ME 586 - Automation Sensors. Objectives Identify commonly used sensor types Identify commonly used...

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ME 586 - Automation ME 586 - Automation ME 586 - Automation ME 586 - Automation Sensors Sensors

Transcript of ME 586 - Automation Sensors. Objectives Identify commonly used sensor types Identify commonly used...

Page 1: ME 586 - Automation Sensors. Objectives Identify commonly used sensor types Identify commonly used sensor types Where, how and why they are usedWhere,

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SensorsSensors

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Objectives

• Identify commonly used sensor types Identify commonly used sensor types

•Where, how and why they are usedWhere, how and why they are used

•Latest and greatest capabilitiesLatest and greatest capabilities

•Bottom Line (cost)Bottom Line (cost)

• Where to go to find out moreWhere to go to find out more

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Proximity Sensors•InductiveInductive

•CapacitiveCapacitive

•Ultrasonic Ultrasonic

•PhotoelectricPhotoelectric

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Inductive Sensors•How they workHow they work

•Creates a radio frequency field using Creates a radio frequency field using an oscillator and a coil. The presence of an oscillator and a coil. The presence of a metal object changes the field and the a metal object changes the field and the sensor is able to detect this.sensor is able to detect this.

*Picture compliments of Baumer Electric Ltd.

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Inductive Sensors•ApplicationsApplications

•Conveyor on/off switchesConveyor on/off switches

•Begin machine cycleBegin machine cycle

•Quality control (sense lids, proper alignment, Quality control (sense lids, proper alignment, etc.)etc.)

•Count, determine direction of Count, determine direction of motion/rotation, positioningmotion/rotation, positioning

•Anytime you want to sense metalAnytime you want to sense metal

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Inductive Sensors• AdvantagesAdvantages

•Can detect metal target even Can detect metal target even through non-metallic barriersthrough non-metallic barriers

•Eliminates need for contactEliminates need for contact

•Operate in harsh conditionsOperate in harsh conditions

•Rapid response timeRapid response time

•Long life, virtually unlimited operating Long life, virtually unlimited operating cycles.cycles.

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Inductive Sensors• LimitationsLimitations

•Can only detect conductive metalCan only detect conductive metal

•Relatively short range. Usually used for less than 1” Relatively short range. Usually used for less than 1” sensing distance.sensing distance.

•May be affected by metal chips collecting on sensor face.May be affected by metal chips collecting on sensor face.

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Inductive Sensors• Things to be Aware OfThings to be Aware Of

•Specified range is for axial approach. If object Specified range is for axial approach. If object approaches from the side, range is decreased.approaches from the side, range is decreased.

•Range depends of metal type!!!!Range depends of metal type!!!!•St37 ( Fe ) St37 ( Fe ) 11

•Aluminium foil ( Al ) Aluminium foil ( Al ) 11

•Nickel chromium ( V2A ) Nickel chromium ( V2A ) 0.90.9

•Mercury ( Hg ) Mercury ( Hg ) 0.60.6

•Lead, brass ( Pb, Ms ) Lead, brass ( Pb, Ms ) 0.50.5

•Aluminium ( solid ) Aluminium ( solid ) 0.450.45

•Copper ( Cu ) Copper ( Cu ) 0.40.4

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Inductive Sensors• Current SpecificationsCurrent Specifications

•Range: up to 40 mmRange: up to 40 mm

•Switching Frequency: Switching Frequency: 25 Hz to 3 kHz. 25 Hz to 3 kHz.

•Time delay: < 2msTime delay: < 2ms

•Repeatability error: < 1% of rangeRepeatability error: < 1% of range

•Cost: $25 to $250 (typically just under $100)Cost: $25 to $250 (typically just under $100)

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Capacitive Sensors

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Capacitive Sensors•How they workHow they work

•Uses two plates to form a linear capacitor (hence the Uses two plates to form a linear capacitor (hence the name). The amount of energy that can be stored between name). The amount of energy that can be stored between the plates depends on the material between them. When a the plates depends on the material between them. When a material other than air is present, the sensor can detect it.material other than air is present, the sensor can detect it.

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Capacitive Sensors•ApplicationsApplications

•conveyorsconveyors

•roboticsrobotics

•jam protectionjam protection

•positioningpositioning

•parts detection or controlparts detection or control

•indexingindexing

•bottle cap or can lid bottle cap or can lid detectiondetection

•countingcounting

•broken or damaged tool broken or damaged tool detectiondetection

•liquid level controlliquid level control

•volume level controlvolume level control

•leak detectionleak detection

•avoid or jam controlavoid or jam control

•semiconductor manufacturingsemiconductor manufacturing

•food processingfood processing

•missing component detectionmissing component detection

•bottle fillingbottle filling

•bottle detectionbottle detection

•thickness monitoringthickness monitoring

•gaming table chip monitoringgaming table chip monitoring

•missing unit in shipping carton detectionmissing unit in shipping carton detection

•bin level in silo detectionbin level in silo detection

•low paper roll monitoringlow paper roll monitoring

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Capacitive Sensors• AdvantagesAdvantages

•Can detect Can detect aaabout anythingabout anything

•Can detect liquid targets through non-metallic barriers Can detect liquid targets through non-metallic barriers (glass, plastic, etc.)(glass, plastic, etc.)

•Operate in harsh conditionsOperate in harsh conditions

•Quick response timeQuick response time

•Can detect difference of object, not just presence Can detect difference of object, not just presence

•Long operational life, with virtually unlimited cycles.Long operational life, with virtually unlimited cycles.

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Capacitive Sensors• LimitationsLimitations

•Typically short range (less than 15mm)Typically short range (less than 15mm)

•Affected by varying temperature, humidity and moisture Affected by varying temperature, humidity and moisture conditionsconditions

•Not as accurate as inductive proximity sensorsNot as accurate as inductive proximity sensors

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Capacitive Sensors• Things to be Aware OfThings to be Aware Of

•Again, range depends upon direction of approachAgain, range depends upon direction of approach

•Range also depends on material Range also depends on material

•Be sure to check for ambient temperature limits Be sure to check for ambient temperature limits

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Capacitive Sensors• Current SpecificationsCurrent Specifications

•Range: typically up to 25 mm (can be as high as Range: typically up to 25 mm (can be as high as 150mm!)150mm!)

•Switching Frequency: up to 200 Hz Switching Frequency: up to 200 Hz

•Time delay: <=25 msTime delay: <=25 ms

•Repeatability: < 2% of rangeRepeatability: < 2% of range

•Cost: $25 - $250 (typically $80-100)Cost: $25 - $250 (typically $80-100)

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Ultrasonic Sensors

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Ultrasonic Sensors•How they workHow they work

•Sends out sound waves above audible frequencies Sends out sound waves above audible frequencies (ultrasonic), and listens for the return. Uses the (ultrasonic), and listens for the return. Uses the time delay, and the speed of sound in air to time delay, and the speed of sound in air to determine distance to object. Also can be used just determine distance to object. Also can be used just to see if object is there.to see if object is there.

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Ultrasonic Sensors•Different TypesDifferent TypesUltrasonic proximity sensor with Ultrasonic proximity sensor with analog output stageanalog output stage

Both current and voltage outputs from the Both current and voltage outputs from the sensor are proportional to the distance of sensor are proportional to the distance of the sensor from the target. This allows the sensor from the target. This allows simple non-contact measurementsimple non-contact measurement

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Ultrasonic Sensors•Different TypesDifferent TypesUltrasonic retro-reflective sensorUltrasonic retro-reflective sensor A fixed machine part is used here as a A fixed machine part is used here as a

reflector. The time difference between the reflector. The time difference between the emission and the reception of an ultrasonic emission and the reception of an ultrasonic signal (known as propagation time) is signal (known as propagation time) is therefore fixed and known. When an object therefore fixed and known. When an object comes within this sensing distance the comes within this sensing distance the output is activatedoutput is activated

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Ultrasonic Sensors•Different TypesDifferent TypesUltrasonic through beam sensorUltrasonic through beam sensor These sensors are ideal for applications in These sensors are ideal for applications in

which objects follow each other in quick which objects follow each other in quick succession. They are also recommended succession. They are also recommended when high switching frequencies are when high switching frequencies are required, up to 200 Hzrequired, up to 200 Hz

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Ultrasonic Sensors• AdvantagesAdvantages

•Can detect more types of objects than other three types of Can detect more types of objects than other three types of sensors (pretty much anything)sensors (pretty much anything)

•Very good for telling distances Very good for telling distances

•Longer range than capacitive and inductive sensorsLonger range than capacitive and inductive sensors

•Can operate in harsh conditionsCan operate in harsh conditions

•Quick response timeQuick response time

•Long operational life, with virtually unlimited cycles.Long operational life, with virtually unlimited cycles.

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Ultrasonic Sensors• LimitationsLimitations

•Have a “dead zone” close to the face of the sensor – can’t Have a “dead zone” close to the face of the sensor – can’t detect very close objectsdetect very close objects

•Can’t detect very small objects (detectable size depends on Can’t detect very small objects (detectable size depends on wavelength)wavelength) (except for really high tech ones – 0.076mm!) (except for really high tech ones – 0.076mm!)

•Speed depends on material (cotton, sponge, etc. require Speed depends on material (cotton, sponge, etc. require slower frequencies)slower frequencies)

•Smooth surfaced objects must be aligned correctly or echo Smooth surfaced objects must be aligned correctly or echo won’t return to sensorwon’t return to sensor

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Ultrasonic Sensors• Current SpecificationsCurrent Specifications

•Range: 50mm to 11.3mRange: 50mm to 11.3m

•Sampling Frequency: up to 2 kHz (usually about Sampling Frequency: up to 2 kHz (usually about 120 Hz or less, depending on distance and material)120 Hz or less, depending on distance and material)

•Maximum Target Speed: up to 400 in/secMaximum Target Speed: up to 400 in/sec

•Time delay: 0.5 msTime delay: 0.5 ms

•Repeatability: 0.1% of rangeRepeatability: 0.1% of range

•Cost: $75 – several hundred (typically just over Cost: $75 – several hundred (typically just over $100)$100)

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Photoelectric Sensors

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Photoelectric Sensors•How they workHow they work

•A photoelectric proximity switch is one in which the light source and A photoelectric proximity switch is one in which the light source and light sensor are housed in the same unit. The sensor picks up the pulse light sensor are housed in the same unit. The sensor picks up the pulse of the LED (light emitting diode), which is usually in either the of the LED (light emitting diode), which is usually in either the infrared or visible light range, as it reflects off of the object being infrared or visible light range, as it reflects off of the object being sensed. sensed.

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Photoelectric Sensors•Thru-BeamThru-Beam A source unit in one location sends a light beam to a A source unit in one location sends a light beam to a

detector unit in another location. An object is detected detector unit in another location. An object is detected when it passes between the source unit and the detector when it passes between the source unit and the detector

unit, interrupting the light beam.unit, interrupting the light beam.

•Reflex Reflex The source and detector are housed in one package and (Retro- The source and detector are housed in one package and (Retro- placed on the same side of the target object’s path. placed on the same side of the target object’s path.

Reflective) Reflective) When the object passes by, the source signal is reflected When the object passes by, the source signal is reflected back to the detector by a retro-reflector.back to the detector by a retro-reflector.

•Diffuse Diffuse The source and detector are housed in one package and The source and detector are housed in one package and ReflectiveReflective placed on the same side of the target object’s path. When placed on the same side of the target object’s path. When

the object passes by, the source signal is reflected back the object passes by, the source signal is reflected back to the detector off the target object itself.to the detector off the target object itself.

•Background Background This is a special type of diffuse reflective sensor that This is a special type of diffuse reflective sensor that Rejection Rejection includes two detectors. This arrangement allows the includes two detectors. This arrangement allows the

sensor to detect targets reliably within a defined range, sensor to detect targets reliably within a defined range, and to ignore objects just outside of this range. Unlike a and to ignore objects just outside of this range. Unlike a standard diffuse reflective sensor, color or reflectivity has standard diffuse reflective sensor, color or reflectivity has

minimal effect on the sensing range.minimal effect on the sensing range.

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Photoelectric Sensors•Applications (just a few)Applications (just a few)•Material HandlingMaterial Handling A sensor can ensure that products move along A sensor can ensure that products move along a conveyor line in an orderly manner. The sensor will stop the a conveyor line in an orderly manner. The sensor will stop the operation if a jam occurs. And items can be counted as they move operation if a jam occurs. And items can be counted as they move down the line.down the line.

•PackagingPackaging Sensors can verify that containers are filled properly, Sensors can verify that containers are filled properly, labeled properly and have tamper-proof seals in place.labeled properly and have tamper-proof seals in place.

•Machine operationMachine operation Sensors can watch to verify that a machine is Sensors can watch to verify that a machine is operating properly, materials are present and tooling is not operating properly, materials are present and tooling is not broken.broken.

•Paper IndustryPaper Industry Sensors can detect web flaws, web splice, clear Sensors can detect web flaws, web splice, clear web and paper presence, while maintaining high web speedsweb and paper presence, while maintaining high web speeds ..

In this cookie kitchen, fiber optic photoelectric sensors are placed in a hot oven. As long as the sensors detect motion as the trays of cookies move by, the oven stays on. If the conveyor stops, the sensors will detect light or dark for too long, and the output device will shut down the oven.

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Photoelectric Sensors• AdvantagesAdvantages

•Much greater sensing rangeMuch greater sensing range

•Can tell how far away the object isCan tell how far away the object is

•Fast response timeFast response time

•Typically very accurate (considering sensing range)Typically very accurate (considering sensing range)

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Photoelectric Sensors• LimitationsLimitations

•Don’t function well in contaminant environmentsDon’t function well in contaminant environments

•Sometimes too powerful (Excess Gain)Sometimes too powerful (Excess Gain)

•Reliability depends on object being sensed (can be too Reliability depends on object being sensed (can be too dark, too transparent, etc.)dark, too transparent, etc.)

•More expensiveMore expensive

•Require more power to operateRequire more power to operate

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Photoelectric Sensors• Current SpecificationsCurrent Specifications

•Range: up to 130m (typically between 0.5 and Range: up to 130m (typically between 0.5 and 10m)10m)

•Switching Frequency: up to 1 kHz (typically 20 – Switching Frequency: up to 1 kHz (typically 20 – 60 Hz)60 Hz)

•Time delay: as low as 0.5 ms (typically 8-50 ms)Time delay: as low as 0.5 ms (typically 8-50 ms)

•Accuracy: as good as 0.5mm or lessAccuracy: as good as 0.5mm or less

•Cost: very low end - $50, typical - $125-150, very Cost: very low end - $50, typical - $125-150, very sophisticated = very expensivesophisticated = very expensive

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Sensors Summary

Who Sells Them? Who Sells Them? (Thomas Register lists 120+ vendors)(Thomas Register lists 120+ vendors)

Rockwell Automation Cutler-Hammer, Sensor Div.

TURCK, Inc. Electro Corp.

SICK, Inc. Stedham Electronics Corp.

Baumer Electric Ltd. Advance Controls, Inc.

Balluff, Inc.

Altech Corp.

Southern Controls, Inc.

Fargo Controls, Inc.

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Sensors Summary

Where to Find out More?Where to Find out More?www.theproductfinder.com/sensors/sensor.htm

((good source for info about how they work and lists of vendors)good source for info about how they work and lists of vendors)

www.ch.cutler-hammer.com/training/slfstudy/sensors/welcome.htm

(excellent website for more technical information about various types of (excellent website for more technical information about various types of sensor and their applications)sensor and their applications)

http://www.thomasregister.com/

(great source for finding vendors of a specific type of sensor)(great source for finding vendors of a specific type of sensor)

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EncodersEncoders

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Objectives

•Present background and function of encodersPresent background and function of encoders

•Discuss where, when, and why encoders are usedDiscuss where, when, and why encoders are used

•Introduce types, models, and current technology of encodersIntroduce types, models, and current technology of encoders

• Delineate benefits and limitationsDelineate benefits and limitations

• Cite references and locations of further informationCite references and locations of further information

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BackgroundBackgroundA vast number of sensor products exist to detect all types of A vast number of sensor products exist to detect all types of

events. There are sensors to detect the presence of objects, the events. There are sensors to detect the presence of objects, the speed, the size, the structure, the color, the exact dimensions, the speed, the size, the structure, the color, the exact dimensions, the location, etc. Once the detection occurs, there is also a wide variety location, etc. Once the detection occurs, there is also a wide variety of ways a sensor can communicate, or convert, this information. of ways a sensor can communicate, or convert, this information.

Analog-to-digital conversion begins with sampling, or Analog-to-digital conversion begins with sampling, or measuring the amplitude of the analog waveform at equally spaced measuring the amplitude of the analog waveform at equally spaced discrete instants of time.discrete instants of time.

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As theAs the signal is sampled the signal is sampled the amplitude at each interval is amplitude at each interval is quantized, and the values are mapped quantized, and the values are mapped into a series of binary digits, or bits. into a series of binary digits, or bits. The information is then transmitted The information is then transmitted as a digital signal to the receiver, as a digital signal to the receiver, where it is decoded and the analog where it is decoded and the analog signal reconstituted.signal reconstituted.

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In order for a sampled signal In order for a sampled signal to be stored or transmitted in digital to be stored or transmitted in digital form, each sampled amplitude must form, each sampled amplitude must be converted to one of a finite number be converted to one of a finite number of possible values, or levels. For ease of possible values, or levels. For ease in conversion to binary form, the in conversion to binary form, the number of levels is usually a power of number of levels is usually a power of 2--that is, 8, 16, 32, 64, 128, 256, and 2--that is, 8, 16, 32, 64, 128, 256, and so on, depending on the degree of so on, depending on the degree of precision required. In the figure, an precision required. In the figure, an analog waveform is shown being analog waveform is shown being quantized on an 8-level scale (0 quantized on an 8-level scale (0 through 7). through 7).

2288

=256=256

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Encoder exampleEncoder example – – An absolute optical encoder has 8 An absolute optical encoder has 8 rings, 8 LED sensors, and 8 bit resolution. If the output rings, 8 LED sensors, and 8 bit resolution. If the output

pattern is 10010110, what is the shaft’s angular position?pattern is 10010110, what is the shaft’s angular position?

RingRing Angle (deg)Angle (deg) PatternPattern Value (deg) Value (deg)11 180180 11 180 18022 9090 0033 4545 0044 22.522.5 11 22.5 22.555 11.2511.25 0066 5.6255.625 11 5.625 5.62577 2.81252.8125 11 2.8125 2.812588 1.406251.40625 00

Angular Position = 180 + 22.5 + 5.625 + 2.8125Angular Position = 180 + 22.5 + 5.625 + 2.8125

Total = 210.94Total = 210.94

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Absolute EncodersAbsolute EncodersThe term The term absolute absolute defines the defines the type of information that is type of information that is relayed to the processor. There relayed to the processor. There are only two options available are only two options available here, either here, either absolute or absolute or incrementalincremental..

The absolute encoder differs from the The absolute encoder differs from the incremental encoder in that each angular incremental encoder in that each angular location is represented by a different location is represented by a different digital word.digital word.

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Absolute EncodersAbsolute EncodersIn the case of the incremental encoder, it is only possible In the case of the incremental encoder, it is only possible

to know your location relative to another location. The absolute to know your location relative to another location. The absolute encoder solves this problem by making each encoder solves this problem by making each angular position unique. (An image of an angular position unique. (An image of an absolute encoder disk is shown to the right.) absolute encoder disk is shown to the right.) Each separate location can be represented Each separate location can be represented by a binary number, determined by the by a binary number, determined by the sequence of light transmission or blockage sequence of light transmission or blockage as you progress inward to the center. as you progress inward to the center.

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Absolute EncodersAbsolute Encoders

Contrary to incremental encoders, absolute Contrary to incremental encoders, absolute encoders supply a clear code (information) in each encoders supply a clear code (information) in each angular position. This process offers the advantage angular position. This process offers the advantage that even in case of a power failure the actual that even in case of a power failure the actual position will be transmitted to the evaluation position will be transmitted to the evaluation electronics. Furthermore, errors of measurement electronics. Furthermore, errors of measurement due to missing pulses and cumulative errors are due to missing pulses and cumulative errors are excluded. excluded.

The primary advantage of the absolute The primary advantage of the absolute encoder is that the position is not lost in the case of encoder is that the position is not lost in the case of power loss or noise bursts. The largest disadvantage power loss or noise bursts. The largest disadvantage is added complexity and price. is added complexity and price.

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Absolute EncodersAbsolute EncodersTop of the Line – AstroCODER 150 Top of the Line – AstroCODER 150

• The only programmable absolute encoder that allows the user toThe only programmable absolute encoder that allows the user tochange programs on the fly. change programs on the fly.

• Industry leading 680 µsecond scan time virtually eliminates error, Industry leading 680 µsecond scan time virtually eliminates error, allowing for faster machine speeds while maximizingallowing for faster machine speeds while maximizingproductivity. productivity.

• Built-in scalable resolution displays user defined units between Built-in scalable resolution displays user defined units between 16 and 4096.16 and 4096.

• Includes resolver based transducers enhancing ruggedness while Includes resolver based transducers enhancing ruggedness while maintaining absolute position even after loss of power. maintaining absolute position even after loss of power.

• Accepts inputs from one or two transducers providing independent Accepts inputs from one or two transducers providing independent dual axis control. dual axis control.

• Position data available in three user selected forms: Serial Digital, Parallel Digital and Analog Position data available in three user selected forms: Serial Digital, Parallel Digital and Analog Voltages. Voltages. • Factory installed Astro data latch reacts to signal from PLC thereby accommodating any Factory installed Astro data latch reacts to signal from PLC thereby accommodating any predetermined scan rate.predetermined scan rate.• Available with WindowsAvailable with Windows®® or DOS or DOS®® based start-up software based start-up software

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Incremental EncodersIncremental EncodersLike any other position feedback device, theLike any other position feedback device, the incremental incremental

encoder is used to determine rotary or linear position. The term encoder is used to determine rotary or linear position. The term “incremental” describes the type of information that the encoder “incremental” describes the type of information that the encoder sends out, being either incremental or absolute. sends out, being either incremental or absolute.

The encoder provides relative position information. As The encoder provides relative position information. As rotation or linear translation occurs, the incremental encoder sends rotation or linear translation occurs, the incremental encoder sends out one pulse for each set incremental distance of travel. These out one pulse for each set incremental distance of travel. These pulses can be counted to determine the linear or rotary position pulses can be counted to determine the linear or rotary position relative to another position. Motion is quantified by a certain relative to another position. Motion is quantified by a certain number of pulses.number of pulses.

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Incremental EncodersIncremental Encoders Usually, the incremental encoder will come with three Usually, the incremental encoder will come with three channels, referred to as A, B, and Z. A and B are placed 90' out of channels, referred to as A, B, and Z. A and B are placed 90' out of phase. With these two channels, the phase. With these two channels, the processor determines the distance processor determines the distance traveled by the number of steps, and traveled by the number of steps, and the direction traveled by the leading the direction traveled by the leading wave form. The third channel is the wave form. The third channel is the reference. Usually the Z channel will have only one pulse per reference. Usually the Z channel will have only one pulse per revolution or per length of the encoder, so it can be used to revolution or per length of the encoder, so it can be used to determine an actual location, rather than just an incremental determine an actual location, rather than just an incremental number. These encoders can be either magnetic, optical, number. These encoders can be either magnetic, optical, contacting, or capacitive. contacting, or capacitive.

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Incremental EncodersIncremental EncodersThe disadvantage of the incremental encoder is that it is The disadvantage of the incremental encoder is that it is

unable to determine its location upon start-up, but this problem unable to determine its location upon start-up, but this problem can be overcome by taking the time to do a homing or reference can be overcome by taking the time to do a homing or reference pulse sequence, and then moving the desired amount of steps from pulse sequence, and then moving the desired amount of steps from there. The added expense and setup time of an absolute encoder there. The added expense and setup time of an absolute encoder should be avoided unless completely necessary.should be avoided unless completely necessary.

Another benefit of the Another benefit of the incremental encoder is the large incremental encoder is the large range of possible sizes and the high range of possible sizes and the high degree of compatibility.degree of compatibility.

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Incremental Functions: QuadratureIncremental Functions: QuadratureIncremental optical encoders generate two data Incremental optical encoders generate two data

signals that are electrically 90° out of phase with each other, signals that are electrically 90° out of phase with each other, as shown below. The term as shown below. The term quadraturequadrature refers to this 90° refers to this 90° phase relationship. Since each full cycle contains four phase relationship. Since each full cycle contains four transitions, or edges, an encoder that generates 2500 transitions, or edges, an encoder that generates 2500 cycles/rev, for example, provides 10,000 edges per cycles/rev, for example, provides 10,000 edges per revolution.revolution.

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QuadratureQuadrature20+ years ago, the prevalent electronic circuitry of 20+ years ago, the prevalent electronic circuitry of

the day was based on "edge detection". The transitions the day was based on "edge detection". The transitions coming from the encoder would act as the "trigger" to coming from the encoder would act as the "trigger" to cause a count. At each transition, the electronics not only cause a count. At each transition, the electronics not only generates a count, but also determines direction of travel generates a count, but also determines direction of travel so that it knows whether to count up or down. This is so that it knows whether to count up or down. This is done by establishing whether the transition is going high done by establishing whether the transition is going high or going low, and what the state of the other signal is.or going low, and what the state of the other signal is.

HighHigh

LowLow

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FROM TO FROM TO

0,1 1,1 0,1 0,0

1,1 1,0 1,0 1,1

1,0 0,0 1,0 1,1

0,0 0,1 0,0 1,0

QuadratureQuadratureHowever, modern electronics looks not at transitions, but at changes of state. However, modern electronics looks not at transitions, but at changes of state.

Basically, the user's electronics contains a high-speed clock and constantly samples Basically, the user's electronics contains a high-speed clock and constantly samples the states of A and B. When it sees a change, it counts up or down based on the the states of A and B. When it sees a change, it counts up or down based on the following table, where 0,1 represents the states of A and B, respectively. Instead of following table, where 0,1 represents the states of A and B, respectively. Instead of waiting for a triggering event from the encoder, the electronics generates its own waiting for a triggering event from the encoder, the electronics generates its own triggering based on its detection of a state change triggering based on its detection of a state change from the encoder. A subtle difference, but critical to from the encoder. A subtle difference, but critical to the operation of modern digital circuitry.the operation of modern digital circuitry.

Forward

Reverse

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Quadrature – PulsesQuadrature – Pulses(For the interested reader)(For the interested reader)

Back when people were counting edges, it was often convenient to Back when people were counting edges, it was often convenient to have the encoder vendor provide an output that not only identified a specific have the encoder vendor provide an output that not only identified a specific number of edges per cycle (1, 2 or 4), but also gave direction information number of edges per cycle (1, 2 or 4), but also gave direction information directly. Pulse output was introduced for this purpose. Pulses differ from square directly. Pulse output was introduced for this purpose. Pulses differ from square waves in 2 important ways:waves in 2 important ways:

•      •       Pulse widths are of fixed time duration, whereas the width of a square Pulse widths are of fixed time duration, whereas the width of a square wave ON state is a function of speed. (The distance between pulses is, wave ON state is a function of speed. (The distance between pulses is, of course, a function of position.)of course, a function of position.)

•      •       "Quadrature" has no meaning with pulse output; you get FWD pulses "Quadrature" has no meaning with pulse output; you get FWD pulses on one line, and REV pulses on another. (Or pulses on one line and on one line, and REV pulses on another. (Or pulses on one line and direction information on the other.)direction information on the other.)

             Pulse output options were fairly popular at one time, but it's been Pulse output options were fairly popular at one time, but it's been dwindling for quite a while. With quad decode chips that are available, the dwindling for quite a while. With quad decode chips that are available, the requirement has pretty much become obsolete.requirement has pretty much become obsolete.

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Although many companies have attempted to develop a new method of Although many companies have attempted to develop a new method of encoding, time and again they have returned to the absolute and incremental encoding, time and again they have returned to the absolute and incremental methods. Until now….methods. Until now….

A new type of encoder is currently being researched by Gurley Precision A new type of encoder is currently being researched by Gurley Precision Instruments. A Gurley Instruments. A Gurley Virtual AbsoluteVirtual AbsoluteTMTM encoder is absolute in essence or effect encoder is absolute in essence or effect without being formally recognized as such. (That's what without being formally recognized as such. (That's what virtualvirtual means.) In reality, means.) In reality, it is neither an incremental encoder, nor an absolute encoder. It is a whole new it is neither an incremental encoder, nor an absolute encoder. It is a whole new kind of encoder based on kind of encoder based on pseudorandompseudorandom encoding technology, which has certain encoding technology, which has certain details of construction similar to an incremental encoder, and certain kinds of details of construction similar to an incremental encoder, and certain kinds of behavior similar to an absolute encoder. Pseudorandom output codes directly behavior similar to an absolute encoder. Pseudorandom output codes directly from the disc or scale are not especially useful, so they've invented means for from the disc or scale are not especially useful, so they've invented means for decoding those signals into a natural binary format you can use like any other decoding those signals into a natural binary format you can use like any other encoder. This decoder (patent pending) stands in place of the quadrature decoder encoder. This decoder (patent pending) stands in place of the quadrature decoder and up/down counter used with an incremental, so total cost need not be much and up/down counter used with an incremental, so total cost need not be much more than an incremental encoder of comparable resolution. Yet it's more than an incremental encoder of comparable resolution. Yet it's effectivelyeffectively absolute!absolute!

A 3A 3rdrd Method!? Method!?

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A 3A 3rdrd Method!? Method!?A Virtual AbsoluteA Virtual Absolute™™ encoder encoder

uses just cyclic and index tracks, like an uses just cyclic and index tracks, like an incremental encoder. However, the index incremental encoder. However, the index track is a serial code similar to a bar code track is a serial code similar to a bar code instead of just a single line. You do not instead of just a single line. You do not know position immediately upon start-up, know position immediately upon start-up, as you do in a conventional absolute, but as you do in a conventional absolute, but after a very short travelafter a very short travel, in either direction , in either direction and starting from anywhereand starting from anywhere, you know , you know exactly where you are. In a rotary VA™ exactly where you are. In a rotary VA™ encoder, this encoder, this initializationinitialization angle is angle is typically about one degree, depending on typically about one degree, depending on the encoder's line count; in a linear VA™ the encoder's line count; in a linear VA™ encoder, about 1/2 mm motion is needed. encoder, about 1/2 mm motion is needed. In a sense, from then on the encoder is In a sense, from then on the encoder is truly absolute.truly absolute.

A Virtual Absolute Encoder

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A 3A 3rdrd Method!? Method!?Advantages of the Virtual Absolute™ technology are:Advantages of the Virtual Absolute™ technology are:• The initialization distance or angle is a fixed and very small motion, regardless of the The initialization distance or angle is a fixed and very small motion, regardless of the

starting position or direction of travel. Just "bump" it to find out where you are.starting position or direction of travel. Just "bump" it to find out where you are.

• The encoder contains inherent built-in-test functions not found in any conventional The encoder contains inherent built-in-test functions not found in any conventional encoder. It reports not only various encoder malfunctions, but can also help detect encoder. It reports not only various encoder malfunctions, but can also help detect system problems such as too high a temperature or excessive speed.system problems such as too high a temperature or excessive speed.

• The encoder generates the same whole-word information as a conventional absolute, The encoder generates the same whole-word information as a conventional absolute,

so it is very easy to interface to computers, PLC's, servo controls, etc.so it is very easy to interface to computers, PLC's, servo controls, etc.

• With its simpler optics, a rotary VA™ encoder can be smaller than a conventional With its simpler optics, a rotary VA™ encoder can be smaller than a conventional absolute of equal resolution. And you can use a linear VA™ encoder for applications absolute of equal resolution. And you can use a linear VA™ encoder for applications where a suitable conventional absolute linear would be very hard to find.where a suitable conventional absolute linear would be very hard to find.

• Because of its simpler electronics, reduced parts count, and less critical internal Because of its simpler electronics, reduced parts count, and less critical internal alignments, a VA™ encoder is inherently more reliable than a conventional absolute.alignments, a VA™ encoder is inherently more reliable than a conventional absolute.

• A VA™ encoder is usually dramatically less expensive than a conventional absolute.A VA™ encoder is usually dramatically less expensive than a conventional absolute.

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Principal Types of EncodersPrincipal Types of Encoders

•Rotary (77 Companies)Rotary (77 Companies)

•Linear (42 Companies)Linear (42 Companies)

•Optical (69 Companies)Optical (69 Companies)

•Magnetic (17 Companies)Magnetic (17 Companies)

List obtained from www.plantautomation.com

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Rotary EncodersRotary Encoders

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Rotary EncodersRotary Encoders•How they workHow they work

Most actuator systems contain some form of rotary motion. Most actuator systems contain some form of rotary motion. Often times, it is necessary to accurately locate the rotary position Often times, it is necessary to accurately locate the rotary position of that motion. One way of accomplishing this is with a rotary of that motion. One way of accomplishing this is with a rotary

encoder. This device is used to encoder. This device is used to convert a pattern on a rotary disc into convert a pattern on a rotary disc into an electrical signal which can be an electrical signal which can be processed to determine angular processed to determine angular position.position.

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Rotary EncodersRotary EncodersRotary encoders can be classified by two different characteristics:Rotary encoders can be classified by two different characteristics:

1) technology used to convert rotary position to an electrical 1) technology used to convert rotary position to an electrical signal signal

2)2) type of electrical output type of electrical output

Several technologies are now used to convert rotarySeveral technologies are now used to convert rotary information into an electric signal. The original method was information into an electric signal. The original method was through physical contacts. This created obvious through physical contacts. This created obvious limitationslimitations in inspeed, resolution, and life expectancy. This led to the evolution ofspeed, resolution, and life expectancy. This led to the evolution ofoptical, magnetic, and capacitive techniques. The two most optical, magnetic, and capacitive techniques. The two most commonly used encoders today are the commonly used encoders today are the opticaloptical encoders and the encoders and the magnetic magnetic encodersencoders.

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Rotary EncodersRotary Encoders•ApplicationsApplications

The rotary encoders are most often mounted to the back of The rotary encoders are most often mounted to the back of a motor to determine the shaft position, but they are definitely not a motor to determine the shaft position, but they are definitely not limited to this. They can be mounted to rotary positioning tables, limited to this. They can be mounted to rotary positioning tables, screw drives, gearheads, machining tools, or any other application screw drives, gearheads, machining tools, or any other application where a rotary actuator exists. Many drives and motion controllers where a rotary actuator exists. Many drives and motion controllers

can process common rotary encoder signals. Since can process common rotary encoder signals. Since the range of rotary encoders is so broad, there is one the range of rotary encoders is so broad, there is one for almost every application requiring position for almost every application requiring position feedback.feedback.

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Rotary EncodersRotary Encoders•Current SpecificationsCurrent Specifications

•Measurement range of up to 360°Measurement range of up to 360°•Contactless : no wear, no friction, high reliabilityContactless : no wear, no friction, high reliability•Magnetic : high mechanical ruggednessMagnetic : high mechanical ruggedness•Temperature range from -40°C to +85°CTemperature range from -40°C to +85°C•Provides absolute positionProvides absolute position•Accuracy range of 1° to 0.05°Accuracy range of 1° to 0.05°•Digital or analog outputDigital or analog output•Low costLow cost•Built-in self-testBuilt-in self-test

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Rotary EncodersRotary EncodersTop of the Line – MicroE Systems G1400Top of the Line – MicroE Systems G1400

FEATURESFEATURES•Miniature Sensor PackageMiniature Sensor Package •Line Counts from 82K to 2.68B CPRLine Counts from 82K to 2.68B CPR •Safe Transmissive DesignSafe Transmissive Design •Broad Alignment TolerancesBroad Alignment Tolerances

APPLICATIONSAPPLICATIONS•Servo Track WritersServo Track Writers •Head/Media TestersHead/Media Testers •Precision Stage FeedbackPrecision Stage Feedback •Grating Period: 5 µmGrating Period: 5 µm•Resolution from 76.6 µrad to 2.37 nanoradiansResolution from 76.6 µrad to 2.37 nanoradians •Signal Period: 2.5 µmSignal Period: 2.5 µm•Power Supply: VDC +/- 5% @100 mA, 12 VDC +/- 5% @1 mAPower Supply: VDC +/- 5% @100 mA, 12 VDC +/- 5% @1 mA•Speed: 1714 rpmSpeed: 1714 rpm

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Linear EncodersLinear Encoders

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Linear EncodersLinear Encoders•How they workHow they work

This device is used to convert This device is used to convert linear position information into an linear position information into an electrical output signal. The electrical output signal. The linear linear encoder consists of a linear tape scaleencoder consists of a linear tape scale made up of glass or steel, a light source made up of glass or steel, a light source (e.g. LED, laser), and a photoreceptor. (e.g. LED, laser), and a photoreceptor. The light source, photoreceptor, and The light source, photoreceptor, and additional scale are usually housed together. This housing either additional scale are usually housed together. This housing either surrounds the tape scale in through beam encoders or resides on surrounds the tape scale in through beam encoders or resides on one side of the tape scale in reflective linear encodersone side of the tape scale in reflective linear encoders. .

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Linear EncodersLinear Encoders

Light is projected through or off the tape scale and is Light is projected through or off the tape scale and is detected by the photoreceptor. The fixed scale modulates the light detected by the photoreceptor. The fixed scale modulates the light

as the receptor and light source progress. as the receptor and light source progress. The The receptor detects these modulations and receptor detects these modulations and

converts the input into an electrical output converts the input into an electrical output usually in the form of a quadrature signal usually in the form of a quadrature signal (shown here). The two channels are always (shown here). The two channels are always 90' out of phase. The direction of the motion 90' out of phase. The direction of the motion can be determined by the leading channel. can be determined by the leading channel. The output is the same as that of the The output is the same as that of the incremental encoder.incremental encoder.

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Linear EncodersLinear EncodersTop of the Line - Top of the Line - GEL 221 Linear Scale IP66 - motor technologyGEL 221 Linear Scale IP66 - motor technology

FeaturesFeatures • Magnetic sensing principle Magnetic sensing principle Corrosion resistant 12 mm measuring rod Corrosion resistant 12 mm measuring rod Easy mounting and adjustment Easy mounting and adjustment 0.01 mm resolution (w/ external edge-evaluation) 0.01 mm resolution (w/ external edge-evaluation) 200kHz maximum output frequency 200kHz maximum output frequency Temperature range 0...+70°C or -20...+85ºC Temperature range 0...+70°C or -20...+85ºC Supply voltage 5VDC±5% or 10...35VDC Supply voltage 5VDC±5% or 10...35VDC IP66 protection IP66 protection

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Optical EncodersOptical Encoders

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Optical EncodersOptical Encoders•How they workHow they work

This feedback device is used to detect rotary or linear position and convert it to This feedback device is used to detect rotary or linear position and convert it to an electrical output. A light source, usually either an LED or a laser, is projected through an electrical output. A light source, usually either an LED or a laser, is projected through thin slits in a rotary disc for rotary encoders, or a thin tape scale for linear. The LED is thin slits in a rotary disc for rotary encoders, or a thin tape scale for linear. The LED is adequate for most applications, although the laser has found niches in several high adequate for most applications, although the laser has found niches in several high

precision, high resolution applications. precision, high resolution applications. The disk and tape can either be made of The disk and tape can either be made of covered glass with thin etchings in the covered glass with thin etchings in the cover, or thin metal with etchings cover, or thin metal with etchings through it. Each has appropriate through it. Each has appropriate applications. As light is transmitted, a applications. As light is transmitted, a photo receptor on the opposite side of photo receptor on the opposite side of the disc or tape detects the light and the disc or tape detects the light and converts it to an electrical output. converts it to an electrical output. Different optical encoders can create a Different optical encoders can create a wide range of signals, (e.g. silicon cell, wide range of signals, (e.g. silicon cell, analog, sinusoidal).analog, sinusoidal).

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Optical EncodersOptical EncodersOptical encoders offer a higher resolution Optical encoders offer a higher resolution and accuracy than all other encoders. Some and accuracy than all other encoders. Some can offer in excess of 1 million counts per can offer in excess of 1 million counts per Revolution (cpr). Often times the best wayRevolution (cpr). Often times the best way

to decide what feedback device you should use for to decide what feedback device you should use for your application is to determine what type of your application is to determine what type of information your information your controller, PLC, smart drive, or controller, PLC, smart drive, or

other other processor that you are using is capable of processing processor that you are using is capable of processing without too much trouble. Frequently many types of without too much trouble. Frequently many types of feedback will fit your needs, but only a couple will be feedback will fit your needs, but only a couple will be simple to integrate. Due of the different signal options simple to integrate. Due of the different signal options and versatility of the optical encoder, this is a very and versatility of the optical encoder, this is a very popular position feedback device. popular position feedback device.

AdvantagesAdvantages

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Optical EncodersOptical Encoders Pos. /DescriptionPos. /Description1 Circlip1 Circlip2 Washer2 Washer3 Spacer3 Spacer4 Ball bearing4 Ball bearing5 Housing5 Housing6 LED support6 LED support7 LED 7 LED 8 Spacer ring8 Spacer ring9 Codewheel 9 Codewheel 10 Stator disk 10 Stator disk 11 Printed circuit 11 Printed circuit 12 Cover12 Cover13 Ribbon cable13 Ribbon cable14 Connector 14 Connector 

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Optical EncodersOptical EncodersTop of the Line - Top of the Line - S5S single-ended optical shaft encoderS5S single-ended optical shaft encoder

The S5S single-ended optical shaft encoder is a non-contacting rotary to digital converter. The S5S single-ended optical shaft encoder is a non-contacting rotary to digital converter. Useful for position feedback or manual interface, the encoder converts real-time shaft Useful for position feedback or manual interface, the encoder converts real-time shaft angle, speed, and direction into TTL-compatible quadrature outputs with or without index. angle, speed, and direction into TTL-compatible quadrature outputs with or without index. The encoder utilizes an unbreakable mylar disk, metal shaft & bushing, LED light source, The encoder utilizes an unbreakable mylar disk, metal shaft & bushing, LED light source, and monolithic electronics. It may operate from a single +5VDC supply. and monolithic electronics. It may operate from a single +5VDC supply.

FeaturesFeatures •Small size Small size

•Low costLow cost

•Positive finger-latching connector Positive finger-latching connector

•2-channel quadrature,2-channel quadrature,

•TTL squarewave outputs 3rd channel index option TTL squarewave outputs 3rd channel index option

•Tracks from 0 to 100,000 cycles/sec Tracks from 0 to 100,000 cycles/sec

•Ball bearing option tracks to 10,000 RPM Ball bearing option tracks to 10,000 RPM

•-40 to +100°C operating temperature-40 to +100°C operating temperature

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Magnetic EncodersMagnetic Encoders

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Magnetic EncodersMagnetic Encoders

This device is used to convert position information into an electrical This device is used to convert position information into an electrical output that can be interpreted by a system controller. The two main components output that can be interpreted by a system controller. The two main components

of a magnetic encoder are the read of a magnetic encoder are the read head and head and the magnetic disc. The the magnetic disc. The read head contains a read head contains a magneto resistive magneto resistive sensor, which is basically sensor, which is basically an inductor that an inductor that detects changes in the detects changes in the magnetic flux. magnetic flux. The disc is magnetically The disc is magnetically coded. The coded. The magnetic code is interpreted by magnetic code is interpreted by the the sensor as a series of on and off states. sensor as a series of on and off states.

One magnetic code is interpreted as a 0 bit One magnetic code is interpreted as a 0 bit value and the next as a 1 bit value. Through value and the next as a 1 bit value. Through

this combination the magnetic encoder is this combination the magnetic encoder is able to transmit pulses representing able to transmit pulses representing

incremental rotary motionincremental rotary motion.

•How they workHow they work

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Magnetic EncodersMagnetic Encoders•AdvantagesAdvantages

•The magnetic encoder offers good resolutionThe magnetic encoder offers good resolution

•can operate in a wide variety of conditionscan operate in a wide variety of conditions

•requires low power for operation requires low power for operation

•DisadvantagesDisadvantages

•they cannot achieve very high speedsthey cannot achieve very high speeds

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Magnetic EncodersMagnetic Encoders

 Pos. /DescriptionPos. /Description1 DC-Micromotor1 DC-Micromotor2 Terminals2 Terminals3 End cap3 End cap4 Housing4 Housing5 Magnet disk5 Magnet disk6 Hall sensor 6 Hall sensor 7 Printed circuit 7 Printed circuit 8 Isolation8 Isolation9 Cover 9 Cover 10 Ribbon cable10 Ribbon cable11 Connector11 Connector

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Who Sells Them? Who Sells Them? (Thomas Register lists 100+ vendors)(Thomas Register lists 100+ vendors)

>ACC>ATS>AVG Automation>Astrosystems Automation>Balluff Inc>Baumer Electric Ltd.>Computer Conversions Corp.>Dynamics Reseach Corp.>Eastern Air Devices>Globetron Electronics>Gurley Precision Instruments

>MicroE>Motor Technology UK Limited>NC Servo Technology>Omron Electronic Inc.>Ormec Systems Corp.>Parvex Inc.>Quin Systems Ltd.>Southern Power Inc>Space Age Control Inc>Stegmann Inc.>U.S. Digital Corporation

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Where to Find out More?Where to Find out More?www.theproductfinder.com/sensors/sensor.htmwww.theproductfinder.com/sensors/sensor.htm

((good source for info about how they work and lists of vendors)good source for info about how they work and lists of vendors)

http://www.gpi-encoders.com/http://www.gpi-encoders.com/

(excellent website for more technical information about various types of (excellent website for more technical information about various types of encoders and their applications. Also source of VA encoders.)encoders and their applications. Also source of VA encoders.)

http://www.microesys.com/http://www.microesys.com/

(source of several leading encoders)(source of several leading encoders)

http://www.thomasregister.com/http://www.thomasregister.com/

(great source for finding vendors of a specific type of sensor)(great source for finding vendors of a specific type of sensor)

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Glossary of Encoder NomenclatureGlossary of Encoder NomenclatureACCURACY is a measure of how close the output is to where it should be. It is usually expressed in units of distance, such as ±30 arc seconds or ±0.0001 inch. If it's expressed as a percent, make sure to state whether it's a percent of full scale (not usually meaningful with a rotary encoder) or a percent of nominal resolution.

BIT is an abbreviation for Binary digit; it refers to the smallest element of resolution.

CPR can mean either cycles/rev or counts/rev. To avoid confusion, this term should not be used.

ERROR is the algebraic difference between the indicated value and the true value of the input.

FREQUENCY RESPONSE is the encoder's electronic speed limit, expressed in kilohertz (1 kHz = 1000 Hz = 1000 cycles/sec). For calculations, rotational speed must be in rev/sec (rps = rpm/60); linear speed must be either in/sec or mm/sec, depending on the scale line count.

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Glossary of Encoder NomenclatureGlossary of Encoder NomenclatureINDEX SIGNAL is a once-per-rev output used to establish a reference or return to a known starting position; also called reference, marker, home, or Z

INTERPOLATION involves an electronic technique for increasing the resolution from the number of optical cycles on the disc or scale to a higher number of quadrature square waves per revolution or per unit length. These square waves can then be quadrature decoded.

MEASURING STEP is the smallest resolution element; it assumes quadrature decode. (see also QUANTUM)

PPR (pulses per revolution) Commonly (but mistakenly) used instead of cycles/rev when referring to quadrature square wave output.

QUADRATURE refers to the 90-electrical-degree phase relationship between the A and B channels of incremental encoder output.

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Glossary of Encoder NomenclatureGlossary of Encoder NomenclatureQUADRATURE DECODE (or 4X Decode) refers to the common practice of counting all 4 quadrature states (or square wave transitions) per cycle of quadrature square waves. Thus, an encoder with 1000 cycles/rev, for example, has a resolution of 4000 counts/rev.

QUANTIZATION ERROR is inherent in all digital systems; it reflects the fact that you have no knowledge of how close you are to a transition. It is commonly accepted as being equal to ±1/2 bit.

QUANTUM (plural is “quanta”) = BIT. It is the smallest resolution element. (quanta and bit are more commonly used with absolute encoders; counts/rev or measuring steps are more common with incremental encoders.)

REPEATABILITY is a measure of how close the output is this time to where it was last time, for input motion in the same direction. It's not usually specified explicitly, but it is included in the accuracy figure. (As a rule of thumb, the repeatability is generally around 1/10 the accuracy.)

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Glossary of Encoder NomenclatureGlossary of Encoder Nomenclature

RESOLUTIONRESOLUTION is the smallest movement detectable by the encoder. It can be expressed in is the smallest movement detectable by the encoder. It can be expressed in either electrical terms per distance (e.g., 3600 counts/rev or 100 pulses/mm) or in units of either electrical terms per distance (e.g., 3600 counts/rev or 100 pulses/mm) or in units of distance (e.g., 0.1° or 0.01 mm). distance (e.g., 0.1° or 0.01 mm).

SLEW SPEEDSLEW SPEED is the maximum allowable speed from mechanical considerations. It is is the maximum allowable speed from mechanical considerations. It is independent of the maximum speed dictated by frequency response.independent of the maximum speed dictated by frequency response.

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Conversion FactorsConversion FactorsANGULAR MEASURE ANGULAR MEASURE

1 revolution = 360° = 21,600 minutes = 1,296,000 seconds » 2pi radians (rad)

1° = 60 minutes (min) = 3600 seconds (s) » 0.0175 rad

1 min = 60 s = 0.0167° » 0.291 mrad

1 s = 0.0167 min = 0.000278° » 4.85 µrad

1 rad » 57.3°; 1 mrad » 3.48 min; 1 µrad » 0.206 s

Sometimes the terms "arcminutes" and "arcseconds" are used to differentiate the units of angle from the units of time. If the context makes the meaning clear, the "arc" prefix need not be used.

Occasionally, the symbols ' and " are used to indicate arcminutes and arcseconds, respectively. Because they can be confused with feet and inches, they should not be used.

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LINEAR MEASURE LINEAR MEASURE

1 foot (ft) = 12 inches (in) = 304.8 millimeters (mm)

1 in = 25.4 mm

0.001 in = 25.4 micrometer (µm)

1 meter (m) » 3.281 ft » 39.37 in

1 mm » 0.0394 in

1 µm » 39.37 µin

The terms "mil" (= 0.001 in; short for milli-inch) and "micron" (= 1 µm) should not be used.

Conversion FactorsConversion Factors

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SPEED SPEED

1 rev/min (rpm) = 1/60 rev/s (rps)

1 rad/s » 57.3 deg/s » 0.159 rev/s

1 in/min » 0.423 mm/s

1 mm/min » 0.000657 in/s

Conversion FactorsConversion Factors