Introduction
The strain measurement is a very straight forward
method in experimental stress analysis. The strains obtained from an experiment
at room temperature are considered to be accurate, and actually it is accurate
with some minor errors if it is performed at unchanged environmental condition.
The case arises when the temperature changes, and the specimen is subjected to
a different temperature during performing the test. In this case, the strain
reading will be affected by several factors that cause error in the reading.
When the temperature changes, the specimen will expand, and this expansion causes
and increases or decreases in strain reading. The temperature change also
affects the gage itself, and the gage can’t read correctly.
This strain change
in the specimen and the gage is called thermal output. The change in strain
gage by temperature causes the gage factor to be changed. This variation of
gage factor is also another factor of error. The error that is caused by
different factors can be fixed either by error correction or compensation.
There are several methods that can be used for error correction or
compensation. The purpose of this
experiment was using different compensation and correction methods to obtain
actual strain. The experimental procedure and details for each method will be
discussed here.
Experimental Method
A 6061-T651 type aluminum cantilever beam, with
specified dimensions in Figure 1, was used in this experiment. Firstly this
beam was loaded at room temperature to obtain the strain as baseline strain.
Then, four different methods of test were performed in this experiment. Two
tests were performed for the correction purpose. Two tests were performed for
the compensation purpose. The other two methods
were used to show that there isn't any way to correct or compensate them. These
were using two-wire connection and using wrong strain gage.
Correction Methods
Single beam, 3-wire (simple)
A single beam with a strain gage, as presented in
Figure 1, was tested by changing temperature. The temperature was increased
from room temperature to 180F˚. The thermal output is calculated from the
following equation.
where T is the increased
temperature, and A is coefficient for the equation. The gage factor for this
equation is set to 2.0, and the coefficients for an advance (constantan) gage
are as following
Since the gage factor is 2.0 and
the gage factor for P-3500 was 2.055, there is a correction for thermal output
as following.
Therefore, the correction for the strain can be calculated as following.
The result for the correction is
presented in Table 1.
Single beam, 3-wire (more correction)
It is already mentioned earlier
when the temperature changes, the gage factor in the gage also will be affected
by the temperature change, so there should be an advance correction method to
correct the gage factor change or correct the error due to strain gage change.
Therefore, there is an advance correction method to correct this error. The
correction for the gage factor can be obtained from the following equation.
where
FT is the corrected gage factor at increased temperature, FRT
is the provided gage factor by
manufacturer
which is 2.055, and delta F(%) 
is a factor obtained from Figure 7 in TN 504 for the gage
is a factor obtained from Figure 7 in TN 504 for the gage
factor
change. This factor was obtained 0.7% at 180F˚ for A-alloy strain gage.
Combining equations (4) and (5),
the actual or corrected strain can be obtained as following.
where F* is the gage
factor of P-3500 which was 2.0. The result is given in Table 1.
Compensation Methods
The compensation method is a method
that does not need any kind of equation to correct the error, but there are
some techniques to the wiring of the gages to compensate the thermal output.
Two techniques were used in this experiment to compensate the thermal output,
self-temperature-compensated strain gage and half-bridge with dummy arm.
STC Single beam, 3-wire
A self-temperature-compensated
strain gage is a gage that can compensate the thermal output to the possible
minimum. This gage uses a 3-wire connection to the P-3500 as quarter-bridge, so
bridge can compensate the thermal output at a range of temperature change. A
STC, 3-wire strain gage was used on a single cantilever beam, the same as
previous parts, to read the strain change by changing the temperature. This
reading is also presented in Table 1. This experiment doesn’t need any
calculation because of its self-temperature-compensation. Figure 2 shows the
diagram of quarter-bridge with a single-self-compensated strain gage.
Half-bridge (dummy gage)
Half-bridge with active and dummy arms and full-bridge
with active elements are the methods that can be used as temperature
compensation. There are five methods to build a fully temperature compensated
Wheatstone bridge. There was only one method used to fully compensate the
thermal output effects. This method was using a dummy gage on a cantilever beam
along with the previous single beam with an active gage. They were constructed
as half-bridge. These two beams were simultaneously subjected to temperature
change. Therefore, the thermal output effects from these two gages canceled
each others, and there wasn’t any change in the reading due to temperature
changes. The reading is presented in Table 1. Figure 3 shows a half-bridge
construction.
Uncorrectable/No Compensation
Incorrect Compensation/Correction
Aluminum beam with -0.6-gage
The last experiment was about using a wrong strain
gage for a specified material. A strain gage was built as a
temperature-compensated strain gage for steel by the manufacturer, but it was
used with an aluminum beam in this experiment. There wasn’t any load application,
but the strain increased with a drastic range by variation of temperature
Discussion
The results from Table 1 show that
the baseline part of the experiment didn't have any compensation or correction
procedure because there is no temperature variation. This part of experiment
was performed at room temperature, and the result from this test is considered
as actual strain. We need to compare other results with this actual strain.
The
simple correction method, which was used to obtain the actual strain due to
thermal effect, shows that the result obtained from this method is larger than
the actual strain. This means that there is still some source of errors. The
strain gage type used in this experiment was unknown, so we picked up a gage
factor of 2.055 for this strain gage. Therefore, there was a difference in the
actual strain and corrected strain. The vibration of the cantilever beam during
experiment can be counted as another factor of causing the error because the
testing table was vibrated by some students during performing the test. Another
factor is due to initial reading of the strain from P-3500 and expansion of the
strain gage itself. The more correction method was used similar to simple
method, but the thermal effect was also calculated to the strain gage, i.e. the
gage factor was also corrected. The result from this correction method is also
similar to the simple method, but it is quite bit smaller in value because the
gage factor was corrected. The same errors as simple method were considered to
this method.
The
result obtain from the self-temperature-compensated, 3-wire strain gage shows
that there is a small difference with the actual strain. There is still some
effects due to the temperature variation but isn’t that much crucial. The
result obtained from the half-bridge, 3-wire construction shows that the
readout and actual strains are the same because the thermal output from dummy
gage cancels the active one. Therefore, an actual strain can be obtained from
direct reading.
The
result from a 2-wire connection strain gage shows that there is a large
variation due to the thermal output. This method cannot be corrected, or there
isn’t any way to compensate it. Therefore, this method is wrong. The result
from last part of this experiment shows that there is a large variation in the
strain reading even though there wasn’t any load application. The reason was
because of selecting incorrect strain gage. This gage was manufactured for a
steel substrate, and it was calculated from the steel’s thermal coefficient to
be temperature-compensated. This gage was used for an aluminum beam in this
experiment. Therefore, the readout was incorrect, and there isn’t any equation
to correct it.
Conclusion
As a conclusion,
we can say that the correction and compensation methods in this experiment were
reasonable. The errors due to some factors were because of uncertainties in the
process of the experiment. The advance correction method was more accurate than
simple correction because the correction for gage factor was also calculated.
The half-bridge temperature compensation method was more accurate than the
self-temperature-compensated strain gage. Two-wire connection of strain gage
and improper selection of the strain gage were wrong methods for the thermal
output, and there weren’t any way to compensate or correct them. An exaggerated
reading was seen for these last two parts. This experiment was an opportunity
to get familiar with the methods of error correction and temperature
compensation that was caused due to thermal output. In addition, knowing that
improper selection of strain gage or incorrect wiring of the strain gage causes
a big error.
