Page 17 - Mechanical Engineers' Handbook (Volume 2)

6 Instrument Statics

term ‘‘residual’’ refers to the deviations of output readings from their corresponding
values on the straight line fitted through the data.
Hysteresis is the maximum difference in output, at any measured value within the spec-
ified range, when the value is approached first with increasing and then with decreas-
ing measurand. Hysteresis is typically caused by a lag in the action of the sensing
element of the transducer. Loading the instrument through a cycle of first increasing
values, then decreasing values, of the measurand provides a hysteresis loop, as shown
in Fig. 1b. Hysteresis is usually expressed in percent of full-scale output.
Error band is the band of maximum deviation of output values from a specified refer-
ence line or curve. A static error band (see Fig. 1c) is obtained by static calibration.
It is determined on the basis of maximum deviations observed over at least two
consecutive calibration cycles so as to include repeatability. Error band accounts for
deviations that may be due to nonlinearity, nonrepeatability, hysteresis, zero shift,
sensitivity shift, and so forth. It is a convenient way to specify transducer behavior
when individual types of deviations need not be specified nor determined. 5

2 STATIC CALIBRATION
2.1 Calibration Process
Calibration is the process of comparison of the output of a measuring system to the values
of a range of known inputs. For example, a pressure gage is calibrated by a device called a
‘‘dead-weight’’ tester, where known pressures are applied to the gage and the output of the
gage is recorded over its complete range of operation.
The calibration signal should, as closely as possible, be the same as the type of input
signal to be measured. Most calibrations are performed by means of static or level calibration
signals since they are usually easy to produce and maintain accurately. However, a measuring
system calibrated with static signals may not read correctly when subjected to the dynamic
input signals since the natural dynamic characteristics and the response characteristics of the
measurement system to the input forcing function would not be accounted for with a static
calibration. A measurement system used for dynamic signals should be calibrated using
known dynamic inputs.
A static calibration should include both increasing and decreasing values of the known
input signal and a repetition of the input signal. This allows one to determine hysteresis as
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well as the repeatability of the measuring system, as shown in Fig. 1c. The sensitivity of
the measuring system is obtained from the slope of a suitable line or curve plotted through
the calibration points at any level of the input signal.

2.2 Fitting Equations to Calibration Data
Though linear in most cases, the calibration plot of a specific measurement system may
require a choice of a nonlinear functional form for the relationship that best describes the
calibration data, as shown in Fig. 1d. This functional form (or curve fit) may be a standard
polynomial type or may be one of a transcendental function type. Statistics are used to fit a
desired function to the calibration data. A detailed description of the mathematical basis of
the selection process used to determine the appropriate function to fit the data can be found
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elsewhere. Most of today’s graphing software allow the user to select the type of fit required.
A very common method used to describe the quality of ‘‘fit’’ of a chosen functional form is