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

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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

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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

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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

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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

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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

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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