DeVeloPMent of A MethoD for MeAsureMents of the PArAMeters of the externAl MAGnetIC fIelD of

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Introduction
At present, the sphere of application of magnetic mea surements is constantly expanding. These measurements are in demand in many fields of science, engineering and industry, such as electric power engineering, design, deve lopment and operation of electrical machines and apparatus, space research, navigation, military science, electromagnetic ISSN 2226-3780 compatibility, etc. The solution of a wide range of scientific and practical problems is directly related to the use of measured values of magnetic quantities such as magnetic field strength, magnetic flux and dipole magnetic moment. Measurements of these quantities are carried out using appropriate methods and means of measurement.
Technical facilities, which include electroradio equipment, are considered as sources of external magnetic fields (EMF). Such technical objects form an electromagnetic state in the area of the surrounding space and have a negative impact on the functioning of other objects sensitive to the EMF impact. The EMF term denotes a magnetic field that arises in the region of the outer space relative to the surface of the technical means, which is the EMF source [1]. In connec tion with this, the task of measuring the EMF parame ters, which is created by technical means, becomes topical. The resulting problems of electromagnetic compatibility, mag netic ecology, navigation and magnetic protection of equip ment go beyond the capabilities of individual countries [2]. To solve these problems, the International Radiation Pro tection Association has developed recommendations for the application in European countries of the permissible and maximum permissible EMF levels in production and nonproduction conditions, on the basis of which national standards are developed.
One of the components of the solution of these prob lems is creation of effective methods and means for mea suring the regulated magnetic parameters of the sources of magnetic fields. According to regulatory documents, such regulated parameters for sources of magnetic fields are their dipole magnetic moments, which, in contrast to the strength of the magnetic field, depend on the coor dinates of the observation points. The dipole magnetic moment ( , ) M A m ⋅ 2 is the cumulative characteristic of the EMF of the technical object, through which it is possible to determine the field strength at any point in space, the structure and spatial configuration of the magnetic field of the technical field [3][4][5][6].
Therefore, there arises the need to solve interrelated problems of creating highprecision methods and systems for measuring dipole magnetic moments. This includes ap propriate analytical EMF modeling, development of methods and means for its measurement, compensation of multipole interference and external electromagnetic interference [7,8].

the object of research and its technological audit
The object of the research is methods and means of measuring the EMF parameters of technical objects. The main characteristic of the method and means of measure ment is the measurement accuracy or the measurement error, inversely proportional to the accuracy.
The accuracy of measuring the EMF parameters of the object is determined by the nature of the field source, the choice of observation points, the degree of correspondence of the proposed mathematical model of the magnetic field of a real EMF. In addition, the task of monitoring the parameters of magnetic fields is complicated by the pre sence of nonstationary interference from external sources.
One of the most important stages of the measurement procedure is the stage of constructing or selecting the model of the measurement object. This stage is the most important in the planning of measurements, since errors made at this stage can not be corrected in the future. In the course of measurements, the object model can only be clarified. The discrepancy of the chosen model with the real object is the source of the error, by classification refers to the methodological component of the overall measurement er ror. This error is always present, because it is impossible to build or choose a model that is completely adequate to the object of measurement. The more accurately the model reflects the object, the less the methodical compo nent of the error. Therefore, the problem of choosing the EMF source model requires more detailed consideration.
One of the most problematic areas of existing methods for measuring the magnetic moments of sources of mag netic fields is the presence of a significant methodological error. For magnetometric methods, its value is 10 %, for integral 20-30 % [8,9]. This is due to the imperfection of the theoretical foundations of the method.

the aim and objectives of research
The aim of research is development and improvement of the metrological support of magnetic measurements by creating effective methods and means of measuring the parameters of electromagnetic objects of technical objects that ensure an increase in the measurement accuracy.
To achieve this aim, the following tasks must be solved: To propose a mathematical model describing EMF created by a technical object.
2. To develop a method for measuring the magnetic moments of magnetic fields of technical objects.
3. To evaluate the effectiveness of the developed method.

research of existing solutions of the problem
The existing methods for measuring the dipole magnetic moment can be divided into: -magnetometric -the socalled point, magneticfield based values of the magnetic field strength at one or more points in space; -integral, based on the measurement of the magnitude of the magnetic flux [9][10][11][12]. The shortcomings of the integral method are given in [8,9]. This is the complexity of the design and large dimensions of the primary measuring transducer when measuring the magnetic moment of large objects, as well as significant measurement errors (up to 20-30 %). Point methods of measurement are considered in [13,14]. They are distinguished by the simplicity and low cost of the primary measuring transducers. However, such methods also have low accuracy (for example, the methodological error of the standardized chitritic method is 10 %) due to the insufficient selectivity of the dipole magnetic moment by the sensor system from the full field spectrum. This is due to the imperfection of the theoretical foundations of the method.
The use of point methods that use inductive sensors as primary measuring transducers greatly simplifies the implementation of measurement systems that implement point methods. This gives them the property of mobility, which makes it possible to use pointbased magnetometric devices for their small working volume to control EMF sources in industrial conditions and on stationary mag netometric test benches [10].

ISSN 2226-3780
In [5,6], the character of the distribution of the magnetic field is investigated. The need to improve the metrological characteristics, the used measuring instruments is established. In work [7] it is shown that in the development of systems for measuring magnetic parameters, it is important to in crease the accuracy of measurement and to compensate for interference from external sources. In [15], the importance of choosing an adequate mathematical model for the theoreti cal justification of methods for measuring the parameters of a magnetic field is shown. In [11,12] alternative methods for measuring the magnetic moment are proposed, but certain limitations of the application of these methods to magnetic field sources of various sizes are shown.
Thus, the need to increase the accuracy of measuring dipole magnetic moments requires: -development of effective pointbased magnetometric methods and new more noiseproof measuring devices; -methods to assess the methodological error and the degree of interference immunity of measuring devices from the magnetic field of external sources.

Methods of research
To achieve the aim set in the study, methods of EMF analytical representation and its simulation, magnetometric methods for measuring the magnetic field strength, and methods for processing the measurement results are used. Theoretical studies related to the application of mathe matical models are based on the use of the method of multipole analysis of EMF, the classical method of EMF representation, methods for solving systems of algebraic equations and methods of matrix algebra.
6. research results 6.1. results of the development of a method for measuring the parameters of the external magnetic field of technical means. Any EMF source at each instant of time can be represented as a set of a finite number of elementary magnetic dipoles, each of which is located in the center of a small volume element. According to the principle of superposition, the sum of the elements of elementary dipoles is equal to the equivalent dipole moment, which is shifted relative to the origin of the adopted coordinate system, which is related to the EMF source [1,3].
To represent the mathematical model of the external magnetic field of a source in order to estimate the level of its magnetic field strength, it is sufficient to clarify the nature of the function. This function describes the distribution of the components of the field strength of an equivalent displaced then arbitrarily oriented in space magnetic dipole. The magnetic field of the source in the surrounding space outside the conductors with current, that is, in the region of space where the current density is zero and rot H = 0 can be characterized with the help of a scalar magnetic potential U . In this case, the vec tor of magnetic field strength H is defined as a vector equal in magnitude and directed opposite to the poten tial H gradU = − . The magnetic potential U is a solution of the Laplace equation ∇ = 2 0 U with the corresponding boundary conditions, which are plotted on a closed outer surface surrounding the source of the external magnetic field [15]. The components of the magnetic field strength are determined by differentiating the magnetic potential U with the current coordinates x, y, z. The classical method describes the intensity of the magnetic field of a source through the parameters of its eccentric equivalent magnetic dipole, the components of the resulting dipole magnetic moment of the source of the field, and the coordinates of the eccentricity of the magnetic dipole. For a magnetic field source of the «black box» type, these parameters are unknown quantities and for this reason to determine by the classical method the total value of the magnetic field strength of such source at given points of the external space is very problematic. In this case, EMF describe with sufficient accuracy the dipole model through the magnetic parameters of the components of the equivalent dipole magnetic moment of the field source, determined experimentally for the black box source. Thus, the magnetic field of the source of the magnetic dipole, displaced and arbitrarily oriented in space, found by the classical method, can be described with a given accuracy by the dipole model. In this case, it is necessary to determine experimentally the components of the dipole moment M M M x y z , , of the EMF source of the «black box» type. Then calculate the values of the magnetic field strength of this source in given zones of external space.
The multipole model of the EMF representation [15,16] can be obtained by expanding the magnetic potential in a stepwise series with respect to the radius of the observa tion point. The magnetic potential of the EMF source is described by the spherical harmonic Gaussian series (1) as a sum of multipoles of spatial harmonics of the dipole, quadrupole, octupole, and so on. The components are: The constant coefficients g nm and h nm in expressions (2)-(4) have a certain physical meaning, since they are equal to the magnetic moments of elementary multipoles of the mth order of the spatial nth harmonic. The co efficients g 10 , g h 11 11 ,  , , -the measured dipole magnetic moment of the magnetic field source along the three orthogonal directions X, Y, Z, respectively; 1...8 -twocomponent sensors which longitudinal mag netic coil axes are indicated by arrows, the beginning and the end of these arrows is determined by the rule of the right screw connected with the direction of winding turns of the sensor coils; R R 1 2 , -the radii of the circles on which the sensors 1-4 and 5-8 are placed, respectively; j -angular coordinate.
The magnetic field strength H R affects the magnetic axes of the sensor coils 1...4 and 5...8, located on the circles of radii R 1 and R 2 , and brings electrical signals into them. The effective value of the electrical signals for the measuring channels X, Y, Z is described by the expressions (5), (6). , , of the field source, from the harmonic of the EMF of even order. Therefore, the structure of the resulting signal, given by the radial, tangential and axial components of the source magnetic field strength in the measuring circuits of the sensor system coils, consists of a useful harmonic signal n = 1 and multipole interference of odd harmonics (5), (6).
The structure of the resulting electrical signals E R ( ) 1 and E R ( ) 2 of channels X, Y, Z consists of a useful signal of the first harmonic n = 1 and signals of odd harmonics n = 3 5 7 , , ..., introducing a methodical error in the results of measuring the dipole magnetic moment. Therefore, in order to improve the accuracy of measuring dipole mag netic moments M M M x y z , , , it is first of all necessary to exclude E R ( ) 1 and E R ( ) 2 from the structure of the signals and the most significant minterference of the harmonics n = 3. This is done analytically by solving the system of equations (5), (6). As a result, let's obtain an algorithm for determining the resulting signals E of the measuring channels X, Y, Z: where k k -the coefficients which values for a given ratio of radii R R 2 1 on which the sensor groups 1...4 and 5...8 are arranged according to the scheme in Fig. 1 To display the structure of the resulting signal E of the X, Y, Z channels, let's substitute the signal values in a harmonic series E R ( ) 1 and E R ( ) 2 , as described by the ISSN 2226-3780 expressions (5), (6), taking into account the value M in in the expression (7) and obtain expressions of the form: where R R = 1 -the distance, is taken as the base one when measuring the dipole magnetic moments of the EMF sources.
The analysis of expressions (9)- (11) shows that the signal structure E E E The sensitivity of the channels X, Y, Z of the mea suring system to the useful signal of the dipole component of the EMF source is determined by expressions: S k According to the results of measuring the components of the magnetic moment M x , M y , M z of magnetic field of the blackbox type source, it is possible to calculate the level of the magnetic field strength of the source in any zones of the surrounding space. It is also possible to determine the spatial configuration of the external magnetic field of the source by using expressions (2)-(4) and made computer simulation [17].Practical implementation of the method for measuring the dipole magnetic moments of EMF sources is carried out by a threechannel measuring system, the structural diagram of which is shown in Fig. 2.
Electrical signals, indicated by the magnetic field of the investigated source, in the circles of the radial and axial coils of the sensors are fed into the switching device SD. SD generates the resulting electrical signals E R x ( ), -in the measuring channel Z by appropriate commutation of the radial and axial coils. The resultant electrical signals of the measuring channels X, Y, Z are fed to the threeposition switch of the CS, which sets the preset mode of operation of the threechannel measuring system to alternately measure the dipole magnetic moments M M M x y z , , of the EMF sources. After the set measurement mode has been established, the resulting signals E R ( ) 1 and E R ( ) 2 of the measuring circuit of the corresponding channel of the measuring system are fed to the amplifiers A1 and PA2 to amplify them in accordance with (7)  = are then coupled with the compensating signal U k of the external interference compensator and the external interference signal E P to the input of the adder AD and the measuring device MD for displaying the measurement result.
6.2. effectiveness evaluation of the developed measurement method. Determination of the value of the meth odological error of the developed method and obtaining its mathematical expressions is based on the use of the multipole theory of the representation of EMF sources and the classical method of representing the source mag netic field, based on the theory of a magnetic dipole. This makes it possible to obtain reliable and convenient mathematical expressions on the basis of a comparative analysis for a methodical error in evaluating the efficiency and determining the metrological characteristics of the measuring system.
Let's determine the value of the methodical error for the first three odd harmonics n = 5 7 9 , , where E x y z , , 1 -useful signals of channels X, Y, Z of the mea suring system, created by the dipole component of the magnetic field; k x y z L x y z x y z , , , system, ensures the interrelation of the field parameters, allows to calculate the field at any point in space. 2. A point magnetometric method has been developed for measuring the magnetic moments of the dipole com ponent of the intensity of the external magnetic field of the source. The structural scheme of a measuring system that implements the developed method is proposed. Typical differences of this scheme is the presence of the block, it ensures the elimination of the third order harmonic from the resulting signal and the presence of a block that compensates for interference from extraneous sources.