New magnetostrictive materials and transducers—II

J. Sound Vib. (1968) 8 (3), 431-456

NEW MAGNETOSTRICTIVE

MATERIALS

AND TRANSDUCERS-II

E. A. NEPPIRAS Department of Physics, University of Vermont, Burlington, Vermont, U.S.A. (Received 8 February 1968) This paper introduces new design techniques and transducer materials now becoming available which appear very promising for use in medium and high-intensity ultrasonics (sonar and industrial processing). Comparisons are made with the more conventional materials and systems.

1. MATERIALS

AND TRANSDUCERS

1.1. INTRODUCTORY Measurements have been carried out on transducers made from new magnetostrictive alloys whose properties have previously been discussed [l]. These are nickel-base alloys with small additions of cobalt and chromium. The measurements reported previously were done on what may be termed “idealized” types of transducer, chosen for convenience in obtaining the type of measurement sought. The performance of these alloys was outstanding by comparison with nickel. The aim of the present work was to see whether these good results could be reproduced on the types of transducer that are actually used in industrial ultrasonics. The work has uncovered some interesting new facts about these materials.

1.2. MATERIALS Four carefully-chosen alloys were used; compositions are given in Table 1. A-nickel was chosen as a standard to compare the others against. 4-Cobalt-nickel is the critical cobaltnickel alloy with zero magnetocrystalline anisotropy. Its electromechanical coupling and initial permeability are therefore at critical maxima. This material has been available TABLE 1 Materials used in experimental A-Nickel 4-Cobalt-nickel 2.3-1*4-Chromium-cobalt-nickel 2.25-Chromium-nickel

(with (with (with (with

approx. approx. approx. approx.

0.25 % 0.20 % 0.27% 0.27%

Mn; Mn; Mn; Mn;

work 0.15 % 0.05 % 0.03% 0.03 %

Fe; Fe; Fe; Fe;

0.06 % 0.06 % 0.06% 0.06%

C; C; C; C;

0.05 % 0.02 % a01 % 0.01%

Cu) Cu) Cu) Cu)

commercially for several years, but no measurements of its performance in practical transducers have been reported. 2*3-I.4 Chromium-cobalt-nickel is the high-resistivity ternary alloy containing the maximum practicable amount of chromium, which Clark’s measurements [2] suggest would give a good compromise of properties. 2.25 Chromium-nickel is the zero-anisotropy chromium-nickel alloy with high coupling and high resistivity. It is the same as the “optimum” ternary alloy above, but without the cobalt content. It should therefore behave a little worse in some respects, but somewhat better in others, than the ternary. 431

432

E. A. NEPPIRAS

Being a binary alloy, it would be easier and cheaper to manufacture in controlled quality. These last two alloys also have never before been assessed in practical systems. 1.3. LAMINATION DESIGN Sample quantities of these four materials were obtained in the form of 5 cm wide half-hard cold-rolled strip, O-025 cm thick. All the measurements on single, unloaded and unmounted, transducers were done on transducers made from one lamination size and shape, of an efficient window pattern, as in Figure l(1). When plate-coupled systems were studied later, a lamination of higher inherent resonant frequency was used so as to compensate for the mass of the coupling plate and to bring the system resonance near that for the free transducers (165 kHz). This provided a better comparison. The dimensions of this lamination are given in Figure l(2).

iI

41

1

k-b-M----u----+ Thickness a

b

(I)

3.7

2.9

(2)

3.7

2.2

cm

e

1

R(=c/2)

I.65

1.53

4.7

13.2

0,825

I.2

I.6

4.4

Il.8

0.60

c

I 54 I .36

0,025

d

M(=e/2d)

Figure 1. Laminations used in experimental work. All laminations of all transducers were the same thickness and width and were given the standard “soft” anneal of 800°C for 1 hr with free access to air, cooling at about 5°C per minute. During the anneal, the laminations take on an oxide coating which is available for interlaminar insulation in solid-stack transducers. For A-nickel and 4-cobalt-nickel the coating was a uniform texture and highly-insulating. But for the two chromium-containing alloys the layer was patchy, the hard coating covering only part of the surface; in other parts, the oxide was flakey and could be rubbed off. It was found that by hand-stacking, the laminations could easily be stacked so as to avoid any electrical contact. The lamination thickness (0.025 cm) was selected to bring the chosen resonant frequency of the nickel laminations near to the characteristic frequency for this thickness. This means that laminations will be a little below optimum thickness for the chromium-containing alloys, and a little above for the cobalt-nickel alloy. This is illustrated by the design curves of Figure 2, from which it can be seen that the thickness used is a good average choice for the four materials. The window lamination shape was chosen as giving a closed magnetic circuit with space and anchorage for windings in a robust structure. For this design, three otherwise independent geometrical quantities : a (half limb length); b (end-section length); M (ratio of end-section area to total limb area) are related through the propagation constant k by the following formula : cot ka cot kb = M. (1)

.

Here, k = w/v where o = 2nf is the angular frequency and v = v;~ = (Y,B,/p)“’ is the extensional-mode sound velocity at the constant flux (short-circuit) resonant frequency. If the constant-field (open-circuit or free) resonant frequency is used instead, this is expressed in terms of vysand YE where YIJ = Y&(1 - k&). The use of Young’s modulus as the appropriate

NEW MAGNETOSTRICTIVE

433

MATERIALS

elastic constant implies that lateral dimensions are everywhere small compared with the wavelength. The simple formula (1) is the one generally used; it implies that an abrupt area-discontinuity exists between the limbs and end-section. But this is not advisable in practice: radiusing should be used to avoid stress-raising at the sharp corners. When the radius (R) is half the r; = 109p7/2n2 p7 Microhm-cm 8.0 IO.5 29 0 27.0 I III 2.3-I-4-Chmmium-cobalt-

A- Nickel 4- Cobolt-nickel 2-3-l.4-Chromium-cobalt-nickel 2 25-Chromium-nickel

Lamination

thickness

pt2 ,uLRy 45 75 45 42

(mild

Figure 2. Characteristic frequency for eddy-currency loss as a function of lamination thickness for nickel-base alloys. window width and the lamination shape is near-optimum (qa) it is found empirically that the formula (1) is modified in the following way : cot&-0.215R).cotk(b+0.215R)=M.

(2)

This formula has been used for the lamination design in the present work. This equation is the only restriction on the choice of the three quantities a, b and M relative to any design frequency, so there is scope for satisfying other practical requirements, such as adequate winding space (determined by window-width); adequate area of active material (limb-width); and low-reluctance end-section (end-section depth). The design chosen, where c % d and b z 2d, has been found to be a useful compromise. We may note that for shapes near the optimum, the frequency equation reduces to any one of the following three approximate expressions, which are often preferred, as they give the frequency explicitly in terms of the geometrical quantities, whereas the exact equation has the frequency implicit and can only be solved geometrically or by some other approximate method. w* = Yfs A/a(m, + mJ3) (3) where A is the transducer limb area and m, and m, are the masses of one end-section and of one limb, respectively. Equation (3) can be re-expressed as o2 = v2/a(2bM + a/3),

(4)

w2=+u2/4(a+b)(a+b+e).

(5)

434

E. A. NEPPIRAS

The window shape, although convenient to use, is not considered as efficient as the “ideal ” radial-mode ring or the straight bar. Its mechanical Q-value is reduced somewhat due to the effect of lateral magnetostriction in the end-sections. There are also other deleterious effects which are less well understood which will be considered later. Performance of window transducers therefore cannot be inferred directly from data taken from measurements on bartransducers. 1.4.

TRANSDUCER CONSTRUCTIONS

Three types of transducer were used in the basic measurements, all constructed from the one lamination design shown in Figure l(1). (i) Solid square stacks. These consisted of 150 laminations stacked up to a thickness of 3.8 cm. The excitation winding was twenty turns per limb of 24 s.w.g. enamelled copper wire, close-wound in one layer on tape over the centre of each limb. The polarization winding was 60 turns per limb of stranded P.V.C. flex, wound over spacers, such that with the spacers removed the windings hung very loosely on the limbs, with negligible damping. After stacking and winding, the transducers were partially consolidated by running coldsetting epoxide-resin carefully into the end-sections only. This held the laminations in position, preventing relative motion, even at high intensities, with the minimum of mechanical damping. This avoided uncertainties of performance which often occur with transducers which are bonded in the limbs. Mechanical Q-values were appreciably higher than is usual with conventional window constructions. (ii) Thin stuck transducers. These were similar partially-consolidated stacks, but only 44 laminations, approximately 1 cm thick. Transducers were wound with 40 turns per limb of 22 s.w.g. enamelled copper wire close-wound over about 2 cm length at the limb-centre. In some measurements, the one winding was used for both polarization and excitation. Later, when a lower impedance was found desirable, a second winding of 20 turns per limb was used for excitation, the other being reserved for polarization. These thin-stack transducers were intended for high-energy excitation and the particular size was chosen for three reasons : the limb section was small enough to permit saturation with the input power available (about 2 kw); because of the short heat-conduction path from the limb-centre, such a slim transducer is very effectively water-cooled without danger of local overheating; the size is also convenient for making spaced-transducer-coupled systems for sonar and liquid-processing. All measurements on these transducers were taken with the transducers standing in cold water, with the bottom surface and underside of the limbs pressure-relieved by closed-cell sponge-rubber. (iii) Spaced-lamination transducers. These are designs in which the laminations are spaced separately from one another. This construction is likely to come into wide use and has many advantages. Because of the large area exposed to the cooling medium, they are effectively cooled even by air-flow, and safely operated at high intensities. It is a significant advantage that water-cooling is avoided with its attendant dangers and inefficiency. Another advantage of these transducers is that they make much easier the calorimetric assessment of loaded transducers, as the heat dissipated in the transducer is easily separated from the load by using a suitably-directed air-blast. This type of transducer, coupled through thin plates, was used in all measurements under liquid-loaded conditions; examples will be given later. They show surprisingly little tendency to vibrate in unwanted flexural modes, and potential efficiencies are not appreciably less than for solid stacks. In sonar applications, frequencies needed now are so low that very thick laminations with wide spacing would be used, and handling and assembly are facilitated. Large-area systems can be constructed with no danger of coupling into unwanted lateral modes, as the spacing automatically decouples vibrations in these directions. The spacing ratio can be increased above the efficiency-optimum to

NEW MAGNETOSTRICTIVE

MATERIALS

435

achieve whatever bandwidth is desired and to allow full utilization of the theoretical powerhandling capacity. No insulation is needed between laminations. With all these advantages, these transducers are potentially of great value. The spaced-lamination transducers used in the main series of measurements were of the same overall dimensions as the square solid-stack transducers. A total of 22 laminations were stacked over spacers consisting of plastic strips of suitable thickness (1.5 mm). The laminations were held in position by sticking four strips of thin, stiff insulating material about 2 cm wide, over the nodal regions. Two square pieces of the same material were similarly stuck over the two end-faces. In this way the laminations were held in a rigid stack. The clamps over the nodal regions were also used as formers to carry the excitation coil (20 turns per limb). The polarization coil was 60 turns per limb of stranded P.V.C. flex, very loosely wound, as for the solid-stack transducers. These spaced transducers were measured unloaded and driven up to very high power densities, always with only forced-air cooling. 1.5.

SYSTEMS DESIGN

We may in principle couple to the medium through either thin plates, comparatively thick plates moving piston-wise, giving area-match, or a fully-resonant X/2 impedance transformer stub. Advantages of the thick plate and resonant-stub couplings are that impedance-matching is obtained with piston-motion, and that the vibrator can be nodally-mounted with no loss in efficiency. Erosion is not such a serious problem and long life is assured. Disadvantages are that the system becomes massive and probably expensive at the low frequencies of interest. Also it may be necessary for the transducer-plate bond to be in a high-stress plane, with some danger of mechanical failure. The alternative technique, in which many transducers of small area are spaced on a thin coupling plate, or its logical extension, a fully spaced-lamination system, is small, light, economical, easily-cooled with better and more uniform area-matching. The only disadvantages of this method are that life may be limited by cavitation erosion of the thin plates, and that the potential efficiency may be reduced by some decrease in each of the three parameters : coupling (kerJ; magnetic Q-value (Q;) ; and mechanical Q-value (Q,B). The reduced coupling is due to unavoidable leakage and loss of flux from the limbs of such thin transducers; leakage-flux linking the coupling-plate may reduce Q;, and flexure of either transducer or plate may increase mechanical losses. The product k$, Q; Qi, in terms of which the potential efficiency is expressed, may therefore be reduced. But with careful design the combined effect of these losses need not be severe; certainly it does not overwhelm the practical advantages of these spaced designs. The best materials for the plates are stainless steels or age-hardened grades of Monel or titanium alloys [3]. Both stuband plate-coupled systems were constructed and measured. Examples are given later. Plate-coupled spaced-lamination transducers, assessed calorimetrically, were used in all measurements under liquid-load conditions; in these cases, the laminations used were those of Figure l(2). 2. MEASURING

2.1.

TECHNIQUES

INTRODUCTORY

Measurements were done over a very wide range of power-densities on unloaded transducers. The low-level measurements were usually done on the square-stack transducers in two ways: by plotting out the impedance locus point-by-point using bridge-balance; or, where possible and convenient, by a few measurements taken from the total impedanceor admittance-frequency response at constant-current or constant-voltage. The highintensity measurements on unloaded transducers were all done by bridge-balance, using a 29

436

E. A. NEPPIRAS

specially-constructed high-intensity impedance bridge. Efficiency measurements loaded systems were obtained by measuring heat dissipation calorimetrically. 2.2.

MAGNETIZATION

on water-

MEASUREMENTS

Magnetization characteristics were first obtained for each transducer. The virgin B-H curves were measured. The total flux linking one limb was obtained using a search coil of thin wire wound tightly over the centre of the limb. The magnetizing d.c. was taken through a polarization winding of 60 turns per limb and increased in small steps. The core was demagnetized between each reading by taking a.c. through the magnetizing coil, of peak value greater than the maximum d.c. used. In calculating the flux density for the solid-stack transducers, a lamination stacking factor of 0.85 was assumed, previous experience having shown that this is a reliable figure for this type of transducer. 7000 -

6000~

5000 ‘j; Y g Q

4000-

3000 -

2000 -

IOOOI 0

Figure

3.

20 240

40 480

,

60 720

I

60 960

1

Effective /-/ (oersteds) Total amp- tums

Virgin magnetization curves for nickel-base alloys.

In window-type transducers there is always some leakage due to flux generated in one limb not linking the other. This cannot easily be calculated but was measured by confining the polarization field to one limb while recording the flux in the two limbs separately. Using the incremental permeability obtained from the B-H curve, the true permeability can be estimated for any operating condition. The virgin B-H curves are shown in Figures 3 and 4. Those of Figure 3 were measured on solid-stack transducers only. As to be expected, the binary cobalt-nickel alloy shows the highest saturation B and the highest permeabilities and the binary chromium-nickel alloy the lowest. It is clear from the curves of Figure 4 that flux leakage is always small in the usable induction ranges for all alloys. Leakage is even only moderate for the spaced-lamination designs, where it might reasonably be expected to be high. In Figure 4 the ordinate scale for the spaced-lamination transducer is the apparent B, not taking account of the l-in-7 spacing. Multiplying by this factor brings the characteristics almost into coincidence with those for the solid-stack transducer. The curves show that the permeabilities, although high enough to make the correction for leakage unimportant, are much lower than have been measured on ring laminations of the same or similar materials [4]. This discrepancy has previously been noted for window transducers, but its reason is unknown.

NEW MAGNETOSTRICTIVE

437

MATERIALS

stock

,oool , ;;,Fryi 0

IO

20

30 Effective H

40

50

60

berstedsl

Figure 4. Magnetization curves for transducers in 4-cobalt-nickel alloy showing effect of fluxleakage in solid-stack and spaced-lamination transducers. (1) Field applied in both limbs; flux measured in either. (2) Field applied in one limb; flux measured in same limb. (3) Field applied in one limb; flux measured in the other.

2.3.

ELECTRICAL

MEASUREMENTS

AT LOW

EXCITATION

ON UNLOADED

TRANSDUCERS

Experience shows that at low excitation there are two extreme ranges of efficiency for which electromechanical assessment of magnetostrictors is easy and accurate; but in the intermediate range measurements are not so meaningful. 2.3.1. High-eficiency transducers These are transducers characterized by the parameter k$, Qz being 4 1, in practice, greater than about 8. This implies that the ratio Rmax/Rminis greater than about 60 (see Figure 7) and the potential efficiency greater than about 75 %. In these cases, all relevant information about the unloaded transducer can be obtained from a few measurements taken from the total impedance- or admittance-frequency response recorded at either constantcurrent or constant-voltage. The shapes of typical impedance- and admittance-frequency characteristics are given in Figure 5, which also includes a list of the formulae used to make deductions from the measurements. It is not necessary to record the full characteristic; just six quantities are needed: the frequencies of maximum and minimum impedance,f, and fa and the quadrantal frequencies relative to either of these (f, and fi or f3 and fJ; also the values of the total impedances at fr and f, (Z,,,,, and Z,,,i,J. Measurement of these two impedances involves making two voltage and current measurements. A total of eight separate measurements is therefore needed to get the six quantities Z,,,,,, Z,,,‘,,,fr, f., fi and f2. From these we deduce : (a) the real part of k,,, which under these conditions is given to a good approximation by & = (1 - U/D*), since, for a transducer as efficient as we here assume, fr and f, almost coincide with f Hand f B,respectively;

438

E. A. NEPPIRAS

(b) for the same reason, Q,” is given approximately byf,/(f, -f,); (c) Qli: is similarly fp/(f4 -f3) ; alternatively, QE is obtainable from the approximate formula (Q3' = Pk&d(1 - &)2/kk (d) Qz is then obtained from the relation k&/Q; = I/Q: - l/Q:, that is, P,=& Q!LQXQ:- Q3. All the elements of the equivalent circuit are now deducible, as well as the potential efficiency. The complete admittance or impedance locus can also now be located if required. The simplest way to do this is to note that the centre of the impedance circle lies on the circle,

Q: ~:fil(A -.fi) Q: =Mh

-A)

k:rr s 1 - CfxJY

x; = cG., - &iJk:n xc=-GaxZ*inlX~

Qf

Q,Z = k:rr Q: Q:/tQ: - Q!l2 a

cz(1 + k:rr Q: Q:)-“’

?Ipot= (1 - 4/u

+ 4

v& Obtained from f, and the frequency equation

y,“, = p(v!,)* p;, x IX;. 109/8.rr2Ad f. k:, = &u h:, = k:, Y,B,IP:, 4, =&/Ml

I,

- k:,)

r,

Figure 5. Total impedance- and admittance-frequency characteristics. centre the origin, radius (Z,,,,, +2,,,)/2, since the impedance circle must touch the two circles, centre origin, radii Z,,, and Zmin. Also, the clamped reactance is given by Qz and since to a good approximation, the reactance co-ordinate J$ = (Z,,, - Z,&f, of the centre of the impedance circle is XCwhere X; . Xc = Z,,, .Zmin, the circle can be located exactly. The procedure is illustrated in Figure 9. Having located the circle we can obtain f n and f Bexactly if we assume linearity of the response. To do this, the motional diameter and the diameter normal to it are drawn in. A linear scale of frequencies is set up on this normal on a scale determined by the intersections off, and fi projected through the clamped point, as illustrated in Figure 9. The frequencies corresponding to f HandfB and their quadrantal points can now be read off from their projections on the linear scale. kerf is then obtained more exactly from ki&= (1 - (f"/f73. Similarly, the more exact values of the other frequency-dependent parameters Q,B, Qi, etc., are obtained. However, for the condition noted above, where k& Qg 4 about 8, this correction is insignificant and to the accuracy required, f, and facan be taken to coincide with f Hand f B. For the transducers used in the low-intensity measurements, care was taken in the mechanical construction to achieve a high value of Qm. For some of the unloaded transducers at

439’

NEW MAGNETOSTRICTIVE MATERIALS

low level, the above efficiency condition was found to hold, and the simple analysis was therefore used. The experimental set-up is shown in Figure 6. The series resistor R was large and the parallel resistor R, small compared with any impedance in the resonant range of the transducers. The voltage across the small series resistor R2 was used as a measure of the transducer current. With high-efficiency transducers, the impedance reaches such a low value around fn that precautions are needed to eliminate or correct for leakage impedances (leakage inductance and copper loss in windings). In the method advocated by Piggott and Kendig, a self-compensating method is used to balance out both the clamped and leakage impedances [5]; Van der Burgt balances exactly the leakage impedance once and for all [6]. In the present work, with the excitation coil wound closely and directly on the limb, leakage inductance can be neglected. The leakage resistance, including lead-resistance was measured

Constant-current

measurements

R >a Z,.,

Constont-voltage

measurements

R~BR2c
L, IOOmH

L, 100

m/f

Figure 6. Experimental set-up used for measurements using the total impedance and admittancefrequency characteristics. on a precision impedance bridge to be 0.1 ohm typically. Where significant, a correction was made by shift-of-origin of the impedance plot. Polarization of the transducer was at d.c. using batteries. Some exploratory measurements, using rectified mains, showed that even a minute ripple remaining interfered too much with the voltage measurements to be tolerable. The inductance of the choke L,, which had low d.c. resistance, was at least 100 times that of any transducer tested. Referring to the typical characteristics shown in Figure 5, it is clear that the impedance-frequency response can be used to locate f, accurately, but because of the flat minimum, the indication it gives forf, is not precise. To locate this frequency we can make use of the admittance-frequency response, which does peak sharply. To locate A, therefore, measurements were done at constant-current, while for fU constant-voltage was used. The eight quantities fr, f., fi, fi, V,, V,, Z, and Z, were measured at a large number of increasing values of the polarization field for each of the twelve transducers, and the above deductions and transformations made. The transducer core was demagnetized between each setting of Z,. 2.3.2 Low-eficiency

transducers

These are transducers for which the parameter k$r QE is not much greater than unity, in practice, less than about 3. This implies that the ratio Rmax/Rmin is less than about

440

E. A. NEPPIRAS

10 and the potential efficiency below 50 %. For such transducers, the impedance or admittance circles do not approach the reactance axis very closely. The approximate method of measurement outlined above is now hopelessly inaccurate and performance is best assessed by bridge balance. The latter method is now very accurate because measurement of small resistancedifferences is not required as the circles do not approach closely to the reactance axis. Once the circle has been located and the origin shifted to take account of leakage impedance, the

i+, X,, R,, R,, 4 fR,fB, fl ad A arereadoff directly from the impedance circle L; = X,l2wfH

Q; = &YR, Q:: -f”Kfz -fA R, = Z,$ D - R, L,,, = Q:(R, + R,,,)/2nf H - L,, y* cm = 1/L###(27rf ktn = 1 - (f H/f 9’ = LpKL, + Lm) Q: = 2vf BLmIR, a = ~Rmi.lRm.3”’ q,t z (1 - 4/u + 4 p, = (pdprw)

(R3/6An”)

Figure 7. Geometrical relations of the impedance circle plots. analysis for separation of the elements of the equivalent circuit and other parameters of interest is straightforward. The geometrical constructions and relevant formulae are given in Figure 7. A special impedance bridge was constructed to cope with these measurements, one object being to make the bridge useful at very high intensities. A Maxwell-Wein circuit was used, as in Figure 8, which also shows a block-schematic of the complete measuring set-up. One

Figure 8. Impedance bridge used in experimental work. C, 1000 pF; R, 50,000; R,, 1M; R1, 0.75 100 W; L, low-resistance goes capacitive; L,, polarization choke 100 mH.

inductor added only when transducer

arm of the bridge through which the transducer excitation current flows, is a very small resistor. Measurements were always taken at constant-current, measured as the voltage across this resistor, The bridge was calibrated against standard inductors and resistors at a frequency of 16 kHz, near the resonant frequency for all transducers.

NEW MAGNETOSTRICTIVE

2.3.3. Medium-eficiency

MATERIALS

441

transducers

These are transducers for which the parameter k& Qi is between about 3 and 8. This is between about 10 and 60 and the potential efficiency implies that the ratio Rmax/Rmin between 50 and 75%. This is a region where neither bridge-balance nor direct deductions from the total impedance-frequency characteristics are quite adequate. But a judicious combination of the two methods may be used. Alternatively, a method of successive approximation based on the measured impedancefrequency response can be applied. The apparent position of the circle is first located as explained in section 2.3.1 above, and f H,f*,QE and keff obtained. We may now derive

f, 16085

Figure 9. Sketchillustrating the method of successive approximation for plotting out the impedance circles from information from the total impedance-frequency characteristic. From the measured values of fi, f., f, , f2, Z,, Z. we deduce : k& = 0.0393 ; Q,” = 88.5 ; X, = 22.5 ; XC = 5-3 ; k&Q,” = 3.48. After locating the impedance circle from these data and applying a linear interpolation to get the values off H,f B,f; and fi we deduce: k& = 0.0375; QE = 98.0; X, = 21.4; X, = 5.6; k& Q,w = 3.68. values for Xi, and therefore XC, more exact than those from which the circle was drawn. This locates the circle more accurately, from which, in turn, more precise values for the above parameters can be derived. The position of the circle is approached by a series of approximations. The method becomes very laborious if more than about two applications are necessary. Figure 9 illustrates the technique. 2.4.

MEASUREMENTS AT HIGH EXCITATION

Measurements involving deductions from the impedance- or admittance-frequency characteristics are restricted to low-intensity, as constant-current or constant-voltage drive must be used. For high-intensity measurements on unloaded transducers the impedance

442

E. A. NEPPIRAS

plot must be obtained by bridge-balance. The method is generally accurate enough because, due to increased magnetic loss at high drive, the circles do not approach closely to the reactance axis. Excessive heating of the transducer may limit accuracy at high excitation. Measurements were taken on either the thin-stack transducers, which were water-cooled, or the spacedlamination types, cooled by airflow only. For the thin-stack transducers, all exposed radiating surfaces-end-faces and undersides of the window-spaces-were pressure-relieved using thin sponge-rubber, and the transducer placed in a large tank of water. To further avoid possible over-heating, the drive current was switched on for just enough time to permit the bridge to be balanced, usually a few seconds only. 3. EXPERIMENTAL

3.1.

MEASUREMENT

OF FUNDAMENTAL

RESULTS

AND

DISCUSSION

CONSTANTS

Low-intensity measurements were done on the square-stack transducers under unloaded conditions. All results are displayed in Figures 10 to 17. Figure 10(l) gives the measured electromechanical coupling for A-nickel and the 4-cobaltnickel alloy. It must be remembered that these are “effective” values for the window shape. 03

o,2-

jf&yQ

0.1

I I

2 3/p.’ -I 4-

,,_

1 I

I I

I I

I I

I I

Chromium-copalt

- nickel -_x

0.1 -

4-Cobalt-nickel

2 5 Chromium-nickel

*

+.:

0304-

-

oz-

0 I’

1 IO

I 20

I 30 Effective

I 40 H (oersteds) (1)

I 50

I 60

0

I IO

I 20

I 30

I 40

I 50

I 60

Effective H (owsieds) (2)

Figure 10. Effective electromechanical coupling as a function of effective HP.

For the cobalt-nickel alloy, coupling is rather critically dependent on magnetization, especially near the maximum, due to the critical nature of the alloy, near zero anisotropy. as to be expected, although the H-value required to The peaks of coupling occur at 0.7 B,,,, achieve this is greater than would be expected from other published results [4]. However, this sort of discrepancy has been previously noted for window-type transducers. Figure lO(2) gives the corresponding measurements of effective coupling for the chromium-containing alloys. For these, the measured values of coupling are appreciably less than would be expected from Clark’s results [2]. The reduced coupling must be due to the effect of oxygen penetration

NEW MAGNETOSTRICTIVE

443

MATERIALS

into the laminations during the heat-treatment.

The laminations used by Clark were treated in an oxygen-free atmosphere, so this complication did not arise. In Figure 11 are plotted material coupling constants which have been deduced from the “effective” couplings recorded in the previous figure. The effective coupling depends on the shape of the transducer in so far as it affects the distribution of stress and magnetic flux in the material. The correction-factor to be applied to convert to the material-constant can therefore be calculated from the dimensions [7]. The factor does not depend on the nature of

lG$z~~ 2.3-l.4-Chromium-cobalt-nickel I 10

0

I 20

I 30

Effective

I 40

/ 50

I 60

\

H (oersteds)

Figure 11. Coupling material constant k3, as a function of effective Hp. the material, but only on the transducer shape and its mode of vibration. Referring to reference 7, this factor has the value (7r2/8. 1*02)‘/2= 1.1 for the particular lamination shape used. After making this correction, the coupling is obtained as it would be measured on a radialmode ring transducer of the same material carrying the same polarization flux, and is the material-constant k,,.

0

I

IO

I

I

t

20

30

40

Effective

H

(oerstedsl

a

50

I

60

Figure 12. Reversible permeability as a function of effective H,. For A-nickel, the material-constant peaks at O-30, which is the generally-accepted figure; that for the binary cobalt-nickel alloy is O-50, very near the figure quoted by Clark [4]. On the other hand, the values for the chromium-containing alloys-about 0.24 and O-26-are much less than those measured by Clark (about 0.37).

444

E. A.

NEPPIRAS

Figure 12 shows the reversible permeability for A-nickel and 4-cobalt nickel as a function of the polarizing field. The data were deduced from off-resonant reactance measurements, taken on either side of resonance. The reactance is given by XP = 4~rAwN~~.,,,/l. lo9 ohms, where A is the limb cross-sectional area, o the angular frequency, and N the total turns on the excitation winding. In our case, taking the resonant frequency to be 16,000 Hz, prey = _%‘p. l-26, with XP expressed in ohms. Strictly, the relation between XP and preVwill be modified by leakage, but we have shown this to be a small effect, and it was ignored in the calculations. The results are just about what might be expected. The binary cobalt-nickel alloy shows the highest permeability, approaching an initial value of about 200. The characteristics should not continue to rise steeply to zero field, but will bend back to some extent. Another parameter obtainable from off-resonant impedance measurements is the dynamic resistivity of the core material @,.). The ratio @,/p-L),where p is the d.c. incremental permeability, is valuable as a magnetic figure-of-merit for the material. At low enough frequencies, the clamped impedance locus is a circular arc, radius R = (3/2)(X,)(f,/f,) where f0 is the resonant frequency and f, the characteristic frequency of the material for eddy-currents cfC = 109p,/4n2@*, where t is the thickness of the lamination). In our case, where the

15.7 15+ .

L IO

I 20 Effective

Figure 13. geometrical

I 30

t 40

I 50

I 60

.

HP (oersteds)

and antiresonant frequencies cf, and f.) as a function of effective

factors are t = 0.025; A = 6; N= 40; I= 15, all in c.g.s. units, we obtain microhm-ems. From the geometry of the impedance W/4 = ~W~rcv circle (Figure 7), R = Q,X,,/2 = Xi/2R,. This parameter is independent of frequency at low frequencies. It is clear that the resistivity defined in this way is dependent on magnetic condition, and so can be expected to vary with polarization and drive level. In fact, the measured values do show wide variations and near maximum-coupling induction are appreciably less than the figures generally quoted for these alloys. The constant-field and constant-flux resonant frequencies of the solid-stack type transducers were recorded as functions of polarization field. Results are displayed in Figure 13. The constant-flux resonant frequency (shown by the upper curves) is not very dependent on magnetic condition and increases very slowly with Hp. The changes in the constant-field resonant frequencies are much greater, and reflect the changes in coupling. The relative difference between the two frequencies at any point is approximately half the square of the coupling.

pr = W*bfN*)

NEW

MAGNETOSTRIMVE

MATJBIALB

445

Using these resonant frequencies and the geometry of the window shape used, the sound velocities z$ and D&and the elastic constants Yry and Y,: were derived, using the modified form of Camp’s formula : cot k(u - 0~215R). cot k(b + 0.215R) = M = e/2d = 1.54 where R = O-825; a = 3.7; b = 2.9 cm. This gives k = 0.2054 cm-‘, Camp’s equation being cot (O-2054.3.077). cot (0.2054.3.523) = 1.54. The sound velocities trj3 are now obtained from u33= (w/k) = (2rf/k) = 30~59f cm/set and the elastic constants Y3, from Y33= pt$3 = 4n2pf2/k2 = 8330f 2 dyne/cm2, taking p = 8.9 andfin Hz, the constants referring either to the constant-field or constant-flux conditions. Results are recorded in Figure 14.

Effective

Figure 14. Extensional-mode

H (cersteds)

elastic constant calculated fromf’ as a function of effective H,,,

Having obtained the relevant magnetic, elastic and magnetoelastic constants k33, pS3 and Y& we can now deduce, without further measurement, the two sensitivity constants of interest: the magnetostriction constant h,, = (&/8B)S and the stress-sensitivity d33= @B/&T)~. These are related by II,,.~~~ = k:,/(l -k:,), where kg, = h:3 .P;~/ Y&. This gives the five magnetization-dependent constants of greatest interest: k,, ; pT3; Yt3 ; h3, ; and d33. These are listed together with other data in Table 2. The other parameter of interest is the potential efficiency. This is a symmetrical function of the three constants of the free transducer: coupling; Q; and Qg. Coupling we have already shown. By way of example, Figure 15 gives measured values of Q, for the binary chromiumnickel alloy taken at low excitation on all types of transducers, at different times. They include direct measurements from impedance plots, and derivations from the more accuratelymeasured quantities kefr, QE and Qi. The scatter reflects the wide range of different measurements from which the information was obtained. The Q-values increase steadily with increasing magnetization, and become large near saturation. Although not shown in the figure, Q-values for the other chromium-containing alloy fall a little below these, followed by nickel, with those for the binary cobalt-nickel least of all. From the measured d.c. incremental permeability (p) and resistivity, it is possible to calculate the contribution of eddy-current loss, and therefore the magnetic Q-value which relates to this. Bozorth [8] quotes the formula: Q, = (sinhe + sinB)/(sinh8 - sin@. Here 0 = ~&(JL./~J’/~. The dependence of Q,, obtained from this formula, on the magnetic field, is shown by the broken-line curve in Figure 15. Not surprisingly, calculated Q-values lie well

446

E. A. NJZPPIRAS TABLE 2 Measured constants for nickel alloys

Material

A-Nickel 4-Cobalt-nickel 2.3-l .CChromiumcobalt-nickel 2.25-Chromiumnickel

0,265 044

69 60

56 58

0.30 0.50

56 80

2.2.10” 2.13

1.7.104 2.3

0.23

75

66

0.26

44

2.22

1.6

4.5

0.215 ,

80

53

0.24

35

2.185

1.7

3.65 240 -34 ---JWJ From other published data

From the measurements

reported in the text

260

-33

Z25 Chromium-nickel

Alltransducers I

6. 1O-6 360 -42. 1O-6 13.3 410 -38

I

I

I

I

I

IO9-

2l-

0

1

I

I

I

I

I

I

IO

20

30

40

50

60

Effective

I

H (oersteds)

Figure 15. Q”,as a function of effective HP for 2.25 chromium-nickel

transducers.

above the measured values. The calculated values take into account only eddy-current loss in the laminations, whereas other losses, notably hysteresis, must be involved in practice. Mechanical Q-values Qi and QE were measured or deduced for both resonant frequencies. These were both obtained in three different ways : from the total impedance- and admittancefrequency responses; by fixing the quadrantal points on the measured impedance circles; and from the approximate formulae :

QZ = CL,,/&)

(1 - &YkGf

and

QE = GL/Zmd’~2

(1 - k&P&.

447

NEW MAGNETOSTRICTIVE MATERIALS

The constant-field (or open-circuit) Q,-values (Qt) must be very magnetization-dependent, as they include all the effects of electromechanical coupling. Measurements also show that the response aboutf, (orf”) may be very asymmetric even at low level. This asymmetry is very marked at low polarization, and reduces as the magnetic bias is increased. Eventually it almost disappears near saturation. It is much the greatest for the binary cobalt-nickel alloy, less for A-nickel and very small for the chromium-containing alloys, except at low polarization. The constant-flux Q,-values (QE) also depend on the state of magnetization. The variation is large for the binary cobalt-nickel alloy, less for A-nickel and extremely small for the chromium-containing alloys. The loss-factors (QE)-i are plotted out as functions of the effective field in Figure 16 for all alloys. The (Qg- * - H, characteristic is also shown for the binary chromium-nickel alloy. The total loss is sometimes large at zero magnetization Constont-flux

mechanical

loss factor

4-Cobalt-nickel

0.03

-

I. _E 0

2.3-I’4-Chromium-

0

I

I

I

I

I

I

I

IO

20

30

40

50

60

Effective

J

H (oersteds)

Figure 16. (Q,,J-l as a function of effective HP. and decreases towards saturation. The results refer to transducers of the same mechanical construction (square-stack transducers) and it can be seen that the loss approaches about the same value for all transducers as saturation is approached. This limit clearly refers to constructional mechanical losses-interlaminar friction, winding friction, etc.-which will be about the same for all transducers, and is rather low for the efficient constructions used here. It seems clear that the magnetization-dependent part of the loss in the case of Qz which is not affected by coupling, must be due to micro-eddy-currents. On the other hand, Qt will include the effects of all magnetic losses and must also be affected by the contribution of the varying coupling on the elastic compliance. At zero and saturation magnetization, keff is zero. At these extremes, therefore, QE and Qi coincide. In both cases, the difference between the loss at zero magnetization and that at saturation must be due to micro-eddycurrents. This can therefore easily be separated from the total loss. The effect is so great for the cobalt-nickel alloy that further investigation is called for.

448

E. A. NEPPlRAS

Micro-eddy-current losses are due to local stress-interaction between individual domains. The magnetization vectors add to zero on the macroscopic scale, but the integrated energy is finite and may be large. The loss factor from this cause is Q-’ = 6 = 471~J,’ Y12f/pq: where J, is the saturation magnetization, Y is Young’s modulus, f frequency, Us internal stress, pI electrical resistivity, and I is a characteristic length which defines the range of action of internal stresses. This component of loss is therefore proportional to frequency, inversely proportional to resistivity and to the square of internal stresses, but independent of the external stress. Since external magnetization permits less freedom of motion between domains, these micro-eddycurrent losses will be greatest at zero magnetization and will decrease with applied field. This is just what we observe. Note that Q-l = 47r2Ji Y12f/pra: = (l/t)2 d2 since 8 the eddycurrent phase-angle = 2rtOtflp,)“2 and Jt/p = u:/ Y. It seems we must assume that this I

I

301

I

I

I

I

2.3~1.4-Chromium-cobalt-nickel

60-

I

I

I

I

I

I.2

2.4

3.6

4.8

6.0

I 7.2.10’

Totol amp-turns

Figure 17. rlpOcas a function of effective Hp. formula will break down if any dimension of the material becomes comparable with, or less than, the characteristic length 1. For well-chosen laminations, the lamination thickness, t, will be near the penetration depth for eddy-currents: (pr/pf)- ‘i2. In this case, it is realistic to substitute t for 2 giving Q-l E 02. The lamination thickness therefore becomes all-important in determining both macro- and micro-eddy-current losses and therefore in fixing both the magnetic and mechanical Q-values. We conclude that laminations should be chosen much thinner than would be predicted from normal macro-eddy-current theory. This applies especially to the binary cobalt-nickel alloy. Alternatively, the polarization may be pushed well towards saturation, with substantial increases in both magnetic and mechanical Q-values, even at the expense of reduced coupling. We see the effect of this on the potential efficiency in Figure 17. From the effective coupling and the two Q-values, we can calculate the theoretical potential efficiency, which is a symmetric function of all three. The “transducer loss factor” a = (1 + /& Q, Q3-‘/2 is first derived. The potential efficiency is then given accurately by qpOl= (1 - a)/(1 + a). Results for the four alloys at low intensities are displayed in Figure 17. The efficiencies obtained are all quite high, considering that they refer to window-type

NEW

MAGNETOSTRICTIVE

449

MATERIALS

transducers, which usually show up rather badly in this respect compared with rings and straight bars. This inferior performance is due to the effect of lateral magnetostriction in the end-sections of the window structure reducing the mechanical Q-value. Our construction is appreciably better than average and frictional losses are quite low. The two chromiumcontaining alloys show peak efficiencies around 75 to 78 %. These high values reflect their high magnetic and mechanical Q-values at high polarization. They are believed to be the highest ever recorded for laminated window transducers. The peak for the cobalt-nickel alloy (59%) occurs at a relatively high polarization due to the significant increase in eP and Qi as saturation is approached, despite the reduced coupling. For all materials, the peak efficiency occurs at a polarization much greater than that required for maximum coupling. The curves were calculated using figures for keff and the window shape. Substituting k,, for keff the efficiency figures would of course be somewhat greater. 3.2.

MEASUREMENTS

ON UNLOADED

TRANSDUCERS

AT HIGH INTENSITY

Two types of transducer were used in these measurements : thin stacks, which were watercooled after pressure-release; and square-section spaced-lamination transducers, cooled by air flow. To avoid excessive heating, the impedance measurements were got by bridgebalance, with the excitation switched on for the minimum time needed to get a balance at each frequency. A few frequencies were chosen in the resonant range and a balance obtained I

I

I

I

I

Figure 18. Electrical impedance plots for thin-stack transducers of 2.25 chromium-nickel alloy at increasing excitation. Excitation current: x ,05 A; 0, 1.0 A; 0, 2.0 A; A, 3.0 A; A, 4.0 A. at several increasing values of excitation at each frequency, the polarization remaining at a constant set value. In this way we could see how the impedance vector at each frequency was affected by the drive intensity. A typical set of results for the chromium-nickel thin-stack transducer is shown in Figure 18. A circular locus is always obtained at first and this decreases in diameter with increasing intensity. The circle later distorts, becoming squashed inwards in the direction of reducing R and also pushed upwards in the direction of increasing reactance. It is of course questionable how much meaning can be attached to impedance measurements under non-linear conditions, as the bridge balance is obtained only at the fundamental frequency.

450

E. A. NEPPIRAS

It seems likely that three different physical effects combine to account for the effects of increased excitation on the impedance locus. (i) The reduced diameter of a circular locus is probably due mainly to distortion of the drive flux wave-form by operating on a non-linear part of the magnetization characteristic. In this case, the flux wave-form has a steady component which will subtract from the set value of polarization if the transducer was initially polarized above the knee of the curve. If, as in our case, the polarization was initially set near the maximum-efficiency value, the efficiency and therefore the circle diameter will reduce, as observed. But, depending entirely on the position of the biassing point, the efficiency might have increased or decreased, and the circle diameter might move in either direction. Reduced efficiency from this cause could be compensated by adjusting the polarization at the same time as the excitation level is changed.

Maximum

input power density (w/cm* of limb section)

Figure 19. Maximum resistive component of measured impedance as a function of maximum input power density for all alloys. It is not clear whether this effect could also be responsible for any of the non-circular distortion. (ii) Non-circular distortion of the sort observed has usually been ascribed to local heating of the transducer [9]. If the temperature in the high-stress region approached the Curie point the magnetomechanical constant would fall rapidly. Although the Curie point for the alloy shown is indeed low (about 240°C) we can reasonably suppose that, because of the precautions taken, any effect from this cause must be small. (iii) Another possible reason for non-linear distortion is increased magnetomechanical hysteresis. This is hysteresis between the magnetomechanical constant, hi,, and the stress u. The loss-factor from this is 6 = 4 YZ5/3a/3, where fl is the coefficient defining the stressdependence of the coupled elastic compliance, /I = a(l/ YjT)/%. Although independent of frequency, this loss factor is proportional to the stress amplitude. Its effects would therefore be seen between certain frequencies in the resonant range where the stress exceeds some threshold value, as we observe. This loss-factor is also proportional to the second-order constant /I which must be rather high for this binary alloy. It is of interest to note that distortion of the impedance circle in the other direction, the so-called cusp distortion, is obtained with low-Q transducers and is due to variation of the clamped electrical impedance round the locus. Our transducers, being unloaded, were operating at rather high Q-values, so this distortion is not great. For loaded transducers, it is possible for the two types of distortion to appear to compensate one another giving a spurious circular locus.

NEW

MAGNETOSTRICTIVE

451

MATERIALS

Clearly, we cannot apply the routine methods of analysis to distorted impedance plots. But it is instructive to see how the maximum resistive component of impedance depends on the power density. This is a convenient way of showing the degree of the distortion. The relevant plots are given in Figure 19 for all four alloys together. The binary cobalt-nickel alloy shows up best in that the impedance circles retain their size up to high intensity; they show hardly any distortion up to power densities of about 50 w/cm2. Therefore, despite the fact that this alloy showed the lowest vPot at low excitation, it should retain its efficiency at high level. By contrast, the binary chromium-nickel alloy seems rather inferior in this respect. In making these pronouncements, we must remember that a fixed polarization was used, that for maximum qDotat low excitation. The material would have shown up better if the polarization had been increased in step with the drive to compensate the rectifying effect mentioned above.

0

2

4

6

8

IO

12

14

R (ohms1

Figure 20. Electrical impedance plots for spaced-lamination transducers of 2.25 chromiumnickel alloy at increasing excitation. Excitation current: X, 0.5 A; ?? , 1.0 A; o, 2.0 A; A, 3.0 A; A, 4.0 A; v, 5.0 A.

Figure 20 shows results similar to those of Figure 18, taken at increasing drive for the same alloy, but using the square-section spaced-lamination transducer with only air flow cooling. The inner locus refers to an input intensity of 60 w/cm’ of the limb cross-section. We can estimate potential efficiency for the circular plots; this starts at about 60% and reduces to about 45 ‘A before the severe distortion sets in. 3.3.

MEASUREMENTS

ON WATER-LOADED

TRANSDUCERS

AT HIGH INTENSITY

Spaced-lamination transducers were used for these measurements, chiefly because with this construction it is easy to match to the acoustic load, and also to separate transducer losses from power-dissipation in the load. A typical system for which measurements are reported here consisted of 300 laminations of A-nickel spaced at a previously determined optimum ratio, about I-in-6. The transducer was fixed with epoxide resin adhesive to a thin (0.1 cm thick) stainless-steel coupling plate, working into a large tank of water. The lamination dimensions are given in Figure l(2). They are of the same thickness, but somewhat shorter 30

452

E. A. NEPPIRAS

than those used in the other measurements reported above. The dimensions were chosen to bring the resonant frequency, plate-coupled, near that for the free transducer. To measure the acoustic power dissipated in the water, the outside of the tank, including exposed parts of the base-plate carrying the laminations, was lagged with glass fibre sheets. The transducer was cooled by a number of forced-air jets, directed through and across the laminations, carrying the heated air away from the coupling plate. An advantage of spaced laminations is that they are easily cooled in this way. Calorimetric assessment of output power is therefore simple and reliable. The input power to the transducer was measured by a thermocouple wattmeter. Preliminary measurements were done to decide the optimum spacing needed to match into water at the intensities used in practical systems (about 1.5 w/cm2 at the work-face). This optimum spacing arises not only because the area-matching runs through an optimum, but also because the potential efficiency falls off slowly with increased spacing. The curve showing the effect of spacing on the electroacoustic efficiency (Figure 21) suggests an optimum spacing of about I-in-6.

0

/

I

2

4

I

6

Lamination

spacing ratio

I

I

8

IO

1

(air-nickel)

Figure 21. Optimum spacing for spaced- lamination transducers. E. B. Wright measured an optimum spacing ratio, for a water-loaded nickel transducer of about I-in-11, compared with l-in-6 recorded here [lo]. This difference may be due to his use of a thicker plate, although he states that the result was independent of plate thickness, which suggests that plates of all thicknesses vibrate piston-wise at all spacings. But although the optimum shown by the curve of Figure 21 is only I-in-6, the peak of the curve is very flat, and it may well be more economical to use a larger spacing ratio, economizing in material at the expense of only a slightly reduced efficiency. The power-handling capacity of the material will allow this. 100 60-

I

I

I

1’

I

for maximum

I

I

C.W. excitation,polarized efficiency

_P

I /

0 1

0 Input electrical

power (w)

I 12 w/cm’ in the material 2 w /cm2 in the liquid

Figure 22. Calorimetric measurements on water-loaded spaced-lamination (300 laminations of A-nickel, spaced l-in-6 on 0.1 cm thick steel plate).

transducer

system.

NEW MAGNETOSTRICTIVE

MATERIALS

453

Results of the calorimetric measurements are given in Figure 22. They refer to two different methods of excitation and polarization. For C.W.excitation on d.c. polarization set at the low-drive maximum-efficiency point, the measured efficiency is 51%. This must be near vpot. In the other method, polarization was a.c. at line frequency, and the excitation was also modulated at the line frequency and in phase with the polarization. I,, was adjusted so that the peak polarization flux was near that for maximum potential efficiency. This is a very economical method to use with liquid-loaded industrial equipment. A useful efficiency of 42 % was obtained, which seems to be almost independent of the drive intensity up to the maximum used. This is in fair agreement with impedance measurements previously reported for nickel. 4. GENERAL DISCUSSION

4.1.

SUMMARY OF RESULTS ON MAGNETOSTRICTIVE

ALLOYS

The transducer parameters of interest in sonar and industrial ultrasonics divide into four groups: (i) fundamental constants; (ii) parameters defining stability; (iii) limiting constants; (iv) practical, constructional and economic factors. Not all these quantities were investigated in the present work. The first 8 columns of Table 2 give constants inferred from our measurements and the complete table covers data in the groups (i) and (iii) above. 4.1.1. Fundamental constants The five important magnetization-dependent material-constants are given in columns 4 to 8 of the table. psjr was deduced from off-resonant measurements of reactance; kj3 from the effective coupling; and Y& from the measured constant-flux resonant frequency. A33 and ds3 were then deduced from formulae without further measurement (see Figure 5) yPot was calculated from three measurements on the free transducer : keff, es, and Qi. The most important parameters in this category are the coupling and thepotentialeficiency. The measurements confirm the high value of coupling for the binary cobalt-nickel alloy, previously reported [4]. This figure (51%) is higher than for any other magnetostrictive material in this mode of vibration, so this alloy is clearly the one to use when high bandwidth is essential. The measured coupling for both of the chromium-containing alloys was appreciably less than quoted elsewhere [2]. Q-values are all high for these alloys, leading to high potential efficiencies under linear drive. To retain these efficiencies at high excitation, the biassing point must be taken well towards saturation. For the 4-cobalt-nickel alloy, efficiencies are lower but also less dependent on the level of excitation. They can be increased at high excitation either by taking polarization further towards saturation-where increased Q-values more than compensate for reduced coupling-or by using much thinner laminations than would be predicted from macro-eddy-current calculations to reduce the abnormally high micro-eddy-current losses which occur in this material. With these reservations our results are in fair agreement with data communicated by International Nickel Limited [I, 111. 4.1.2. Parameters defining stability

The properties of the Ccobalt-nickel alloy are found very dependent, sometimes critically so, on the magnetic biassing point. But this is not likely to limit its value seriously, as the bias can usually be held very stable. Dependence on time, temperature and stress were not measured. Time-dependence of properties is probably too small to be worrying for any metallic materials. Temperature dependence has recently been measured by others [12] and found to be small.

454

E. A. NEPPIRAS

All nickel-base alloys have negative magnetostriction. This means that the saturation value is reduced by positive stress, as would arise in deep-sea sonar. But it has been shown elsewhere that the vital parameters are not much affected by the stresses likely to occur [13]. 4.1.3. Limiting constants The last two entries in Table 2-saturation magnetostriction (LI) and Curie temperature (C)-have not been measured but are extracted from reliable sources [2, 11, 141. rl and F limit the power-handling capacity of the material [14]. It has often been stated that the comparatively low strain obtainable from magnetostrictive materials compared with piezoelectric ceramics will restrict their power-handling capacities, so as to make them uncompetitive for sonar applications. But this may be due to a misunderstanding. It has been shown both theoretically and experimentally [14, 151 that the power-handling capacity for nickel (and therefore also for the nickel-base alloys) is sufficiently high so that the practical limit will be set by the efficiency of removing heat from the material, not by II or F. In this respect, metallic materials are all clearly superior to ceramics: not only is the thermal conductivity greater and the effects of thermal strains less, but the transducer designs we have described are much more easily cooled, even by air-flow. The value of spaced-lamination designs has been demonstrated. Alloying chromium with nickel reduces the Curie point at the rate of about 50°C per 1% added chromium. Starting with nickel (C = 358°C) or the binary cobalt-nickel alloy (C = 410°C) about 2.5% chromium is as much as could be tolerated. But we can note that the other binary cobalt-nickel alloy which shows a peak of coupling (18-cobalt-nickel) has a much higher Curie point (C = 570°C). This would stand the addition of at least 5 % chromium before its Curie point became dangerously low. Such an alloy would show higher resistivity than any other tested so far; its coupling would also be high. On the other hand, with 18 % cobalt, it would be more expensive than any of the others. 4.1.4. Practical, constructional and economic factors All the nickel-base alloys are easily worked, soldered and hard-soldered, are sufficiently corrosion-resistant and only a little more expensive than nickel itself. An advantage of all metallic materials is their mechanical and thermal robustness and the fact that the impedance can be made easily-variable and as low as desired, so that electrical break-down need never be a problem. With regard to reproducibility and ease of manufacture, the supplier would probably prefer to handle nothing more complex than a binary alloy; it is therefore fortunate that the two zero-anisotropy binary alloys (4-cobalt-nickel and 2.25 chromium nickel) have shown up with such favorable properties. Criticisms of magnetostrictive transducers are: the inconvenience of having to provide windings, with the unavoidable copper loss that must occur in them; and the need for external polarization. These are valid, but minor, objections, especially now that new drive techniques have largely avoided the expense involved in polarization supplies [ 11. As well as those discussed above, the following points arise out of the present work. (i) The importance of micro-eddy-currents has not before been emphasized in transducer work. The contribution from this loss-mechanism is important for the 4-cobalt-nickel alloy. The only satisfactory way to reduce these losses is to use much thinner laminations than would be chosen on the basis of macro-eddy-current calculations. Since manufacturers of industrial equipment prefer not to have to handle material thinner than about 0.025 cm, a practical limitation is imposed here. (ii) Very high efficiencies at high excitation are only obtainable at polarization well above that required for maximum coupling. This has not been fully realized by transducer designers.

NEW

MAGNETOSTRICTIVE

MATERIALS

455

Even at low excitation, the potential efficiency peaks at a polarization well above the 0.7 B,,, needed for maximum coupling (Figure 17). At higher excitation, even more polarization amp-turns are needed to compensate the reduced bias caused by drive flux distortion. Increasing the polarizing field implies more d.c. power loss unless one of the more economical drive methods is used [l]. (iii) Although the present measurements were confined to the new nickel-base alloys, the new design factors that have emerged make it advisable to look again at other available alloys, in particular the nickel-irons (especially 45-50 Permalloys); the aluminium-iron alloys (especially 13-Alfer); and high-cobalt-irons (Hiperco, Permendur and 65-cobalt-iron). These all have the advantage of positive magnetostriction, adequate coupling and high theoretical power-handling capacity. The high cobalt-irons in particular show about the same coupling as nickel, but higher power-handling capacity, both rl and F being greater. However, these materials are expensive, difficult to work, brittle and not easy to manufacture in reproducible quality.

4.2.

CHOICE

OF TRANSDUCER

SYSTEM

From the above discussion, we reach a broad conclusion that the best system to use in sonar and industrial ultrasonics may be a spaced-lamination or spaced-transducer device constructed from one of the new chromium-containing nickel-base alloys. It is instructive to compare this type of magnetostrictive system with the best modern ceramic-based vibrator for the applications of interest. In the latter category, the prestressed sandwich transducer, using LZ piezoelectric ceramic plates, is currently used. (i) Both types of transducer are limited to rather lowfrequencies-below about 50 kHzthe magnetostrictor through magnetic losses and the sandwich through mechanical losses in the rather complex structure. (ii) Limiting peak intensities are fixed by power-handling capacity which is theoretically greater for the ceramic, but adequate for both types. (iii) The magnetostrictive system is more robust mechanically and electrically. (iv) The potential efficiency of the magnetostrictive system may be in the range 80 to 85 % at very high intensities, about the same as ceramic sandwiches using the best construction. (v) The magnetostrictor is more easily matched acoustically to a water medium. (vi) The magnetostrictor is more easily bonded reliably to the coupling plate, since only the thickness of single laminations or a thin transducer is involved, whereas for sandwiches a large area needs to be bonded. (vii) The impedance-level of the magnetostrictor is infinitely-adjustable and can therefore be kept low. For the ceramic sandwich, the impedance may be unavoidably high unless the system is large enough to employ many transducers connected in parallel. (viii) The properties and operating characteristics of the magnetostrictor are probably more reproducible. (ix) The magnetostrictor shows less temperature-, time- and stress-dependence. (x) The magnetostrictor requires some form of external polarization; the ceramic can always be operated at remanance. (xi) Running costs should be about the same for both systems. (xii) Material and assembly costs, referred to the transducer alone, are, as near as can be assessed at present, about the same for both types. (xiii) Motional self-excitation, if required, can be applied equally readily to both types. (xiv) For the magnetostrictor, there is a disadvantage in the need to provide excitation and polarization windings, which also account for some loss.

456

E. A. NJZPPIRAS

The relative importance of these factors should be carefully assessed by equipment designers. But it seems that, on balance, magnetostrictors using the new nickel-base alloys may be preferable to ceramic sandwiches and therefore to all other types. ACKNOWLEDGMENTS The nickel-base alloys were provided by International Nickel Ltd. Thanks are also due to Kerry’s (Ultrasonics) Ltd. who carried out the stamping and heat-treatment of the laminations by their normal production technique. REFERENCES 1. E. A. NEPPIRAS1968 J. Sound Vib. 8 (3). New magnetostrictive materials and transducers. 2. C. A. CLARK 1961 J. acoust. Sot. Am. 33,930. Improved nickel-base alloys for magnetostrictive transducers. 3. E. A. NEPPIRAS1963 Acustica 13,368. Mechanical transformers for producing very large motion. 4. C. A. CLARK 1956 Brit. J. appl. Phys. 7, 355. The dynamic magnetostriction of nickel-cobalt alloys. 5. M. T. PIGGOT~and P. M. KENDIG 1954J. acoust. Sot. Am. 26,974. Rapid method of evaluating magnetostrictive materials for electromechanical transducers. 6. C. M. VANDERBURGT 1963 Ultrasonics 1, 199. 7. E. A. NEPPIRAS1965 Acustica 15,58. The effect of shape and internal impedance on the efficiency and power handling capacity of ultrasonic transducers. 8. R. M. BOZORTH1951 Ferromagnetism New Jersey: D. van Nostrand Co., Inc., 774. 9. E. A. NEPPIRASUnpublished research. 10. E. B. WRIGHT Instn Radio Engrs International Convention Record 8 (Part 6). A spaced-lamination transducer for industrial use. 11. Unpublished research sponsored by International Nickel Ltd. 12. C. A. CLARK and J. J. MASON 1963 J. acoust. Sot. Am. 35, 1665. Temperature dependence of dynamic magnetostrictive properties of nickel-cobalt-chromium alloys. 13. R. R. WHYMARKand J. M. WITTING 1961 J. acoust. Sot. Am. 33,172O. Resonant displacement of nickel and permendur magnetostrictors under static compressive stress. 14. E. A. NEPPIRAS1968 Acustica 19,54. Some remarks on the maximum power-handling capacity of resonant electromechanical transducers. 15. R. R. WHYMARK1961 J. acoust. Sot. Am. 33, 725. Utilization of magnetostrictive materials in generating intense sound.