Study On Modeling And Distribution Of Magnetic Field And Eddy Current In Rectangular Conductive Plates

Eddy currents occur in conductors subjected to time-varying electromagnetic fields.The thermal effects,magnetic effects and mechanical effects of eddy currents exist widely in practical life and engineering.On the one hand,eddy current effects can be used effectively in induction furnace,non-destructive testing,electromagnetic braking,magnetic eddy current hyperthermia system,etc.On the other hand,eddy current effects can also cause unnecessary power losses and equipment overheating,which we need to avoid.Therefore,it is necessary to analyze the eddy current of devices that placed in time-varying electromagnetic fields and to make a priori judgment of eddy current heat losses.In the design of devices,it is also necessary to calculate the magnetic field intensity or magnetic induction intensity of materials.The research on magnetic field and eddy current has been developed into a multidisciplinary subject in the fields of heat,electricity,force and magnetism.However,there are few researches on the internal magnetic field of materials,especially on the rectangular plate with some characteristics.In view of this,based on Maxwell's equations theory,this dissertation studies the distribution of magnetic field intensity and eddy current density in a rectangular material plate placed in time-varying magnetic field,which provides theoretical support for the design of some devices.The major work of this paper is summarized as follows.Firstly,based on the Maxwell's equations,the magnetic field models in a rectangular plate with isotropic conductivity and with orthotropic conductivity are established,respectively.The equations are solved by double Fourier sine transformation,and the analytical expressions of magnetic field intensity expressed by double series are given.The error in the result that obtained by R.L.Stoll which used Fourier transformation method to solve the former model is corrected.The result obtained in this paper is in good agreement with that obtained by R.L.Stoll using separation of variables,which verify the correctness of the result in this paper.Secondly,on the base of the analytical expressions of magnetic field intensity in rectangular plates with isotropic conductivity and orthotropic conductivity,the formulas of eddy current density and eddy current loss in the two kinds of plates expressed by double series are obtained correspondingly.The distributions of magnetic field intensity and eddy current density in the two kinds of plates mentioned above with different dimensions are simulated intuitively by using MATLAB software,and the regularities of distributions are given.Thirdly,the effects of excitation frequency,relative permeability and conductivity of materials on the distributions of magnetic field intensity and eddy current density in rectangular conductive plates with different sizes are analyzed in their two cross sections which perpendicular to each other.With the change of the above factors,regardless of the size of the rectangular conductive plate,the magnetic field and eddy current always follow the same change rules in the edge part of the plate,but the distribution rules in other areas of the plate will become more complex with the increase of the plate.Fourthly,the governing equation for determining electromagnetic field in an isotropic bi-layered laminate is established based on the magnetic field model of single material plate with isotropic conductivity.The equation is solved by using the combination of double Fourier transformation and approximate substitution.By simulating the distribution of magnetic field intensity and eddy current density in the two groups of bi-material plates,it can be concluded that the higher the conductivity ratio between the two layers materials,the more significant the magnetic field intensity decreases in the material layer with higher conductivity,and the more obvious the eddy current density decreases in the material layer with lower conductivity.When the two layers of the bi-material plate are the same,the bi-material plate can be attributed to the single material plate.The relative errors of the two magnetic field intensities of the bi-material plate with the same layers and the single material plate are benchmarked.The maximum relative errors are less than 0.5%,which verify the validity of the method and result for calculating the magnetic field intensity inside the bi-material is verified.