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ME 515 Mechatronics 12/12/2006

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ME 515 Mechatronics

Introduction to Sensors IAsanga Ratnaweera

Department of Mechanical EngineeringFaculty of Engineering

University of PeradeniyaTel: 081239 (3627)

Email: [email protected]

12 December 2006 Asanga Ratnaweera, Department of Mechanical Engineering

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Overview of Computer based Control System


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Sensors and TransducersA sensor is an element in a mechatronic or measurement system that acquires a physical parameter and changes it into a signal that can be processed by the systemActive element of a sensor is referred to as a transducer


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Sensors: ClassificationSignal Characteristics

Analogue or Digital

Power supply Active or passive

Method of operationResistive, Capacitive or Inductive, piezoelectric

Subject of Measurement Acoustic, Biological, Chemical, Electrical, Mechanical, Optical, Thermal, Other


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Sensors : Types

Temperature sensorsPressure sensorsStrain sensors (Strain gauges)Piezoelectric sensorsPosition sensorsProximity sensorsVelocity sensorsLight sensors


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Physical Sensors

TemperatureThermistors

TemperatureThermocoupleThermal

AccelerationAccelerometer

VelocityVelocimeterKinematic

DisplacementEncoderDisplacementPotentiometerDisplacementLVDTStrainStrain Gauge

Geometry

Force/TorqueLoad cellForce-TorqueFlow rateFlow meter

PressurePressure transducerFluid

VariableSensorPhysical Quantity


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Sensor Performance CharacteristicsTransfer Function:

The functional relationship between physical input signal and electrical output signal.For sensors which are individually calibrated, this might take the form of the certified calibration curve.

InputO

utput(usually an electrical signal)


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Sensor Performance Characteristics

Span or Dynamic Range: The range of input physical signals which may be converted to electrical signals by the sensor.

Signals outside of this range are expected to cause unacceptably large inaccuracy.

Span is the difference between the max. and the min. values of the input. EX:

sensor measures force might have a range of 0-50 kN and a span of 50 kN


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ErrorThe discrepancy between the instrument reading and the true value is called error.

Absolute error = measured value - actual valueRelative error = absolute error / true value

Hysteresis ErrorTransducers can give different outputs from the same value of quantity being measured according to whether that value has been reached by a continuously increasing change or a continuously decreasing change.


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Non-Linearity ErrorFor many transducers a linear relation-ship between the input and output is assumed over the working range. Few transducers, however, have a truly non-linear relationship and thus errors occur as a result of the assumption of linearity. Various methods are used for the numerical expression of the non-linearity error

End-range valuesBest straight line for all valuesBest straight line through zero point


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Non-Linearity Error

Best straight line through zero point

Best straight line for all values

End-range values


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Non-linearity

Maximum non-linearity

OIDEAL (I)

O(I)


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SensitivityThe sensitivity K is defined as the rate of change of the output (O) with respect to the input (I).

For a linear sensor:

For a non-linear sensor

Ex: Thermometer would have "high sensitivity" if a small temperature change resulted in a large voltage change.


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Environmental effectsEnvironmental effects can lead to variations in the degree of non-linearity, the sensitivity and the offsets


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Sensor Performance CharacteristicsResolution

Resolution is defined as the largest change in I that can occur without a corresponding change in O:

R =

In most applications, we want the best possible resolution (ie. the finest) without paying too much for it.


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StabilityThe stability of a transducer is its ability to give the same output when used to measure a constant input over a period of time. The term drift is often used to describe the change in output that occurs over time. The drift may be expressed as a percentage of the full range output.


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Error bandsIt is often impractical to separate and determine non-linearity, resolution and other such effects in these cases, non-ideal performance is classified by one broad term: the error band

Accuracy: Generally defined as the largest expected error between actual and ideal output signals.


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Dead-bandThe dead-band or dead space of a transducer is the range of input values for which there is no output. The dead time is the length of time from the application of an input until the output begins to respond and change.

NoiseAll sensors produce some output noise in addition to the output signal. The noise of the sensor limits the performance of the system based on the sensor.


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Resistive sensorsThere are number of ways in which resistance can be changed by a physical phenomenon.At a constant temperature, the resistance of a conductor can be expressed as;

AlR ρ

=

ρ – Resistivity, ΩmR – Resistance, Ωl – Length, mA – Cross section area, m2


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Resistive sensorsOutput voltage is proportional to the change in resistance of the sensor.

Obey the Ohms law: V =IR

PotentiometersStrain gauge

Ex:


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Inductive sensorsThe basic principle of operation of inductive sensors is based on Faraday’s law of induction in a coil.

Inductance (L) of a circuit is defined as the total flux linkage per unit current

dtdiLVvoltgeOutput =

iNL φ

=RNi

=φR – Reluctance of the flux pathN – Number of turns of the coilΦ – magnetic flux

RN

RNi

iNL

2

=⎟⎠⎞

⎜⎝⎛=


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Inductive sensorsReluctance is expressed as

Therefore inductance can be expressed as:

AlRµ

=Where,µ – Effective permeability of the medium in and around the coill – Length of the coil, mA – Cross sectional area of the coil, m2

lANL µ2=


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Inductive sensorsThe inductance change can be caused by any of the following :

Variation in Area or/and length of the coilChange in the effective permeability of the medium in and around the coilChange in reluctance of the magnetic path or variation in air gapChange in mutual inductance (by changing the coupling between coils 1 and 2 with siding or opposing field.

Ex:


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Capacitive SensorsIn capacitive sensors, the measurement of physical phenomena is made based on the variation in capacitance between two separate members or electrodes.

The capacitance C:

q= CVdtdVCI =

dA

Cεε 0=

εo- Permittivity of free space (=8.85pF/m);ε - Relative PermittivityA - overlapping area of plates (m2)d - Plate separation (m)


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Capacitive SensorsA change in capacitance can be brought about by varying any one of the three parameters listed below.

Changing distance between two parallel electrodes

Distance, d

Cap

acita

nce,

C

d

dA

Cεε 0=


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Capacitive SensorsChanging the dielectric constant, permittivity of dielectric medium ε

Ex:

dA

Cεε 0= A linear relationship


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Capacitive SensorsChanging the area of the electrodes A

Ex:

A linear relationship


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Piezoelectric sensorsA piezoelectric material produces voltage by redistributing charge when mechanical strain/stress is applied.

Strain causes a redistribution of charges and results in a net electric dipole (a dipole is kind of a battery!)


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Piezoelectric sensorsSome piezoelectric materials are;

Quartz Crystal (SiO2) - Most commonly used materialRochelle saltPZT (lead zirconium titanate)PVDF (polyvinylidene fluoride)BaTiO3 (barium titanate)LS (lithium sulfate)

Ex: Quartz Crystal

Si

O2F F F F

- +

-


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The Piezoelectric EffectCrystal material at rest: No forces applied,

so net current flow is 0

Crystal

Current Meter= 0

+ - + - + -

+ - + - + -Charges canceleach other, sono current flow


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The Piezoelectric EffectCrystal material with forces applied in direction of arrows

Crystal

Current Meterdeflects in + direction

- - - - -

+ + + + +Due to properties of symmetry,charges are net + on one side & net - on the opposite side: crystal getsthinner and longer

Force


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The Piezoelectric EffectChanging the direction of the applied force………..

Crystal

Current Meterdeflects in -direction

+ + + +

- - - - -…. Changes the direction of current flow, and the crystal getsshorter and fatter.

Force


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Piezoelectric sensorsThe Charge Generation

dFQ =

F

F

Conductive surface

Piezoelectric material

Voltage

badFQ =

Longitudinal effect Transverse effect F

Voltage

b

a

F

d – piezoelectric coefficient


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Piezoelectric sensorsThe piezoelectric coefficient , d, also known as charge sensitivity factor is a constant for a given piezoelectric martial. If the ratio a/b is greater than 1, the transverse effect produces more charge than the longitudinal effect.If the thickness of the crystal is t and change in thickness due to the force F is ∆t, the stress strain relationship (Young’s Modulus) is:

tAFt

ttA

F

StrainStressE

∆∆===

A - area of the crystal


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Piezoelectric sensorsTherefore, the force F,

tt

AEF ∆=

The capacitance of the piezoelectric material

tAC r0εε=

However,

dFQ =For Longitudinal effect

Therefore,

tt

AEdQ ∆=F

Adt

CQV

orεε==

Therefore, the voltage V

εo- Permittivity of free space (=8.85pF/m);εr - Relative Permittivity of the piezo. material

CVQ =

However, Charge Q


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Piezoelectric sensorsTherefore the voltage V,

gtPFAtgV ==

Where,

or

dgεε

= is crystal voltage sensitivity factor

P – Pressure or the stress


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Piezoelectric sensorsBasic characteristics of Piezoelectric material

20 -300.3121.78PVDF

1108.312007.5PZT

781117005.7Barium Titanate(BaTiO3)

2.37.74.52.65Quartz (SiO2)

Piezoelectric charge sensitivity (d) pF/N

Young’s Modulus (E), 1010 N/m2

Permittivity(εr)

Density (ρ)103 kg/m3

Material

or

dgεε

=The crystal voltage sensitivity factor can be calculated using


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Sensors: position and speed measurementTranslational and Rotational Potentiometers

Translational or angular displacement is proportional to resistance.


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Position sensor: Potentiometer

Translational Potentiometers

iRVVV =+= 21

11 iRV = 22 iRV =

1RRVVout =

VxVout =

21 RRR +=

RxR =1 )1(2 xRR −=

V2

= V1


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Position sensor: Potentiometer

Rotational Potentiometers

iio vv φ=


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Position sensor: PotentiometerEffect of loading

This is a non-linear function of x with the degree of non-linearity dependent on the ratio .

⎥⎦

⎤⎢⎣

⎡+−

=1)1( xx

RR

VxV

L

OUT

LRR


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Position sensor: PotentiometerThus, we desire RL>>R in order to achieve a linear response from the potentiometer we should therefore measure the output voltage Voutusing apparatus of high input impedance. Devices with this characteristic often use ‘buffers’, one form of which can be made using ‘operational amplifiers (op-amps)’.Some of the disadvantages of potentiometer sensors are its slow dynamic performance, low resolution and susceptibility to vibration and noise.


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Position sensor: Linear Variable Differential Transformer (LVDT)An Inductive Sensor

lANL µ2=

µ – Effective permeability of the medium in and around the coil


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Position sensor: Linear Variable Differential Transformer (LVDT)

An inductor is basically a coil of wire over a “core” (usually ferrous)

It responds to electric or magnetic fields

A transformer is made of at least two coils wound over the core: one is primary and another is secondary

Primary Secondary Displacement Sensor

Inductors and transformers work only for ac signals


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Position sensor: Linear Variable Differential Transformer (LVDT)Basic features

High resolutionHigh accuracyGood stability

Therefore, ideal for applications involving short displacement measurements.


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Position/Velocity sensor: Digital Sensors

Optical encoders are widely used in applications involving measurement of linear or angular position, velocity and direction of movement.

Ex: rotary optical encoders.


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Position/Velocity sensor : Optical Encoders

Optical encoders are usually used to measure rotational movement precisely. The major advantages of these sensors are simplicity, high accuracy, suitability for sensitive applications.

There are two types of optical encoders: absolute and incremental.


48Ideal

Relative position mask/diffuser

grating

light emitter

light sensor

decode circuitry

Real

Position/Velocity sensor : Optical Encoders


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Position/Velocity sensor : Incremental Encoders

Incremental encoders provide a simple pulse each time the object to be measured has moved a given distance.

These encoders are usually used for counting applications

There are two types of incremental encoders: tachometer type

quadrature type.


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Tachometer type Incremental encodersThe tachometer type encoders used for relative position velocity measurement, and have one output channel. The velocity measurement is done by looking at the pulses during a certain time interval.

Direction of rotation cannot be measured

output

Resolution = 360/ no. of slots


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Quadrature type.Have dual channels A and B The output waveform is arranged in such a way that channel A is 90 degrees out of phase with channel B. By utilizing quadraturedetection and decoding output signals, one can obtain precise direction, distance and velocity information.


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Position/Velocity sensor : Absolute Encoder

An absolute encoder provides a unique binary word coded to represent a given position of an object.

Wheel with 4 tracks

Resolution = 360/24 = 22.50


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Position/Velocity sensor : Optical Encoders disc

Incremental encoder discAbsolute encoder disc

Wheel with 8 tracks

Resolution = 360/28 = 1.410

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