McGraw-HillCreateTM Review Copyfor InstructorNicolescu.Notfordistribution.412Signal Processing andEngineering Measurements5CHAPTERForce, Torque, andShaftPowerMeasurement5.1STANDARDSANDCALIBRATIONForce is defined by the equation F = MA; thus a standard for force depends on stan-dardsformassand acceleration.Mass is considered a fundamentalquantity,and itsstandard is a cylinder of platinum-iridium, called the International Kilogram,keptin a vaultatSevres,France.Othermasses(such asnational standards)maybecomparedwiththis standard bymeans ofanequal-armbalance,withaprecisionofa few parts in 109 for masses of about I kg. Tolerances on various classes of stan-dardmassesavailablefromNiSTmaybefoundinitspublications.!Acceleration is not a fundamental quantity,but rather is derived from lengthand time,twofundamental quantities whose standardsarediscussed in Chap.4.Theacceleration ofgravity,g,is a convenient standard which can be determined with anaccuracy of about I part in 1oby measuring the period and effective length of apendulum orby determiningthe changewithtime of the speed of a freelyfallingbody.2Theactual valueofgvarieswithlocationand also slightlywithtime (inaperiodic predictable fashion)at a given location.It also may change (slightly)unpredictablybecause of local geological activity.The so-called standard value ofgrefersto thevalueat sea level and 45°latitudeand isnumerically980.665cm/s?.Thevalueatanylatitudedegreesmaybecomputedfromg =978.049(1 +0.0052884 sin2b0.0000059 sin?2)cm/s2(5.1)IT. W. Lashof and L. B. Macurdy, “Precision Laboratory Standards of Mass and Laboratory Weights," Nanl.Bur.Std.(U.S.),Circ.547,sec.1,1954:P.E.Pontius,Massand MassValues."Natl.Bur.Std.(U.S.)Monograph133.1974.2A.Bray,G.Barbato,and R.Levi,"Theory and Practice ofForce Measurement," Academic Press, NewYork, 1990, chap. 3; W. Torge,"Gravimetry," de Gruyter, Berlin, 1989.432
Doebelin: Measurement Systems, Application and Design, Fifth Edition II. Measurement Devices 5. Force, Torque, and Shaft Power Measurement © The McGraw−Hill Companies, 2004 432 5 CHAPTER Force, Torque, and Shaft Power Measurement 5.1 STANDARDS AND CALIBRATION Force is defined by the equation F MA; thus a standard for force depends on standards for mass and acceleration. Mass is considered a fundamental quantity, and its standard is a cylinder of platinum-iridium, called the International Kilogram, kept in a vault at Sèvres, France. Other masses (such as national standards) may be compared with this standard by means of an equal-arm balance, with a precision of a few parts in 109 for masses of about 1 kg. Tolerances on various classes of standard masses available from NIST may be found in its publications.1 Acceleration is not a fundamental quantity, but rather is derived from length and time, two fundamental quantities whose standards are discussed in Chap. 4. The acceleration of gravity, g, is a convenient standard which can be determined with an accuracy of about 1 part in 106 by measuring the period and effective length of a pendulum or by determining the change with time of the speed of a freely falling body.2 The actual value of g varies with location and also slightly with time (in a periodic predictable fashion) at a given location. It also may change (slightly) unpredictably because of local geological activity. The so-called standard value of g refers to the value at sea level and 45˚ latitude and is numerically 980.665 cm/s2. The value at any latitude f degrees may be computed from g 978.049(1 0.0052884 sin2 f 0.0000059 sin2 2f) cm/s2 (5.1) 1T. W. Lashof and L. B. Macurdy, “Precision Laboratory Standards of Mass and Laboratory Weights,” Natl. Bur. Std. (U.S.), Circ. 547, sec. 1, 1954; P. E. Pontius, “Mass and Mass Values,” Natl. Bur. Std. (U.S.), Monograph 133, 1974. 2A. Bray, G. Barbato, and R. Levi, “Theory and Practice of Force Measurement,” Academic Press, New York, 1990, chap. 3; W. Torge, “Gravimetry,” de Gruyter, Berlin, 1989. 412 Signal Processing and Engineering Measurements McGraw-Hill Create™ Review Copy for Instructor Nicolescu. Not for distribution.
McGraw-HillCreateTM ReviewCopyforInstructorNicolescu.NotfordistributionMeasurement Systems, Application and Design,Fifth Edition413433CHAPTER5Force, Torque, and Shaft Power MeasurementLKI8/64OnepartAccuracyof forcemeasurementin10542/"NewU-Wmachines10°/Smoll D-W machineo3/ LargeD-W712M-1BmachinemachineUelo5/ Multiple pravinging6Multiple load cells102Present facilitiesFuturefacilities1010210310410510610710810Pounds force110510610810210310410710Kilograms force (1kgf:9.80665Newtons)Figure 5.1Force standards.["Future facilities"are now.available.]whilethe correction for altitudeh in meters above sea level isCorrection=-(0.00030855+0.00000022cos2b)hhcm/s2+0.000072(5.2)1,000Local valuesofgalsomaybeobtainedfromtheNationalOceanSurvey,NationalOceanicandAtmosphericAdministrationWhen thenumerical value of g has been determined at aparticular locality,thegravitationalforce(weight)onaccuratelyknownstandardmassesmaybecomputedto establish a standard of force.This is the basis of the"deadweight"calibration offorce-measuringsystems.TheNationalBureauof Standards(nowNIST)capability(Fig. 5.1)3 for such calibrations is an inaccuracy of about 1 part in 5,000 for therangeof1to1millionlbf.Abovethisrange,directdeadweightcalibrationisnotpresently available.Rather,proving ringstor load cells of a capacity of 1million Ibforlessarecalibratedagainstdeadweights,andthentheunknownforceisappliedtoamultiplearrayoftheseinparallel.TherangeIto10millionlbfiscoveredbysucharrangementswithsomewhatreducedaccuracy.Atthelow-forceendofthescale,3Accuracy in Measurements and Calibrations," Natl. Bur. Std. (U.S.), Tech. Note 262, 19654Proving Rings for Calibrating Testing Machines,"Nal. Bur.Std. (U.S.).Cire. C454,1946
Doebelin: Measurement Systems, Application and Design, Fifth Edition II. Measurement Devices 5. Force, Torque, and Shaft Power Measurement © The McGraw−Hill Companies, 2004 CHAPTER 5 Force, Torque, and Shaft Power Measurement 433 while the correction for altitude h in meters above sea level is Correction (0.00030855 0.00000022 cos 2f)h 0.000072 cm/s2 (5.2) Local values of g also may be obtained from the National Ocean Survey, National Oceanic and Atmospheric Administration. When the numerical value of g has been determined at a particular locality, the gravitational force (weight) on accurately known standard masses may be computed to establish a standard of force. This is the basis of the “deadweight” calibration of force-measuring systems. The National Bureau of Standards (now NIST) capability (Fig. 5.1)3 for such calibrations is an inaccuracy of about 1 part in 5,000 for the range of 10 to 1 million lbf. Above this range, direct deadweight calibration is not presently available. Rather, proving rings4 or load cells of a capacity of 1 million lbf or less are calibrated against deadweights, and then the unknown force is applied to a multiple array of these in parallel. The range 1 to 10 million lbf is covered by such arrangements with somewhat reduced accuracy. At the low-force end of the scale, ¢ h 1,000≤ 2 Figure 5.1 Force standards. [“Future facilities” are now available.] 3“Accuracy in Measurements and Calibrations,” Natl. Bur. Std. (U.S.), Tech. Note 262, 1965. 4“Proving Rings for Calibrating Testing Machines,” Natl. Bur. Std. (U.S.), Circ. C454, 1946. Measurement Systems, Application and Design, Fifth Edition 413 McGraw-Hill Create™ Review Copy for Instructor Nicolescu. Not for distribution.
McGraw-Hill CreateTM Review Copyfor Instructor Nicolescu.Notfordistribution.414Signal Processingand Engineering Measurements434PART 2 Measuring Devicesthe accuracy of standard masses ranges from about I percent for a mass of 10-5Ibm to 0.0001 percent for the 0.1 to 10 Ibm range to 0.001 percent for a 100-1bmass.Theaccuracyofforcecalibrationsusingthesemassesmustbesomewhatlessthan the quoted figures because of error sources in the experimental procedures.6Acommerciallyavailablecalibrating machineusingdeadweights,knife edges,andleverscoverstherangeof0to10,000lbf(or0to50kN)withanaccuracyof0.005percentofappliedloadandaresolutionof±0.0062percentofapplied load.Computerized calibration systems based on strain gage load cells and hydraulic loadframes are also available.8Themeasurementof torque is intimatelyrelated toforcemeasurement; thustorque standards as sucharenot necessary,sinceforceand length are sufficient todefine torque.Atorque standard may,however,be convenient,and one was underdevelopment in 1998.9 The power transmitted by a rotating shaft is the product oftorque and angular velocity.Angular-velocity measurement was treated in Chap.4.5.2BASICMETHODSOFFORCEMEASUREMENTAn unknown forcemay be measuredbythefollowing means:1.Balancing it against theknowngravitational forceon a standard mass,eitherdirectly orthrough a system of levers2.Measuringtheaccelerationof abodyofknownmasstowhichtheunknownforceis applied3.Balancing it against amagneticforce developed byinteraction of a current-carrying coil and a magnet4.Transducing theforce to a fluid pressure and then measuring the pressure5. Applying the force to some elastic member and measuring the resultingdeflection6.Measuring the change in precession of a gyroscope caused by an appliedtorque related to the measuredforce7.Measuring the change in natural frequency of a wire tensioned by theforce5R. M. Schoonover and F. E. Jones, "Examination of Parameters That Can Cause Errors in MassDetermination," CAL LAB, Julyl/Aug. 1998, pp. 2631.6Calibration of Force-Measuring Instruments for Verifying the Load Indication of Testing Machines,"ASTM Std. E-74, 1974.7w.C.Dillon Co. (www.dillonnews.com).$Gold Standard System, Interface, Inc., Scottsdale,AZ, 800-947-5598 (www.interfaceforce.com); C.Ferreroet al.,"Main Metrological Characteristics of IMGC Six-Component Dynamometer,"RAM, vol 2,1986pp.21-28; R.Hellwig,"Precision Force Transducer for International Comparison Measurements onForce Standard Machines," RAM, vol. 3, 1987, pp. 1722; HBM, Norcross, GA, 888-816-9006(www.hbm-home.com).°F. A. Davis,"Design of the Ist UK National Standard Static Torque Calibration Machine," NationalPhycalaboraory,Queens Road,Teddington,Middesex,United KingdomW11LW,1943-694
Doebelin: Measurement Systems, Application and Design, Fifth Edition II. Measurement Devices 5. Force, Torque, and Shaft Power Measurement © The McGraw−Hill Companies, 2004 434 PART 2 Measuring Devices the accuracy5 of standard masses ranges from about 1 percent for a mass of 105 lbm to 0.0001 percent for the 0.1 to 10 lbm range to 0.001 percent for a 100-lb mass. The accuracy of force calibrations using these masses must be somewhat less than the quoted figures because of error sources in the experimental procedures.6 A commercially available7 calibrating machine using deadweights, knife edges, and levers covers the range of 0 to 10,000 lbf (or 0 to 50 kN) with an accuracy of 0.005 percent of applied load and a resolution of 0.0062 percent of applied load. Computerized calibration systems based on strain gage load cells and hydraulic load frames are also available.8 The measurement of torque is intimately related to force measurement; thus torque standards as such are not necessary, since force and length are sufficient to define torque. A torque standard may, however, be convenient, and one was under development in 1998.9 The power transmitted by a rotating shaft is the product of torque and angular velocity. Angular-velocity measurement was treated in Chap. 4. 5.2 BASIC METHODS OF FORCE MEASUREMENT An unknown force may be measured by the following means: 1. Balancing it against the known gravitational force on a standard mass, either directly or through a system of levers 2. Measuring the acceleration of a body of known mass to which the unknown force is applied 3. Balancing it against a magnetic force developed by interaction of a currentcarrying coil and a magnet 4. Transducing the force to a fluid pressure and then measuring the pressure 5. Applying the force to some elastic member and measuring the resulting deflection 6. Measuring the change in precession of a gyroscope caused by an applied torque related to the measured force 7. Measuring the change in natural frequency of a wire tensioned by the force 5R. M. Schoonover and F. E. Jones, “Examination of Parameters That Can Cause Errors in Mass Determination,” CAL LAB, July/Aug. 1998, pp. 26–31. 6“Calibration of Force-Measuring Instruments for Verifying the Load Indication of Testing Machines,” ASTM Std. E-74, 1974. 7W. C. Dillon Co. (www.dillonnews.com). 8Gold Standard System, Interface, Inc., Scottsdale, AZ, 800-947-5598 (www.interfaceforce.com); C. Ferrero et al., “Main Metrological Characteristics of IMGC Six-Component Dynamometer,” RAM, vol. 2, 1986, pp. 21–28; R. Hellwig, “Precision Force Transducer for International Comparison Measurements on Force Standard Machines,” RAM, vol. 3, 1987, pp. 17–22; HBM, Norcross, GA, 888-816-9006 (www.hbm-home.com). 9F. A. Davis, “Design of the 1st UK National Standard Static Torque Calibration Machine,” National Physical Laboratory, Queens Road, Teddington, Middlesex, United Kingdom, TW 11 OLW, 0181-943-6194. 414 Signal Processing and Engineering Measurements McGraw-Hill Create™ Review Copy for Instructor Nicolescu. Not for distribution.
McGraw-Hill CreateTM Review Copyfor lnstructor Nicolescu.Not fordistributionMeasurementSystems,ApplicationandDesign,FifthEdition415CHAPTER5435Force,Torque,and Shaft Power MeasurementLLLLLL-TapeTape4OC口T14UnknownStandardforcemassCounter-Analytical bolan.ceweightsSteel18tapesTfPendulumscaleOFCFStandordmoss 2I"Poise weight")]白 Stondord mossI("Panweighr")16;PlotformAmtof6-Platform scole(1)Accelerometer(2)Figure 5.2Basicforce-measurementmethods.InFig.5.2,method1isillustratedbytheanalyticalbalance,thependulumscale,and theplatform scale.Theanalytical balance,whilesimpleinprinciplerequires careful design and operation to realize its maximum performance.ioThebeam isdesigned sothatthe center ofmass is onlyslightly(afewthousandthsof aninch)belowtheknife-edgepivot and thus barelyin stableequilibrium.Thismakesthebeamdeflection(which insensitiveinstruments isreadwithan optical1oL.B.Macurdy,"Performance Tests for Balances," Inst.& Cont.Syst.,pp. 127-133, September 1965
Doebelin: Measurement Systems, Application and Design, Fifth Edition II. Measurement Devices 5. Force, Torque, and Shaft Power Measurement © The McGraw−Hill Companies, 2004 CHAPTER 5 Force, Torque, and Shaft Power Measurement 435 In Fig. 5.2, method 1 is illustrated by the analytical balance, the pendulum scale, and the platform scale. The analytical balance, while simple in principle, requires careful design and operation to realize its maximum performance.10 The beam is designed so that the center of mass is only slightly (a few thousandths of an inch) below the knife-edge pivot and thus barely in stable equilibrium. This makes the beam deflection (which in sensitive instruments is read with an optical Figure 5.2 Basic force-measurement methods. 10L. B. Macurdy, “Performance Tests for Balances,” Inst. & Cont. Syst., pp. 127–133, September 1965. Measurement Systems, Application and Design, Fifth Edition 415 McGraw-Hill Create™ Review Copy for Instructor Nicolescu. Not for distribution
McGraw-Hill CreateTM ReviewCopyforInstructorNicolescu.Notfordistribution416Signal Processingand EngineeringMeasurements436PART2MeasuringDevices+++++++Flexiblebearings(3a)Pan?Suspension?Parallel guideOFlexiblebearing(①???OCouplingQLeverFlexible fulcrumOCoil?O①Permanent magnet@oFlux lines?8DiaphragmOpticalpositionCindicator?Temperature sensor-O④(3)@3(3b)Figure 5.2(Continued)micrometer)a very sensitive indicator of unbalance.For the low end of a particularinstrument's range, often the beam deflection is used as the output reading ratherthanattemptingtonullbyaddingmassesoradjustingthearmlengthof apoiseweight.This approachisfasterthannullingbut requiresthat thedeflection-angleunbalancerelationbeaccuratelyknownand stable.Thisrelationtendstovarywiththe load on the balance,because of deformation of knife edges, etc., but carefuldesigncankeepthistoaminimum.Forhighlyaccuratemeasurements,thebuoyantforceduetotheimmersionof thestandardmass inairmustbetaken intoaccount.Also,themost sensitivebalancesmustbe installedintemperature-controlled cham-bers andmanipulatedby remote control to reduce the effects ofthe operator's bodyheatandconvection currents.Typically,a temperaturedifferenceof1/20'Cbetweenthe two arms of a balance can cause an arm-length ratio change of Ippm, sig-nificant in some applications.Commerciallyavailable analyticalbalancesmaybeclassified asfollows:11"f, Baur, "The Analytical Balance," Ind. Res., . 64, JulyAugust 1964
Doebelin: Measurement Systems, Application and Design, Fifth Edition II. Measurement Devices 5. Force, Torque, and Shaft Power Measurement © The McGraw−Hill Companies, 2004 436 PART 2 Measuring Devices micrometer) a very sensitive indicator of unbalance. For the low end of a particular instrument’s range, often the beam deflection is used as the output reading rather than attempting to null by adding masses or adjusting the arm length of a poise weight. This approach is faster than nulling but requires that the deflection-angle unbalance relation be accurately known and stable. This relation tends to vary with the load on the balance, because of deformation of knife edges, etc., but careful design can keep this to a minimum. For highly accurate measurements, the buoyant force due to the immersion of the standard mass in air must be taken into account. Also, the most sensitive balances must be installed in temperature-controlled chambers and manipulated by remote control to reduce the effects of the operator’s body heat and convection currents. Typically, a temperature difference of 1/20˚C between the two arms of a balance can cause an arm-length ratio change of 1 ppm, significant in some applications. Commercially available analytical balances may be classified as follows:11 Pan Suspension Parallel guide Flexible bearing Coupling Lever Flexible fulcrum Coil Permanent magnet Flux lines Diaphragm Optical position indicator Temperature sensor 1 1 2 2 3 3 4 4 4 3 4 5 5 6 6 7 7 8 8 9 9 10 10 11 12 11 12 13 13 Flexible bearings (3a) (3b) G Figure 5.2 (Continued) 11F. Baur, “The Analytical Balance,” Ind. Res., p. 64, July–August 1964. 416 Signal Processing and Engineering Measurements McGraw-Hill Create™ Review Copy for Instructor Nicolescu. Not for distribution