by A.
Shatat and David L. Atherton*
|
This article demonstrates how
the remote field eddy current technique might be extended to
measure support plate fretting wear in heat exchanger tubes.
A finite element analysis was used to examine the plate's effect
on the eddy current signal. Experimental data lend support to
a suggested multifrequency method for sizing fretting grooves.
G.P. Singh
Associate Contributing Editor
|
In heat exchangers, vibrations induced by high velocity fluids
cause fretting of the tubes at the support plate locations. Support
plate vibration wear (fretting) has been recognized as the second leading
cause of heat exchanger failure after corrosion. Blevins (1979) showed
that the wear rate increases as the tube support clearance is enlarged.
It is therefore important that fretting wear is determined as early
as possible.
Proper assessment of vibration wear is often problematic
(Krzywosz and Dau, 1990). This is mainly due to two factors. First of
all, fretting wear is a form of external wall loss and therefore difficult
to measure in ferromagnetic pipes. Secondly, the interference caused
by the support plate is so complicated that measured signals are often
hard to analyze. The remote field eddy current technique is a well established
through-wall inspection method that detects external and internal wall
losses with approximately equal sensitivity, and is therefore frequently
used for the inspection of ferromagnetic tubing. However, the same mechanism
that makes the remote field sensitive to external wall loss also makes
it sensitive to the presence of external conducting objects, such as
support plates. In fact, the remote field eddy current technique is
exceptionally sensitive to support plate interference. The technique
has a very characteristic support plate response, which depends on a
number of pipe and plate parameters. A commercial finite element package
was used here to investigate the effect of the support plate on the
remote field signal.
The proper assessment of vibration wear in heat exchangers is
often problematic.
Remote Field Eddy Current Support
Plate Signals
The remote field eddy current technique is used for the inspection of
relatively thick walled ferromagnetic tubes. The typical remote field
probe consists of two coaxial coils, spaced 2.5-3 pipe diameters apart
(Schmidt, 1984). One coil carries a low frequency AC current, generating
an AC field. The other coil is used to measure the field of the exciter
coil. There are two different paths that couple the energy from the
exciter to the detector. One is along the inside of the pipe and is
a direct coupling path; the other is along the outside of the pipe and
is an indirect (external) coupling path (Figure1). The dominant path
is determined by the axial distance between the two coils. For axial
distances smaller than 1 pipe outer diameter (OD), the predominant energy
coupling path is the internal one. Because of circumferential eddy currents
induced in the pipe wall, the energy in the internal path drops rapidly
and exponentially as the distance from the exciter is increased. At
axial distances greater than about 2 pipe ODs, the energy of the internal
path has been so heavily reduced that the external energy coupling becomes
dominant. The external path contains information from two pipe wall
transits, and as such provides the remote field eddy current method
with its through-wall inspection characteristic.
Figure 1 - Remote field eddy current energy
coupling. In the remote field zone, only the external energy coupling
remains.
The effect of the support plate is due to its influence
on the external energy coupling path. The plate effectively intercepts
the external coupling between exciter and detector and causes a significant
drop in detector signal. A typical strip chart recording of a remote
field eddy current support plate scan is shown in Figure 2. Because
of the relatively large distance between exciter and detector, the interference
of the support plate extends over a significant axial range (probe length
+ plate thickness = 2.5-3.5 pipe ODs).
Figure 2 - Strip chart recording of remote
field eddy current support plate signal. The plate is 6.4 mm (0.26
in.) thick, with no defect present. Current = 250 mA at 220 Hz.
Pipe OD is 19 mm (0.8 in.), coil separation is 50 mm (2 in.).
The amplitude and phase information of the detector
signal can be combined in one display by plotting the corresponding
in phase and quadrature components in the complex plane. The result,
referred to as the voltage plane polar plot display, is often used for
improved signal interpretation (Atherton et al., 1993). Axial information
is lost on the voltage plane display, but is obtained from the strip
charts. Before calculating the in phase and quadrature components, the
detector signal is normalized with respect to the nominal full wall
signal. The nominal full wall signal, therefore, corresponds to the
(1,0) point on the voltage plane display, and anomalies will appear
as deviations from the (1,0) point. The skin depth spiral, included
in Figure 3, indicates deviations as predicted by the skin depth model
(Schmidt et al., 1989).
Figure 3 - Calculated ideal voltage plane
display for support plate, no defect case. Plate to tube gap = 0.476
mm (0.02 in.). Exciter carries 300 mA at 200 Hz and is 50 mm (2
in.) from the receiver. The detector is approaching the plate.
On the voltage plane polar plot, the support plate
response exhibits a characteristic signature (illustrated in Figure
3). The tail of the signature corresponds to the signal drop caused
by the plate when it separates transmitter and receiver. Because the
signal drop continues over a long axial range, the support plate signature
trace has a relatively long tail. There is also a slight increase in
amplitude when either of the two coils approaches the plate.
Finite Element Analysis
The remote field eddy current support plate response was investigated
using Infolytica's Magnet 5.03 finite element software package. The
package was run on a 486 computer with 64 MB of RAM. The investigation
was performed using an axisymmetric model comprising slightly over 9,500
elements. Geometric details of the model are shown in Figure 4. In order
to improve accuracy and provide resolution in the region of interest,
the mesh density at the pipe-plate interface was made high. To give
an impression of the refinement of the mesh, the region around the support
and pipe is shown in Figure 5. Fretting wear was modelled using full
circumferential rectangular grooves with the same width as the thickness
of the support plate. The mesh in the pipe wall was constructed such
that it allows groove depths that are 20 percent multiples of the wall
thickness. The pipe and plate are made of linear isotropic material
(see Table 1).
Figure 4 - Outline of the finite element
model used in the support plate investigation. Variable coil positions
simulate the pull-through of a remote field probe. Each exciter
area consist of a 3.2 x 3.2 mm (0.13 x 0.13 in.) region through
which a total of 300 mA is carried.
Figure 5 - Zoom in of the mesh in the
top region of the model. The region has been divided into three
different areas, each shown separately. The total model consist
of 9,500 triangle elements (10,000 is the maximum the solver
can handle).
Table 1 - Dimensions
and material parameters used in the finite element model
The exciter coil is modelled as having a square
cross section, carrying a total current of 300 mA at 200 Hz. A remote
field scan is simulated by moving the exciter towards the plate (see
Figure 4). The detector signal is obtained by finding the modified magnetic
vector potential at an axial distance of 50 mm (2 in.) from the center
of the exciter. The modified magnetic vector potential is equal to the
product of the magnetic vector potential, A, and the radial coordinate,
r. Except for the axis of the model and the boundary nodes of the plate,
all borders were constrained using Dirichlet boundary conditions. The
model was solved as a second order problem.
Energy Flow Analysis
Figure 6 shows the direction of average
energy flow in a 40 ´ 40 mm (1.6 ´ 1.6 in.) subsection of
the model using arrow plots. The average energy flow was calculated
using the time averaged Poynting vector, which in turn was calculated
from the magnetic vector potential. The energy is directed from the
source towards the conducting sections of the model (pipe and plate),
where it is dissipated.
Figure 6 - Time averaged Polynting vector
calculated at the pipe-plate interface. The pipe has no defect;
the air gap is 0.476 mm (0.02 in.) wide. The exciter is located
at 46.4 mm (1.86 in.) from mid plate, at the position shown, and
carries 300 mA at 200 Hz. The figure shows a 40 x 40 mm (1.6 x
1.6 in.) zoom in. The widths of the arrows are proportional to
the logarithm of the local Polynting vector.
There is an apparent tendency for the energy to
be funnelled into the air gap between pipe and plate. Both the plate
and the pipe are ferromagnetic and offer a path of low reluctance to
the flux. The air gap separates the two, and couples the flux from one
into the other. The big permeability difference between the air gap
and the ferromagnetic material of pipe and plate causes a significant
increase in the magnetic field H across the gap. This
results, by definition of the Poynting vector, in large energy densities
in the gap region, which in addition has only limited dissipation. As
a result, the energy at the far side of the plate has emanated predominantly
from the gap.
This energy flow can be used to explain qualitatively
the shape of the support plate trace. There is an increase in amplitude
just before the detector enters the area below the support plate (point
2 on Figure 3). This increased amplitude is the result of the funnelling
of energy through the air gap. The funnelling of energy provides the
time-averaged Poynting vector with a significant radial component, which
is highest at the edge of the plate. When the detector approaches the
plate, it will register the higher energy densities as a slight increase
in amplitude. The maximum detector amplitude is reached several millimeters
from the support plate edge.
Position 4 on Figure 3 corresponds to the situation
when transmitter and receiver are located on different sides of the
support plate. In this case, the plate blocks most of the energy from
reaching the receiver. The support plate signature will become shorter
when the gap width is increased, allowing more energy to reach the other
side.
Depth Sizing of Fretting Grooves
Information on the depth of fretting grooves could be obtained when
the detector coil is located directly underneath the plate. On the support
plate trace this corresponds to a position slightly to the right of
point 3 in Figure 3. This was investigated by placing the exciter at
an axial distance of 46.4 mm (1.87 in.) from the plate edge, while calculating
the detector signal underneath the support plate. The detector phase
was determined for five different depths of full circumferential fretting
grooves. The results are presented in Figure 7. The phase change induced
by a groove seems to be roughly proportional to the depth of the groove,
indicating that the phase velocity in the air gap is significantly higher
than in the pipe wall.
Figure 7 - Calculated phase of the dector
signal, when located underneath the plate. Exciter at 50 mm (2 in.)
distance, carrying 300 mA at 200 Hz.
There are, however, some practical aspects that
complicate the application of these findings. First of all, the nominal
full wall phase is not always available. The nominal phase is a reference
that allows the calculation of the phase change caused by the fretting.
Without this reference, accurate fretting sizing can not be performed.
The difficulty is that it is not always easy to accurately predict what
the phase underneath the support plate would be if there were no fretting.
The nominal full wall phase depends on the width of the air gap, the
thickness of the support plate, and the local values of the permeability
and conductivity of pipe and plate. These factors (and their influences)
are not accurately known.
Instead of the nominal full wall phase, the phase
at a different frequency can be used as the reference. This second frequency
should be of about the same order of magnitude as the first frequency
to ensure that the behavior of the pipe and the plate remain practically
the same. In Figure 8 the calculated detector phase is plotted as a
function of the frequency for different fretting groove depths under
the support plate. The calculated phase seems to be proportional to
the square root of the frequency and as such obeys the skin depth relationship.
According to the skin depth equation, the slope of the phase-frequency
curve is also linearly proportional to the thickness of the remaining
pipe wall. A reference slope for the nominal full wall case is easily
obtained, because (surprisingly) the slope does not change with the
presence of a support plate. The slopes can therefore be used to yield
an estimation of the depth of the grooves.
Figure 8 - Calculated influence of frequency
on detector signal when detector is directly beneath the plate. The
exciter carries 300 mA at 200 Hz and is at 50 mm (2 in.) from plate
center. Exciter-detector spacing is 50 mm (2 in.).
We then attempted to verify the finite element results
using an experimental mock-up of a heat exchanger. A 500 ´ 500
mm (20 ´ 20 in.) steel plate with a thickness of 6.4 mm (0.25
in.) was used to represent the support plate. A hole was drilled in
the plate with a diameter of 19.8 mm (0.78 in.). The plate supported
a carbon steel pipe with an OD of 19 mm (0.75 in.) and a wall thickness
of 2.3 mm (0.09 in.). The remote field probe consisted of a 20 mm (0.8
in.) long exciter and a 5 mm (0.2 in.) long detector, which were spaced
50 mm (2 in.) apart.
First the slope of phase-frequency curve was determined
for the no-plate case and found to be -19.8 degrees/Hz½
(Figure 9). Then the remote field probe was positioned such that its
detector coil was located directly under the support plate. Again the
slope of the phase-frequency curve was determined. The slope was found
to vary only slightly from the no-plate case: -20.0 degrees/Hz½.
Figure 9 - Experimental depth gaging of full
circumferential grooves under 6.34 mm (0.25 in.) thick support plate.
Detector is centered under plate. Exciter-dector spacing is 50 mm
(2 in.) and I= 300 mA.
To model fretting wall loss, full circumferential
grooves were cut in the outside of the pipe. The grooves were made 6.4
mm (0.26 in.) wide, with depths of 37 percent and 81 percent of the
wall thickness. When the grooves were placed under the support, the
slopes of the phase-frequency curves changed significantly. The slopes
were used in combination with the skin depth equation to estimate the
depth of the full circumferential grooves, yielding 31 percent and 76
percent. Both depth estimations are close to the actual depths and well
within 10 percent of the wall thickness. The depth estimation depends
on plate thickness and wear depth, and in general will improve as the
plate becomes thinner and the fretting deeper.
In order to further improve the performance of the
multi-frequency sizing method, it is suggested that a second exciter
could be placed at an equal distance on the other side of the detector.
Not only will this boost signal strength, it will also provide a means
of identifying when the detector is directly beneath the support plate.
Conclusions
Using finite element analysis, the support plate response of the remote
field eddy current method was examined. The characteristic support plate
response was explained in terms of the funnelling of energy through
the air gap. It was found, both numerically and experimentally, that
the phase-frequency behavior of the remote field eddy current signal
is independent on the presence of a support plate. A multi-frequency
method was suggested for sizing of full circumferential fretting grooves
under support plates.
References
Atherton, D.L., D.D. Mackintosh, S.P. Sullivan, J.M.S. Dubois, and T.R.
Schmidt, "Remote Field Signal Representation," Materials
Evaluation, Vol. 51, No. 7, Jul. 1993, pp 782-789.
Blevins, R.D., "Fretting Wear of Heat Exchanger
Tubes (Part 1: Experiments)," Journal of Engineering for Power,
Oct. 1979, Vol. 101, pp 625-629.
Krzywosz, K., and G. Dau, "Comparison of Electromagnetic
Techniques for Nondestructive Inspection of Ferromagnetic Tubing,"
Materials Evaluation, Vol. 48, No. 1, Jan. 1990, pp 42-45.
Schmidt, T.R., "The Remote-Field Eddy Current
Inspection Technique," Materials Evaluation, Vol. 42,
No. 2, Feb. 1984, pp 225-230.
Schmidt, T.R., D.L. Atherton, and S.P. Sullivan,
"Use of One-Dimensional Skin-Effect Equations for Predicting Remote-Field
Characteristics, Including Wall-Thickness versus Frequency Requirements,"
Materials Evaluation, Vol. 47, No. 1, Jan. 1989, pp 76-79.
-
- * Department of Physics, Queen's University, Kingston, Ontario
K7L 3N6, Canada; (613) 545-2701; fax (613) 545-6463.
Copyright © 1997 by the American
Society for Nondestructive Testing, Inc. All rights reserved.
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