ME 368
Laboratory 5
Cantilever Beam / Wheatstone Bridge
Laboratory 5
Calibration of a Cantilever Beam / Wheatstone Bridge system
Equipment
NI myDAQ connected to computer running LabVIEW
solderless breadboard, 50-ohm potentiometer, etc. from kit
Omega BCM-1 module
Flexible metal ruler with a single strain gage mounted halfway along the length
Hairdryer
Large black-oxide coated steel beam with 2 strain gages each side and ¼-20” screw eye on end
Set of masses up to 1 kg
Additional masses (slotted weights and metal hook-hanger)
Goals and Objectives
 Become familiar with strain gages with the Wheatstone bridge circuit and similarities /
differences/ pros / cons relative to the voltage divider circuit
 Become familiar with strain gages
 Use your linear fitting and uncertainty analysis skills to characterize a cantilever beam
Background reading
See lab_5_background.docx on the course website.
1.0 Measuring the resistance of a single strain gage: any myDAQ-based method
Select the flexible metal ruler with a single strain gage mounted half-way along the length. Build a
myDAQ-based instrument to measure the resistance of the gage every 0.5 s. Gently flex the ruler (not
more than 30° angle between the 2 ends) and observe the changes in its value.
completion a: have your lab instructor observe you making a measurement of the stain gage, both
unstrained and max strained (~ 30° angle between the 2 ends).
completion b: determine the precision interval [ohms] for your measurement of the unstrained gage.
2.0 Wheatstone bridge basics
Consider the basic Wheatstone bridge shown in Figure 1 below:
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Laboratory 5
RA
Cantilever Beam / Wheatstone Bridge
RB
+ Vout -
RD
+
Vin
RC
-
Figure 1: Conventional Wheatstone bridge
The bridge can be operated in full bridge mode, where all of the resistors are occupied by sensors
(strain gages), half bridge mode, where half of the resistors are sensors, and quarter bridge mode,
where only one resistor is a sensor.
3.0 Measuring the resistance of a single strain gage: quarter-bridge method
You may disassemble whatever you wish from the previous step. Locate the Omega BCM-1 module.
This module contains the bridge circuitry described in the background reading.
Connect the strain gage on the flexible metal ruler to terminals +BRG and +SIG on the left side of the
BCM.
Jumper terminals +SIG to 350 using a short wire.
Connect the myDAQ +15V output to +EX on the right side of the BCM. Also connect the AGND
terminal by +15V to –EX.
Connect terminals +VOUT and –VOUT to ai0+ and aio-.
Write a LabVIEW program to measure and display the voltage out of the bridge, with one data point
every 0.2 s. Write your program such that you achieve the best possible precision interval in these
measurements.
Compute the strain gage resistance from the measured bridge voltage. One approach to do this is to
solve equation 7 from Lab_5_background.docx for RA. Display the resistance on the front panel.
Run the program. Adjust the zero control on the BCM to obtain the minimum output signal.
Flex the ruler and observe the changes in voltage and resistance.
completion c: determine the precision interval [ohms] for your measurement of the unstrained gage.
by what factor is this precision interval better or worse than the value you obtained in completion b?
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Does the strain gage reading change when you place your hand on the gage to warm it up?
Does the reading change when you use the blow dryer to warm up the gage? Don’t get the gages above
50 °C; they can come unglued.
completion d: Estimate: by how many ohms does the strain gage appear to drift per degree C.
4.0 Wheatstone bridge analysis
The basic analysis of the Wheatstone bridge (Figure 1) begins with performing a voltage divider
calculation on each side, resulting in Equation (1).
Vout
RC
RD


Vin
R A  RD RB  RC
(1)
In the quarter bridge arrangement you experimented with above, the sensor is placed in one position,
here assumed to be position D, such that the response of the bridge becomes
Vout
RC
RD  RD


Vin R A  RD  RD RB  RC
(2)
One way to operate the bridge is in “null” mode. In this mode, another resistor in the bridge, here
assumed to be RC, is variable; the user adjusts this resistance until Vout = 0 V. The user then measures
the value of RC and calculates the sensor resistance. This mode is tedious if performed manually, using
a mechanically variable resistance (screw-driven trim potentiometer). However, it can be performed
automatically, using, for example, a voltage-controlled resistance in position C.
You have seen already in this lab that one advantage of the bridge is that it can be used to convert a
changing resistance into a changing voltage signal and that this voltage signal can be set near 0 V,
making it possible to use very sensitive voltage-measurement instruments.
The bridge response simplifies nicely if RB = RC and RA = RD. In this case, Equation (2) becomes
1  RD
Vout
RC
RD  RD
RD 1




Vin
RD  RD  RD RC  RC 2  RD
2
RD
Vout
Vin
R
  2  RD

RD
21  D
 

R
R
RD
GF
D 
D 
 
 


4  2GF
 2 2  RD
 4  2 RD
2 2  RD



R
R
R
D
D 
D 


where the gage factor (GF) has been introduced.
4.1 An important quarter bridge application
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Cantilever Beam / Wheatstone Bridge
One of the most important quarter bridge applications does not involve strain gages, but rather the
varying resistance of a platinum wire exposed to a flowing fluid. The concept is simple. The
resistance of a platinum wire (or many conductors, actually) can be expressed as
R  R0 1  T 
(4)
The bridge is energized such that a small current flows through the platinum wire, causing it to
generate thermal energy. The bridge is balanced when there is no flow of the fluid that you desire to
measure, but while the wire is slightly heated. The wire will reach an equilibrium temperature due to
natural convection to the surrounding fluid. When fluid flows past the wire, the heat transfer from the
wire will increase, causing its temperature to fall and a voltage signal to appear at the Vout terminals.
The input voltage can be controlled such that the current through the wire increases when the heat
transfer from the wire increases, causing the temperature to rise back to its original value and the
bridge to maintain balance. As a result of this feedback circuit, a signal is generated that is
proportional to the mass flow of fluid past the wire. Once the sensor is calibrated, this setup can
provide very fast and quite accurate measurements of the fluid mass flow. Sensors like this are very
common, e.g., as inlet air mass flow sensors in automobiles.
5.0 Measurements with a Full Wheatstone Bridge
Examine the stiff metal beam at your station. It has two strain gages on one side and two on the other
side.
Using the breadboard at your station, connect the gages into a Wheatstone bridge circuit, as shown in
Figure 2. The variable potentiometer should be located as shown in the figure. The physical on-beam
locations of each gage should be located electrically in the bridge so the result provides maximum
output voltage change with a bending load.
Power the bridge with 15 V as above.
Connect the bridge output voltage to ai0. Write a LabVIEW program to measure and display the ai0
voltage every 0.2 s.
Run LabVIEW and adjust the potentiometer until the output voltage is as close to zero as possible. It
may be helpful to make the voltage display on the front panel a dial gage as well as a numeric indicator
and a graph indicator. Use any indicators you like to help you balance the bridge. It may also be
helpful to adjust the time it takes your indicator(s) to update by adjusting the digital sampling
parameters.
Below, we are going to be concerned with the accuracy of the measurements. Therefore, we care about
how close the +15 V source comes to providing exactly 15 V as bridge excitation. In hardware, add
wires in your setup connecting the + 15 V terminal to the red DMM terminal appropriate for voltage
measurements, and connecting the nearby AGND terminal to the black DMM terminal. In software,
add a single DMM voltage measurement (1 sample, on demand) ahead of the rest of your code and
wire things up so this voltage measurement occurs first before the rest of the code kicks off.
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Laboratory 5
RA
RB
+ Vout -
+
Vin
RC
RD
Cantilever Beam / Wheatstone Bridge
-
50  variable
potentiometer
Figure 2: Detail of how the variable resistor (potentiometer) helps to balance the bridge.





R
 VinGF . Note that in practice this ΔR value
R
will be the average ΔR value (averaged over all 4 strain gages located on the beam).
Modify your LabView VI to display ΔR in Ohms on the Front Panel, as calculated from the
DMM measurement of Vin and the ai0 measurement of Vout.
Generate a display on the front panel for the strain reading of the strain gage using the
relationship
R
o
 GF
R
o GF is the gage factor. Omega specified the GF at 2.08 +/- 1.0 % for these strain gages.
o It may be convenient to display the strain output in microstrain (  106) since the strain
is << 1.
Gently bend the beam slightly in both directions and note the readings. If your setup is correct,
you should observe positive strain for tension on the top sensors.
By studying a mechanics of materials book, you should be able to determine that the strain at
the location of the strain gages on a rectangular cantilever beam under bending is given by
6 PL

Ebt 2
where E is the Young’s modulus for the material (2.1x1011 Pa for mild steel), P is the force [N]
Starting from Eq (1), show that Vout  Vin
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applied at the end of the beam, L is the distance from the center of the strain gage to the force
application point, b is the width of the beam, and t is the thickness of the beam. Using this
equation, have LabVIEW display the mass [kg] placed on the end of the beam. It should read
zero initially.
completion e: what is the precision interval [kg] for your setup?
6.0 Uncalibrated static mass measurements
You will be hanging masses from the hook suspended from the end of the ruler. Measure your
unlabeled masses using the digital scale in the back so you know what you have. Choose the
maximum mass assembly you intend to hang on the beam. Hang this mass assembly from the end of
the beam. If the mass measurement is off by more than 20%, check carefully for errors in your setup.
Is the precision interval [kg] higher or lower than the precision interval with no mass on the beam?
For the next step, you may wish to increase the sample compression factor in your code, because our
goal is to have negligible precision intervals so that we can focus on system accuracy. Begin with no
mass on the beam. It may be helpful to re-balance the bridge and then place the potentiometer in a
location where it can’t be easily disturbed. Hang at least 6 nonzero masses (including the
aforementioned heaviest mass assembly) from the beam.
mini report 1: Prepare a table in which the first column is applied mass [kg] and includes zero as well
as the “known” values of the masses you used. The second column is measured mass [kg]. The third
column is (measured – applied mass) [kg]. The fourth column is (measured – applied mass)/(applied
mass). Based on the third column or the fourth column (whichever makes more sense to work with),
state the accuracy of your uncalibrated system for use as a mass measurement instrument.
7.0 Calibrated static mass measurements
Using your recent measurements, plot (measured mass) vs. (applied mass). Use a fit to this data to
calibrate your beam. This calibration should improve the accuracy, by reducing the effects of details
not present in our equations and model such as small variations in the “unstrained” strain gages as well
as the mass of the strain gages, wires, etc.
mini report 2: Prepare the same table as in 1, except this time for the calibrated instrument. Based on
the third column or the fourth column (whichever makes more sense to work with), state the accuracy
of your calibrated system for use as a mass measurement instrument.
Try to measure really small masses. Start with several pennies and work your way down. If you can
measure 1 penny, go down to a paper clip, etc.
completion f: What is the smallest mass you can measure? How does it relate to your answer to
completion e?
7.1 Temperature effects
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Laboratory 5
Cantilever Beam / Wheatstone Bridge
Use a hairdryer to heat the ruler setup from different angles. Don’t get the strain gages above 50 °C,
we don’t want them to come unglued. How sensitive is your setup to temperature? Should
temperature effects cancel due to the locations of the gages in the bridge? Does it matter from where
you apply heat?
completion g: How would your answer to completion f change if you had to measure small masses in
the presence of unknown hairdryer heating (if someone was randomly applying hairdryer heat, what
then would be the smallest mass you could reliably measure)?
mini report 3: This time you will write a results and discussion section. It should be 1 pg. max. The
result you are to discuss is the plot provided in the file lab5_report_plot.docx.
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