RESULTADOS DE LAS PREGUNTAS DE LA ENCUESTA

Having demonstrated the sensitivity of the eddy current system to changes in the lift-o between the surface of the sample and the probe, the reliability of the proposed measurement technique must be evaluated. This has been done using a high precision stage which is capable of controlling the lift-o between a probe and a at sample to an accuracy of 0.3μm as discussed in section 7.3. The

single frequency technique was evaluated on three steel samples, provided by the industrial partners, which were approximately 200 by 200 mm with a thickness of 10 mm. The exact composition of these three samples is not known, as they represent the intellectual property of the client, although they are representative of the industrial materials, and they are referred to using the codes provided with the samples; C40, FE370, and FES10.

In order to meet the criterion for sensitivity of the measurement system discussed in section 7.1, the eddy current probe must demonstrate a 1μm sensitivity to changes in lift-o over the operating

range of 2 mm in a repeatable manner. The reliability of the measurement was assessed at a number of nominal values of lift-o, in order to ensure that the performance of the measurement system was acceptable across the entire operating range. While the desired resolution of the measurement system to lift-o variations was 1μm, early results suggested that this may not be achievable, and

so in addition to the tests at 0.9 μm resolution using the precision stage the performance of the

measurement system at a resolution of 3.0μm was also investigated.

In order to test the reliability of the measurement technique at a given lift-o and for a given accuracy, the stage was rst used to increase the lift-o to the nominal value, for example 2 mm, as conrmed by the linear encoder. As discussed previously, due to the uncertainty in the contact measurement the error in the nominal lift-o may be larger than the resolution of the linear encoder, but should still be of the order of 10μm. At this point the lift-o would then be reduced

(a) 20 40 60 80 100 990 995 1000 1005 1010 Measurement Number Lift−off ( µ m) (b) 20 40 60 80 100 −0.37 −0.3695 −0.369 −0.3685 −0.368 Measurement Number Phase (Radians)

Figure 8.6: (a) The lift-o of each measurement using the precision stage for 5 scans with a resolution of 0.9μm at a nominal lift-o of 2 mm. (b) The change in the phase data as a function

of the measurement number on the C40 sample.

0.9μm or 3.0μm. This typically moved ten measurement steps below the nominal value, and the

lift-o was then increased to ten measurement steps above the nominal value, and the amplitude and phase data was recorded at each position. Once the scan had been completed it was then repeated multiple times, typically at least ten, in order to provide a statistically reliable number of measurements of the change in amplitude and phase data with controlled changes in lift-o. The relationship between the total lift-o and the measurement number is shown in gure 8.6 (a) for a nominal lift-o of 1 mm, where the repeated scans over the same lift-o values gives rise to the saw-tooth pattern. Figure 8.6 (b) shows the phase response of the measurement to the changes in lift-o on the sample C40 and shows the same saw-tooth pattern in the data. There is a gradual increase across the phase measurements, which is due to a temperature drift in the electronics, although due to the focus of this measurement being on the dierence between adjacent points this can be ignored.

In order to calculate the sensitivity of the measurement to changes in lift-o the dierence in measured phase between adjacent points was calculated for the phase data, and this is shown in gure 8.7 (a). In this gure the dierence between the phase change due to the 0.9 μm steps

and due to the resetting of the stage can be seen, where the data points corresponding to the stage returning to the initial scan position are marked by red crosses. A statistical analysis of the response of the coil is then required to determine the reliability of the measurement under these conditions. A histogram of the coil responses is shown in gure 8.7 (b), plotting the number of position changes for which a given phase dierence occurs. The histogram is split into 50 equally sized bins across the phase dierence range, and shows that the response of the coil to lift-o changes of 0.9 μm follows a roughly Gaussian distribution centred around -76.6μRadians.

(a) 20 40 60 80 100 0 0.5 1 1.5 Measurement Number

Phase Change (mRadians)

(b) −100 −50 0 0 5 10 15

Phase Difference (µRadians)

Number of Occurrences

Figure 8.7: The phase response for the C40 sample at a nominal lift-o of 2 mm to changes in lift-o of 0.9 μm, shown as (a) a function of the measurement number, and (b) as a histogram.

−100 −50 0 50 100

0 5 10 15

Deviation from the mean (%)

Number of Occurrences

Figure 8.8: The deviation from the mean as a percentage of the mean for the phase data at 2 mm lift-o and 0.9μm resolution on the C40 sample.

the lift-o change of 0.9μm, and assessing the deviation of each measurement from that mean value

of -76.6μRadians. This deviation is presented as a percentage of the mean value in gure 8.8, where

the vertical red lines show the ± 50 % boundaries. These boundaries mark the region within which the measurement can be considered reliable, and are dened by assuming that the measurement is quantised, and that all changes in the phase are related to changes in the lift-o which are integer steps of the resolution of 0.9μm. If the deviation from the mean lies between -150 and -50 % of

the mean then the quantised lift-o change from that measurement will be underestimated, in this case resulting in a measurement of 0μm, while if the deviation from the mean lies between 50 and

150 % of the mean then the quantised lift-o change will be overestimated, in this case giving a measurement of 1.8μm. This method of classifying the reliability is chosen as a simple and easily

quantiable method suitable for an industrial environment. For this experiment the percentage of the measurements which fall within the boundaries, and thus can be considered reliable, is 98.5 %. An estimation of the uncertainty in the measurement can be obtained by considering the

−6000 −400 −200 0 200 400 600 5 10 15 20 25 30

Deviation from the mean (%)

Number of Occurrences

Figure 8.9: The deviation from the mean as a percentage of the mean for the amplitude data at 2 mm lift-o and 0.9μm resolution on the C40 sample.

uncertainty in a binned histogram which has equal weightings for each bin [164,165], using

σ2[Nk] =Nk 1−Nk N , (8.1)

where Nk is the number of samples in the bin for which the uncertainty is calculated,N is the

total number of samples andσ2_[N

k]is the variance of the number of samples in the bin. For the

measurement presented here the bin is considered to be the region between ± 50 % of the mean, which allows the measurement to be expressed together with its uncertainty as 98.5 ± 1.7 %. It is important to note that the uncertainty here will tend to zero as the proportion of the points within 50 % of the mean increases to 100 % and an alternative uncertainty could be presented based on the Poisson statistics of the number of samples acquired in the measurement as√N_/N, which for

the 200 data points presented in this measurement would be 7.1 %.

An example of the histogram showing the deviation from the mean in gure 8.8 using the amplitude instead is shown in gure 8.9. The amplitude data can be seen to be markedly less reliable than the phase data for the same measurement conditions, shown by the large number of points which occur outside of the ± 50 % boundaries. The reliability of the measurement for the amplitude on the C40 sample for a lift-o of 2 mm and a resolution of 0.9μm is 66.0 ± 6.7 %.

Using this method the reliability of the measurement technique for a given resolution can be calculated for a variety of samples and lift-os, for both the phase and amplitude data by nding the variation around the average change in amplitude or phase for a given resolution for all samples at the chosen values of nominal lift-o. This is shown for a resolution of 0.9 μm in gure 8.10 for

both the amplitude and phase data in (a) and (b) respectively, for nominal lift-os of 1 and 2 mm. There is a considerable dierence between the reliability of the amplitude and phase data, where the phase data meets the client specied reliability of 90 % under all of the measurement conditions

(a) 1 2 0 20 40 60 80 100 Lift−off (mm) Reliability (%) C40 FE370 FES10 (b) 1 2 0 20 40 60 80 100 Lift−off (mm) Reliability (%) C40 FE370 FES10

Figure 8.10: The results across the full range of samples and at multiple nominal lift-os of either 1 or 2 mm with a nominal resolution of 0.9μm for (a) the amplitude data, and (b) the phase data.

(a) 1 2 0 20 40 60 80 100 Lift−off (mm) Reliability (%) C40 FE370 FES10 (b) 1 2 0 20 40 60 80 100 Lift−off (mm) Reliability (%) C40 FE370 FES10

Figure 8.11: The results across the full range of samples and at multiple nominal lift-os of either 1 or 2 mm with a nominal resolution of 3.0μm for (a) the amplitude data, and (b) the phase data.

tested, while the amplitude data only meets this criterion for one measurement.

A similar relationship can be seen in the measurements on the same samples performed at a resolution of 3.0 μm, where the amplitude and phase data are shown in gure 8.11 (a) and (b)

respectively, for all of the samples and at nominal lift-os of 1 and 2 mm. Again the phase data considerably outperforms the amplitude data, achieving almost 100 % reliability across all the measurement conditions tested. The amplitude data also performed well on two of the samples, although the performance on the C40 sample is very poor at the higher lift-o.

A summary of all of these results can be seen in table 8.1. The reliability of this measurement technique across the samples is very positive, particularly for the phase measurements, although the measurements at 0.9μm only just meets the desired reliability of 90 % for the sample C40. Ad-

ditionally there are large dierences between the samples in the amplitude data. These dierences may be due to the selected operating frequency of the coil, and thus the improvement discussed in section 7.5, where the coil is continuously operated at resonance, was proposed.

Sample Lift-o P. Rel. @0.9μm A. Rel. @0.9μm P. Rel. @3.0μm A. Rel. @3.0μm

C40 1 mm_{2 mm} 90.0 %_{98.5 %} 36.5 %_{66.0 %} 98.0 %_{100 %} 93.5 %_{44.5 %} FE370 1 mm_{2 mm} 95.5 %_{97.0 %} 93.5 %_{88.5 %} 99.5 %_{100 %} 100 %_{100 %} FES10 1 mm_{2 mm} 99.5 %_{98.8 %} 88.9 %_{58.8 %} 100 %_{100 %} 99.5 %_{97.5 %}

Table 8.1: A summary of the reliability measurements across all samples for nominal lift-os of 1 and 2 mm and resolutions of both 0.9 and 3.0 μm for the single frequency technique. The phase

reliability for a given resolution is marked as P. Rel., while the amplitude reliability is marked as A. Rel.

X

Y

sample

probe

scanning directions

crest

Figure 8.12: Schematic diagram showing the scanning directions (X and Y) used when assessing the sensitivity of the eddy current probe to transverse misalignments.