| Eddy-current testing is one of non-destructing testing methods based on the electromagnetic theory. It is an experiment method that uses the electric and magnetic properties presented by the material in the electromagnetic field to estimate the inner constitution, function, and the geometry shape of the test specimen. In the eddy-current testing, testing coil is the sensitive component connecting the specimen and the instrument, so it is called transducer. The information of the test specimen is reflected by the variation of the coil impedance (or induced voltage) . But it is well known that there are many limits in the present design formula on transducer. Therefore, it is very meaningful for both the electromagnetic theory and practical applications to study the electromagnetic field caused by testing coil and analyze the dependence of the coil impedance on the parameters that affect the coil impedance. Based on the electromagnetic theories, this dissertation presents an analytical method to analyze the electromagnetic field caused by the solenoid coil with ferrite core that is popularly used in eddy-current non-destructing test (NOT). Both numerical method and experiments are given to verify the analyzed results. Below are the work and results of the dissertation:1. Analytical Solution to the Eddy-current Transducer with Ferrite CoreAccording to the practical eddy-current transducer used in eddy-current NOT, the analytical model described by a solenoid coil with a coaxial cylindrical ferrite core of finite length' is established. For the scattering field caused by the finite-length conducting and permeable cylinder, the boundary condition that the normal component of electrical strength is zero inconducting medium, i.e. En=0, was used to determine the separation constant of boundary value problem in the past. Because the field caused by the eddy-current transducer in the dissertation is not only axially symmetrical, but also plane symmetrical, there is no normal component of the electrical field strength and we cannot apply the condition En = 0 to solve such a problem. Considering that the ferrite core is often made from good permeable material, the dissertation presents the condition that the normal component of the magnetic field strength is zero approximately at the inside surface of good permeable material, i.e. Bn=0 to determine the eigenvalues for the separation constant. During the solving process, the solenoid coil is supposed to be wound closely by infinite symmetrical delta-coils. Firstly, the field caused by two symmetrical carrying current delta-coils with finite-length ferrite core is solved. The solving steps are as follows: The field is divided into three regions by the cylindrical surface of the finite-length cylinder and the location of the delta-coils. Because 'the surface current source is placed at the interface, the non-homogenous restricted equation on the magnetic vector potential is transformed into the homogenous Helmholtz equation. By using the method of separation of variables to solve equation and according to the interface conditions and the condition at infinity to determine the unknown constants, the expressions for the magnetic vector potential of the three regions are solved out. Then, using the principle of superposition and integrating the delta-coils, we can obtain the expressions for the magnetic vector potential caused by the cylindrical coils carrying current. Finally, the impedance analytical expression for the solenoid coil with a finite-length ferrite core carrying time-harmonic current is obtained through the magnetic vector potential.2. Numerical Analysis of the Electromagnetic Field Caused by the Eddy-current TransducerThe dissertation calculates the field caused by the solenoid coil with a finite-length ferrite core carrying time-harmonic current by the finite element method. The main work is as follows: For the magnetic vector potential,the principle of calculus of variations is applied to convert the elliptical boundary value pr...
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