UDC: 681.2.088

Errors in strain measurement at high frequency by M Dixon, Cambridge Consultants Ltd, Science Park, Milton Road, Cambridge CB4 4DW.

Two possible sources of error in strain measurement at high frequency were considered. The performance of the strain gauge itself was measured by comparison with a reference transducer. Several installations were shown to he satisfactory at up to 100 H z hut another showed a progressive attenuation with frequency. Attempts to reproduce the f a u l t with another installation were unsuccessful . The sources of error within the instrumentation were also considered and measurements made on the dynamic performance of several voltmeters.

minimise the mass of the gauge and to maximise the stiffness of the adhesive layer. The following guidelines may be set:

1) Gauges with a thin hard backing layer, such as epoxy or glass fibre reinforced epoxy resin should be used in preference to thicker, more flexible, materials such as pol yimide.

2) Adhesives with a low solids content giving a thin, very hard, glue line should be used wherever possible.

Key words: Dynamic strain measurement, transducer, calibration, instrumentation bandwidth.

3) For high accuracy measurements, two installations of different specifications should be used and the outputs compared.

Measurements of strain gauge performance Introduction

Errors can occur when strain gauges and their measurement systems that have been calibrated statically are used to measure dynamic strains. This paper will highlight some of the measurement errors that can arise and give some guidance on how to minimise or remove them.

Two sources of error are considered. The first is that the strain gauge will fail to record the dynamic strain correctly due to imperfect coupling between the foil, its backing material and the specimen surface. The second source of error is that the instrumentation may not be suitable or calibrated for the frequency range in use.

The dynamic performance of the foil strain gauge

As far as is known, the performance of a foil strain gauge installation has never been measured accurately at high frequency. Simplifying the construction to a lumped mass model, the strain gauge may be considered as a mass, connected to the specimen via a spring, damper system known as the adhesive. The higher the mass of the strain gauge, and the higher the compliance of the adhesive layer, the lower the resonant frequency of the system will be. The model of the strain gauge may be subdivided into one mass, the foil, attached to a second mass, the backing material, via a second spring and damper. The performance of this subsystem is probably less important than that of the first.

It is therefore apparent that strain gauge installations for measurement at high frequency should be chosen to

These principles were used in the construction of the standard dynamic force transducer at the National Physical Laboratory (NPL) 1. This provides a traceable system for dynamic force measurement of sinusoidal amplitudes over the frequency range of 0.1 to 100Hz. The system consists of an elastic loadcell element, constructed of a material with known low damping and instrumented with two independent strain measurement systems. These two systems were a bridge of 8 foil strain gauges, and a capacitance displacement gauge made up of two annular electrodes.

Two elements were made of different materials, and three types of strain gauge used, all from Micro-Measurements Inc. The first element was made from EN 24T, a high strength nickel chromium molybdenum steel, and gauged with one bridge of type TK-06- 125-VB-350 gauges.

The second element was made of HE 15 TF, an aluminium alloy, commonly known as duralumin, and gauged with two bridges, one of type MA-06-125-VA-350 gauges and the other of type EA-13-125-TM-120 gauges. All gauges were attached with MBond 610 adhesive from Micro- Measurements Inc, chosen for its low solids content.

Both the TK and the MA gauges conformed to the guidelines set out above, having thin, hard backings. The EA gauges, however, are polyimide backed and therefore formed a useful comparison.

The instrumentation was first calibrated from traceable electrical standards and the two strain measurement systems then calibrated statically in the 20 kN deadweight force standard machine at the NPL. The transducer was

‘Strain’, August 1991 105

then operated dynamically in a materials testing machine and the two force outputs compared. The difference between the two was less than 0.2% over the frequency range tested, 0.1 to 100Hz. An uncertainty analysis established the overall uncertainty of dynamic force measurement to be k 0.4%.

In addition, comparisons between the individual strain gauge bridges, made by mounting the two transducers in series in the testing machine, showed that there was no measurable difference between the outputs from the three strain gauge bridges. Experiments were carried out at strain levels up to k 350 microstrain.

This standard system was then used to measure the dynamic performance of other strain gauge installations on steel specimens. Three other installations showed no measurable difference from the standard loadcell, but a fourth installation of EA-06- 125-TM- 120 gauges showed a progressive attenuation with frequency, to a maximum of -1.5% at 100Hz. The error was found to be linear with strain level up to the maximum tested, 350 microstrain. This experiment was repeated several times over a period of months and after recalibration of the instrumentation, but the attenuation remained constant. Further experiments were therefore undertaken to establish the reason.

The deviations from correct practice were as follows:

1st bridge: The metal surface was not abraded or cleaned properly. An excess of adhesive was applied, in several layers.

2nd bridge: An excess of adhesive was again used, and the specimen placed i n an oven already at the cure temperature. The recommended practice is to heat and cool the oven with the gauged installation in place. The clamps were removed after 10 minutes in the oven, and the specimen removed, 50 minutes later, while the oven was still hot.

3rd bridge: An excess of adhesive was again used, and the clamps only applied for two minutes, while the specimen was transported to the oven.

As shown in Figure 1, all three bridges were found to have constant sensitivity with frequency above 1Hz. Below 1 Hz, their sensitivities were reduced due to creep, of greater magnitude than would normally be expected from a transducer.

0.5

0

Attempts to re-create the poor installation

It was necessary to establish first whether the sensitivity of the strain gauge bridge was frequency dependent or whether the elastic modulus of this particular specimen was a function of frequency. A second strain gauge bridge, of the same type of gauges, was therefore attached to the specimen.

It was not possible to use the same type of adhesive as for the first bridge, as the high temperature cure required would have altered the characteristics of the protective coating and possibly the soIdered joints of the first bridge. MBond 200, a quick setting, room temperature cure adhesive, also from Micro-Measurements Inc but with a higher solids content than MBond 610, was used instead. This resulted in a thicker glue line but it was intended, that if this bridge also showed a reduction in sensitivity with frequency, to then verify the performance of MBond 200 adhesive by a separate test on a different specimen.

The sensitivity of this second bridge however, when tested against the standard loadcell, was constant with frequency to within 0.05%. From this i t was evident that the reduction in sensitivity of the original bridge was not caused by a variation of the elastic modulus of the element with frequency.

Another reference specimen of the same design was produced, and three attempts were made to produce deliberately a poor bond between the gauge and the metal.

-0.5 G z

- 1 0

.1 5

I I I I I 0 01 0 1 1 10 100

Frequency (Hz)

- . Orlglnal reference specimen

Fig. 1 Dynamic calibration of strain gauge installations.

Instrumentation errors

The instrumentation used to condition the signal from a strain gauge installation may be split into three components;

1) The excitation for the bridge, which may be either DC or AC.

2) The amplification of the signal from a millivolt level to a volt level.

3) The measurement of the signal amplitudes.

If the bridge has DC excitation, then the bandwidth of the amplification stage may be limited by low pass filters which are usually included to remove high frequency

106 ‘Strain’, August 1991

noise. These may be calibrated individually if required for Tracking D V M

330 Hr

180Hz

lOOHz - ’ 0 ° 8 80

high accuracy measurements by applying a known amplitude to the input and measuring the output amplitude at different frequencies.

0 0

A system with AC excitation will also have a low pass filter to remove the carrier frequency from the output. Calibration of this type of system is more difficult but can be achieved from measurements on the individual sidebands 2.

It is in the measurement of the signal amplitudes that the largest errors usually occur. Methods for measurement of the signal amplitude can be divided into those that only look at the peaks and troughs of the signal and those that take information from the entire signal.

0 20 40 60 80 100

Frequency (Hz)

F i g 2 Performance of 5DVMs and a tracking voltmeter.

Measurement of the maxima and minima Using information from the entire signal

There are 3 possible algorithms.

1) Detect the maximum and minimum from a single cycle of the waveform.

2) Detect a succession of maxima and minima and take the highest maximum and the lowest minimum.

3) Detect a succession of maxima and minima and average them.

Method 2 will usually give the highest answer from a ‘real’ signal because any noise or variation in mean level will tend to increase the maximum and decrease the minimum. Method 1 will give a lower answer, but is less repeatable unless the noise is consistent from cycle to cycle. Method 3 will provide the most accurate and repeatable answer, but requires more advanced hardware.

The peak monitor found on many testing machines, and now available as a stand alone unit known as a tracking voltmeter, usually operates by method 2 and has a reasonably high bandwidth. There i s normally an automatic reset after a few seconds and a manual reset. Note that if this instrument is used at low frequencies where the reset time is similar to the period of the waveform then the algorithm will approximate to method 1.

An AC DVM with a max-min facility may also be used, but with caution as many of these instruments have a low sampling rate and therefore a low bandwidth. A comparison of the performance of five DVMs and a tracking voltmeter is shown in Figure 2.

Method 3 is not, as far as is known, available in any analogue instruments. It is therefore necessary to digitise the signal, transfer it to a computer and to detect and average the maxima and minima in software.

There are three methods that use information from the entire signal.

1) The RMS function of an AC DVM.

If the signal is sinusoidal and has low harmonic content, then the RMS function of an AC DVM may be used and the reading converted into an amplitude. The instrument will normally have a higher frequency bandwidth than is required, but problems may occur at low frequencies due to the AC coupling of the input. Typically the instrument will not function in this mode below 10 or 20 Hz.

2) The Fast Fourier Transform (FFT).

Spectral analysis is the most widely known method and the most popular technique is the FFT. This converts the information from the time domain into the frequency domain, the signal appearing as a series of frequency lines on a plot of frequency against amplitude. This gives information about the ent i re signal, including any harmonics and noise. The resolution of the method is dependent on the number of frequency increments which in turn is decided by the number of points in the original sampled signal.

3) The cross correlation method.

The frequency of the excitation waveform is usually known, and for most applications, the largest component of the output signal will be at this frequency. The cross correlation method compares the signal with reference sine and cosine waveforms of that frequency and derives a measure of the similarity between the two. This method rejects all information that is not a t the fundamental frequency and is a very accurate method of amplitude measurement when the excitation frequency is known.

‘Strain’, August I991 107

Conclusions Acknowledgement

Two sources of error from strain measurement at high frequency have been considered. The performance of the strain gauge itself has been measured and the likely errors arising from the instrumentation have been quantified.

The author wishes to express his thanks to Mr R F Jenkins of the National Physical Laboratory for advice and assistance during the work on which this paper is based.

Of seven strain gauge installations, six showed no measurable change in sensitivity with frequency. Three types of gauge and two adhesives were used successfully, including EA gauges which have a thick, flexible backing, applied with MBond 200, an adhesive giving a relatively thick glue line. The only degradation in performance occurred below O.IHz, where an increase in creep was observed.

The seventh installation showed a reduction in sensitivity with frequency. No explanation was found for this and the conclusion reached was that the adhesive or strain gauges References used in the original installation were defective in some way. (1) Dixon, M., “A traceable dynamic force transducer”,

Experimental Mechanics, 30, 2, (June 1990). Measurements on several voltmeters showed that the tracking voltmeter had the highest bandwidth and was (2) Dixon, M., “Dynamic calibration methods f o r therefore generally more suitable for dynamic transducer instrumentation”, Experimental Techniques, measurements. (Dec 1990), 51 - 54.

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