Magnetostrictive Force Research Articles

ON ANALOG FEEDBACK CONTROL FOR MAGNETOSTRICTIVE TRANSDUCER LINEARIZATION

The magnetostrictive transducer output force, displacement, and bandwidth characteristics are well suited for a variety of active vibration control applications. However, their use is limited in part because these transducers are known to be non-linear. The transducer in this study is assumed to be a linear system and its output harmonics are assumed to be disturbance inputs. Two feedback control models are proposed and one is used to obtain expressions for predicting the change in harmonic amplitudes of displacement and acceleration as functions of frequency and parameters for the controller, load, and transducer. An approach based on magnetostrictive transduction modelling is presented for experimentally determining appropriate transducer model parameters for use in the feedback control model. Experimental measurements using simple, analog, PD (proportional plus derivative) acceleration feedback control are presented to validate the expressions. The closed loop feedback control system model resulted in predicted changes in harmonic acceleration amplitudes ranging from +2 to −30 dB (depending upon the frequency of the disturbance input) that were verified experimentally. A significant extension of the linear range of transducer behaviour, due to feedback control, is also demonstrated.

4HE EXPERIMENTS NEAR TLAMBDA IN A LOW-GRAVITY SIMULATOR

We report on our latest measurements of gravity cancellation in the low-gravity simulator using a magnetostrictive force. We made these measurements using a new thermal conductivity cell design that is 0.5cm in diameter and 0.5cm in height. Gravity cancellation was verified by measuring both the reduction in the Tλvariation across the cell and the suppression of thermal convection as a function of the magnetic field. Full gravity cancellation was achieved in the simulator with B(dB/dz) ≈ 21 T2/cm, agreeing well with the calculated value and the valve found from levitating drops of helium.

Precise crystal and magnetic structure determinations. Part I: a neutron diffraction study of Nd 2Fe 14B at 20 K

Nd 2Fe 14B is the well known basis of the best performing hard magnets. It exhibits a spin reorientation transition (SRT) at 140 K, where the easy axis magnetisation turns to a canted magnetic structure at low temperature. An accurate neutron diffraction experiment performed on a single crystal, allows us to precisely determine the low temperature non-collinear magnetic structure and to compare it with the Ho parent compound. Moreover, a lowering of the crystal symmetry (space group C m) is shown to take place in addition to the SRT. High magnetostrictive forces and negative Nd Nd interactions make possible such a crystal and magnetic symmetry lowering, which is complicated by the SRT induced by high order crystal electric fields terms.

SIGNIFICANCE OF THE ELECTROMAGNETIC FORCES ON THE MECHANICAL RESONANCES OF STATOR LAMINATIONS

The laminated structure of the stator core of fractional horsepower electric motors consists of plates of ferromagnetic materials that can have unusually large deformation coefficients when an electric field is applied. The influence of the compressive stresses is the cause of significant changes in the harmonics that can be explained by the effect of the stress on the harmonic content of the flux density waveform. Magnetostriction harmonics are important when considering the significant contribution to audible noise of electric motors. The significance of magnetostrictive forces increases when they excite the lamination plates around their mechanical resonances. The combined effects of the radial components of the electromagnetic forces and the magnetostrictive deformation can cause further problems of amplification of noise by setting the core and frame in motion. This study investigates the effects of magnetostrictive forces on the laminated mechanical structure of the stator core by referring to changes of the plate materials depending upon the heat treatments, magnetic properties, and the percentage of silicon alloying that were all considered as factors which modify the effects of magnetostriction.

Mechanisms of noise generation of model transformer cores

The audible noise of transformer cores is generated by vibrations due to both magnetostriction and magnetic forces which gain relevance in the case of highly oriented SiFe. The Maxwell stress vector depends strongly on the flux distribution in the core corners which show maximum dislocations δ z normal to the sheet planes. Multi-step-lap assembling increases δ z but reduces harmonic distortions which can be assumed to be one reason for the decrease in A-weighted noise.

Bulk-Wave Generation in a Ferromagnetic Metal by Electromagnetic Acoustic Transduction.

Bulk-wave generation in plates of aluminum, stainless steel, and carbon steel by a spiral elongated coil and a static magnetic field is analyzed experimentally and numerically. First, the field dependences of the wave amplitudes are investigated using the electromagnetic acoustic resonance (EMAR). The magnetic field is applied parallel to the sample surface. A theoretical model developed to explain the considerable difference in the field dependence between nonmagnetic and ferromagnetic metals is presented, which shows the dominant contribution of the magnetostrictive forces to bulk wave generation in ferromagnetic metal rather than the Lorentz force and the magnetization force, especially in the shear wave generation. The model is further developed by the FEM simulation of the two-dimensional body force profile within the metal. The simulation is Performed for a practical bulk-wave electromagnetic acoustic transducer (BW-EMAT), which has an elongated coil and a pair of permanent magnets of the coil. The calculation strictly predicts several important features of the BW-EMAT, and has significant implications for the practical use of the EMAT.

THE MAGNETOSTRICTION FORCES IN THE INDUCTION MOTOR

The paper describes how the classical formula of the Maxwell magnetic stress tensor may be extended to cover the magnetostriction phenomena. It is assumed that the ferromagnetic continuum is isotropic and conservative. The method takes into account the magnetic nonlinearity and it assumes that mechanical deflections are sufficiently small to neglect the nonlinearity of the Hooke's law. The paper presents also the experimental method, which has been used to measure the magnetostriction intensity for electrotechnical laminations. As the final result, the distribution of the volume magnetostriction forces acting on the stator core of the induction motor has been calculated.

A magnetostrictive force sensor

A new magnetostrictive force sensor is presented and its operation is verified experimentally. The sensor has a single excitation coil and a single detection coil, which utilize the magnetostrictive effect. The cores of the coils function as ‘‘spring elements’’ of the sensor, and are linked together by rigid end plates. The magnetostrictive force sensor is compensated for asymmetric magnetostrictive behavior, and measures both tensile and compressive forces. Force sensitivity increases with excitation current and coil turns, but is less influenced by excitation frequency.

Tb-Fe Sputtered Films with Large Magnetostriction for Use in Magnetomechanical Thin-Film Devices

We examined the magnetostriction and coercive force of amorphous Tb-Fe films sputter-deposited under different conditions (rf input power, Ar gas pressure, Tb content, etc.). Here we discuss the possibility of obtaining both soft magnetic properties and a large magnetostriction in this system. Soft magnetic properties and large magnetostriction were obtained simultaneously in sputtered Tb-Fe thin films prepared with a Tb content of 45 to 50 at%, under an Ar gas pressure of 4 mTorr and with an rf input power of 200 W. This material has strong potential for use in magnetomechanical thin-film devices.

電気機械変換薄膜素子用Ｔｂ‐Ｆｅスパッタ薄膜の磁歪

We examined the magnetostriction and coercive force of amorphous Tb-Fe films while varying the sputtering conditions (rf input power, Ar gas pressure, Tb content, and so on). Here we discuss the possibility of obtaining both soft magnetic properties and large magnetostrictionin this system. Soft magnetic properties and large magnetostriction were obtained simultaneously in sputtered Tb-Fe thin films prepared with a composition of 45∼50 at% Tb-Fe. Ar gas pressure of 4 mTorr, and rf power of 200 W. This material has astrong potential for use in magnetomechanical thin-film devices.

Vibration Reduction of Power Transformer Core.

Recently, demand has increased for low-noise power transformers as well as large-capacity and small-size power transformers. To reduce transformer noise, it is necessary to reduce vibration of their iron cores, which is caused by magnetostrictive forces of silicon iron sheets. In this paper, a method for calculating core vibration was introduced and techniques for reducing the vibration were investigated. First, magnitudes and phases of higher-harmonic components of the magnetostriction were clarified. Then, a calculation method of core vibration using analytical solutions for a uniform beam was introduced. Calculated values for natural frequencies agreed with measured ones within 5%. Also, the vibration characteristics of a single-phase two-legged core, a three-phase three-legged core, and a three-phase five-legged core were clarified. Finally, it was found that the participation factors of magnetostriction in various portions of the core had different values for the displacement of core, and that arbitrary vibration modes could be eliminated by adjusting the magnetostriction values. Optimum combinations of magnetostriction which reduce core vibration were obtained. The preferable ratios for dimensions such as the ratio of the sectional areas of the core and yoke, or the ratio of the area moments of the inertia of the core and yoke, were proposed. In many cases, it was found that participation factors of magnetostriction in yokes were larger than those of legs, although the yokes were shorter than the legs.

Crystal and non-colinear magnetic structures of R2Fe14B, R = Nd, Ho

The boride series R 2 Fe 14 B (R = rare earth metal) develops very hard magnetic properties such as to be most promising magnet materials. Owing to the large magnetostrictive forces and the reorientation phenomenon (SR) setting at low temperature, the crystal and magnetic symmetry were seen to lower from P4 2/mnm to Cm with temperature

Low temperature crystal and magnetic structures of Ho 2Fe 14B

Ho 2Fe 14B belongs to the hard magnetic material series and, like the prototype neodymium compound, exhibits a spin reorientation transition phenomenon. An accurate neutron diffraction experiment performed on a single crystal allows us to establish the exact low temperature non-collinear magnetic structure. Moreover, a lower crystal symmetry (space group Cm) is shown to occur far above T = 58 K, the spin reorientation transition. The previously reported tetragonal symmetry (space group P4 2/ mnm) can be regarded as a reasonable approximation at room temperature. High magnetostrictive forces and negative Ho-Ho interactions make possible such a crystal and magnetic symmetry lowering that is complicated by the low temperature easy axis reorientation induced by high order CEF terms.

Effect of ordering on magnetic properties of 6.5-percent silicon-iron alloy

The effect of ordering on the magnetic properties such as magnetostriction, magnetic anisotropy, permeability, and coercive force of 6.5-percent silicon-iron alloy has been studied. The alloys were heat-treated at various temperature, and then quenched into oil. It was found that magnetostriction decreases with the growth of DO 3 structure and magnetic anisotropy decreases with the growth of B 2 structure. By oil-quenching from 500°C, permeability became a maximum and coercive force became a minimum. The effect is caused by the growth of DO 3 structure. The improvement of the magnetic properties of 6.5-percent silicon-iron alloy was attained by controlling the ordering in this alloy through the double heat treatment. The values obtained were maximum permeability μm = 52 000, initial permeability \mu_{i} = 4000 , and coercive force H c = 0.088 Oe measured at the maximum induction of 10 kG.

Impact-induced demagnetization, magnetostriction and coercive force in co-doped iron oxide recording tapes

The saturation magnetostriction constant (λ s ) determines the remanence loss of a recording tape when an impact is applied normal to the plane of the tape. The addition of Co to iron oxide particles alters λ s and increases the coercive force. As Co is added to γ-Fe 2 O 3 , λ s becomes more negative and the stress demagnetization is greater; when Co is added to Fe 3 O 4 , λ s is less positive and the stress demagnetization becomes smaller. Impact-induced losses of up to 30% of the remanence are measured on Co doped γ-Fe 2 O 3 tapes with \lambda_{s} = -15 \times 10^{-6} ; this compares with a 1% loss in CrO 2 tapes where \lambda_{s} \sim 1 \times 10^{-6} . \lambda_{s} is measured on particle compacts using a strain gage; its value can also be estimated from the coercive force change produced when applying uniaxial tension to a tape.

Variational formulation of the electrodynamics of fluids and its application to the radiation pressure problem

A covariant formulation of classical electrodynamics is given for nonviscous, compressible, nondispersive, polarizable, and magnetizable fluids. The part of the Lagrangian density accounting for the various interactions to be existent in such fluids under the influence of the electromagnetic fields is constructed rather intuitively by introducing two four-vector variables, one to describe the states of polarization and the other to describe those of magnetization. The energy-momentum conservation law can be derived separately for the material and the field subsystems. The energy-momentum tensor of the total system cannot be split in a unique way into the material and the field parts. However, physically reasonable ways of splitting can be found so as to give one and the same result as to the electromagnetic radiation pressure in electromagnetic fluids. This pressure is shown to be $\frac{(\stackrel{\ensuremath{\rightarrow}}{\mathrm{D}}\ifmmode\times\else\texttimes\fi{}\stackrel{\ensuremath{\rightarrow}}{E})}{4\ensuremath{\pi}{(\ensuremath{\mu}\ensuremath{\nu})}^{\frac{1}{2}}}$, in agreement with experiment. This indicates that the pressure observed in experiment consists almost entirely of the "true" electromagnetic radiation pressure. For the sake of consistency, the mechanical pressure arising both from the electro- and magnetostrictive forces and the forced motions of the fluid particles under the influence of the electromagnetic radiation fields is also estimated and found, in fact, to be negligible in ordinary experimental conditions.

The tilted helix: an intermediate magnetic phase

In a system of localized spins interacting via an exchange favouring helical ordering there is a region of 'forbidden' axial anisotropy separating normal flat and conical spirals as the stable orders. The stable phase in the intermediate region is shown to be a tilted helix corresponding to tilting the planes of a normal flat spiral together with additional perturbations of pitch and out-of-plane wobble. An investigation is presented of the ordering, stability and excitation of this intermediate phase. It is proposed that the model provides an explanation of intermediate phases seen in Er-Tb, Er-Dy alloys and also Er metal itself. It is suggested that similar intermediate phases may exist in Ho and certain other alloys, although unconsidered magnetostrictive or other forces could lead to discontinuities which prevent their manifestation.

Natural frequencies and mode shapes of vibration of transformer cores

Transformer-core vibrations, which are caused by magnetic and magnetostrictive forces, are responsible for the noise radiated by the tank. Since the core is a structure consisting of distributed mass and stiffness, it has an infinite number of natural frequencies, one of which may coincide with one of the harmonics of the above forces, resulting in increased noise level. Because of the nonuniformity of the core steel, vibrations may be excited, both in the plane of the core and normal to it. The paper sets out to show how these natural frequencies can be calculated for both directions, taking longitudinal vibrations, shear deformation and rotational inertia into account. A distinction is made between cores having a large overlap at the joints and those having mitred joints with small overlap. The correctness of the mathematical model and the validity of the assumptions made for the calculations were checked on two models and two transformer cores. Satisfactory correlation was achieved between the experimentally determined natural frequencies and those calculated with the help of a computer programme.

The Effect of Dislocations on Magnetization Near Saturation

The effect of dislocations on the magnetization curve at high fields is calculated by direct use of dislocation theory. The deviation from saturation is assumed to be due to magnetostrictive forces, localized in the stress field about the dislocation rather than at the dislocation itself; their effect is more complicated than that of the simple "line concentrations of force" considered in an earlier article. Pairs of dislocations of opposite sign, separated by a short distance, contribute a term $\frac{a}{H}$ to the deviation from saturation; in this respect they resemble line concentrations. Pairs separated by a long distance and surplus dislocations of one sign contribute a term $\frac{b}{{H}^{2}}$, with $b$ theoretically not a constant but a logarithmically varying function of $H$. From data on the variation of the empirical $a$ and $b$ with plastic strain, it is possible to calculate the density of dislocations and the "block" length if a value is assumed for the distance $Y$ between the members of a dislocation pair. The orders of magnitude obtained agree with those obtained in the theory of hardening if $Y$ is taken $\ensuremath{\cong}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ cm. It appears that all but about 1 percent of the dislocations are members of such pairs.

Static and Motional Impedance of a Magneto-Striction Resonator

The equivalent series inductance and resistance of a long solenoid with nickel-steel bar has been investigated in relation to the excitation frequency for frequencies up to 14000 cycles per second. Beyond 400 cycles per second, after which only a negligible flux penetrates to the center of the bar, the inductance varies inversely with the square root of the frequency, and the resistance directly with the square root of the frequency. The product of the resistance and inductance is substantially constant over the frequency range; also, the power factor angle of the bar is substantially constant. The field for the higher frequencies is shown to be confined largely to the circumference of the bar, at which zone the greater part of the magnetostrictive force is produced. The results are discussed in relation to the theory of flux distribution in the bar. The effect of motion of the bar under the action of magnetostriction has been measured in terms of the motional impedance, and a circle diagram obtained. The ratio of motional resistance to reactance, in the vicinity of mechanical resonance of the bar, is of the order of magnitude of one to six thousand. The theory of total impedance, static and motional, is given, and the nature of the angular displacement of the resonant circle indicated.