Effective Coupling Coefficient Research Articles

New low sound velocity magnetostrictive transducer

The magnetic and magnetostrictive properties of a magnetostrictive scroll wound ring transducer made from “cube textured” nickel developed by Inco were measured and compared to the corresponding properties of a conventional nickel ring transducer. The conventional ring was fabricated by the Naval Underwater Systems Center and the “cube textured” ring; with nearly identical dimensions, by Inco. Both transducers were separately excited in air under identical conditions and their electrical input impedances measured with a pulse vector immittance meter. Using Butterworth and Smith and NDRC analyses of a magnetostrictive ring transducer, the following parameters were obtained as a function of the bias induction (1 ⩽ B ⩽ 5kG): sound velocity, Young's modulus, reversible permeability, effective coupling coefficient, magnetostrictive and stress sensitivity constants. The Young's modulus of the “cube textured” ring was 40% lower than that of the conventional nickel ring, resulting in a 20% lower sound velocity and radial resonance frequency. This reduction was obtained without any appreciable sacrifice of electrochemical coupling coefficient or magnetostrictive constant. The “cube textured” ring also exhibited a much lower loss angle.

Excitation of Two Adjacent Resonances with a Chosen Frequency Separation in a Ceramic Piezoelectric Resonator

Abstmct-In the crystal class Car (piezoelectric ceramics) the excitation and propagation of elastic waves in arbitrary directions are theoretically investigated. It is shown that among other modes a transverse wave and a quasi-transverse wave may be excited piezoelectrically. Accordingly, resonators with two adjacent resonances are possible. Conditions for the simultaneous excitation of these two mode6 are derived. The frequency separation of these two resonances may be controlled by the angle between the direction of polarization and the wave normal while the amplitude ratio is governed by the direction of the applied ac field in the resonator. An experimental verification of the theoretical results is presented for piezoelectric ceramics. H Is~rl~oI~L~~~rto s PI; conventiorlal 1)iezoclcctric ceramic rcso~~ators the direction of the e~cit~ing electric ac field is eit,ller perpet~licular or parallel to the direction of the permanent polarizatio~~. To our knon-ledge, little use is made of oblique cuts. In a Japanese patent’ [l] oblique cuts have been proposed to reduce the effective coupling coefficient of resonators being employed as F11 discriminators. 111 a paper on thin-film transducers, Foster et al. [2] use a special oblique cut for the excitation of only one mode. This paper deals with the simultaneous excitation of two thickness modes that are not, mechanically coupled. This is made possible by an appropriate choice of the direction of the ac field.

Predicting the Effective Dynamic Coupling Coefficient of the Flextensional Transducer (Preliminary Design Considerations)

Expressions for the effective dynamic coupling coefficient of the flextensional transducer have been approximated. The approximate solutions are illustrated and compared with experimental data.

Electromechanical Coupling and Composite Transducers

Measurements with composite types of transducers indicate that both the classical definition of the electromechanical coupling factor and the equivalent circuit for a piezoelectric transducer require revisions for improved consistency. The effective coupling coefficient depends on the proportion of the piezoelectric material that is employed electromechanically rather than being independent of it as implied by existing definitive formulations. Furthermore, the inherently usable coupling decreases below the fundamental resonance frequency so that it approaches zero at very low frequencies. At higher frequencies the inherent coupling factor may approach the ultimate value at a frequency specified by the dimensions and characteristics of the piezoelectric specimen in a transducer. For the equivalent circuit, the measurements favor a parallel rather than a series form for the motional or transformed mechanical impedance because the frequency for parallel resonance remains invariant with the proportion of the piezoelectric specimen that is excited electromechanically.

Effect of a Longitudinal Static Pressure upon a Magnetostrictive Ferrite

Double-dumbbell transducer elements of two commercial nickel-copper-cobalt-ferrous ferrites (Ferroxcube 7A1 and 7A2) with acoustic “pressure-release” material at each end were placed between the jaws of a hydraulic pressure testing machine. The effective electromechanical coupling coefficient for the sample was measured for various magnetizing currents and static loads. As the load was increased to 5600 lb, corresponding to 4600 psi in the narrow “limbs” of the element, the effective coupling coefficient at optimum bias decreased from 0.21 to 0.05, and the clamped inductance (which is proportional to the incremental permeability) decreased by 40 per cent.

Effect of High Static Pressure upon a Magnetostrictive Ferrite

A double-dumbbell transducer element of a commercial nickel-copper-cobalt-ferrous ferrite (Ferroxcube 7AI) with acoustic “pressure-release” material at each end was placed between the jaws of a hydraulic pressure testing machine. The effective electro-mechanical coupling coefficient for the sample was measured for various magnetizing currents and static loads. As the load was increased to 5600 lb, corresponding to 4600 psi in the narrow “limbs” of the element, the effective coupling coefficient at optimum bias decreased from 0.21 to 0.05. the resonant frequency increased by 8%. and the clamped inductance (which is proportional to the incremental permeability) decreased by 40%.

Form Factors inβDecay andμCapture

We suppose that $\ensuremath{\beta}$ decay and $\ensuremath{\mu}$ capture are described by a universal vector and axial vector Lagrangian and we consider, via dispersion relation techniques, the properties of the corresponding $S$-matrix elements. Owing to the strong interactions of the nucleons, the structure of the $S$ matrix is expected to be more complicated than that of the Lagrangian. In the former, vector and axial vector terms appear, but with coefficients which in general depend on the invariant nucleon momentum transfer; they can be thought of as Fermi interaction form factors. Moreover, two additional kinds of terms can appear in the $S$-matrix elements: one which simulates a direct pseudoscalar coupling and one which simulates a direct coupling involving derivatives of the nucleon wave functions. The latter is probably too small to have any experimental significance. The former, though negligible in $\ensuremath{\beta}$ decay, may be appreciable in $\ensuremath{\mu}$ capture. We estimate the effective pseudoscalar coupling coefficient there to be about eight times as large as the axial vector coefficient. More generally, we investigate the structure of the various form factors; and we also reconsider, in further refinement, a recent quantitative discussion which we have given of $\ensuremath{\pi}\ensuremath{\rightarrow}\ensuremath{\mu}+\ensuremath{\nu}$ decay.

Effect of Firing Cycle on Structure and Some Dielectric and Piezoelectric Properties of Barium Titanate Ceramics

In the preparation of barium titanate ceramics for dielectric and piezoelectric applications, careful attention must be given to many factors which determine the ultimate performance of the ceramic. In this study structural differences were observed with the aid of electron micrographs as the time and temperature of firing were varied. At lower temperatures and shorter firing intervals crystals remained small, grain‐boundary areas were relatively large, and there were numerous voids where several crystals joined. As the time and/or temperature were increased, crystals became larger with an improved grain‐boundary condition that resulted in better structure. An optimum condition was soon reached beyond which rounding of edges at grain boundaries where several crystals joined became more pronounced. This caused an increase in the number of voids. Accompanying these changes, the 1‐kc. dielectric constant, the piezoelectric constants (thickness mode), and coupling coefficients first improved, reached optimum values, and then declined slightly, but the resistance to depoling continually decreased as the crystal size increased. An experimental technique of rapid heating and cooling was used to prepare dense specimens of chemically pure barium titanate with relatively small average crystal sizes. Dielectric constants as high as 3000 with Q values of 80 were obtained for these high‐density ceramics, accompanied by low effective piezoelectric constants and coupling coefficients.

The Dynamic Magnetostrictive Properties of Alfenol

The magnetostrictive properties of Alfenol, a cold-rolled Fe-Al alloy, for use as the active element in electromechanical transducers were compared with those of nickel. The aluminum content of the Alfenol was varied from ten to sixteen percent. After a suitable heat treatment a maximum effective electromechanical coupling coefficient of 0.31 was obtained with 12-Alfenol biased to four oersteds. The maximum effective coupling coefficient of 13-Alfenol was observed to be approximately the same as that of nickel, 0.27. While the effective coupling coefficient of 13-Alfenol is smaller than that of 12-Alfenol, the product of the characteristic frequency times the thickness squared for 13-Alfenol biased to twelve oersteds was twice that of 12-Alfenol biased to four oersteds and four times that of nickel biased to thirteen oersteds. Performance is given for similarly constructed Alfenol and nickel transducers.