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: 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

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)

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)

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

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

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

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

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

- 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

FIRST RESULTS

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

Test at 77K: Set up

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

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 %

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 +/- 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

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!

Questions?

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

Last study k factor changing with temperature last study: 1995

LVDT 1 calibration at room temperature Micrometer

LVDT 2 calibration at room temperature

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

Sample

LVDT: Principle