mechanical measurement lab , 17.06.2011 t.dijoud
DESCRIPTION
Characterisation of the Strain Gauge Factor at Cryogenic Temperature. Mechanical Measurement Lab , 17.06.2011 T.Dijoud. Summary. Introduction Goal of the study Method Results Conclusion. Introduction : Strain gauges. APPLICATION : Strain measurement Stress analysis MATERIALS : - PowerPoint PPT PresentationTRANSCRIPT
Mechanical Measurement Lab, 17.06.2011
T.Dijoud
Characterisation of the Strain Gauge Factor at Cryogenic Temperature
2Mechanical Measurement Lab [email protected]
2011.17.06
• Introduction
• Goal of the study
• Method
• Results
• Conclusion
Summary
3Mechanical Measurement Lab [email protected]
2011.17.06
• APPLICATION:
Strain measurement Stress analysis
• MATERIALS:
Measuring grid (5μm thickness) : Chromium-Nickel alloys, Copper-Nickel alloys
Support (25μm thickness):Polyimide
All type for several applications
Introduction : Strain gauges
Between 0.6 and 160 mm Between 0.6 and 160 mm
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2011.17.06
Close bond between the strain gauge and the object
Strain on the object transferred without loss to the strain gauge
PRINCIPLE:
WIRE RESISTANCE CHANGING WITH LENGTH OF WIRE
R = ρL/S (ρ: resistivity (Ω.m); L: length (m); S: section (m2))
∆R/R = ε (1 + 2ν) + ∆ ρ/ ρ (ε: strain = ∆L/L (μm/m); ν: Poisson coefficient)
Introduction : Strain gauges
F (N)
F (N)
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2011.17.06
Bridgman’s law: ∆ρ/ρ = C ∆v/v (C: Bridgman constant, ranging from 1.13 to 1.15)
∆R/R = ε ((1 + 2ν) + C(1 – 2ν)) k = (1 + 2ν) + C(1 – 2ν)
∆R/R = k ε
k : Strain gauge factor = Strain gauge sensitivity
Depends on: • Material of measuring grid• TEMPERATURE
Introduction : Strain gauges
∆L/L (μm/m)
∆R/R (μΩ/Ω)
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2011.17.06
Goal of the study
• GOAL: Characterise the strain gauge factor at 293K, 77K and 4.2K
NEW STRAIN GAUGES, NEW ADHESIVE, MORE ADVANCED DATA ACQUISITION SYSTEM
• WHY? Measurement conditions at CERN: 1.9 K to 500 K Strain measurements must be accurate
Application: Stress measurements during assembly and cryogenic cool down at 4.2 K of short magnet coil
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2011.17.06
COMPARISON BETWEEN 2 TECHNIQUES OF STRAIN MEASUREMENT
Reference sensor Strain gauges
Strain Resistance relative change
(∆L/Lo)Ref ∆R/Ro = (∆V/Vo)SG
Tests procedure
k =
�̃
• STEPS:
Find a way to measure strain with a great accuracy
Identify the set up for the measurements at room and cryogenic temperature
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2011.17.06
Strain measurement
Cryogenic temperature = cryostat
• WHAT IS NEEDED:
Sensor inside the cryostat Must work at low temperature Not too big, easy to install Great accuracy
• TECHNIQUE:
STRAIN = EXTENSION (∆L) / INITIAL LENGTH (L)
LVDT (Inductive sensor) : Infinite resolution Low linearity error
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2011.17.06
Method
LVDT and extension support
Strain gauge on each side
(¼ Bridge (X2))
LVDT
LO = 60 mm
Sample instrumentation
TENSILE TEST
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2011.17.06
Method: Set up
CRYOSTAT
77 K Nitrogen 4.2 K Helium
Sample
Fmax = 5kN
Vacuum
Tensile machine
Bellow
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2011.17.06
Sample design
F max 5 kNWidth 12 mm
Thickness 1,5 mmSection 18 mm2
L0 60 mmStress 278 MPa
E 193000 MPaε (μm/m) 1439 µm/m
(∆L)LVDT 90.7 µm
Aluminum Copper Stainless Steel
Young modulus E (MPa) 69000 128000 193000
Yield limit σe (MPa) 50 70 290
Max strain εm (μm/m) 725 547 1503 εm = e
Requirements:
- Strain does not exceed the yield limit of the material
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2011.17.06
Test at 293K
y = 2.1823x + 13.166R² = 1
0
500
1000
1500
2000
2500
0 500 1000 1500
Output signal (μV/V)
Strain (μm/m)
293K (Up#1)
Gauge factor
UP#1 2.18
UP#2 2.17
UP#3 2.16Force (kN) LVDT 1 (μm) LVDT 2 (μm)
1 3 292 11 553 24 77
3,8 36 91
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2011.17.06
Test at 77K: Results
Gauge factor
UP#1 2.32
UP#2 2.32
UP#3 2.32
y = 2.3176x - 18.468R² = 1
0
500
1000
1500
2000
2500
0 500 1000 1500
Output signal (μV/V)
Strain (μm/m)
77K (Up#1)
Force (kN) LVDT 1 (μm) LVDT 2 (μm)1 11 182 23 393 36 584 49 78
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2011.17.06
Accuracy of the measurements
• Displacement (LVDT)- DAQ Linearity : 0.02 % FS
ULDAQ = (0.02*2)/3 = 0.013 %- DAQ Precision : (0.05 % Meas. Value + 0.05 % FS)
UPDAQ = (0.05*4)/3 = 0.067 % UDis = 0.18 %- Linearity error LVDT : 0.25 % FS
UL = (0.25*2)/3 = 0.17 % UStrain = 0.19 %
• Initial length - Resolution of the caliper + Repeatability:
ULength = 0.071 %• Output signal (SG)
- DAQ Linearity: 0.013 %- DAQ Precision: 0.067 % UOS = 2.67 %- Accuracy of strain gauge measurement: 2.67%
GAUGE FACTOR ACCURACY : Uk = (0.192+2.672)1/2 = +/- 5.35 %
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2011.17.06
Conclusion
Gauge factor (293K) Gauge factor (77K)
UP#1 2.18 +/- 0.12 2.32 +/- 0.12
UP#2 2.17 +/- 0.12 2.32 +/- 0.12
UP#3 2.16 +/- 0.12 2.32 +/- 0.12
Average 2.17 2.32
Theoretical 2.2 +/- 0.022 /
• k-factor value satisfactorily close to the value given by the manufacturer • What we are looking for: Variations of the gauge factor • Between 293K and 77K, k-factor increases by 6.9%• Set up (sample instrumentation) validated for the measurements
NEXT STEPS:
• Tests with others samples Check the reproducibility of the experiment• Use the original cryostat for the tests at 293K, 77K and 4.2K
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2011.17.06
Thanks to
Thanks to Ofelia Capatina and Ramon Folch for this period at CERN
Thanks to Michael, Eugenie, Andrey, Raul, Alex, Robin,
Jean-Michel, Kurt and Rosmarie
Thank you for your attention!
20Mechanical Measurement Lab [email protected]
2011.17.06
Stress versus strain
Steel 304 L (AISI) 293 K 77 K
Young Modulus(MPa) 193000 208000
y = 0.2004x + 6.1235R² = 0.9998
0.0
50.0
100.0
150.0
200.0
250.0
0 500 1000 1500
Stress (MPa)
Strain (μm/m)
293K (Up#1)
y = 0.2164x + 5.5506R² = 1
0
50
100
150
200
250
0 500 1000 1500
Stress (MPa)
Strain (μm/m)
77K (Up#1)
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2011.17.06
Last study
k factor changing with temperature
last study: 1995
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2011.17.06
y = 198,93x + 1,5105R² = 0,9999
y = 199.08x - 3.0614R² = 0.9999
-250
-200
-150
-100
-50
0
50
100
150
200
250
-1,5 -1 -0,5 0 0,5 1 1,5
Output sig(mV/V)
Displacement (mm)
Signal versus displacement
Up #1
Down #1
Linear (Up #1)
Linear (Down #1)
LVDT 1 calibration at room temperature
y = 1.003x - 0.9999R² = 1
y = 1.002x - 22.954R² = 0.9998-1500
-1000
-500
0
500
1000
1500
-1500 -1000 -500 0 500 1000 1500
LVDT (μm)
Displacement (μm)
Up 3Down 3Linear (Up 3)Linear (Down 3)
Micrometer
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2011.17.06
LVDT 2 calibration at room temperature
y = 197.31x - 0.2624R² = 0.9999
y = 197.24x + 4.4976R² = 0.9999
-250
-200
-150
-100
-50
0
50
100
150
200
250
-1,5 -1 -0,5 0 0,5 1 1,5
Signal output (mV/V)
Displacement (mm)
Up #1
Down #1
Linear (Up #1)
Linear (Down #1)
y = 1.0009x - 11.286R² = 0.9999
y = 0.9996x + 13R² = 0.9999
-1500
-1000
-500
0
500
1000
1500
-1500 -500 500 1500
Displacement (μm)
Displacement (µm)
Up1
Down 1
Linear (Up1)
Linear (Down 1)
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2011.17.06
Wheatstone bridge
Bridge equation:
Vout/Vin =
Application with strain gauges:
Vout/Vin =
Configuration:- ¼ bridge- half bridge- full bridge
For the experiment: 1/4 bridge
R1+∆R1
R2+∆R2
Very low ∆R can be measuredFor 2000 µm/m, ∆R = 11µΩ
R3+∆R3
R4+∆R4
