Analytic Solutions To Magnetic Field For Eddy Current Testing With Natural Defects In Metal

In the daily engineering application,the metal components may have defects in the interior or surface due to the bad working environment and complex working conditions,which will lead to the failure of the metal components and cause heavy losses.Therefore,it is of great significance to detect and identify the defects in the metal components.In this thesis,analytical method and numerical simulation are used to study the forward problem of eddy current testing for defects in electromagnetic eddy current nondestructive testing.The contribution is to derive the analytical expression of magnetic field of eddy current nondestructive testing system when there are natural defects in metal components,which lays a theoretical foundation for the application of electromagnetic eddy current nondestructive testing technology in the detection of natural defects.At present,in the field of analytical calculation for the forward problem of eddy current nondestructive testing,there are more researches on the analytical model without defects,less on the analytical model with defects;in the analytical model with defects,there are more researches on the analytical model of regular shape defects,but less on the analytical model of natural defects.Aim to above two problems existing in the analytical model calculation of the forward problem of eddy current nondestructive testing,the following research work has been carried out:(1)The analytical solution of is extended to obtain the magnetic field in coil region.First of all,for the previous analytical calculation model of cylindrical defects,according to the needs of the actual application scenario,the solution domain is extended,and the series expression of the magnetic field signal in the region where the rectangular coil is located is obtained.Then,the time domain solution of the region is obtained by the inverse Laplace transform.The analytical solution is applied to deduce the analytical calculation model of the magnetic field of the selected frequency band electromagnetic eddy current testing system.The selected frequency band electromagnetic eddy current detection method improves the shortcomings of the sinusoidal excitation signal detection frequency is too single and the pulse eddy current excitation signal frequency is too dispersed in the traditional eddy current detection.The energy is concentrated in the effective frequency band to avoid energy waste and is apromising non-destructive testing technology.(2)An analytic solution to eddy current nondestructive testing with natural defect in metal is derived.In reality,the shape of natural defects is irregular,the wall surface is not smooth,and there are different degrees of local thinning,which is difficult to be represented by function.Fortunately,the main influencing factor of local thinning in the analytical calculation is conductivity,so a region between the metal and the air is set to simulate the rough wall surface of the natural defect.In this region,the conductivity is larger than that of in air region and smaller than that of in metal region.The mathematical model of analytical calculation of magnetic field in eddy current nondestructive testing of metal components with natural defects is established.The governing equations of the mathematical model about the vector potential are derived from the Maxwell equations.The integral expressions of the magnetic field signals in each solving domain are solved by the method of separating variables.The series expressions of the magnetic field signals in each solving domain are obtained by the method of truncation region.Finally,the analytical solutions in time domain are obtained by the Laplace Inverse Transform.Through the comparison between the analytical results and the numerical simulation results,the calculation method of electromagnetic nondestructive testing signal of natural defects obtained in this paper not only has a high calculation accuracy,but also the calculation efficiency is more than30 times of the simulation calculation.Finally,the influence of the conductivity in the surface area of natural defects on the calculation results of magnetic field is analyzed and compared.(3)An analytic solution to eddy current nondestructive testing with or cone defect in metal is derived.In the previous research,the mathematical model is mainly used to solve the vertical boundary,but in reality,there are a large number of inclined cracks,such as V-type fatigue cracks and other inclined boundary defect shapes.Therefore,this paper proposes an analytical calculation model of conical defects on metal components,which uses the equivalent boundary method to solve the inclined boundary equivalent to the vertical boundary,and obtains the analytical solution of the magnetic field.Then,a three-dimensional finite element simulation model of conical defect is built.By comparing the analytical results with the numerical simulation results,the calculation method of electromagnetic nondestructive testing signal of conical defect in this paper is not only of high accuracy,but also of ten times more efficiency than the simulationcalculation.