1. Mechanical Measurement Lab, 17.06.2011 T.Dijoud
Characterisation of the Strain Gauge Factor
at Cryogenic Temperature
Mechanical Measurement Lab,
T.Dijoud

2. Summary
Introduction
Goal of the study
Method
Results
Conclusion

3. Introduction : Strain gauges
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
Between 0.6 and 160 mm

4. Introduction : Strain gauges
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)
F (N)

5. Introduction : Strain gauges
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
∆R/R (μΩ/Ω)
∆L/L (μm/m)

6. NEW STRAIN GAUGES, NEW ADHESIVE, MORE ADVANCED DATA ACQUISITION SYSTEM
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

7. COMPARISON BETWEEN 2 TECHNIQUES OF STRAIN MEASUREMENT
Tests procedure
COMPARISON BETWEEN 2 TECHNIQUES OF STRAIN MEASUREMENT
Reference sensor Strain gauges
Strain Resistance relative change
(∆L/Lo)Ref ∆R/Ro = (∆V/Vo)SG ̃
k =
STEPS:
Find a way to measure strain with a great accuracy
Identify the set up for the measurements at room and cryogenic temperature

8. Cryogenic temperature = cryostat
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

9. LO = 60 mm Method TENSILE TEST LVDT Strain gauge on each side
(¼ Bridge (X2))
LO = 60 mm
LVDT and
extension support
Sample instrumentation

10. Method: Set up Fmax = 5kN Bellow Vacuum CRYOSTAT 77 K  Nitrogen
4.2 K  Helium
Sample
Tensile machine

11. - Strain does not exceed the yield limit of the material
Sample design
Requirements:
- Strain does not exceed the yield limit of the material
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
F max 5 kN
Width 12 mm
Thickness
1,5
Section 18
mm2 L0 60
Stress
278
MPa E
193000
ε (μm/m)
1439
µm/m
(∆L)LVDT
90.7 µm

12. FIRST RESULTS

13. Test at 293K Gauge factor UP#1 2.18 UP#2 2.17 UP#3 2.16 Force (kN)
LVDT 1 (μm)
LVDT 2 (μm) 1 3 29 2 11 55 24 77
3,8 36 91

14. Test at 77K: Set up

15. Test at 77K: Results Gauge factor UP#1 2.32 UP#2 UP#3 Force (kN)
LVDT 1 (μm)
LVDT 2 (μm) 1 11 18 2 23 39 3 36 58 4 49 78

16. Accuracy of the measurements
Displacement (LVDT)
- DAQ Linearity : 0.02 % FS
ULDAQ = (0.02*2)/3 = %
- DAQ Precision : (0.05 % Meas. Value % FS)
UPDAQ = (0.05*4)/3 = % 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 = %
Output signal (SG)
- DAQ Linearity: %
- DAQ Precision: % UOS = 2.67 %
- Accuracy of strain gauge measurement: 2.67%
GAUGE FACTOR ACCURACY : Uk = ( )1/2 = +/ %

17. Conclusion
Gauge factor (293K)
Gauge factor (77K)
UP#1
2.18 +/- 0.12
2.32 +/- 0.12
UP#2
2.17 +/- 0.12
UP#3
2.16 +/- 0.12
Average
2.17
2.32
Theoretical
2.2 +/ /
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

18. Thank you for your attention!
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!

19. Questions?

20. Stress versus strain 293 K 77 K 193000 208000 Steel 304 L (AISI)
Young Modulus
(MPa)
193000
208000

21. Last study
k factor changing with temperature
last study: 1995

22. LVDT 1 calibration at room temperature
Micrometer

23. LVDT 2 calibration at room temperature

24. Very low ∆R can be measured
Wheatstone bridge
 Bridge equation:
Vout/Vin =
 Application with strain gauges:
Configuration:
¼ bridge
half bridge
full bridge
For the experiment: 1/4 bridge
R1+∆R1
R3+∆R3
R2+∆R2
R4+∆R4
Very low ∆R can be measured
For 2000 µm/m, ∆R = 11µΩ

25. Sample

26. LVDT: Principle