Randall D. Peters and Eric Daine
Copyright Aug 2012
Described is an extensometer that functions with a MEMS capacitive to digital converter chip (AD7745, 24-bits). Power to this chip and its ancillary components, all of which are mounted on a small board ( 2 in x 3 in ), is supplied by the computer through a USB cable.
The hardware component of this instrument, which is pictured in Fig. 1, was once marketed by Tel-Atomic, Inc . At that time the instrument functioned with an analog control box that was designed to be compatible with the patented symmetric differential capacitive (SDC) sensor that is employed by the instrument .
Figure 1. Photograph of the extensometer connected to its electronics support board. The nichrome wire holding the boom in its nominally level position is of too small diameter to be visible. One end of the USB cable is shown connected to the board, but not the other end that connects to the computer during operation of the tiltmeter.
The boom of this instrument is secured to the frame (on its end opposite the weight pan) by means of a fine bearing. Because typically measured wire length changes are small; there is insignificant nonlinearity associated with boom rotation. Bearing friction is also insignificant, at least for usual cases in which background environmental (mechanical) noises provide enough dithering influence to prevent stiction effects.
For the examples shown in this document, a very small Nichrome wire (dia. 60 m m) was tied on its bottom end to the boom that holds the weight pan. Where it runs through a pair of nylon washers at its top end, the wire was then secured with the knurled nut. For maximum dynamic range of the sensor, the boom is nominally level when there is no mass on the weight pan.
An extensometer similar to the instrument pictured in Fig. 1 (but using the analog SDC box) was used to study a solder wire undergoing creep. The data of that study was used in the generation of an article concerned with the prediction of catastrophes .
Built by Eric Daine and shown close-up in Fig. 2 is a picture of the complete electronics support now employed by the instrument.
Figure 2. Populated with all of its parts, detailed features of the components are visible in this photograph of the small self-contained pc-board.
The electronics of this setup is virtually the same as was used in some other instruments described on our webpage .
Example data records
Linearity of the instrument is known from other experiments to be excellent. Here greater attention is given to measurement sensitivity. As an example of the instrument's capabilities for purpose of mass measurement, Fig. 3 is provided.
Figure 3. Example of the extensometer functioning as a mass balance. Departure from a perfect r2 = 1 in the trendline fit to the data is the result of nichrome wire creep under load of the masses. By work hardening the nichrome or using a different, more stable material (such as tungsten), this performance could be improved.
A measure of instrument noise is provided by Fig. 4.
Figure 4. Record showing level of noise with the 60 micron nichrome wire.
In a separate part of this study, the calibration constant was crudely estimated to be in the neighborhood of 1 to 2 nm/count, which is essentially the same as reported for the instrument that used the analog electronics SDC box and a 24 bit adc, to obtain the data that resulted in the paper of ref. .
The present rms noise level of approx. 200 capacitive to digital converter (CDC) counts, corresponds to a lowest detectable wire length change of approximately 400 nm. Although the following hypothesis was not rigorously tested, it is believed that a substantial fraction of the 200 CDC cts of noise in Fig. 4 is the result of fluctuations in the length of the nichrome wire. Sensitivity to temperature was gauged by quickly moving a lighted match past the center of the wire, with a closest approach of about 1 cm. The results are shown in Fig. 5.
Figure 5. Example of system sensitivity to the temperature of the wire.
The maximum excursion, at 75000 cts, corresponds to a rapid wire length increase of about 0.1 mm, followed by a slower near-exponential recovery. Although 75 kcts may seem initially like a large number, the number of counts associated with the full range of boom motion is nearly 3 million, corresponding to 2 mm of boom displacement where the wire attaches. For displacements greater than about plus or minus 0.25 mm, nonlinearity begins to become important, because of boom rotation as opposed to the ideally preferred translation.
The recovery time through cooling of the wire, after passage of the match, is seen to be only of the order of 1 s. This is consistent with the very small mass of the fairly long (13 cm) thermally conductive specimen.
As sold by Tel-Atomic, the instrument could be used to do two separate experiments: measurement of either (i) the thermal coefficient of expansion of wire specimens, or (ii) Young's modulus for the same wires. For the thermal experiments, a clamp was mounted on the frame, so that a hollow wire-wound power resistor could surround the wire. The temperature within the resistor was measured with a solid state thermometer.
 Company webpage at http://telatomic.com
[3 R. Peters, Martine Le Berre, and Yves Pomeau, "Prediction of Catastrophes, an experimental model", online at http://arxiv.org/abs/1204.1551
 Links in http://symcdc.com/ to (i) ``Precision pendulum'' http://symcdc.com/index.php/cpp/ (ii) ``computerized micro-barometer'' http://symcdc.com/index.php/micro-barometer and (iii) "State-of-the-art digital tiltmeter" http://symcdc.com/index.php/state-of-the-art-digital-tiltmeter/