Table of Contents ECNDT '98 Session: Electromagnetic Methods

New Aspects for Remote Field Eddy Current Probe Development. H. Ostermeyer - Test Maschinen Technik. D. Stegemann - Uni. Hannover. Germany. Corresponding Author Contact: Email: stegemann@mbox.ikph.uni-hannover.de

Introduction

The Remote Field Eddy Current Technique is an electromagnetic NDT method which is more and more used for the inspection of ferrous heat exchanger and boiler tubes. One main advantage of the method is the high sensibility to large wallthickness reductions without sharp edges. The fact that the field application of the technique is relatively young causes fewer experience in the probe development than in the conventional eddy current technique. Additionally some phenomena of the Remote Field Technique are not easy to understand. To allow a better understanding a short description of the basic principle is given first.

Principle of the Remote Field Eddy Current Technique

Fig. 1: Principle of Remote Field Sensing Effect

An RFEC probe consists basicly of a exciter coil and a detector coil in a certain distance between each other. The probe is passed through the tube which shall be inspected. The exciter coil is fed with a low frequency alternating current (normally sinusoidal). This exciter current causes an electromagnetic field around the exciter coil. The energy of the field spreads out in axial direction inside the tube as well as into the tube wall. The eddy currents which are induced in the tube wall generate a secondary field which can be measured outside the tube. This secondary field is much weaker than the primary field directly at the exciter coil inside the tube and has a significant phase shift. The direction of the energy flow is from tube inside to tube outside. This area is called Near Field.

The slope in the Near Field in axial direction is very fast because it has to provide the energy for the induction of the eddy currents in the tube wall. The slope of the secondary field at the tube outside is much smaller. Thus in a certain axial distance from the exciter coil there is an area at which the secondary field is stronger than the primary field. This area is called Remote Field. The area between Near field and Remote Field is called Transition Zone. Here the direction of the energy flow is reverted. If a detector coil is placed in this area an electromagnetic field will be measured which is induced by energy which has passed two times the tube wall. Thus it is spoken from two different energy paths. On the direct coupling path the energy comes directly fro exciter coil, on the indirect coupling path the energy has passed to the tube outside and is transmitted back to the tube inside. If a defect is located in the tube wall on the indirect coupling path, it can be detected by the change of the electromagnetic field the Remote Field.

As probes must be manufactured individually for each different tube type, the probe development is an important factor for the economic use of the method. The classical procedure of probe development is a combination of experience and experiment. The new probe design is based on the experience with already manufactured probes. For an evaluation of the new design the probe must be manufactured. If the probe design is complicated, for example due to dual exciter coil arrangement or segmented differential detector coil systems, the costs of the development can be very high. Therefore a method for the pre- calculation of the probe performance is extremely useful.

Calculation of the Electromagnetic Field around an Exciter Coil

Maxwell's equation are the basis for the calculation of electromagnetic fields. An exact solution of these equations can be given only in special cases, so that numerical approximations are used. If the problem is two-dimensional, a considerable reduction of the computation expenditure can be obtained by the introduction of the magnetic vector potential A = x B With the assumption that all field variables are sinusoidal, the time dependence can be simplified by the use of complex numbers for all field variables. With this assumptions the differential equation which has to be solved is in cylindrical coordinate system:

with
A Vector Potential
r, z Cylindrical Coordinates
µ Permeability
s elektrical Conductivity
w Exciter Frequency


For the determination of the approximated solution of this equation the finite difference method and the finite element method (FEM) can be used. FEM has advantages because of lower requirements to the discretization. If the material properties within one element are estimated to be constant the last term of the equation becomes zero. Figure 2 shows the principle discretization for the field computation.

Fig.2: Discretization of the Tube and Exciter Coil

The accuracy of the calculated solution is highly depending of realistic values for Conductivity and permeability of the tube material. While the conductivity can be found in the literature for most materials, the right permeability is harder to determine. In the RFEC technique the exciter current and thus the exciter field strength is often to high to assume a linear material behaviour with constant properties. This requires the use of the magnetization curve of the tube material. if this curve cannot be found in the literature it can be determined experimental with a ring specimen from the tube material. Figure 3 shows the magnetization and permeability curves measured at a riser pipe and the principle experimental setup.

A ring specimen is cut from the tube. Two coils are wrapped around this ring, one exciter coil and one receiver coil. The exciter coil NI should cover the entire ring so that there are no field losses when ring is saturated. The sinusoidal exciter current which can be measured at

Fig.3: Experimental Determination of the Permeability

the resistor R is proportional to the magnetic field H. The voltage which is induced in the receiver coil N2 is proportional to the change of the flux, df/dt, in the specimen. The flux density B can be calculated after integration of this voltage.

For the field calculation it more convenient to use a µ(B) curve than the normal µ(H) curve because the calculated vector potential A is derived from the flux density B. This u(B) curve however can be calculated easily from the measured values.

Fig.4: Iteration Procedure

Now since the material properties of the tube are known the electromagnetic field of the probe can be calculated with an iterative procedure. Beginning with an assumed value for the permeability a solution for the field equation is calculated. With this solution the flux density at any point in the computation domain can be determined. Using the µ(B) curve an actualized permeability distribution in the tube wall is found. With this improved permeability distribution the field eququalion for the vector potential is solved again.

This procedure is repeated until the previous defined convergence criteria are reached. The actualization of the permeability has to be done with an under-relaxation process to avoid numerical instability. The final solution of the vector potential equation is the complex flux distribution. The real part of this solution can be seen as the field lines at t = 0. It gives a good overview over the electromagnetic field which is generated by the exciter coil. Figure 5 shows these field lines which were calculated for a tube with a diameter of 88 m thickness of 6.5 mm with the magnetization curve shown in figure 3. The exciter data were was 80 Hz.

Fig. 5: Real Part of Calculated Field Distribution around Exciter Coil

It can bee seen that there are two areas with totally different behaviour. While in the vicinity of the exciter coil the field lines are encircling the exciter coil (the Near Field), there is another area in a larger distance were the field lines are directed away from the exciter coil (the Remote Field). The Transition Zone between both areas is a sharp separation. The zone inside the tube wall in which both areas are separated, is called in the literatur "Potential valley". It can be seen in Figure 5 as well clearly.

Calculation of Probe Signals and Parameters

Fig.6: Defect Signal Simulation Procedure

The field distribution itself gives information about the location where the detector coil or coils should be placed. It can however be used as a basis for the calculation of defect signals of the probe as well as for the optimization of probe parameters. For this purpose a detector coil is assumed at a certain distance to the exciter coil. The voltage which is induced in this receiver can be calculated from the coil data (area, number of windings,etc.) and the flux density at the location of the coil which was determined from the computed field distribution. This induced voltage is again a complex number with real and imaginary Part.

It gives the detector coil working point for the simulated arrangement of tube, probe and inspection parameters. The procedure which is used to simulate defect signals is explained with figure 6. An arrangement with a defect in the tube wall is computed. If motion induced signals are neglected, it makes no difference to the simulation whether the defect is moved towards the probe or the probe is moved towards the defect. Therefore a loop is programmed in which the field distribution an the induced detector voltage is calculated for different defect positions. In the beginning the defect is located in front of the detector coil. In each calculation it is moved a certain distance in axial direction until the defect has passed the detector coil and the entire defect signal has been determined. The signal when the exciter coil is passing the defect can be simulated as well as the different signals at different defect depths or lengths. Figure 7 shows calculated defect signals of an absolute probe in the described arrangement. Both amplitude change and phase shift between the different defect signals can be seen.

Fig.7: Calculated Defect Signals of Absolute Probe Fig.8: Detector Coil Voltage as Function of Exciter Current

An important parameter for the probe development is the amplitude Of the exciter current, because of its influence on the diameter of the wire which is used for the coil. For an estimation of the required current the previous described simulation of defect signals is performed with different exciter currents. The result of this calculation is shown in figure 8. The induced detector voltage for an assumed detector coil is calculated for different exciter current amplitudes at a frequency of 80 Hz. As a comparison the calculation is done with a linear approach with constant permeability (µ_r-40) and using the measured magnetization curve of the tube.

It can be seen that the curve which is based on measurements deviates from the linear slope already at lower exciter currents. The linear calculation is thus not sufficient for the prediction of probe signals. The amplitudes of the detector are calculated too high. Another effect which can be observed is the fact that the use of higher exciter currents will not result in the expected increase of detector signal amplitude. Reason for this is that the increase of exciter current increases the flux density in the tube wall directly at the exciter coil and thus also the permeability.

This increased permeability however acts shielding against the energy distribution to the Remote Field. Therefore the small detector signals are better enlarged by high quality signal amplifiers than by power amplifiers for the exciter current.

Conclusion

The development of Remote Field Eddy Current probes requires experience and expensive experiments. The numerical simulation of electromagnetic fields can be used not only for a better understanding of the Remote Field effect but also for the probe lay out. Geometrical parameters of the probe can be derived from calculation results as well as inspection parameters. An important requirement for a realistic prediction of the probe performance is the consideration of material properties of the tube for which the probe is designed. The experimental determination of magnetization curves is necessary and can be satisfactory done with a simple experimental setup.

References

1. Lord,W., Sun,Y., Udpa,S., Nath,S., Physics of the Remote Field Eddy Current Effect, Review of Progress in Quantitative NDE, Vol. 7A
2. Palanisamy,R., Finite Element Study of the Anomalous Behaviour of Remote Field Eddy Currents, Proc. 7th Int. Conf. on Offshore Mechanics, Houston, Texas 1988
3. Schmidt, T.R., Atherton, D.L., Sullivan, S., Use of One-Dimensional Skin-Effect Equations for Predicting Remote Field Characteristics, Materials Evaluation Vol.47 / Jan.89
4. Ostermeyer, H., Methodische Entwicklung von Fernfeld-Wirbelstromsonden zur Prüfungferromagnetischer Stahlrohre, Dissertation, Universität Hannover 1997