Campbell Scientific 4WFBS120, 4WFBS350, 4WFBS1K 4 Wire Full Bridge Terminal Input Modules User Manual
Page 42
4WFBS120, 4WFBS350, 4WFBS1K 4 Wire Full Bridge Terminal Input Modules (TIM)
In this circuit, R1 and R2 are 1000 ohm resistors making up the back plane of
the Wheatstone bridge, as is done in the TIM design. R
D
is the complementary
resistor that has a nominal resistance of the un-strained gage. The 4
th
resistive
element is the active strain gage. In most applications, the gage is some
distance from the other components of the Wheatstone bridge. R
L
represents
the resistance of the wire leads returning from the two sides of the gage. It is
normally assumed that the length of the two wires is equal and thus the two
lead resistances are equal; R
L.
. As can be seen in this circuit, the two R
L
s are
both included in the arm of the bridge containing the strain gage. This results
in equation 4.4.12 for solving the strain from the voltage ratio (V
r
:reference
equation 3.14).
GF
R
R
V
R
R
V
L
r
G
L
r
⎟
⎞
⎜
⎛
⎟
⎠
⎞
⎜
⎝
⎛ +
−
⎟
⎠
⎞
⎜
⎝
⎛ +
=
1
2
1
1
4
2
ε
G
⎠
⎝
4.4.12
This results in a non-linear relationship between the strain and line resistance.
In addition to this non-linear relationship in the gain, having both lines in the
same arm of the bridge results in an offset error as the line resistance (R
L
)
changes due to temperature effects. These offset errors can easily outweigh
any legitimate measurements.
Take for example a 120 ohm 2 wire gage with 100 foot leads of 20 gage copper
wire. Copper wire has a Temperature Coefficient of Resistance of about
+3930 ppm (or 0.393%) per degree C. The initial resistance for the 200 foot
combined leads is 2.000 ohms @ 24 degrees C. If the temperature were to drop
20 degrees C, the change in resistance would be 0.127 ohms:
2Ω
Ω
Ω
0.127Ω
×
=
C
0.00393
C
20
°
×
°
Equation 3.2, from Section 3, derives strain as a function of resistance:
G
R
GF
•
G
R
Δ
=
ε
(
)
As mentioned before in Section 3, strain is typically reported in microstrain
με
. Microstrain is strain expressed in parts per million, i.e: a change in
length by one millionth of the length. Equation 3.3, again from Section 3,
derives microstrain as a function of resistance.
(
)
G
G
R
GF
R
•
Δ
×
=
6
10
1
με
Entering 0.127
Ω
for
Δ
R
g
, 2 for the Gage Factor (GF), and 120
Ω
for R
g
, the
apparent or false strain reading indicated would be 529
με.
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