Mechanical Engineering - 22.302 ME Lab I
ME 22.302
Mechanical Lab I
Strain Gage Measurements
Note: Some material was obtained from unidentified web sources and origin cannot be determined at this time
Dr. Peter Avitabile
University of Massachusetts Lowell
Strain Gages - 122601 - 1
Copyright © 2001
Mechanical Engineering - 22.302 ME Lab I
A “transducer” is a device that converts some mechanical quantity
into some measurable electrical quantity.
Through a calibration procedure, the “sensitivity” of the
transducer can be obtained
OUTPUT
INPUT
transducer
Physical Phenomenon
Pressure, Temperature,
Strain, Displacement,
Velocity, Acceleration,
etc
Dr. Peter Avitabile
Volts
per
Engineering
Unit
University of Massachusetts Lowell
Electrical Signal related
to Physical Phenomenon
DC voltage, AC voltage,
current, resistance, etc
V/EU
Strain Gages - 122601 - 2
Copyright © 2001
Mechanical Engineering - 22.302 ME Lab I
There are a wide variety of methods to measure stress & strain
Moire Fringe Techniques
Holographic Interferometry
Brittle Coat Methods
Photoelasticity
Strain Gages
Only strain gages will be considered here.
Strain gages are used for a variety of transducer designs for the
measurement of force, acceleration, torque and others
Dr. Peter Avitabile
University of Massachusetts Lowell
Strain Gages - 122601 - 3
Copyright © 2001
Mechanical Engineering - 22.302 ME Lab I
Strain Gage Construction
- Can be made with straight wires
- More common to etch them from thin metal
foil sheets bonded to a plastic backing which
is then glued to the structure
- Size can be as small as 0.2 mm
which is relatively small
Points to Note
- Remember that stress is average stress over gage area
SIZE IS IMPORTANT !!!
- Orientation is equally important for single direction gages
- Rosettes combine 3 gages to form one integral gage
- Accurate to 1% typically but mounting (bond & orientation) and
environmental effect may introduce 1% to 3% additional error
OR WORSE !!!
Dr. Peter Avitabile
University of Massachusetts Lowell
Strain Gages - 122601 - 4
Copyright © 2001
Mechanical Engineering - 22.302 ME Lab I
Review of Stress-Strain Relationships
D
F
(axial stress)
A
dL
strain = ε a =
(axial strain)
L
dD
strain = ε t =
(traverse or lateral strain)
D
stress = σ a =
F
L
Poisson' s ratio = ν = −
E=
σ
σ
ε
εt
dD / D
(typically = 0.3)
=−
dL / L
εa
(Young Modulus or Modulus of elasticity)
Elastic Limit
ε
Dr. Peter Avitabile
University of Massachusetts Lowell
Strain Gages - 122601 - 5
Copyright © 2001
Mechanical Engineering - 22.302 ME Lab I
Electrical Resistance Strain Gage
A relationship exists between the strain and change in resistance
in many materials (Lord Kelvin). Using this relationship, the
resistance R, the cross sectional area A, the length of the wire L
and the resistivity are related as
ρL
R=
A
The strain gage factor is defined as
S = SG = gage factor =
dR / R
εa
The strain gage factor is the slope of
the curves shown in the plot
Note: Some material was obtained from unidentified web sources and origin cannot be determined at this time as is the case for the plot
Dr. Peter Avitabile
University of Massachusetts Lowell
Strain Gages - 122601 - 6
Copyright © 2001
Mechanical Engineering - 22.302 ME Lab I
Electrical Resistance Strain Gage
Assuming small changes in resistance to changes in the resistivity,
length, and area,
a relationship referred to as the Gage Factor can be developed as
dR / R dR / R dρ / ρ
SG = gage factor =
=
=
+ 1 + 2υ
dL / L
εa
εa
The gage factor and resistance of the gage are typically
specified by the manufacturer
Gage factors are typically between 1.5 and 4.0 but can be as
high as 6.0 (other special materials have higher values)
Dr. Peter Avitabile
University of Massachusetts Lowell
Strain Gages - 122601 - 7
Copyright © 2001
Mechanical Engineering - 22.302 ME Lab I
Strain Gage Factor - Related Information
If the resistivity does not change significantly with strain, then
dρ / ρ
SG =
+ 1 + 2υ
εa
The electrical resistance R is generally 120 or 350 Ohm
Cross sensitivity generally refers to the distortion of the strain
due to the gage deformation itself and is generally small
However, the gage is generally very sensitive to loads and stress
perpendicular to the main sensing axis of the strain gage
Dr. Peter Avitabile
University of Massachusetts Lowell
Strain Gages - 122601 - 8
Copyright © 2001
Mechanical Engineering - 22.302 ME Lab I
Strain Gage Factor for Different Materials
dR / R dR / R dρ / ρ
SG = gage factor =
=
=
+ 1 + 2υ
dL / L
εa
εa
Note: Some material was obtained from unidentified web sources and origin cannot be determined at this time as is the case for this table
Dr. Peter Avitabile
University of Massachusetts Lowell
Strain Gages - 122601 - 9
Copyright © 2001
Mechanical Engineering - 22.302 ME Lab I
The strain gage resistance change is very small
Therefore, the signal is amplified in the signal conditioner
Dr. Peter Avitabile
University of Massachusetts Lowell
Strain Gages - 122601 - 10
Copyright © 2001
Mechanical Engineering - 22.302 ME Lab I
Wheatstone Bridge - Quarter Bridge Circuit
Using Ohm’s Law, the current is
I ABC =
Vs
(R 1 + R
4
)
I ADC =
Vs
(R 2 + R
3
)
Combining terms and rewriting, the following is obtained
R3 R1 − R4 R2
Vo = Vs
(R2 + R3 )(R1 + R4 )
The bridge is said to be balanced if
R3 R1 = R4 R2
Dr. Peter Avitabile
University of Massachusetts Lowell
or
R1 R4
=
R2 R3
Strain Gages - 122601 - 11
Copyright © 2001
Mechanical Engineering - 22.302 ME Lab I
Wheatstone Bridge - Quarter Bridge Circuit
When the strain gage is strained, there
is a change in resistance in the strain
gage. Noting this as ∆R3 and
substituting, using the gage factor
relationship and neglecting relatively
small terms in this equation, then
AFTER MUCH ALGEBRA !!!
Vo (R 2 + R 3 )2
εa =
VS SG R 2 R 3
and if equal resistors are used for R1, R2, R3, R4, then
Vo 1
εa = 4
VS SG
Dr. Peter Avitabile
University of Massachusetts Lowell
Strain Gages - 122601 - 12
Copyright © 2001
Mechanical Engineering - 22.302 ME Lab I
Wheatstone Bridge - Half Bridge Circuit
Temperature can have an effect on the measured strain. This
can be dealt with using a half bridge to balance the effects.
If R1 is the active gage, then R2 can be used for temperature
compensation (in an unstrained environment)
Dr. Peter Avitabile
University of Massachusetts Lowell
Strain Gages - 122601 - 13
Copyright © 2001
Mechanical Engineering - 22.302 ME Lab I
Wheatstone Bridge - Half Bridge Circuit
Using two gages on either side on a beam in bending (and
measuring the same but opposite stress/strain) yields a strain
measurement which is twice as large as a single gage
Dr. Peter Avitabile
University of Massachusetts Lowell
Strain Gages - 122601 - 14
Copyright © 2001
Mechanical Engineering - 22.302 ME Lab I
Strain Gage Wiring Considerations
Dr. Peter Avitabile
University of Massachusetts Lowell
Strain Gages - 122601 - 15
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Mechanical Engineering - 22.302 ME Lab I
Wheatstone Bridge - Some Compensation Considerations
Dr. Peter Avitabile
University of Massachusetts Lowell
Strain Gages - 122601 - 16
Copyright © 2001
Mechanical Engineering - 22.302 ME Lab I
Wheatstone Bridge - Some Compensation Considerations
Dr. Peter Avitabile
University of Massachusetts Lowell
Strain Gages - 122601 - 17
Copyright © 2001
Mechanical Engineering - 22.302 ME Lab I
Wheatstone Bridge - 2311 Signal Conditioner
Trim
Low Pass
Filter
Excitation
Voltage
Gain
Power
Dr. Peter Avitabile
University of Massachusetts Lowell
Strain Gages - 122601 - 18
Copyright © 2001