On Resolution, Accuracy and Calibration of Digital ...

On Resolution, Accuracy and Calibration
of Digital Ultrasonic Thickness Gauges

by Peter Hammond Cygnus Instruments Ltd *

ABSTRACT

The difference between resolution and accuracy is highlighted with respect to ultrasonic thickness gauges. After briefly describing the principles of operation, sources of errors are discussed, and where possible quantified. It is shown that calibration to national standards has no place in this field.

It is concluded that while the thickness gauge is a valuable tool for routine inspection, the accuracy of its readings should not be accepted with unquestioning faith.

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Table of contents


1. Introduction
   Accuracy and Resolution, The digital time of flight gauge, What is calibration?
2. Principles of Operation
   Obtaining a Time of Flight, Converting to Thickness
3. Sources of error
   Time of Flight errors, Variations in speed of sound, Temperature
4. Conclusions

Introduction

Digital ultrasonic thickness gauges are versatile instruments for measurement of engineering structures which can only be accessed from one side. Their most common uses are in quality control (e.g. during the fabrication of large tanks), and corrosion monitoring (e.g. ship hull condition surveys). They are easy to use, requiring the minimum of setup, and operate on a wide range of materials.

Display resolution as good as 0.01mm is commonly offered. However, in this paper, it will be shown that the situation is not as simple as it may seem. There are many factors which can reduce both the accuracy and resolution of the thickness reading obtained. These will be discussed, after first outlining the principles of operation of thickness gauges.1.

1 Throughout this paper, the term "thickness gauge" will be taken to mean only digital ultrasonic wall thickness gauge.

Accuracy and Resolution


Figure 1: Distribution of readings taken on a component, showing the difference between accuracy and resolution. It may be worthwhile first to clarify the terms "accuracy" and "resolution". Refer to figure 1, which represents schematically the distribution of a number of readings taken on a component. Note that the observations are not evenly distributed, but a bunched at discrete reading values. Resolution is the smallest increment of the quantity that can be recognised. Here, that means the smallest possible change in the displayed reading. In figure 1, it can be seen that the readings recorded appear at discrete values with none in between. When applied to a flaw detector, resolution means the closest together that two echoes can be and still be distinguished. This is an important difference. For high resolution in a flaw detector, a very short pulse is required, so that overlap in minimised. This is not the case in a thickness gauge, where the pulse width affects the minimum reading, but not the resolution.

Accuracy is a measure of the statistical error in the readings that may be obtained, as a result of the imperfections in the instrument. It is a combination of a number of terms representing uncertainty in the measurement and calibration processes.

A third term that is used is repeatability. This is the error in readings caused by a combinaton of the instrument and its use. Repeatability cannot be better than accuracy, and can be much worse. For example, a screw micrometer may have a resolution of 0.01mm, that being its scale division. The accuracy is limited by the cutting of the thread, hysteresis in the screw, the setting of the zero point and the reading of the measurement. The latter two are both equal to the resolution, so even if the former two are negligible, the accuracy cannot be better than 0.02mm. Such a relation between accuracy and resolution is common. The use of a micrometer requires a degree of skill to get the tension right. In the hands of an unskilled user, the repeatability can be 0.05mm or worse.

The digital time of flight gauge

The term "thickness gauge" is to some extent a misnomer. The gauge in fact measures the time of flight (TOF) of an ultrasonic pulse. Before the result is displayed to the user, it is converted into a thickness, which requires a conversion factor to be applied - in effect, a speed of sound value (a factor of two is also introduced, as the TOF is a two-way transit time). The resolution of the reading is therefore dependent on the speed of sound calibration in use. Resolution quoted by manufacturers is often that of the display hardware, as it is inconvenient to quote resolution as a function of material.

The conversion step can greatly reduce both accuracy and resolution. The speed of sound (c) is calibrated by the user prior to a survey, and is therefore outside the control of any notional standard approval.

What is calibration?

Most industrial instruments are subjected to periodical recalibration procedures. For example, a micrometer will be sent away once a year to verify that it reads a series of blocks to within the required error limits. Absolute values traceable to national standards can be used.

This kind of certified standard calibration is meaningless for a thickness gauge. In our laboratory we have two 99 mm cubic test blocks, both made to the same drawing specification from EN3B steel. Both have NAMAS calibration certificates (Coventry Gauge Co. numbers and ), stating that the dimensions between prescribed faces are 99.013 +-0.010 mm and 99.009 +-0.007 mm. When a Cygnus 3 gauge with resolution 0.05 mm is calibrated to read 99.00 on one of these blocks, its calibration is traceable to national standards. However, it then reads 100.0 mm on the other: reductio ad absurdum.

Time of flight measurement could be verified against absolute standards, but there would be no point to such a test. The time is measured in some arbitrary units and only becomes meaningful when processed for display.

In terms of thickness gauges, "calibration" means setting the speed of sound for the material under test. For single echo gauges, the probe delay time must also be set. One of two methods can be used to set the speed of sound. Either an absolute value can be entered, or the gauge can be set to read a known sample and its thickness entered. Both methods assume that the material under test is the same as that used for calibration. It will be shown later that this assumption is not always valid.

Principles of Operation

Obtaining a Time of Flight


Figure 2: Time of flight detection in echo to echo mode. A thickness gauge uses an internal clock to measure the time of arrival of one or more echoes, assumed to be from the backwall of the test object. The frequency of this clock determines the resolution of TOF measurement. The time of flight is determined either by subtracting the time of arrival of consecutive echoes (echo to echo or multiple echo modes), or by subtracting a calibrated offset value from the first time of arrival. Figure 2 represents the detection in echo-to-echo mode. There are three sources of error in this process, described below. Therefore, we can say that
T = Rø + ø +
where
T = error in TOF
Rø = resolution (frequency) of clock
ø = error in clock frequency and
other timing electronics
= phase angle error.
(1)

Of these three, Rø is the most significant.

Clock resolution


Figure 3: Improving resolution by repeated measurement with offset. TOF cannot be known to greater accuracy than the clock resolution. It can be seen from figure 2 that the error in (t1 - t0) is still 1 clock tick, as the times are rounded down. Resolution can be improved by applying digital signal processing (DSP) techniques to the received signal. The high level of computing power required to implement a sophisticated DSP algorithm is unlikely to be found in a general purpose handheld gauge. Resolution can be improved by averaging a number of readings taken with a known small shift in the start of timing, relative to the drive pulse. Figure 3 illustrates this. Here the shift is Rø/ 4. Implementing this requires the offset to be accurately known, usually by using a higher speed clock.

Electronic precision

The clock frequency itself and the detection of echoes both have errors associated with them. With modern crystal oscilators and precision electronics, ø is negligible within the manufacturer's specified working range.

Phase angle error

The echoes are detected by comparing the signal level with a reference value. If the two peaks are of different amplitude, the peaks will cross the reference at slightly different phase angles. In theory, could approach 1/4 wavelength () if the threshold was near the base of one peak and the top of the second. In practice, less than /16 would be expected.
A related problem occurs when noise is superimposed on the wave. The small change in overall signal level can cause the detection point to move, and that can cause jitter in the reading. It can be overcome by averaging a number of readings for display. Averaging in this way improves accuracy, but not resolution.

Converting to Thickness

Having established the TOF in internal clock ticks, there are two ways to convert it to a reading - fixed clock or fixed conversion. Each has its own limitations. In addition, both are limited by the accuracy with which c is known for the material under test. The error introduced by differences between the calibration sample and the actual test material is denoted c. Sources of this error are discussed in the next section.

Fixed clock

The more common method is to use a fixed clock frequency, and to use digital arithmetic to multiply TOF by c to get the reading. In this type of gauge, the speed of sound can be set or displayed in normal engineering units. However, there is a limit to the resolution of the setting (for example, 5 ms-1 steps). The limitations will be more noticeable at lower c, for example in plastics. Also rounding errors can be introduced in the calculation, although this should not be a significant effect with well designed software. Thus
L = T + Rc + p + c
where
L = error in thickness reading
Rc = error due to resolution of velocity setting
p = precision of calculation
(2)

At low velocity settings, each clock tick will represent a small thickness, so measurement resolution will be smaller than display resolution. At the high end of the velocity range, the measurement resolution will become comparable to, or exceed, the resolution of the digital display. Consider a hypothetical gauge with a fixed clock frequency of 50 MHz, calibrated to ms-1. Each tick thus represents 0.059 mm. The gauge has a four digit display. As the probe is moved along a continuous wedge from 10 to 11 mm, readings 10.03, 10.09, 10.15, 10.21 etc. are observed. Although the last digit of the display can take any value 0-9, only certain readings can be displayed. For a true measurement resolution of 0.01 mm at a maximum velocity setting of ms-1, the clock would need to run at 500 MHz. This is an extremely high speed for a simple hand held instrument.

Fixed conversion

Another method is to vary the clock frequency so that one count always represents one increment of the displayed digits. Before the widespread use of microprocessors, this was the only way. The setting of c is analogue, and is thus not subject to any limitation of resolution. It is set by measuring a known sample and adjusting a trimmer to get the correct displayed thickness.

It may seem that this would be liable to the same errors as normal measurement, and so the total system error would be doubled. However, it is possible to get much more accurate setting by adjusting the gauge one digit too far in each direction, and then setting the trimmer to the midway position. The actual value of c is unknown to the user. The total error is then

L = T + c in the best case (3) or
L = 2T + c in the worst case (4)

Measurement resolution is, by definition, equivalent to display resolution in this type of instrument.

Sources of error

Time of Flight errors

In addition to the fixed calibration errors outlined above, there are several sources of random error in the use of the gauge, which affect the repeatability of readings.

The thickness of the couplant layer can have a marked effect on the reading from a single echo gauge, especially when reading on a rough corroded surface. The velocity of sound in the couplant is around 1/4 that in steel, so 0.5mm of couplant in a pit will increase the indicated reading by 2mm. A similar effect can be observed when reading pitted substrates. A relatively deep and flat bottomed pit, when filled with couplant, can give a reading. For example a 1mm pit on an 8mm steel wall could give a reading of 4mm. The user might erroneously believe this to be some acoustic effect or probe fault leading to halved readings. Usually a multipe echo gauge will ignore both of these effects, as with other coatings, but occasionally a pit can be measured. As a wave is propagated through the material, it is attenuated and diffracted. Both processes reduce the proportion of high frequency components in the wavelet, thus changing its shape, which can alter the measured time of flight. In laboratory measurements of velocity, these phase shift effects are accounted for mathematically. [1]. As the gauge does not make the same corrections, entering literature values for velocity will introduce a small error. Fowler et al [3] list a number of additional factors which can reduce accuracy, including curvature of the test piece and surface roughness. These are only significant when working at the highest accuracy.

Variations in speed of sound

The nature of the work implies that calibrating thickness gauges on the actual material under test is not normally practicable. Gauges are normally calibrated using some kind of reference sample - either a standard velocity for the material, or a test block of a similar material. This assumes that the two materials have the same speed of sound; an assumption which can be very poor. We will discuss some of the many factors which can affect speed of sound in materials.

It has been postulated [2] that for corrosion monitoring, knowing the absolute thickness is less important than knowing the rate of loss year on year. Therefore, accurate calibration is not necessary, only repeatable calibration. This pragmatic approach may be appropriate in many cases, providing the survey results are used with this assumption in mind.

Material grade

The most significant factor is the grade of material. Simply knowing a type of material, such as "steel" or even "stainless steel", is not enough, as table 1 shows. (It should be noted that there are no procedures or estimates of error given with these values.)
Table 1: Literature values for speed of sound in steels. Description velocity /ms-1 Ref Mild steel 3 Steel 4 Stainless steel 3 Stainless steel 302 4 Stainless steel 347 4 Stainless steel 410 4

Process history

The speed of sound in any given sample will be influenced by processes applied to it. Heat treatment of metals (hardening and tempering) will have a small effect, as will cold working.[5]. These differences are estimated to be up to 5%, which can significantly compromise the quoted accuracy of a thickness gauge.

When a material is subjected to any forming process, the microstructure will become aligned. This leads to differences in properties, including speed of sound, in different directions - an effect termed anisotropy. It can be demonstrated using one of the 99 mm mild steel calibration blocks described earlier. A Cygnus thickness gauge with 0.05mm resolution was calibrated to read 99.00 on one pair of faces. It then repeatably read 98.80 and 99.30 on the other two. However the block measured 99.00mm +-0.02 in each direction using a certified digital caliper.

If you want to learn more, please visit our website Ultrasonic Thickness Gauge Suppliers.

Process history has even more marked effect on plastics materials. Anisotropy is very significant, owing to the highly directional nature of plastics forming processes such as injection moulding and extrusion. Cooling rate, and therefore wall thickness, also has an effect. Reliable calibration can only be acheived using a sample of the exact structure under test. Fortunately, thickness gauges are mostly used for process control on plastics, where such procedures can be incorporated easily.

Temperature

Temperature affects the indicated reading through four mechanisms:
• Speed of sound
  
• True thickness of material
  
• Electronics drift
  
• Probe characteristics

The speed of sound in a material depends on the elastic modulus E and the density (, both of which are affected by temperature. Speed of sound will fall as the temperature rises, which makes the material appear thicker. The effect can be estimated quantitatively as follows.[6]. Compressional speed of sound cl is given by

and subscript 0 represents a reference condition.


Figure 4:
Variation of speed of sound in steel with temperature. Using literature values, the variation of speed of sound with temperature can be estimated for mild steel, and is presented in figure 4. It can be seen that the effect can be quite strong.

The material will expand as the temperature rises. This is usually a small effect, but must be considered when comparing a reading at high temperature with a drawing which refers to the room-temperature dimension.

A large departure in ambient temperature can cause the gauge's internal clock to drift from its specified frequency, which will increase the term ø in eq. 1. Similarly, the zero offset and responsivenes of the probe can be altered by changing temperature. The manufacturer's recommendations for service conditions should therefore be observed.

Conclusions

The total accuracy in a digital thickness gauge reading can be stated as the sum of a number of sources of error. The largest are the variation in speed of sound between components, and the resolution of the timing circuit. The user must be aware that the manufacturer's stated resolution is only the reading resolution. This is not the same as accuracy, which may be significantly reduced by uncertainty in the speed of sound for the material under test.

As with any measurement, spurious accuracy should be avoided when reporting. The fact that a gauge's display can show 0.01 mm does not imply that it can resolve between test blocks of 10.01 and 10.02 mm. The limitations of extrapolating from a calibration block to a real structure must be considered when reporting absolute thickness values.

Factory calibration of thickness gauges against traceable standards is meaningless. Careful field calibration is necessary and sufficient. Comparative measurements on the same component need not be compromised by uncertainty in speed of sound, provided the same calibration is used for repeat surveys.

REFERENCES

1. McCann, C and Sothcott, J, Laboratory Measurements of the Seismic Properties of Sedimentary Rocks, in Hurst, A, Griffiths, C M and Worthington, P F (eds), Geological Applications of Wireline Logs II, Geological Society Special Publication 65, 285-297 ()
   
2. Fowler, K A; Elfbaum, G M; Smith, K A and Nelligan, T J, Theory and Application of Precision Ultrasonic Thickness Gauging, Insight 38 582 - 587 ()
   
3. Bell, M S and Haupt, J D, Accuracy of Ultrasonic Digital Thickness Gauging for Corrosion Monitoring, International Chemical and Petroleum Industry Inspection Technology III Topical Conference, Houston, TX, June , pub. American Society for Nondestructive Testing, pp 130-134.
   
4. Kaye, G W C and Laby, T H, Tables of Physical and Chemical Constants, 15th ed. pub. Longman, Essex, 75-77 ()
   
5. Anon, Table of Ultrasonic Properties, Xactex corp, WA, ()
   
6. Kraukrämer, J and Krautkrämer, H, Ultrasonic Testing of Materials, 4th ed. pub. Springer-Verlag, Berlin, trans. Hislop, J D, p 497 ()
   
7. loc cit 3, pp 30, 32, 33, 56, 75.

AUTHOR

Peter Hammond graduated from Brunel University in with BSc (hons) in materials science. This was followed in by a PhD from the same university, on "The uses of overpressure in the removal of binder from ceramic injection mouldings". In he joined Cygnus Instruments as a Teaching Company Associate, to investigate methods of thickness gauging at elevated temperatures. On the completion of that contract in , he was taken on as a full member of the R & D staff. This has lead to some understanding of the challenges of thickness gauging on a wide range of materials. While not at work, he relaxes with cycling, water skiing and real ale.
Cygnus Instruments Ltd Ultrasonic NDT equipment
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Homepage: http://www.cygnus-instruments.co.uk

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For more information see: Focus on Thickness Measurement in UTonline 10/97

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