Campbell Scientific 4WFBS120, 4WFBS350, 4WFBS1K 4 Wire Full Bridge Terminal Input Modules - Manual (Page 43)

4WFBS120, 4WFBS350, 4WFBS1K 4 Wire Full Bridge Terminal Input Modules (TIM)
4.5 Calculation of Strain for ¼ Bridge Circuits
H
L
G
Vx
H
L
or AG
H
R1
R2
R3
Rg
FIGURE 4.5-1. Strain gage in full bridge
Figure 4.5-1 is the diagram of the strain gage in the full bridge configuration
provided by the terminal input module. The result of the datalogger's full
bridge measurement when a multiplier of 1 and an offset of 0 is used is the
measured bridge output in millivolts divided by the excitation in volts (1000
mV=1V):
1000 1000
3
2
1 2
⋅ = ⋅
+
−
+
⎛ ⎞
⎝
⎜
⎠
⎟
Vout
Vin
R
R R
R
R R
g
g 4.5.1
The result is output in the units of millivolts output per volt of excitation
because the output voltage is small relative to the excitation voltage; these
units allow the result to be a larger number easier for the datalogger to display
and store (see data format discussion in the datalogger manual). The output is
a ratio because: 1) the datalogger's ratio metric measurement technique allows
this ratio to be more accurate than the measurement of the output voltage
(errors in the excitation and measured output cancel). 2) This ratio can be used
directly in the calculation of strain.
When strain is calculated, the direct ratio of the voltages (volts per volt not
millivolts per volt) will be used:
Vout
Vin
R
R R
R
R R
g
g
=
+
−
+
3
2
1 2 4.5.2
If the previous equation is taken as the result when the gage is unstrained, then
when the gage is strained it will change resistance by
Δ R
g
. The equation for
the bridge output is:
R R
R R R
R
R R
strained
g g
g g
=
+
Vout
Vin + +
−
+
Δ
Δ
3
2
1 2 4.5.3
37