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.

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The proper assessment of vibration wear in heat exchangers is often problematic.

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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/Hz^½ (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/Hz^½.

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.

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