52512.2SensorsThe angular velocity can be found either from the amplitude or the frequency of the output signal.Thevoltageamplitudesignal is susceptibletonoiseand loadingerrors.Thus,lesserroris introduced ifthefrequencyis usedtodetermine theangularvelocity:typically,somemeansof counting thepulseselectronically is employed. This frequency information can be transmitted digitally for recording,which eliminates the noise and loading error problems associated with voltage signals.Force MeasurementThe measurement of force is most familiar as the process of weighing, ranging from weighingmicrograms of a medicine to weighing trucks on the highway.Force is a quantity derived fromthe fundamental dimensions of mass, length, and time. Standards and units of measure for thesequantitiesare defined in Chapter 1.The mostcommon techniques for force measurement aredescribed in this section.Load Cells"Load cell" is a term used to describe a transducer that generates a voltage signal as a result of anappliedforce,usually along aparticular direction.Suchforcetransducers often consistof an elasticmember and a deflection sensor. These deflection sensors may employ changes in capacitance,resistance, or the piezoelectric effect to sense deflection. Atechnology overview for such devices isprovided elsewhere (5).Consider first load cells that are designed using a linearly elastic memberinstrumented with strain gauges.Strain Gauge Load CellsStrain gauge load cells are most often constructed of a metal, and have ashape such that the range of forces to be measured results in a measurable output voltage overthedesired operating range.The shape of the linearly elastic member is designed to meet the followinggoals: (1) provide an appropriate range of force-measuring capability with necessary accuracy, (2)provide sensitivity to forces in a particular direction, and (3) have low sensitivity to forcecomponents in other directions.A variety of designs of linearly elastic load cells are shown in Figure 12.20. In general, loadcells may be characterized as beam-type load cells,proving rings,or columnar-type designs. Beam-type load cells may be characterized as bending beam load cells or shear beam load cells.Abending beamload cell,as shown inFigure12.21,isconfigured such that the sensingelementof the load cellfunctions as a cantileverbeam. Strain gauges are mounted on the top and bottom ofthebeam tomeasurenormal orbending stresses.Figure 12.21 providesqualitative indication of theshear and normal stress distributions in a cantilever beam. In the linear elastic range of theload cell,the bending stresses are linearly related to the applied load.In a shear beam load cell the beam cross section is that of an I-beam.The resulting shear stress inthe web is nearly constant, allowing placement of a strain gauge essentially anywhere in the web withreasonable accuracy. Such a load cell is illustrated schematically in Figure 12.22, along with the shearstress distribution in the beam.In general, bending beam load cells are less costly due to theirconstruction; however, the shear beam load cells have several advantages, including lower creep andfaster response times. Typical load cells for industrial applications are illustrated in Figure 12.23.Piezoelectric Load CellsPiezoelectric materials are characterized by their ability to develop a chargewhen subject toa mechanical strain.The mostcommon piezoelectric material is single-crystal quartz.The
E1C12 09/14/2010 13:54:11 Page 525 The angular velocity can be found either from the amplitude or the frequency of the output signal. The voltage amplitude signal is susceptible to noise and loading errors. Thus, less error is introduced if the frequency is used to determine the angular velocity; typically, some means of counting the pulses electronically is employed. This frequency information can be transmitted digitally for recording, which eliminates the noise and loading error problems associated with voltage signals. Force Measurement The measurement of force is most familiar as the process of weighing, ranging from weighing micrograms of a medicine to weighing trucks on the highway. Force is a quantity derived from the fundamental dimensions of mass, length, and time. Standards and units of measure for these quantities are defined in Chapter 1. The most common techniques for force measurement are described in this section. Load Cells ‘‘Load cell’’ is a term used to describe a transducer that generates a voltage signal as a result of an applied force, usually along a particular direction. Such force transducers often consist of an elastic member and a deflection sensor. These deflection sensors may employ changes in capacitance, resistance, or the piezoelectric effect to sense deflection. A technology overview for such devices is provided elsewhere (5). Consider first load cells that are designed using a linearly elastic member instrumented with strain gauges. Strain Gauge Load Cells Strain gauge load cells are most often constructed of a metal, and have a shape such that the range of forces to be measured results in a measurable output voltage over the desired operating range. The shape of the linearly elastic member is designed to meet the following goals: (1) provide an appropriate range of force-measuring capability with necessary accuracy, (2) provide sensitivity to forces in a particular direction, and (3) have low sensitivity to force components in other directions. A variety of designs of linearly elastic load cells are shown in Figure 12.20. In general, load cells may be characterized as beam-type load cells, proving rings, or columnar-type designs. Beamtype load cells may be characterized as bending beam load cells or shear beam load cells. A bending beam load cell, as shown in Figure 12.21, is configured such that the sensing element of the load cell functions as a cantilever beam. Strain gauges are mounted on the top and bottom of the beam to measure normal or bending stresses. Figure 12.21 provides qualitative indication of the shear and normal stress distributions in a cantilever beam. In the linear elastic range of the load cell, the bending stresses are linearly related to the applied load. In a shear beam load cell the beam cross section is that of an I-beam. The resulting shear stress in the web is nearly constant, allowing placement of a strain gauge essentially anywhere in the web with reasonable accuracy. Such a load cell is illustrated schematically in Figure 12.22, along with the shear stress distribution in the beam. In general, bending beam load cells are less costly due to their construction; however, the shear beam load cells have several advantages, including lower creep and faster response times. Typical load cells for industrial applications are illustrated in Figure 12.23. Piezoelectric Load Cells Piezoelectric materials are characterized by their ability to develop a charge when subjectto a mechanical strain. The most common piezoelectric materialis single-crystal quartz. The 12.2 Sensors 525
526Chapter12Mechatronics:Sensors,Actuators,andControlsColumnColumn withHollow columnstress concentrationFigure12.20Elastic load cellFlexuredesigns.Normal stress distributionAppliedloadStrain/gaugelocations Normal stressShear stress distributionBending beam load cellShear stressFigure12.21Bending beamload cell and stress distributions
E1C12 09/14/2010 13:54:11 Page 526 Column Column with stress concentration Hollow column Flexure Figure 12.20 Elastic load cell designs. y y Normal stress distribution Normal stress Shear stress distribution Applied load Strain gauge locations Bending beam load cell Shear stress Figure 12.21 Bending beam load cell and stress distributions. 526 Chapter 12 Mechatronics: Sensors, Actuators, and Controls
52712.2SensorsAppliedloadShearstress inI-beam正7Center line of webStraingauge locationsShear stressFigure12.22 Shear beamload cell and shear stress distributionFigure12.23Typicalloadcells.(CourtesyofTransducerTechniques, Inc.)basic principle of transduction that occurs in a piezoelectric element may best be thought of as a chargegenerator and a capacitor. The frequency response of piezoelectric transducers is very high, since thefrequency response is determined primarily by the size and material properties of the quartz crystal. Themodulus ofelasticity ofquartz is approximately 85 GPa,yieldingload cells withtypical static sensitivitiesrangingfrom0.05to10mV/N,and a frequencyresponse upto15,000Hz.Atypical piezoelectricload cellconstructionisshowninFigure12.24.Proving RingA ring-type load cell can be employed as a local force standard. Such a ring-typeload cell, as shown in Figure 12.25,is often employed in the calibration of materials testingmachines because of the high degree of precision and accuracy possible with this arrangement of
E1C12 09/14/2010 13:54:11 Page 527 basic principle of transduction that occurs in a piezoelectric element may best be thought of as a charge generator and a capacitor. The frequency response of piezoelectric transducers is very high, since the frequency response is determined primarily by the size and material properties of the quartz crystal. The modulus of elasticity of quartz is approximately 85 GPa, yielding load cells with typical static sensitivities ranging from 0.05to 10 mV/N, and a frequency response upto 15,000 Hz. Atypical piezoelectricload cell construction is shown in Figure 12.24. Proving Ring A ring-type load cell can be employed as a local force standard. Such a ring-type load cell, as shown in Figure 12.25, is often employed in the calibration of materials testing machines because of the high degree of precision and accuracy possible with this arrangement of Applied load Strain gauge locations Shear stress Shear stress in I-beam y Center line of web Figure 12.22 Shear beam load cell and shear stress distribution. Figure 12.23 Typical load cells. (Courtesy of Transducer Techniques, Inc.) 12.2 Sensors 527
528Chapter12Mechatronics:Sensors,Actuators,andControlsLoad-bearingsurfaceQuartz crystalsCharge pickupCablemountImpedanceFigure12.24Piezoelectricconverterload cell design.(Courtesy ofMounting threadMounting surfacethe Kistler Instrument Co.)transducer and sensor. If the sensor is approximated as a circular right cylinder, the relationshipbetweenappliedforceanddeflectionisgivenbyFnD3(12.17)Oy16EI1AppliedloadStrainStraingaugesgaugesDisplacementMethodMethod 2Method 2sensor1AppliedloadFigure12.25Ringtype load cell, or provingring
E1C12 09/14/2010 13:54:11 Page 528 transducer and sensor. If the sensor is approximated as a circular right cylinder, the relationship between applied force and deflection is given by dy ¼ p 2 4 p FnD3 16EI ð12:17Þ Load-bearing surface Quartz crystals Charge pickup Cable mount Impedance converter Mounting thread Mounting surface Figure 12.24 Piezoelectric load cell design. (Courtesy of the Kistler Instrument Co.) Strain gauges Strain gauges 2 dohteM Method 2 dohteM 1 Applied load Applied load Displacement sensor Figure 12.25 Ring type load cell, or proving ring. 528 Chapter 12 Mechatronics: Sensors, Actuators, and Controls
52912.2SensorswhereOy=deflection along the applied forceFn=applied forceD=diameterE= modulus of elasticityI=moment of inertiaThe application of the proving ring involves measuring the deflection of the proving ring inthe direction of the applied force.Typical methods for this displacement measurement includedisplacementtransducers,whichmeasureoveralldisplacement,andstraingauges.Thesemethodsareillustrated inFigure12.25TorqueMeasurementsTorque and mechanical power measurements are often associated with the energy conversionprocesses that serve to provide mechanical and electrical power to our industrial world.Suchenergy conversion processes are largely characterized by the mechanical transmission ofpower produced by prime movers such as internal combustion engines.From automobiles toturbine-generator sets,mechanical power transmission occurs through torque acting through arotating shaft.Themeasurement of torque is important in avariety of applications,including sizing ofload-carrying shafts. This measurement is also a crucial aspect of the measurement of shaftpower, such as in an enginedynamometer.Strain-gauge-based torque cells are constructed inamannersimilartoload cells,inwhichatorsional straininanelasticelementissensedbystraingauges appropriately placed on the elastic element. Figure 12.26 shows a circular shaftinstrumented with strain gauges for the purpose of measuring torque,and a commerciallyavailabletorque sensor.ADirection of principal stressesTorque cellStraingaugesStrain gaugesBridge setupGauge positionGauge positionfront viewrearview(mirror image of front view)Figure12.26Shaftinstrumentedfortorquemeasurement
E1C12 09/14/2010 13:54:11 Page 529 where dy ¼ deflection along the applied force Fn ¼ applied force D ¼ diameter E ¼ modulus of elasticity I ¼ moment of inertia The application of the proving ring involves measuring the deflection of the proving ring in the direction of the applied force. Typical methods for this displacement measurement include displacement transducers, which measure overall displacement, and strain gauges. These methods are illustrated in Figure 12.25. Torque Measurements Torque and mechanical power measurements are often associated with the energy conversion processes that serve to provide mechanical and electrical power to our industrial world. Such energy conversion processes are largely characterized by the mechanical transmission of power produced by prime movers such as internal combustion engines. From automobiles to turbine-generator sets, mechanical power transmission occurs through torque acting through a rotating shaft. The measurement of torque is important in a variety of applications, including sizing of load-carrying shafts. This measurement is also a crucial aspect of the measurement of shaft power, such as in an engine dynamometer. Strain-gauge–based torque cells are constructed in a manner similar to load cells, in which a torsional strain in an elastic element is sensed by strain gauges appropriately placed on the elastic element. Figure 12.26 shows a circular shaft instrumented with strain gauges for the purpose of measuring torque, and a commercially available torque sensor. Gauge position front view Gauge position rear view (mirror image of front view) Direction of principal stresses seguag niartS seguag niartS 45 54 54 45 1 4 4 B' E0 A' B A T 2 4 1 3 3 1 2 2 3 Bridge setup Torque cell – – – – + + + + 1 2 3 4 Figure 12.26 Shaft instrumented for torque measurement. 12.2 Sensors 529