In eddy current testing, the law of attenuation of eddy current(EC) is of great concern. In conductive half space under the excitation of uniform magnetic field, the EC density decreases exponentially in the depth dir...In eddy current testing, the law of attenuation of eddy current(EC) is of great concern. In conductive half space under the excitation of uniform magnetic field, the EC density decreases exponentially in the depth direction. However, in conductor with finite thickness tested by coil, the distribution of EC in the depth direction is more complicated. This paper studies the characteristics of EC attenuation in metallic plate of finite thickness. Simulation results show that there is an EC reflection at the bottom of plate, which changes the law of EC attenuation. A new concept, namely the equivalent attenuation coefficient, is proposed to quantify the speed of EC attenuation. The characteristics of EC attenuation are utilized to explain the nonmonotonic relation between coil voltage and plate thickness. Procedure of selecting frequency is discussed. Thereafter, measurement of plate thickness is carried out and accurate result is obtained.展开更多
Based on the Maxwell equations, the nonlinear magneto-elastic vibration equations of a thin plate and the electrodynamic equations and expressions of electromagnetic forces are derived. In addition, the magneto-elasti...Based on the Maxwell equations, the nonlinear magneto-elastic vibration equations of a thin plate and the electrodynamic equations and expressions of electromagnetic forces are derived. In addition, the magneto-elastic combination resonances and stabilities of the thin beam-plate subjected to mechanical loadings in a constant transverse magnetic filed are studied. Using the Galerkin method, the corresponding nonlinear vibration differential equations are derived. The amplitude frequency response equation of the system in steady motion is obtained with the multiple scales method. The excitation condition of combination resonances is analyzed. Based on the Lyapunov stability theory, stabilities of steady solutions are analyzed, and critical conditions of stability are also obtained. By numerical calculation, curves of resonance-amplitudes changes with detuning parameters, excitation amplitudes and magnetic intensity in the first and the second order modality are obtained. Time history response plots, phase charts, the Poincare mapping charts and spectrum plots of vibrations are obtained. The effect of electro-magnetic and mechanical parameters for the stabilities of solutions and the bifurcation are further analyzed, Some complex dynamic performances such as perioddoubling motion and quasi-period motion are discussed.展开更多
This paper presents a closed expression of the layered-plate factor used to calculate the coil eddy-current impedance over the multi-layer plate conductor. By using this expression, the general series of eddy-current ...This paper presents a closed expression of the layered-plate factor used to calculate the coil eddy-current impedance over the multi-layer plate conductor. By using this expression, the general series of eddy-current impedance can be written directly without solving the undetermined constant equations. The series expression is easy to use for theoretical analysis and programming. Experimental results show that calculated values and measured values are in agreement. As an application, when the bottom layer of the layered plate is a non-ferromagnetic thin layer conductor and the product of the thickness and conductivity of the layer remains unchanged, using the layered-plate factor expression proposed in this paper, it can be theoretically predicted that the eddy-current impedance curves corresponding to different thin layer thickness values will coincide.展开更多
The effect of the Hall current on the magnetohydrodynamic (MHD) natural convection flow from a vertical permeable flat plate with a uniform heat flux is analyzed in the presence of a transverse magnetic field.It is ...The effect of the Hall current on the magnetohydrodynamic (MHD) natural convection flow from a vertical permeable flat plate with a uniform heat flux is analyzed in the presence of a transverse magnetic field.It is assumed that the induced magnetic field is negligible compared with the imposed magnetic field.The boundary layer equations are reduced to a suitable form by employing the free variable formulation (FVF) and the stream function formulation (SFF).The parabolic equations obtained from FVF are numerically integrated with the help of a straightforward finite difference method.Moreover,the nonsimilar system of equations obtained from SFF is solved by using a local nonsimilarity method,for the whole range of the local transpiration parameter ζ.Consideration is also given to the regions where the local transpiration parameter ζ is small or large enough.However,in these particular regions,solutions are acquired with the aid of a regular perturbation method.The effects of the magnetic field M and the Hall parameter m on the local skin friction coefficient and the local Nusselt number coefficient are graphically shown for smaller values of the Prandtl number P r (= 0.005,0.01,0.05).Furthermore,the velocity and temperature profiles are also drawn from various values of the local transpiration parameter ζ.展开更多
To determine the wall thickness, conductivity and permeability of a ferromagnetic plate, an inverse problem is established with measured values and calculated values of time-domain induced voltage in pulsed eddy curre...To determine the wall thickness, conductivity and permeability of a ferromagnetic plate, an inverse problem is established with measured values and calculated values of time-domain induced voltage in pulsed eddy current testing on the plate. From time-domain analytical expressions of the partial derivatives of induced voltage with respect to parameters,it is deduced that the partial derivatives are approximately linearly dependent. Then the constraints of these parameters are obtained by solving a partial linear differential equation. It is indicated that only the product of conductivity and wall thickness, and the product of relative permeability and wall thickness can be determined accurately through the inverse problem with time-domain induced voltage. In the practical testing, supposing the conductivity of the ferromagnetic plate under test is a fixed value, and then the relative variation of wall thickness between two testing points can be calculated via the ratio of the corresponding inversion results of the product of conductivity and wall thickness. Finally, this method for wall thickness measurement is verified by the experiment results of a carbon steel plate.展开更多
The present numerically study investigates the influence of the Hall current and constant heat flux on the Magneto hydrodynamic (MHD) natural convection boundary layer viscous incompressible fluid flow in the manifest...The present numerically study investigates the influence of the Hall current and constant heat flux on the Magneto hydrodynamic (MHD) natural convection boundary layer viscous incompressible fluid flow in the manifestation of transverse magnetic field near an inclined vertical permeable flat plate. It is assumed that the induced magnetic field is negligible compared with the imposed magnetic field. The governing boundary layer equations have been transferred into non-similar model by implementing similarity approaches. The physical dimensionless parameter has been set up into the model as Prandtl number, Eckert number, Magnetic parameter, Schmidt number, local Grashof number and local modified Grashof number. The numerical method of Nactsheim-Swigert shooting iteration technique together with Runge-Kutta six order iteration scheme has been used to solve the system of governing non-similar equations. The physical effects of the various parameters on dimensionless primary velocity profile, secondary velocity profile, and temperature and concentration profile are discussed graphically. Moreover, the local skin friction coefficient, the local Nusselt number and Sherwood number are shown in tabular form for various values of the parameters.展开更多
基金Supported by National Natural Science Foundation of China(Grant No.51277154)Xiamen Key Laboratory of Optoelectronic Transducer Technology+1 种基金Fujian Key Laboratory of Universities and Colleges for Transducer TechnologyInnovative Talents Program of Far East NDT New Technology&Application Forum
文摘In eddy current testing, the law of attenuation of eddy current(EC) is of great concern. In conductive half space under the excitation of uniform magnetic field, the EC density decreases exponentially in the depth direction. However, in conductor with finite thickness tested by coil, the distribution of EC in the depth direction is more complicated. This paper studies the characteristics of EC attenuation in metallic plate of finite thickness. Simulation results show that there is an EC reflection at the bottom of plate, which changes the law of EC attenuation. A new concept, namely the equivalent attenuation coefficient, is proposed to quantify the speed of EC attenuation. The characteristics of EC attenuation are utilized to explain the nonmonotonic relation between coil voltage and plate thickness. Procedure of selecting frequency is discussed. Thereafter, measurement of plate thickness is carried out and accurate result is obtained.
文摘Based on the Maxwell equations, the nonlinear magneto-elastic vibration equations of a thin plate and the electrodynamic equations and expressions of electromagnetic forces are derived. In addition, the magneto-elastic combination resonances and stabilities of the thin beam-plate subjected to mechanical loadings in a constant transverse magnetic filed are studied. Using the Galerkin method, the corresponding nonlinear vibration differential equations are derived. The amplitude frequency response equation of the system in steady motion is obtained with the multiple scales method. The excitation condition of combination resonances is analyzed. Based on the Lyapunov stability theory, stabilities of steady solutions are analyzed, and critical conditions of stability are also obtained. By numerical calculation, curves of resonance-amplitudes changes with detuning parameters, excitation amplitudes and magnetic intensity in the first and the second order modality are obtained. Time history response plots, phase charts, the Poincare mapping charts and spectrum plots of vibrations are obtained. The effect of electro-magnetic and mechanical parameters for the stabilities of solutions and the bifurcation are further analyzed, Some complex dynamic performances such as perioddoubling motion and quasi-period motion are discussed.
基金supported by the National Natural Science Foundation of China(Grant No.51577004)
文摘This paper presents a closed expression of the layered-plate factor used to calculate the coil eddy-current impedance over the multi-layer plate conductor. By using this expression, the general series of eddy-current impedance can be written directly without solving the undetermined constant equations. The series expression is easy to use for theoretical analysis and programming. Experimental results show that calculated values and measured values are in agreement. As an application, when the bottom layer of the layered plate is a non-ferromagnetic thin layer conductor and the product of the thickness and conductivity of the layer remains unchanged, using the layered-plate factor expression proposed in this paper, it can be theoretically predicted that the eddy-current impedance curves corresponding to different thin layer thickness values will coincide.
文摘The effect of the Hall current on the magnetohydrodynamic (MHD) natural convection flow from a vertical permeable flat plate with a uniform heat flux is analyzed in the presence of a transverse magnetic field.It is assumed that the induced magnetic field is negligible compared with the imposed magnetic field.The boundary layer equations are reduced to a suitable form by employing the free variable formulation (FVF) and the stream function formulation (SFF).The parabolic equations obtained from FVF are numerically integrated with the help of a straightforward finite difference method.Moreover,the nonsimilar system of equations obtained from SFF is solved by using a local nonsimilarity method,for the whole range of the local transpiration parameter ζ.Consideration is also given to the regions where the local transpiration parameter ζ is small or large enough.However,in these particular regions,solutions are acquired with the aid of a regular perturbation method.The effects of the magnetic field M and the Hall parameter m on the local skin friction coefficient and the local Nusselt number coefficient are graphically shown for smaller values of the Prandtl number P r (= 0.005,0.01,0.05).Furthermore,the velocity and temperature profiles are also drawn from various values of the local transpiration parameter ζ.
基金supported by the National Defense Basic Technology Research Program of China(Grant No.Z132013T001)
文摘To determine the wall thickness, conductivity and permeability of a ferromagnetic plate, an inverse problem is established with measured values and calculated values of time-domain induced voltage in pulsed eddy current testing on the plate. From time-domain analytical expressions of the partial derivatives of induced voltage with respect to parameters,it is deduced that the partial derivatives are approximately linearly dependent. Then the constraints of these parameters are obtained by solving a partial linear differential equation. It is indicated that only the product of conductivity and wall thickness, and the product of relative permeability and wall thickness can be determined accurately through the inverse problem with time-domain induced voltage. In the practical testing, supposing the conductivity of the ferromagnetic plate under test is a fixed value, and then the relative variation of wall thickness between two testing points can be calculated via the ratio of the corresponding inversion results of the product of conductivity and wall thickness. Finally, this method for wall thickness measurement is verified by the experiment results of a carbon steel plate.
文摘The present numerically study investigates the influence of the Hall current and constant heat flux on the Magneto hydrodynamic (MHD) natural convection boundary layer viscous incompressible fluid flow in the manifestation of transverse magnetic field near an inclined vertical permeable flat plate. It is assumed that the induced magnetic field is negligible compared with the imposed magnetic field. The governing boundary layer equations have been transferred into non-similar model by implementing similarity approaches. The physical dimensionless parameter has been set up into the model as Prandtl number, Eckert number, Magnetic parameter, Schmidt number, local Grashof number and local modified Grashof number. The numerical method of Nactsheim-Swigert shooting iteration technique together with Runge-Kutta six order iteration scheme has been used to solve the system of governing non-similar equations. The physical effects of the various parameters on dimensionless primary velocity profile, secondary velocity profile, and temperature and concentration profile are discussed graphically. Moreover, the local skin friction coefficient, the local Nusselt number and Sherwood number are shown in tabular form for various values of the parameters.