Study On Analytical Modelling For Eddy Current Response From Driver–Pickup Coils

In manufacturing fields,safety in production is one of the core issues for a country.A large number of alloys and metal materials are usually needed in these fields,such as aeronautics and astronautics,shipbuilding,weapons manufacturing,nuclear industry and railway transportation.The quality of metal materials is closely related to the safety of the industrial production process and the quality of the products.Eddy current testing(ECT)has unique advantages for detecting the properties and structure of conductive materials,such as: no coupling agent,sensitivity to crack signal,multi parameter detection of material properties.Therefore,ECT technology is widely used in the industrial manufacturing field.Usually,there are various samples with complicated structure in the process of ECT.In order to improve the sensitivity,signal-to-noise ratio and thermal drift immunity of specimen,driver–pickup probe is applied.Compared with the traditional absolute probe,the mutual inductance probe has better sensitivity and flexibility.Analytical model is of great significance for understanding the principles of ECT,designing new probes,improving detection efficiency,evaluating defect detection rate,and constructing inversion models.Consequently,it is important to establish the analytical model of eddy current field for mutual inductance probe.Dodd-Deeds model is the earliest and most widely used analytical model that describes eddy current electromagnetic field.Whereas it has some shortcomings: physical meaning of the model is not clear;expression is in the form of generalized double integral with numerical difficulties;solution area is a typical axisymmetric field;the process of establishing non-coaxial mutual inductance probe model is complicated.In order to establish the impedance model of mutual inductance probe signal,the author starts from Dodd-Deeds model,and establishes the theoretical model of mutual impedance probe signal.In the second chapter,the analytical model of a non-coaxial driver–pickup probe is established.A partial differential equation of vector magnetic potential is derived from Maxwell's equations,and the analytical model of magnetic field in the ideal single turn coil is set up.The analytical model of coil excitation magnetic field and the eddy current field of multilayer conductive structure is established and solved by the superposition principle,and the reflection and transmission theory of electromagnetic fields is applied to multilayered specimens.The frequency domain expression of absolute probe voltage can be deduced by using the analytical model of the vector potential.Afterwards based on the principle of coordinate transformation,the integral of the eddy current field that induced by the excitation field on the pickup coil is adopted,the mutual inductance voltage is obtained,and the change in mutual impedance is deduced.In the third chapter,the analytical model of a non-coaxial tilted driver-pickup probe is established.Basically,the core of the formulation is to obtain the projection of magnetic vector potential(MVP)from the driver coil onto the vector along the tilted pickup coil,which is divided into two key steps.The first step is to make a projection of MVP along the pickup coil onto a horizontal plane,and the second one is to build the relationship between the projected MVP and the MVP along the driver coil.Afterwards,an analytical model for the case of a layered plate is established with the reflection and transmission theory of electromagnetic fields.Fourier transform and Lorenz reciprocity theorem are usually applied to solve the mutual inductance model,so the solution domain of the eddy field is infinite in form of integral.In this chapter,the author combines the mapping theory to with Dodd-Deeds model effectively,so the change in impedance of the model is in form of series,which greatly improves the computation efficiency of the model.In the fourth chapter,the analytical model of mutual inductance probe is set up considering the source of excitation.Eddy current field is regarded as a quasi-static field in Dodd-Deeds model.The equation of alternating magnetic field is similar with that of the steady magnetic field due to that the influence of displacement current is ignored under the low frequency excitation.However,the influence of displacement current is amplified under high frequency excitation,there are differences between the theoretical values of the magnetic vector potential in the alternating electromagnetic field and the steady electromagnetic field.The research shows that high frequency eddy current testing can be applied to measure the thickness of some insulating materials and characterize the dielectric constant of low conductive materials.In this paper,the analytical model of high frequency eddy current mutual inductance probe is established from the Maxwell equation,and the relationship between the eddy current impedance of the coil and the relative dielectric constant of the conductive material under high frequency excitation is simulated and studied,which provides guidance for the characterization of the dielectric constant of the materials with poor insulation or electrical conductivity by high frequency eddy current testing.In this paper,an analytical modeling of mutual impedance change from a noncoaxial driver-pickup probe is established.The model is verified with the finite element model and experiment,and the correctness of the model is proved.