UM-0085-B09
DT80 Range User Manual
Page 327
RG
Converting Frequency to Strain
As mentioned above, the strain experienced by a VWSG is proportional to the change in the square of the resonant
frequency. That is:
𝑆𝑡𝑟𝑎𝑖𝑛
=
𝐺
(
𝑓
2
− 𝑓
0
2
)
where:
•
G
is the gauge factor (supplied by the manufacturer)
•
f
is the measured frequency
•
f
0
is the zero or "at rest" frequency
It is therefore necessary to take a zero reading, after installation of the gauge. This value should be recorded; it can then
be used in a DT80 program in order to return strain, e.g.
BEGIN
RA1M
1FW("freq",W)
'read the frequency
'calculate the strain, given gauge factor G and zero frequency f
0
CALC("strain")=
G
*(&freq^2-
f
0
^2)
END
Temperature Correction
As the temperature of the VWSG changes, the steel wire will expand or contract. Its change in length is proportional to
the change in temperature. A temperature change will therefore cause an addition or reduction to the measured strain.
That is:
𝑆𝑡𝑟𝑎𝑖𝑛
=
𝐺�𝑓
2
− 𝑓
0
2
�
+
𝐶
(
𝑇
2
− 𝑇
0
2
)
where:
•
C
is the temperature correction factor (supplied by the manufacturer; this is basically the coefficient of thermal
expansion for the grade of steel used for the wire)
•
T
is the current temperature
•
T
0
is the temperature at which the zero frequency measurement was taken
So if the gauge incorporates a YS04 thermistor and is wired as per
VS1 – Vibrating Wire Strain Gauge and Thermistor
then a typical program might be:
BEGIN
RA1M
1FW("freq",W)
'read the frequency
1*YS04("temp") 'read the temperature
'calculate the strain and apply temperature correction
CALC("strain")=
G
*(&freq^2-
f
0
^2)+
C
*(&temp-
T
0
)
END
Strain Gauges – Carlson Meter
A Carlson meter consists of two tensioned steel wires (connected in series) whose resistance changes as they are
strained. The wires are arranged so that a given strain causes the resistance of one wire to increase and the other to
decrease. The strain is then proportional to the ratio of the two resistances.
The resistance labelled R1 in the wiring diagrams is the
expansion
wire (its resistance increases as the gauge is
stretched), while R2 is the
compression
wire (its resistance increases as the gauge is compressed). Thus when the
gauge is stretched, the ratio R1/ R2 will increase, resulting in a positive strain reading. Conversely, compression will
cause a decrease in ratio R1/ R2 and a negative strain reading.
The wire resistances are also temperature dependent. The temperature is proportional to the total resistance, i.e. the
sum of the two resistances.
A Carlson stress meter uses the same principle as a strain meter but is designed to indicate
stress
(force per unit area,
unit MPa) rather than
strain
(displacement). Stress and strain proportional to each other according to the modulus of
elasticity of the material.
Carlson meters are supplied in 3, 4, 5 or 6 wire configurations. The extra wires allow the logger to properly compensate
for the cable resistance, which is often an important issue given that meters typically have a total resistance in the range
50-100
Ω
. Standard wire colours are normally (although not universally) used, as shown in the wiring diagrams.
Due to their low resistance, Carlson meters should normally be measured using the high (2.5mA) excitation setting (
II
channel option). If higher excitation current is required the Series 4 models provides built-in 16-bit DAC converter at
V/I
DAC
terminal. It capable to supply currents up to 25mA max.
