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WSachse; 2/2012;
Load Measurement System:
Force
Force
M&AE 3272 - Supplementary Lecture Materials: Strain Gages
Elastic Member
1
M&AE 3272: Mechanical Propertyand Performance Laboratory
Excitation
Signal Conditioning and Processing
Display and Analysis via LabVIEW
Strain Gage
Load Cell
WSachse; 2/2012;
Resistance Strain Gage – Brief History:
M&AE 3272 - Supplementary Lecture Materials: Strain Gages 2
The electrical resistance of a conducting wire increaseswith elongation and decreases with compression.
Lord Kelvin’s Experiments:Strain ε and electrical resistance of wires
1856
WSachse; 2/2012;
Resistance Strain Gage – Brief History 2:
1936-1938 Ruge (MIT) and Simmons (CalTech) plus 2 Students!
SR-4 (Simmons+Ruge+4 Others) joined with DeForest
Ruge-DeForest Partnership; SR-4 Gages distributed
SR-4 Strain Gages distributed by Baldwin
M&AE 3272 - Supplementary Lecture Materials: Strain Gages 3
Simmons Patent, 1944
“…He’s a familiar figure around the CalTech campus, which he considers a ‘suitable local amusement park.’”Simmons: Near Genius; Brilliant EE; “Lab Rat”;64 μV/με ! Failed to realize the significance of his invention.
Ruge: Bonded wire gage; Stymied by low-level signals;
Realized at once the significance of their
invention.
WSachse; 2/2012;
Resistance Strain Gage – Brief History 3:
1952 Development of foil gage by Saunders-Roe, UK
1960-70’s Improved Control and understanding of gage materials,design, photolithography, chemical etching; vacuumdeposition; manufacturing
Today Used in most applications; Many, many configurations
M&AE 3272 - Supplementary Lecture Materials: Strain Gages 4
Single-element foil gages
WSachse; 2/2012;
Foil Strain Gages - Various:
(a)-(c) Single-element gages
(d)-(e) Two-element rosette
(f) Two-element, stacked rosette
(g)-(h) Three-element rosette
(i) Three-element, stacked rosette
(j) Torque gage
(k) Diaphragm gage
(l) Stress gage
(m) Gages for use on concrete
M&AE 3272 - Supplementary Lecture Materials: Strain Gages 5
WSachse; 2/2012;
Semi-conductor Strain Gage – Brief History:
1954 Piezoresistive properties of Si and Ge discovered
1957 Mason and Thurston (Bell Labs); Transducer development (theory and experiment)
1960 Commercial piezoresistive strain gages available
1990’s -Current
Development of MEMS strain gages with electronics (analog/digital); telemetry
M&AE 3272 - Supplementary Lecture Materials: Strain Gages 6
• Usually have a larger Gage Factor (-50 to -200) than foil gages (typically +2.0 to 2.5)
• Highly non-linear resistance/strain behavior (Calibration?)• More expensive• More sensitive to temperature changes• More fragile than foil gauges.
Characteristics:
WSachse; 2/2012;
Strain Gage Specifications:
M&AE 3272 - Supplementary Lecture Materials: Strain Gages 7
WSachse; 2/2012;
Strain Gage Operation:
M&AE 3272 - Supplementary Lecture Materials: Strain Gages 8
http://www.rdpe.com/ex/hiw-sglc.htm
Essential Assumption:
The deformation of the gage accurately mimics the deformation of the material to which it is attached.
• Minimal loading effect of the gage on the test specimen
• Strain sign tensile/compressive)
• Strain magnitude
• Secondary effects negligible or accounted for
WSachse; 2/2012;
Strain Gage Applications:• Material property sensor
• Monitor and control loads/deformations in mechanical systems; e.g. Scales, Tools, Thermal sensor, Flow, Motion, etc.; Multi-B$ industry.
M&AE 3272 - Supplementary Lecture Materials: Strain Gages 9
“ … Real-time Computer Graphics for Character Animation. … we use strain gages as the input device. By using this, we can get the relative moving data between two human surfaces with no pains.”テレビジョン学会技術報告 17(55) pp.31-36 19930930
Alinghi; America’s Cup (IEEE Trans Neural Sys Rehab Eng, 2009)New Minneapolis I-35W BridgeGreen: Strain Gage Monitoring System
WSachse; 2/2012;
Strain Gages – Desired Characteristics:
M&AE 3272 - Supplementary Lecture Materials: Strain Gages 10
• Low mass: Minimal loading effect in dynamic
measurements
• Low stiffness: Minimal loading effect on deformation
• Gage calibration stable wrt temperature and time
• Wide operating temperature range
• High Gage resolution: ±1 μm/m
Large Dynamic range: ±5% strain (±50, 000 μm/m)
(High ε-sensitivity)
• Gage length small ⇒ point-like measurement
• Linear response: Simplified data process
• Good fatigue life - in dynamic measurements
WSachse; 2/2012;
Strain Gage Sensitivity:
M&AE 3272 - Supplementary Lecture Materials: Strain Gages 11
Factional Change of Gage Resistance with Strain:
ΔR
R= (1 + 2ν)εaxial︸ ︷︷ ︸
Dimensional
+Δρ
ρ︸ ︷︷ ︸piezo−resistive
The fractional change of gage resistance per unit strain –Strain gage Sensitivity :
ΔR
R· 1
εaxial⇒ Gage Factor ≡ Sgage = (1 + 2ν) +
Δρ
ρ· 1
εaxial
When ν ≈ 0.3 : the Gage Factor is given by
Sgage � 1 + 0.6 + (0.4 to 2.0) Metallic conductors
Sgage � 1 + 0.6 + (−125 to 175) Semiconductors
P − type (e. g. Boron) Sgage > 0
N − type (e. g. Arsenic) Sgage < 0
Sgage > 0 → Rg ∝ +ε > 0 [T] Sgage < 0 → Rg ∝ −ε < 0 [C]
• Numerical Example : Metal foil gage, 120 Ω ; Sgage ≈ 2.0 ,then for εaxial = 1 με (i. e. 1 × 10−6 in/in) :
ΔRg = Sg Rg εaxial � 2·120·10−6 � 2.4×10−4 [Ω] = 240 [μΩ]
WSachse; 2/2012;
Strain Gage: Performance Factors - 1
M&AE 3272 - Supplementary Lecture Materials: Strain Gages 12
Installation - It is assumed that a properly selected gage hasbeen correctly bonded to the material under test.
Transverse Sensitivity - Sensitivity of a gage to transversestrains (non uniaxial)
ΔR
R= Sgage(εaxial + Kt εtrans) where: Kt ≡ Strans
Saxial
Sgage = Saxial (1 − ν Kt)
True : εaxial =ΔR/R
Sgage
1 − ν Kt
1 + Kt(εaxial/εaxial)App : ε′axial =
ΔR/R
Sgage
Error in neglecting εtrans : Error =εaxial − ε′axial
εaxial100 %
Percent error of actual axial strain as a function of εtrans/εaxial
WSachse; 2/2012;
Strain Gage: Performance Factors - 2
M&AE 3272 - Supplementary Lecture Materials: Strain Gages 13
Cyclic Straining -May result innonlinearity, hysteresisand zero-shift.
Possible resultsof strain cycling
Temperature Sensitivity - Important if measurements aremade over a large ΔT . Possible effects:1. Gage Factor Saxial changes2. Gage dimensions change: ΔL/L = α ΔT3. Specimen dimensions change: ΔL/L = β ΔT4. Gage resistance changes: ΔR/R = γ ΔT#1 is relatively small; Mismatch between #2 and #3 leads tothermal straining of gage (unable to separate from specimen).
Apparent
strain for
two gage
alloys
Corrections - For measurements over a broad range oftemperature measured strains must be corrected.
WSachse; 2/2012;
Strain Gage: Performance Factors - 3
M&AE 3272 - Supplementary Lecture Materials: Strain Gages 14
Power Dissipation - Depends on gage size; design; material properties;adhesive/thickness; specimen material/thermal properties; coating; cooling.
WSachse; 2/2012;
Strain Gage: Performance Factors - 4
M&AE 3272 - Supplementary Lecture Materials: Strain Gages 15
Loading Effects - The gage/backing has an effective modulus,Egage = 7 ∼ 20 GPa (1 to 3 × 106 psi).
Effect of mechanical behavior of specimen under test isaffected locally and globally .
• Example of local effect:
Effective gage modulus: 1.15×106 psi (8.0 GPa);
Thickness of gage installation: 0.0023 in (0.06 mm)
• Global effects of the gage also arise affecting the entirecross-section of the specimen.
• Solution - Use the lowest modulus gage; smallest in size –or – use optical, capacitive techniques.
WSachse; 2/2012;
Wheatstone Bridge Circuit – Static Measurements:
M&AE 3272 - Supplementary Lecture Materials: Strain Gages 16
• Constant voltage (or current) excitation; Resistors R1, R2, R3 and
R4 and load resistance RM → ∞ .
Constant voltage circuit
Output Voltage:
E0 =R1 R3 − R2 R4
(R1 + R2))R3 + R4)Ei
At balance :
E0 = 0 when R1 R3 = R2 R4
⇒ Static Measurements
WSachse; 2/2012;
Wheatstone Bridge Circuit – Dynamic Measurements:
M&AE 3272 - Supplementary Lecture Materials: Strain Gages 17
• Dynamic Measurements: R1 → R1 + ΔR1;R2 → R2 + ΔR2; R3 → R3 + ΔR3 and R4 → R4 + ΔR4
then . . .
ΔE0 =R1 R2
(R1 + R2)2
(ΔR1
R1− ΔR2
R2+
ΔR3
R3− ΔR4
R4
)Ei + h. o. t.
The omitted higher-order-terms lead to an error given by
Error : =∑4
i=1 ΔRi/Ri∑4i=1 ΔRi/Ri + 2
• When ΔR1 = −ΔR4 and ΔR2 = ΔR3 = 0
– or : ΔR2 = −ΔR3 and ΔR1 = ΔR4 = 0 ⇒ Error equals zero.
WSachse; 2/2012;
Common Strain Gage Wheatstone Bridge Circuits:
M&AE 3272 - Supplementary Lecture Materials: Strain Gages 18
4-Arm Active (4X Output)
1-Arm Active (Quarter Bridge)
2-Arm Active (Temp Comp)
2-Arm Active (Temp Comp)
WSachse; 2/2012;
Common Strain Gage Wheatstone Bridge Circuits:
M&AE 3272 - Supplementary Lecture Materials: Strain Gages 19
Dummy Gage: Temperature
Compensation
WSachse; 2/2012;
Amplification of Bridge Signals:
M&AE 3272 - Supplementary Lecture Materials: Strain Gages 20
Pressure Sensor Application:
Circuit compensates for sensor-to-sensor offset and gain variations
Functional Block Diagram:
WSachse; 2/2012;
Measurement/Analysis of Dynamic Effects with Strain Gages:
M&AE 3272 - Supplementary Lecture Materials: Strain Gages 21
• Strain gage
detecting a
stress pulse :
Transmission of
dynamic strains
from specimen
into gage
• Dynamic response
of the strain gage
• Time-spatial signal
convolution:
ΔR(t) = Sgage(�0/C) ∗ ε(t) R0
• Examples - Dynamic, Axial Impact Loadings
Shock tube generated stress waves in rods; (a) Measurementsystem; (b) Longitudinal strain record at 1.51 m from impact
(Fox and Curtis, 1958)
Pneumatic rifle pellet excitation of stress wave in a rod; (a)Measurement system; (b) Longitudinal strain record showing
compressive and tensile pulses (Pao and Kowal, 1965)
WSachse; 2/2012;
Strain Gage as a Dynamic Pressure Sensor:
M&AE 3272 - Supplementary Lecture Materials: Strain Gages 22
Experiment : Two strain gages were bonded to the sides of a full can (Aluminum) ofsoda. The can was opened and the voltage signals from each gage were recorded using adigital waveform recorder.
Recorded unloading strains when opening a can of soda.
We only used one gage measuring the hoop strain, εhoop , of the can during unloadingto evaluate the internal pressure p prior to opening. The relationship is
Released Pressure, p =E t
r (1 − ν/2)εhoop
where
εhoop Measured hoop strain difference � 800 μεE Material’s Young’s modulus � 10.5 × 106 [psi]ν Material’s Poisson’s ratio ν � 0.33t Can wall thickness = 0.0040 [in]r Can inside radius = 1.3125 [in]
⎫⎪⎪⎪⎪⎪⎪⎪⎪⎪⎬⎪⎪⎪⎪⎪⎪⎪⎪⎪⎭
=⇒ 28.8 [psi]
Principle : A fluid (gas or liquid) under pressure inside of a can resultsin stresses and strains (deformations) in the material making up the can.
Stresses in a cylindrical pressure vessel. (from Gere, Mechanics of Materials (2004))
σhoop → ← σaxial
Biaxial State of Stress:
Hoop stresses : σhoop
2 · σhoop (t · Δx) � p (2r · Δx)
σhoop =p r
t
Axial stresses : σaxial
σaxial (2πr · t) � p (πr2)
σaxial =p r
2 t
Procedure : A strain gage is used to measure the hoop strain, εhoop , of the can.
εhoop =σhoop
E− ν
σaxial
EFor an aluminum can :
ν � 0.33E � 10.5 × 106 [psi]
Gives . . .
Pressure, p =E t
r (1 − ν/2)εhoop
WSachse; 2/2012;
Measuring Large (Plastic) Strains with Elastic Strain Gages:
M&AE 3272 - Supplementary Lecture Materials: Strain Gages 23
• Permits measurement of large, inelasticdeformations.
• Useful for measurements in hostile environments.
• Re-useable gage.
Semi-circular,thin beam
extensometer
Applied Load, P , deflection δ :
Bending Stress: σb =6 P R
b h2
Bending Strains: εb =6 P R
b h2 ECastigliano’s 2nd Theorem to findbending strain energy:
U =∫ π0
(P R sin θ)2
2 E IR dθ =
3 π P 2 R3
b h3 E
Axial deflection: δ =∂U
∂P=
π 6 P R3
b h3 E
Deflection Sensitivity:
δ
εb=
π R2
2 h
When connected to aquarter-bridge Wheatstonebridge for which the excitationis Ei gives the Output Signal :
ΔE0
Ei=
⎛⎜⎝Sg h δ
2π R2
⎞⎟⎠
Extensometer Sensitivity:
Sδ =ΔE0
δ
=Sg h
2π R2
WSachse; 2/2012;
Hot, New Ideas with Strain Gages:
M&AE 3272 - Supplementary Lecture Materials: Strain Gages 24
Silver Ink: Before/After Sintering 350^C, 60-min
A Digital MEMS-Based Strain Gage for Structural Health Monitoring
B. J. MacLean, M. G. Mladejovsky, M. R. Whitaker, M. Oliver, S. C. Jacobsen
Mat Res Soc Symposium Procedings, 503, 309-320 (1998)
Arthroscopically Implantable Force Probe: μ-Forces
Fiber-Optic Strain Gage
WSachse; 2/2012;
Back to us and M&AE 3272:
M&AE 3272 - Supplementary Lecture Materials: Strain Gages 25
We’re going to learn how to mount strain gages onto an elastic member in order to
fabricate a Load cell, or Force transducer.