Page 105 - Mechanical Engineers' Handbook (Volume 2)

94 Bridge Transducers

1. Zero-measurand output verification
2. Sensitivity verification
3. Linearity and hysteresis verification
4. Repeatability verification
Zero-measurand output verification starts with a measurement of system output with
zero measurand applied to the transducer. Zero measurand is an important measurement for
several reasons:

1. In many measurement systems, the transducers are exposed to zero measurand before
the test begins.
2. For many transducers, zero measurand means that no external input to the transducer
is required, thus greatly simplifying the test procedure.
3. Measurement system malfunctions, including drift, will frequently appear when the
system output is monitored over some reasonable time period with zero measurand
applied.
4. In some measurement systems with no external measurand input, the ambient envi-
ronment will furnish an important reference point for the system calibration. For
example, for an absolute-pressure-measuring system, the ambient atmospheric pres-
sure provides this reference. Similarly, for certain accelerometer systems, the meas-
urable attitude of the test vehicle prior to launch represents a known component of
the earth’s gravitational field as input to the accelerometer.

For a measurement system with a linear response, the slope of the line characterizing
the input measurand versus system output represents the sensitivity of the system. There are
a number of straight lines which may be chosen to provide this sensitivity verification. These
include the following:
1. Endpoint line—The straight line between the outputs at the specified upper and lower
limits of the range.
2. Best straight line—The line midway between the two parallel straight lines closest
together that enclose all output versus measurand values on a calibration curve.
3. Terminal line—The straight line for which the endpoints are 0 and 100% of both
measurand and output.
4. Theoretical slope line—The straight line connecting the specified points between
which a specified theoretical curve has been established.
5. Least-squares line—The straight line for which the sum of the squares of the residuals
is minimized for all calibration points.
Procedures used in the verification of sensitivity will depend on specific accuracy, cal-
ibration time, and expense trade-off choices for each system. For unidirectional transducers,
it is typical to calibrate from zero to full scale and back again in 10% of full-scale increments
(21 points). For bidirectional transducers, a 21-point calibration cycles the transducer from
negative full scale to positive full scale and back again in 20% of full-scale increments.
Data extracted from these calibrations are typically linearity and hysteresis. Linearity is
the closeness of a calibration curve to the specified straight line, expressed as the maximum
deviation of any calibration point from that line during any one calibration cycle. Hysteresis
is the maximum difference in output at any measured value within the specified range when
the value is approached first with increasing and then with decreasing measurand.