite; (2) hysteresis loops at fields from 9.5 to 1020 gausses, some obtained with a rotating field (Figs. 6, 7, 8, 9, 11), the others with an alternating field (Figs. 10, 11); (3) a graph representing components of magnetization parallel and perpendicular to the field (Fig. 12).Deduction, The normal magnetization curve of hematite consists of a sharp rise followed by a slow increase, which is proportional to the field strength. The hysteresis energy loss increases with an increase in the maximum field applied up to a certain field, and thereafter the area of the hysteresis loop remains constant. For the specimen on which most of the present measurements were made, the hysteresis loss is constant for field strengths above about 150 gausses.