476Chapter11StrainMeasurementlengths,silicon semiconductorstraingaugetechnologyprovidesfor theconstruction of very smalltransducers.For example,flush-mount pressure transducers having diameters of less than 8mmprovide pressure measurements up to 15,o00 psi, with excellent frequency response characteristics.However, silicone diaphragm pressure transducers require special proceduresformeasuring inliquid environments such as deposition of a thin film of next material over the silicone diaphragm.Semiconductor strain gauges are somewhat limited in the maximum strain that they can measure,approximately 5000 μe for tension,but larger in compression.Because of the possibility of aninherent sensitivity to temperature,careful consideration must be given to each application toprovide appropriate temperature compensation or correction.Temperature effects can result, for aparticular measurement, in zero drift for the duration of a measurement.11.4STRAINGAUGEELECTRICALCIRCUITSA Wheatstone bridge is generally used to detect the small changes in resistance that are the outputof a strain gauge measurement circuit. A typical strain gauge measuring installation on a steelspecimen has a sensitivity of 10-6 Q2/(kN m). As such, a high-sensitivity device such as aWheatstone bridge is desirablefor measuring resistance changes for strain gauges. The fundamentalrelationships for the analysis of such bridge circuits are discussed in Chapter 6.Equipment iscommercially available that can measure changes in gauge resistance of less than 0.0005 (0.000001μs).A simple strain gauge Wheatstone bridge circuit is shown in Figure 11.9. The bridge outputunder these conditions is given by Equation 6.15:(Ri + 8R)R4 - RR2(6.15)Eo+Eo=E(RI + 8R +R2)(R3 + R4)where Eo is the bridge output at initial conditions, Eo is the bridge deflection associated with thechange in the strain gauge resistance SR.Consider the case where all the fixed resistors and the straingauge resistance are initially equal, and the bridge is balanced such that Eo = O. If the strain gauge isthen subjected to a state of strain, the change in the output voltage,Eo, from Equation 6.15WRRR3W心Figure11.9Basic straingauge Wheatstone bridgeE,circuit
E1C11 09/14/2010 13:14:2 Page 476 lengths, silicon semiconductor strain gauge technology provides for the construction of very small transducers. For example, flush-mount pressure transducers having diameters of less than 8 mm provide pressure measurements up to 15,000 psi, with excellent frequency response characteristics. However, silicone diaphragm pressure transducers require special procedures for measuring in liquid environments such as deposition of a thin film of next material over the silicone diaphragm. Semiconductor strain gauges are somewhat limited in the maximum strain that they can measure, approximately 5000 me for tension, but larger in compression. Because of the possibility of an inherent sensitivity to temperature, careful consideration must be given to each application to provide appropriate temperature compensation or correction. Temperature effects can result, for a particular measurement, in zero drift for the duration of a measurement. 11.4 STRAIN GAUGE ELECTRICAL CIRCUITS A Wheatstone bridge is generally used to detect the small changes in resistance that are the output of a strain gauge measurement circuit. A typical strain gauge measuring installation on a steel specimen has a sensitivity of 106 V/(kN m2 ). As such, a high-sensitivity device such as a Wheatstone bridge is desirable for measuring resistance changes for strain gauges. The fundamental relationships for the analysis of such bridge circuits are discussed in Chapter 6. Equipment is commercially available that can measure changes in gauge resistance of less than 0.0005 V (0.000001 me). A simple strain gauge Wheatstone bridge circuit is shown in Figure 11.9. The bridge output under these conditions is given by Equation 6.15: E0 þ dE0 ¼ Ei ð Þ R1 þ dR R4 R3R2 ð Þ R1 þ dR þ R2 ð Þ R3 þ R4 ð6:15Þ where E0 is the bridge output at initial conditions, dE0 is the bridge deflection associated with the change in the strain gauge resistance dR. Consider the case where all the fixed resistors and the strain gauge resistance are initially equal, and the bridge is balanced such that E0 ¼ 0. If the strain gauge is then subjected to a state of strain, the change in the output voltage, dE0, from Equation 6.15 Ei R3 R4 Gauge R2 Eo R1 Figure 11.9 Basic strain gauge Wheatstone bridge circuit. 476 Chapter 11 Strain Measurement
11.4477StrainGaugeElectricalCircuitsCircuit arrangementfor shunt balanceDifferential shuntbalancearrangementRhWMNNRRRR.R.RWN2NEw川RFigure11.10Balancingschemesforbridgecircuitsreduces toSE.SR/RSR/R(11.14)4E;4+2(8R/R)under the assumption thatR/R<1.This simplified form of Equation6.15is suitablefor all butthose measurements that demand the highest accuracy,and is valid for values of SR/R1.Usingthe relationship from Equation 11.11 that SR/R=GFg,SE。GFeGF(11.15)Ei44+2GFEquations 11.14 and 11.15 yield two practical equationsfor strain gauge measurements using asingle gauge in a Wheatstone bridge.The Wheatstone bridge has several distinct advantages for use with electrical resistance straingauges.The bridge may be balanced by changing the resistance of one arm of the bridge.Therefore,once thegaugeismounted in place on thetestspecimen under a condition of zero loading,theoutputfromthebridgemaybezeroed.TwoschemesforcircuitstoaccomplishthisbalancingareshowninFigure11.10.Shuntbalancingprovidesthebestarrangementforstraingaugeapplications,sincethechanges in resistance for a strain gauge are small. Also,the strategic placement ofmultiple gauges ina Wheatstone bridge can both increase the bridge output and cancel out certain ambient effects andunwantedcomponentsofstrainasdiscussedinthenexttwosections.Example 11.3A strain gauge,having a gauge factor of 2,is mounted on a rectangular steel bar (Em=200×x 10°kN/m),as shown inFigure11.11.Thebar is 3cm wideand1 cm high,and is subjected
E1C11 09/14/2010 13:14:2 Page 477 reduces to dEo Ei ¼ dR=R 4 þ 2ð Þ dR=R dR=R 4 ð11:14Þ under the assumption that dR=R 1. This simplified form of Equation 6.15 is suitable for all but those measurements that demand the highest accuracy, and is valid for values of dR=R 1. Using the relationship from Equation 11.11 that dR=R ¼ GFe, dEo Ei ¼ GFe 4 þ 2GFe GFe 4 ð11:15Þ Equations 11.14 and 11.15 yield two practical equations for strain gauge measurements using a single gauge in a Wheatstone bridge. The Wheatstone bridge has several distinct advantages for use with electrical resistance strain gauges. The bridge may be balanced by changing the resistance of one arm of the bridge. Therefore, once the gauge is mounted in place on the test specimen under a condition of zero loading, the output from the bridge may be zeroed. Two schemes for circuits to accomplish this balancing are shown in Figure 11.10. Shunt balancing provides the best arrangement for strain gauge applications, since the changes in resistance for a strain gauge are small. Also, the strategic placement of multiple gauges in a Wheatstone bridge can both increase the bridge output and cancel out certain ambient effects and unwanted components of strain as discussed in the next two sections. Example 11.3 A strain gauge, having a gauge factor of 2, is mounted on a rectangular steel bar (Em ¼ 200 106 kN=m2), as shown in Figure 11.11. The bar is 3 cm wide and 1 cm high, and is subjected Circuit arrangement for shunt balance Differential shunt balance arrangement Ei R3 R4 R R2 1 Ei R3 R4 R1 R2 Figure 11.10 Balancing schemes for bridge circuits. 11.4 Strain Gauge Electrical Circuits 477