7/27/2019 CH8_1.PDF

1/20

- 1 -

8. SENSORS

8.2. POSITION AND SPEED MEASUREMENT

(1) Proximity Sensors and Switches

Magnetic, electrical capacitance, inductance, and eddy current methods are used.

Photoemitter-detector pair: interruption or reflection of a light beam is used to detect an

object in a noncontact manner as illustrated in Fig. 8.1.

Applications of proximity sensors and limit switches: counting moving objects (e.g., cans

on a convey belt), and limiting the traverse of a mechanism.

Switches are characterized by the number of poles (P) and throws (T) and whether

connections are normally open (NO) or normally closed (NC).

7/27/2019 CH8_1.PDF

2/20

- 2 -

(2) Potentiometer

Variable resistance device (a wiper makes contact with a resistive element, and as the

contact point moves, the resistance between the wiper and end leads of the device changes).

Through voltage division, the change in resistance can be used to create an output voltage

that is proportional to the input displacement.

(3) Linear Variable Differential Transformer (LVDT)

Operation Thoery

Transducer for measuring linear displacements.

It consists of primary and secondary windings and a movable iron core.

As with any transformer, the voltage of the induced signal in the secondary coil is linearly

related to the number of coils, i.e.,in

out

in

out

N

N

V

V= .

As the core is displaced, the number of coils in the secondary coil changes linearly.

Therefore the amplitude of the induced signal varies linearly with displacement.

7/27/2019 CH8_1.PDF

3/20

- 3 -

With two secondary coils connected in series-opposing configurations, the output signal

includes both the magnitude and direction of the core motion.

At the null position (midpoint in the cores position), the voltage induced in each coil will

be of the same amplitude and 180o

out of phase, producing a null output.

As the core moves from the null position, the output amplitude will increase a proportional

amount over a linear range around null.

Demodulation and Low-pass filter

The diode bridges in this circuit produce a positive or negative rectified sine wave

depending on what side of the null position the core is on.

7/27/2019 CH8_1.PDF

4/20

- 4 -

A low-pass filter is used to convert the rectified output into a smoothed signal. The cutoff

frequency of the low-pass filter should be higher than that of the core motion (at least 10

times the maximum expected frequency of the core motion).

Characteristics

Advantages: accuracy over the linear range, an analog output that may not require

amplification, and insensitivity to wide ranges in temperature.

Disadvantages: limited range of motion and limited frequency response.

(4) Digital Optical Encoder

Encoders have both linear and rotary configurations.

The absolute encoder where a unique digital word corresponds to each rotational position

of the shaft, and the incremental encoder, which produces digital pulses as the shaft rotates,

allowing measurement of relative position of shaft.

Rotary encoders are composed of a glass or plastic code disk and photoemitter-detector

pairs. As redial lines in each track interrupt the beam between a photoemitter-detector pair,

digital pulses are produced.

7/27/2019 CH8_1.PDF

5/20

- 5 -

Absolute Encoder

Producing a digital word that distinguishes Ndistrict positions of the shaft. For example, if

there are 8 tracks, the encoder is capable of producing 28=256 district positions or angular

resolution of 1.406o

(360o/256).

Gray and binary codes for numerical encoding of the absolute encoder.

[4-bit Gray code] [4-bit Binary code]

For the gray code, the uncertainty during a transition is only one count, unlike with the

binary code, where the uncertainty could be multiple counts.

The gray code provides data with the least uncertainty, but the binary code is the preferred

choice for direct interface to computers.

7/27/2019 CH8_1.PDF

6/20

- 6 -

A simple circuit to convert from gray to binary code (binary bit (iB ), gray bit ( iG ), and

is the exclusive OR gate):

01012123233 ,,, GBBGBBGBBGB ====

Incremental Encoder

It consists of two tracks and two sensors whose outputs are called channels A and B.

The A and B channels are used to determine the direction of rotation by assessing which

channel leads the other. The signals from the two channels are a 1/4 out of phase with

each other and are known as quadrature signals.

7/27/2019 CH8_1.PDF

7/20

- 7 -

The third channel, called INDEX, yields one pulse per revolution, which is useful in

counting full revolution. It also useful as a reference to define a home base or zero position.

There are two separate tracks for the A and B channels, but a more common configuration

uses a single track with the A and B sensors offset a 1/4 cycle on the track to yield the same

signal pattern.

Decoder circuits: A= with B=1 implies a CW pulse, and B= with A=1 implies a CCW

pulse, in the 1X mode. The D flip-flops decode whether the shaft is rotating CW or CCW,

and this information is used to drive an up-down counter to keep the current pulse count.

An incremental encoder can be used in conjunction with a limit switch to define absolute

position relative to some home position defined by the switch.

7/27/2019 CH8_1.PDF

8/20

- 8 -

8.3. STRESS AND STRAIN MEASUREMENT

- Stress, force, pressure and temperature can be determined from strain measurements, i.e.,

the electrical resistance strain gage.

(1) Electrical Resistance Strain Gage

The metal foil strain gage illustrated in Fig. 8.17 consists of a thin foil of metal (usually

constantan) and etched in a grid pattern onto a thin plastic backing material (usually

polyimide). The foil pattern is terminated at both ends with large metallic pads for allowing

leadwires to be attached with solder. The size of gage is typically 5mm to 15 mm long.

The gage is adhesively bonded directly to the surface of a mechanical component, usually

with epoxy.

Fig. 8.17 Metal foil gage.

When the component is loaded, the resistance of the metal foil changes, and if this

resistance change is measured accurately, the strain on the surface of the component can be

determined in the following ways:

The metal foil grid lines in the active portion of the gage can be approximated by a single

rectangular conductor. The total resistance is given by

A

LR

=

where is the foil metal resistivity, L is the total length of the grid lines, and A is the

cross-sectional area.

To see how the resistance changes under deformation, we need to take the differential of

the above equation.

ALR lnlnlnln += AdALdLdRdR //// += (Eq. 8.4)

7/27/2019 CH8_1.PDF

9/20

- 9 -

The resistance increase ( 0>dR ) with increased resistivity and increased length, and

decreases with increased cross-sectional area.

The cross-sectional area and the area differential are

whA = w

dw

h

dh

hw

dwhdhw

A

dA+=

+=

From the Poissons Ratio (see Appendix 2),

L

dL

h

dh= and

L

dL

w

dw= axial

L

dL

A

dA 22 ==

where axial is the axial strain. When the conductor is elongated ( 0>axial ), the cross-

sectional area decreases ( 0/

7/27/2019 CH8_1.PDF

10/20

- 10 -

(2) Measuring Resistance Changes with a Wheatstone Bridge

- It consists of a four-resistor network excited by a dc voltage, in order to measure small

changes in resistance.

Static Balanced Mode

2R and 3R are precision resistors, 4R is a precision potentiometer with an accuratescale for displaying the resistance value, and

1R is the strain gage resistance.

To balance the bridge, the variable resistor is adjusted until the voltage between nodes A

and B is zero.

In the balanced state, the voltages at A and B must be equal so

2211 RiRi = (Eq. 8.14)

With the high-input impedance voltmeter,

41

41RR

Vii ex

+== , and

32

32RR

Vii ex

+== .

Substituting these expressions into Eq. 8.14 gives

3

2

4

1

R

R

R

R= .

So, we can calculate the unknown resistance 1R as (the result is independent of exV )

3

241

R

RRR =

Dynamic Deflection Mode

The changes in the strain gage resistance 1R that occur when the mechanical component

is loaded can be determined from changes in the output voltage.

The output voltage is expressed in terms of the resistor currents as

324122110RiRiRiRiV +==

7/27/2019 CH8_1.PDF

11/20

- 11 -

The excitation voltage can be related to the same current as

)()(322411

RRiRRiVex

+=+=

Eliminating the currents from these equations results in

++= 322

41

10RR

R

RR

RVV ex

When the bridge is balanced,0V is zero and 1R has a known value. When 1R changes

value, the voltage change0

V can be related to the change in resistance1

R . To find

this relation, we can replace 1R by 11 RR + and 0V by 0V .

+

++

+=

32

2

411

110

RR

R

RRR

RR

V

V

ex

1

132

20

32

20

1

4

1

1

+

++

=

RR

R

V

V

RR

R

V

V

R

R

R

R

ex

ex

By measuring the change in the output voltage 0V , we can determine the gage resistance

change 1R .

Leadwire Effects

When using a strain gage located far from the bridge circuit, each of the leadwire

resistances R add to the resistance of the strain gage. The problem is that if the leadwire

temperature changes, it will cause changes in the resistance of the bridge.

As shown in Fig. 8.22b, a 3-wire connection can solve this problem. Equal resistances are

added to adjacent branches in the bridge so the effects of changes in the leadwire

resistances offset each other.

7/27/2019 CH8_1.PDF

12/20

- 12 -

Fig. 8.22 Leadwire effects in 1/4 bridge circuit.

Temperature Compensation

In addition to temperature effects in leadwires, temperature changes in the actual strain

gage can cause significant changes in resistance.

A method for eliminating this effect is to use a 1/2 bridge circuit where two of the four

bridge legs contain strain gages.

7/27/2019 CH8_1.PDF

13/20

- 13 -

(3) Measuring Different States of Stress with Strain Gages

Uniaxial Stress (1 strain gage)

When a component is loaded only in one direction in tension and compression.

By measuring the strain x , the stress is known from Hooks Law to be

xx E = . The axial stress in the bar

x is given by

A

Px=

where A is the bars cross-sectional area.

The force P can be determined from the strain gage measurement:

xAEP =

Biaxial Stress (2 strain gages)

7/27/2019 CH8_1.PDF

14/20

- 14 -

When a component is loaded in two orthogonal direction in tension or compression.

By measuring the strainsx and y , the stresses in the tank shell can be determined by

EE

yx

x

= and

EE

xy

y

=

Solving for the stress components gives

)(1 2

yxx

E

+

= and )(

1 2xyy

E

+

= .

For a thin-walled pressure vessel (i.e., t/r < 1/10), the stresses are given by

t

prx= and

t

pry

2= .

The pressure of vessel can be calculated by

)()1(2 yx

x

r

tE

r

tp

+== or )()1(

222 xy

y

r

tE

r

t

p

+== .

General Planar Stress (3 strain gages)

For uniaxial and biaxial loading, we already know the directions of principal stresses.

However, when the loading is more complex or when the geometry is more complex, we

have to use three gages in three different directions.

An assembly of strain gages is referred to as astrain gage rosette.

7/27/2019 CH8_1.PDF

15/20

- 15 -

(4) Force Measurement with Load Cells

A load cell is a sensor used to measure a force. It contains an internal flexural element,

usually with several gages mounted to its surface. The flexural elements shape is designed

so that the strain gage outputs can be related to the applied force.

A typical connection is that

Strain gage (or load cell) Amplifier Low-pass filter A/D Converter.

7/27/2019 CH8_1.PDF

16/20

- 16 -

8.4. TEMPERATURE MEASUREMENT

(1) Liquid-in-Glass Thermometer

(2) Bimetallic Strip

It is composed of two or more metal layers having different coefficients of thermal

expansion. So, the deflection is related to the temperature of the strip.

It is used in household thermostats where the mechanical motion of the strip makes or

breaks an electrical contact to turn a heating or cooling system on or off.

(3) Electrical resistance Thermometer

Resistance Temperature Device (RTD)

It is constructed of metallic wire wound around a ceramic or glass core and hermetically

sealed.

The resistance-temperature relationship is approximated by

)](1[ 00 TTRR += .

The most common metal used in RTDs is platinum, and the operating range for a typical

platinum RTD is 220oC to 750

oC.

Thermistor

It is a semiconductor device whose resistance changes exponentially with temperature

given by

=)

11(

00TTeRR

The accuracy of thermistors is better than that of RTDs, but thermistors have much

narrower operating ranges than RTDs.

7/27/2019 CH8_1.PDF

17/20

- 17 -

(4) Thermocouple

Two dissimilar metals in contact form a thermoelectric junction that produces a voltage

proportional to the temperature of the junction known as the Seebeck effect.

The wires of metals A and B form junctions at different temperatures1

T and2

T , resulting

in a potential V that can be measured. The thermocouple voltage V depends on the

metal properties of A and B and the difference between the junction temperatures1T and

2T given by

)(21 TTV = where is called the Seebeck coefficient.

A standard configuration is shown in Fig. 8.40. The reference junction is used to establish a

temperature reference.

7/27/2019 CH8_1.PDF

18/20

- 18 -

8.5. VIBRATION AND ACCELERATION MEASUREMENT

Accelerometer

It detects acceleration along one axis and is insensitive in orthogonal directions.

As a position transducer, strain gages or piezoelectric elements converting vibration into a

voltage signal are used.

Through the frequency response analysis, we can relate the displacement transducer output

to acceleration of the object.

The relative displacementrx between the seismic mass ( 0x ) and the object ( ix ) is

defined asirxxx = 0 .

The equation of the motion for the seismic mass is

0xmFF bk &&= 0xmxbkx rr &&& = )( irrr xxmxbkx &&&&& +=

irrrxmkxxbxm &&&&& =++

whererik

kxxxkF == )(0

,ribxbxxbF &&& == )(

0and

irxxx &&&&&& +=

0.

Referring to the analysis of a second order system in Chapter 4, the amplitude ratio and

phase angle can be obtained as

2/12

2

22

2

41

)/(

+

=

nn

n

i

r

X

X

and

=

2

1

1

2

tan

n

n

where the input and output displacements are )sin()( tXtxii

= and

)sin()( += tXtx rr .

7/27/2019 CH8_1.PDF

19/20

- 19 -

To relate the output displacement signal rx to the input acceleration ix&& , differentiate the

displacements:

)sin()( 2 tXtx ii =&& and )sin()(2 += tXtx rr&&

Rearranging the amplitude ratio with the amplitudes of the input and output acceleration

gives

2/12

2

22

2

2

41

1)(

+

==

nn

i

nra

X

XH

.

If we design the accelerometer so that )(aH is nearly 1 over a large frequency range,

then the input acceleration amplitude is given directly in terms of the relative displacement

amplitude scaled by a constant factor 2n :

rni XX )(amplitude,onAccelerati22 =

The largest frequency range resulting in a unity amplitude ratio occurs when the damping

ratio is 0.707 and when the natural frequency n is as small as possible. We can

make the natural frequency, mkn /= , large by choosing a small seismic mass and a

large spring constant.

Vibrometer

Instead of measuring acceleration, this device measures displacement.

The displacement ratio can be defined asi

rd

X

XH =)( . The input displacement amplitude

iX is related to the measured relative displacement amplitude rX as

r

d

ri X

H

XX =

)(

where )(dH is nearly 1 over a large frequency range.

As seen in Fig. 8.47, the largest frequency range resulting in a unity amplitude ratio occurs

when the damping ratio is 0.707 and when the natural frequency n is as small as

possible.

We can make the natural frequency small by choosing a large seismic mass and a small

spring constant. This explains the large size of seismographs used to measure the earths

displacement during an earthquake.

7/27/2019 CH8_1.PDF

20/20

- 20 -

Piezoelectric Accelerometers

As a displacement sensor, high quality accelerometers use a piezoelectric crystal, a

material whose deformation results in charge polarization across the crystal. In a reciprocal

manner, application of an electric filed to a piezoelectric material results in deformation.

An equivalent circuit for a piezoelectric crystal is shown in the following figure. The

crystal is effectively a capacitor and a charge source Q generating charge across the

capacitor plates proportional to the deformation of the crystal. By a Thevinin equivalent

circuit, the open circuit voltage V is equal to the charge (typically in pico-coulomb)

divided by the capacitance (typically in the pico-farad range):

pC

QV =

The sensitivity of the accelerometer is the ratio of the charge output to the acceleration of

the housing expressed in pC/g, (rms pC)/(rms g), or (peak pC)/(peak g), where g is the

gravity acceleration.

(read Ch 8.6 and 8.7)