Experiment #5 Pressure Transducers / Gages:

http://egweb.mines.edu/eggn250/exp5.htm

3 ways to measure pressure:

1.) Bourdon Tube Pressure Gauge
http://www.wika.com/web/ProductInformation/ProductInformation_Technical_BourdonTubeOperatingPrinciple.html

1. Pointer
2. Bourdon tube
3. End piece
4. Link
5. Quadrant
6. Movement
7. Connection (or socket)
8. Dial

Bourdon tube pressure gauges are widely used in all branches of

industry. The construction is simple yet rugged, and operation does not
require any additional power source. The Bourdon tube element is directly
exposed to the medium being measured and is normally made of copper
alloy (brass) or stainless steel as the application demands. Except for
absolute pressure gauges, WIKA Bourdon tube gauges measure pressure
relative to the pressure of the surrounding air.
The Bourdon tube measuring element is made of a thin-walled tube
that is either bent into a semicircle (C-shape tube) or spirally wound (coiled
safety tube). When pressure is applied to the measuring system through the Pressure
port, the pressure causes the Bourdon tube to straighten itself, thus causing the End
piece to move upward (or downward for vacuum measurements). The movement of the
end piece is transmitted via the Link to the Movement. The movement converts the
linear motion of the Bourdon tube end piece to a rotational movement which
in turn causes the Pointer to indicate the measured pressure.
Bourdon tube pressure gauges are designed for the measurement
of pressure and vacuum and are generally suitable for all clean and non-
clogging liquid and gaseous media.
Various types of Bourdon tubes are used. C-shape Bourdon
tubes are typically used for ranges up to 800 psi. Higher ranges use coiled
Bourdon tubes for safety. All WIKA Bourdon tube pressure gauges are
capable of withstanding pressures up to 30% above their full span without a shift in
calibration.
Bourdon tube pressure gauges are available to measure full vacuums, compound and
pressure ranges from 0-10 psi to 0-60,000 psi with an accuracy from ±0.1% to ±3/2/3%
of span (ASME Grade 4A to Grade B).

2.) CSM Pressure transducer:

The CSM made transducer has a strain gage mounted on a
circular flat plate of brass/copper.
 Air is confined in a chamber with a copper/brass
spherical cap (E ~ 16*106 psi)
 Air pressure
causes the
Pressurized spherical cap to
Chamber Air bulge
 Knowing
o the modulus
of elasticity of this spherical cap
o the strain associated with the bulging cap
o the geometry of the cap (spherical)
allows you to calculate the pressure inside the chamber

Use a ¼ Wheatstone bridge to measure the strain of the deflecting plate:

Air
To find P from CSM pressure transducer:
Record Vout from CSM transducer as a function of the
pressure
- Check for hysteresis: (Q7, Q11,
Get data points while both loading and unloading the gage
- Check for repeatability: (Q11)
Get two sets of data taken by two different people

The stress on a circular surface whose outer edge is supported and has a
uniform load over the entire area is:

39/80)(pa2/T2),

where:
p = differential pressure,
Note:
Differential pressure = inside p – outside p
Outside pressure:
http://www.srh.noaa.gov/data/forecasts/COZ039.php?
warncounty=COC059&city=Golden

http://www.crh.noaa.gov/den/products/webpres.html
Absolute pressure = inside pressure, or pressure measured relative to a
vacuum
a = radius = 0.75 in
T = thickness = 0.03 in

Psiatm

Force Balance:
Psig = inside – outside
= Psiabs - Psiatm
 Psiabs

For #7 Use the following excel spreadsheet:

Point Vout R/R strain Pressure (gage) Pressure

CSM Omega CSM CSM gage CSM - calc Omega - calc abs

Example graph from CSM transducer (Notice hysteresis, nonlinearity

in data…)
 Expt 5 -- CSM Pressure Tranducer w/ Cu Plate

0.0025

0.002

0.0015
e
g
a
tl
o
V
0.001

0.0005

0
0 10 20 30 40 50 60
Pres sure (psig)

3.) Omega manufactured transducer

http://www.omega.com//Pressure/pdf/PX178.pdf
Sensitivity:
60mv for 0-150 PSIG

With a 10V bias:

150 psig 100mV
P  Vout  2500Vout
60mV 1V
With a 5V bias
P  5000Vout

PX236 Pressure transducer:

This transducer has a full bridge built in
All you have to do is
provide excitation voltage (10 V)
ground it
measure the signal out of it
Three wires:
+ excitation voltage (red)
ground (black)
signal = Vout across bridge (Green and white wires)
Omega Transducer

Red = +10 V excitation

Green = output – to channel 0
White = output – to channel 8
Black = ground

Example graph from OMEGA transducer… (It is allot more linear and
repeatable than CSM…)
 Expt 5 -- Om ega PX 236 Pressure Transduce

1.00E-02

9.00E-03

8.00E-03

7.00E-03

6.00E-03
Voltage (v)

5.00E-03

4.00E-03

3.00E-03

2.00E-03

1.00E-03

0.00E+00
0.00 5.00 10.00 15.00 20.00 25.00 30.00 3
-1.00E-03
Pressure (psig)

Note:
Max Pressure at Each Lab Bench Station in CTLM 125
Spring ‘03
 3 52 psig 4 45 psig 9 46 psig 10 22 psig

2 53 psig 5 31 psig 8 45 psig 11 45 psig

1 50 psig 6 37 psig 7 46 psig 12 46 psig

Avoid using benches 5, 6, & 10 for Expt. 5, so the students can obtain a larger range of
data.
These pressures haven’t changed since Fall ’02.

Experiment #5 Prelab:
#1)
in short…
pressure to stress:
The stress on a circular surface whose outer edge is supported and has a
uniform load over the entire area is:

39/80)(pa2/T2),

where:
p = differential pressure,
Note:
Differential pressure = inside p – outside p = gage pressure = psig
Outside pressure:
http://www.srh.noaa.gov/data/forecasts/COZ039.php?
warncounty=COC059&city=Golden

http://www.crh.noaa.gov/den/products/webpres.html
Absolute pressure = inside pressure, or pressure measured relative to a
vacuum = psia
a = radius = 0.75 in
T = thickness = 0.03 in

Stress to strain: Remember, E = stress over strain

Use Young’s modulus E = 16*106 psi (this is inbetween values for brass
and copper) (see
http://www.csuchico.edu/~jpgreene/itec104/m104_c12/tsld015.htm)

Strain: use calcs from previous labs…

Gage factor = 2.7

#5, #6:
go to the reference on: http://egweb.mines.edu/eggn250/
read through the error stuff…

Lab report:
#1 - #4 ) Bourdon tube pressure gauge. Put these back together when you are
done for the next section to use!
#5 ) Measure pressure with the PX236 pressure transducer while simultaneously
measuring Vout from the CSM ¼ bridge…
#7) C = CSM, O = omega
- Check for hysteresis:
Get data points while both loading and unloading the gage
- Check for repeatability:
Get two sets of data taken by two different people
Use this spreadsheet:
Pressure
Point Vout   R/R strain   (gage)   Pressure

  CSM Omega CSM CSM gage CSM - calc Omega - calc abs

1               

2               

3               

Show the equations that you are using in the spreadsheet!!

#10) This one is worth 20 points – do a good job!

#13) Plastic vs elastic deformation…
#16) string = letters (abc, labels on graphs, etc.)
integer = 1, 2, 3, = blue lines
Boolean = true/False, On/off, green stuff
floating point = 1.3256741… = orange stuff
array = column of numbers

Experiment 5 – Big Picture, Corrections, Guidance & PreLab Help

So far, you’ve experimented with a couple of electro-mechanical devices, Thermistors
and Strain Gages. And you’ve used them to measure several useful mechanical
properties: temperature, temperature sensor response, cantilever beam response to force
and vibration, and coefficient of thermal expansion for 2 different materials.

Big Picture: For this experiment you will be working with a New Electromechanical
Device – a Pressure Transducer. You’ll be measuring the response from 2 transducers
simultaneously, commercial (OMEGA) and homemade (CSM). The Homemade one
uses a brass or copper plate with a bonded metallic Strain Gage1, whereas the
Commercial one uses a semi-conductor Strain Gage2 (more info in class).

A ¼ Bridge Circuit will be required for the CSM pressure transducer. The commercial
transducer’s bridge circuit is on a silicon chip inside, but you will need to supply an
excitation voltage, obtain the output voltage, and ground it, of course.

Experiment 5 – Corrections/Clarifications to Lab Manual

1) Dr. King has made some useful additions to the list of reference material & fixed
some of the errors with this lab. Thanks Dr. King. Use the references listed, esp.
MatWeb, and Current Atmospheric Pressure.
2) We actually have only One OMEGA pressure transducer. The PX-236. This
model has been discontinued at OMEGA, so you won’t find specifics at the
omega website. See “Some Useful Info” below.
3) The CSM Pressure transducer is made using either a round brass or a square
copper plate, as shown in class last week. However, if you use the Copper
information given in the manual it will send you to the right value for Young’s
Modulus (E). Any of the states given (cold drawn, cold worked or annealed) will
yield the same value for E.
4) Use the plate thickness, T = 0.035” stated on the Pressure sheet, pg. 158, versus
the 0.03” in the experiment write-up.

1
This is the type we’ve been using so far. The fine metallic foil bonded to a polyimide backing.
2
This type has an advantage of being much more sensitive & much smaller than the bonded metallic type.
They are typically made from Silicon that is doped with a semi-metallic atom, like Boron. And the silicon
is etched to the desired shape and size.
 Experiment 5 – Some Useful Info

1) For the OMEGA X-ducer -- You’ll need the Specifications and Application
Notes. They are on pages B-14 and Z-14 of the OMEGA manuals in the back of
the lab.
a. John Synhorst has been nice enough to make a double-sided copy for each
MEL I student.
b. They are on the table right inside the door of CTLM 125.
c. You can go by sometime tonight (Tues) before 8 PM or Wed 10:30 AM –
5 PM to pick one up.

2) The spec sheet lists the pressure range, max voltage output, and model#. The
model # on this transducer is 236PC150G V.
a. OMEGA transducer(s) specified excitation voltage is 10 volts. We use 5
volts excitation. Therefore our maximum output at 150 psig would be 30
mV, not 60.
PX 236 0-150 psig 60 mV @ 10 V (excitation)
PX 236 0-150 psig 30 mV @ 5 V (excitation)
The equation at the bottom of the sheet shows the sensitivity with this 5V
excitation.

3) The application notes (pg Z-14) describe linearity, sensitivity, hysteresis, zero
(null), and repeatability errors. They also define Absolute, Differential and Gage
pressure.

4) One other important note. I would read the page on Grounding, if you haven’t
already. The data taking, especially for the CSM transducer, will be next to
impossible without proper grounding of your circuit.

Experiment 5 – Help on PreLab Questions

Q1) Use atmospheric pressure at Jeff Co airport from the NOAA website
given, under additional reference material. Use gage pressure for p.
Remember that E = /, or =/E. Use the MatWeb site to find E for
copper (Cu). You may have to review your notes on strain gages and ¼
bridge calculations for Vout. The Gage factor on this strain gage is 2.07,
as stated on the pressure sheet.
General
Semiconductor strain gages are devices which vary in resistance as strain
is applied to them. This property makes them very useful in measuring
extremely small amounts of force with accuracy and precision. Creative
uses for these gages have ranged from the measurement of internal
pressures inside solid rocket engines to delicate medical apparatus used
in microsurgery.
Gages made from semiconductor materials have advantages over more
conventional types of strain gages. These include homogeneity,
increased sensitivity, and decreased size. Gages made by Micron
Instruments range down to 0.027" (0.69 mm) in length.
Micron semiconductor strain gages are made from Czochoralski pulled
boron doped bulk silicon. They have no P/N junction. The silicon is
etched to shape, eliminating the potential for molecular dislocation or
cracks, thereby optimizing performance.
All gages manufactured by Micron must pass through rigorous tests
before they are approved for use by our customers. The behavior of each
gage at different temperatures is measured and the gages are matched to
each other based upon these measurements. Customers may specify
matched sets of 2, 4, or more gages, or purchase unmatched sets of bulk
gages.
Bar Semiconductor Strain Gages
Home
Download this data
sheet

Lead Resistance @ 78 Gage

Part Number X dim Y dim Z dim Thickness
Attachment deg F Factor
SS-027-013-
0.027" 0.013" 0.009" Ball Bond 0.0004" 540 ± 50 Ohms 155 ± 10
500P
SS-080-050-
0.080" 0.050" 0.008" Welded 0.0004" 120 ± 20 Ohms 120 ± 10
120P
SS-090-060-
0.090" 0.060" 0.008" Welded 0.0004" 540 ± 50 Ohms 140 ± 10
500P
SS-150-125-
0.150" 0.100" 0.009" Welded 0.0008" 25 ± 3 Ohms 100 ± 10
25P
SS-250-225-
0.250" 0.225" 0.009" Welded 0.0004" 120 ± 20 Ohms 100 ± 10
120P

* per 100 degrees F

 "U"-shaped
Semiconductor Strain
Gages

Lead Resistance @ 78 Gage

Part Number X dim Y dim Z dim Thickness
Attachment deg F Factor
SS-037-022-
0.037" 0.022" 0.016" Welded 0.0004" 540 ± 50 Ohms 150 ± 10
500PU
SS-047-025-
0.047" 0.025" 0.016" Welded 0.0004" 540 ± 50 Ohms 140 ± 10
500PU
SS-060-033-
0.060" 0.033" 0.016" Welded 0.0004" 325 ± 40 Ohms 100 ± 10
300PU
SS-060-033-
0.060" 0.033" 0.016" Welded 0.0004" 540 ± 50 Ohms 140 ± 10
500PU
SS-060-033-
0.060" 0.033" 0.016" Welded 0.0004" 2000 ± 100 Ohms 155 ± 10
2000PU
SS-080-050- 10000 ± 1000
0.080" 0.050" 0.013" Welded 0.0004" 175 ± 10
10000PU Ohms
SS-095-060-
0.095" 0.060" 0.016" Welded 0.0004" 350 ± 50 Ohms 120 ± 10
350PU
* per 100 degrees F
 
"M"-shaped Semiconductor
Strain Gages
 Lead Resistance @ 78 Gage
Part Number X dim Y dim Z dim Thickness
Attachment deg F Factor
SS-060-040-
0.060" 0.040" 0.032" Welded 0.0004" 2500 ± 150 Ohms 140 ± 10
2500-PM
* per 100 degrees F
 
DEFINITIONS
GAGE FACTOR

The gage factor (G.F.) of strain gage is a dimensionless number defined

by the formula
G.F. = (R - Rm)/RE
where
R = nominal unstrained resistance of the gage,
Rm = the measured resistance of the gage under some known strain, E,
and
E = the strain on the gage.

Thermal Coefficient of Gage Factor (TCGF)

The Thermal Coefficient of Gage Factor (TCGF) is due to thermal effects

in the silicon matrix of the strain gage inhibitiing the flow of electrons.
The formula for TCGF is
TCGF = (100 x (GF2 - GF1))/(GF1 x (T2 - T1))
where
GF1 = Gage factor at ambient temperature T1;
GF2 = Gage factor at elevated temperature T2;
T1 = ambient temperature (78 deg F);
and
T2 = elevated temperature.
Thermal Coefficient of Resistance (TCR)

The Thermal Coefficient of Resistance (TCR) is also due to thermal

effects in the silicon matrix affecting the flow of electrons. The formula
for TCR is given by
TCR = (100 x (R2 - R1))/(R1 x (T2 - T1))
where
R1 = Resistance at ambient temperature T1;
GF2 = Resistance at elevated temperature T2;
T1 = ambient temperature (78 deg F);
and
T2 = elevated temperature.
For further information, request a set of strain gage specifications from
our technical support staff.
 

Strain Gage Technical Data

Strain Gage Measurement

The most universal measuring device for the electrical measurement of mechanical
quantities is the strain gage. Several types of strain gages depend on the proportional
variance of electrical resistance to strain: the piezoresistive or semi-conductor gage,
the carbon-resistive gage, the bonded metallic wire, and foil resistance gages.

The bonded resistance strain gage is by far the most widely used in experimental
stress analysis. These gages consist of a grid of very fine wire or foil bonded to the
backing or carrier matrix. The electrical resistance of the grid varies linearly with
strain. In use, the carrier matrix is bonded to the surface, force is applied, and the strain is found by measuring
the change in resistance. The bonded resistance strain gage is low in cost, can be made with a short gage length,
is only moderately affected by temperature changes, has small physical size and low mass, and has fairly high
sensitivity to strain.

In a strain gage application, the carrier matrix and the adhesive must work together to transmit the strains from
the specimen to the grid. In addition, they serve as an electrical insulator and heat dissipator.

The three primary factors influencing gage selection are operating temperature, state of strain (gradient,
magnitude, and time dependence) and stability required.

Because of its outstanding sensitivity, the Wheatstone bridge circuit is the most frequently used circuit for static
strain measurements. Ideally, the strain gage is the only resistor in the circuit that varies and then only due to a
change in strain on the surface.

There are two main methods used to indicate the change in resistance caused by strain on a gage in a
Wheatstone bridge. Often, an indicator will rebalance the bridge, displaying the change in resistance required in
micro-strain. the second method installs an indicator, calibrated in micro-strain, that responds to the voltage
output of the bridge. This method assumes a linear relationship between voltage out and strain, an initially
balanced bridge, and known V in. In reality, the V out-strain relationship is nonlinear, but for strains up to a few
thousand micro-strain, the error is not significant.

Potential Error Sources

In a stress analysis application, the entire gage installation cannot be calibrated as can some pressure
transducers. Therefore, it is important to examine potential error sources prior to taking data.
Some gages may be damaged during installation. It is important therefore to check the resistance of the strain
gage prior to stress.

Electrical noise and interference may alter your readings. Shielded leads and adequately insulating coatings may
prevent these problems. A value of less than 500 M ohms (using an ohmmeter) usually indicates surface
contamination.

Thermally induced voltages are caused by thermocouple effects at the junction of dissimilar metals within the
measurement circuit. Magnetically induced voltages may occur when the wiring is located in a time varying
magnetic field. Magnetic induction can be controlled by using twisted lead wires and forming minimum but equal
loop areas in each side of the bridge.

Temperature effects on gage resistance and gage factor should be compensated for as well. This may require
measurement of temperature at the gage itself, using thermocouples, thermistors, or RTDs. Most metallic gage
alloys, however, exhibit a nearly linear gage factor variation with temperature over a broad range which is less
than ±1% within ±100°C.

Prime Strain Gage Selection Considerations

• Gage Length
• Number of Gages in Gage Pattern
• Arrangement of Gages in Gage Pattern
• Grid Resistance
• Strain Sensitive Alloy
• Carrier Material
• Gage Width
• Solder Tab Type
• Configuration of Solder Tab
• Availability

Strain gage dimensions

The active grid length, in the case of foil gages, is the net grid length without the tabs and comprises the return
loops of the wire gages. The carrier, dimensions are designed by OMEGA for the optimum function of the strain
gage.
Strain gage resistance
The resistance of a strain gage is defined as the electrical resistance measured between the two metal ribbons or
contact areas intended for the connection of measurement cables. The range comprises strain gages with a
nominal resistance of 120, 350, 600, and 700 Ohms.
Gage Factor (Strain Sensitivity)
The strain sensitivity k of a strain gage is the proportionality factor between the relative change of the resistance.
The strain sensitivity is a figure without dimension and is generally called gage factor.
The gage factor of each production lot is determined by sample measurements and is given on each package as
the nominal value with its tolerance. Reference Temperature The reference temperature is the ambient
temperature for which the technical data of the strain gages are valid, unless temperature ranges are given. The
technical data quoted for strain gages are based on a reference temperature of 23°C.
Temperature Characteristic
Temperature dependent changes of the specific strain gage grid resistance occur in the applied gage owing to the
linear thermal expansion coefficients of the grid and specimen materials. These resistance changes appear to be
mechanical strain in the specimen. The representation of the apparent strain as a function of temperature is
called the temperature characteristic of the strain gage application. In order to keep apparent strain through
temperature changes as small as possible, each strain gage is matched during the production to a certain linear
thermal expansion coefficient. OMEGA offers strain gages with temperature characteristics matched to ferritic
steel and aluminum.
Service Temperature Range
The service temperature range is the range of ambient temperature where the use of the strain gages is
permitted without permanent changes of the measurement properties. Service temperature ranges are different
whether static or dynamic values are to be sensed.
Maximum Permitted RMS Bridge Energizing Voltage
The maximum values quoted are only permitted for appropriate application on materials with good heat
conduction (e.g., steel of sufficient thickness) if room temperature is not exceeded. In other cases temperature
rise in the measuring grid area may lead to measurement errors. Measurements on plastics and other materials
with bad heat conduction require the reduction of the energizing voltage or the duty cycle (pulsed operation).

THE STRAIN GAGE IS ONE OF THE MOST IMPORTANT TOOLS of the

electrical measurement technique applied to the measurement of mechanical
quantities. As their name indicates, they are used for the measurement of
strain. As a technical term "strain" consists of tensile and compressive strain,
distinguished by a positive or negative sign. Thus, strain gages can be used
to pick up expansion as well as contraction. The strain of a body is always
caused by an external influence or an internal effect. Strain might be caused
by forces, pressures, moments, heat, structural changes of the material and
the like. If certain conditions are fulfilled, the amount or the value of the
influencing quantity can be derived from the measured strain value. In
experimental stress analysis this feature is widely used. Experimental stress
analysis uses the strain values measured on the surface of a specimen or
structural part to state the stress in the material and also to predict its safety
and endurance. Special transducers can be designed for the measurement of
forces or other derived quantities, e.g., moments, pressures, accelerations,
and displacements, vibrations and others. The transducer generally contains
a pressure sensitive diaphragm with strain gages bonded to it.