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 easily 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 voltages 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 secondary. 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 output 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 frequency of this low-pass filter must be chosen carefully to filter out the high frequencies 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 frequency 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 position 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 digital 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 demonstration 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 illustrate the action of an absolute encoder, the gray code and natural binary code disk Video Demo 9.5 Voice coil 9.6 Magnetostrictive 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 demonstration (8.0 MB) 1.2 Adept One robot internal design and construction (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 photodetectors 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