NDT.net  August 1999,
Vol. 4 No. 8
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 twodimensional, 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 underrelaxation 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
 Lord,W., Sun,Y., Udpa,S., Nath,S.,
Physics of the Remote Field Eddy Current Effect,
Review of Progress in Quantitative NDE, Vol. 7A
 Palanisamy,R.,
Finite Element Study of the Anomalous Behaviour of Remote Field Eddy
Currents,
Proc. 7th Int. Conf. on Offshore Mechanics, Houston, Texas 1988
 Schmidt, T.R., Atherton, D.L., Sullivan, S.,
Use of OneDimensional SkinEffect Equations for Predicting Remote Field
Characteristics, Materials Evaluation Vol.47 / Jan.89
 Ostermeyer, H.,
Methodische Entwicklung von FernfeldWirbelstromsonden
zur Prüfungferromagnetischer Stahlrohre,
Dissertation, Universität Hannover 1997
Top
© NDT.net,
info@ndt.net
/DB:Article /SO:ECNDT /AU:Ostermeyer_H /AU:Stegemann_D /CN:DE /CT:ET /CT:RFEC /ED:199908