Engineering Instrumentation and Measurement Experiments

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Experiment No. 2 Calibration of a Electronic Load Cell and a Bourdon Tube-Type Pressure Gage 6 Discussion of results 6.1 Bourdon Gage The Bourdon data was reported to a precision of +/- 10 psi, however the output gage increment was 100 psi so the nominal precision should be reported at +/- 50 psi. The Bourdon gage calibration showed high correlation with a linear curve fit to the data throughout the range. The hysteresis in the unload cycle was in all cases less then the nominal precision of the output gage which means that one calibration curve for both loading directions would be sufficient for most applications. Comparatively, a second order polynomial curve fit to the data produced a comparable correlation coefficient. The plot of the errors associated with the calibration curves show increasing correlation with higher loading as might be expected from losses associated with friction and other mechanical factors. If the Bourdon gage was going to be used exclusively in the lowers section of the range, errors are a lot smaller. The calculated standard error from the linear curve fit was less than the nominal precision of the gage which reaffirms the suitability of a simple first order polynomial. 6.2 Strain Gage The strain gage data was reported to a precision of .001 mv, however the fluctuation in the last digit dictated a nominal precision of +/- .005 mv. The strain gage calibration data was less linear throughout the range, but not irregular. Visual inspection of the raw data in Figure 3 shows that a nonlinear fit would have better correlation with even the data points. The standard error associated with the linear curve fit was about .027 mv. The lower number of data points in the curve-fit range was a factor in the relatively high standard error. The strain gage scale also showed high hysteresis or bias error in the unload direction. With a device like this, it is important to a specific procedure to obtain accurate and repeatable results. A plot of the errors of the data to the analytical curve show decreasing correlation with increasing load, which is self-evident in the raw data plot. 7 Conclusions and recommendations A mechanical and an electronic scale were evaluated by students to familiarize them with calibration procedures and the analytical methods of least squares curve fitting. The scales were incrementally loaded with nominal weights and the gage outputs were recorded. The procedure was repeated in the unload direction. Statistical evaluation comparing the data to the analytical results with consideration for the nominal gage precision was used to determine the most suitable reporting precision. The Bourdon mechanical scale calibration data showed good correlation with a linear curve. The electronic strain gage calibration data was more nonlinear but a first order polynomial was used for a good fit over the entire set of the range. The standard error was calculated for both data sets. For both experiments, the standard error exceeded the output precision (the load precision being close). Since Bourdon errors were smaller the Strain Gage errors, the first experiment would be more reliable. This exercise was effective for illustrating the procedures and limitations of calibration methodology as might be applied to a quality control process. The different apparatuses also contrasted the different character of calibration data from linear throughout the range for the Bourdon gage, to a more non-linear with for the strain gage. The concepts of bias error and precision error were illustrated by hysteresis between the load and unload calibration direction. 10
Experiment No. 2 Bibliography References [1] Rahai, H.R et al, 2007, ”MAE 300 Instrumentation and Measurement”, CSULB MAE Department. [2] Velleman, Paul F., 1984, ”Applications, Basics, and Computing of Exploratory Data Analysis ”, Wadsworth Pub Co. 11
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Engineering Instrumentation and Measurement Experiments

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