Chap 3 Analog sensors

3.1 Introduction

● to prevent error ⇒ error measurement sensor are used (type and

characteristics have to be found) ● size (length) measurement is important in precision machines sensors measuring length error are mostly studied (in the course)

● sensor limitations sometimes machine structure can be changed

3.1 Introduction

● sensor is a device that responds to or detects a physical quantity and transmits the resulting signal to a controller

● transducer: transforms energy types

▶ piezo material: electric E ⇔ mechanical E (sensor or actuator)▶ shape memory alloy: thermal E ⇒ mechanical E (transform: change to original shape)

Definitions

● absolute: output is always relative to a fixed reference regardless of the initial condition● incremental: output is a series of binary pulses ● analog: continuous output (proportional to physical quantity being measured)● digital: discrete output ▶ series of binary pulses▶ each pulse represents sensor’s resolution

Sensor performance

ex) accuracy, resolution, repeatability  ● average outputaverage value of sensor output from many data ⇒ As N increases, random error decreases at the ratio of (N)1/2 (noise level decrease) ⇒ resolution increases

sampling rate

● v: max. slew rate (related to measurand change)● increase resolution() by a factor of N (resolution δ is limited by random noise) ● total sampling time: ttotal sampling = δ/Nv(during this time, measurand will not change by more than 1/N times the resolution)● in order to increase resolution by averaging random noise ⇒ N2 data points have to be taken⇒⇒ minimum required sampling period

tsample = /N3v

frequency response

● effect on the output of sensor of the physical quantity being measured

frequency()

1

Sensor outputphys quan

Definitions● hysteresis: maximum difference in sensor output between measurements made from 0 to 100% full scale output and 100 to 0%● linearity: variation in proportionality constant (between output signal and measured physical quantity)● mapping: measuring sensor response to a known input under known conditions and storing results in a look-up table or fitting mathematical expression to the data⇒ nonlinearity, hysteresis, and temperature effects can be compensated

Definitions ● noise: magnitude of any part of the sensor output that is not directly related to the physical quantity being measured ● noise input margin: maximum noise input level (ex, deviation in supply voltage) that can be tolerated without affecting desired sensor performance ● resolution: smallest detectable change in the measured physical quantity

Definitions

● sensitivity: variation in sensor output caused by a variation of physical quantity

● slew rate error: how the accuracy of sensor changes with the rate of change of measured physical quantity ● standoff distance: distance between sensor and target 

Definitions● step response: time-varying change in sensor output given a step change in the measured physical quantity

Delay timeRise time

Storage time

Fall time

Time

Sen

sor

oup

ut

10%

90%

100%

Ideal response to a step input

Actual response to a step input

3.1.2 System dynamics

● sensor frequency response ⇒ system’s ability to respond to changes in the measurand(fast process ⇒ inaccurate measurement) ⇒ frequency that a sensor’s output tends to decrease because it can no longer accurately detect changes in a rapidly changing measurand ⇒ determined experimentally or analytically How quickly system accuracy can be degraded with increasing frequency

Mathematical modeling of a Dynamic system

● sensor system (complicated in machine tools)

2

'' ' ( )

( )( )

mx bx kx u t

U sG s

ms bs k

( )( )

( )

log ( ) log ( ) log ( )

i

j

i j

N sG s

D s

G s N s D s

log-log ⇒ graphical addition

Mathematical modeling of a Dynamic system

● Most sensor frequency response is given in terms of 3 dB response pt (1st order system)- = n

- response = 0.707 of the response at zero frequency input(dc) (30% error)- Operates well before its -3dB frequency

● response (dB) = 20 /log10G

frequency()

1

센서출력물리량

0.7

n frequency()n

phaselag

3.2 Nonoptical sensor systems

● generating analog signals or digital pulses in response to a physical process by other than optical means

3.2.1 capacitance sensors

● determines the distance (gap) between probe and target surface ⇒ measures capacitance formed by two parallel plates● non-contact● performance (accuracy, linearity) determined primarily by probe capacitance

▶ large probe: 10∼100 pF ▶ small probe: 0.01∼0.1 pF

target

sensor

3.2.1 capacitance sensors ● target material: metal (conductor), dielectric, semiconductor ⇒ affects the sensor output ▶ metal : affects sensor output equallyex) calibrated over STS measurement over brass and aluminum▶ dielectric material : different calibrations

Applications of capacitance sensors

● motion of rotating parts (spindles, bearings)● mapping flatness of delicate objects (lens, silicon wafers)● thickness (two probes are used)

- metal thicknessl1 l2

t

1 2( )t l l l

Applications of capacitance sensors

● thickness of dielectric plateone probe is used in conjunction with a grounded metal surface dielectric material is introduced into the gap resultant change in capacitance thickness of material is determined

metal metal대상

부도체

Applications of capacitance sensors

● pressure measurementrigid frame + diaphragmThe diaphragm deforms due to pressure ⇒ capacitance change between diaphragm and sensor  

- proximity (presence/no presence) of nonmetal and liquid level (cf, cheap inductive proximity sensor for metal)

diaphragm

p

probe design for capacitance sensors

● depends on application and electronic circuit configuration- matching probe shape to target surface ⇒ performance improve ● stray capacitance (between probe sensor and outer body) – removed or reduced by using guard electrode (10-14∼10-16 F) ▶ operate guard and electrode by same voltage waveform ⇒ reduce stray capacitance effect▶ collimate electric field line between sensor and target ⇒⇒ capacitance between parallel plates

probe design for capacitance sensors

body guard

CGB

target

CGT

CSGCST

sensor

bodyguard

sensor

Dielectric constant

● dielectric constant, ε ⇒ how easily electromagnetic waves can travel through a medium

ε = f(temp, pressure, humidity, media type)

/C A d

probe design for capacitance sensors

● temperature, humidity ⇒ easy to control● pressure ⇒ difficult to control ⇒ reference gage (against a fixed gap) is used to compensate pressure change● cutting oil, oil shower (affecting ε) should not affect guard can be used ● A (area) ⇒ affecting accuracy▶ depending on temperature (temperature affects machine and sensor)▶ As A/d increases, accuracy, resolution better ▶ A’s surface finish large average effect

small topography effect

3.2.2 Hall effect sensors

● Lorentz's law: charged particle moves in a magnetic field ⇒ force acting ⇒ motion trajectory of the particle changes ⇒ Lorentz force  ● Hall effect: result of Lorentz force acting on electrons flowing through a semiconductor ⇒ potential produced in direction orthogonal to the excitation current and magnetic fieldOutput voltage ∼ order of millivolts ⇒ electronics is necessary to amplify voltage⇒ combination of (Hall element + amplifier electronics) into one: Hall effect transducer

3.2.2 Hall effect sensors

3.2.2 Hall effect sensors

Design Hall effect sensors to be sensitive to magnetic pole (triggering)

V=0

V=VHall

3.2.2 Hall effect sensors

bipolar digital on/off Hall effect sensor  ● combined with transistor⇒ ‘+’ (south pole) maximum trigger pt, ‘-’ (north pole) release pt ● with a magnet, Hall effect sensor produces an analog voltage proportional to the magnetic field strength⇒ distance measuring sensor (voltage is proportional to magnetic strength, and the magnetic strength is related to the distance)

Characteristics

● magnet is needed (attached to the target)- strength changes depending on time ⇒ inadequate to ultra high precision (resolution > 5 m)- other magnets and electric field magnetic strength changes● inexpensive compared with capacitance sensor by 2 orders of magnitude● accuracy depends on the accuracy of power supply (supply voltage to semiconductor: 5V±0.001V)

Typical applications

● unipolar head-on modeone magnet triggers Hall effect sensor (moving parallel to the direction of magnetic field)

G1

G2

D1 D2

S

B

Gau

ss

Typical applications

● unipolar slide-by modeone magnet triggers Hall effect sensor (perpendicular, large motion)

S

B

Typical applications

● bipolar slide-by mode

Have directionality- analog : voltage = f(distance)- digital : trigger, release

Gau

ss

Distance

B

NS

Typical applications

● bipolar slide-by mode

B

NN

S

B

S

S

NN

Typical applications

● Hall effect sensor can be used as a digital on/off proximity sensor

- Monitors position of objects hidden from view as long as the barrier does not block magnetic field lines⇒ sensing through dielectric and nonferrous metals

3.2.3 Inclinometers

● electromechanical levelPrecisely measures small angle of a body (wrt horizontal or vertical reference)

▶ movement data during construction▶ motion of local geologic formation▶ machine platform stability measurement▶ machine orientation, slope measurement 

Types

● precision pendulums are used

● mercury bubble wets a linear resistor (the more device tilts, the more resistor wet and the greater the change in the output voltage)▶ surface tension low resolution▶ inexpensive

inclinometer● inclinometer tilts ⇒ position sensor generates an electric signal (amplified and fed back to galvanometer ⇒ galvanometer produces torque ⇒ mass to original position ⇒ current applied to galvanometer to generate balancing torque is proportional to sinθ(current x resistance = voltage) ● natural frequency depends on (g/l)1/2

3.2.4 Inductive digital on/off proximity sensors

● consists of wire-wound ferrite (iron) core, oscillator, detector, solid-state switch    

● oscillatorproduces (high-frequency) electromagnetic field centered on core

Metal target

Coil and core

Oscillator

Detector

Output

3.2.4 Inductive digital on/off proximity sensors

Target motion

Housing

Ferrite core

Shield

Target motion

Housing

Ferrite core

3.2.4 Inductive digital on/off proximity sensors

● metal object moves inside electromagnetic field ⇒ eddy current inside object ⇒ receives energy from field ⇒ amplitude of oscillation decreases ⇒ if amplitude change > a value, transistor in sensor is triggered on- Object is removed⇒ transistor is back to original state (off) ● sensor response time depends on effective inductance of circuit (L), resistance(R) time delay occurs (analogous to mechanical mkb system)

3.2.4 Inductive digital on/off proximity sensors

● other trigger, release pt ⇒ the difference is embeddied in the sensor- Small sensitive to noise- normally 2∼15% of full-scale range (decided by manufacturer) ● sensor diameter – proportional to allowable standoff distance (larger longer distance) 

head on sensor

● shield to make field in front of sensor sharp⇒ count parts

Targer motion

Housing

Ferrite core

Shield

slide-by sensor

● wide field without shield (oscillating field of sensor recovered after target passes ⇒ should be released before next object triggers)

Targer motion

Housing

Ferrite core

inductive digital on/off proximity sensor

● no magnet (cf, Hall effect sensor) ● metal powder should not be attached● non-contact (cheap)● large standoff distance(∼25mm) is possible● conductive targets are needed● no moving parts ⇒ low failure possibility(replacing mechanical switch)

3.2.5 Inductive distance measuring sensors

Target

referencecoil

active coil

3.2.5 Inductive distance measuring sensors

● apply AC current to reference coil⇒ electromagnetic field occurs⇒ current is inducted in conductor⇒ inductive current generates magnetic field and reduces intensity of original field⇒ changes effective impedance of active coil⇒ impedance change is detected⇒ analog voltage (related to distance between sensor and target) is produced

3.2.5 Inductive distance measuring sensors

● performance depends on material properties- Homogeneous electric properties- Good conductivity, small magnetic permeability (good for aluminum, copper, brass) requiredFerrous metal is not good ⇒ thin target material is plated or bonded (epoxy)

- 0.5mm (gold, silver, copper, aluminum)

- 1.3mm (magnesium, brass, bronze, lead)

Characteristics ● output affected by conductive material - dirt (if nonmetal) has no problem (in optical, big problem)● thickness, diameter measurement, concentricity, 2 axis alignment● range ↑ resolution ↑

Sheet thickness

Orbit tracing and shaft error motions diameter

Shaft and dynamic displacement

ConcentricityTwo axis alignment

Precision measurement

differential mode sensor is used for precision measurement (2 sensors)

● one against fixed object only environmental effect occurs

● difference between outputs of two sensors error compensated

● two sensors should have similar characteristics (environmental effect to be similar)

3.2.6 Inductosyns

● copper sheet on metal plate by insulating adhesive (0.07mm), square wave ● inductive coupling is used between two coils (many overlapping windings used ⇒ error averaging) ● linear Inductosyn is a linear motion transducer having scale and slider

3.2.6 Inductosyns

Slider

Scale

Slider

Two windings 90 out of phase

Scale

scale

● thin STS plate is covered with insulating adhesive

● wire strip is attached onto insulating surface by printed circuit technology⇒ continuous square wave (pitch = 0.1", 0.2", 2mm)

● fixed onto machine axis

slider

● attached onto carriage (table)

● moving above scale surface (0.1mm)(required straightness of slider = 10∼20μm)

Slider output ● scale is excited by 5∼10kHz signal (A sint) ⇒ slider output 

B, X determined from two outputsB: amplitudeX: linear displacementS: waveform period – known

13

24

sin sin(2 / )

sin cos(2 / )

S B t X S

S B t X S

13 24/ tan(2 / )S S X S

● precision, resolution (∼ 0.12 μm) depends on number of waveforms per unit length

● overlapping of many coils in slider, scale averaging effect noise removed, high precision ● coarse/fine position sensing system

- waveform: coarse position information- sine wave interpolation: fine position resolution

Characteristics ● most simple (almost no problem)

● performance is affected only when dirt particle breaks circuit(dirt is fatal in optical sensors)

Tyes of commercial linear Inductosyn

● standard (∼ 250mm)

● tape-type- One end attached to machine element and the other mounted for tension control- Tension adjustment when installed ⇒ precision is fine adjustable

● adjustable InductosynClamp and tension adjusting screw at each 3”, and adjustable independently

rotary Inductosyn ● stator (slider)- Two separated square waveforms (sine track, cosine track are repeated) ⇒ two tracks cover entire stator

● rotor (scale)- square waveform covers entire circumference (overlapping occurs) extremely good random noise reduction (∵averaging effect)- Periodic error does not decrease ⇒ compensated by mapping

rotary Inductosyn ● many sine, cosine waveforms

- averaging effect error reduction- High resolution (0.1 μrad)- high repeatability (0.5 μrad) ⇒ used in precision rotary table

● if too many ⇒ sine, cosine waveforms are crowded ⇒ coupling between two occurs ⇒ resolution↑, accuracy ↓

3.2.7 Linear and rotary variable differential transformers (LVDT,

RVDT) ● electromagnetic induction principle is used- linear motion detection (<10∼20 cm)- rotary motion detection (1 rotation)

Vout

Vreference

3.2.7 Linear and rotary variable differential transformers (LVDT,

RVDT)

core

e1 e2

e1- e2

Linear operating region

X motion

Output (e1- e2)

LVDT components

● armature (or core) – made of ferritic (magnetic) alloy

● stem - nonmagnetic alloy- fix core to object

● transformer- Consists of a primary ac excited coil and 2 secondary coils

LVDT components

● armature moves in coil (noncontact)  ● if primary is excited by AC power⇒ armature position affects output voltages of two secondary coil(one +, the other - ⇒ directionality determined) ● relative distance between two objects ⇒ core fixed on one, and transformer fixed on the other

Characteristics of operation

● non-contact between winding and armature ⇒ no friction, wear, hysteresis ⇒ theoretically infinite life, extremely high reliability

● if core is properly supported, no stick/slip ⇒ theoretically infinite resolution(accuracy, resolution depends on signal conditioning electronics and A/D converter)

● stable AC excitation source is needed

Characteristics of operation

● signal conditioner converts AC voltage in secondary coil to DC

● high output ⇒ simple circuit

● measurement length can be easily increased

● less sensitive to core radial motion

● simple, shock resistant ⇒ theoretically no maintenance is necessary

RVDT

● similar to small electric motor ⇒ generates output voltage varying linearly depending on shaft angle

● rotation is analogous to linear motion in LVDT

● generates output voltage in secondary coil depending on shaft angle

3.2.8 Magnetic scales

● sliding sensing head is used ⇒ detects magnetic field strength from magnetically recorded scale (sine and cosine outputs) ● scale: wire (many north, south pole pairs)  wire imprinted scale

sliding sensing head

N S S N N S

3.2.8 Magnetic scales

                                     

3.2.8 Magnetic scales

● merit (compared with optical sensors) – less affected by dirt, fluid contamination ● incremental⇒ slide produces two waves ⇒ electronics interprets moving distance and produces digital signal ● magnitude scale: thin wire ⇒ scale minor misalignment (0.1mm wrt moving axis) causes measurement error, irrelevant to wear

3.2.9 Magnetostrictive sensors

● "magnetostriction" - length change of ferromagnetic material in magnetic field- magnetization change under mechanical stress

● non-contact torsion sensormeasures torsional stress of a rotating shaft ⇒ power measurement (to prevent excessive stress in rotating shaft)

● strain gage was used (attached on shaft)(expensive, electric noise, unreliable due to wear)

Villari effect

● magnetic field change in the direction of mechanical strain (shaft twiated ⇒ strain in 45°) ● several Villari differential torque transformers along circumference ⇒ torsional stress can be precisly measured ● initial calibration is necessary (ferrous material behaves differently under similar conditions) ● sensor mounted close to the shaft ⇒ large output signal (∼ mV)

Villari effect

Guillemen effect

● magnetic material is in magnetic field size changes ● diameter of a long small rod changes locally

v

L

2L=vt

Guillemen effect

⇒ diameter change stress wave reflecting point

⇒ ultrasonic transducer sends stress wave and measures time (wave reflected)

⇒ time is related to distance (magnetic field and ultrasonic transducer)

3.2.11 Piezo material bonded sensors

● force is applied to crystalline structure oscillation ⇒ high-energy electrons emits (current flow) ⇒ stress is predicted by measuring current ● examples) accelerometer, precision loadcell, ultrasnic transducer

piezoelectric accelerometer

● speed control, vibration sensing, position measurement

● resolution (1 μg)

● frequency response ∼ 100 kHz (good response)

● small size

precision load cells

● thin film crystalline piezo material is used ⇒ measures nanostrains

● more sensitive than metal strain gage (2∼3 orders of magnitude)

● load range limit (maximum strain level ~ μ strain)

ultrasonic piezoelectric sensors

● piezoelectric, magnetostrictive and electrostatic are possible

● stress wave generating/receiving sends pressure wave and receives echo pulse measure time determines distance to impurities or shape change

3.2.12 Potentiometers

● change in electric resistance resulting from change in physical process ⇒ definition of “potentiometer” ● consists of coil or high-resistance film and wiper (used mostly)

3.2.12 Potentiometers

● wiper position target motion

● DC voltage is applied to entire length of coil ⇒ wiper picks off intermediate voltage (variable resistance) ⇒ determine wiper position ● plastic film (large resistance)Film is continuous, potentiometers are analog devices ⇒submicron resolution is possible, but relies on DC power supply and D/A converter

potentiometer

● most expensive

● high output voltage (no amplification necessary)

● mechanical contact between wiper and film ⇒ contaminated by dust or oil ⇒ resistance change, error ⇒ preventing contamination by using various seals

● friction and wear exist

● very small overhead compared with size

3.2.13 Synchros and resolvers

● electromagnetic induction ⇒ (rotary) transformer (between 1st and 2nd coil)

● used in shaft positioning

● can measure infinite revolutions

Characteristics

● high precision, inexpensive, insensitive to contamination (compared with potentiometer or optical sensor)

● disadvantage: analog device (∵ mostly used with digital control system)

synchro

● variable transformer (output voltage is varying):The magnitude of the electromagnetic coupling between primary and secondary coils (which determines output voltage) varies with the relative angular position of the coils ● 2 modes- control synchro: electric signal depending on shaft rotation- torque synchro: shaft rotation depending on electric signal

control synchro

● transmitters, differentials, controltransformers, receivers

● used in servo control axes

torque synchro

● transmitters, differentials, receivers

● dial of instrument is rotated by transferring rotating angle from transmitter

synchro applications

● long distance transmission from transmitter to receiver (up to 4km)

● used in remote devices

ex) remote steering in ships, opening/closing water gates in a power plant

transmitters and receivers

● single-phase rotorpower supply via a slip ring (brush)● three-phase stator (electromagnetically coupled with rotor )● rotor winding is excited by AC (60∼400Hz) ⇒ voltage is inducted in stator winding (proportional to cone of angle between rotor coil and stator coil)

rotor

statorS1

S2

S3

R1

R2

transmitters and receivers

● accuracy, repeatability and linearity depends on winding quality● exciting voltage at the rotor

2 1

2 1

2 1

2 1

1 3

2 1

3 2

max

sin

sin

sin( / 3)

sin( / 3)

/out

rotor o

rotor

rotor

rotor

in

V V t

V kV

V kV

V kV

k V V

transmitters and receivers

● transmitter sends information

● receiver receives information- analog signal- converted to digital signal ⇒ information decoding device

synchro-to-digital converter (SDC)

torque synchro

● torque transmitter and receiver are the same● angle information is transferred electrically (not mechanically)● a gage dial is rotated by the angle

Vin

S2

S1

S3

S2

S1

S3R1

R2

R1

R2

CG CR

control synchro

● control transmitter, control transformer, control differential transmitter are used ⇒ signals are combined electrically and amplified ⇒ rotates motor(because of being amplified, control transmitter winding does not have to be as good as torque synchro)

● synchro performance- positioning accuracy: ±10 arcminutes- Maximum torque: 3 g-mm per receiver angle

differential

● used with transmitter and receiver● three-phase stator, three-phase rotor● via slip rings (brushes) current is transferred to rotor winding

rotorstator

S2

S3 R1

R2

S1 R3

control transformer

● stator, rotor coil structures are the same as in transmitter

● transmitter sends position information through 3 wires to control transformer transformed to voltage and amplified to drive the motor

● angle of motor axis is mechanically coupled to angular motion of the control transformer

● if the angles of motor and transmitter are different the shaft rotates because voltage is applied

control transformer

Vin

S2

S1

S3

S2

S1

S3R1

R2

R1

R2

CG CR motorAmp

resolver

● special form of synchro● better accuracy, resolution than synchro● resolver transmitter: ends of rotor windings connected ⇒ one frequency excitation is needed

rotor

R1

R2

S2

S1

S4

S3

resolver

● windings added ⇒ resolution ↑

13

24

13

24

sin

sin sin

sin cos

tan

V A t

S kA t

S kA t

S

S

synchro, resolver-to-digital converters

● device to transform signal to digital (in order to be used in digital control) ● SDC, RDC 16 bit resolution ⇒ total rangeis divided into 216

⇒ resolution = total range/216

3.2.14 ultrasonic sensors

● stress wave generating/ receiving ⇒ pressure wave to medium ⇒ measures amplitude and return time of the echo

Time is related to the distance to impurities or shape change in material ● piezoelectric transducers

- used in NDT (∼100 kHz) - measurement of thickness and surface

roughness (resolution: 10 to 12 bits)

3.2.14 ultrasonic sensors

● magnetostriction transducers ● electrostatic transducers- Use metal film, metallic backing dish- oscillating applied to film ⇒ inductive current in dish due to electric field ⇒ current in field generates force ⇒ attracting and pusjing forces between dish and metalized film act repeatedly ⇒ ultrasonic wave occurs

- dish, film are small mass ⇒ fast response

- high frequency used ⇒ high precision, high resolution in small range

3.2.15 Velocity sensors

● velocity feedback is needed for position, velocity control ● position signal differentiated ⇒ noise spikes● relative motion between magnet and (moving) coil induces voltage- Proportional to relative velocity between coil and magnet and rate of magnetic flux change (due to moving magnet)

Linear velocity transducers (LVT)

● measures linear velocity

● similar to LVDT, but does not use excitation voltage ● uses two coils ⇒ voltage difference represents speed, and sign of voltage represents direction

Linear velocity transducers (LVT)

● modeled as pure inductance, resistor ⇒ behaves as 1st order system

= 2 L/R (time constant: ~0.001 sec) ● speed ↑ ⇒ time lag ↓⇒ linearity ↓

N S

V1 V2

Tachometer

● velocity transducer

● types: - permanent magnet stator dc tachometers- drag-torque tachometers- capacitor tachometers- digital tachometers- dc brushless tachometers

permanent-magnet stator dc tachometers

● consists of rotor winding, commutator assembly● armature (rotor winding) rotates ⇒ windings passes stator magnetic field ⇒ voltage is induced in windings proportional to rotational speed● reverse of dc motor● voltage is transferred by brush, slip-ring● number of armature coils is discrete ⇒ ripple occurs ⇒To reduce ripple, filtering techniques and many coils are used● other error source: commutator interface contamination, temperature change, magnetic field

permanent-magnet stator dc tachometers

                                        

brushless tachometers

● magnetic rotor, wound stator ⇒ rotor and stator in brushed tachometer are switched

● no problem of brush wear

● to produce homogeneous DC signal proportional to speed, switching to other windings is required ⇒ expensive, complicated, noise reduction, no brush wear