Mechanical Engineering - 22.302 ME Lab Ifaculty.uml.edu/pavitabile/22.302/web_download/... · ......
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Dr. Peter Avitabile University of Massachusetts Lowell Strain Gages - 122601 - 1 Copyright © 2001
Mechanical Engineering - 22.302 ME Lab I
Strain Gage Measurements
ME 22.302
Mechanical Lab I
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 - 2 Copyright © 2001
Mechanical Engineering - 22.302 ME Lab I
A “transducer” is a device that converts some mechanical quantityinto some measurable electrical quantity.
Through a calibration procedure, the “sensitivity” of thetransducer can be obtained
transducerINPUT OUTPUT
Physical Phenomenon
Pressure, Temperature,Strain, Displacement,Velocity, Acceleration,etc
Electrical Signal relatedto Physical Phenomenon
DC voltage, AC voltage,current, resistance, etc
Voltsper
EngineeringUnit
V/EU
Dr. Peter Avitabile University of Massachusetts Lowell Strain Gages - 122601 - 3 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 themeasurement of force, acceleration, torque and others
Dr. Peter Avitabile University of Massachusetts Lowell Strain Gages - 122601 - 4 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 - 5 Copyright © 2001
Mechanical Engineering - 22.302 ME Lab I
Review of Stress-Strain Relationships
)elasticity of Modulusor Modulus (Young E
0.3) (typically //ratio sPoisson'
strain) lateralor (traverse strain
strain) (axial strain
stress) (axial
a
t
t
a
εσ
εε
ν
ε
ε
σ
=
=−=−==
==
==
==
LdLDdD
DdDLdLAFstress a
σ
ε
Elastic Limit
FD
L
Dr. Peter Avitabile University of Massachusetts Lowell Strain Gages - 122601 - 6 Copyright © 2001
Mechanical Engineering - 22.302 ME Lab I
Electrical Resistance Strain Gage
A relationship exists between the strain and change in resistancein many materials (Lord Kelvin). Using this relationship, theresistance R, the cross sectional area A, the length of the wire Land the resistivity are related as
aG
R/dRfactor gageSSε
===
ALR ρ=
The strain gage factor is defined as
The strain gage factor is the slope ofthe 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 - 7 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
υ++ερρ
=ε
=== 21/dR/dRL/dLR/dRfactor gageS
aaG
The gage factor and resistance of the gage are typicallyspecified by the manufacturer
Gage factors are typically between 1.5 and 4.0 but can be ashigh as 6.0 (other special materials have higher values)
Dr. Peter Avitabile University of Massachusetts Lowell Strain Gages - 122601 - 8 Copyright © 2001
Mechanical Engineering - 22.302 ME Lab I
Strain Gage Factor - Related Information
If the resistivity does not change significantly with strain, then
υ++ερρ
= 21/dSa
G
The electrical resistance R is generally 120 or 350 Ohm
Cross sensitivity generally refers to the distortion of the straindue to the gage deformation itself and is generally small
However, the gage is generally very sensitive to loads and stressperpendicular to the main sensing axis of the strain gage
Dr. Peter Avitabile University of Massachusetts Lowell Strain Gages - 122601 - 9 Copyright © 2001
Mechanical Engineering - 22.302 ME Lab I
Strain Gage Factor for Different Materials
υ++ερρ
=ε
=== 21/dR/dRL/dLR/dRfactor gageS
aaG
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 - 10 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 - 11 Copyright © 2001
Mechanical Engineering - 22.302 ME Lab I
Wheatstone Bridge - Quarter Bridge Circuit
( )( )4132
2413
RRRRRRRRVV so ++
−=
Using Ohm’s Law, the current is
Combining terms and rewriting, the following is obtained
( )41
sABC RR
VI+
=
( )32
sADC RR
VI+
=
3
4
2
12413 or
RR
RRRRRR ==
The bridge is said to be balanced if
Dr. Peter Avitabile University of Massachusetts Lowell Strain Gages - 122601 - 12 Copyright © 2001
Mechanical Engineering - 22.302 ME Lab I
Wheatstone Bridge - Quarter Bridge Circuit
( )32G
232
S
oa RRS
RRVV +
=ε
When the strain gage is strained, thereis a change in resistance in the straingage. Noting this as ∆R3 andsubstituting, using the gage factorrelationship and neglecting relativelysmall terms in this equation, then
AFTER MUCH ALGEBRA !!!
and if equal resistors are used for R1, R2, R3, R4, then
GS
oa S
1VV4=ε
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
Temperature can have an effect on the measured strain. Thiscan be dealt with using a half bridge to balance the effects.If R1 is the active gage, then R2 can be used for temperaturecompensation (in an unstrained environment)
Dr. Peter Avitabile University of Massachusetts Lowell Strain Gages - 122601 - 14 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 (andmeasuring the same but opposite stress/strain) yields a strainmeasurement which is twice as large as a single gage
Dr. Peter Avitabile University of Massachusetts Lowell Strain Gages - 122601 - 15 Copyright © 2001
Mechanical Engineering - 22.302 ME Lab I
Strain Gage Wiring 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 - Some Compensation Considerations