《工程测试与信号处理》课程教学资源（文献资料）Sensors_proximity

McGraw-Hill CreateTM ReviewCopyforInstructorNicolescu.Notfordistribution31IntroductiontoMechatronicsandMeasurementSystems,FourthEdition9HHAPTERSensorshis chapterdescribes various sensorsimportantin mechatronic systemdesign.MECHANICAL SYSTEMsystem modeldynamic responseINPUT SIGNALACTUATORSSENSORSCONDITIONINGsolenoids, voice coilsswitchesstrain gageANDINTERFACING-DC motorspotentiometerthermocouple- stepper motorsphotoelectricsaccelerometer- servo motors-discrete circuits-fltersMENSdigital encoder- hydraulics, pneuma-A/D, D/D-amplifiersOUTPUT SIGNALDIGITAL CONTROLGRAPHICALCONDITIONINGARCHITECTURESDISPLAYSANDINTERFACING- sequencing and timinglogic circuits- LEDs-LCDrocontroller- logic and arithmeric-DIA, D/D - power transistors.-SBC-CRT- digital displays- control algorithmsampifiespowerop amps-PLC- communication-PWMCHAPTER OBJECTIVESAfteryouread,discuss,study,andapplyideas inthis chapter,youwill1.Understandthefundamentals of simpleelectromechanical sensors,includingproximity sensors and switches,potentiometers,linear variable differentialtransformers,optical encoders,straingages,loadcells,thermocouples,andaccelerometers2.Beabletodescribehownatural andbinarycodesareusedtoencodelinearandrotationalpositionindigitalencoders3.Be able to apply engineering mechanics principles to interpret data from asinglestraingageorstraingagerosette375

Confirming Pages 375 C H A P T E R 9 Sensors T his chapter describes various sensors important in mechatronic system design. ■ INPUT SIGNAL CONDITIONING AND INTERFACING - discrete circuits - amplifiers - filters - A/D, D/D OUTPUT SIGNAL CONDITIONING AND INTERFACING - D/A, D/D - PWM - power transistors - power op amps GRAPHICAL DISPLAYS - LEDs - digital displays - LCD - CRT SENSORS switches potentiometer photoelectrics digital encoder strain gage thermocouple accelerometer MEMs ACTUATORS - solenoids, voice coils - DC motors - stepper motors - servo motors - hydraulics, pneumatics MECHANICAL SYSTEM DIGITAL CONTROL ARCHITECTURES - logic circuits - microcontroller - SBC - PLC - sequencing and timing - logic and arithmetic - control algorithms - communication - amplifiers system model dynamic response CHAPTER OBJECTIVES After you read, discuss, study, and apply ideas in this chapter, you will: 1. Understand the fundamentals of simple electromechanical sensors, including proximity sensors and switches, potentiometers, linear variable differential transformers, optical encoders, strain gages, load cells, thermocouples, and accelerometers 2. Be able to describe how natural and binary codes are used to encode linear and rotational position in digital encoders 3. Be able to apply engineering mechanics principles to interpret data from a single strain gage or strain gage rosette alc80237_ch09_375-430.indd 375 lc80237_ch09_375-430.indd 375 10/01/11 10:09 PM 0/01/11 10:09 PM Introduction to Mechatronics and Measurement Systems, Fourth Edition 31 McGraw-Hill Create™ Review Copy for Instructor Nicolescu. Not for distribution

McGraw-Hill CreateTM ReviewCopyforInstructorNicolescu.Notfordistribution.32MeasurementSystems376CHAPTER9Sensors4.Beabletomakeaccuratetemperaturemeasurementsusingthermocouples5.Know howtomeasure acceleration and understand thefrequency response ofaccelerometers6.Understand whata microelectromechanical (MEM)system is9.1INTRODUCTIONA sensor is an element in a mechatronic or measurement system that detects themagnitudeof aphysicalparameterandchanges it intoasignal thatcanbeprocessedby the system.Often the active element of a sensor is referred to as a transducer.Monitoring and control systems require sensors to measure physical quantities suchas position,distance,force,strain,temperature, vibration, and acceleration.Thefollowing sections present devices and techniques for measuring these and otherphysicalquantities.Sensor and transducer design always involves the application of some law orprincipleof physics orchemistry thatrelates thequantityof interestto somemeasur-ableevent.AppendixB summarizesmanyof thephysical lawsandprinciplesthathavepotentialapplicationinsensorandtransducerdesign.Someexamplesofapplications are also provided.This list is useful to a transducer designer who is searchingfor amethodto measure a physical quantity.Practically every transducer applies oneormoreof theseprinciples initsoperation.Internet LinkInternet Link 9.1 provides links to numerous vendors and online resources forawiderangeof commerciallyavailablesensorsandtransducers.TheInternetis9.1Sensoronlinea good resource for finding the latest products in the mechatronics field. This isresourcesandespecially true for sensors,where new technologies and improvements evolvevendorscontinuously.9.2POSITIONANDSPEED MEASUREMENTOther than electrical measurements (e.g.,voltage,current,resistance),themostcommonlymeasured quantityinmechatronic systemsisposition.Weoften need toknowwherevarious parts of a systemare in orderto control the system.Section 9.2.1presents proximity sensors and limit switches that area subset of position sen-sors that detect whether or not something is close or has reached a limit of travel.Section9.2.2presentsthepotentiometer,whichisaninexpensiveanalogdeviceformeasuring rotary or linear position.Section 9.2.3 presents the linear variable differ-ential transformer,which is an analog device capable of accurately measuring lineardisplacement.Finally,Section 9.2.4 presents the digital encoder,which isusefulformeasuring a position with an output in digital form suitable for direct interface to acomputerorotherdigital system.Because most applications involvemeasuring and controlling shaft rotation(e.g., in robot joints, numerically controlled lathe and mill axes,motors,and gen-erators),rotarypositionsensorsaremorecommonthanlinearsensors.Also,linear

Confirming Pages 376 C H A P T E R 9 Sensors 4. Be able to make accurate temperature measurements using thermocouples 5. Know how to measure acceleration and understand the frequency response of accelerometers 6. Understand what a microelectromechanical (MEM) system is 9.1 INTRODUCTION A sensor is an element in a mechatronic or measurement system that detects the magnitude of a physical parameter and changes it into a signal that can be processed by the system. Often the active element of a sensor is referred to as a transducer. Monitoring and control systems require sensors to measure physical quantities such as position, distance, force, strain, temperature, vibration, and acceleration. The following sections present devices and techniques for measuring these and other physical quantities. Sensor and transducer design always involves the application of some law or principle of physics or chemistry that relates the quantity of interest to some measur￾able event. Appendix B summarizes many of the physical laws and principles that have potential application in sensor and transducer design. Some examples of appli￾cations are also provided. This list is useful to a transducer designer who is searching for a method to measure a physical quantity. Practically every transducer applies one or more of these principles in its operation. Internet Link 9.1 provides links to numerous vendors and online resources for a wide range of commercially available sensors and transducers. The Internet is a good resource for finding the latest products in the mechatronics field. This is especially true for sensors, where new technologies and improvements evolve continuously. 9.2 POSITION AND SPEED MEASUREMENT Other than electrical measurements (e.g., voltage, current, resistance), the most com￾monly measured quantity in mechatronic systems is position. We often need to know where various parts of a system are in order to control the system. Section 9.2.1 presents proximity sensors and limit switches that are a subset of position sen￾sors that detect whether or not something is close or has reached a limit of travel. Section 9.2.2 presents the potentiometer, which is an inexpensive analog device for measuring rotary or linear position. Section 9.2.3 presents the linear variable differ￾ential transformer, which is an analog device capable of accurately measuring linear displacement. Finally, Section 9.2.4 presents the digital encoder, which is useful for measuring a position with an output in digital form suitable for direct interface to a computer or other digital system. Because most applications involve measuring and controlling shaft rotation (e.g., in robot joints, numerically controlled lathe and mill axes, motors, and gen￾erators), rotary position sensors are more common than linear sensors. Also, linear Internet Link 9.1 Sensor online resources and vendors alc80237_ch09_375-430.indd 376 lc80237_ch09_375-430.indd 376 10/01/11 10:09 PM 0/01/11 10:09 PM 32 Measurement Systems McGraw-Hill Create™ Review Copy for Instructor Nicolescu. Not for distribution

McGraw-Hill CreateTM Review Copyfor Instructor Nicolescu.Not fordistributionIntroduction to Mechatronics and Measurement Systems,Fourth Edition333779.2PositionandSpeedMeasurementmotion can often be easily converted to rotary motion (e.g., with a belt, gear, orwheel mechanism),allowing the use of rotary position sensors in linear motionapplications.Speedmeasurements canbeobtainedbytakingconsecutivepositionmeasure-mentsatknowntimeintervals andcomputingthetimerateof changeof thepositionvalues.A tachometerisan exampleof a speed sensorthatdoes thisfora rotatingshaft.9.2.1ProximitySensorsandSwitchesAproximitysensorconsists ofanelementthatchangeseitherits stateorananalogsignal when it is close to, but often not actually touching, an object. Magnetic,electrical capacitance,inductance,and eddy current methods areparticularly suitedtothedesign ofaproximity sensor.VideoDemo9.1showsanexampleapplicationforamagneticproximity sensor.Aphotoemitter-detectorpairrepresents anotherapproach, where interruption or reflection of a beam of light is used to detect anobjectin anoncontact manner.The emitter can bea laser or focused LED,andVideo Demothe detector is usually a phototransistor orphotodiode.Various configurations for9.1Magneticphotoemitter-detector pairs are illustrated in Figure 9.1. In the opposed and ret-pickuptachom-roreflective configurations,the objectinterrupts the beam; and in the proximityeterused inaPIDconfiguration,the objectreflectsthebeam.Figure9.2showsa commercial sensorspeedcontrollerthat canbe used in theretroreflective orproximity configurations.Video Demo9.2test-standshows an interesting studentprojectexampleoftheproximityconfiguration.Com-9.2Automatedmon applicationsforproximitysensorsand limitswitchesaredetectingthepres-laboratoryratence of an object (e.g., a man in front of a public urinal), counting moving objectsexercisemachine(e.g.,passingbyon a conveyorbelt),and in limiting thetraverseof a mechanismwithinfrared(e.g., bydetecting the end of travel of a slider or joint).sensorandThere are many designs for limit switches, including pushbutton and leveredsteppermotormicroswitches.All switches are used to open or close connections withincircuitsAs illustrated inFigure9.3, switchesarecharacterized bythenumber of poles(P)Proximity (Diffuse) Mode AlignmentOpposedModeAlignmentRetroreflective Mode AlignmentModeAligr:MoveEminterective Mode AligDiffuse Mode AlignrMove Target Up-Down, Lef-RighRotate Up-Down, Leff-Rightciver Up-Down,Left-Right, and RotateFigure 9.1 Various configurations for photoemitter-detector pairs.(Courtesy of Banner Engineering,Minneapolis,MN)

Confirming Pages Figure 9.1 Various configurations for photoemitter-detector pairs. (Courtesy of Banner Engineering, Minneapolis, MN) 9.2 Position and Speed Measurement 377 motion can often be easily converted to rotary motion (e.g., with a belt, gear, or wheel mechanism), allowing the use of rotary position sensors in linear motion applications. Speed measurements can be obtained by taking consecutive position measure￾ments at known time intervals and computing the time rate of change of the position values. A tachometer is an example of a speed sensor that does this for a rotating shaft. 9.2.1 Proximity Sensors and Switches A proximity sensor consists of an element that changes either its state or an analog signal when it is close to, but often not actually touching, an object. Magnetic, electrical capacitance, inductance, and eddy current methods are particularly suited to the design of a proximity sensor. Video Demo 9.1 shows an example application for a magnetic proximity sensor. A photoemitter-detector pair represents another approach, where interruption or reflection of a beam of light is used to detect an object in a noncontact manner. The emitter can be a laser or focused LED, and the detector is usually a phototransistor or photodiode. Various configurations for photoemitter-detector pairs are illustrated in Figure 9.1 . In the opposed and ret￾roreflective configurations, the object interrupts the beam; and in the proximity configuration, the object reflects the beam. Figure 9.2 shows a commercial sensor that can be used in the retroreflective or proximity configurations. Video Demo 9.2 shows an interesting student project example of the proximity configuration. Com￾mon applications for proximity sensors and limit switches are detecting the pres￾ence of an object (e.g., a man in front of a public urinal), counting moving objects (e.g., passing by on a conveyor belt), and in limiting the traverse of a mechanism (e.g., by detecting the end of travel of a slider or joint). There are many designs for limit switches, including pushbutton and levered microswitches. All switches are used to open or close connections within circuits. As illustrated in Figure 9.3 , switches are characterized by the number of poles (P) Video Demo 9.1 Magnetic pickup tachom￾eter used in a PID speed controller test-stand 9.2 Automated laboratory rat exercise machine with infrared sensor and stepper motor alc80237_ch09_375-430.indd 377 lc80237_ch09_375-430.indd 377 10/01/11 10:09 PM 0/01/11 10:09 PM Introduction to Mechatronics and Measurement Systems, Fourth Edition 33 McGraw-Hill Create™ Review Copy for Instructor Nicolescu. Not for distribution

McGraw-Hill CreateTM ReviewCopyforInstructorNicolescu.Notfordistribution.34MeasurementSystems378CHAPTER9SensorsFigure9.2Exampleofaphotoemitter-detectorpair in a single housing. (Courtesy of BannerEngineering,Minneapolis,MN)SPSTNO pushbuttonNCNOSPDTNC pushbuttonFigure9.3Switches.andthrows (T)and whether connectionsarenormallyopen (NO)ornormallyclosed (NC). A pole is a moving element in the switch that makes or breaks con-nections,and a throw isa contactpointfor a pole.The SPST switch is a single-pole(SP),single-throw(ST)devicethatopens or closes a singleconnection.The SPDTswitch changes thepolebetweentwo different throwpositions.There aremanyvari-VideoDemoations on thepole and throw configurations of switches,but theirfunction is easilyunderstoodfromthebasicterminology.Figure9.4andVideoDemo9.3showvari-9.3Switchesous types of switches with the appropriate designations.Video Demo 9.4 shows an9.4 Thermostatinteresting example ofa normally open mercury switch that is used to turn on or offwithbimetallican air conditioning or heating unit when a bimetallic strip coil (see Section 9.4.2)strip and mercuryrotatesacertain amount.switchWhen mechanical switches are opened or closed, they exhibit switch bou-nce,where many break-reconnect transitions occur before a new state is estab-lished.If a switch is connected toa digital circuit that requires a singletransition,the switch outputmustbedebounced using a circuit or softwareas described inSection 6.10.1

Confirming Pages Figure 9.2 Example of a photoemitter-detector pair in a single housing. (Courtesy of Banner Engineering, Minneapolis, MN) Figure 9.3 Switches. SPST NC SPDT NO pushbutton NC pushbutton NO 378 C H A P T E R 9 Sensors and throws (T) and whether connections are normally open (NO) or normally closed (NC). A pole is a moving element in the switch that makes or breaks con￾nections, and a throw is a contact point for a pole. The SPST switch is a single-pole (SP), single-throw (ST) device that opens or closes a single connection. The SPDT switch changes the pole between two different throw positions. There are many vari￾ations on the pole and throw configurations of switches, but their function is easily understood from the basic terminology. Figure 9.4 and Video Demo 9.3 show vari￾ous types of switches with the appropriate designations. Video Demo 9.4 shows an interesting example of a normally open mercury switch that is used to turn on or off an air conditioning or heating unit when a bimetallic strip coil (see Section 9.4.2 ) rotates a certain amount. When mechanical switches are opened or closed, they exhibit switch bou￾nce, where many break-reconnect transitions occur before a new state is estab￾lished. If a switch is connected to a digital circuit that requires a single transition, the switch output must be debounced using a circuit or software as described in Section 6.10.1. Video Demo 9.3 Switches 9.4 Thermostat with bimetallic strip and mercury switch alc80237_ch09_375-430.indd 378 lc80237_ch09_375-430.indd 378 10/01/11 10:09 PM 0/01/11 10:09 PM 34 Measurement Systems McGraw-Hill Create™ Review Copy for Instructor Nicolescu. Not for distribution

McGraw-Hill CreateTM Review Copyfor lnstructor Nicolescu.Not fordistribution35IntroductiontoMechatronicsandMeasurementSystems,FourthEdition3799.2PositionandSpeedMeasurementNOSPST SPSTtogglepushbuttonswitchswitchtNODPST(dual SPST)2NOpushbuttonSPSTswitchesresetswitchSPDTmicroswitchesFigure9.4Photographofvarioustypesofswitches.CLASS DISCUSSIONITEM 9.1Household Three-WaySwitchAhouseholdthree-wayswitch isusedtoallowlightstobe controlledfromtwoloca-tions (e.g., at the top and bottom of a stairwell). Note that the term three-way refersto the number of terminals (3)on each switchand not the number of switches (2).Athree-way switchistheSPDTvariety.Drawa schematicof howACpowerandthe two switches can be wired to a light fixture to achieve the desired functionality,whereeither switchcan beused toturn the light on oroff9.2.2PotentiometerThe rotarypotentiometer (akapot)is a variableresistance device that canbeusedto measure angularposition.It consists of awiperthatmakes contactwitha resis-tive element,and as this point of contact moves, theresistance between the wiperand endleadsofthedevicechanges inproportiontothe angulardisplacement.Figure 9.5 illustrates the form and internal schematic for a typical rotary potenti-ometer.Figure 9.6 shows two common typesof potentiometers.The one on the leftis called a trim pot.It has a small screw on the left side that can be turned with aMMUUOwiperFigure9.5Potentiometer

Confirming Pages Figure 9.4 Photograph of various types of switches. NO SPST reset switch SPST toggle switch NO DPST (dual SPST) pushbutton switches SPDT microswitches NO SPST pushbutton switch 9.2 Position and Speed Measurement 379 ■ C L A S S D I S C U S S I O N I T E M 9 . 1 Household Three-Way Switch A household three-way switch is used to allow lights to be controlled from two loca￾tions (e.g., at the top and bottom of a stairwell). Note that the term three-way refers to the number of terminals (3) on each switch and not the number of switches (2). A three-way switch is the SPDT variety. Draw a schematic of how AC power and the two switches can be wired to a light fixture to achieve the desired functionality, where either switch can be used to turn the light on or off. 9.2.2 Potentiometer The rotary potentiometer (aka pot ) is a variable resistance device that can be used to measure angular position. It consists of a wiper that makes contact with a resis￾tive element, and as this point of contact moves, the resistance between the wiper and end leads of the device changes in proportion to the angular displacement. Figure 9.5 illustrates the form and internal schematic for a typical rotary potenti￾ometer. Figure 9.6 shows two common types of potentiometers. The one on the left is called a trim pot. It has a small screw on the left side that can be turned with a Figure 9.5 Potentiometer. wiper alc80237_ch09_375-430.indd 379 lc80237_ch09_375-430.indd 379 10/01/11 10:09 PM 0/01/11 10:09 PM Introduction to Mechatronics and Measurement Systems, Fourth Edition 35 McGraw-Hill Create™ Review Copy for Instructor Nicolescu. Not for distribution

McGraw-Hill CreateTM ReviewCopyforInstructorNicolescu.Notfordistribution36MeasurementSystems380CHAPTER9SensorsFigure9.6Photographofatrimpotand arotarypot.screwdriverto accuratelymake small changes in resistance (i.e."trim"or adjust theresistance).On theright is a standard rotarypot with aknob allowing a userto eas-ilymakeadjustmentsbyhand.Throughvoltage division,thechangein resistanceof a pot can be used to create an output voltage that is directly proportional to theinput displacement.Thisrelationshipwas derived in Section4.8.9.2.3Linear Variable Differential TransformerThe linear variabledifferential transformer (LVDT) is a transducer formeasuringlinear displacement.As illustrated in Figure 9.7,it consists of primary and secondarywindings andamovable iron core.Itfunctionsmuch likea transformer,wherevolt-ages are induced in the secondary coil in response to excitation in the primary coil.The LVDTmust beexcitedby an AC signal to induce an AC response in the second-ary. The core position can be determined by measuring the secondary response.With two secondary coils connected in the series-opposing configuration asshown, the output signal describes both the magnitude and direction of the coremotion.TheprimaryAC excitation V.and the output signal Voutfor two differentcore positions are shown in Figure 9.7.There is a midpoint in the core's positionwhere the voltage induced in each coil is of the same amplitudeand 180°out ofphase,producing a"null"output.As the coremoves fromthe null position,the out-put amplitude increases a proportional amount over a linear range around the null asInternet Linkshown in Figure 9.8.Therefore, by measuring the output voltage amplitude, we caneasily and accurately determine the magnitude of the core displacement.Internet9.2AnimationofLVDT functionLink 9.2points to an interesting animation that illustrates how the output voltage oftheLVDTchanges with core displacement.To determine the direction of the core displacement, the secondary coils can beconnected to a demodulation circuit as shown in Figure 9.9.The diodebridges in thiscircuitproduceapositiveor negativerectified sinewave,dependingon which sideofthenull positionthecoreislocated(seeClassDiscussionItem9.2)

Confirming Pages Figure 9.6 Photograph of a trim pot and a rotary pot. 380 C H A P T E R 9 Sensors screwdriver to accurately make small changes in resistance (i.e. “trim” or adjust the resistance). On the right is a standard rotary pot with a knob allowing a user to eas￾ily make adjustments by hand. Through voltage division, the change in resistance of a pot can be used to create an output voltage that is directly proportional to the input displacement. This relationship was derived in Section 4.8. 9.2.3 Linear Variable Differential Transformer The linear variable differential transformer (LVDT) is a transducer for measuring linear displacement. As illustrated in Figure 9.7 , it consists of primary and secondary windings and a movable iron core. It functions much like a transformer, where volt￾ages are induced in the secondary coil in response to excitation in the primary coil. The LVDT must be excited by an AC signal to induce an AC response in the second￾ary. The core position can be determined by measuring the secondary response. With two secondary coils connected in the series-opposing configuration as shown, the output signal describes both the magnitude and direction of the core motion. The primary AC excitation Vin and the output signal Vout for two different core positions are shown in Figure 9.7 . There is a midpoint in the core’s position where the voltage induced in each coil is of the same amplitude and 180 out of phase, producing a “null” output. As the core moves from the null position, the out￾put amplitude increases a proportional amount over a linear range around the null as shown in Figure 9.8 . Therefore, by measuring the output voltage amplitude, we can easily and accurately determine the magnitude of the core displacement. Internet Link 9.2 points to an interesting animation that illustrates how the output voltage of the LVDT changes with core displacement. To determine the direction of the core displacement, the secondary coils can be connected to a demodulation circuit as shown in Figure 9.9 . The diode bridges in this circuit produce a positive or negative rectified sine wave, depending on which side of the null position the core is located (see Class Discussion Item 9.2). Internet Link 9.2 Animation of LVDT function alc80237_ch09_375-430.indd 380 lc80237_ch09_375-430.indd 380 10/01/11 10:09 PM 0/01/11 10:09 PM 36 Measurement Systems McGraw-Hill Create™ Review Copy for Instructor Nicolescu. Not for distribution.

McGraw-Hill CreateTM Review Copyfor lnstructor Nicolescu.Not fordistribution37IntroductiontoMechatronicsandMeasurementSystems,FourthEdition9.2PositionandSpeedMeasurement381magnetic ficldVinexcitation voltageVoutmtoutput voltage withVoucore left of null2primaryoutput voltage withmovableVoutlcore right of nulliron coreC2core centered(null position)Figure 9.7 Linear variable differentialtransformer.Vout amplitudelinearrange!leftrightcore displacementFigure9.8LVDTlinearrange.cxcitation voltaggutput voltage withcore left of nullVodtconeaecondar50005000coreoutput voltage withVont1core right of null000magnetic fieldsprimaryand associatedVin voltage polaritiesFigure9.9LVDTdemodulation.CLASSDISCUSSIONITEM9.2LVDTDemodulationTrace the currents through the diodes in the demodulation circuit shown inFigure9.9fordifferent corepositions (null, left ofnull,and rightofnull)and explainwhy the output voltage behaves as shown.Assume ideal diodes.Also,explain whythe output is O when the core is in the null or center position

Confirming Pages Figure 9.7 Linear variable differential transformer. Vout Vin core centered (null position) secondary primary movable iron core Vin Vout Vout excitation voltage output voltage with core left of null output voltage with core right of null + − + − − + +− − + magnetic field Figure 9.8 LVDT linear range. Vout amplitude core displacement left right linear range Figure 9.9 LVDT demodulation. Vin primary secondary Vout secondary core Vin Vout Vout excitation voltage output voltage with core left of null output voltage with core right of null − + − + magnetic fields and associated voltage polarities + − + − − + 9.2 Position and Speed Measurement 381 ■ C L A S S D I S C U S S I O N I T E M 9 . 2 LVDT Demodulation Trace the currents through the diodes in the demodulation circuit shown in Figure 9.9 for different core positions (null, left of null, and right of null) and explain why the output voltage behaves as shown. Assume ideal diodes. Also, explain why the output is 0 when the core is in the null or center position. alc80237_ch09_375-430.indd 381 lc80237_ch09_375-430.indd 381 10/01/11 10:09 PM 0/01/11 10:09 PM Introduction to Mechatronics and Measurement Systems, Fourth Edition 37 McGraw-Hill Create™ Review Copy for Instructor Nicolescu. Not for distribution

McGraw-Hill CreateTM Review Copyfor Instructor Nicolescu.Not fordistribution.38Measurement Systems382CHAPTER9SensorsAs illustrated inFigure 9.10, a low-passfilter mayalso be used to convert therectified output into a smoothed signal that tracks the core position.The cutoff fre-quency of this low-pass filter must be chosen carefully to filter out the high fre-quencies in the rectified wave but notthe frequency components associated with thecoremotion.The excitation frequencyis usually chosen to be at least 1 times themaximumexpectedfrequencyofthecoremotiontoyieldagoodrepresentationofthetime-varyingdisplacement.Commercial LVDTs, such as the one shown in Figure 9.1l, are available incylindrical forms with different diameters,lengths, and strokes.Often, they includeinternal circuitry that provides a DC voltage proportional to displacement.The advantages of the LVDT are accuracy over the linear range and an analogoutput that may not require amplification.Also, it is less sensitive to wide rangesin temperature than other position transducers (e.g,potentiometers,encoders,andsemiconductordevices).TheLVDT's disadvantages includelimitedrange ofmotionand limitedfrequency response.The overall frequency response is limited by inertialeffects associated withthe core's mass and thechoiceof the primaryexcitationfre-quency and the filter cutoff frequency.R+.W0V'autlow-pass filterVoutr1ooutput voltage withoutput voltage withcore left of nullcore right of nullV'otV'outFigure 9.10 LVDT output filter.Figure9.11Commercial LVDT.(CourtesyofSensotec,Columbus, OH)

Confirming Pages Figure 9.10 LVDT output filter. + − Vout V'out R C low-pass filter output voltage with core left of null output voltage with core right of null Vout Vout V'out V'out Figure 9.11 Commercial LVDT. (Courtesy of Sensotec, Columbus, OH) 382 C H A P T E R 9 Sensors As illustrated in Figure 9.10 , a low-pass filter may also be used to convert the rectified output into a smoothed signal that tracks the core position. The cutoff fre￾quency of this low-pass filter must be chosen carefully to filter out the high fre￾quencies in the rectified wave but not the frequency components associated with the core motion. The excitation frequency is usually chosen to be at least 10 times the maximum expected frequency of the core motion to yield a good representation of the time-varying displacement. Commercial LVDTs, such as the one shown in Figure 9.11 , are available in cylindrical forms with different diameters, lengths, and strokes. Often, they include internal circuitry that provides a DC voltage proportional to displacement. The advantages of the LVDT are accuracy over the linear range and an analog output that may not require amplification. Also, it is less sensitive to wide ranges in temperature than other position transducers (e.g., potentiometers, encoders, and semiconductor devices). The LVDT’s disadvantages include limited range of motion and limited frequency response. The overall frequency response is limited by inertial effects associated with the core’s mass and the choice of the primary excitation fre￾quency and the filter cutoff frequency. alc80237_ch09_375-430.indd 382 lc80237_ch09_375-430.indd 382 10/01/11 10:09 PM 0/01/11 10:09 PM 38 Measurement Systems McGraw-Hill Create™ Review Copy for Instructor Nicolescu. Not for distribution

McGraw-Hill CreateTM Review Copyfor Instructor Nicolescu.Not fordistributionIntroduction to Mechatronics and Measurement Systems,Fourth Edition39383PositionandSpeedMeasurement9.2CLASSDISCUSSION ITEM9.3LVDTSignal Filtering田Given the spectrum of a time-varying core displacement, what effect does thechoiceoftheprimaryexcitationfrequencyhave,andhowshouldthelow-passfilterbedesignedtoproduceanoutputmostrepresentativeofthedisplacement?Aresolveris an analog rotaryposition sensor that operates verymuchliketheLVDT. It consists of a rotating shaft (rotor) with a primary winding and a stationaryhousing (stator)with two secondary windings offset by 90°.When the primary isexcited with an AC signal, AC voltages are induced in the secondary coils,which areproportional tothe sine and cosine of the shaft angle.Because of this,the resolver isVideo Demouseful inapplicationswheretrigonometricfunctions ofpositionarerequired.Two other types of linear position sensors that measure linear displacement9.5Voice coildirectly,based on magnetic principles,are the voice coil and magnetostrictive posi-9.6Magneto-tion transducers.Video Demos 9.5 and 9.6 show two example devices and describestrictive positionhowtheywork.sensor9.2.4DigitalOpticalEncoderA digital optical encoder is a device that converts motion into a sequence of dig-ital pulses.By counting a single bit or decoding a set of bits, the pulses can beconvertedtorelativeorabsolutepositionmeasurements.Encodershaveboth linearand rotaryconfigurations,butthemost commontypeis rotary.Rotaryencoders areVideo Demomanufactured intwobasicforms:theabsoluteencoderwhereauniquedigital word9.7Encodercorresponds to each rotational position of the shaft, and the incremental encoder,componentswhichproducesdigitalpulsesastheshaftrotates,allowingmeasurementof relative9.8Computerdisplacementof theshaft.AsillustratedinFigure9.12,mostrotaryencodersaremouse relativecomposed of a glass or plastic code disk with a photographicallydeposited radialencoderpattern organized in tracks. As radial lines in each track interrupt the beam between9.9 Adept robota photoemitter-detector pair,digital pulses are produced.digital encoderVideoDemo9.7showsanddescribesallof theinternal componentsof a smallcomponentsdigital encoder.In this case the code disk is made of stamped sheetmetal.Video1.1AdeptOneDemos9.8and9.9describetwointerestingapplicationsof encoders:acomputerrobot demon-mouse and an industrial robot.View Video Demos 1.1 and 1.2 to see a demonstra-stration (8.0MB)tionof howtherobotworksand howtheencoders are incorporated intothe internal1.2AdeptOnedesign.Video Demo 1.5 shows another application of encoders where cost is a majorrobot internalconcern and a custom design is necessary.designand conThe optical disk of theabsoluteencoder is designedtoproducea digital wordstruction (4.6 MB)that distinguishes N distinct positions of the shaft. For example, if there are eight1.5 Inkjet printertracks,the encoder is capableofmeasuring256(2)distinct positions correspondingcomponents withto an angular resolution of1.406°(360°/256).Themost common types ofnumericalDCmotorsandencoding used in the absolute encoder are gray and natural binary codes.To illus-piezoelectricinkjetheadtrate the action of an absolute encoder, thegray code and natural binary code disk

Confirming Pages 9.2 Position and Speed Measurement 383 A resolver is an analog rotary position sensor that operates very much like the LVDT. It consists of a rotating shaft (rotor) with a primary winding and a stationary housing (stator) with two secondary windings offset by 90 . When the primary is excited with an AC signal, AC voltages are induced in the secondary coils, which are proportional to the sine and cosine of the shaft angle. Because of this, the resolver is useful in applications where trigonometric functions of position are required. Two other types of linear position sensors that measure linear displacement directly, based on magnetic principles, are the voice coil and magnetostrictive posi￾tion transducers. Video Demos 9.5 and 9.6 show two example devices and describe how they work. 9.2.4 Digital Optical Encoder A digital optical encoder is a device that converts motion into a sequence of dig￾ital pulses. By counting a single bit or decoding a set of bits, the pulses can be converted to relative or absolute position measurements. Encoders have both linear and rotary configurations, but the most common type is rotary. Rotary encoders are manufactured in two basic forms: the absolute encoder where a unique digital word corresponds to each rotational position of the shaft, and the incremental encoder, which produces digital pulses as the shaft rotates, allowing measurement of relative displacement of the shaft. As illustrated in Figure 9.12 , most rotary encoders are composed of a glass or plastic code disk with a photographically deposited radial pattern organized in tracks. As radial lines in each track interrupt the beam between a photoemitter-detector pair, digital pulses are produced. Video Demo 9.7 shows and describes all of the internal components of a small digital encoder. In this case the code disk is made of stamped sheet metal. Video Demos 9.8 and 9.9 describe two interesting applications of encoders: a computer mouse and an industrial robot. View Video Demos 1.1 and 1.2 to see a demonstra￾tion of how the robot works and how the encoders are incorporated into the internal design. Video Demo 1.5 shows another application of encoders where cost is a major concern and a custom design is necessary. The optical disk of the absolute encoder is designed to produce a digital word that distinguishes N distinct positions of the shaft. For example, if there are eight tracks, the encoder is capable of measuring 256 (2 8 ) distinct positions corresponding to an angular resolution of 1.406 (360 /256). The most common types of numerical encoding used in the absolute encoder are gray and natural binary codes. To illus￾trate the action of an absolute encoder, the gray code and natural binary code disk Video Demo 9.5 Voice coil 9.6 Magneto￾strictive position sensor ■ C L A S S D I S C U S S I O N I T E M 9 . 3 LVDT Signal Filtering Given the spectrum of a time-varying core displacement, what effect does the choice of the primary excitation frequency have, and how should the low-pass filter be designed to produce an output most representative of the displacement? Video Demo 9.7 Encoder components 9.8 Computer mouse relative encoder 9.9 Adept robot digital encoder components 1.1 Adept One robot demon￾stration (8.0 MB) 1.2 Adept One robot internal design and con￾struction (4.6 MB) 1.5 Inkjet printer components with DC motors and piezoelectric inkjet head alc80237_ch09_375-430.indd 383 lc80237_ch09_375-430.indd 383 10/01/11 10:09 PM 0/01/11 10:09 PM Introduction to Mechatronics and Measurement Systems, Fourth Edition 39 McGraw-Hill Create™ Review Copy for Instructor Nicolescu. Not for distribution.

McGraw-Hill CreateTM ReviewCopy forInstructorNicolescu.Notfordistribution.40MeasurementSystems384CHAPTER9Sensorscode disktrackshaftOphototransistor1 or more LEDphotodetectorsphotoemitters楚文SS文adigital outputsignals(a) schematicElectronics board(Signal conditioning)LED light sourceRotatingencoder diskStationary maskPhotodetector(b) typical construction (Courtesy ofLucas LedexInc., Vandalia, OH)Figure9.12Componentsofanopticalencodertrack patterns fora simplefour-track (4-bit)encoder areillustrated inFigures9.13and 9.14. The linear patterms and associated timing diagrams are what the photo-detectors sense as the code disk circular tracks rotate with the shaft.The output bitcodesforbothcoding schemesare listed inTable9.1.Thegray code is designed so that only one track (one bit) changes state for eachcount transition, unlike the binary code where multiple tracks (bits) can change duringcounttransitions.This effect canbe seen clearly inFigures9.13and9.14and in thelasttwo columns of Table 9.1.For the gray code,the uncertainty duringa transition is onlyonecount,unlikewiththebinarycode,wheretheuncertaintycouldbemultiplecounts.CLASS DISCUSSIONITEM 9.4EncoderBinaryCodeProblemsWhat is the maximum countuncertaintyfora 4-bit gray codeabsolute encoder anda 4-bit natural binaryabsolute encoder?At whatdecimal codetransitions doesthemaximum count uncertainty occur in a 4-bit natural binary absolute encoder?

Confirming Pages Figure 9.12 Components of an optical encoder. 1 or more LED photoemitters phototransistor photodetectors code disk shaft tracks digital output signals (a) schematic (b) typical construction (Courtesy of Lucas Ledex Inc., Vandalia, OH) Electronics board (Signal conditioning) Rotating encoder disk LED light source Stationary mask Photodetector 384 C H A P T E R 9 Sensors track patterns for a simple four-track (4-bit) encoder are illustrated in Figures 9.13 and 9.14 . The linear patterns and associated timing diagrams are what the photo￾detectors sense as the code disk circular tracks rotate with the shaft. The output bit codes for both coding schemes are listed in Table 9.1. The gray code is designed so that only one track (one bit) changes state for each count transition, unlike the binary code where multiple tracks (bits) can change during count transitions. This effect can be seen clearly in Figures 9.13 and 9.14 and in the last two columns of Table 9.1. For the gray code, the uncertainty during a transition is only one count, unlike with the binary code, where the uncertainty could be multiple counts. ■ C L A S S D I S C U S S I O N I T E M 9 . 4 Encoder Binary Code Problems What is the maximum count uncertainty for a 4-bit gray code absolute encoder and a 4-bit natural binary absolute encoder? At what decimal code transitions does the maximum count uncertainty occur in a 4-bit natural binary absolute encoder? alc80237_ch09_375-430.indd 384 lc80237_ch09_375-430.indd 384 10/01/11 10:09 PM 0/01/11 10:09 PM 40 Measurement Systems McGraw-Hill Create™ Review Copy for Instructor Nicolescu. Not for distribution