Syllabus€¦ · · 2012-10-16Syllabus Measurement Characteristics Transducers-Fundamentals of Vibration- ... Fundamentals of Rotating Machinery Diagnostics,

Vib

ration

Mea

sure

men

t Sys

tems

H.Ahmad

ian

Intr

oduc

tion

Syllabus

Mea

sure

men

t C

hara

cter

isti

cs

Tra

nsd

uce

rs

-F

un

da

men

tals

of

Vib

rati

on

-V

ibra

tion

Tra

nsd

uce

rs

Fu

nd

am

enta

ls o

f S

ign

al

An

aly

sis

Fau

lt D

etec

tion

an

d D

iagn

osi

s in

Rota

tin

g M

ach

iner

y

Case

His

tori

es

Mea

sure

men

t Char

acte

rist

ics

Ch

aracte

ris

tics o

f In

str

um

en

tati

on

Op

erati

on

al

Mo

des o

f In

str

um

en

tati

on

s

Sta

tic a

nd

Dyn

am

ic C

haracte

ris

tics o

f In

str

um

en

tati

on

Measu

rem

en

t A

ccu

racy

Measu

rem

en

t S

tan

dard

s

Sim

ple

instr

um

ent

model

Sensitiv

ity

Accura

cy a

nd E

rror

Tra

nsduc

ers

Fun

dam

enta

ls o

f Vib

ration

s

SD

OF S

yste

ms

Undam

ped

Fre

e V

ibra

tion

Dam

ped F

ree V

ibra

tion

Harm

onic

Forc

ing

Arb

itra

ry F

orc

ing

MD

OF S

yste

ms

…

Tra

nsduc

ers

Vib

ration

Tra

nsduc

ers

Accele

rati

on

Vib

rati

on

an

d S

ho

ck

Measu

rem

en

t

Accele

rom

ete

r D

ynam

ics

Ele

ctr

om

echanic

al Forc

e-B

ala

nce (

Serv

o)

Accele

rom

ete

rs

Tra

nsduc

ers

Vib

ration

Tra

nsduc

ers

Pie

zoele

ctr

ic A

ccele

rom

ete

rs

Pie

zore

sis

tive

Accele

rom

ete

rs

Diffe

rential-

Capacitance

Accele

rom

ete

rs

Tra

nsduc

ers

Vib

ration

Tra

nsduc

ers

Str

ain

-Gage A

ccele

rom

ete

rs

Seis

mic

Accele

rom

ete

rs

Inert

ial Types,

Cantile

ver,

and S

uspended-

Mass C

onfigura

tion

Ele

ctr

osta

tic F

orc

e F

eedback A

ccele

rom

ete

rs

Mic

roaccele

rom

ete

rs

Cro

ss-A

xis

Sensitiv

ity

Sele

ction,

Full-S

cale

Range,

and O

verload

Capability

Sig

nal Conditio

nin

g

Fun

dam

enta

ls o

f Signa

l Ana

lysis

Tim

e,

Freq

uen

cy a

nd

Mo

dal

Do

main

s

•The T

ime D

om

ain

•The F

requency D

om

ain

•In

str

um

enta

tion for

the F

requency D

om

ain

Fun

dam

enta

ls o

f Signa

l Ana

lysis

•The M

odal D

om

ain

•In

str

um

enta

tion for

the M

odal D

om

ain

Fun

dam

enta

ls o

f Signa

l Ana

lysis

Un

dersta

nd

ing

Dyn

am

ic S

ign

al

An

aly

sis

FFT P

ropert

ies

Sam

pling a

nd D

igitiz

ing

Aliasin

g

Band S

ele

cta

ble

Analy

sis

Win

dow

ing

Avera

gin

g

Real Tim

e B

andw

idth

Overlap P

rocessin

g

Usin

g D

yn

am

ic S

ign

al

An

aly

sers

Fau

lt D

etec

tion

and

Diagn

osis in

Rot

ating

Mac

hiner

y

Fau

lt D

etec

tion

and

Diagn

osis in

Rot

ating

Mac

hiner

y

Im

bala

nced

Ro

tor

Fau

lt D

etec

tion

and

Diagn

osis in

Rot

ating

Mac

hiner

y

Belt

an

d p

ull

yp

ro

ble

ms

Fau

lt D

etec

tion

and

Diagn

osis in

Rot

ating

Mac

hiner

y

RP

M

2*R

PM

2*B

PF

O

Lu

bri

cati

on

De

fect

Ro

tor

Mis

alig

nm

en

t

Ro

tor

Un

ba

lan

ce

Rad

ial T

en

sio

n

of

Beari

ng

Mis

alig

nm

en

t o

f

ou

ter

Ra

ce

Slip

of

Race i

n

the

Mo

un

tin

g S

ea

t

2*R

PM

1*R

PM

2*B

PF

O

Harm

on

ics

of

RP

M

Incre

ase o

f

Backg

rou

nd

level

RP

M

Ref

eren

ces

& C

ours

e Eva

luat

ion

Ref

eren

ces:

Measure

ment,

Instr

um

enta

tion,

and S

ensors

H

andbook C

RCnetB

ase

1999.

Fundam

enta

ls o

f Rota

ting M

achin

ery

Dia

gnostics,

Donald

E.

Bently,

2002.

Cou

rse

Eva

luat

ion

Sch

eme

Mid

-Term

30

%

Co

urse P

ro

ject

20

%

Fin

al

Exam

5

0%

Vib

ration

Mea

sure

men

t Sys

tems

H.A

hm

adia

n

Mea

sure

men

tChar

acte

rist

ics

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 2

2

Pres

enting

Top

ics

Char

acte

rist

ics

of

Inst

rum

enta

tion

Sim

ple

Inst

rum

ent

Model

Pass

ive

and A

ctiv

e Sen

sors

Cal

ibra

tion

Modifyi

ng a

nd I

nte

rfer

ing I

nputs

Acc

ura

cy a

nd E

rror

Oper

atio

nal

Modes

of

Inst

rum

enta

tion

Def

lect

ion I

nst

rum

ent

Null

Inst

rum

ent

Anal

og a

nd D

igital

Sen

sors

Anal

og a

nd D

igital

Rea

dout

Inst

rum

ents

Input

Imped

ance

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 2

3

Mea

sure

men

t Char

acte

rist

ics

Sim

ple

In

stru

men

t M

od

el

Mas

s of an

obje

ct

Wei

ght

(Obse

rvab

le P

hys

ical

Var

iable

)

Key

fun

ctio

nal

ele

men

t

Mec

han

ical

or

Ele

ctrica

l

(Can

be

Man

ipula

ted in a

Tra

nsm

issi

on S

yste

m)

The

Mea

sure

men

t

(Obse

rved

Outp

ut)

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 2

4

Mea

sure

men

t Char

acte

rist

ics

Oth

er

Exam

ple

s o

f P

hysi

cal an

d S

ign

al V

ari

ab

les

CommonMechanical

CommonElectrical

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 2

5

Mea

sure

men

t Char

acte

rist

ics

Need

fo

r o

ther

devic

es

If t

he

outp

ut

is t

o inte

rfac

e w

ith a

co

mpute

r-bas

ed d

ata

acquis

itio

n

or

com

munic

atio

n s

yste

m

Use

d w

hen

the

outp

ut

signal

is

smal

l

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 2

6

Mea

sure

men

t Char

acte

rist

ics

Sen

sor

or

Tra

nsd

uce

r !?

Sen

sor

:Sen

sing e

lem

ent

itse

lf

Tra

nsd

uce

r:

Sen

sing e

lem

ent

plu

s an

y as

soci

ated

circu

itry

The

sensi

ng p

roce

ss

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 2

7

Mea

sure

men

t Char

acte

rist

ics

Pass

ive &

Act

ive S

en

sors

Sen

sors

•P

ass

ive :

Do n

ot

add e

ner

gy

but

may

rem

ove

(t

her

moco

uple

,...

)

•A

ctiv

e :

Add e

ner

gy

to t

he

mea

suring e

nvi

ronm

ent

(rad

ar,…

)

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 2

8

Mea

sure

men

t Char

acte

rist

ics

Calib

rati

on

Sensor

Input

Outp

ut

(Know

n)

Wh

at

is C

alib

rati

on

!?

Dyn

am

ic R

an

ge

resu

lts

in a

. .

.[C

alib

ration S

tandar

ds]

Satu

rati

on

. .

.

Cali

bra

tio

n C

urv

e

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 2

9

Mea

sure

men

t Char

acte

rist

ics

Mo

dif

yin

g a

nd

In

terf

eri

ng

In

pu

ts

Y,

as s

truct

ura

l vi

bra

tion d

uring forc

e m

easu

rem

ent

Z,

com

mon

ly t

emper

ature

-M

an

y d

evic

es

calib

rate

d a

t sp

eci

fied

tem

pera

ture

s.

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 2

10

Mea

sure

men

t Char

acte

rist

ics

Mo

dif

yin

g a

nd

In

terf

eri

ng

In

pu

ts

Typ

es

of

Inp

uts

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 2

11

Mea

sure

men

t Char

acte

rist

ics

Err

or,

Acc

ura

cy &

Pre

cisi

on

Err

or

Syst

em

ati

c (b

ias)

Ran

do

m (

no

ise)

Acc

ura

cy :

How

clo

se t

o t

he

true

valu

e

-10m

, a

very

acc

ura

te m

easu

rem

ent

if t

he

truth

is

10.0

00001m

Pre

cisi

on

: H

ow

fin

e th

e le

vel of m

easu

rem

ent

-22.0

234578m

very

pre

cise

, but

not

accu

rate

if 10m

is t

he

truth

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 2

12

Mea

sure

men

t Char

acte

rist

ics

Err

or,

Acc

ura

cy &

Pre

cisi

on

Bia

sed a

nd n

ot

pre

cise

Bia

sed b

ut

pre

cise

Not

Acc

ura

teN

ot

Acc

ura

te

Acc

ura

teN

ot

Acc

ura

te

Unbia

sed b

ut

not

pre

cise

Unbia

sed a

nd p

reci

se

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 2

13

Mea

sure

men

t Char

acte

rist

ics

Err

or

sou

rces

Syst

em

ati

c (b

ias)

Err

or

So

urc

es

Mis

-cali

bra

tio

ndue

to m

odifyi

ng inputs

lik

e

-te

mper

ature

-ag

ing

Invasi

ven

ess

(m

easu

rem

ent

pro

cess

its

elf ch

anges

the

mea

sure

d)

-la

rge

war

m t

her

mom

eter

for

smal

l co

ld v

olu

me

of

fluid

-si

gnal

pat

h o

f m

easu

rem

ent

pro

cess

-hum

an o

bse

rver

s lik

e par

alla

x

Can

be R

em

oved

by c

om

pen

sati

on

meth

od

s

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 2

14

Mea

sure

men

t Char

acte

rist

ics

Err

or

sou

rces

seviation

standard

:

68%

95% 9

9.7

% (Wid

th o

f dis

trib

ution)

Ran

do

m (

no

ise)

Err

or

So

urc

es

-G

auss

ian d

istr

ibution

Rep

eata

bil

ity o

f m

easu

red

as

in r

ough s

urf

aces

’hei

ght

mea

sure

men

t

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 2

15

Mea

sure

men

t Char

acte

rist

ics

Err

or

sou

rces

Ran

do

m (

no

ise)

Err

or

So

urc

es

(cont.

)

Sta

ges

in p

roce

ss

Fig

ure

of

meri

t w

hen

an

aly

zin

g n

ois

e i

s S

ign

al

to n

ois

e r

ati

o (

SN

R)

an

d

no

t th

e l

evel

of

com

bin

ed

no

ise .

.

.

.

Wh

y?

-SN

R >

>1

idea

lly

-Poss

ible

SN

R <

1so

met

imes

as in h

um

an h

earing a

bili

ty in a

nois

y en

viro

nm

ent

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 2

16

Cov

ered

Top

ics

Char

acte

rist

ics

of

Inst

rum

enta

tion

Sim

ple

Inst

rum

ent

Model

Pass

ive

and A

ctiv

e Sen

sors

Cal

ibra

tion

Modifyi

ng a

nd I

nte

rfer

ing I

nputs

Acc

ura

cy a

nd E

rror

Oper

atio

nal

Modes

of

Inst

rum

enta

tion

Def

lect

ion I

nst

rum

ent

Null

Inst

rum

ent

Anal

og a

nd D

igital

Sen

sors

Anal

og a

nd D

igital

Rea

dout

Inst

rum

ents

Input

Imped

ance

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 2

17

Mea

sure

men

t Char

acte

rist

ics

Defl

ect

ion

In

stru

men

t

For

eith

er s

tatic

or

dyn

amic

mea

sure

men

ts

Hig

h d

ynam

ic r

esponse

Ener

gy

dra

in fro

m t

he

mea

sure

d…

load

ing

err

or

Op

era

tio

nal M

od

es

of

Inst

rum

en

tati

on

: D

efl

ect

ion

In

stru

men

t

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 2

18

Mea

sure

men

t Char

acte

rist

ics

Op

era

tio

nal M

od

es

of

Inst

rum

en

tati

on

: N

ull I

nst

rum

en

t

Nu

ll I

nst

rum

en

t

-K

ey f

eatu

res

-Com

par

ator

for

Iter

ativ

e bal

anci

ng o

per

atio

n-

Feed

bac

k to

ach

ieve

bal

ance

-N

ull

def

lect

ion a

t parity

Hig

h a

ccura

cy for

smal

l in

put

valu

esLo

w load

ing e

rror

Not

suitab

le for

hig

h s

pee

d m

easu

rem

ents

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 2

19

Mea

sure

men

t Char

acte

rist

ics

An

alo

g S

en

sors

-

continuous

in m

agnitude

& t

empora

l (t

ime)

, or

spat

ial (s

pac

e) c

onte

nt

Dig

ital S

en

sor

-D

igital

sig

nal

exi

sts

at d

iscr

ete

valu

es o

f tim

e or

spac

e-bas

ical

ly b

inar

y•

bin

ary

num

ber

ing s

yste

m for

logic

alan

d n

um

ber

ing

info

rmat

ion

•M

-bit d

evic

enum

ber

s (E

x. 0

0,0

1,1

0,1

1)

An

alo

g a

nd

Dig

ital S

en

sors

M 2

-D

iscr

ete

sam

ple

d s

ign

al dis

cret

eoutp

ut

both

in t

ime

or

spac

e &

m

agnitude

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 2

20

Mea

sure

men

t Char

acte

rist

ics

An

alo

g R

ead

ou

t In

stru

men

t

-def

lect

ion o

f a

poin

ter,

ink

trac

e on a

gra

duat

ed s

cale

, in

tensi

ty o

f a

bea

m

Dig

ital

Read

ou

t In

stru

men

t

An

alo

g a

nd

Dig

ital R

ead

ou

t In

stru

men

ts

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 2

21

Mea

sure

men

t Char

acte

rist

ics

Lo

ad

ing

Err

or

-Should

be

Min

imiz

ed b

y im

ped

ance

mat

chin

g o

f so

urc

e w

ith m

easu

ring inst

rum

ent

And in a

sig

nal

chai

n

22/Z

EP

Inp

ut

Imp

ed

an

ce

Input

Imped

ance

Sourc

e vo

ltag

e pote

ntial

bei

ng m

easu

red

Th

e m

ore

is,

the less

th

e lo

ad

ing

err

or

12/Z

Z

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 2

22

Nex

t Ses

sion

Top

ics

Char

acte

rist

ics

of In

stru

men

tation

Sim

ple

Inst

rum

ent

Model

Pass

ive

and A

ctiv

e Sen

sors

Cal

ibra

tion

Modifyi

ng a

nd I

nte

rfer

ing I

nputs

Acc

ura

cy a

nd E

rror

Oper

atio

nal

Modes

of In

stru

men

tation

Def

lect

ion I

nst

rum

ent

Null

Inst

rum

ent

Anal

og a

nd D

igital

Sen

sors

Anal

og a

nd D

igital

Rea

dout

Inst

rum

ents

Input

Imped

ance

Char

acte

rist

ics

of In

stru

men

tation

Sta

tic

and D

ynam

ic

Mea

sure

men

t Acc

ura

cyM

easu

rem

ent

Sta

ndar

ds

Vib

ration

Mea

sure

men

t Sys

tems

H.A

hm

adia

n

Mea

sure

men

tChar

acte

rist

ics

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 3

2

Pres

enting

Top

ics

Sta

tic

& D

ynam

ic C

har

acte

rist

ics

of

Inst

rum

enta

tion

Sta

tic

Char

acte

rist

ics

of In

stru

men

t Sys

tem

sO

utp

ut/

Input

Rel

atio

nsh

ipD

rift

Hys

tere

sis

Sat

ura

tion

Bia

sErr

or

of N

onlin

earity

Dyn

amic

Char

acte

rist

ics

of In

stru

men

t Sys

tem

sFo

rcin

g f

unct

ions

Char

acte

rist

ic E

quat

ions

dev

elopm

ent

Res

ponse

of

the

diffe

rent

linea

r sy

stem

s ty

pes

Zer

o o

rder

,1

stord

er,

and

2nd

ord

er b

lock

s

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 3

3

Mea

sure

men

t Char

acte

rist

ics

Dyn

am

ic V

ari

ati

on

sChan

ges

in m

easu

rand

itse

lfTim

e ta

ken b

y th

e in

stru

men

t to

follo

w t

he

chan

ges

Corr

ect

info

rmat

ion c

onsi

der

ing t

he

stat

ic a

nd d

ynam

ic

char

acte

rist

ics

of

both

the

mea

sura

nd

and t

he

inst

rum

enta

tion..

Sta

tic

& D

yn

am

ic C

hara

cteri

stic

s o

f In

stru

men

tati

on

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 3

4

Mea

sure

men

t Char

acte

rist

ics

Ou

tpu

t/In

pu

t R

ela

tio

nsh

ip

Inst

rum

en

ts f

orm

ed

fro

m b

lock

s-co

nn

ect

ion

Blo

cks

repre

sente

d b

y co

nce

ptu

al &

mat

hem

atic

al m

odel

s

Tra

nsf

er f

unct

ion

(dyn

amic

& s

tatic

)

Val

ue

afte

r tr

ansi

ents

hav

e se

ttle

d t

o f

inal

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 3

5

Mea

sure

men

t Char

acte

rist

ics

Sta

tic

beh

avio

r o

f th

e b

lock

Off

set

Err

or

when

not

des

ired

Bia

sw

hen

del

iber

atel

y se

t

Ran

ge

(span

)ze

ro t

o a

saf

e m

axim

um

for

use

Dyn

amic

ran

ge

ratio o

f th

e sp

an t

hat

the

outp

ut

will

cove

r

Sen

sitivi

ty

Sta

tic

Ch

ara

cteri

stic

s o

f In

stru

men

t S

yst

em

s

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 3

6

Mea

sure

men

t Char

acte

rist

ics

Dri

ft Cau

se Var

iations

in p

arts

ove

r tim

e (C

hem

ical

, m

echan

ical

, …

)Envi

ronm

enta

l par

amet

ers

(Tem

per

ature

, P

ress

ure

, H

um

idity

, …

)

Obse

rved

eff

ects

Chan

ge

in o

ffse

t ,

sensi

tivi

ty ,

acc

ura

cy

Tak

es m

any

form

sSte

ady

drift

ove

r tim

e of

a m

easu

ring s

pring

Sta

tic

Ch

ara

cteri

stic

s o

f In

stru

men

t S

yst

em

s

tim

e

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 3

7

Dri

ft(c

ont.

)

Tak

es m

any

form

sel

ectr

onic

am

plif

ier

sett

le b

y tim

e to

fin

al v

alue

afte

r pow

er s

upply

elec

tronic

am

plif

ier

gai

n v

aria

tion w

ith t

emper

ature

of oper

atio

n(d

ue

to c

han

ge

of

elec

tric

al r

esis

tance

)

Mea

sure

men

t Char

acte

rist

ics

Sta

tic

Ch

ara

cteri

stic

s o

f In

stru

men

t S

yst

em

s

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 3

8

Mea

sure

men

t Char

acte

rist

ics

Sta

tic

Ch

ara

cteri

stic

s o

f In

stru

men

t S

yst

em

s

Hyst

ere

sis

diffe

rent

resu

lts

as s

ignal

s va

ry in

direc

tion o

f th

e m

ove

men

tlo

w h

yste

resi

sas

in:

-tr

ansf

orm

er iro

n lam

inat

ions

-cl

ock

spring w

ire

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 3

9

Mea

sure

men

t Char

acte

rist

ics

Sta

tic

Ch

ara

cteri

stic

s o

f In

stru

men

t S

yst

em

s

Satu

rati

on

Sig

nal

, a

mplif

ied d

iffe

rently

bas

ed o

n g

ain/a

mplit

ude

curv

e

amplif

ying e

lem

ents

only

able

to a

mplif

y one

pola

rity

of si

gnal

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 3

10

Mea

sure

men

t Char

acte

rist

ics

Sta

tic

Ch

ara

cteri

stic

s o

f In

stru

men

t S

yst

em

s

Satu

rati

on

(cont.

)

signal

too lar

ge

that

the

top is

not

amplif

ied

signal

pas

ses

from

neg

ativ

e to

posi

tive

pola

rity

:cr

oss

ove

rdis

tort

ion

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 3

11

Mea

sure

men

t Char

acte

rist

ics

Sta

tic

Ch

ara

cteri

stic

s o

f In

stru

men

t S

yst

em

s

Bia

s Nee

d f

or

input

signal

pro

cess

at

a hig

her

ave

rage

valu

eAs

in o

ne

pola

rity

am

plif

icat

ion b

y a

sem

iconduct

or

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 3

12

Mea

sure

men

t Char

acte

rist

ics

Err

or

of

No

nli

neari

tyLi

nea

rity

:co

nst

ant

gai

n f

or

all le

vels

Err

or

of nonlin

earity

ther

e ex

ist

man

y w

ays

to e

xpre

ss e

rror

of

nonlin

earity

4 m

ethods

are

usu

ally

use

d :

Com

par

ing w

ith b

est

fit

line

Sta

tic

Ch

ara

cteri

stic

s o

f In

stru

men

t S

yst

em

s

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 3

13

Mea

sure

men

t Char

acte

rist

ics

Sta

tic

Ch

ara

cteri

stic

s o

f In

stru

men

t S

yst

em

s

Err

or

of

No

nli

neari

tyCom

par

ing w

ith b

est

fit

line

thro

ugh z

ero

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 3

14

Mea

sure

men

t Char

acte

rist

ics

Sta

tic

Ch

ara

cteri

stic

s o

f In

stru

men

t S

yst

em

s

Err

or

of

No

nli

neari

tyCom

par

ing w

ith lin

e jo

inin

g 0

% a

nd 1

00%

poin

ts

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 3

15

Mea

sure

men

t Char

acte

rist

ics

Sta

tic

Ch

ara

cteri

stic

s o

f In

stru

men

t S

yst

em

s

Err

or

of

No

nli

neari

tyCom

par

ing w

ith t

heo

retica

l lin

e

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 3

16

Mea

sure

men

t Char

acte

rist

ics

Deali

ng

wit

h d

yn

am

ic s

tate

s

Ex.

: s

pee

d a

t w

hic

h t

he

pen

can

follo

w t

he

input

chan

ges

Mat

hem

atic

s to

des

crib

e lin

ear

dyn

amic

sys

tem

s

Dyn

am

ic C

hara

cteri

stic

s o

f In

stru

men

t S

yst

em

s

Forc

ing f

unct

ions

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 3

17

Mea

sure

men

t Char

acte

rist

ics

Dyn

am

ic C

hara

cteri

stic

s o

f In

stru

men

t S

yst

em

s

Fo

rcin

g f

un

ctio

ns

The

typic

al o

nes

for

dyn

amic

res

ponse

anal

ysis

:

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 3

18

Mea

sure

men

t Char

acte

rist

ics

Ch

ara

cteri

stic

Eq

uati

on

Develo

pm

en

tLi

nea

r beh

avio

r

Dyn

am

ic C

hara

cteri

stic

s o

f In

stru

men

t S

yst

em

s

char

acte

rist

ic e

quat

ion

spec

ific

to b

lock

’s inte

rnal

pro

per

ties

not

alte

red b

y th

e w

ay t

he

blo

ck is

use

d.

Com

bin

ed f

orc

ing

funct

ions

Blo

ck c

har

acte

rist

ic

equat

ion

Outp

ut

resp

onse

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 3

19

Mea

sure

men

t Char

acte

rist

ics

Dyn

am

ic C

hara

cteri

stic

s o

f In

stru

men

t S

yst

em

s

Ch

ara

cteri

stic

Eq

uati

on

Develo

pm

en

tN

ature

of ch

arac

terist

ic e

quat

ion…

blo

ck b

ehav

ior

Hig

hest

ord

er u

sual

lyn

ece

ssary

to

co

nsi

der

in f

irst

-cu

t in

stru

men

t an

aly

sis

: 2

nd

-ord

er

class

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 3

20

Mea

sure

men

t Char

acte

rist

ics

Zero

-ord

er

blo

cks

No fre

quen

cy d

epen

den

t te

rmN

ot

even

for

phas

e sh

ift

Just

For

amplif

icat

ion (

) 0a

Dyn

am

ic C

hara

cteri

stic

s o

f In

stru

men

t S

yst

em

s

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 3

21

Mea

sure

men

t Char

acte

rist

ics

Fir

st-o

rder

blo

cks

Tim

e dep

enden

t te

rms

Outp

ut

resp

onse

to s

tep

forc

ing f

unct

ion

Dyn

am

ic C

hara

cteri

stic

s o

f In

stru

men

t S

yst

em

s

Ste

p a

mplit

ude

Sta

tic

gai

n o

f th

e blo

ck

)1(

)(

/te

AKt

y

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 3

22

Mea

sure

men

t Char

acte

rist

ics

Fir

st-o

rder

blo

cks

(cont.

)

Outp

ut

resp

onse

to s

ine-

wav

e fo

rcin

g funct

ion

Dyn

am

ic C

hara

cteri

stic

s o

f In

stru

men

t S

yst

em

s

Eff

ect

s to

be u

nd

ers

too

d w

hen

in

terp

reti

ng

measu

rem

en

t re

sult

s

Sig

nal

fre

quen

cy

)(

tan1

t

Sin

e-w

ave

amplit

ude

Gai

n o

f th

e blo

ck

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 3

23

Dyn

am

ic C

hara

cteri

stic

s o

f In

stru

men

t S

yst

em

s

Seco

nd

-ord

er

blo

cks

You r

emem

ber

how

to f

ind t

he

resp

onse

!?

Mea

sure

men

t Char

acte

rist

ics

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 3

24

Mea

sure

men

t Char

acte

rist

ics

Dyn

am

ic C

hara

cteri

stic

s o

f In

stru

men

t S

yst

em

s

Seco

nd

-ord

er

blo

cks

(cont.

)Ste

p input

Sin

e-w

ave

input

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion 3

25

Cov

ered

Top

ics

Sta

tic

& D

ynam

ic C

har

acte

rist

ics

of

Inst

rum

enta

tion

Sta

tic

Char

acte

rist

ics

of In

stru

men

t Sys

tem

sO

utp

ut/

Input

Rel

atio

nsh

ipD

rift

Hys

tere

sis

Sat

ura

tion

Bia

sErr

or

of N

onlin

earity

Dyn

amic

Char

acte

rist

ics

of In

stru

men

t Sys

tem

sFo

rcin

g f

unct

ions

Char

acte

rist

ic E

quat

ions

dev

elopm

ent

Res

ponse

of

the

diffe

rent

linea

r sy

stem

s ty

pes

Zer

o o

rder

,1

stord

er,

and

2nd

ord

er b

lock

s

Mea

sure

men

t S

yste

ms

H.A

hm

adia

n

Mea

sure

men

tChar

acte

rist

ics

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion3

2

Prese

nting

Top

ics:

Mea

sure

men

t Acc

ura

cyErr

or:

The

Norm

al D

istr

ibution a

nd t

he

Uniform

D

istr

ibution

Unce

rtai

nty

(Acc

ura

cy)

Mea

sure

men

t U

nce

rtai

nty

Model

Cal

cula

tion o

f Tota

l U

nce

rtai

nty

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion3

3

Measu

rement

Acc

uracy

Acc

ura

cy is

mer

ely

an o

ptim

istic

word

for

erro

r, t

he

diffe

rence

bet

wee

n t

he

outp

ut

of

a m

easu

rem

ent

syst

em a

nd t

he

true

valu

e :

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion3

4

Measu

rement

Acc

uracy

Imag

ine

a te

st t

o e

xam

ine

the

beh

avio

r of

a w

ing

spar

.A p

osi

tion s

enso

r on t

he

spar

rec

ord

s th

e si

gnal

fro

m it

at c

ruis

ing c

onditio

ns.

What

do t

he

mea

sure

men

ts m

ean?

Do t

he

say

anyt

hin

g a

bout

the

aver

age

load

on t

he

spar

?Is

the

spar

vib

rating e

xces

sive

ly?

Could

it

be

in d

anger

of

dev

elopin

g a

fra

cture

?

To a

nsw

er t

hes

e ques

tions

does

not

just

req

uire

a phys

ical

and t

heo

retica

l under

stan

din

g o

f th

e si

tuat

ion b

ut

also

som

e an

alys

is o

f th

e m

easu

rem

ents

mad

e.

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion3

5

Measu

rement

Acc

uracy

In t

hes

e si

tuat

ions

a good f

irst

ste

p w

ould

be

to c

alcu

late

the

mea

n a

nd s

tandar

d

dev

iation o

f th

e m

easu

rem

ents

:

Note

that

the

stan

dar

d d

evia

tion is

calc

ula

ted d

ivid

ing

by

N-1

rath

er t

han

N.

This

is

bec

ause

only

N-1

of th

e sa

mple

s ar

e in

dep

enden

t of th

e m

ean.

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion3

6

Measu

rement

Acc

uracy

The

mea

n o

f si

gnal

:W

ould

be

the

aver

age

def

lect

ion o

f th

e sp

ar.

Could

be

use

d t

o e

stim

ate

its

aver

age

load

.

The

stan

dar

d d

evia

tion o

r va

rian

ce a

re:

Mea

sure

s of

how

wid

ely

the

mea

sure

men

ts a

re

spre

ad a

round t

he

mea

nThey

could

be

take

n a

s in

dic

atio

ns

of

the

inte

nsi

ty o

f vi

bra

tions

in t

he

spar

.

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion3

7

Measu

rement

Acc

uracy

Anoth

er w

ay o

f pre

senting d

ata

in a

sta

tist

ical

way

is

a his

togra

m:

The

range

of

the

quan

tity

bei

ng m

easu

red (

def

lect

ion in o

ur

exam

ple

) is

div

ided

up into

a n

um

ber

of

equal

inte

rval

s, o

r 'b

ins'

.W

e th

en m

erel

y ad

d u

p t

he

num

ber

of

sam

ple

s fa

lling in e

ach b

in.

His

tog

ram

of

spar

defl

ect

ion

s

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion3

8

Prob

ability d

ens

ity f

unct

ions

-th

e n

ormal distr

ibut

ion

Ther

e is

a c

lose

co

nnec

tion b

etw

een

his

togra

ms

and

pro

bab

ility

.Consi

der

mea

sure

men

ts o

f th

e hei

ghts

of w

aves

hitting a

n o

il rig

during a

sea

son.

A h

isto

gra

m o

f th

ese

mea

sure

men

ts c

an

be

use

d t

o e

stim

ate

the

pro

bab

ility

of

wav

es o

f a

cert

ain

size

hitting t

he

oil

rig

in t

he

futu

re

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion3

9

Prob

ability d

ens

ity f

unct

ions

-th

e n

ormal distr

ibut

ion

The

pro

bab

ility

of

a w

ave

with a

hei

ght

(h)

bet

wee

n 2

0 a

nd 3

0 fee

t hitting t

he

rig:

the

ratio o

f th

e ar

ea o

f th

e his

togra

m b

etw

een

h=

20 a

nd h

=30 a

nd d

ivid

ing b

y th

e to

tal ar

ea

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion3

10

Prob

ability d

ens

ity f

unct

ions

-th

e n

ormal distr

ibut

ion

Mat

hem

atic

ally

this

may

be

writt

en a

s:

Obvi

ousl

y th

e to

tal ar

ea u

nder

p(x

) (t

he

pro

bab

ility

of

a sa

mple

hav

ing a

ny

valu

e)

must

be

unity,

i.e

.:

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion3

11

Prob

ability d

ens

ity f

unct

ions

-th

e n

ormal distr

ibut

ion

It is

a m

atte

r of

exper

ience

that

the

vast

m

ajority

of

random

pro

cess

es (

incl

udin

g

random

exp

erim

enta

l er

ror)

pro

duce

the

norm

al (

or

Gau

ssia

n)

pro

bab

ility

den

sity

fu

nct

ion.

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion3

12

Prob

ability d

ens

ity f

unct

ions

-th

e n

ormal distr

ibut

ion

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion3

13

Prob

ability d

ens

ity f

unct

ions

-th

e n

ormal distr

ibut

ion

The

pro

bab

ility

Pof

a giv

en v

alue

xof

a quan

tity

gove

rned

by

a norm

al d

istr

ibution

falli

ng w

ithin

a r

ange

x 0to

x 1is

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion3

14

Prob

ability d

ens

ity f

unct

ions

-th

e n

ormal distr

ibut

ion

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion3

15

Prob

ability d

ens

ity f

unct

ions

-th

e n

ormal distr

ibut

ion

Exam

ple

A s

enso

r is

use

d t

o d

etec

t th

e flow

ra

te o

f fu

el t

o a

jet

engin

e. T

he

follo

win

g a

re

21 s

uch

rea

din

gs

(in a

rbitra

ry u

nits)

,

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion3

16

Prob

ability d

ens

ity f

unct

ions

-th

e n

ormal distr

ibut

ion

Det

erm

ine

the

mea

n a

nd s

tandar

d d

evia

tion:

Cal

cula

te t

he

pro

bab

ility

that

a r

eadin

g t

aken

at

ran

dom

will

hav

e a

valu

e bet

wee

n .

5 a

nd .

7

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion3

17

Prob

ability d

ens

ity f

unct

ions

-th

e n

ormal distr

ibut

ion

What

per

centa

ge

of

a la

rge

num

ber

of

read

ings

are

likel

y to

lie

above

a v

alue

of

.8?

What

per

centa

ge

of

a la

rge

num

ber

of

read

ings

are

likel

y to

lie

within

tw

o

stan

dar

d d

evia

tions

from

the

mea

n?

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion3

18

Com

mon

Sta

tist

ical Distr

ibut

ions

No

rmal

(Gau

ssia

n)

dis

trib

uti

on

Log N

orm

al D

istr

ibution

Pois

son D

istr

ibution

Wei

bull

Dis

trib

ution

Bin

om

ial D

istr

ibution

Stu

den

t t

Dis

trib

uti

on

2D

istr

ibution

Un

ifo

rm D

istr

ibu

tio

nBet

a D

istr

ibution

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion3

19

Unc

ert

ainty

Ana

lysis

It is

esse

ntial

that

the

engin

eer

hav

e a

good

idea

of

the

likel

y ac

cura

cy o

f th

e dat

a.Est

imat

es o

f ex

per

imen

tal ac

cura

cy a

re

refe

rred

to a

s 'U

nce

rtain

ty E

stim

ate

s'An u

nce

rtai

nty

inte

rval

def

ines

a s

ymm

etrica

l ban

d a

round a

mea

sure

men

t.Id

eally

it

should

be

chose

n s

o t

hat

ther

e is

a 9

5%

pro

bab

ility

that

the

true

valu

e lie

s w

ithin

it.

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion3

20

Unc

ert

ainty

Ana

lysis

On g

ener

al,

unce

rtai

nty

anal

ysis

may

be

div

ided

into

tw

o p

arts

: U

nce

rtain

ty i

n p

rim

ary

measu

rem

en

ts,

A p

rim

ary

mea

sure

men

t is

one

that

is

not

der

ived

fr

om

any

oth

er,

e.g.

voltag

e fr

om

a v

oltm

eter

, te

mper

ature

fro

m a

ther

mom

eter

, hea

d fro

m a

m

anom

eter

, dis

tance

fro

m a

dia

l gag

e et

c

Un

cert

ain

ty i

n a

resu

ltder

ived

fro

m t

hose

m

easu

rem

ents

.

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion3

21

Dete

rmining

the u

ncert

ainty

in

prim

ary

measu

rement

s

Invo

lves

mak

ing a

n e

duca

ted g

ues

s bas

ed o

n

seve

ral so

urc

es o

f in

form

atio

n:

1.

Dig

ital

res

olu

tion,

size

of sm

alle

st d

ivis

ions

in s

cale

. The

low

est

poss

ible

unce

rtai

nty

is

hal

f th

e dig

ital

res

olu

tion.

2.

Man

ufa

cture

rs info

rmat

ion,

calib

ration info

rmat

ion.

3.

Rep

eate

d m

easu

rem

ents

of th

e sa

me

quan

tity

4.

Com

par

ison w

ith o

ther

indep

enden

t m

easu

rem

ents

of th

e sa

me

quan

tity

5.

Oth

er fac

tors

, va

lidity

of th

e m

easu

rem

ent

schem

e e.

g.

oper

atin

g a

n inst

rum

ent

outs

ide

its

des

ign r

ange

6.

Exp

erie

nce

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion3

22

Dete

rmining

the u

ncert

ainty

in

a r

esu

lt

In g

ener

al e

xper

imen

tal dat

a is

pro

cess

ed

to g

ener

ate

resu

lts.

The

connec

tion b

etw

een t

he

raw

prim

ary

mea

sure

men

tsan

d t

he

resu

lts

is a

lway

s a

mat

hem

atic

al f

unct

ion o

f so

me

kind

The

unce

rtai

nty

in R

resu

ltin

g f

rom

the

unce

rtai

nties

in a

,b,

c

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion3

23

Exam

ple:

Pow

er

dissipa

ted in

a

resist

or

The

resi

stan

ce R

has

a n

om

inal

val

ue

of

100 o

hm

.

The

voltm

eter

rea

ds

28.0

volts,

with a

res

olu

tion o

f 0.1

V.

Est

imat

e th

e unce

rtai

nty

in t

he

pow

er

mea

sure

men

t.Res

ista

nce

: A g

lance

thro

ugh a

ny

man

ufa

cture

rs

spec

ific

atio

ns

will

show

you t

hat

most

oft

en n

om

inal

re

sist

ance

s ar

e only

acc

ura

te t

o w

ithin

±5%

. W

e sh

all

ther

efore

tak

e our

prim

ary

unce

rtai

nty

her

e as

(R)=

5 o

hm

.

Voltag

e: T

he

unce

rtai

nty

in t

he

read

ing o

f a

dig

ital

voltm

eter

is

usu

ally

hal

f th

e re

solu

tion (

the

true

voltag

e co

uld

lie

an

ywher

e bet

wee

n 2

7.9

5 a

nd 2

8.0

5).

We

ther

efore

hav

e(V

)=0.0

5V.

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion3

24

Exam

ple:

Pow

er

dissipa

ted in

a

resist

or

ab

ou

t 5

%

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion3

25

Exam

ple:

Pow

er

dissipa

ted in

a

resist

or

This

anal

ysis

show

s th

at t

he

likel

y er

ror

in

our

pow

er m

easu

rem

ent

is a

lmost

entire

ly

due

to t

he

unce

rtai

nty

in r

esis

tance

. To im

pro

ve t

he

accu

racy

we

should

co

nce

ntr

ate

on r

educi

ng t

he

unce

rtai

nty

of

the

resi

stan

ce m

easu

rem

ent,

not

on

impro

ving t

he

voltm

eter

. This

kin

d o

f in

form

atio

n c

an s

ave

a lo

t of

tim

e an

d m

oney

(vo

ltm

eter

s ar

e ex

pen

sive

, re

sist

ors

are

not)

.

H.

Ahm

adia

nM

easu

rem

ent

Sys

tem

s,

Ses

sion3

26

Cov

ere

d T

opics:

Mea

sure

men

t Acc

ura

cyErr

or:

The

Norm

al D

istr

ibution a

nd t

he

Uniform

D

istr

ibution

Unce

rtai

nty

(Acc

ura

cy)

Mea

sure

men

t U

nce

rtai

nty

Model

Cal

cula

tion o

f Tota

l U

nce

rtai

nty

Measurement Systems

H.Ahmadian

MeasurementCharacteristics

H. Ahmadian Measurement Systems, Session4 2

Measurement StandardsStandard is a unit of known quantity or dimension to which other measurement units can be compared.

A Historical PerspectiveWhat Are Standards?

Standards of Practice (Protocol Standards) • Legal Metrology •Forensic Metrology • Standard Reference Materials

A Conceptual Basis of MeasurementsThe Need for StandardsTypes of Standards

Basic or Fundamental Standards • Derived Standards • TheMeasurement Assurance System

Numbers, Dimensions, and UnitsMultiplication Factors


A Historical PerspectiveMany early standards were based on the human body:

Length of man’s hand, Width of his thumb,Distance between outstretched fingertips, Length of one’s foot,…

The logical person to impose a single standard was the ruler of the country

12-inch or other short measuring stick is still called a ruler.

This right has since been assumed by all governments.


A Historical PerspectiveStandards defined by regional authorities, often caused problems in commerce and early scientific investigation.In 1790, the French National Assemblydirected the French Academy of Sciencesto “deduce an invariable standard for all measures and all the weights”

The Academy proposed the metric system,Unit of length in terms of the earth’s circumference.Units of volume and mass derived from the unit of lengthAll multiples of each unit be a multiple of 10.


A Historical PerspectiveIn 1875, the 17 countries signed the “Treaty of the Meter,”

It also established an International Bureau of Weights and Measures (BIPM)The BIPM assigned system of units by meter and kilogram called the Système International d’Unités (SI).

As the level of scientific sophistication improved, the basis for the measurement system changed dramatically.

Attempts were made to base them on “natural” phenomena:The second was defined as 1/86,400th of a mean solar day.The meter is the distance that light travels in an exactly defined fraction of a second (the speed of light in a vacuum is now defined as a constant of nature).


What Are Standards?There are several kinds of standards:

“measurement standards,”“standards of practice or protocol standards”

Produced by the various standards bodies:International Organization for Standardization (ISO), International Electrotechnical Commission (IEC), American National Standards Institute (ANSI),Institute of Standards & Industrial Research of Iran (ISIRI)


Standards of Practice (Protocol Standards)

Such standards can be defined as documents describing the operations and processes that must be performed in order for a particular end to be achieved:

Dimensions and electrical characteristics of a flashlight batteryShape of the threads on a machine screw Size and shape of an IBM punched card Quality Assurance Requirements for Measuring Equipment.

They are called a “protocol” by Europeans to avoid confusion with a physical standard.


Standards of Practice


Legal MetrologyLegal Metrology: application of measurement standards to the control of the daily transactions of trade and commerce

It is more commonly known as Weights and Measures.

Internationally, coordination among nations on Legal Metrology matters is, by the International Organization for Legal Metrology (OIML).Domestic uniformity in legal metrology matters is the responsibility of National Institute of Standards of each country.


Forensic Metrology

Forensic Metrology: Application of measurements and hence measurement standards to the solution and prevention of crime.It is practiced within the laboratories of law enforcement agencies throughout the world.Worldwide activities in Forensic Metrology are coordinated by Interpol.


Standard Reference Materials (SRM)

Discrete quantities of substances or minor artifacts that have been certified as to their composition, purity, concentration, or some other characteristic. Useful in the calibration of the measurement devices and the measurement processes normally used in the process control of those substances.The essential calibration standards in stoichiometry.


A Conceptual Basis of MeasurementsIn order to achieve quality/to do things right:

It is necessary to make some decisionsCorrect decisions needs good numerical data on which to base those decisions.Those numerical data must come from measurements and they must be based on the “right” numbers.The only way to get “good” numerical data is to make accurate measurements using calibrated instruments that have been properly utilized.If it is important to compare those measurements to other measurements made at other places and other times, the instruments must be calibrated using traceable standards.


The Need for StandardsStandards define the units and scales in use, and Allow comparison of measurements made in different times and places.

In any commercial transaction there is need to agree on the units, conditions, and method(s) of measurement to be used.

Daily measurement needs use lower-level standards that can be checked against those national or international standards.This chain of calibrations or checking is called “traceability”.A proper chain of traceability must include a statement of uncertainty at every step.


Types of Standards

Basic or Fundamental StandardsIn the SI system, there are seven basic measurement units from which all other units are derived.


Types of Standards

Derived StandardsAll of the other units are derived from the seven basic units


The Measurement Assurance System


Numbers, Dimensions, and Units

A measurement is always expressed as a multiple (or submultiple) of some unit quantity.

Amperes, milliamperes or even microamperes.

Multiplication factors has been defined used in conjunction with the units to them to a more reasonable size.


Multiplication Factors

Vibration Measurement Systems

H.Ahmadian

VibrationTransducers

H. Ahmadian Measurement Systems, 2

Covering TopicsVibration Transducers

Ch 17, Measurement, Instrumentation, and Sensors HandbookIntroduction Acceleration, Vibration and Shock MeasurementAccelerometer DynamicsElectromechanical Force-Balance (Servo) AccelerometersPiezoelectric AccelerometersPiezoresistive AccelerometersDifferential-Capacitance AccelerometersStrain-Gage AccelerometersSeismic AccelerometersInertial Types, Cantilever, and Suspended-Mass ConfigurationElectrostatic Force Feedback AccelerometersMicroaccelerometersCross-Axis SensitivitySelection, Full-Scale Range, and Overload CapabilitySignal Conditioning


Transducers

The Measurement Chain

Remember : System never stronger than the weakest link in the chain.

Vibration Transducers


Transducers

Vibration TransducersCommonly referred to as pickups or sensors

Early Methods of vibration measurementMeasurement !!?. . . . . . . “ Evaluation ” sounds better !


Touching finger Transfer through a rod Transfer through a doctor’s stethoscope


Transducers

Vibration TransducersMechanical Lever

ApplicationObsolete !! but still found in a few old power stations.

Measures Displacement Advantages

Self generatingTrace availableInexpensive

LimitationsNo electrical outputLow frequency onlyHigh amplitudes requiredProne to wearLoads the vibrating structureSensitive to orientation



Vibration TransducersEddy current proximity probe

Measures DisplacementDynamic range : 500:1Frequency range : DC-10 KHz (Theoretical)

DC-2000Hz (Practical)How it works ?

DriverProbeExtension cable

TransducersVibration Transducers


Vibration TransducersEddy current proximity probe

How it works ? (cont.)Produces 2 signals :

AC proportional to vibrationDC proportional to the gap size



Vibration TransducersEddy current proximity probe (cont.)

ApplicationRelative motionShaft eccentricityOil film thickness & etc.Generally

Smooth running rotor is critical (Turbines & Compressors)High speed or very low speed rotors

AdvantagesNon-contactingNo moving parts, no wearWorks to DC



Vibration TransducersEddy current proximity probe (cont.)

LimitationsShaft magnetic properties VariationsShaft geometric irregularities

Local calibration necessaryLimited practical frequency range as displacement relatively small at high frequencies


erroneous signal components


Vibration TransducersVelocity Pickup

2 primary types :Moving coil typePiezoelectric type

Moving coil typeHow it works ?

Induced voltage proportional to Magnetic field B, length of winding, & velocityDynamic range : 1000:1




Vibration TransducersVelocity Pickup

Moving coil type (cont.)Induced voltage proportional to

Magnetic field B, length of winding, & velocityDynamic range : 1000:1

AdvantagesSelf generatingLow impedance

LimitationsMoving parts prone to wearLarge sizeSensitive to orientationSensitive to magnetic fieldsHigh lower limiting frequency(>10 Hz) operating above resonanceReduced output signal because of friction of moving element



Vibration TransducersVelocity Pickup (cont.)

Piezoelectric typeSimilar to the piezoelectric accelerometer It has a built-in piezoelectric acceleration detection element and converts the input signal to a voltage signal proportional to velocity vibration by an internal integrating circuit.Charge proportional to velocityPiezoelectric disks responding to the stress of whatever applied forces

AdvantagesNot affected by magnetic fieldsCan measure accurately down to 60 cpm or less.

LimitationsBuilt-in amplifier due to the extremely small signal Thermal sensitivities and ambient temperature limitations involved



Vibration TransducersAccelerometers

The most common and versatile types of transducers

TypesPiezoelectric

Charge modeInternally amplified

Strain gaugePiezoresistiveVariable Capacitance…



Vibration TransducersPiezoelectric Accelerometers

How it works ?Sensing element put under load by a massCrystal squeezed or released as “stack” vibratesCharge output proportional to force



Vibration TransducersPiezoelectric Accelerometers (cont.)

Measures accelerationDynamic range ContactingMeasures absolute casing motion

AdvantagesSelf generatingRuggedNo moving parts, no wearVery large dynamic rangeWide frequency & amplitude rangeCompact & often low weightOrientation not importantVelocity or displacement output available

)160(1:108 dB



Vibration TransducersPiezoelectric Accelerometers (cont.)

LimitationsHigh impedance outputNo true DC response

TypesCompression type design

Traditional simple constructionVery stable but high environmental influenceTypically used for high shock levels

P :piezoelectric element B :Base

M :Seismic mass S :Spring




Types (cont.)Shear type design

Piezoelectric arranged subjected to shear forces from seismic massRather insensitive to environmental parameters like temperatures

DeltaShear Design3 piezoelectric elements & 3 masses arranged in triangular configurationExcellent overall specificationsVery low sensitivity to environmental influences

P :piezoelectric element B :Base

M :Seismic mass R :Clamp ring




Types (cont.)Planar-Shear Design

Simplified DeltaShear Design with 2 elementsAnnular-Shear DesignTheta-Shear DesignOrtho-Shear Design

P :piezoelectric element B :Base E :Built-in Electronics

M :Seismic mass R :Clamp ring


TransducersAccelerometer Dynamics

Full understanding of accelerometer dynamics Characteristics of acceleration, vibration, and shock

Vibrating MotionPeriodicStationary RandomNon-Stationary RandomTransient



Periodic VibrationSinusoidal



Periodic VibrationBut not necessarily sinusoidal !!

Fourier Analysis

As in . . .

Elements of the frequency Spectrum



Stationary RandomNever repeat themselves exactly (random)Statistical properties of vibrations do not vary in time (stationary)Infinitely long time record necessary

BUT. . . Statistical methods & Probability theory applicableprobability distributionsprobability densitiesfrequency spectracross- & auto-correlationsDigital Fourier Transforms (DFT)Fast Fourier Transforms (FFT)Auto spectral analysisRMS valuesDigital filter analysis …



Non-Stationary RandomNever repeat themselves exactly (random)Statistical properties of vibrations do vary in time (non-stationary)



Transients and ShocksShort-duration sudden-occurrence vibrationStatistical methods and Fourier Transforms applicable



Seismic AccelerometerA Deflection type accelerometer

Considering only the mass-spring system

Adding the motion of the base . . .

A 2nd order System


Seismic Accelerometer (cont.)

What are they good for then !?Design for different characteristics by selection of parameters

Further discussion later !


A 2nd order System


Covered TopicsVibration Transducers

Introduction Acceleration, Vibration and Shock MeasurementAccelerometer DynamicsElectromechanical Force-Balance (Servo) AccelerometersPiezoelectric AccelerometersPiezoresistive AccelerometersDifferential-Capacitance AccelerometersStrain-Gage AccelerometersSeismic AccelerometersInertial Types, Cantilever, and Suspended-Mass ConfigurationElectrostatic Force Feedback AccelerometersMicroaccelerometersCross-Axis SensitivitySelection, Full-Scale Range, and Overload CapabilitySignal Conditioning


H.Ahmadian


H. Ahmadian Measurement Systems 2

Covering TopicsVibration Transducers (Chapter 17)

IntroductionAcceleration, Vibration and Shock MeasurementAccelerometer DynamicsElectromechanical Force-Balance (Servo) AccelerometersPiezoelectric AccelerometersPiezoresistive AccelerometersDifferential-Capacitance AccelerometersStrain-Gage AccelerometersSeismic AccelerometersInertial Types, Cantilever, and Suspended-Mass ConfigurationElectrostatic Force Feedback AccelerometersMicroaccelerometersCross-Axis SensitivitySelection, Full-Scale Range, and Overload CapabilitySignal Conditioning


Transducers

Principle of OperationNull-Balance type

Magnetic field equivalent of Spring force Capability of testing static & dynamic characteristicsBetter accuracy than force-to-displacement transducer

Different typesCoil & Magnetic typeInduction Types…

Electromechanical Force-Balance Accelerometers


Transducers

Coil & Magnetic TypeAmpere’s lawHow it works ?

Downward acceleration field

ConsiderationsExternal magnetic disturbancesTemperature rise due to losses


Ri2

Scale factor or bias change


Transducers

Coil & Magnetic TypeRotational type servo-accelerometerHow it works ?

Motion from null of M caused by accelerationMagnetic torque to return the mass to neutral


More in Doebelin 1990


Transducers

Principle of OperationPolarization principle

Mass in direct contact with piezoelectricProportional electric charge

Piezoelectric Accelerometers

Generator action Motor action


Transducers

Principle of Operation (cont.)Typical frequency response for a PZTDetermining resonant frequency

Mathematically a 3rd order system


Not for crystal itself but the electric circuit


Transducers

Principle of Operation (cont.)2 commonly used crystals

Lead-zirconate titanate [PZT]Quartz

Low frequency response limited by piezoelectric Why ?High frequency response related to mechanical response

2 basic design configurationsCompression type

Good mass/sensitivity ratioHousing as an internal part of the mass/spring system

Shear stress type


(150 times more sensitive)


Transducers

Principle of Operationsemiconductor strain gages with large gage factorsmaterial resistivity dependent on stress, not only on dimensionsMostly two or four active gages arranged in a Wheatstone bridge

AdvantageLow frequencies : true static acceleration measurement devicesTypical Characteristics are as above

Piezoresistive Accelerometers

Sensitivity :

Freq. range :

Resonance freq. :

Amplitude range :

Shock rating :

Temp. range :

Total mass :


Transducers

Principle of OperationBased on change of capacitance due to acceleration

One of different types as :Mass constrained in null by a springUnder acceleration, variable frequencies obtained in electric circuit

Differential Capacitance Accelerometers


Transducers

Principle of Operation (cont.)

For example if the oscillation frequency of RC circuit sensed was

Substituting C results in…

Differential Capacitance Accelerometers

m = the proof mass

K = the spring constant


Transducers

Principle of OperationStrain gages for any mechanical variable including force or torqueHow ? Strain-gage-instrumented spring element

As in a strain-gage-based accelerometer like . . .

Strain Gage Accelerometers


Transducers

Principle of Operation (cont.)Based on resistance properties of electrical conductors

Stretched or compressed, conductors change resistance due to :Dimension changeMaterials’ fundamental properties > piezoresistance

Dependence as the Gauge factor

Strain Gage Accelerometers


Transducers

Principle of OperationBase vibrationProper selection of mass, spring & damper

Displacement measurement [ Large mass & soft spring ]Acceleration measurement [ small mass & stiff spring ]

Governing equation

Harmonic vibratory motion for the base . .

Seismic Accelerometers


Transducers

Principle of Operation (cont.)With this the equation modifies to …

The steady-state solution of which is . . .

Which can be rearranged to . . .



Transducers

Principle of Operation (cont.)seismic instrument with low displacement sensor to measure z

seismic instrument with high displacement sensor to measure z

Displacement sensingVoltage divider potentiometer


output proportional to case displacement

n

n output proportional to case acceleration

Full scale

Natural freq.

Damping ratio

Cross-axis sensitivity

Size

mass

gg 501

HzHz 8912

8.05.0

%1

350mm

g120


Transducers

Principle of Operation (cont.)Displacement sensing

Linear variable differential transformers (LVDT)

Electric resistance strain gage


Full scale

Natural freq.

Damping ratio

Cross-axis sensitivity

Size

mass

gg 7002

HzHz 62035

7.06.0

%1

350mm

g120

Natural freq. Hz300


Transducers

Principle of OperationForce to constrain mass in presence of the acceleration by an inertial system

Vibrating string type

Cantilever typeSuspended mass configuration

Inertial types

held constant by servoingtension in strings

)( 21 ff


Transducers

Principle of OperationBased on Coulomb’s law between to charged electrodes

voltage in terms of force required to sustain a movable known electrode

force per unit area of the charged conductor

One stationary and one moveable electrode…. The attraction force

Electrostatic force feedback accelerometers

K is the dielectric constant


Transducers

Principle of Operation (cont.)In presence of acceleration is to restrain the electrode in null

The device, measuring acceleration in one direction, has a quadratic output

If the servo applies a to the fixed electrode

Force balance equation of movable electrode for downward acceleration is

bias potential V1 held constant & high gain of the control loopvariations in gap negligible



Transducers

Principle of Operation (cont.)Main advantages

Extreme mechanical simplicityLow power requirementsAbsence of inherent sources of hysteresiserrorszero temperature coefficientsEease of shielding from stray fields

Main difficultiesRelatively high electric field intensity requiredExtremely good bearings necessaryDamping provided electrically, or by viscosity of gaseous atmosphere




Introduction

Acceleration, Vibration and Shock Measurement

Accelerometer Dynamics

Electromechanical Force-Balance (Servo) Accelerometers


Piezoresistive Accelerometers

Differential-Capacitance Accelerometers

Strain-Gage Accelerometers


Inertial Types, Cantilever, and Suspended-Mass Configuration

Electrostatic Force Feedback Accelerometers

Microaccelerometers

Cross-Axis Sensitivity

Selection, Full-Scale Range, and Overload Capability

Signal Conditioning


H.Ahmadian



Covering TopicsVibration Transducers



Transducers

A Vibrating structure may have been subjected to

Torsional vibrationCompressional vibrationTransverse vibration…

Cross-Axis sensitivityResponse to a plane perpendicular to the main axis Expressed in percent of the main

Cross-Axis sensitivity


Transducers

First glance categorizationGeneral purpose

various sensitivities, frequencies, full scale, & overload ranges

Special types

Characteristics to be consideredTransient responseCross-axis sensitivityFrequency rangeSensitivityMass & dynamic rangeEnvironmental conditions

Accelerometer Selection


Transducers

Frequency RangeUpper limit

Rule of thumbUpper limit : one-third of resonance

vibrations measured less than 1 dB in linearityApplications with lower linearity (e.g., 3 dB)

As for internal conditions of machines (reputability more important)½ or 1/3 of natural freq.

Lower limit2 factors

Amplifier’s cut-offAmbient temperature fluctuations

Accelerometer Selection : Some Hints

r1

Slide 5

r1 itrafieian, 5/9/2005


Transducers

Sensitivity, Mass & Dynamic RangeSure better if higher is the sensitivity . . . BUT compromises may have to be made

versusFrequencyRangeOverload capacitySize

Mass…for small & light test objectsShould not load the test objectRule of thumb

Dynamic rangeShould match high or low acceleration levelsGeneral purpose linear up to 5000g or 10,000g



Transducers

TransientsReleases of energy in short-duration pulses : various shapes and rise times

Overall linearity limited toHigh frequencies by Zero Shift

Phase nonlinearity in preamplifiersNot returning to steady-state conditions after subjected to high shocks

Low frequencies by RingingHigh frequency components of excitation near resonance

Environmental effectsBase strain

Reduced byThick baseDelta shear type

HumidityFor the connectorUse silicon rubber sealants

. . .



Transducers

Main requirementClose mechanical contact

Bad mounting reduces the usable frequency range

Stud mountingCementing studWith Beeswax (limited by temp.)Isolated mounting

Accelerometer mounting-Fixed


Transducers

3 different approaches asPermanent magnet

Limited by Ferro-magnetic surfacesDynamic range limited due to magnet force

Hand held probeLow overall stiffness

On a long rodWhere inaccessibleSuperior to hand held

Accelerometer mounting-Handheld


Transducers

Typical reasons of coupling errors

Comparison of typical mounting techniques (ISO-5348)

Accelerometer mounting


TransducersAccelerometer mounting

Isolating the accelerometerElectrical

Preventation of ground loops

MechanicalProtection against high shocks


TransducersAccelerometer mounting

Choosing a mounting positionDesired measuring direction coincides with the main axis sensitivityWhy you measure vibration dictates where to mount it !

If the bearing is of importanceA, B, C, or D ?

Handle carefullyA drop on a hard floor

Several thousands of gChange in sensitivityDamage….

Recalibration if happened however !A check of frequency response curve


TransducersCalibration

Why Calibration !?To find the sensitivity

Why Recalibration !?Legal obligation – QA requirementGood instrument practiceTest for damage

Accelerometer checkIn the field

Sensitivity checkTotal system check

In the LabFrequency responseSensitivity calibration



Mounted resonance testThe test is done to check

Cable connectionLoose mountinggood mounting not a low mechanical impedance at mounting location

Done as followsAccelerometer excited by a suitable square pulseResponse obtained is filteredFrequency is counted



Back-to-back methodUsing a Reference Standard Accelerometer

Accelerometers with very high accuracy (1%)At a reference frequency (normally 160 or 80 Hz)Over wider frequency ranges with slightly less accuracy

Details in ISO 5347-3

ISO 5347

Methods for Calibration and Characterization of Vibration and Shock

Transducers


TransducersSignal Conditioning

PreamplifierFunctions done bye

Impedance conversionAmplificationMatching output signal to measuring instrumentation input sensitivity (Conditioning)FilteringIntegration to obtain velocity or displacement output signalsWarning of overloads anywhere before the following instrumentation



PreamplifierVoltage preamplifiers

sensitivity varies dramatically with cable lengthLower limiting frequency affected by cable length and resistance

Charge preamplifiersA short-circuit in which the current flowing is integrated

Charge = Current × Time

Charge = Voltage × Capacitance



PreamplifierThe complete transfer function

selected to be large compared to system gain independent of cable length

Low-frequency response a function of well-defined electronic components2 time constants, external & internal for system

fC )1/()( GCC ca



Pieoresistive transducersHigh amplitude outputsLow output impedancesLow intrinsic noise

Many configured as full-bridge devices

MicroaccelerometersSignal conditioning circuitry integrated within chip with sensorTypical of signal conditioning circuitry as

output : frequency-modulated acceleration signaloutput can be read directly into a digital device





H.Ahmadian

Fundamentals of Signal Analysis


Covering TopicsFundamentals of Signal Analysis

Introduction

Time and Frequency Domains: A matter of Perspective

The Time DomainThe Frequency Domain

Understanding Dynamic Signal AnalysisSee Section 83.1 Spectrum Analysis and Correlation

FFT PropertiesSampling and DigitizingAliasingLeakageWindowing



The Measurement Chain

Now : Ways of analyzing the output signals of the preamplifier.

Introduction



The Time DomainTraditional way of observing signals

Hopelessly ideal !!

More practical to convert the parameter to electrical signal by a transducer

So you can adjust the gain

The Time and Frequency Domains



The Frequency DomainShown by Fourier over one hundred years agoEvery Sine wave as a straight line

It’s Height ?It’s position ?

Called the “ Spectrum ” of the signal Each sine wave line a “ Component” of the signal

Relationship between Time and Frequency Domain




The Need for decibelSmall signals in presence of large ones

A logarithmic scaleCompress the larger onesExtend the smaller ones

Alexander Graham Bell human ear responds logarithmically to power difference The unit Bel ….One tenth of a Bel, a deciBel (dB) :most common unit used




When linear & when logarithmic scales !?Depends on the unit to be scaled

LinearWhen the absolute value is importantTypical examples : Time & displacement

LogarithmicWhen the ratio between values is of importanceAs in coins !!




Linear vs. Logarithmic frequency scaleLinear frequency scale

to identify harmonically related components

Logarithmic frequency scalemuch wider frequency range can be covered




Linear vs. Logarithmic amplitude scaleOften the case : interesting components much lower than the dominants

Advantages of logarithmic amplitude scaleConstant factor changes equally displayed for all levelsDisplaying a large dynamic range




Take careChanging from time domain to frequency domain

We have neither gained , nor lost information, JUST representing differently

Frequency Domain a natural domain !!You pick up a small sound in a loud background (a friend speaking)? Don’t you !?

Frequency spectrum or overall level

Overall levelRMS detectorExpressing vibration energy levelNot for diagnosis

The role of frequency analysisMany kinds of diagnosis to be made




Why Frequency domain then !?Detect small sine wave in the presence of large onesSignal sources as in a gearbox

Frequency Domain a natural domain !!How do you pick up a small sound in a loud background (a friend speaking) ?


the gear mesh frequencies



When frequency spectrum & when overall levelWhat the most likely faults in your machine are, dictates!!

Monitoring a fanThe most likely fault : unbalance

Monitoring a gear boxDamaged or worn gears at tooth meshing frequencies and harmonicsLevels much lower than the highest in spectrum




Spectrum Examples




Network (System) AnalysisFrequency analysis not only for extracting signals’ components !Frequency domain used in network analysis

How a structure will behave in high windsHow effective a sound absorbing is reducing machinery noise . . .

One-port Network Analysis

Two-port Network Analysis

N-port Network Analysis


Capacitor Shock mount

Sound transmission through a barrier



Linear Network

Non-linear NetworkSome systems

Linear for small deflections

Non-linear for large deflections


Some otherNonlinear inherently

Mass & stopper

Backlash in gear trains



Time recordConsecutive, equally spaced samples of inputTo make it simpler and faster, N a multiple of 2

Discrete Fourier Transform (DFT) / SeriesAssumption

The signal is periodic

Understanding Dynamic Signal Analysis

Sampling function

Digitized Signal

1s

s

ft Sampling frequency

sT Nt

( ) ( )x t x t T


Fundamentals of Signal AnalysisUnderstanding Dynamic Signal Analysis

Discrete Fourier Series / TransformFourier Series

0

1( ) ( ) ( )

2 n n n nn

ax t a Cos t b Sin t

2n

nT

0

2 ( ) ( )T

n na x t Cos t dtT

0

2 ( ) ( )T

n nb x t Sin t dtT

or

( ) ni tnx t X e

0

1 ( ) n

Ti t

nX x t e dtT

*n nX X

Re( )2n

naX Im( )

2n

nbX

12

0

1

2 2( ) ( )2

N

k n nn

a nk nkx a Cos b SinN N

1,2,....,k N1

0

2 2( )N

n kk

nka x CosN N

1

0

2 2( )N

n kk

nkb x SinN N

or21

0

inkNN

k nn

x X e2

1

1 inkN

n kk

X x eN

1,2,....,n N


Another way of representing

Each element a unit vector with an angular orientationThe sampling frequency :

The frequency rangeThe resolution

0

0 1

1

1

1

. . . ... . . .

. .. . . . . . . .

. .. . . . . . . .

. .. . . . . . . ... . . . . .N

N

xX xX

Xx

Fundamentals of Signal AnalysisUnderstanding Dynamic Signal Analysis

2

1

1 inkN

n kk

X x eN

2 inkNe1 2 2

s ss s

N Nft T t T

max max2 2s sf Nf

T

The Nyquist frequency

1 2,fT T


Covered TopicsFundamentals of Signal Analysis

Introduction

Time and Frequency Domains: A matter of PerspectiveThe Time DomainThe Frequency Domain

Understanding Dynamic Signal Analysis

FFT PropertiesSampling and DigitizingAliasingLeakageWindowing

Documents

Syllabus€¦ · · 2012-10-16Syllabus Measurement Characteristics Transducers-Fundamentals of Vibration- ... Fundamentals of Rotating Machinery Diagnostics,