instrumentation

Kheirallah, S. M. 1

INSTRUMENTATION AND MEASUREMENTS

Course Lectures For Mech. Eng. Students

Kheirallah, S. M.

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Kheirallah, S. M. 2

INSTRUMENTATION AND MEASUREMENTS

REFERENCES Doebelin, “Measurement System:

Design and application”; Patranabis, D., “Principles of

Industrial Instrumentation”, Beckwith, T. & Buck, N. L.,

“Mechanical measurements”,

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Kheirallah, S. M. 3

Course Contents Introduction to Instrumentation; Static Performance Characteristics; Dynamic Performance Characteristics; Calibration and Evaluation of Instruments; Transducers and Intermediate Elements of

Instruments; Motion Measurements; Force, Torque and Power Measurements; Pressure measurements; Temperature Measurements; Flow Measurements; Miscellaneous Measurements;

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Kheirallah, S. M. 4

INTRODUCTION TO INSTRUMENTATION • GENERAL CONCEPTS

- MEASUREMENT – is the comparison or determination or controlling of physical variable quantity or values;

- MEASUREMENT METHODS

1. Direct Method – Direct comparison with standards (primary, etc.); 2. Indirect Method – Indirect comparison with standards through calibration curve of instrument;

- INSTRUMENTATION – is the technological use of instruments;

- CLASSIFICATION OF INSTRUMENTS – By applications instruments are classified as,

1. Monitoring Instrument: – Device serves monitoring function of operations and/or processes. It, generally, indicates the quantity or condition of its input and have no controlling function; Examples: Balances, Barometers, Thermometers, Electric- or Gas-meters.

2. Controlling Instrument: – Instrument serve controlling functions and forms element of automatic control system. Examples: Thermostat, etc.

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Kheirallah, S. M. 5

Input (energy or material)

Role and Location of Measuring Instrument in Control System

PROCESS

Measuring Instrument

Controller

Final Control Element

Disturbances

Output controlled variable

Desired value of controlled variable

3. Instruments for Experimental Analyses – Instruments are designed to serve a special purpose required for experimental engineering analysis. Examples: Dynamometers, Vibration analyzer, Noise-meter, etc.

Consider the closed-loop control system:

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Kheirallah, S. M. 6

Obse-rver

Primary Sensing Element

PSE

• FUNCTIONAL ELEMENTS OF MEASURING SYSTEM

Medium

Data Storage Element

DSE

Variable Conversion

Element VCE

Variable Manipulating

Element VME

Data Transmitting

Element DTE

Data Presenting Element

DPE

Functional element consists of one or more physical elements serving a certain function;

1 2 1 – Quantity to be measured (sensed) 2 – Output presented Quantity;

PSE – produces a physical variable (output) proportional to sensed quantity (its input); Bulb of thermometer, etc. VCE – Converts the sensed quantity (its input) to another physical variable (output) preserving the information about its input; Hg in thermometer VME – modifies (amplifies, filters, etc.) the physical variable (its input) to another way preserving the physical nature of its input; Gimbal suspension, etc. DTE – Transmits the physical variable to another location (when the functional elements are physically separated or far away from each others); Connecting rod, Telemetry, etc. DPE – Presents information about the measured quantity in a form recognizable and convenient to human senses; Pointer and scale, etc. DSE – Stores some information in order to be used or played-back later on during the process of measurement;

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Kheirallah, S. M. 7

x F F p p Divisions

φ VME

Pointer

Piston rod

Pressure-gauge housing

Fluid Pressure

Pipe

Piston

Scale

Supporting plate

Spring

Pressure-Gauge Functional Elements to measure fluid pressure inside a pipe

Pivot pin

Block diagram showing functional elements

PSE VCE P i s t o n

p DTE VCE

Piston rod Spring

Lever-type pointer

DPE

Pointer & scale Medium Observer

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Kheirallah, S. M. 8

• TYPES OF INSTRUMENTS - Two types of instruments can be:

1. Null-Type instrument – maintains balance at one point between effect generated by quantity to be measured and opposing effect applied on suitable application; Examples: Pressure Gauge on the basis of standard weights; Simple, French and Roman Lever-type Balances; etc.

2. Deflection-Type Instrument – is recognized by physical effect produced by quantity to be measured on one part, which causes an effect similar in magnitude but opposite in direction on another part of the instrument system; Examples: Pressure Gauge on basis of springs; D’Arsonval Galvanometer; Spring Balances; etc.

- Comparison of the two types reveals the followings:

i. The accuracy of null-type instrument is higher than that of corresponding deflection-type instrument;

ii. For large quantity to be measured, deflection-type instrument should be larger, more rugged and hence less sensitive than null-type instrument;

iii. Null-type instruments are very difficult to be used in measurement of dynamic quantities i.e., when quantities to be measured are varied by time;

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Kheirallah, S. M. 9

p1

Output due to inputs qi & qm

+

- Possible Inputs on pressure gauge

Desired Input

Total Output

Interfering Input

qd

• INPUT-OUTPUT OPERATIONAL DISCRIPTION OF INSTRUMENT

FD

FMD

FMI

FI

Modifying Input

+

qm

qi

qo

qd – Desired Input is the input for which instrument had been designed to measure;

qi – Interfering input is the input to which the instrument is unintentionally sensitive;

qm – Modifying input is the input, which modifies the interfering and/or modifying functions;

Output due to inputs qd & qm

h1 h2

p2

p1

p1

p1 p1

h3

(a) (b) (c) φ

Acceleration and tilt-angle are Interfering

inputs

Temperature is a modifying

input

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Kheirallah, S. M. 10

+

–

ei

FD Coil

N S

Spring

+

–

• METHODS OF MINIMIZATION OF THE INTERFERING AND/OR MODIFYING INFLUENCES

–

FMD1 T

FMD

1. Inherent Insensitivity Method – Use elements that are insensitive to the undesired inputs, e.g., change of strain-gauge material on which temperature affects its resistance, by invar alloy insensitive to temperature;

2. Compensation Method – Introducing additional input that may cancel the undesired ones; e.g., galvanometer coil (for voltage measurement) is effected by temperature (modifying input);

ei

Rcomp

θ

Scale Rcomp

Rco

il

Rco

il

Rco

mp

T, ºC T, ºC T, ºC

Rto

t

ei θ

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FMD1 qim3

ei + –

KFb eb = KFb θo

3. High-Gain Feedback Method – Introducing a feedback link that may reduce the undesired inputs or changing the open-loop system to a closed-loop system;

Consider the block diagram of the galvanometer given above;

FMD1

qim1

KMo ei

Volts T

FMD2

qim2

KSp θo

Motion T

FMD1

qim1

KMo

FMD2

qim2

KSp θo

KAm

KAm

qim4

(a) Open-loop system

(b) Closed-loop system

- For system (a), θo = KMo KSp ei ;

- For system (b), θo = KAm KMo KSp (ei – eb); or, θo = KAm KMo KSp (ei – KFb θo), hence,

ee

;1 i

FbSpMoAm

SpMoAmo e

KKKKKKK

+=θ Or, for very large KAm; ;1

iFb

o eK

=θ

4. Output Correction Method – If a simple subtraction (or addition) of the preliminary known outputs due to interfering and modifying inputs from (or to) total (overall) output, then the output due to the desired input should remain and observe, i.e., corrected output is determined. www.Engg-Know.com



qo,d

qodm

Zero Filter qoim

Output qo,dm

+

+

qim

qii

qid FD

FMD

FMI

FI Output qo,im

0

5. Signal (input or output) filtering Method – Providing measuring system with filters that should block the undesirable signals combined with inputs and/or outputs;

Output qo,im

Output qo,d

qo

qim

qii

+

qid FD

FMD

FMI

FI

+

Zero Filter

0

Zero Filter

qo

0

0

Zero Filter

i. Filtering of undesired inputs ii. Filtering of undesired outputs

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2 60 f,

ei θx

θy

- Examples on Signal filtering (blocking) of interfering input

(a) Gimbal Suspension, mechanical filter for

filtering inclination φi-angle of U-tube pressure- gauge

R R

R R

Ee

e o

R R

R R Ee

e o

Rf

Cf

(b) Magnetic Shielding of strain-gauge bridge from the effect of

50/60Hz field

t

(a) R-C Filter to block undesired frequencies www.Engg-Know.com


Kheirallah, S. M. 14 VME

Mass & arm Tm

Tm

Core, Coil & Magnet

Ia I θ Te T +

a a DPE eo

Operational Amplifier

Power Source

Inductive Pick-up

Mass Filter

Damper

Support

Spring

N S

Core and coil

Support

Spring

Magnet

r

• Problems Give all functional elements in the form of block diagram

a

θ

eo Rl

R

R

L

L

PSE

Mass

VCE VCE VCE VME

Medium

Mass Spring & damper

Inductive Pickup

Amplifier & Filter

VME

VCE

Resistance –

Ia

Volt-meter

1. Accelerometer Scheme

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Kheirallah, S. M. 15 div.

θ1 Pointer and scale

x Gear sec. and pinion

p T T

Temp., T, ˚C

θ2 θ1

2. Pressure Thermometer

Hg

Container

Fluid

Bulb with mercury (Hg)

Gear sector

Pinion (Gear)

Scale

Pointer Bourdon tube

x

25 75

50

Process of measurement Capillary

T input

Reading output

T, ˚C

PSE VCE VCE VME

Link

VME DPE Observer

Bulb and Hg

Bulb, Hg and

capillary Bourdon

tube

Link and arm of

gear sec.

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ei + ea

3. Servomechanism

Amplifier (KA) ∑

Motor (dc)

Rake

Potentiometer

– efb EA

Em

Pinion

Shaft Scale

Pointer

Controlling-Measuring

Process

Input Output

Ep

R

10 15 20 25 30

x

- Scheme of the device

- Block-Diagram of Functional Elements

PSE DME DME VCE DTE VME DPE

VCE

M-um Ob-er

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Static Performance Characteristics (SPC)

- Performance characteristics (PC) specify the functional characteristics indicating the capabilities and limitations of instruments in applications;

- Static performance characteristics (SPC) are the characteristics determined when the input is insignificantly varied or not varied by time;

- SPC include: static calibration, error, uncertainty, Linearity, sensitivity, accuracy, threshold, resolution and hysteresis of measuring instruments;

• Static Calibration; Calibration Curve - Performance Parameters of instrument are checked by means of calibration process performed by imposing instrument to known input (desiring, modifying or interfering) and observing and registering the resulted output; - Input – Output Relation may be presented by one of the following forms:

Tabular form

qi qo 0 2 5 16

… …

… …

qi

qo

Graphical form

For example,

qo = f(qi) = a qi2 + b qi + c

Mathematical form www.Engg-Know.com



- Steps for Static Calibration Process 1. Study the construction of instrument and pick out and define all possible inputs; 2. Decide, which input is significant to be varied during calibration; 3. Depending on instrument application select the device for applying and varying

the decided input within a definite and assigned range; Standard inputs applied by selected device should be of 10 times as accurate as calibrated instruments;

4. Varying the decided input and keeping the others constant, determine the static input / output relation and represent it by any suitable form given before.

• ERRORS AND UNCERTAINTY OF INSTRUMENTS Errors, E, in measurement may be one or more of the following types,

1. Systematic Errors (SE) have same magnitude & sign for given set of condition. SE may be termed as Instrument Bias (if they alter instrument reading with fixed magnitude and sign), or as Cumulative Errors (if they accumulate). SE appear due to:

• Errors in instrument parts; e.g., Irregular cross section of springs, Divisions of scales, etc.

• Loading errors; e.g., Restrictions (orifices) in flow-rate meter may partially change or disturb flow conditions, etc.

• Environmental errors;

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2. Random Errors (RE) are variable in magnitude, may have opposite signs and appeared on the basis of chances alone.

3. Miscellaneous Errors (ME) can’t belong to both mentioned types, i.e., measurement may include

- errors due to human beings or operators;

- errors due to wrong adjustments / parts;

- errors due due to improper applications Uncertainty, U, of instruments, characterizes the dispersion, variance or scatter in

measuring data from normal one. Two uncertainty types may be,

1. External Estimate of Uncertainty, Ue, generally characterized by resolution, is determined from limitations of measuring apparatus, manufacturer’ literature, etc.

2. Internal Estimate of Uncertainty, Ui, is the difference in output value (scatter in values) every time the given input is imposed on instrument. Ui is estimated as,

- Data ‘population’ including all possible values of particular measurement, is obtained;

- Random sampling of equitable distribution of the population is selected;

- The means and standard deviation (estimated true value and uncertainty respectively) of each sample is evaluated. The best estimate of the mean value is the mean of the sample means (the population mean).

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Note: If the two external and internal estimates of uncertainties are of the same magnitude order (i.e., minimum overall uncertainty in the experiment) then the experiment is considered consistent, otherwise if the two estimates are considerably different, then the higher among them is the experiment uncertainty and the experiment itself is inconsistent.

• LINEARITY: INDEPENDENT, PROPORTIONAL AND COMBINED

- Output – input relation is linear if it is represented graphically by straight line or mathematically by straight-line equation qo = a + b qi; (a and b are constants).

- As absolute linearity of commercial instruments could not be achieved, still the relation can be considered linear if it follows one of the following forms:

a. Independent Linearity if the output deviations from a best fitting (idealized) straight line (blue-dotted line) will remain within two parallel straight lines spaced by a value ±x% of full scale output on both +ve and –ve sides of the idealized straight line;

qo

qi

Max.dev. in +ve side

Max. dev. in -ve side

Ideal straight line

±x%

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b. Proportional Linearity if the output deviations from a best fitting (idealized) straight line (blue-dotted line) will remain within two straight lines drawn from the origin and joining the maximum deviations of the true calibration curve on both +ve and –ve sides of the idealized straight line;

Max. dev.

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Dynamic Performance Characteristics (DPC) Input Types

• Periodic input (harmonic or non-harmonic)

• Non-periodic input

Inpu

t

Inpu

t

Inpu

t

Time

T T

Time Time

T (a) (b) (c)

T T T Time Time Time

Inpu

t

Inpu

t

Inpu

t (d) (e) (f)

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Input, Cont., • Random input

Measurement System Equations Dynamic response: Input – output relation as linear (or

linearized) differential equation:

Inpu

t

Time, t

iimi

m

moo

no

n

nno

n

n bqqbdt

qdbqadt

dqadt

qdadt

qda =++=++++ −

−

− 0011

1

1 ...........

;opiocfo qqq +=

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MOTION MEASUREMENT; Introduction

- Motion measurement includes: displacement of elements (velocity and acceleration as well) and vibration of machines, etc

Types of measured motion (instruments)

o Absolute motion {seismic motion (instrument)} – Xo, & Relative motion, with respect to a fixed reference – yo ;

o Form – translational & rotational; o By time – static & dynamic; o Linkage – contact & contactless

Dash- pot Scale

Mass Frame

Spring Xo

Moving body

M

B

k yo

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MOTION, Cont., …… Displacement Measurement

Mechanical methods – Caliper, micrometers, dial gauges, etc. (most of them are manual)

Pneumatic methods – flapper (moving object) / nozzle assembly. Displacement (thickness) of value 0.2 microns and magnification of order 105; Accuracy depends on supply pressure constancy;

Electrical (electromechanical) methods - the conversion of displacement to electrical quantity like resistance, voltage, etc.; strain gauges, linear variable differential transformers, capacitances, or piezoelectric crystals, etc.

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Displacement, Cont., Resistance strain gauge transducers

o Types and fixation of strain gauges Paper - 0.08mm in thickness Force

Force

Motion

Moving frame

d

h

1 3

2 4 Wire type

Foil type

Fixed frame

(b) Bonded Strain Gauges 3. Un-Bonded Strain Gauges

(a) Tensioned Elastic Element Wire diameter (foil thickness) = 0.01

up to 0.03 mm

Conductor, G=2.0 up to 3.5

Semiconductor, G=100 up to 200

Wire dimensions: Length = 25mm &

Diameter = 0.025mm; Wires are preloaded by

more than expected compressive load

Resistance strain gauges (of both types) are arrangement in Wheatstone bridge

Strain gauges

x

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Resistance Strain, Cont., …. o Analyisis of strain gauges

Gldl

dldlRdR

=++=ρρµ21

;Eldl

d ψρρ=Moreover:

Where,

E – Modulus of elasticity; Ψ – Bridgman coefficient

Where, G – Gauge factor

227.1D

lA

lR ρρ==

AdA

DdD

ldl

ta 2; −=−== εεAxial and transverse

strains; Poison’s ratio ldlDdD

a

t −==

εεµ

AdAd

ldl

RdR

−+=ρρ

Differentiate and divide by R

Wire resistance

R Rs

Rs Rs

Rg

G

a

b c

d

Rb

Vb

Vg

Connection of strain gauge R, in Wheatstone bridge

2s

s

se

RRR

RRR ++

=

Effective bridge resistance

Current ig through G, if Rb ≈ 0:

ge

gg RR

Vi

+=

Continue,…… www.Engg-Know.com



Resistance Strain, Cont., …. ( )

s

sso

bo

ob RR

RRRRandRR

RVV3

2++

=

+

=

.21

−

+=

sg RR

RVVThen for balanced conditions, i.e., ig = 0, voltage between b & c is,

Introduction of the values,

As the strain gauge resistance R, changes to R+ΔR, then ,

21

1

1

21

−+∆+

∆+=−

+∆+∆+

=

RR

RR

RR

RRRRR

VV

ss

g 1

21

21

−−

+

=∆

VV

VV

RR

RR

g

gs

Then knowing the unbalance voltage Vb (in case of large value of Rg → ∞), the strains can be easily found.

( )s

s

gesgeg RR

RRRR

VRR

RRR

Vi+−

×+

=

−

++=

221In case of bridge balance

R = Rs, the current is,

( ) ( )ggeg RRR

RVRR

RRR

Vi+∆

=∆+

∆×

+=

422Due to change in R, using Re

Continue, …… www.Engg-Know.com



Using gauge factor relation, aG

RdR ε=

Resistance Strain, Cont., …. ( )

ggs

a ikGV

iRR=

+=

4ε

R1 R2

R3 R4

Rg

G

a

b c

d

V

Vo

Similarly, if R1 & R2 are strain gauges and the other two R3 & R4 are standard ones, then,

( )

∆−

∆+

=2

2

1

1

14 RR

RR

RRVi

gg

( )

∆−

∆+

∆−

∆+

=4

4

3

3

2

2

1

1

14 RR

RR

RR

RR

RRVi

gg

By same manner if all arms of the bridge are strain gauges.

Unbalance current across galvanometer is,

Arrangement of strain gauges in

full bridge

Continue ……..

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R1

R3

Resistance Strain, Cont., …. 1) Larger output current ig, (i.e., higher sensitivity) will be

developed if the strain gauges of the bridge opposite arms (R1 and R3) or (R2 and R4) are subjected to the same nature of straining (tensile or compressive);

2) Exciting voltage V, of the bridge may be dc or ac voltage. Both cases require the use of amplifier (dc or ac amplifier) as the bridge output is very small (i.e., small strain).

o Compensation of temperature effect - By introducing in the circuit a thermally sensitive

compensating resistances Rc/2 (deterministic value); - By special mounting & arrangement of strain gauges on the

elastic element to be strained.

Rc / 2

Rc / 2

V

Vo

P P

R1

R2 R2

R4

Continue,…. www.Engg-Know.com



Resistance Strain, Cont., …. Suppose strain gauges R1 = R2 = R3 = R4 = R, are correctly arranged. If the bridge factor n, is considered

RRn

c+=

1

1Then,

+

×∆

×=×∆

×=

RRR

RmnRRm

VV

c

o

1

144

Where, m is the signal enhancement factor that depends on number of active strain gauges and their arrangement in the bridge circuit. Value of m & arrangements may be:

(a) m = 1 ; No temp. comp-n; (b) m = 1+ μ;

(comp-n for temp.) (c) m = 2;

(No temp. comp-n)

(d) m = 2 (1 + μ) (comp-n for temp.)

R1

(e) m = 4 ; (ensure temp. comp-n)

R1 R2 R1

R3 R1,3

R1 R2

R3 R4

R1,3 R2,4

R1,3

R2,4

R3,4 R1,2

P P P P

P P

P P

P P

P P

P

Continue,…… www.Engg-Know.com



Resistance Strain, Cont., ….

For arrangement in Fig. (d); [ ]

EAGPG

EA

PG

RR

a ===∆ ε

( ) ARG

RREmV

PV

c

o ×+

×=1

4Substitute in the voltage relation and simplify,

Temperature affects the value E(R+Rc), hence, ( ) ( ) ( )[ ]

( ) ( )[ ] ( )211

TEcbRRRcRbTERRE

TbRRTcERRE

cccc

cc

∆+++∆++=

=∆++∆+=+

where, c – temperature coefficient (usually negative) of Young’s modulus; b – temperature coefficient of electrical resistivity and ∆T – temperature change.

Accordingly, ( )bc

cRReiRRcRb c

cc +−==++ .,.,0

bccARARl ccc

c +×==

ρρHence, the length of compensating resistance Rc, can be found

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Capacitance-Type Transducer

Dielectric medium

Fixed plate

Movable plate

Reference linkage

l

y 1

2

l y

1

2

3

3'

Dielectric medium

V1

V2

V

C1

C2

Types: plate and cylidrical capacitances

;. l

AKlAC εε

π==

631

2lAK

lCS ε−=∂∂

=

Where, ε – dielectric constant, A – cross area, and l – thickness of dielectric medium

Sensitivity:

,,ylAKCand

ylAKC

−=

+=

εε21

- Differential capacitance transducer

VlylV

CCCVandV

lylV

CCCV

22 21

12

21

21

−=

+=

+=

+= ,

Hence,

====−l

Vdy

dVSitysensisitivandyl

VVVVdifferenceVoltage oo ;21

Fixed plates

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Secondary coil 1

Primary coil

Secondary coil 2

Linear-Variable Differential Transformer (LVDT) o Construction & electrical circuit

Secondary coil 1

Secondary coil 2

Primary coil

Rod Core

Insulating former

Core

V1

Vo

V2

Vi

Housing y

- Core is usually made of nickel – iron alloy, which moves in a slot to reduce eddy currents. Core is positioned with a rod of nonmagnetic material. - The primary coil is supplied with alternating (ac) voltage Vi, of amplitude between 5V to 25V and frequency from 50 cycle/s to 20 kilo-cycle/s.

- Range of LVDT between 0.025mm to several millimeters.

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