Applying the Wheatstone Bridge Circuit
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Applying the Wheatstone Bridge Circuit Applying the Wheatstone Bridge Circuit Dirk Eberlein dirk.eberlein@hbm.com www.hbm.com 19.03.2008, Folie 1 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit The relationship between the applied strain ε and the relative change of the resistance of a strain gauge A A strain strain gauge gauge converts converts aa mechanical mechanical strain strain into into aa change change of of an an electrical electrical resistance. resistance. “gauge factor”: characteristic of the strain gauge and has to been checked experimentally: ∆R = k ⋅ε R 19.03.2008, Folie 2 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit Test of the gauge factor Thomas Kleckers, HBM 19.03.2008, Folie 3 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit Value of the relative change of the resistance • ∆R/R 0 = k · ε ε k ~ 2 R(typ.) = 120Ω or 350Ω for example – (strain level for transducers) 1000 µm/m = 1mm/m (0,1%) E.g.:120Ω-strain E.g.:120Ω-straingauge gaugeat at1mm/m 1mm/m==0,24Ω 0,24Ωchange changeof of the theresistance resistance Measurements with an ohmmeter are impossible 19.03.2008, Folie 4 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit Basics U1 R1 = U 0 R1 + R2 R1 U1 = U 0 R1 + R2 U1= 5V U2= 5V R1= 5 Ω R2= 5 Ω U0=10V 19.03.2008, Folie 5 Hottinger Baldwin Messtechnik GmbH Spannungsabfall = voltage drop potential divider Dirk Eberlein Applying the Wheatstone Bridge Circuit Basics U1= 4V U2= 6V R1= 4 Ω R2= 6 Ω U0=10V U1 R1 = U0 R1 + R 2 19.03.2008, Folie 6 U1 = U 0 R1 R1 + R 2 Hottinger Baldwin Messtechnik GmbH potential divider Dirk Eberlein Applying the Wheatstone Bridge Circuit Basics U1= 5V U2= 5V R1= 5 Ω R2= 5 Ω Ua=0V R4= 5 Ω R3= 5 Ω U4= 5V U3= 5V U0=10V 19.03.2008, Folie 7 Hottinger Baldwin Messtechnik GmbH potential divider Dirk Eberlein Applying the Wheatstone Bridge Circuit Basics U1= 5,45V R1= 6 Ω U2= 4,54V + R2= 5 Ω Ua=0,45V R4= 5 Ω - U4= 5V R3= 5 Ω U3= 5V U0=10V increasing of R1 output voltage Ua will be positive decreasing of R1 output voltage Ua will be negative 19.03.2008, Folie 8 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit Basics U1= 4,54V R1= 5 Ω U2= 5,45V - R2= 6 Ω Ua= - 0,45V + R3= 5 Ω R4= 5 Ω U4= 5V U3= 5V U0=10V increasing of R2 output voltage Ua will be negative decreasing of R2 output voltage Ua will be positive 19.03.2008, Folie 9 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit Basics U1 R1 R1 + R 2 U2 U1 = U0 U3 U4 = U0 Ua U4 R4 R3 + R 4 U0 R1 R4 U a = U 0 − R1 + R2 R3 + R4 R1 + ∆R1 R4 + ∆R4 U a = U 0 − R1 + ∆R1 + R2 + ∆R2 R3 + ∆R3 + R4 + ∆R4 19.03.2008, Folie 10 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit Basics R1 + ∆R1 R4 + ∆R4 U a = U 0 − R1 + ∆R1 + R2 + ∆R2 R3 + ∆R3 + R4 + ∆R4 the resistance changes in the strain gauges are very small : ∆R << R the two halves of the bridge must have the same resistance: R1 = R2 19.03.2008, Folie 11 und R3 = R4 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit Basics U a ∆R1 ∆R2 ∆R3 ∆R4 = − + − U0 R1 R2 R3 R4 with: ∆R = k ⋅ε R that implies: Ua k = ⋅ (ε1 − ε 2 + ε 3 − ε 4 ) U0 4 19.03.2008, Folie 12 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit Basics • we use every time the Wheatstone Bridge Circuit with 4 resistors • these 4 resistors could be 1, 2 or 4 strain gauges • modern amplifiers completing “missing“ resistors in the Wheatstone Bridge Circuit • with 4 active strain gauges we get the largest output value 19.03.2008, Folie 13 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit Basics R4 R1 UB R3 R2 UA 19.03.2008, Folie 14 UA k = (ε1 − ε 2 + ε 3 − ε 4 ) UB 4 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit Elementary circuits with strain gauges Quarter bridge 1 active strain gauge ε1 ( +) R4 R1 (R1) R4 ε2 (−) R2 R3 Half bridge 2 active strain gauges ε1 ( + ) (R1) ε2 (−) (R2) 19.03.2008, Folie 15 (R2) R3 Full bridge 4 active strain gauges ε1 ( + ) R4 (R1) ε2 (−) R3 (R2) Hottinger Baldwin Messtechnik GmbH ε4 (−) (R4) ε3 (+) (R3) Dirk Eberlein Applying the Wheatstone Bridge Circuit Measurements on a bending beam (Quarter Bridge) R1 F strain gauge 1 R3 R2 F R4 UA tensile bar / bending load strain gauge 1: + UA k = (ε1 ) UB 4 19.03.2008, Folie 16 Temperature compensation: No! Hottinger Baldwin Messtechnik GmbH Dirk Eberlein UB Applying the Wheatstone Bridge Circuit Calibrating measurement equipment (Quarter Bridge) UA k = (ε1 − ε 2 + ε 3 − ε 4 ) UB 4 k = 2 gauge factor (written on the strain gauge package) estimated strain level ε = 1000 µm/m (estimation!) UA k = (ε1 − ε 2 + ε 3 − ε 4 ) UB 4 UA k 2 = (ε1 ) = (1000µm / m) = 0,5 ⋅ 1000 ⋅ 10 −6 = 0,5 ⋅ 10 −3 UB 4 4 UA = 0,5mV / V UB 19.03.2008, Folie 17 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit Measurements on a bending beam (Half Bridge) R1 F UA strain gauge 2 UA k = (ε1 − ε 2 ) UB 4 19.03.2008, Folie 18 R3 R2 strain gauge 1 R4 bending load strain gauge 1: + strain gauge 2: Temperature compensation: Yes! Hottinger Baldwin Messtechnik GmbH Dirk Eberlein UB Applying the Wheatstone Bridge Circuit Measurements on a bending beam (Half Bridge) R1 R3 R2 strain gauge 1 F strain gauge 2 UA k = (ε1 − ε 2 ) UB 4 19.03.2008, Folie 19 R4 UB UA Superimposed normal strains are compensated strain gauge 1: + strain gauge 2: + Temperature compensation: Yes! Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit Calibrating measurement equipment (Half Bridge) k = 2 gauge factor (written on the strain gauge package) estimated strain level ε = 1000 µm/m (estimation!) UA k = (ε1 − ε 2 + ε 3 − ε 4 ) UB 4 UA k 2 = (ε1 − ε 2 ) = (1000µm / m − [− 1000µm / m]) UB 4 4 UA = 0,5 ⋅ 2000 ⋅ 10 − 6 = 1⋅ 10 −3 UB UA = 1 mV / V UB 19.03.2008, Folie 20 2 times the output value of a 1/4-bridge Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit Optimisation Optimisationof ofaawish wishmop mop 19.03.2008, Folie 21 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit Measurements on a bending beam (Full Bridge) R1 F UA strain gauge 4 strain gauge 2 UA k = (ε1 − ε 2 + ε 3 − ε 4 ) UB 4 19.03.2008, Folie 22 R3 R2 strain gauge 3 strain gauge 1 R4 bending load strain gauge 1: + strain gauge 2: strain gauge 3: + strain gauge 4: Temperature compensation: Yes! Hottinger Baldwin Messtechnik GmbH Dirk Eberlein UB Applying the Wheatstone Bridge Circuit Measurements on a bending beam (Full Bridge) R1 R3 R2 strain gauge 3 strain gauge 1 F strain gauge 4 strain gauge 2 UA k = (ε1 − ε 2 + ε 3 − ε 4 ) UB 4 19.03.2008, Folie 23 R4 UB UA Superimposed normal strains are compensated strain gauge 1: + strain gauge 2: +strain gauge 3: + strain gauge 4: +Temperature compensation: Yes! Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit Calibrating measurement equipment (Full Bridge) k = 2 gauge factor (written on the strain gauge package) estimated strain level ε = 1000 µm/m (estimation!) UA k = (ε1 − ε 2 + ε 3 − ε 4 ) UB 4 UA 2 = (1000µm / m − [− 1000µm / m] + 1000µm / m − [− 1000µm / m]) UB 4 UA = 0,5 ⋅ 4000 ⋅ 10 −6 = 2 ⋅ 10 −3 UB UA = 2 mV / V UB 19.03.2008, Folie 24 4 times the output value of a 1/4-bridge Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit ... and the right strain gauge for this application DY11... 19.03.2008, Folie 25 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit Measurements on a tension/compression bar (Half Bridge) R1 R3 R2 strain gauge 2 strain gauge 1 F −ν = F R4 UA tensile bar εq εl ⇒ ε q = −νε l ⇒ ε 2 = −νε1 ν KPoisson' s ratio (steel ≈ 0,3 ) UA k k = (ε1 − ε 2 ) = [ε1 − (− νε1 )] UB 4 4 19.03.2008, Folie 26 strain gauge 1: + strain gauge 2: Temperature compensation: Yes! Hottinger Baldwin Messtechnik GmbH Dirk Eberlein UB Applying the Wheatstone Bridge Circuit Measurements on a tension/compression bar (Half Bridge) R1 F strain gauge 1 R4 R3 R2 UA strain gauge 2 Superimposed bending strains occur in the result strain gauge 1: + strain gauge 2: - UA k k = (ε1 − ε 2 ) = [ε1 − (− νε1 )] UB 4 4 Temperature compensation: Yes! 19.03.2008, Folie 27 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein UB Applying the Wheatstone Bridge Circuit Calibrating measurement equipment (Half Bridge) k = 2; ν = 0,3 estimated strain level ε = 1000 µm/m (estimation!) UA k = (ε1 − ε 2 + ε 3 − ε 4 ) UB 4 UA k k 2 = (ε1 − ε 2 ) = [ε1 − (− νε1 )] = (1000µm / m − [− 0,3 ⋅ 1000µm / m]) UB 4 4 4 UA = 0,5 ⋅ (1000µm / m − [− 300µm / m]) = 0,5 ⋅ 1300 ⋅ 10 −6 = 0,65 ⋅ 10 −3 UB UA = 0,65 mV / V UB 19.03.2008, Folie 28 1.3 times the output value of a 1/4-bridge Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit Measurements on a tension/compression bar (Full Bridge) R1 R3 R2 F strain gauge 2 strain gauge 1 strain gauge 4 strain gauge 3 UA k = (ε1 − ε 2 + ε 3 − ε 4 ) UB 4 UA k = [ε1 − (− νε1 ) + ε 3 − (− νε 3 )] UB 4 19.03.2008, Folie 29 F R4 UA tensile bar strain gauge 1: + strain gauge 2: strain gauge 3: + strain gauge 4: Temperature compensation: Yes! Hottinger Baldwin Messtechnik GmbH Dirk Eberlein UB Applying the Wheatstone Bridge Circuit Measurements on a tension/compression bar (Full Bridge) R1 F strain gauge 4 strain gauge 3 UA k = (ε1 − ε 2 + ε 3 − ε 4 ) UB 4 19.03.2008, Folie 30 R3 R2 strain gauge 2 strain gauge 1 R4 UA Superimposed bending strains are compensated strain gauge 1: + strain gauge 2: strain gauge 3: strain gauge 4: + Hottinger Baldwin Messtechnik GmbH Dirk Eberlein UB Applying the Wheatstone Bridge Circuit Calibrating measurement equipment (Full Bridge) k = 2; ν = 0,3 estimated strain level ε = 1000 µm/m (estimation!) UA k = (ε1 − ε 2 + ε 3 − ε 4 ) UB 4 UA k = [ε1 − (− νε1 ) + ε 3 − (− νε 3 )] UB 4 UA 2 = (1000µm / m − [− 0,3 ⋅ 1000µm / m] + 1000µm / m − [− 0,3 ⋅ 1000µm / m]) UB 4 UA = 0,5 ⋅ 2600 ⋅ 10 − 6 = 1,3 ⋅ 10 −3 = 1,3 mV / V UB 19.03.2008, Folie 31 Hottinger Baldwin Messtechnik GmbH 2.6 times the output value of a 1/4-bridge Dirk Eberlein Applying the Wheatstone Bridge Circuit ... and the right strain gauge for this application XY11... 19.03.2008, Folie 32 XY31... Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit Measurements on a shaft under torsion (Full Bridge) R1 R3 R2 strain gauge 1 R4 strain gauge 4 UA strain gauge 3 Torsion shaft strain gauge 2 UA k = (ε1 − ε 2 + ε 3 − ε 4 ) UB 4 19.03.2008, Folie 33 strain gauge 1: + strain gauge 2: strain gauge 3: + strain gauge 4: Temperature compensation: Yes! Hottinger Baldwin Messtechnik GmbH Dirk Eberlein UB Applying the Wheatstone Bridge Circuit Measurements on a shaft under torsion (Full Bridge) F R1 R3 R2 strain gauge 1 strain gauge 4 UA strain gauge 3 Superimposed normal and bending strains are compensated strain gauge 2 F UA k = (ε1 − ε 2 + ε 3 − ε 4 ) UB 4 19.03.2008, Folie 34 R4 strain gauge 1: + strain gauge 2: strain gauge 3: strain gauge 4: + Temperature compensation: Yes! Hottinger Baldwin Messtechnik GmbH Dirk Eberlein UB Applying the Wheatstone Bridge Circuit Calibrating measurement equipment (Full Bridge) k=2 estimated strain level ε = 1000 µm/m (estimation!) UA k = (ε1 − ε 2 + ε 3 − ε 4 ) UB 4 UA 2 = (1000µm / m − [− 1000µm / m] + 1000µm / m − [− 1000µm / m]) UB 4 UA = 0,5 ⋅ 4000 ⋅ 10 −6 = 2 ⋅ 10 −3 UB UA = 2 mV / V UB 19.03.2008, Folie 35 4 times the output value of a 1/4-bridge Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit ... and the right strain gauge for this application XY11... 19.03.2008, Folie 36 XY31... Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit strain gauge rosettes for stress analysis two basic shapes (geometries): 0°/45°/90°-rosettes 0°/60°/120°-rosettes a c b 19.03.2008, Folie 37 strain measurement in 3 directions (a, b, c) Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit strain gauge rosettes for stress analysis Connection at the amplifier always as three different quarter bridges! measuring grid a, b, c 19.03.2008, Folie 38 Hottinger Baldwin Messtechnik GmbH e.g. Spider8-30 Dirk Eberlein Applying the Wheatstone Bridge Circuit Calibrating measurement equipment (3 different quarter bridges) 1000µm/m correspond to 2mV/V (at a gauge factor of 2), valid for amplifier channel (measuring grid) a, b, c a c b 19.03.2008, Folie 39 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit ε active strain gauge passive strain gauge or resistor εϑ strain gauge for temperature compensation Mb-bending moment; Md-torque; T-temperature; F-normal force 19.03.2008, Folie 40 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit 19.03.2008, Folie 41 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit 19.03.2008, Folie 42 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit 19.03.2008, Folie 43 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit Reduction and elimination of measurement errors, especially temperature effects • temperature error can be corrected mathematically • temperature compensation using Wheatstone bridge circuit -quarter bridge with compensating strain gauge -half and full bridges 19.03.2008, Folie 44 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit Basics Every strain gauge gives out a value when the temperature varies – without any mechanical load. Cause: • Work piece expansion with temperature • Change in specific resistance of strain gauge • Strain gauge grid expansion with temperature HBM, Thomas Kleckers (Januar 1999) 19.03.2008, Folie 45 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit Basics Thermal output of a quarter bridge ∆R = k ⋅ (εM + ε ϑ ) R0 F Strain gauge 1 19.03.2008, Folie 46 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit Temperature compensated strain gauges (series Y) 11 33 55 66** 77** 88** 99** -6 for αα == 10,8 forferritic ferriticsteel steel 10,8·10 ·10-6//KK -6 for αα == 23 foraluminium aluminium 23··10 10-6//KK -6 for αα == 16 foraustenitic austeniticsteel steel 16··10 10-6//KK -6 for αα == 0,5 forquartz quartz 0,5·10 ·10-6//KK -6 for fortitanium titanium/grey /greycast castiron iron αα == 99·10 ·10-6//KK -6 for αα == 65 forplastic plasticmaterial material 65·10 ·10-6//KK -6 for αα == 5,4 formolybdenum molybdenum 5,4·10 ·10-6//KK * not for all measuring grid length available 19.03.2008, Folie 47 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit Temperature TemperatureCompensation Compensation (Material, (Material,thermal thermalexpansion expansioncoefficient coefficient remaining remainingtemperature temperaturevariation variation polynomial polynomial(of (ofthe theremaining remaining temperature temperaturevariation) variation) so sothat thatthe thearising arisingmeasurement measurementfault fault can canbe becorrected correctedmathematically mathematically 19.03.2008, Folie 48 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit temperature compensation using Wheatstone bridge circuit R1 F (εM + εϑ ) strain gauge 1 (+ ε ϑ ) F=0! R4 R3 R2 UA quarter bridge with compensating strain gauge strain gauge 2 19.03.2008, Folie 49 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein UB Applying the Wheatstone Bridge Circuit temperature compensation using Wheatstone bridge circuit quarter bridge with compensating strain gauge strain R4 gauge1 strain R3 gauge2 Ue strain gauge 1 ⇒ (εM + ε ϑ ) strain gauge 2 ⇒ (+ ε ϑ ) Ua k = (ε1 − ε 2 ) Ue 4 Ua 19.03.2008, Folie 50 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit quarter bridge with compensating strain gauge The compensating strain gauge: - must be applied in a spot where it will be subjected to the same interference effect as the active strain gauge - must have the same physical properties as the active strain gauge (same package or batch) - must only be subjected to the interference effect and never to the quantity to be measured εM or its side effects - must be applied at the same material (e.g. steel) as the active strain gauge 19.03.2008, Folie 51 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit temperature compensation using Wheatstone bridge circuit Advantages: - it is not necessary to measure the temperature during the strain measurement - it is not absolutely necessary that the strain gauges are adjusted to the material 19.03.2008, Folie 52 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein Applying the Wheatstone Bridge Circuit temperature compensation using Wheatstone bridge circuit Changes of the strain gauge resistance of the same sign appearing in neigh boring arms will be subtracted with respect to the bridge output signal εϑ (+) R1 R4 R3 R2 UA strain gauge 1 strain gauge 1: + strain gauge 2: + strain gauge 2 half bridge 19.03.2008, Folie 53 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein UB Applying the Wheatstone Bridge Circuit temperature compensation using Wheatstone bridge circuit R1 Changes of the strain gauge resistance of the same sign appearing in neigh boring arms will be subtracted with respect to the bridge output signal strain gauge 1 strain gauge 2 strain gauge 3 strain gauge 4 R3 R2 εϑ (+) R4 UA εϑ (+) s. g. 1: + s. g. 2: + s. g. 3: + s. g. 4: + full bridge 19.03.2008, Folie 54 Hottinger Baldwin Messtechnik GmbH Dirk Eberlein UB Applying the Wheatstone Bridge Circuit Hottinger Baldwin Messtechnik GmbH Im Tiefen See 45 D-64293 Darmstadt www.hbm.com thank you... Dirk Eberlein Tel. 06151/803-763 ... for your attention 19.03.2008, Folie 55 Hottinger Baldwin Messtechnik GmbH dirk.eberlein@hbm.com Dirk Eberlein
