Page 107 - Mechanical Engineers' Handbook (Volume 2)

96 Bridge Transducers

If the measurement system cannot be verified to be linear, it should not be used to acquire
time-varying measurements.
The concept of a measuring system having a unique amplitude–frequency and phase–
frequency response is only meaningful for systems which have been verified to be dynam-
ically linear. Amplitude–frequency response tests consist essentially of a series of dynamic
sensitivity determinations at a number of frequencies within the bandwidth of the system.
Three is the minimum number of test frequencies. One test should be performed close to the
upper limit of the frequency band where the response has not been affected by the high-
frequency roll-off characteristic of the system. The second frequency should be sufficiently
higher than the first to provide some indication of the roll-off rate of the system. The third
frequency should be about halfway between zero frequency and the first test frequency to
verify a flat response to the upper band edge. More improved definition obviously can be
provided by increasing the number of test frequencies.
Phase–frequency response characteristics of a measuring system can often be acquired
simultaneously with the amplitude–frequency response. An output recording device is re-
quired with two identically responding channels. The system output is recorded on one
channel. The second channel records the measurand, which is typically acquired by a pre-
viously calibrated monitoring transducer whose amplitude–frequency and phase–frequency
response characteristics are well established. A time correlation between the system output
and this monitoring transducer can establish measuring system phase–frequency response.
For systems measuring signals whose time history is important, a linear phase response with
frequency is required. For those signals about which only statistical information is to be
acquired (e.g., random vibration), phase response is not an important system characteristic.
With today’s technology, frequency response functions can also be characterized by
transient or random system excitation. Dual-channel spectrum analyzers can ratio input-to-
output measuring system Fourier transforms in near-real time. Recall that the system input
stimulus must contain significant signal content at all frequencies of interest.

6.3 Electrical Substitution Techniques
If actual values of the measurand cannot be used to calibrate resistance bridge transducers,
electrical substitution techniques can be used. Test equipment required includes a precision
voltage source, precision resistors or decade box, and a signal generator. The techniques
include shunt calibration, series calibration, and bridge substitution. Shunt calibration tech-
niques are discussed first.
Inserting a resistor of known value in parallel with one arm of a strain gage bridge is
single-shunt calibration. The calibration resistor is inserted across the arm opposite the strain
gage conditioning system. The conditioning system may contain a balance potentiometer, a
limit or pad resistor, modulus resistors, and temperature compensation resistors. Standard
practice is to insert the shunt resistor between the negative input (excitation) and the negative
output (Fig. 19). This reduces errors caused by shunting some of the bridge-conditioning
resistors.
The value of the shunt resistor R is determined by first applying a value of the mea-
c
surand to the transducer and monitoring the voltage change at the transducer output terminals
(Fig. 19). With the measurand removed, a decade box is substituted for R and its resistance
c
adjusted until a voltage change results with a magnitude equal to that caused by the mea-
surand. For subsequent calibrations, a fixed resistor R can be substituted for the decade box.
c
When the switch in series with R is closed, it will produce a step voltage through the
c
measuring system of amplitude equal to that produced by the measurand. When shunting
2
one arm of the bridge, the resistance change produced in that arm is R /(R R).
c