UDC 621.318.38.001.5 : 389.0

E L E C T R O M A G N E T W I T H A U N I F O R M

F I E L D FOR M E T R O L O G I C A L WORK

A N D S T A B L E M A G N E T I C

V. I . Z i n g e r m a n

Translated from Izmer i t e l ' naya Tekhnika, No. 2, pp. 19-23, February, 1964

Magnetic fields which are stable with t ime and vary but l i t t le in space are required for investigating modern high-precision magnet ic induction meters. Special requirements are specified for magnet ic field sources when mag- netic balances are used for measuring induction. Such sources are required, in part icular , for determining the proton gyromagnet ic ratio when the magnet ic induction must be of the order of tenths of a tesla, the magnet ic field distr i- bution must be carefully studied over a large volume (to a distance up to 600ram from the center of the field), and its variations within that volume should not exceed several hundredths of one percent, with the field distribution re- maining the same for long periods of t ime.

Either magnets or e lectromagnets can be used as sources for such fields. The advantage of electromagnets con- sists in the faci l i ty they provide for adjusting over wide ranges the magnet ic induction they produce. Methods for computing and designing magnet ic circuits and magnet iz ing coils have now been developed sufficiently well. There is, however, very l i t t le published data on designing field magnets. Certain considerations on computing field mag-

nets are contained in [1]. The basic a im of these authors is to obtain magnet ic fields of a maximum power, therefore their recommendat ions are not suitable for the specific requirements of medium-power magnets used for met ro logica l

work.

The proton gyromagnetic ratio was determined at the KhGIMIP (Khar 'kov State Institute of Measures and Mea- suring Instruments) [2, 3] in the field of an e lect romagnet , whose exper imenta l investigation led to certain general recommendat ions on the production of field magnets for met ro logica l work.

This e lec t romagnet has a double yoke and tapered cores. The dimensions of the magnet ic c i rcui t and m a g - net iz ing coils have been chosen according to normal considerations [4]. The magnet iz ing coils provide an a i r -gap induction up to 0.5 T with a dissipated power of 120 W. The heating of the windings is so smal l (less than I~ owing to the large dissipating surface, that no forced cooling is necessary. The temperature field around the e lec t romagnet is, therefore, free of large gradients, thus providing favorable conditions for the operation of high-precis ion magnet ic balances. The e lec t romagnet ic pole pieces consist of p l ane -pa ra l l e l plates made of Armco steel 30.8 mm thick and 280 mm in d iameter . The upper part of the pole pieces is cut off horizontal ly at a distance of 100 mm from the center in order to fac i l i t a te the adjustment of magnet ic balances [3]. k s imilar part is cut off the bottom of the pole pieces so as to make the magnet ic circui t symmetr ica l with respect to the horizontal plane. The surfaces of the cores

were lapped to each other in an assembled e lec t romagnet before fi t t ing the pole pieces, so that the distance between the cores remained fixed at 2/~. The surfaces of the pole pieces were machined to obtain a high degree of flatness (a deviat ion of less than 0.2 p over a d iameter of 160 ram). The required mechan ica l s tabil i ty was obtained by fi t t ing the pole pieces t ightly over the cores. The deviat ion of the po l e -p i e c e surfaces from paral le l ism is then of the order of 1 g. The length of the effect ive air gap is equal to 42 ram.

A s tabi l iz ing system based on nuclear magnet ic resonance [8] was used for e l imina t ing a i r -gap magnet ic indue- tion changes due to possible variations in the magnet iz ing current or the parameters of the magnet ic circuit . The

auxi l iary windings fed by the s tabi l izer current were located in the immedia t e proximity of the pole pieces. The s tabi l iz ing system was usually adjusted so that the ampere-turns of the s tabi l iz ing windings amounted to 5-10% of the ma in windings supplied from storage batteries without any sudden surges in the windings. The very large s t ab i l i za -

t ion coeff ic ient (up to 15000) of the device ensured for any slow main current variat ion encountered in prac t ice a

constant magnet ic induction in the air gap over long periods of t ime with an error not exceeding 1 �9 10"6

The magnet ic field distribution between the e lec t romagnet poles was studied in de ta i l by means of a proton magne t ic resonance transducer which provided for a single measurement of magnet ic induction a random error not exceeding 5 . 1 0 - 6

A deta i led study of the magnet ic f ield distribution in the large volume of the effect ive air gap leads to several general conclusions.

121

~'Bo CD j

I1"

.z~ r mm

,=Z5 rl

:m

r 5o o 5o m m Distance from the axis of the poles

Fig. 1. Magnetic induction in the hor izonta lp lane passing through the axis of the poles. B 0 = 0.2848 T,

z is the distance in mm from the symmetry plane

of the air gap.

It will be seen from Figs. 1 and 2 that the induction

in the e lec t romagnet under consideration rises slightly from

the center of the pole to its periphery, and that this rise is

present in the large volume of the air gap. This phenom- enon prevents the magnet ic induction drop at the edges, which is normal ly considered to be the main cause for the

magnet ic field irregulari ty in the air gap, having any no- t i ceab le effect on the f ield in the central part of the air

gap. The effect of a magnet ic induction rise away from

the center towards the periphery of the poles is par t icular ly pronounced at a short distance from their surface. Thus,

in a plane at 6.5 mm from the pole surface a rise in the

magnet ic induction towards the periphery was observable

even at a distance of 100 mm from the center.

A drop in the magnet ic induction towards the center

of the pole is not a feature character is t ic only of the e l e c -

t romagnet under consideration. The above phenomenon was studied in detai l by examining the magnet ic fields in the

air gaps of laboratory electromagnets and permanent mag-

nets of different designs. It was possible from the avai lab le published data to determine the nature of the magnet ic field distribution for various designs of magnets with po l e -p i ece diameters of 98 to a20 ram. a i r -gap widths of 24 to 60 ram, and magnet ic inductions of 0.28 to 0.95 T. The magnet pole pieces had a thickness of 20 to 78 mm with either cyl indr ica l or tapered side surfaces. Some of the examined f ield magnets had nonoperative air gaps between the pole

pieces and cores.

An analysis of the results thus obtained shows that a decreasing magnet ic induction towards the center of the pole is character is t ic for the overwhelming major i ty of carefully made electromagnets and permanent magnets with a ratio of the po l e -p i ece diameter D to the effect ive a i r -gap length l exceeding 4. For smaller ratios D~ l this phenomenon is lacking, and the ordinary irregularity of the magnet ic field is produced by the edge effects.

Magnets with a ratio of D/l > 4 lack almost comple t e - ly any regular relationship between the dimensions of the poles and the position of the maximum induction points with respect to the edge of the pole on the curve representing the relationship of induction to the distance from the center

of the pole piece. In the a i r -gap symmetry plane this m a x - imum is at a distance of 1.2-1.7 l from the edge of the pole in magnets of comple te ly different designs.

Fig. 2. Lines of equal magnet ic induction in the a i r -gap symmetry plane para l le l to the pole sur-

faces. The figures over the lines denote the values

of (B -- B 0 )" 104/B0 ; B0 = 0.2848 T. The nature of the above phenomena can be changed

if the magnet ic state of pole pieces is affected by first passing through the magnet iz ing windings a current which is larger than that required for obtaining the required magnet ic induction in the air gap. This method, which reduces the drop in the magnet ic induction at the center of the gap, should not, however, be appl ied to magnets intended for met ro logica l work, since the magnet ic field distribution thus obtained changes wi threpea ted switching of the magnet .

The appearance m magnets with a ratio D/I > 3 of an area in which the magnet ic induction rises from the center towards the edges has been theore t ica l ly demonstrated in [1]. However, the authors of this work have assumed that this phenomenon can only exist with magne t i ca l ly - saturated tapering pole pieces. Measurements of a large number of different magnets have demonstrated the existence of such an area with pole pieces which are neither tapering nor any-

where near magnet ic saturation.

122

iiI 1

-~0 80

\ / 0 50 mm

Distance from the axis of the poles

Fig. 3. Magnetic induction along a line through the center of the air gap para l le l to the po le - p iece surfaces. B 0 = 0.2348 T. Shim dimensions: 1) thickness 1.5 ram, width 7 ram; 2)thickness

1.2 ixlm, width 7 mm.

It is thus possible to arrive at the conclusion that i t is

not advisable to increase appreciably the d iameter of pole pieces in order to reduce the nonuniformity of the magnet ic

field at the center of the air gap. Increasing the d iameter beyond an opt imum size only results in the replacement of the magnet ic field irregularity due to edge effects by an i rregular-

ity produced by the drop of induction at the center of the pole. From this point of view the minimum permissible ratio of D/l = 5, which is widely recommended in l i terature, should be considered unjustifiably large for magnets requiring a uniform field over only a few cubic centimeters . Experiments have shown that with such a value of D/I the uniformity of the m a g - netic field near the a i r -gap center does not improve, but can even deteriorate a l i t t le as compared with magnets which have a ratio of D/I = 3 . 5 - 4 It is advisable to make magnets with a ratio D/l exceeding 4 only when it is required to e l imina te

the edge effects over large volumes of the magnet ic field. The e lec t romagnet used at the KhGIMIP is of that type.

It is widely recommended, but comple te ly inadvisable to use peripheral shims for reducing the air gap at the edges of pole pieces [5] in order to raise the magnet ic field uniformity at the central operating part of the air gap in magnets with l a rge-d iamete r pole pieces. It is obvious that shims canpro - duce a desirable reaction only on those parts of the field where there exists an edge effect, i . e . , to a distance from the edge of the pole not exceeding 1.2-1.7 l .

Figure 3 shows the results obtained by fitting shims of different sizes to the 200-ram round poles of theKhGIMIP elect romagnet . These poles were mounted especial ly for the experiment , since the technique of ca lcula t ing shims

has not been developed for poles of a complex form. It will be seen from these experiments that for the a i r -gap symmetry plane, shown in Fig. 3, the effect of shims is useful only within a re la t ively narrow range. Nearer to the poles the effect of shims is even smaller. A high-precis ion adjustment of the shim dimensions is diff icult and, although they lead to an extension of the uniform field size, they at the same t ime often disruptits symmetry.

The placing on the pole surface of winding turns with an addit ional current [6] is also ineff ic ient for magnets with l a rge -d iamete r pole pieces. Such a circular winding improves the magnet ic field uniformity over a small area with a dia ineter of 10-20 ram, whereas it increases nonuniformity in the remaining parts of the field.

Shims or current rings are not used, therefore, in the KhGIMIP electromagnet , but main at tention is paid to

careful adjustment of the pole pieces.

The distribution of the magnet ic field in the working air gap can be affected not only by the lack of para l le l - ism and flatness in the pole surfaces but also by their deviat ion from coaxia l i ty . The coax ia l i t yo fpo le s ~ith a complex

shape is difficult to check by means of l inear measurements; however, experiments have shown that their coaxia l i ty can be ascertained by examining the magnet ic field distribution charts in two planes located at equal distances on either side of the a i r -gap symmetry plane. An example given in Fig. 4 shows field distribution charts in planes loca ted at a distance of 6.5 m m from the pole surfaces, with the axis of pole A displaced by 1 mm with respect to that of pole B in the direction shown by an arrow. It wil l be seen from these charts that the areas with a sharply-r is inggra- dient (denser spacing of lines) are located in each of the planes on the side of the axis to which the pole nearest to

the surface has been displaced. The mutual d isplacement of the pole axes distorts the magnet ic field over the whole volume of the air gap despite the large d iameter of poles (D/l = 6). In the above case the mutual d isplacement of the two chart centers (points with a min imum induction) amounts to approximately 40 ram, i.e., i t is tens of t imes greater than the displacement between the pole axes. It is possible by means of this pecul iar i ty of the f ield d isp lace- ment charts to discover re la t ive shifts in the pole axes of the order of 0.03-0.05 ram, which indicates the necessity

of adjusting the pole coaxia l i ty approximate ly with the same precision. The positions of the lines of equal induct ion in two similar planes of the KhGIMIP magnet did not differ from each other by more than 2 ram.

123

. F Direction of displacement +t ~'

/ I

X * r X

_ _ C0ntoursofpole A j " \ . contours of pole g -I I

Fig. 4. Lines of equal magnetic induction in planes with z = 14,a mm with the axis of pole A displaced by 1 mm with respect to that of pole B.

The correct mutual location of poles, their parallelism and coaxiality are expecially important for measuring induction by means of magnetic balances. The calculation of magnetic induction from the force operating on a current with a conductor requires knowledge of the angle between the direction of the magnetic field lines and that of the current. Direct determination of the direction of the magnetic induction vectors is impossible with the preci- sion required for metrological work, since it is possible to measure by the nuclear magnetic resonance method only the magnitude of magnetic induction, whereas the other methods are insufficiently sensitive, k is, therefore, desir- able for working with magnetic balances to place the current-carrying circuit perpendicular to the direction of the magnetic induction vectors. Their mutual perpendicularity is normally checked in the following manner, the angle between the magnetic poles and the plane of the current circuit is adjusted for a maximum interaction force meas- ured by the balance. This technique does not take into account the possible lack of mutual parallelism between the magnetic induction vectors of the measured field in various parts of the current-carrying circuit, which could produce an underestimated value of the induction. It is highly probable that this error is one of the reasons for the systematic difference between the values of proton gyromagnetic ratios obtained by means of magnetic balances and ratios obtained by means of computed magnetic field coils,

The magnetic field of the KhGIMIP electromagnet is distributed in the air gap very symmetrically with respect to the vertical plane which passes through the center of the gap parallel to the pole surfaces, Figure 5 shows meas- urements of magnetic induction in the direction perpendicular to the pole surfaces in various parts of the field, It is reasonable to assume that with such symmetry the magnetic induction vectors are perpendicular to the symmetry plane at that plane. The perpendicularity of the magnetic induction vectors to the current-carrying circuit of mag- netic balances was also tested by an indirect method. A current-carrying loop was suspended in the air gap of an electromagnet free to rotate about its vertical axis under the effect of the electrodynamic interaction force. The position of the loop was checked by means of an optical system. Displacements of the loop in the horizontal direction in the symmetry plane of the air gap over large distances (up to 50 mm from the axis of symmetry) did not produce a rotation of the loop, whereas its displacements in other planes which were also parallel to the poles produced rota- tions through an angle whose value increased with the displacement from the air-gap vertical axis of symmetry, The lack of torque when the current-carrying loop is in the air-gap symmetry plane, despite the inequality between the magnetic induction in the areas occupied by the vertical conductors on either side of the rotation axis of the loop, indicates that the magnetic induction vectors are perpendicular to the plane of the loop,

Nomlal operation of magnetic balances also requires that the horizontal component of the magnetic field paral- lel to the magnetic induction vector of the measured field should approach zero along the upper side of the current- carrying loop. Normally this condition is :-net by compensating the stray magnetic fields by Helmholtz ring fields. However, it is impossible to produce along the entire horizontal length (up to 100 ram) or the loop by means of Helmholtz rings a field with the required space distribution for compensating the irregular stray fields.

A satisfactory result has been obtained by means of compensation coils (Fig. 6). These coils are not provided with a rigid frame, but are fixed to supports by means of which it is possible to change the shape and position of each

124

r .... / " -

x=3 g5 ~ / y-S7

0 j

- - ' - x-'-~ x=3e ~i-0 9=0.

Ce 8 O e z, mm Fig. 5. Magnetic induction in horizontal planes. B0 = 0.2348 T. The direction of coordinates X and Y is shown in Fig. 2.

Direction of ~ / ~ thecompen-.//~:~\ / , / //.-v ~ed

Fig. 6. Coil for compensating the stray

fields of the electromagnet.

1,

2.

3,

4o 5,

6.

7.

coil. By regulating the current through the compensation coils and adjusting their configuration it is possible to compensate stray fields over the required volume even at small distances (120-150 mm) from the magnetizIng coils of the electromagnet, where these fields are still very irregular. It was found conve- nient to use for testing purposes a measuring generator with a phase-sensitive voltmeter [7]. The magnetic induction of the stray fields is determined ahnost entirely by the main coils, since the diameter of the electromagnet windings fed by the magnetic induction stabilizer current is considerably smaller than that of the main magnetizing coils. Variations in the current of the main coils produce changes in the stray fields even when the magnetic induction in the air gap is maintained constant by the induction stabilizer. It is necessary to maintain the current through the magnetizIng coils at a constant value in order to ensure the compensation of stray fields over a long period of time.

The magnetic induction for the existing configuration of the electromagnet at a distance of 500 mm from the center of the working air gap (the location of the magnetic balance's upper conductor) amounted approximately to 0.4~ of the magnetic induction in the operating gap. The current through the mag- netizing windings was maintained at a constant value within 0.03%. The residual uncompensated stray fields due tovariations in the magnetizing current could then be of the order of 1 �9 10-6 of the magnetic induction in the operating air gap.

The provision of the required distribution in space and stability with time of magnetic fields in the air gap of the elec- tromagnet and outside it led to a substantial reduction in the error produced by the magnetic field source in the absolute eval- uation of the proton gyromagnetie ratio.

A magnetic induction stable with time and reproducible at a given value in the required part of the air gap leads to utilization of the electromagnet as a measure of magneticinduc- tion, The error in producing magnetic induction values up to 0.5 T does not exceed 0.003%, including the error of the proton gyromagnetic ratio.

L ITERATURE C I T E D

Y, Ishikawa and S. Chikazumi, Japanese Journal of Applied Physics, 1, No. 3 (1962).

G. K. Yagola, V. L Zingerman, and V. N, 8epetyi, Izmerit. tekh., No. 5 (1962). G. K. Yagola, V. L Zingerman, and V. N. 8epetyi, Transactions of the Institutes of the Committee of Standards, Measures and Measuring Instruments, No. 68 (128) (1962). H. Primas, R. Amdt, and R. Ernst, Zeitschrift ftir Instmmentenkunde, 67, No. 12 (1959). E. Andrew and F. Rushworth, Proc. Phys. 8oc., 65 (1952). H. Primas and H. Gunthard, Helvetica Physica Acta, 30, No. 4 (1957), p. 321.

V. I. Zingerman. V. N. 8epetyi, and G. K. Yagola, Transactions of the Institutes of the Committee of Standards, Measures and Measuring Instruments, No. 67 (127) (1962).

125