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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



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



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



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 !!!



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



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



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)



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



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



The strain gage resistance change is very small

Therefore, the signal is amplified in the signal conditioner



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



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



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)



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



Strain Gage Wiring Considerations



Wheatstone Bridge - Some Compensation Considerations



Wheatstone Bridge - 2311 Signal Conditioner

Low PassFilter

Trim

Power

ExcitationVoltage

Gain

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