McGraw-Hill CreateTM Review Copy forInstructorNicolescu.NotfordistributionMeasurement Systems,Application and Design,Fifth Edition417437CHAPTER5Force, Torque, and Shaft Power MeasurementOperating principleElectromagneticbalanceof themagneticsuspension balanceAAThe controlled electromagnet exerts a magnetic forceon the permanent magnet throughthe nonmagneticvessel wall, supporting the sample weight. This force58Control systemis measured by the electromagnetic balance-ElectromagnetSetpointcontrollerCoupling housingPermanent magnetOCYSensorcoreSensor coilPosifion transducerMany versions of this basic balanceare available for different pressureMeasuringand temperature ranges andLload decouplingLmeasuring fasksSample(3c)Figure 5.2(Continued)DescriptionRange,gResolution,g10-4200-1,000Macro analytical10-550-100Semimicro analytical10-61020Micro analytical10~6Microbalanceless than 110~7Ultramicrobalanceless than 0.01Thependulum scaleis a deflection-typeinstrumentinwhichtheunknownforceis converted to a torque that is then balanced by the torque of a fixed standard massarranged as a pendulum.Thepractical version of this principleutilizes speciallyshaped sectors and steel tapestolinearize the inherentlynonlinear torque-angle rela-tion of a pendulum. The unknown force F, may be applied directly as in Fig.5.2 orthrougha system oflevers,such asthat shownfortheplatform scale,toextend therange.An electrical signal proportional to force is easily obtained from any angular-displacement transducer attachedtomeasuretheangle.The platform scaleutilizes a system of levers to allow measurement of largeforces in terms of much smaller standard weights.The beam is broughtto null byaproper combination of pan weights and adjustment of the poise-weight lever arm
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 437 Description Range, g Resolution, g Macro analytical 200–1,000 104 Semimicro analytical 50–100 105 Micro analytical 10–20 106 Micro balance less than 1 106 Ultramicro balance less than 0.01 107 The pendulum scale is a deflection-type instrument in which the unknown force is converted to a torque that is then balanced by the torque of a fixed standard mass arranged as a pendulum. The practical version of this principle utilizes specially shaped sectors and steel tapes to linearize the inherently nonlinear torque-angle relation of a pendulum. The unknown force Fi may be applied directly as in Fig. 5.2 or through a system of levers, such as that shown for the platform scale, to extend the range. An electrical signal proportional to force is easily obtained from any angulardisplacement transducer attached to measure the angle uo . The platform scale utilizes a system of levers to allow measurement of large forces in terms of much smaller standard weights. The beam is brought to null by a proper combination of pan weights and adjustment of the poise-weight lever arm Electromagnetic balance Electromagnet Coupling housing Permanent magnet Sensor core Sensor coil Measuring load decoupling Sample Control system Set point controller Position transducer Operating principle of the magnetic suspension balance The controlled electromagnet exerts a magnetic force on the permanent magnet through the nonmagnetic vessel wall, supporting the sample weight. This force is measured by the electromagnetic balance Many versions of this basic balance are available for different pressure and temperature ranges and measuring tasks PID controller (3c ) Figure 5.2 (Continued) Measurement Systems, Application and Design, Fifth Edition 417 McGraw-Hill Create™ Review Copy for Instructor Nicolescu. Not for distribution.
McGraw-HillCreateTM ReviewCopyforInstructorNicolescu.Notfordistribution418Signal Processing and Engineering Measurements438PART2MeasuringDevices00Loading heaHardened steel ballSofftrubberClampringFlexible-AibootsupplyBox-Clampp,StayplalePreloodGaugingspringholeBridge ringDiaphrogmCasingHordened steelHydraulicringinsertsffuidPneumatic load cellHydrostatic load cell(4)Column compressionIAElasticCforce-to-deflectiontransducersBinocular bending beam+A- Shear webParollelogramflexures-beam(5)Figure 5.2(Concluded)along its calibrated scale. The scale can be made self-balancing by adding an elec-trical displacementpickupfornulldetectionandanamplifier-motorsystemtoposi-tion thepoiseweighttoachieve null.Another interestingfeature is that ifalb=cld,thereadingofthescaleisindependentofthelocationofF:ontheplatform.Sincethisis quiteconvenient,most commercial scalesprovidethisfeaturebyuse ofthesuspension system shown orothersthatallowsimilarresults.While analytical balances are used almost exclusively for“"weighing"(reallydeterminingthemassof)objectsorchemicalsamples,platformandpendulumscales areemployed alsoforforcemeasurements,such asthose involved in shaftpower determinations with dynamometers.All threeinstruments areintendedmainlyforstaticforcemeasurements
Doebelin: Measurement Systems, Application and Design, Fifth Edition II. Measurement Devices 5. Force, Torque, and Shaft Power Measurement © The McGraw−Hill Companies, 2004 438 PART 2 Measuring Devices along its calibrated scale. The scale can be made self-balancing by adding an electrical displacement pickup for null detection and an amplifier-motor system to position the poise weight to achieve null. Another interesting feature is that if a/b c/d , the reading of the scale is independent of the location of Fi on the platform. Since this is quite convenient, most commercial scales provide this feature by use of the suspension system shown or others that allow similar results. While analytical balances are used almost exclusively for “weighing” (really determining the mass of) objects or chemical samples, platform and pendulum scales are employed also for force measurements, such as those involved in shaft power determinations with dynamometers. All three instruments are intended mainly for static force measurements. A P P A Column compression Hydrostatic load cell Binocular bending beam Shear web s-beam C T T C C T T C (5) Figure 5.2 (Concluded) 418 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,FifthEdition419CHAPTER55Force, Torque, and Shaft Power Measurement439Method 2,the use of an accelerometerforforce measurement, is of somewhatlimited application since the force determined is the resultantforce on the mass.Often several unknown forces are acting,and they cannot be separately measuredby this method.The electromagnetic balancel2 (method 3)utilizes a photoelectric (or otherdisplacement sensor) null detector, an amplifier, and a torquing coil in a servo-system to balancethedifferencebetween the unknown force F,and the gravityforceon a standard mass.Its advantages relative tomechanical balances are ease of useless sensitivityto environment,fasterresponse,smaller size,andeaseofremoteoperation.Also,the electric output signal is convenient for continuous recordingand/or automatic-control applications.Balances with built-in microprocessors13allow evengreater convenience,versatility,and speed ofuse byautomating manyroutine procedures and providing features not formerly feasible. Automatic tare-weight systems subtract containerweightfromtotal weighttogivenetweight whenmaterial isplaced in the container.Statisticalroutines allowimmediatecalculationofmean and standard deviationfora series of weighings."Counting"of small partsby weighing is speeded by programming the microprocessor to read out the partscount directly,rather than the weight. Accurate weighing of live laboratory animals(difficulton an ordinary balancebecause of animal motion)isfacilitated by averag-ing scale readings over a preselected time.Interfacing the balance to (external orbuilt-in)printersforpermanent recording alsois eased bythe microprocessor.Figure 5.2,part 3a,14 shows a design available in range from 22 to 405 grams, withresolutions from 2to 100 μg.Part 3a shows schematically the parallelogram flex-ure system that guides the motion produced by an applied force (weight), whilepart 3b shows details of thecompletesystem (exceptforthe servoand readout elec-tronics).A flexure-pivot lever system (up to 15:1) puts large input forces within therange of a relatively small magnetic force coil.The signal from the opticaldisplacementsensoristheerrorsignal inthe servo system,whichprovides a coilcurrent (and thus magnetic force) to balance the unknown input force and restorethedeflectiontonearzero.Allmotions areconstrained withflexurebearings (ratherthanrolling or slidingbearings)togive thenearlyfrictionlessperformance requiredfor resolutions as small as 2 μg.Temperature effects (observed mainly in themagneticfield strength)arecompensated in software;thetemperatureismeasuredusing the signal from the temperature sensor.The seven-digit readout testifiestotheextremeresolution of these instruments.Figure5.2,part3c,15showsa version thatallowstheweighed sampletobeimmersed inanatmosphereofcontrolledtemper-ature,pressure,and fluid composition,completely sealed off from theweighingbalance,forsensitivedensity,sorbtion,andchemical studies2L.CaEetmaeWeighingInm.ConSyst7eptembr1962;CahnInrumDiv. (www.thermocahn.com).13B. Ludewig,"Microprocessor Balance," Am. Lab., Pp. 8183, May 197914Mettler-Toledo, Inc., Hightstown, NJ, 800-638-8537 (www.mico.mt.com).15Rubotherm GMBH,S.Natick, MA, 508-655-3950 (www.rubotherm.com)
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 439 Method 2, the use of an accelerometer for force measurement, is of somewhat limited application since the force determined is the resultant force on the mass. Often several unknown forces are acting, and they cannot be separately measured by this method. The electromagnetic balance12 (method 3) utilizes a photoelectric (or other displacement sensor) null detector, an amplifier, and a torquing coil in a servosystem to balance the difference between the unknown force Fi and the gravity force on a standard mass. Its advantages relative to mechanical balances are ease of use, less sensitivity to environment, faster response, smaller size, and ease of remote operation. Also, the electric output signal is convenient for continuous recording and/or automatic-control applications. Balances with built-in microprocessors13 allow even greater convenience, versatility, and speed of use by automating many routine procedures and providing features not formerly feasible. Automatic tareweight systems subtract container weight from total weight to give net weight when material is placed in the container. Statistical routines allow immediate calculation of mean and standard deviation for a series of weighings. “Counting” of small parts by weighing is speeded by programming the microprocessor to read out the parts count directly, rather than the weight. Accurate weighing of live laboratory animals (difficult on an ordinary balance because of animal motion) is facilitated by averaging scale readings over a preselected time. Interfacing the balance to (external or built-in) printers for permanent recording also is eased by the microprocessor. Figure 5.2, part 3a,14 shows a design available in range from 22 to 405 grams, with resolutions from 2 to 100 mg. Part 3a shows schematically the parallelogram flexure system that guides the motion produced by an applied force (weight), while part 3b shows details of the complete system (except for the servo and readout electronics). A flexure-pivot lever system (up to 15:1) puts large input forces within the range of a relatively small magnetic force coil. The signal from the optical displacement sensor is the error signal in the servo system, which provides a coil current (and thus magnetic force) to balance the unknown input force and restore the deflection to near zero. All motions are constrained with flexure bearings (rather than rolling or sliding bearings) to give the nearly frictionless performance required for resolutions as small as 2 mg. Temperature effects (observed mainly in the magnetic field strength) are compensated in software; the temperature is measured using the signal from the temperature sensor. The seven-digit readout testifies to the extreme resolution of these instruments. Figure 5.2, part 3c,15 shows a version that allows the weighed sample to be immersed in an atmosphere of controlled temperature, pressure, and fluid composition, completely sealed off from the weighing balance, for sensitive density, sorbtion, and chemical studies. 12L. Cahn, “Electromagnetic Weighing,” Instrum. Contr. Syst., p. 107, September 1962; Cahn Instrument Div. (www.thermocahn.com). 13B. Ludewig, “Microprocessor Balance,” Am. Lab., pp. 81–83, May 1979. 14Mettler-Toledo, Inc., Hightstown, NJ, 800-638-8537 (www.mico.mt.com). 15Rubotherm GMBH, S. Natick, MA, 508-655-3950 (www.rubotherm.com). Measurement Systems, Application and Design, Fifth Edition 419 McGraw-Hill Create™ Review Copy for Instructor Nicolescu. Not for distribution
McGraw-Hill CreateTM Review Copyfor Instructor Nicolescu.Not fordistribution.420Signal Processing and Engineering Measurements440PART2MeasuringDevicesMethod 4 is illustrated in Fig. 5.2 by hydrostaticl6 and pneumatic load cells.Hydraulic cells are completely filled with oil and usually have a preload pressure oftheorderof 30Ib/in?.Application of load increasestheoilpressure,whichisreadon an accurategage.Electrical pressure transducers canbe used toobtain an elec-trical signal.The cells arevery stiff,deflecting onlyafewthousandths of an inchunderfull load.Capacitiesto100,000lbf areavailableas standard while specialunits up to 10 million Ibf are obtainable. Accuracy is of the order of 0.1 percentof full scale; resolution is about 0.02 percent. A hydraulic totalizerl7 is availableto produce a single pressure equal to the sum of up to 10 individual pressures inmultiple-cell systems used for tank weighing, etc. (see Chap. 10).The pneumatic load cell shown uses a nozzle-flapper transducer as a high-gainamplifierinaservoloop.ApplicationofforceF,causesadiaphragmdeflectionx,which in turn causes an increase in pressure P。since the nozzle is more nearly shutoff. This increase in pressure acting on the diaphragm area A produces an effectiveforceF,that tends to return thediaphragmto its formerposition.For any constantFr,the system will come to equilibrium at a specific nozzle opening and correspon-ding pressure Po.The static behavior is given by(5.3)(F, -P。A)KaK, = PoK. diaphragm compliance,in/lbf(5.4)whereKnozzleflappergain,(lb/in2)/in(5.5)Solving for Po we getF(5.6)P。= 1(K,K.)+ANow K, is not strictly constant, but varies somewhat with x,leading to a non-linearity between x and p.However,in practice,theproductK,K, isverylarge,sothat 1/(KK,)ismade negligible compared withA, which givesFi(5.7)Po"Awhich is linear since A is constant. As in any feedback system, dynamic instabilitylimitstheamountofgainthat actuallycanbeused.Atypical supplypressurep,is60Ib/in?,and sincethemaximumvalueofPocannotexceedps,thislimitsF,tosomewhat less than 60 A.A line of commercial pneumatic weighing systems18 usingsimilar principles (combined with lever/knife-edge methods)is available in standardranges to110,000lbf.While allthe previously described force-measuring devices are intended mainlyforstaticor slowlyvaryingloads,theelasticdeflectiontransducersofmethod5are16A. H. Emery Co. (www.emerywinslow.com).17Tbid.1$*An Introduction to the Darenth Gnu-Weigh Pneumatic Weighing System," Darenth Americas,Bridgeville, DE, 1980. (A google search in 2002 could not find this company.)
Doebelin: Measurement Systems, Application and Design, Fifth Edition II. Measurement Devices 5. Force, Torque, and Shaft Power Measurement © The McGraw−Hill Companies, 2004 440 PART 2 Measuring Devices Method 4 is illustrated in Fig. 5.2 by hydrostatic16 and pneumatic load cells. Hydraulic cells are completely filled with oil and usually have a preload pressure of the order of 30 lb/in2. Application of load increases the oil pressure, which is read on an accurate gage. Electrical pressure transducers can be used to obtain an electrical signal. The cells are very stiff, deflecting only a few thousandths of an inch under full load. Capacities to 100,000 lbf are available as standard while special units up to 10 million lbf are obtainable. Accuracy is of the order of 0.1 percent of full scale; resolution is about 0.02 percent. A hydraulic totalizer17 is available to produce a single pressure equal to the sum of up to 10 individual pressures in multiple-cell systems used for tank weighing, etc. (see Chap. 10). The pneumatic load cell shown uses a nozzle-flapper transducer as a high-gain amplifier in a servoloop. Application of force Fi causes a diaphragm deflection x , which in turn causes an increase in pressure po since the nozzle is more nearly shut off. This increase in pressure acting on the diaphragm area A produces an effective force Fp that tends to return the diaphragm to its former position. For any constant Fi , the system will come to equilibrium at a specific nozzle opening and corresponding pressure po . The static behavior is given by (Fi po A)Kd Kn po (5.3) where Kd diaphragm compliance, in/lbf (5.4) Kn nozzle-flapper gain, (lb/in2)/in (5.5) Solving for po , we get po (5.6) Now Kn is not strictly constant, but varies somewhat with x , leading to a nonlinearity between x and po . However, in practice, the product Kd Kn is very large, so that 1/(Kd Kn) is made negligible compared with A, which gives po (5.7) which is linear since A is constant. As in any feedback system, dynamic instability limits the amount of gain that actually can be used. A typical supply pressure ps is 60 lb/in2, and since the maximum value of p0 cannot exceed ps , this limits Fi to somewhat less than 60 A. A line of commercial pneumatic weighing systems18 using similar principles (combined with lever/knife-edge methods) is available in standard ranges to 110,000 lbf. While all the previously described force-measuring devices are intended mainly for static or slowly varying loads, the elastic deflection transducers of method 5 are Fi A Fi 1/(KdKn) A 16A. H. Emery Co. (www.emerywinslow.com). 17Ibid. 18“An Introduction to the Darenth Gnu-Weigh Pneumatic Weighing System,” Darenth Americas, Bridgeville, DE, 1980. (A google search in 2002 could not find this company.) 420 Signal Processing and Engineering Measurements McGraw-Hill Create™ Review Copy for Instructor Nicolescu. Not for distribution.
McGraw-Hill CreateTM ReviewCopyforInstructorNicolescu.NotfordistributionMeasurementSystems,ApplicationandDesign,FifthEdition421CHAPTER5Force, Torque,and Shaft Power Measurement441widely used for both static and dynamic loads of frequency content up to manythousand hertz.Whileall areessentiallyspring-mass systemswith(intentional orunintentional)damping,they differ mainly inthe geometric form of"springemployed and in the displacement transducer used to obtain an electrical signal.Thedisplacement sensedmaybe a gross motion, or strain gages may be judiciouslylocatedtosenseforceintermsofstrain.Bonded straingageshavebeenfoundparticularly useful in force measurements with elastic elements.In addition to serv-ingasforce-to-deflectiontransducers,someelasticelementsperformthefunctionofresolvingvectorforces ormoments intorectangularcomponents.Asan example,theparallelogramflexureof Fig.5.2(part5)is extremely rigid (insensitive)toallappliedforces andmoments except inthedirection shownbythearrow.Adisplace-ment transducer arranged to measure motion in the sensitive direction thus willmeasure only that component of an applied vector force which lies along thesensitiveaxis.Perhaps theaction of thisflexuremaybemost easilyvisualizedbyconsidering it as a four-bar linkage withflexure hinges at the thin sections a, b, c,and d.Because of the importance of elastic force transducers in modern dynamicmeasurements, we devote a considerable portion of this chapter to their considera-tion.Although they may differ widely in detail construction, their dynamic-responseform isgenerallythe same,and so wetreat an idealized modelrepresentative of allsuch transducers in the next section.Discussion of methods 6 and 7is deferred totheend ofthechaptersincetheyarenotascommonasmethodsI through55.3CHARACTERISTICSOFELASTICFORCETRANSDUCERSFigure 5.3 shows an idealized model of an elastic force transducer.Therelationshipbetween inputforceand output displacement is easily established as a simplesecond-orderform:(5.8)F,-K,x。-Bx=Mx。K曾(D)=(5.9)FiD2/+2D/+1区o,4(5.10)whereVMB14(5.11)2VK,M1K4(5.12)K.Notethatdevicesof thistypearealso(unintentional)accelerometersandproduceaspurious outputinresponsetobase vibration inputs (seeProb.5.1).For transducers that do not measure a gross displacement but rather use straingages bonded to the"spring,"the output strain may be substituted for xif K
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 441 widely used for both static and dynamic loads of frequency content up to many thousand hertz. While all are essentially spring-mass systems with (intentional or unintentional) damping, they differ mainly in the geometric form of “spring” employed and in the displacement transducer used to obtain an electrical signal. The displacement sensed may be a gross motion, or strain gages may be judiciously located to sense force in terms of strain. Bonded strain gages have been found particularly useful in force measurements with elastic elements. In addition to serving as force-to-deflection transducers, some elastic elements perform the function of resolving vector forces or moments into rectangular components. As an example, the parallelogram flexure of Fig. 5.2 (part 5) is extremely rigid (insensitive) to all applied forces and moments except in the direction shown by the arrow. A displacement transducer arranged to measure motion in the sensitive direction thus will measure only that component of an applied vector force which lies along the sensitive axis. Perhaps the action of this flexure may be most easily visualized by considering it as a four-bar linkage with flexure hinges at the thin sections a, b, c, and d. Because of the importance of elastic force transducers in modern dynamic measurements, we devote a considerable portion of this chapter to their consideration. Although they may differ widely in detail construction, their dynamic-response form is generally the same, and so we treat an idealized model representative of all such transducers in the next section. Discussion of methods 6 and 7 is deferred to the end of the chapter since they are not as common as methods 1 through 5. 5.3 CHARACTERISTICS OF ELASTIC FORCE TRANSDUCERS Figure 5.3 shows an idealized model of an elastic force transducer. The relationship between input force and output displacement is easily established as a simple second-order form: Fi Ks xo B˙xo M¨xo (5.8) (D) (5.9) where vn (5.10) (5.11) K (5.12) Note that devices of this type are also (unintentional) accelerometers and produce a spurious output in response to base vibration inputs (see Prob. 5.1). For transducers that do not measure a gross displacement but rather use strain gages bonded to the “spring,” the output strain e may be substituted for xo if Ks 1 Ks B 2Ks M B Ks M K D2 /2 n 2D/n 1 xo Fi Measurement Systems, Application and Design, Fifth Edition 421 McGraw-Hill Create™ Review Copy for Instructor Nicolescu. Not for distribution.