International Research Journal of Engineering and Technology (IRJET)
e-ISSN: 2395-0056
Volume: 10 Issue: 07 | July 2023
p-ISSN: 2395-0072
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Analysis of Hysteresis and Eddy Current losses in ferromagnetic plate induced by time-varying electromagnetic field G. D. Kedar1, B. B. Balpande2 1,2 Department of Mathematics, RTM Nagpur University, Nagpur-440033, Maharashtra, India,
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Abstract - Whenever electric devices are exposed to time-
electromagnetic field or when exposed to the time-varying electromagnetic field, Eddy currents are induced. This eddy current creates an internal magnetic field that exactly opposes the external magnetic field. This gives rise to a skin effect in which the current density near the outside of the conducting medium becomes higher than the inside. The eddy current creates a kind of power loss in the medium known as Eddy current loss. The heat produced by Eddy current is used in various applications like heat treatment of metal products, induction furnaces, Induction hardening in steel parts, induction welding/brazing as a way of connecting metal components, or induction annealing which can selectively soften a region of a steel portion, etc. [2-5]. The estimation of Eddy current is also used for one of the inspection methods which is non-destructive testing which serves for a variety of purposes, including flaw detection, measuring material and coating thickness and determining and laying out the heat treatment condition for conducting materials.
Key Words: Eddy current, hysteresis loss, time-varying electromagnetic field, magneto-thermoelasticity, integral transform
Magneto-thermoelasticity is a subject where we study the interactions between magnetic, thermal, and mechanical fields in a thermoelastic solid in the presence of a magnetic field. The theories like heat conduction theory, classical elasticity theory, and electromagnetic theory which are applied to solve the coupling problems of temperature field, electromagnetic field, and elastic field of conductive elastic solids are also included in Magneto-thermoelasticity. The theoretical idea of magneto-thermoelasticity was introduced by [6-7] and later on was developed by [8]. Paria [9] considered a thermo-elastic solid inside a magnetic field and studied the propagation of the plane waves and gave a theoretical framework for the advancement of magnetothermoelasticity. Wilson [10] studied the propagation of magneto–thermoelastic waves in a non-rotating medium. The above studies were based on the theory of classical coupled thermoelasticity, with interaction among the electromagnetic field, the thermal field, and the elastic field, as well as the dispersion relation, taken into consideration. Nayfeh et al. [11] used the Perturbation technique to study the effect of small couplings related to thermoelasticity and magneto-elasticity of an unbounded isotropic medium. Sherief et al. [12] discussed a one-dimensional thermal shock problem of generalized thermoelastic electrically conducting half-space permeated by a primary uniform magnetic field with thermal relaxation. Biswas et al. [13] exemplify a threedimensional electro-magneto-thermoelastic coupled problem for homogeneous orthotropic thermally and
varying electromagnetic field, it brings out two impacts on the devices: Firstly, conducting currents appears in the device, which ultimately gives rise to Joule’s heat which rises the temperature of the device in terms of Eddy current loss, and, secondly due to the time lag between magnetization and demagnetization of the ferromagnetic plate some amount of energy is lost which is termed Hysteresis loss. In this paper, we have treated this total loss as the heat source for the problem. Based on Maxwell’s equations a three-dimensional mathematical model for the magnetic field, temperature field, and elastic field in the plate was established. Then the governing equations for determining magnetic field intensity, temperature, and stresses inside the plate were solved by integral transform technique. The results obtained are displaced graphically to illustrate the influence of wave frequency, skin depth, electrical conductivity, magnetic permeability, hysteresis loss, and Eddy current loss of steel plate on the various fields considered in the problem.
1.INTRODUCTION In many electromagnetic equipment such as magnetic circuits of motors, generators, inductors, magnetically levitated high-speed terrestrial vehicles, energy storage devices in electromagnetic fields, fusion reactors, and devices using electro-magnetic propulsion etc, ferromagnetic materials are widely used. Analogous to conventional structures which experience mechanical loads, the ferromagnetic structures inside the strong magnetic fields typically are exposed to the magnetic force arising due to mutual interaction between time-varying magnetic fields and the magnetization of ferromagnetic materials. Due to this strong magnetic force, the ferromagnetic structures undergo deformation which affects their stability drastically [1]. Eddy current induced in conducting mediums (such as metallic plates) by time-varying magnetic field and its consequences is of great practicable significance due to its magnificent role in a vast range of technical and industrial applications. Many mechanical structures get activated when immersed in the electromagnetic field. Such structures or conducting mediums, when moving through the
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