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Mechanical Measurement Lab , 17.06.2011 T.Dijoud

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 :

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Mechanical Measurement Lab , 17.06.2011 T.Dijoud

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  1. Characterisation of the Strain Gauge Factor at Cryogenic Temperature Mechanical Measurement Lab, 17.06.2011 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) 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. 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. Tests procedure COMPARISON BETWEEN 2 TECHNIQUES OF STRAIN MEASUREMENT Reference sensor Strain gauges StrainResistancerelative 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. 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. 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. Sample design Requirements: - Strain does not exceed the yield limit of the material e εm =

  12. FIRST RESULTS

  13. Test at 293K

  14. Test at 77K: Set up

  15. Test at 77K: Results

  16. 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 %

  17. Conclusion • 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. 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

  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. 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 R3+∆R3 R2+∆R2 R4+∆R4 Very low ∆R can be measured For 2000 µm/m, ∆R = 11µΩ

  25. Sample

  26. LVDT: Principle

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