Hankel Transform Application for Calculation of Ring Coils Inductance. Part 2
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el Transform Application for Calculation of Ring Coils Inductance. Part 2 O. N. Petrischev1*, M. I. Romanyuk2**, and G. M. Suchkov3*** 1
Kyiv Scientific Research Institute of Hydrodevices, Kyiv, Ukraine National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine 3 National Technical University “Kharkiv Polytechnic Institute”, Kharkiv, Ukraine *ORCID: 0000-0001-7529-9076, e-mail: [email protected] **ORCID: 0000-0002-2238-0257, e-mail: [email protected] ***ORCID: 0000-0002-1805-0466, e-mail: [email protected]
2
Received March 13, 2019 Revised March 9, 2020 Accepted April 29, 2020
Abstract—Changes in the geometric parameters of ring coils, which are an essential element of transducer design used for non-destructive testing of ferromagnetic metals, entail a change in the self-induction coefficient (inductance) of alternating magnetic field source. In the article, on the basis of proposed approach [1], the equations for determining the ring coils inductance are obtained, allowing to take into account real dimensions of inductors. They are equally suitable for situations where coil is located in an empty space, as well as near a conductive ferromagnetic or non-ferromagnetic metal. Calculating the inductance of ring coil located near magnetized, conductive ferromagnetic plate, we found that circuit inductance is the frequency-dependent complex-valued function vs distance between plate and ring coil. The measurements of the inductance of a coil located above a conductive ferromagnetic plate with a change in the non-contact value were carried out. The obtained results testify to physical meaningfulness and reliability of theoretical statements and calculations. These qualitative and quantitative results correspond to generally accepted energy definition of self-induction coefficient. DOI: 10.3103/S0735272720070018
1. INTRODUCTION In [1], the fundamentals of new method for calculating the electrical circuits inductances located near metal (conductive and magnetized) objects, using reviews [2–11] and materials [12–16], are formulated. The calculating features of self-induction coefficient of a ring coil, located near a magnetized, i.e., anisotropic in magnetic permeability, conductive ferromagnetic plate is discussed in this paper. 2. INDUCTANCE OF RING COIL LOCATED NEAR MAGNETIZED CONDUCTIVE FERROMAGNETIC PLATE The region of an alternating magnetic field of ring coil (Fig. 1 [1]) is divided into two regions, which significantly different in magnetic and electrical properties. Electrical conductivity is equal to zero and magnetic permeability is equal to m 0 in the first region (z > 0). There are external currents with J f (r , z )e iwt density in this region. The second region (z < 0) is characterized by nonzero electrical conductivity and magnetic permeabilities m ij . We assume that a constant bias field source creates vertically oriented magnetic field with intensity H z0 in ferromagnetic metal volume. It does not change within the region of alternating magnetic field existen
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