Page 106 - Mechanical Engineers' Handbook (Volume 2)

6 Resistance Bridge Transducer Measurement System Calibration 95

The reference straight line selected is often the linear least-squares line. This line is
based on the following principle: The most probable value of an observed quantity is such
that the sum of the squares of the deviations of the observations from this value is a mini-
mum. This is based on the fact that most measurements of physical quantities show a normal
distribution with both positive and negative deviations from the mean probable and very
large deviations less likely than small deviations. The line can be defined unequivocally in
terms of the quantities measured. The line also is statistically significant, and standard de-
viations can be assigned to estimates of the slope, intercept, and other parameters derived
from it.
An additional parameter describing the performance of the measurement system is ob-
tained by repeating the static calibration of the system. A minimum of two, but preferably
three, consecutive static calibrations yield data from which the ‘‘repeatability’’ of the system
is verified. Repeatability is the ability of the measurement system to reproduce output read-
ings when the same measurand value is applied to it consecutively under the same conditions
and in the same direction. It is expressed as the maximum difference between corresponding
values from at least two consecutive calibrations. Although there is no universal agreement
as to the particular values selected, a value close to full-scale output is commonly used.
If the bridge transducer will be used to acquire time-varying measurements, the mea-
suring system must be both dynamically and statically calibrated. The dynamic response of
any system is described by a frequency response function which is a complex function of
frequency. The frequency response function relates system output to system input in the
frequency domain. For measurement systems, this frequency response function is typically
represented by Bode plots which are log amplitude and phase versus log frequency.

6.2 Dynamic Calibration

Dynamic calibrations are inherently more difficult to perform than are static calibrations and
usually require specialized equipment. Dynamic calibrations can be performed using several
types of well-defined input signals, such as applications of sinusoids, transients, or broadband
noise. The principal requirement that the input must satisfy is that it must contain significant
energy at frequencies over the range of the frequency response function of interest.
The dynamic calibration sequence consists of the following steps:

1. Dynamic sensitivity determination
2. Dynamic amplitude linearity determination
3. Amplitude–frequency verification
4. Phase–frequency verification

If the measuring system does not have zero frequency response, its end-to-end calibra-
tion is of necessity made by dynamic methods. The simplest approach to dynamically de-
termining system sensitivity is the application of a sinusoidally varying measurand to the
transducer. The amplitude of the measurand should be equal to the range of the transducer.
For unidirectional transducers, this test involves biasing the transducer to its half-range point.
At the test frequency, it is possible to relate the peak amplitude of the system response to
the amplitude of the measurand and determine system dynamic sensitivity.
It is further desired to acquire dynamic amplitude linearity by performing tests equiv-
alent to dynamic sensitivity determination at several levels of the measurand (usually levels
of 25, 50, 75, and 100% of full scale are adequate). This testing should be performed at
several different frequencies over the range of the frequency response function of interest.