METROLOGY
Cour
seObj
ect
i
v
es:
1.Deal
swi
t
ht
hebasi
cpr
i
nci
pl
esofbasi
cmeasur
i
ngi
nst
r
ument
sandpr
eci
si
on
measur
ementt
echni
ques.
2.Lear
nt
hebaseknowl
edgeofLi
mi
t
s,
Fi
t
sandTol
er
ances.
3.Tounder
st
anddi
f
f
er
entsy
st
em t
omanuf
act
ur
ehol
esandshaf
t
s.
4.Togai
ndomai
nknowl
edgeonl
i
near
,angul
arandopt
i
calmeasur
i
ngdev
i
cesf
or
v
ar
i
ousf
or
msofwor
kpi
eces.
5.Lear
nst
hei
mpor
t
anceofsur
f
acef
i
ni
shf
ort
hepr
eci
si
oncomponent
s,di
f
f
er
ent
met
hodsf
orf
i
ndi
ngandmeasur
i
ngsur
f
acef
i
ni
sh.
6.Lear
nsdi
f
f
er
enti
nst
r
ument
susedf
ormeasur
i
ngt
hedi
mensi
onalaccur
acyof
component
sl
i
kegear
sandscr
ewt
hr
eads.
7.Lear
nst
heneedofsur
f
aceengi
neer
i
nganddi
f
f
er
entmet
hodsofcl
eani
ngand
ov
er
l
ay
i
ng.
Cour
seOut
comes:
1.Whencompl
et
ed,st
udent
swi
l
lhav
eapr
operunder
st
andi
ngonbasi
cconcept
ofmet
r
ol
ogy
.
2.Gai
nsdomai
nknowl
edgeonMet
hodsofmeasur
ement
3.Lear
nsv
ar
i
ousmeasur
i
ngdev
i
ces.
4.Wi
l
l
beabl
et
oanal
y
zet
hemeasur
edv
al
ues.
5.Under
st
andconceptofcal
i
br
at
i
onofequi
pment
s.
6.He gai
nsknowl
edge i
n achi
ev
i
ng qual
i
t
yand r
el
i
abi
l
i
t
yi
n ser
v
i
cesofany
pr
oducti
si
t
sdi
mensi
onal
cont
r
ol
.
STUDYMATERI
ALPage1
METROLOGY
Chapt
er1
Sy
st
em ofLi
mi
t
sandFi
t
s
1.
1
I
nt
r
oduct
i
on:
Theknowl
edgeofmet
r
ol
ogyi
sofv
i
t
ali
mpor
t
ancei
nt
hemoder
ncompet
i
t
i
v
e
i
ndust
r
i
alenv
i
r
onment
.Thi
scour
sei
sdesi
gnedt
of
ami
l
i
ar
i
zeEngi
neer
sand
Sci
ent
i
st
swi
t
hMet
r
ol
ogy
,
t
hesci
enceofmeasur
ement
.Aquant
i
t
at
i
v
eanal
y
si
s
ofdesi
gn based on sound met
r
ol
ogypr
i
nci
pl
es wi
l
lhel
p engi
neer
s and
sci
ent
i
st
st
odesi
gnbet
t
erpr
oduct
sandser
v
i
ces.I
nor
dert
oev
al
uat
emul
t
i
pl
e
sol
ut
i
ons t
ot
he desi
gn,phy
si
calmeasur
ement
s ar
e made and t
he dat
a
anal
y
zed.Pr
edi
ct
i
onsneedt
obemadeonhowwel
lt
hedesi
gnwi
l
lper
f
or
mt
o
i
t
sspeci
f
i
cat
i
onsbef
or
ef
ul
lscal
epr
oduct
i
onbegi
ns.Test
sar
eper
f
or
med
usi
ng pr
ot
ot
y
pe model
s, comput
er si
mul
at
i
on, desi
gned exper
i
ment
s,
dest
r
uct
i
v
eandnondest
r
uct
i
v
et
est
s,scal
emodel
sandst
r
esst
est
samong
t
hemanyot
hermet
hodsofev
al
uat
i
on.I
nt
hi
scour
se,y
ouwi
l
ll
ear
nt
oappl
y
endt
oendmet
r
ol
ogyacr
ossal
ldi
sci
pl
i
nesi
nv
ol
v
edi
npr
oduci
ngapr
oduct
.
Ther
ol
eofmet
r
ol
ogyi
nt
hev
ar
i
ousphasesofapr
oduct
sl
i
f
ecy
cl
ewi
l
lbe
cov
er
ed.
1.
2
Def
i
ni
t
i
on:
Met
r
ol
ogy(
f
r
om Anci
entGr
eekmet
r
on(
measur
e)andl
ogos(
st
udyof
)
)i
st
he
sci
ence ofmeasur
ement
.Met
r
ol
ogyi
ncl
udes al
lt
heor
et
i
caland pr
act
i
cal
aspect
sofmeasur
ement
.
Met
r
ol
ogyi
sconcer
nedwi
t
ht
heest
abl
i
shment
,r
epr
oduct
i
on,conser
v
at
i
on
and t
r
ansf
erofuni
t
sofmeasur
ement& t
hei
rst
andar
ds.Forengi
neer
i
ng
pur
poses,met
r
ol
ogyi
sr
est
r
i
ct
edt
omeasur
ement
sofl
engt
handangl
e&
quant
i
t
i
eswhi
char
eexpr
essedi
nl
i
nearorangul
art
er
ms.Measur
ementi
sa
pr
ocessofcompar
i
ngquant
i
t
at
i
v
el
yanunknownmagni
t
udewi
t
hapr
edef
i
ned
st
andar
d.
Measur
ementi
scol
l
ect
i
onofquant
i
t
at
i
v
edat
a.Ameasur
ementi
smadeby
STUDYMATERI
ALPage2
METROLOGY
compar
i
ngaquant
i
t
ywi
t
hast
andar
duni
t
.Si
ncet
hi
scompar
i
soncannotbe
per
f
ect
,
measur
ement
si
nher
ent
l
yi
ncl
udeer
r
or
.
1.
3
Needf
orI
nspect
i
on:
 Ol
den day
s pr
oduct
i
on was i
n smal
lscal
e,pr
oduct
s used t
o be
assembl
edbysi
ngl
eper
son.
 Duet
ot
echnol
ogi
cal
dev
el
opmentmasspr
oduct
i
onhasst
ar
t
ed
 Handf
i
tmet
hodcannotser
v
et
hepur
pose
 Moder
ni
ndust
r
i
al
masspr
oduct
i
onneedsi
nt
er
changeabl
epr
oduct
i
on
 Pr
oduct
i
onofeachcomponentbecomesi
ndependentpr
ocess
 I
t
’
sessent
i
al
anypr
oduct
schosenatr
andom needt
of
i
tpr
oper
l
y
.
1.
4
Pr
eci
si
onandAccur
acy
:
Pr
eci
si
on:Thepr
eci
si
onofani
nst
r
umenti
ndi
cat
esi
t
sabi
l
i
t
yt
or
epr
oducea
cer
t
ai
nr
eadi
ngwi
t
hagi
v
enaccur
acy
.I
not
herwor
ds,i
ti
st
hedegr
eeof
agr
eementbet
weenr
epeat
edr
esul
t
s.Pr
eci
si
ondat
ahav
esmal
ldi
sper
si
on
(
spr
eadorscat
t
er
)butmaybef
arf
r
om t
het
r
uev
al
ue.
Accur
acy
:
Thedegr
eeofcl
osenesst
ot
r
uev
al
ue.
Ameasur
ementcanbeaccur
at
ebutnotpr
eci
se,pr
eci
sebutnotaccur
at
e,
nei
t
her
,orbot
h.Ameasur
ementsy
st
em i
scal
l
edv
al
i
di
fi
ti
sbot
haccur
at
e
andpr
eci
se.
STUDYMATERI
ALPage3
METROLOGY
Fi
gur
ei
ndi
cat
espr
eci
si
onandaccur
acy
Tabl
ei
ndi
cat
est
hedi
f
f
er
encebet
weenaccur
acyandpr
eci
si
on
Sl
.
No Accur
acy
Pr
eci
si
on
1
I
ti
st
hecl
osenesswi
t
ht
het
r
ue I
ti
sameasur
eofr
epr
oduci
bi
l
i
t
yoft
he
v
al
ue of t
he quant
i
t
y bei
ng measur
ement
s
measur
ed
2
Theaccur
acyofmeasur
ement The t
er
m pr
eci
se means cl
ear
l
y or
meansconf
or
mi
t
yt
ot
r
ut
h
shar
pl
ydef
i
ned
3
Accur
acycanbei
mpr
ov
ed
4
Accur
acydependsuponsi
mpl
e Pr
eci
si
on depends upon manyf
act
or
s
t
echni
quesofanal
y
si
s
and r
equi
r
es many sophi
st
i
cat
ed
t
echni
quesofanal
y
si
s
5
Accur
acyi
snecessar
ybutnot Pr
eci
si
on i
s necessar
y but not a
suf
f
i
ci
ent
condi
t
i
on
f
or suf
f
i
ci
entcondi
t
i
onf
oraccur
acy
pr
eci
si
on
1.
5
Pr
eci
si
oncannotbei
mpr
ov
ed
LI
MI
TSYSTEM:
1.
5.
1
Li
mi
t
:
Themaxi
mum upperv
ar
i
at
i
onorl
owerv
ar
i
at
i
ongi
v
enaboutt
owhi
ch
STUDYMATERI
ALPage4
METROLOGY
acomponentcanbemadei
scal
l
edLi
mi
t
.
Def
i
ni
t
i
on:
Thet
woext
r
emeper
mi
ssi
bl
esi
zesbet
weenwhi
cht
heact
ualsi
ze
oft
heobj
ectl
i
esi
scal
l
edLi
mi
t
.
Themaxi
mum si
zei
scal
l
edupperl
i
mi
t
Themi
ni
mum si
zei
scal
l
edl
owerl
i
mi
t
1.
5.
2
Tol
er
ance
Tol
er
ance:
I
ti
st
hedi
f
f
er
encebet
weenmaxi
mum l
i
mi
tofsi
zeandt
hemi
ni
mum l
i
mi
t
ofsi
ze.I
ti
sal
way
sposi
t
i
v
eandi
sexpr
essedonl
yasanumberwi
t
houta
si
gn.
Theper
mi
ssi
bl
ev
ar
i
at
i
onordev
i
at
i
onwhi
chcanbegi
v
enf
ort
heact
ual
si
zeoft
heobj
ecti
scal
l
edt
ol
er
ance.
Ty
pes:
a)Uni
l
at
er
al
Tol
er
ance.
b)Bi
l
at
er
al
t
ol
er
ance.
a)Uni
l
at
er
alTol
er
ance:-At
ol
er
ancemet
hodusi
ngadev
i
at
i
oni
nonl
yone
di
r
ect
i
on,
ei
t
herpl
usormi
nus,
f
r
om t
hespeci
f
i
eddi
mensi
on
I
tmaybecompl
et
el
yabov
et
heact
ual
si
zeorbel
owt
heact
ual
si
ze.
STUDYMATERI
ALPage5
METROLOGY
Fi
gur
ei
ndi
cat
esuni
l
at
er
al
t
ol
er
ance
b)Bi
l
at
er
alTol
er
ance:-A t
ol
er
ancemet
hodusi
nganequalpl
usandmi
nus
dev
i
at
i
onf
r
om t
hespeci
f
i
eddi
mensi
on.
Tol
er
ancei
sgi
v
enonbot
ht
hesi
desoft
heact
ualsi
ze,andt
heni
t
’
scal
l
edas
bi
l
at
er
al
t
ol
er
ance
Fi
gur
ei
ndi
cat
esbi
l
at
er
al
t
ol
er
ance
1.
5.
3
Dev
i
at
i
on
Dev
i
at
i
on:-I
ti
st
heal
gebr
ai
cdi
f
f
er
encebet
weensi
zes,t
oi
t
scor
r
espondi
ng
basi
csi
ze.I
tmaybeposi
t
i
v
e,
negat
i
v
eorzer
o.
Thedi
f
f
er
encebet
weent
heact
ual
si
zeandbasi
csi
zei
scal
l
eddev
i
at
i
on
Ty
pes:
(
a)
UpperDev
i
at
i
on
(
b)
LowerDev
i
at
i
on
UpperDev
i
at
i
on:-I
ti
st
heal
gebr
ai
cdi
f
f
er
encebet
weenmaxi
mum l
i
mi
tofsi
ze
andi
t
scor
r
espondi
ngbasi
csi
ze.
LowerDev
i
at
i
on:-I
ti
st
heal
gebr
ai
cdi
f
f
er
encebet
weenmi
ni
mum l
i
mi
tofsi
ze
andi
t
scor
r
espondi
ngbasi
csi
ze.
Act
ualDev
i
at
i
on:-I
ti
st
heal
gebr
ai
cdi
f
f
er
encebet
weenact
ualsi
zeandi
t
s
STUDYMATERI
ALPage6
METROLOGY
cor
r
espondi
ngbasi
csi
ze.
Fi
gur
ei
ndi
cat
est
heupperandl
owerdev
i
at
i
on
Shaf
t
:
Hol
e:
1.
5.
4
l
owerdev
i
at
i
onwi
l
l
bemor
e&upperdev
i
at
i
oni
sl
ess
l
owerdev
i
at
i
oni
sl
ess&upperdev
i
at
i
oni
smor
e.
Al
l
owance&Tol
er
ance
Tol
er
ancei
sgi
v
enf
orManuf
act
ur
er
s
Al
l
owancei
sgi
v
enf
orassembl
i
ngpeopl
e
Al
l
owance:
Thedi
f
f
er
encebet
weent
hemat
i
ngpar
t
si
nor
dert
ogett
her
equi
r
edamount
off
i
ti
scal
l
edAl
l
owance
Ty
pesofAl
l
owances:
1)Posi
t
i
v
e
MMC
Cl
ear
anceFi
t
2)Negat
i
v
e
LMC
I
nt
er
f
er
enceFi
t
Tabl
ei
ndi
cat
esdi
f
f
er
encebet
weenAl
l
owance&Tol
er
ance
STUDYMATERI
ALPage7
METROLOGY
TOLERANCE
ALLOWANCE
1)
Per
mi
ssi
bl
e v
ar
i
at
i
on i
n 1) Di
f
f
er
ence Bet
ween t
he
Si
ze/
Di
mensi
on i
s cal
l
ed Di
mensi
ons ofMat
i
ng Par
t
si
s
Tol
er
ance
cal
l
edAl
l
owance
2)
The Di
f
f
er
ence bet
ween 2)TheDi
f
f
er
encebet
weenShaf
t
UpperLi
mi
t&LowerLi
mi
ti
s &Hol
ei
scal
l
edAl
l
owance
Tol
er
ance
3)Tol
er
ance ar
e gi
v
en f
or 3)
Al
l
owance i
s
Manuf
act
ur
er
s
assembl
ypeopl
e
gi
v
en
f
or
4) Tol
er
ance v
al
ues ar
e 4) Al
l
owance ar
e Posi
t
i
v
e &
absol
ut
ev
al
ues
negat
i
v
e
1.
5.
5
MAXI
MUM MATERI
ALCONDI
TI
ON(
MMC)
MMC:
I
t
’
sacondi
t
i
oni
nwhi
cht
hesi
zeshoul
dcont
ai
nmaxi
mum amountofmat
er
i
al
.
Shaf
tshoul
dbepr
epar
edf
ort
heupperl
i
mi
t&Hol
et
ot
hel
owerl
i
mi
tshoul
d
cor
r
espondt
oMMC.
Cl
ear
ancef
i
t
sar
eusual
l
ydi
mensi
onedf
orMMC
STUDYMATERI
ALPage8
METROLOGY
Exampl
e:
+0.
000
0.
015
Shaf
tofØ29.
98
+0.
025
+0.
000
Hol
eofØ30.
00
Shaf
tshoul
dbepr
epar
edt
oUpperLi
mi
tØ29.
98
Hol
eshoul
dbepr
epar
edt
oLowerl
i
mi
tØ30.
00
Di
f
f
er
ence=+0.
02
Fi
tobt
ai
nedi
sCl
ear
ance
1.
5.
6
LOWER/
LEASTMATERI
ALCONDI
TI
ON(
LMC)
LMC:
I
t
’
sacondi
t
i
oni
nwhi
cht
hesi
zeshoul
dcont
ai
nmi
ni
mum
mat
er
i
al
.
amount of
Shaf
tshoul
dbepr
epar
edf
ort
hel
owerl
i
mi
t&Hol
et
ot
he
shoul
dcor
r
espondt
oLMC.
upper l
i
mi
t
I
nt
er
f
er
encef
i
t
sar
eusual
l
ydi
mensi
onedf
orLMC
STUDYMATERI
ALPage9
METROLOGY
Exampl
e:
+0.
035
+0.
020
Shaf
tofØ30
+0.
021
+0.
000
Hol
eofØ30
Shaf
tshoul
dbepr
epar
edt
ol
owerl
i
mi
tØ30.
020
Hol
eshoul
dbepr
epar
edt
oupperl
i
mi
tØ30.
021
Fi
tobt
ai
nedi
sI
nt
er
f
er
ence
1.
5.
7
l
engt
h.
gi
v
en.
Ter
mi
nol
ogy
Si
ze:-I
ti
sanumberexpr
essedi
napar
t
i
cul
aruni
ti
nt
hemeasur
ementof
Basi
cSi
ze:-I
ti
st
hesi
zebasedonwhi
cht
hedi
mensi
onaldev
i
at
i
onsar
e
Act
ualSi
ze:-I
ti
st
hesi
zeoft
hecomponentbyact
ualmeasur
ementaf
t
er
i
ti
smanuf
act
ur
ed.I
tshoul
dl
i
ebet
weent
het
wol
i
mi
t
sofsi
ze.
STUDYMATERI
ALPage10
METROLOGY
Zer
ol
i
ne:-I
ngr
aphi
calr
epr
esent
at
i
onoft
heabov
et
er
ms,t
hezer
ol
i
ne
r
epr
esent
st
hebasi
csi
ze.Thi
sl
i
nei
sal
socal
l
edast
hel
i
neofzer
o
dev
i
at
i
on.
Fi
gur
ei
ndi
cat
est
er
mi
nol
ogyofl
i
mi
tsy
st
em
1.
6
FI
TS:
I
ti
st
her
el
at
i
onshi
pt
hatexi
st
sbet
weent
womat
i
ngpar
t
s,ahol
eandshaf
twi
t
h
r
espectt
ot
hei
rdi
mensi
onal
di
f
f
er
encebef
or
eassembl
y
.
Ty
pesofFi
t
s:
(
1)Cl
ear
ance
STUDYMATERI
ALPage11
METROLOGY
(
2)I
nt
er
f
er
ence
(
3)Tr
ansi
t
i
on
1.
6.
1 Cl
ear
ancef
i
t
:
-(
Posi
t
i
v
eAl
l
owance)
I
ti
saf
i
twhi
chal
way
spr
ov
i
descl
ear
ance.Her
et
he t
ol
er
ancezoneoft
hehol
e
wi
l
l
beabov
et
het
ol
er
ancezoneoft
heshaf
t
.
e.
g.20H7/
g6.
Bot
hMMC&LMCcanbeusedher
e.
Maxi
mum cl
ear
ancei
st
hedi
f
f
er
encebet
weent
he maxi
mum
hol
e
and
mi
ni
mum shaf
t
.LMC
Mi
ni
mum
cl
ear
ancei
st
hedi
f
f
er
encebet
weent
he mi
ni
mum
hol
e
and
maxi
mum shaf
t
.MMC
Fi
gur
esshowcl
ear
ancef
i
t
Ty
pesoff
i
t
si
ncl
ear
ance:
• Pr
eci
si
onsl
i
di
ngf
i
t
• Cl
oser
unni
ngf
i
t
• Nor
mal
r
unni
ngf
i
t
STUDYMATERI
ALPage12
METROLOGY
• Easyr
unni
ngf
i
t
• Looser
unni
ngf
i
t
1.
6.
2I
nt
er
f
er
encef
i
t
:
I
ti
saf
i
twhi
chal
way
spr
ov
i
desi
nt
er
f
er
ence.Her
et
het
ol
er
ancezoneof
t
hehol
ewi
l
l
bebel
owt
het
ol
er
ancezoneoft
heshaf
t
.
e.
g.25H7/
p6.
Maxi
mum i
nt
er
f
er
encei
st
heal
gebr
ai
cdi
f
f
er
encebet
weent
hemi
ni
mum
hol
eandmaxi
mum shaf
t
.MMC
Mi
ni
mum i
nt
er
f
er
encei
st
heal
gebr
ai
cdi
f
f
er
encebet
weent
hemaxi
mum
hol
eandmi
ni
mum shaf
t
.LMC
Ty
pesoff
i
t
si
nI
nt
er
f
er
ence:
•
Shr
i
nkf
i
t
•
Heav
ydr
i
v
ef
i
t
STUDYMATERI
ALPage13
METROLOGY
•
Pr
essf
i
t
•
Medi
um pr
essf
i
t
1.
6.
3 Tr
ansi
t
i
onf
i
t
:
I
ti
saf
i
twhi
ch maysomet
i
mes pr
ov
i
des cl
ear
ance and somet
i
mes
i
nt
er
f
er
ence.When t
hi
s cl
ass off
i
ti
sr
epr
esent
ed gr
aphi
cal
l
y
,t
he
t
ol
er
ancezoneoft
hehol
eandshaf
twi
l
l
ov
er
l
apeachot
her
.
e.
g.75H8/
j
7.
Fi
gur
ei
ndi
cat
est
r
ansi
t
i
onf
i
t
Ty
pesoft
r
ansi
t
i
onf
i
t
•
•
•
•
Li
ghtPr
essFi
t
For
ceFi
t
PushFi
t
EasyPushFi
t
1.
6.
4 Conv
ent
i
onal
r
epr
esent
at
i
onoff
i
t
’
s.
STUDYMATERI
ALPage14
METROLOGY
1.
7
Sy
st
emsf
orobt
ai
ni
ngdi
f
f
er
entt
y
pesoff
i
t
s:
Sy
st
emsar
eoft
wot
y
pes:
(
A)Hol
ebasi
ssy
st
em(
HBS)
(
B)Shaf
tbasi
ssy
st
em(
SBS)
1.
7.
1
Hol
ebasi
ssy
st
em(
HBS)
Wher
et
hesi
zeoft
hehol
ei
skeptconst
antandt
hesi
zeoft
heshaf
ti
s
v
ar
i
edt
ogett
hedi
f
f
er
entcl
assoff
i
t
s,t
heni
ti
sknownast
hehol
e
basi
ssy
st
em.
Fi
gur
ei
ndi
cat
esHBS
1.
7.
2
Shaf
tbasi
ssy
st
em(
SBS)
Wher
et
hesi
zeoft
heshaf
ti
skeptconst
antandt
hev
ar
i
at
i
onsgi
v
ent
ot
he
hol
et
ogett
hedi
f
f
er
entcl
assoff
i
t
s,t
heni
ti
sknownast
heshaf
tbasi
s
sy
st
em.
STUDYMATERI
ALPage15
METROLOGY
1.
7.
3
Fi
t
si
nShaf
tBasi
sandHol
eBasi
sSy
st
em
Fi
gur
ei
ndi
cat
essev
er
al
f
i
t
si
nSBCandHBC
1.
7.
4
Di
f
f
er
encebet
weenSBS&HBS
HOLEBASI
SSYSTEM
SHAFTBASI
SSYSTEM
1)Thesi
zeoft
hehol
ei
sso
pr
epar
edt
hatt
hel
owerdev
i
at
i
on
v
al
uei
sassumedt
obenearzer
o
l
i
ne
1)
Upperdev
i
at
i
onofshaf
ti
st
owar
ds
zer
ol
i
ne&assumedt
obebasi
csi
ze
2)Thi
ssy
st
em i
sr
epr
esent
edby
l
et
t
er(
H)
2)
Thi
ssy
st
em i
sr
epr
esent
edbyl
et
t
er
(
h)
3)Thel
i
mi
t
soft
hehol
ei
skept
const
ant&shaf
ti
sv
ar
i
edt
o
desi
r
edf
i
t
3)Thel
i
mi
t
soft
heshaf
ti
skept
const
ant&hol
esar
ev
ar
i
edt
odesi
r
ed
f
i
t
4)Usedi
nmasspr
oduct
i
on
4)Sy
st
em notsui
t
abl
ef
ormass
pr
oduct
i
on,
5)Costofpr
oduct
i
oni
sl
ess
5)Costofpr
oduct
i
oni
shi
gh
6)St
or
agepl
acef
orkeepi
ngt
he
t
ool
i
sl
ess
6)St
or
agepl
acef
orkeepi
ngt
het
ool
i
smor
e
STUDYMATERI
ALPage16
METROLOGY
1.
8
St
andar
dLi
mi
tSy
st
em:
Thr
eeTy
pesofLi
mi
tSy
st
em Av
ai
l
abl
ear
e
(
1)Br
i
t
i
shSy
st
em,
(
2)I
SO2861988,
(
3)I
S919
1.
8.
1
I
ndi
anSt
andar
dSy
st
em (
I
s)
I
nI
S919t
her
ear
e:
(
a)18t
y
pesofFundament
al
Tol
er
ances(
Gr
ades)
(
b)25t
y
pesofFundament
al
Dev
i
at
i
ons
18Gr
ades:
I
T01,
I
T00I
T1,
I
T2,
I
T3…I
T16.
25Dev
i
at
i
ons:
Capi
t
al
Let
t
er
s-I
ndi
cat
esHol
es:
A,
B,
C,
D,
E,
F,
G,
H,
I
,
JS,
J,
K,
L,
M,
N,
O,
P,
Q,
R,
S,
T,
U,
V,
W,
X,
Y,
Z,
ZA,
ZB,
ZC.
Smal
lLet
t
er
s-I
ndi
cat
esHol
es:a,
b,
c,
d,
e,
f
,
g,
h,
i
,
j
j
,
k,
l
,
m,
n,
o,
p,
q,
r
,
s,
s,
t
,
u,
v
,
w,
x,
y
,
z,
za,
zb,
zc.
STUDYMATERI
ALPage17
METROLOGY
Gr
aphi
cal
I
l
l
ust
r
at
i
onofTol
er
anceZones
Numbersy
mbol
gener
al
l
yr
epr
esent
st
heTol
er
ance(
I
TGr
ade)
.
Eg:
1 40H7
40i
ndi
cat
est
heBasi
cSi
ze
Hi
ndi
cat
esHol
ebasi
ssy
st
em
7i
ndi
cat
esI
TGr
ade(
I
T7)
Eg:
2 43h7
43i
ndi
cat
est
heBasi
cSi
ze
hi
ndi
cat
esShaf
tbasi
ssy
st
em
7i
ndi
cat
esI
TGr
ade(
I
T7)
1.
8.
2 St
andar
dTol
er
ance
St
andar
dt
ol
er
ancesar
edet
er
mi
nedi
nt
er
msofst
andar
dt
ol
er
anceuni
t“
i
”
.(
“
i
”i
n
mi
cr
ons)
“
i
”i
sexpr
essedas
“
i
”
=0.
453√(
D)+0.
001D
Wher
eDi
sgeomet
r
i
calmeanofl
owerandupperdi
amet
erst
epwher
et
heact
ual
si
zeofshaf
t&hol
el
i
es
Var
i
ousst
epsi
nI
S919ar
easf
ol
l
ows
13,
36,
610,
1014,
1418,
1824,
2430,
3040,
4050,
5065,
6580,
80100,
100120,
120
140,
140160,
160180,
180250,
250315,
315400,
400500mm
Tol
er
ancesI
T01I
T5i
scal
cul
at
edasbel
ow.Remai
ni
ngl
i
keI
T2I
T4i
sscal
ed.
STUDYMATERI
ALPage18
METROLOGY
I
T01=0.
3+0.
08D,
I
T10=64i
,
I
T0=0.
5+0.
12D,
I
T11=100i
,
I
T1=0.
8+0.
02D,
I
T12=160i
,
I
T5=7i
,
I
T13=250i
,
I
T6=10i
,
I
T14=400i
,
I
T7=16i
,
I
T15=640i
,
I
T8=25i
,
I
T16=1000i
I
T9=40i
,
1.
8.
3 Fundament
al
Dev
i
at
i
onsf
orhol
esf
orsi
zesupt
o500mm
Not
e:Forshaf
t
st
hesameupperdev
i
at
i
onf
or
mul
ausedwi
l
lbecomel
ower
dev
i
at
i
onwi
t
hachangei
nsi
gn,samewayt
hel
owerdev
i
at
i
onf
or
mul
aofhol
e
becomeupperdev
i
at
i
onwi
t
hchangei
nsi
gn.
UPPERDEVI
ATI
ON(
es)
Shaf
t
I
nMi
cr
ons/Di
nmm
a
=(
265+1.
3D)f
orD≤120
=3.
5Df
or
D≥120
b
=(
140+0.
85D)
f
or
D≤160
=1.
8Df
orD≥160
c
=(
52D0.2)f
orD≤40
=(
9.
5+0.
8D)f
orD≥40
d
STUDYMATERI
ALPage19
=16D0.41
METROLOGY
e
=11D0.41
f
=5.
5D0.41
g
=5.
5D0.34
h
=0
LOWERDEVI
ATI
ON(
ei
)
Shaf
t
I
nMi
cr
ons/Di
nmm
k4k8
=+0.
63√D
m
=(
I
T7I
T6)
n
=+5De0.
24
p
=+I
T7+0t
o5
r
=Geomet
r
i
cmeanof
v
al
uesel
f
orpands
s
I
T8+1t
o4ForD≤50
=+I
T7t
o+0.
4DForD>50
t
=I
T7+0.
63D
u
=+I
T7+D
v
=+I
T7+1.
25D
x
=+177+1.
6D
STUDYMATERI
ALPage20
METROLOGY
y
=+1T7+2D
z
=+1T7+2.
5D
za
=+1T8+3+3.
15D
zb
=+1T9+4D
zc
=+1T10+5D
Quest
i
onBank
1.
2.
3.
4.
5.
6.
7.
8.
a)Expl
ai
nt
heuni
l
at
er
alandbi
l
at
er
alsy
st
emsofwr
i
t
i
ngt
ol
er
anceswi
t
hsui
t
abl
e
exampl
es.Whi
chsy
st
em i
spr
ef
er
r
edi
ni
nt
er
changeabl
emanuf
act
ur
i
ng?Why
?
b)A50mm di
amet
ershaf
ti
smadet
or
ot
at
ei
nt
hebush.Thet
ol
er
ancesf
orbot
h
shaf
tandbushar
e0.
050mm.Det
er
mi
net
hedi
mensi
onoft
heshaf
tandt
hebush
t
ogi
v
eamaxi
mum cl
ear
anceof0.
075mm wi
t
ht
hehol
ebasi
ssy
st
em.
a)Expl
ai
nbr
i
ef
l
yt
hedi
f
f
er
encebet
weent
heI
nt
er
changeabl
emanuf
act
ur
eand
sel
ect
i
v
eassembl
y
?
b)Di
f
f
er
ent
i
at
ebet
ween‘
Hol
ebasi
ssy
st
em’
and‘
shaf
tbasi
ssy
st
em’
off
i
t
s.
Dr
awt
heconv
ent
i
onal
di
agr
am ofl
i
mi
t
sandf
i
t
sandexpl
ai
nt
het
er
ms.
i
)Basi
csi
zei
i
)Upperdev
i
at
i
oni
i
i
)Lowerdev
i
at
i
oni
v
)Fundament
al
dev
i
at
i
on.
a)Def
i
net
het
er
ms:
i
)Al
l
owancei
i
)Li
mi
t
si
i
i
)Tol
er
ancei
v
)Fi
t
s.
b)Expl
ai
n cl
ear
l
ywhati
smeantbysel
ect
i
v
e assembl
y
.Gi
v
e one pr
act
i
cal
exampl
e.
(
a)Di
scusst
hesi
gni
f
i
canceofi
nt
er
changeabi
l
i
t
ywi
t
hr
espectt
oanengi
neer
i
ng
assembl
ysuchasi
nt
hecaseofamot
orcy
cl
e.
(
b)Expl
ai
nt
het
er
msRel
at
i
v
eer
r
or
,r
andom er
r
orandsy
st
emat
i
cer
r
orwi
t
h
sui
t
abl
eexampl
es
I
dent
i
f
ywhet
hert
hef
ol
l
owi
ngf
i
t
sar
ehol
ebasedorshaf
tbased.Conv
er
tt
hem
i
nt
oequi
v
al
entot
hersy
st
em.(
a)H7-f
8(
b)F6-h4(
c)H5-n4(
d)H7-c6.
A35mm di
amet
ershaf
tandbear
i
ngar
et
obeassembl
edwi
t
hacl
ear
ancef
i
t
.
Thet
ol
er
anceandal
l
owancesar
easunderAl
l
owances=0.
003mm Tol
er
anceon
hol
e=0.
007mm Tol
er
anceonshaf
t=0.
002mm Fi
ndt
hel
i
mi
t
sofsi
zef
ort
he
hol
eandshaf
ti
f(
a)Hol
ebasi
ssy
st
em i
sused(
b)Shaf
tbasi
ssy
st
em i
sused
Thet
ol
er
ancesar
edi
sposedofuni
l
at
er
al
l
y
.
Wi
t
hr
ef
er
encet
ot
hemet
r
ol
ogy
,
def
i
neanddi
st
i
ngui
shbet
weent
het
er
ms.
(
a)
Pr
eci
si
onandAccur
acy(
b)Repeat
abi
l
i
t
yandRepr
oduci
bi
l
i
t
y(
c)Nomi
nal
si
zeand
al
l
owance(
d)Tol
er
ancel
i
mi
t
sandCont
r
ol
l
i
mi
t
s.
Assi
gnmentI
:
Q1) Expl
ai
nt
heuni
l
at
er
al
andbi
l
at
er
al
sy
st
emsofwr
i
t
i
ngt
ol
er
anceswi
t
hsui
t
abl
e
STUDYMATERI
ALPage21
METROLOGY
exampl
es.Whi
chsy
st
em i
spr
ef
er
r
edi
ni
nt
er
changeabl
emanuf
act
ur
i
ng?Why
?
Q2) Def
i
net
het
er
ms:
i
)Al
l
owancei
i
)Li
mi
t
si
i
i
)Tol
er
ancei
v
)Fi
t
s.
Q3) I
dent
i
f
ywhet
hert
hef
ol
l
owi
ngf
i
t
sar
ehol
ebasedorshaf
tbased.Conv
er
tt
hem i
n
t
oequi
v
al
entot
hersy
st
em.(
a)H7-f
8(
b)F6-h4(
c)H5-n4(
d)H7-c6.
Chapt
er2
Li
nearmeasur
ement
,
Angul
armeasur
ement
Tapermeasur
ement
,
Li
mi
tgauges
2.
1I
nt
r
oduct
i
on:
Themai
nobj
ect
i
v
eofst
udy
i
ngt
hi
schapt
eri
sknownt
hatanyquant
i
t
ycanbe
measur
edbysomeort
heot
heruni
tandi
tshoul
dbeuni
v
er
salaccept
abl
e.So,
l
i
near
andangul
armeasur
ementi
shel
pf
ul
t
omeasur
et
hesequant
i
t
i
es.
STANDARDSOFMEASUREMENT
Funct
i
onal
:
Wehav
et
odot
hemeasur
ement
NonFunct
i
onal
:wher
ewehav
et
oest
i
mat
et
heuni
tl
i
ke,
Wei
ghtoft
hecomponent
2.
2St
andar
dsy
st
em f
orl
i
nearmeasur
ement
:
Lengt
hcanbemeasur
edasdi
st
ancebet
ween2l
i
nesorasdi
st
ancebet
ween2
f
aces.
I
nst
r
ument
scat
egor
i
esar
eoft
wot
y
pes:
(
a)
Li
nest
andar
d
(
b)
EndSt
andar
d
(
a)
Li
neSt
andar
d:
Lengt
hi
smeasur
edast
hedi
st
anceb/
wcent
er
soft
woengr
av
edl
i
nes.
STUDYMATERI
ALPage22
METROLOGY
Eg:
St
eel
Rul
e
Char
act
er
i
st
i
csofl
i
nest
andar
d:
 Scal
esar
eengr
av
edt
ohi
ghaccur
acy butt
heypossessomet
hi
ckness,
someasur
ementi
snotaccur
at
e
 Scal
ei
squi
ckandeasyt
ouseov
erawi
der
ange
 Scal
emar
ki
ngi
snotsubj
ect
edt
owear
.Howev
erendsar
esubj
ect
edt
o
wear
,
whi
chl
eadst
ounder
si
zemeasur
ement
.
 Par
al
l
axer
r
orwi
l
l
bet
her
e.
 Forhi
gheraccur
acymagni
f
y
i
nggl
assshoul
dbeused
(
b)
EndSt
andar
d:
Lengt
h i
s expr
essed as t
he di
st
ance bet
ween t
wo f
l
at par
al
l
el
f
aces/
sur
f
aces.
Eg:
Mi
cr
omet
er
Char
act
er
i
st
i
csofl
i
nest
andar
d:
 St
andar
dsar
ei
fhi
ghaccur
acyandmeasur
ementcanbemadef
orl
ow
t
ol
er
ances
 Mor
et
i
met
akenpr
ocessf
ormeasur
ement
 Subj
ect
edt
owearont
heendf
aces
 Nopar
al
l
axer
r
or
2.
3Uni
v
er
sal
l
yaccept
edl
i
nest
andar
d:
Theyar
et
wot
y
pesofuni
v
er
sal
l
yaccept
edl
i
nest
andar
ds.
a)YARD(
Engl
i
shSy
st
em)(
Lengt
hSt
andar
d)
b)METER(
Met
r
i
cSy
st
em)
,
(
I
nt
er
nat
i
onal
St
andar
d)
a)
I
mper
i
al
St
andar
dYar
d:
St
andar
dy
ar
dmadebyTr
ought
on&Si
mms,London,1855.Par
l
i
ament
ar
ycopy
No.34oft
heBr
i
t
i
shst
andar
dy
ar
dof1854.Br
onzebari
nwoodencase.They
ar
d
STUDYMATERI
ALPage23
METROLOGY
i
smeasur
edbet
weenf
i
nel
i
nesmar
kedonagol
dpi
ni
nt
hewel
lateachendof
t
hebar
.
Pr
i
mar
yst
andar
dy
ar
df
orVi
ct
or
i
a,1856t
o1966.Thi
sst
andar
dy
ar
dwaspl
aced
i
nt
hecust
odyofRober
tEl
l
er
y
,
Gov
er
nmentAst
r
onomer
,
i
n1860
1y
ar
di
sappr
oxi
mat
el
y91cm.
TheI
mper
i
alSt
andar
dYar
di
sabr
onzebarofonei
nchsquar
ecr
osssect
i
onand
38i
nchesl
ong(
Fi
g.
)andupt
ocent
r
alpl
aneoft
hebar
.A gol
dpl
ug1∕10
di
amet
erhav
i
ngt
hr
eel
i
nesengr
av
edt
r
ansv
er
sel
y
,andt
wol
i
nesl
ongi
t
udi
nal
l
yi
s
i
nser
t
edi
nt
ot
hesehol
essot
hatt
hel
i
nesar
ei
nneut
r
alpl
ane.Yar
di
st
hen
def
i
nedast
hedi
st
ancebet
weent
het
wocent
r
alt
r
ansv
er
sel
i
nesoft
hepl
ugat
62°
F.
STUDYMATERI
ALPage24
METROLOGY
Fi
gur
e’
sshowsi
mper
i
al
st
andar
dYar
d
Br
onzeYar
dwast
heof
f
i
ci
alst
andar
dofl
engt
hf
ort
heUni
t
edSt
at
esbet
ween1855and
1892,
whent
heUSwentt
omet
r
i
cst
andar
ds.1y
ar
d=0.
9144met
er
.They
ar
di
susedas
t
hest
andar
duni
toff
i
el
dl
engt
hmeasur
ementi
nAmer
i
can,Canadi
anandassoci
at
i
on
f
oot
bal
l
,cr
i
cketpi
t
chdi
mensi
ons,swi
mmi
ngpool
s,andi
nsomecount
r
i
es,gol
ff
ai
r
way
measur
ement
s.
2.
4I
nt
er
nat
i
onal
Pr
ot
ot
y
pemet
er
:
I
ti
sdef
i
nedast
hest
r
ai
ghtl
i
nedi
st
ance,
at0oC,
bet
weent
heengr
av
edl
i
nesofpur
e
pl
at
i
numi
r
i
di
um al
l
oy(
90% pl
at
i
num &10% i
r
i
di
um)of1020mm t
ot
all
engt
hand
hav
i
nga‘
Tr
esca’cr
osssect
i
onasshowni
nf
i
g.Thegr
aduat
i
onsar
eont
heupper
sur
f
aceoft
hewebwhi
chcoi
nci
deswi
t
ht
heneut
r
al
axi
soft
hesect
i
on.
STUDYMATERI
ALPage25
METROLOGY
Hi
st
or
i
calI
nt
er
nat
i
onalPr
ot
ot
y
peMet
erbar
,
madeofanal
l
oyofpl
at
i
num and
i
r
i
di
um,
t
hatwast
hest
andar
df
r
om 1889t
o1960.
Thet
r
escacr
osssect
i
ongi
v
esgr
eat
err
i
gi
di
t
yf
ort
heamountofmat
er
i
ali
nv
ol
v
ed
andi
st
her
ef
or
eeconomi
ci
nt
heuseofanexpensi
v
emet
al
.Thepl
at
i
numi
r
i
di
um
al
l
oyi
susedbecausei
ti
snonoxi
di
zabl
eandr
et
ai
nsgoodpol
i
shedsur
f
acer
equi
r
ed
f
orengr
av
i
nggoodqual
i
t
yl
i
nes.
Di
sadv
ant
agesofMat
er
i
al
l
engt
hst
andar
ds:
1.Mat
er
i
all
engt
h st
andar
dsv
ar
yi
nl
engt
h ov
ert
hey
ear
sowi
ng t
o mol
ecul
ar
changesi
nt
heal
l
oy
.
2.The exactr
epl
i
casofmat
er
i
all
engt
h st
andar
dswer
e notav
ai
l
abl
ef
oruse
somewher
eel
se.
STUDYMATERI
ALPage26
METROLOGY
3.I
ft
hesest
andar
dsar
eacci
dent
al
l
ydamagedordest
r
oy
edt
henexactcopi
escoul
d
notbemade.
4.Conv
er
si
onf
act
or
shav
et
obeusedf
orchangi
ngov
ert
omet
r
i
csy
st
em.
2.
5Li
ght(
Opt
i
cal
)wav
eLengt
hSt
andar
d:
Becauseoft
hepr
obl
emsofv
ar
i
at
i
oni
nl
engt
hofmat
er
i
all
engt
hst
andar
ds,t
he
possi
bi
l
i
t
yofusi
ng l
i
ghtasa basi
cuni
tt
o def
i
nepr
i
mar
yst
andar
d hasbeen
consi
der
ed.Thewav
el
engt
hofasel
ect
edr
adi
at
i
onofl
i
ghtandi
susedast
hebasi
c
uni
tofl
engt
h.Si
ncet
hewav
el
engt
hi
snotaphy
si
calone,
i
tneednotbepr
eser
v
ed&
canbeeasi
l
yr
epr
oduci
bl
ewi
t
houtconsi
der
abl
eer
r
or
.
A kr
y
pt
onf
i
l
l
eddi
schar
get
ubei
nt
heshapeoft
heel
ement
'
sat
omi
csy
mbol
.A
col
or
l
ess,odor
l
ess,t
ast
el
essnobl
egas,kr
y
pt
onoccur
si
nt
r
aceamount
si
nt
he
at
mospher
e,i
si
sol
at
edbyf
r
act
i
onal
l
ydi
st
i
l
l
i
ngl
i
quef
i
edai
r
.Thehi
ghpowerand
r
el
at
i
v
eeaseofoper
at
i
onofkr
y
pt
ondi
schar
get
ubescaused(
f
r
om 1960t
o1983)
t
heof
f
i
ci
al
met
ert
obedef
i
nedi
nt
er
msofoneor
anger
edspect
r
al
l
i
neofkr
y
pt
on86.
Met
erasonToday
:I
n1983,
t
he17t
hgener
alconf
er
enceonwei
ght
s&measur
es
pr
oposed t
he use ofspeed ofl
i
ghtasa t
echni
cal
l
yf
easi
bl
e & pr
act
i
cabl
e
def
i
ni
t
i
onofmet
er
.Met
eri
snow def
i
nedast
hel
engt
hofpat
hoft
r
av
el
l
edby
l
i
ghti
nv
acuum i
n(
1/
299792458)second.Thel
i
ghtusedi
si
odi
nest
abi
l
i
zed
hel
i
umneonl
aser
.
STUDYMATERI
ALPage27
METROLOGY
Adv
ant
agesofusi
ngwav
el
engt
hst
andar
ds:
1.Lengt
hdoesnotchange.
2.I
tcanbeeasi
l
yr
epr
oducedeasi
l
yi
fdest
r
oy
ed.
3.Thi
spr
i
mar
yuni
ti
seasi
l
yaccessi
bl
et
oanyphy
si
cal
l
abor
at
or
i
es.
4.I
tcanbeusedf
ormaki
ngmeasur
ement
swi
t
hmuchhi
gheraccur
acy
t
hanmat
er
i
al
st
andar
ds.
5.Wav
el
engt
hst
andar
dcanber
epr
oducedconsi
st
ent
l
yatanyt
i
meandat
anypl
ace.
2.
6 Subdi
v
i
si
onofst
andar
ds:
The i
mper
i
alst
andar
dy
ar
d and t
he i
nt
er
nat
i
onalpr
ot
ot
y
pe met
erar
e mast
er
st
andar
dsandcannotbeusedf
oror
di
nar
ypur
poses.Thusbasedupont
heaccur
acy
r
equi
r
ed,
t
hest
andar
dsar
esubdi
v
i
dedi
nt
of
ourgr
adesnamel
y
;
a.Pr
i
mar
ySt
andar
ds
b.Secondar
yst
andar
ds
c.Ter
i
t
i
ar
yst
andar
ds
d.Wor
ki
ngst
andar
ds
a.Pr
i
mar
yst
andar
ds:
Theyar
emat
er
i
alst
andar
dpr
eser
v
edundermostcar
ef
ulcondi
t
i
ons.Thesear
enot
used f
ordi
r
ect
l
yf
ormeasur
ement
sbutar
e used once i
n 10 or20 y
ear
sf
or
cal
i
br
at
i
ngsecondar
yst
andar
ds.
Ex:I
nt
er
nat
i
onal
Pr
ot
ot
y
pemet
er
,
I
mper
i
al
St
andar
dy
ar
d.
b.Secondar
yst
andar
ds:
Thesear
ecl
osecopi
esofpr
i
mar
yst
andar
dsw.
r
.
tdesi
gn,mat
er
i
al&l
engt
h.Any
er
r
orexi
st
i
ngi
nt
hesest
andar
dsi
sr
ecor
dedbycompar
i
sonwi
t
hpr
i
mar
yst
andar
ds
af
t
erl
ongi
nt
er
v
al
s.Theyar
ekeptatanumberofpl
acesundergr
eatsuper
v
i
si
onand
ser
v
easr
ef
er
encef
ort
er
t
i
ar
yst
andar
ds.Thi
sal
soact
sassaf
eguar
dagai
nstt
he
l
ossordest
r
uct
i
onofpr
i
mar
yst
andar
ds.
c.Ter
i
t
i
ar
yst
andar
ds:
Thepr
i
mar
yorsecondar
yst
andar
dsexi
stast
heul
t
i
mat
econt
r
ol
sf
orr
ef
er
enceatr
ar
e
i
nt
er
v
al
s.
STUDYMATERI
ALPage28
METROLOGY
Ter
t
i
ar
y st
andar
ds ar
et
he r
ef
er
ence st
andar
ds empl
oy
ed by Nat
i
onalPhy
si
cal
l
abor
at
or
y(
N.
P.
L)andar
et
hef
i
r
stst
andar
dst
obeusedf
orr
ef
er
encei
nl
abor
at
or
i
es&
wor
kshops.Theyar
emadeascl
osecopi
esofsecondar
yst
andar
ds& ar
ekeptas
r
ef
er
encef
orcompar
i
sonwi
t
hwor
ki
ngst
andar
ds.
d.Wor
ki
ngst
andar
ds:
Thesest
andar
dsar
esi
mi
l
ari
ndesi
gnt
opr
i
mar
y
,secondar
y&t
er
t
i
ar
yst
andar
ds.But
bei
ngl
essi
ncostandar
emadeofl
ow gr
ademat
er
i
al
s,t
heyar
eusedf
orgener
al
appl
i
cat
i
onsi
nmet
r
ol
ogyl
abor
at
or
i
es.
Somet
i
mes,
st
andar
dsar
eal
socl
assi
f
i
edas;
•Ref
er
encest
andar
ds(
usedasr
ef
er
encepur
poses)
•Cal
i
br
at
i
on st
andar
ds (
used f
orcal
i
br
at
i
on ofi
nspect
i
on & wor
ki
ng
st
andar
ds)
•I
nspect
i
onst
andar
ds(
usedbyi
nspect
or
s)
•Wor
ki
ngst
andar
ds(
usedbyoper
at
or
s)
2.
7Tr
ansf
erf
r
om l
i
nest
andar
dt
o end st
andar
d(
NPLmet
hod ofder
i
v
i
ng End
st
andar
df
r
om l
i
nest
andar
d)
Li
neSt
andar
dCompar
at
or
:
Al
i
nest
andar
dcompar
at
ori
susedt
ot
r
ansf
ert
hel
i
nest
andar
dcor
r
ect
l
yt
ot
heendsof
abar
.I
tconsi
st
soft
womi
cr
oscopesmount
edaboutay
ar
dapar
tov
erat
abl
e.Anend
st
andar
dabout351/
2i
nchi
nl
engt
hi
spr
oducedwi
t
hf
l
at&par
al
l
elf
aces.Two1/
2i
nch
STUDYMATERI
ALPage29
METROLOGY
bl
ockswi
t
hcent
r
al
l
yengr
av
edl
i
nesar
e‘
wr
ung’t
ot
heendsoft
hi
sendst
andar
d,such
t
hatt
hedi
st
ancebet
weent
hecent
erl
i
nesi
sappr
oxi
mat
el
y36i
nches.Thedi
f
f
er
enceof
r
eadi
ngsbet
weent
hel
i
nesont
hel
i
nest
andar
d&t
hel
i
nesont
heendst
andar
dar
e
not
edev
er
yt
i
me,byar
r
angi
ngt
heendbl
ocksi
ndi
f
f
er
entway
st
oel
i
mi
nat
eer
r
or
si
n
wr
i
ngi
ng&ofmar
ki
ngofcent
erl
i
nes.I
ft
heact
uall
engt
hoft
heendst
andar
di
sl
,t
hen
f
ort
hef
ourdi
f
f
er
entway
sofwr
i
ngi
ngt
heendbl
ocks,
wecanwr
i
t
e;
Wher
ed1,
d2,
d3&d4ar
et
hedi
f
f
er
encesnot
edf
ort
hesuccessi
v
eposi
t
i
onsoft
he1/
2
i
nchbl
ocksr
espect
i
v
el
y
.
Takemean,
Nextt
he351/
2i
nchendst
andar
dwr
ungwi
t
honeoft
he1/
2i
nchbl
ocksi
scompar
ed
wi
t
h36i
nchendbar(
t
obecal
i
br
at
ed)onaBr
ooke’
sl
ev
elcompar
at
or&t
hedev
i
at
i
on
D1maybenot
ed.
Thent
heot
her1/
2i
nchbl
ocki
swr
ungwi
t
hi
t&agai
ni
scompar
edwi
t
ht
heendbar(
t
o
becal
i
br
at
ed)&t
hedev
i
at
i
onD2i
snot
ed.I
fLi
st
heact
ual
l
engt
hoft
he36i
nchendbar
,
t
hen;
l+a+b=L+D1,
l
+c+d=L+D2.Combi
net
heequat
i
ons.
2.
8Mi
cr
omet
er
STUDYMATERI
ALPage30
METROLOGY
Ami
cr
omet
eri
samechani
cal
dev
i
cedesi
gnedt
omeasur
esmal
l
di
st
ances
Mi
cr
omet
er
sar
eonl
yonei
nchl
ong.
Themi
cr
omet
eri
susedwi
t
hdi
f
f
er
entt
y
pesandsi
zesoff
r
amest
opr
ov
i
de
pr
eci
semeasur
ement
sofmanydi
f
f
er
entobj
ect
s.
Readi
ngmi
cr
omet
ercal
i
per
par
t
s:
Thef
i
r
stst
epi
nbei
ngabl
et
or
eadami
cr
omet
eri
sl
ear
ni
ngt
henamesoft
he
par
t
s.
 Thef
aceoft
heanv
i
l
andt
hef
aceoft
hespi
ndl
ear
et
hecont
actsur
f
aces.
 Thespi
ndl
eandt
hi
mbl
et
ur
nt
oget
her
.
 Ther
at
chet
/
f
r
i
ct
i
onst
opi
mpr
ov
est
her
epeat
abi
l
i
t
yofmeasur
ement
sf
or
begi
nner
s.
 Ami
cr
omet
ercal
i
peri
sr
eadatt
hepoi
ntwher
et
heedgeoft
het
hi
mbl
e
cr
ossest
hebar
r
el
scal
e
I
nsur
et
hel
ocki
sr
el
easedbef
or
et
r
y
i
ngt
ot
ur
nt
het
hi
mbl
e.
.
Thr
eet
y
pesofmi
cr
omet
er
s:
a)Mi
cr
omet
ercal
i
per
b)I
nsi
demi
cr
omet
er
c)Dept
hgaugemi
cr
omet
er
b)I
nsi
deMi
cr
omet
er
I
nsi
demi
cr
omet
er
shav
ebeenr
epl
acedbydi
alcal
i
per
sandot
hert
ool
sf
or
smal
lgasengi
nes.Thepr
i
nci
pl
esf
orr
eadi
ngar
et
hesame.Thepr
i
mar
y
STUDYMATERI
ALPage31
METROLOGY
di
f
f
er
encei
sdet
er
mi
ni
ngt
hesmal
l
estwhol
euni
t
.Thephy
si
calsi
zeoft
he
mi
cr
omet
erl
i
mi
t
st
hesmal
l
estwhol
euni
tt
o1or11/
2i
nch.Ext
ensi
onsar
e
addedt
osett
hemi
ni
mum si
zet
ot
hedesi
r
edr
angeasshown.
Fi
gur
eshowsi
nsi
dermi
cr
omet
er
I
nsi
demi
cr
omet
er
suseext
ensi
onst
ochanget
her
angeofmeasur
ement
s.
Addi
nganext
ensi
oni
ncr
easest
hemi
ni
mum measur
ement
.I
nt
hi
sexampl
ea
1/
2i
nchext
ensi
onhasbeenadded.
Not
e:whent
hezer
oont
het
hi
mbl
ei
scl
oset
ot
her
ef
er
encel
i
neanda25
t
housandsl
i
nei
scl
oset
ot
heedgeoft
het
hi
mbl
e,i
tmaybedi
f
f
i
cul
tt
o
det
er
mi
nei
ft
hel
astl
i
net
hatshoul
dbecount
ed.I
ft
het
hi
mbl
ezer
oi
sabov
e
t
her
ef
er
encel
i
net
hel
i
nei
snotcount
ed.I
fi
ti
sbel
owi
tshoul
dbecount
ed.
c)Dept
hgaugemi
cr
omet
er
Dept
hgaugemi
cr
omet
er
sar
eusedt
omeasur
et
hedept
hofbl
i
ndhol
es,
sl
ot
s,
STUDYMATERI
ALPage32
METROLOGY
keyway
s,et
c.Thespi
ndl
el
engt
hcanbechangedt
osett
hemi
cr
omet
erf
or
t
hedesi
r
edr
angeofmeasur
ement
.Tor
eadadept
hgaugemi
cr
omet
ery
ou
mustv
i
sual
i
zet
hedi
st
ancet
hathasbeencov
er
edbyt
het
hi
mbl
e.
Fi
gur
eshowsdept
hmi
cr
omet
er
2.
9Ver
ni
erCal
i
per
.
Ver
ni
ercal
i
per
sar
eanol
dt
oolt
hathasbeenmost
l
yr
epl
acedbydi
alanddi
gi
t
al
cal
i
per
s.They ar
e manuf
act
ur
ed wi
t
h deci
malscal
es,met
r
i
c scal
es and
f
r
act
i
onalscal
es.TheVer
ni
erscal
ei
sst
i
l
lusedonmanymechani
calmeasur
i
ng
t
ool
s.
Fi
gur
eshowsv
er
ni
ercal
i
per
2.
10
Ver
ni
erHei
ghtGauge:
STUDYMATERI
ALPage33
METROLOGY
Ahei
ghtgaugei
sameasur
i
ngdev
i
ceusedei
t
herf
ordet
er
mi
ni
ngt
hehei
ghtof
somet
hi
ng,
orf
orr
epet
i
t
i
ousmar
ki
ngofi
t
emst
obewor
kedon.Ver
ni
erhei
ghtgauge
aPr
eci
si
oni
nst
r
ument
.Hasv
ar
i
et
yofsi
zes1272i
n.or3001000mm.Hei
ghtwi
t
hi
n
.
001i
n(
0.
02mm)
Di
gi
t
alhei
ghtgagezer
of
unct
i
on,di
spl
ay.
0001i
n.Of
f
setscr
i
ber
:At
t
achmentt
hat
per
mi
t
sset
t
i
nghei
ght
sf
r
om f
aceofpl
at
eandDept
hgageat
t
achment
.
2.
11
Sl
i
pgauges:
Sl
i
p gauges ar
e bl
ocks ofst
eelt
hathav
e been har
dened and st
abi
l
i
zed byheat
t
r
eat
ment
.Theyar
egr
oundandl
appedt
osi
zet
ov
er
yhi
ghst
andar
dsofaccur
acyand
sur
f
acef
i
ni
sh.Agaugebl
ock(
al
soknownJohanssongauge,
sl
i
pgauge,
orJobl
ock)i
s
apr
eci
si
onl
engt
hmeasur
i
ngst
andar
dconsi
st
i
ngofagr
oundandl
appedmet
alor
cer
ami
cbl
ock.Sl
i
pgaugeswer
ei
nv
ent
edi
n1896bySwedi
shmachi
ni
stCar
lEdwar
d
Johansson.
Sl
i
pgaugesar
er
ect
angul
arbl
ocksofst
eel
hav
i
ngcr
osssect
i
onof30mm f
acel
engt
h&
10mm f
acewi
dt
hasshowni
nf
i
g.
STUDYMATERI
ALPage34
METROLOGY
Fi
gur
eshowssl
i
pgaugebl
ock.
Ty
pesofsl
i
pgauges:
I
NDI
AN STANDARD ON SLI
P GAUGES (
I
S 29841966)
,t
hesear
eav
ai
l
abl
ei
nt
hr
ee
st
andar
dset
s:
M45,
M112,
M87.
Sl
i
pgaugesar
egr
adedaccor
di
ngt
ot
hei
raccur
acyasGr
ade0,
Gr
adeI&Gr
adeI
I
.Gr
ade
I
Ii
si
nt
endedf
orusei
nwor
kshopsdur
i
ngact
ualpr
oduct
i
onofcomponent
s,t
ool
s&
gauges.Gr
adeIi
sofhi
gheraccur
acyf
orusei
ni
nspect
i
ondepar
t
ment
s.Gr
ade0i
sused
i
nl
abor
at
or
i
esandst
andar
dr
oomsf
orper
i
odi
ccal
i
br
at
i
onofGr
adeI&Gr
adeI
Igauges.
M45SetBox:
Basi
cal
l
yconsi
st
sof45Sl
i
pgaugesi
ni
tasshowni
nt
abl
e
Range(
i
nmm) St
ep
STUDYMATERI
ALPage35
No.ofpi
eces
METROLOGY
1.
001t
o1.
009
0.
00
9
1
1.
01t
o1.
09
0.
01
9
1.
1t
o1.
9
0.
1
9
1t
o9
1
9
10t
o90
10
9
M87SetBox:
Basi
cal
l
yconsi
st
sof87Sl
i
pgaugesi
ni
tasshowni
nt
abl
e
Range(
i
nmm)
St
ep
No.ofpi
eces
1.
001t
o1.
009
0.
001
9
1.
01t
o1.
49
0.
01
49
0.
5t
o9.
5
0.
5
19
10t
o90
10
9
1.
0005
-
1
I
mpor
t
antnot
esonbui
l
di
ngofSl
i
pGauges:
•Al
way
sst
ar
twi
t
ht
hel
astdeci
mal
pl
ace.
•Thent
aket
hesubsequentdeci
mal
pl
aces.
•Mi
ni
mum numberofsl
i
p gaugesshoul
d beused bysel
ect
i
ng t
hel
ar
gest
possi
bl
ebl
ocki
neachst
ep.
•I
fi
ncasepr
ot
ect
orsl
i
psar
eused,
f
i
r
stdeductt
hei
rt
hi
cknessf
r
om t
her
equi
r
ed
di
mensi
ont
henpr
oceedasperabov
eor
der
.
Numer
i
cal
pr
obl
em1
Bui
l
dt
hef
ol
l
owi
ngdi
mensi
onsusi
ngM4553.
975
Sol
ut
i
on:
STUDYMATERI
ALPage36
METROLOGY
For
ml
astdeci
mal
pl
ace
1sl
i
p=1.
005
For
m secondl
astdeci
mal
pl
ace
2sl
i
p=1.
07
For
mt
hi
r
dl
astdeci
mal
pl
ace
For
mf
our
t
h
3sl
i
p=1.
9
4sl
i
p=50.
00
53.
975
Wr
i
ngi
ngofSl
i
pGauges:
Sl
i
pgaugesar
ewr
ungt
oget
hert
ogi
v
east
ackoft
her
equi
r
eddi
mensi
on.I
n
or
dert
oachi
ev
et
hemaxi
mum accur
acyt
hef
ol
l
owi
ngpr
ecaut
i
onsmustbet
aken.
•Uset
hemi
ni
mum numberofbl
ocks.
•Wi
pet
hemeasur
i
ngf
acescl
eanusi
ngsof
tcl
eanchamoi
sl
eat
her
.
•Wr
i
ngt
hei
ndi
v
i
dualbl
ockst
oget
herbyf
i
r
stpr
essi
ngatr
i
ghtangl
es,sl
i
di
ng&
t
hent
wi
st
i
ng.
STUDYMATERI
ALPage37
METROLOGY
36Johanssongaugebl
ockswr
ungt
oget
hereasi
l
ysuppor
tt
hei
rownwei
ght
2.
12
Met
hodsofManuf
act
ur
i
ngSl
i
pGauges:
Theyar
et
wodi
f
f
er
entmet
hodsf
ormanuf
act
ur
i
ng
a)Nat
i
onal
phy
si
csl
abor
at
or
ymet
hod
b)Mechani
cal
met
hodofl
appi
ng
a)Nat
i
onal
phy
si
csl
abor
at
or
ymet
hod:
I
nNPLmet
hodmagnet
i
cchucksar
eused.Al
l
t
hesl
i
pgaugesi
nchuckandgr
i
ndi
ng
wi
l
l
bedoneandl
appi
ngpr
ocesswi
l
l
bedonei
nor
dert
ohav
egoodsur
f
acef
i
ni
sh.
Nextt
heywi
l
l
r
ev
er
seal
l
t
hesl
i
pgaugessot
hatt
heyhav
esamepar
al
l
el
i
sm and
f
l
at
nessasshown.
STUDYMATERI
ALPage38
METROLOGY
Manuf
act
ur
i
ngpr
ocedur
e:
• Machi
ni
ng
• Heatt
r
eat
ment
• Gr
i
ndi
ng
• Lappi
ng
• Rev
er
si
ngsl
i
pgauges
• Fi
nal
Lappi
ng
b)Mechani
cal
met
hodofl
appi
ng:
Thr
eedi
f
f
er
entt
y
pes
• Upperl
ap
• Cent
r
al
l
ap
• Bot
t
om l
ap
Upperl
apcanbemov
edi
nanyangl
eanddoesnothav
eanyr
ot
ar
ymot
i
on.I
twi
l
l
bel
i
keasi
mpl
ependul
um.Thecent
r
all
apcont
ai
nssl
ot
s.Thesl
i
pgaugesar
e
hel
di
nt
hi
sl
apbymeansofscr
ews.Thi
sl
aphasar
ot
ar
ymot
i
on.Bot
t
om l
api
s
r
i
gi
dl
ypl
acedont
hebase.
STUDYMATERI
ALPage39
METROLOGY
Manuf
act
ur
i
ngpr
ocedur
e:
• Machi
ni
ng
• Heatt
r
eat
ment
• Gr
i
ndi
ng
• Lappi
ng
• Rev
er
si
ngsl
i
pgauges
• Fi
nal
Lappi
ng
2.
13
Di
al
I
ndi
cat
or
Thedi
ali
ndi
cat
ori
sapr
eci
si
onmeasur
i
ngt
oolt
hatmeasur
esr
el
at
i
v
edi
st
ances.
Usei
tt
omeasur
et
hedi
f
f
er
encei
ndi
st
ancet
ot
woormor
el
ocat
i
ons.Thedi
al
i
ndi
cat
ori
sgr
eatf
orchecki
ngal
i
gnmentandr
unout
.
STUDYMATERI
ALPage40
METROLOGY
Fi
gur
eshowst
hepar
t
sofdi
al
i
ndi
cat
or
.
Di
al
I
ndi
cat
orAppl
i
cat
i
on:
Adi
al
i
ndi
cat
ori
susedt
omeasur
eshaf
tr
unout
,
shaf
tt
hr
ust
,
gearbackl
ash,
f
l
y
wheel
f
acer
unout
,
f
l
y
wheel
housi
ngconcent
r
i
ci
t
y
,
andv
al
v
eseatconcent
r
i
ci
t
y
.
Youcanmountadi
al
i
ndi
cat
oronat
estst
andor
,
wi
t
hcl
ampsandamagnet
i
c
base,
di
r
ect
l
yont
heequi
pmentt
obemeasur
ed.
Fi
gur
eshowsat
y
pi
cal
di
al
i
ndi
cat
orwi
t
hmount
i
ngaccessor
i
es,
mostdi
al
i
ndi
cat
or
shav
ecomponent
ssuchasabezel
,
i
ndi
cat
orpoi
nt
er
,
t
ool
postand
cl
amp,
magnet
i
ct
ool
hol
der
,
andsensorbut
t
ont
hatar
eusedi
nt
aki
ng
measur
ement
s.
Adv
ant
agesofDi
al
I
ndi
cat
or
:
1.Easeofr
eadi
ngadi
al
i
ndi
cat
ori
st
hebi
ggestadv
ant
ageov
erot
her
STUDYMATERI
ALPage41
METROLOGY
conv
ent
i
onal
t
y
pesofl
i
nearmeasur
i
ng
2.Thi
si
sext
r
emel
yusef
ul
f
orqual
i
t
ycont
r
ol
i
nt
hei
nspect
i
onr
oom and
unski
l
l
edl
aborcanbeempl
oy
edf
ori
t
suse
3.Thi
si
sbestsui
t
edf
orpr
eci
si
ondi
mensi
onal
cont
r
ol
4.Di
mensi
onscanbeeasi
l
ycont
r
ol
l
edi
nmasspr
oduct
i
on.
5.Thi
si
snotsubj
ect
edt
opr
obl
emsofgaugewearandt
emper
at
ur
e
v
ar
i
at
i
onset
c
6.Ther
e’
sspeed,
adapt
abi
l
i
t
y
,
andposi
t
i
v
ev
i
si
bi
l
i
t
yofdi
al
i
ndi
cat
orgauges,
i
naddi
t
i
ont
ot
hei
raccur
acy
7.Onecanusei
tf
ormanydi
f
f
er
entmeasur
ement
sbymeansofaf
ew
si
mpl
eat
t
achment
s,
t
husmaki
ngi
tmor
ev
er
sat
i
l
e.
8.Mai
nt
enancecosti
sl
ess
Char
act
er
i
st
i
csofDi
al
I
ndi
cat
or
:
• Robusti
ndesi
gn
• Mechani
cal
st
opshoul
dbepr
ov
i
dedf
ort
hepl
unger
• Pl
ungershoul
dshowbot
hposi
t
i
v
eandnegat
i
v
ev
al
ues
2.
14
Angul
arMeasur
ement
:
Formeasur
i
ngt
heangl
e,noabsol
ut
est
andar
di
sr
equi
r
ed.Themeasur
ementi
sdonei
n
degr
ees,mi
nut
esandseconds.Themeasur
ementofangul
arandci
r
cul
ardi
v
i
si
onsi
san
i
mpor
t
antpar
tofi
nspect
i
on.I
ti
sconcer
nedwi
t
ht
hemeasur
ementofi
ndi
v
i
dualangl
es,
angul
archanges and def
l
ect
i
ons on component
s,gauges and t
ool
s.Forpr
eci
si
on
measur
ement of angl
es mor
e ski
l
li
sr
equi
r
ed.Li
ke l
i
near measur
ement
,angul
ar
measur
ement
shav
et
hei
rowni
mpor
t
ance.Thebasi
cdi
f
f
er
encebet
weent
hel
i
nearand
angul
armeasur
ementi
st
hatnoabsol
ut
est
andar
di
sr
equi
r
edf
orangul
armeasur
ement
.
Ther
ear
esev
er
almet
hodsofmeasur
i
ngangl
esandt
aper
s.Thev
ar
i
ousi
nst
r
ument
sused
ar
eangl
egauges,cl
i
nomet
er
s,bev
elpr
ot
r
act
or
,si
nebar
,si
necent
er
s,t
aperpl
ugandr
i
ng
gauges
STUDYMATERI
ALPage42
METROLOGY
Def
i
ni
t
i
on:
Angl
ei
st
hedi
f
f
er
enceast
hegapi
nbet
weent
wo st
r
ai
ghtl
i
neswhi
char
e
meet
i
ngatasi
ngl
epoi
nt
.
St
andar
dsofMeasur
i
ngAngl
e:
(
a)
Sexagesi
mal
Sy
st
em
Assumet
hatt
her
ei
saCi
r
cl
ewher
et
heCi
r
cl
ei
sdi
v
i
dedi
nt
o360equalpar
t
sand
0
eachpar
ti
scal
l
edasaDegr
ee(
)
.
OneDegr
ee=60mi
nut
es;
1Mi
nut
e=60seconds.
(
b)
Radi
ans
Angl
esubt
endedatt
hecent
r
ebyanar
cofci
r
cl
eofl
engt
hequalt
oi
t
sr
adi
usi
s
cal
l
edRadi
an
2пr
adi
ans=3600
1Radi
an=57.
2958degr
ees.
2.
15
I
nst
r
ument
sf
orAngul
arMeasur
ement
:
a.Ver
ni
erbev
el
pr
ot
r
act
or
b.Si
nebar
c.Angul
argauges
a.
)Ver
ni
erbev
el
pr
ot
r
act
or
:
I
ti
susedt
omeasur
eangl
esaccur
at
el
yt
o5mi
nut
es.I
ti
sf
i
nel
ymadet
oolwi
t
hdi
al
,
gr
aduat
edi
ndegr
ees,abaseandasl
i
di
ngbl
ade.Thebl
adecanbel
ockedagai
nst
di
albyt
i
ght
eni
ngt
hebl
adecl
ampnut
.Thebl
adeanddi
alcanber
ot
at
edasoneuni
t
t
o any posi
t
i
on and l
ocked by t
i
ght
eni
ng t
he di
alcl
amp nutf
or accur
at
e
measur
ement
,av
er
ni
eroraf
i
neadj
ust
mentdev
i
cei
sf
i
t
t
edont
hedi
al
.Thedi
ali
s
gr
aduat
edi
nt
o,It
hr
ead,t
hev
er
ni
erscal
ei
sdi
v
i
dedi
nt
ot
wel
v
eequalpar
t
soneach
si
deofzer
o,
ev
er
yt
hi
r
ddi
v
i
si
oni
snumber
ed0,
15,
30,
45,
60r
epr
esent
i
ngmi
nut
es.
STUDYMATERI
ALPage43
METROLOGY
Fi
gur
ei
ndi
cat
esBev
el
Pr
ot
r
act
or
Fi
gur
eshowsway
si
nwhi
chabev
el
canbeusedt
omeasur
eangl
es
b.
)Si
nebar
:
I
ti
susedf
ormeasur
ementofanangl
eofagi
v
enj
oborf
orset
t
i
nganangl
e.They
ar
ehar
denedandpr
eci
si
ongr
oundt
ool
sf
oraccur
at
eangl
eset
t
i
ng.I
tcanbe
usedi
nconj
unct
i
onwi
t
hsl
i
pgaugesetanddi
algaugef
ormeasur
ementof
angl
esandt
aper
sf
r
om hor
i
zont
alsur
f
ace.Asshowni
nFi
gur
e,t
woaccur
at
el
y
l
appedr
ol
l
er
sar
el
ocat
edatt
heext
r
emeposi
t
i
on.Thecent
ert
ocent
erdi
st
ance
bet
weent
her
ol
l
er
sorpl
ugsi
sav
ai
l
abl
ef
orf
i
xeddi
st
ancei
.
e.l=100,200,250,
300mm.Thedi
amet
eroft
hepl
ugsorr
ol
l
ermustbeoft
hesamesi
zeandt
he
cent
erdi
st
ancebet
weent
hem i
saccur
at
e.Thei
mpor
t
antcondi
t
i
onf
ort
hesi
ne
bari
st
hatt
hesur
f
aceofsi
nebarmustbepar
al
l
el
t
ot
hecent
erl
i
nesoft
hepl
ug
STUDYMATERI
ALPage44
METROLOGY
Pr
i
nci
pl
eofWor
ki
ng:
Asshowni
nFi
gur
et
het
aperangl
eθoft
hej
obWXYZi
st
obemeasur
edbyt
hesi
ne
bar
.Thej
obi
spl
acedov
ert
hesur
f
acepl
at
e.Thesi
nebari
spl
acedov
ert
hej
obwi
t
h
pl
ugorr
ol
l
erofoneendoft
hebart
ouchi
ngt
hesur
f
acepl
at
e.Oneendoft
hesi
ne
bari
sr
est
edont
hesur
f
acepl
at
eandt
heot
herendi
sr
est
edont
hesl
i
pgauges
Theangl
eoft
hej
obi
st
henf
i
r
stmeasur
edbysomenonpr
eci
si
oni
nst
r
ument
,such
asbev
el
pr
ot
ect
or
.Thatangl
egi
v
est
hei
deaoft
heappr
oxi
mat
esl
i
pgaugesr
equi
r
ed,
att
heot
herendofsi
nebar
.Fi
nal
l
yt
heexactnumberofsl
i
pgaugesar
eaddedequal
t
ohei
ghth,sucht
hat
,t
het
opmostsl
i
pgaugest
ouchest
hel
owerendoft
her
ol
l
er
.
Thehei
ghtoft
hesl
i
pgaugesr
equi
r
edi
st
henmeasur
ed.Thent
het
aperangl
ecanbe
measur
edbymaki
ngsi
nebarasahy
pot
enuseofr
i
ghtangl
et
r
i
angl
eandsl
i
degauge
ast
heopposi
t
esi
deoft
het
r
i
angl
easshowni
nFi
gur
e
h=Hei
ghti
nmm
L=Cent
erdi
st
ancei
nmm
Si
nθ=Opp/Hy
p=(
h/L)
STUDYMATERI
ALPage45
METROLOGY
Whent
hesi
zeoft
hej
obi
sl
ar
gehav
i
ngt
apert
henweusesl
i
pgaugesf
ort
hebot
h
t
hesi
det
of
i
ndt
het
aperangl
eoft
hej
ob
Forasmal
lcomponent
,t
hecomponentorwor
kpi
ececanbepl
acedov
erasi
nebar
asshowni
nFi
gur
e.Thej
obi
shel
dont
hesi
nebarwi
t
hsomesui
t
abl
eaccessor
i
es.
Thedi
ali
ndi
cat
or
sar
epr
ov
i
dedatt
het
opposi
t
i
onandt
her
eadi
ngi
st
akenatA
posi
t
i
on.Thedi
ali
ndi
cat
ori
st
henmov
edt
ot
her
i
ghthandsi
deandt
her
eadi
ngi
s
t
akenatposi
t
i
onB.I
ft
her
ei
sadi
f
f
er
encebet
weenr
eadi
ngatposi
t
i
onAandB,
t
hen
t
hehei
ghtoft
hesl
i
pgaugesi
sadj
ust
edunt
i
lt
hedi
ali
ndi
cat
orshowst
hesame
r
eadi
ngatAandB.Thent
heangl
ei
scal
cul
at
edsi
mi
l
art
opr
ev
i
ousmet
hodas
Si
nθ=Opp/Hy
p=(
h/L)
STUDYMATERI
ALPage46
METROLOGY
UseofSi
neBar
:
(
1)
Measur
i
ngknownangl
esorl
ocat
i
nganywor
kt
oagi
v
enangl
e
Fort
hi
spur
poset
hesur
f
acepl
at
ei
sassumedt
obehav
i
ngaper
f
ect
l
yf
l
atsur
f
ace,
sot
hati
t
ssur
f
acecoul
dbet
r
eat
edashor
i
zont
al
.Oneoft
hecy
l
i
nder
sorr
ol
l
er
sof
si
nebari
spl
acedont
hesur
f
acepl
at
eandot
herr
ol
l
eri
spl
acedont
hesl
i
pgaugesof
hei
ghth.Lett
hesi
nebarbesetatanangl
eθ.Thensi
nθ=h/
l
,
wher
el
i
st
hedi
st
ance
bet
weent
hecent
r
esoft
her
ol
l
er
s.Thusknowi
ngθ,
hcanbef
oundoutandanywor
k
coul
dbesetatt
hi
sangl
east
het
opf
aceofsi
nebari
si
ncl
i
nedatangl
eθt
ot
he
sur
f
acepl
at
e.Theuseofangl
epl
at
esandcl
ampscoul
dal
sobemadei
ncaseof
heav
ycomponent
s.Forbet
t
err
esul
t
s,bot
ht
her
ol
l
er
scoul
dal
sobepl
acedonsl
i
p
gauges,
ofhei
ghth1andh2r
espect
i
v
el
y
.
Thensi
nθ=(
h2h1)
/
l
(
2)Checki
ngofunknownangl
es.
Manyat
i
mes,
angl
eofacomponentt
obecheckedi
sunknown.I
nsuchacase,
i
ti
s
necessar
yt
of
i
r
stf
i
ndt
heangl
eappr
oxi
mat
el
ywi
t
ht
hehel
pofabev
elpr
ot
r
act
or
.
STUDYMATERI
ALPage47
METROLOGY
Lett
heangl
ebeθ.Thent
hesi
nebari
ssetatanangl
eθandcl
ampedt
oanangl
e
pl
at
e.Next
,t
hewor
ki
spl
acedont
hesi
nebarandcl
ampedt
ot
heangl
epl
at
eas
showni
nFi
g.andadi
ali
ndi
cat
ori
ssetatoneendoft
hewor
kandmov
edt
ot
he
ot
her
,anddev
i
at
i
oni
snot
ed.Agai
nsl
i
pgaugesar
esoadj
ust
ed(
accor
di
ngt
ot
hi
s
dev
i
at
i
on)t
hatdi
al
i
ndi
cat
orr
eadszer
oacr
osst
hewor
ksur
f
ace.
I
fdev
i
at
i
onnot
eddownbyt
hedi
ali
ndi
cat
ori
sδhov
eral
engt
hl
‘
ofwor
k,
t
henhei
ght
ofsl
i
pgaugesbywhi
chi
tshoul
dbeadj
ust
edi
sequal
t
oδh*(
l
/l
‘
)
(
3)Checki
ngofunknownangl
esofheav
ycomponent
.
I
nsuchcaseswher
ecomponent
sar
eheav
yandcan’
tbemount
edont
hesi
nebar
,
t
hensi
ne
bari
smount
edont
hecomponentasshowni
nFi
g.Thehei
ghtov
ert
her
ol
l
er
scant
henbe
measur
edbyav
er
ni
erhei
ghtgauge;
usi
ngadi
alt
estgaugemount
edont
heanv
i
lofhei
ght
gaugeast
hef
i
duci
ali
ndi
cat
ort
oensur
econst
antmeasur
i
ngpr
essur
e.Theanv
i
lonhei
ght
gaugei
sadj
ust
edwi
t
hpr
obeofdi
alt
estgaugeshowi
ngsamer
eadi
ngf
ort
het
opmost
posi
t
i
onofr
ol
l
er
sofsi
nebar
.Fi
g.8.
18showst
heuseofhei
ghtgaugef
orobt
ai
ni
ngt
wo
r
eadi
ngsf
orei
t
heroft
her
ol
l
erofsi
nebar
.Thedi
f
f
er
enceoft
het
wor
eadi
ngsofhei
ght
gaugedi
v
i
ded byt
hecent
r
edi
st
anceofsi
nebargi
v
est
hesi
neoft
heangl
eoft
he
componentt
obemeasur
ed.Wher
egr
eat
eraccur
acyi
sr
equi
r
ed,t
heposi
t
i
onofdi
alt
est
gaugepr
obecanbesensedbyadj
ust
i
ngapi
l
eofsl
i
pgaugest
i
l
ldi
ali
ndi
cat
ori
ndi
cat
es
same-r
eadi
ngov
err
ol
l
erofsi
nebarandt
hesl
i
pgauges.
STUDYMATERI
ALPage48
METROLOGY
Adv
ant
agesofsi
nebar
:
1.I
ti
susedf
oraccur
at
eandpr
eci
seangul
armeasur
ement
.
2.I
ti
sav
ai
l
abl
eeasi
l
y
.
3.I
ti
scheap.
Di
sadv
ant
ages:
1.Theappl
i
cat
i
oni
sl
i
mi
t
edf
oraf
i
xedcent
erdi
st
ancebet
weent
wopl
ugsor
r
ol
l
er
s.
2.I
ti
sdi
f
f
i
cul
tt
ohandl
eandposi
t
i
ont
hesl
i
pgauges.
3.I
ft
heangl
eexceeds45°
,
si
nebar
sar
ei
mpr
act
i
cabl
eandi
naccur
at
e.
4.Lar
geangul
arer
r
ormayr
esul
t
sduet
osl
i
ghter
r
ori
nsi
nebar
.
Si
neCent
er
s:
I
ti
st
heext
ensi
onofsi
nebar
swher
et
woendsar
epr
ov
i
dedonwhi
chcent
er
s
canbecl
amped,asshowni
nFi
gur
e.Thesear
eusef
ulf
ort
est
i
ngofconi
cal
wor
kcent
er
edateachend,
upt
o60°
.Thecent
er
sensur
ecor
r
ectal
i
gnmentof
t
hewor
kpi
ece.Thepr
ocedur
eofset
t
i
ngi
st
hesameasf
orsi
nebar
.Thedi
al
i
ndi
cat
ori
smov
edont
ot
hej
obt
i
l
lt
her
eadi
ngi
ssameatt
heext
r
eme
posi
t
i
on.Thenecessar
yar
r
angementi
smadei
nt
hesl
i
pgaugehei
ghtandt
he
angl
ei
scal
cul
at
edasθ=Si
n1(
h/
L)
STUDYMATERI
ALPage49
METROLOGY
c.
)Angul
argauges:
I
nt
hi
smet
hod,t
heaut
ocol
l
i
mat
orusedi
nconj
unct
i
onwi
t
ht
heangl
egauges.I
t
compar
est
heangl
et
obemeasur
edoft
hegi
v
encomponentwi
t
ht
heangl
egauges.
Angl
esgaugesar
ewedgeshapedbl
ockandcanbeusedasst
andar
df
orangl
e
measur
ement
.Theyr
educet
hesetupt
i
meandmi
ni
mi
zet
heer
r
or
.Thesear
e13
pi
eces,di
v
i
dedi
nt
ot
hr
eet
y
pessuchasdegr
ees,mi
nut
esandseconds.Thef
i
r
st
ser
i
esangl
ear
e1°
,3°
,9°
,27°and41°Andt
hesecondser
i
esangl
ear
e1'
,3'
,9'
and27'Andt
het
hi
r
dser
i
esangl
ear
e3"
,6"
,18"and30"Thesegaugescanbeused
f
orl
ar
genumberofcombi
nat
i
onsbyaddi
ngorsubt
r
act
i
ngt
hesegauges,
f
r
om each
ot
her
.
2.
16
TAPERMEASUREMENT
Ext
er
nal
t
apermeasur
ement
:
Pl
acet
hesmal
l
erendoft
het
aper
edpl
uggaugeont
hesur
f
acepl
at
e.Pl
aceequal
hei
ghtofsl
i
pgaugecombi
nat
i
ons(
h1)onei
t
hersi
deofgaugeandmeasur
eM1
usi
ngami
cr
omet
er
.I
ncr
easehei
ghtofsl
i
pgaugecombi
nat
i
ons(
h2>h1)onei
t
her
si
deofgaugeandmeasur
eM2usi
ngmi
cr
omet
er
.
Then,
t
anα=(
M2M1)/
2(
h2-h1)
,
STUDYMATERI
ALPage50
METROLOGY
Wher
e
M1=Di
st
ancebet
weent
wor
ol
l
er
satl
owerposi
t
i
on
M2=Di
st
ancebet
weent
wor
ol
l
er
satupperposi
t
i
on
h1=Sl
i
pgaugecombi
nat
i
onhei
ghtatl
owerposi
t
i
on
h2=Sl
i
pgaugecombi
nat
i
onhei
ghtatupperposi
t
i
on
α=Hal
ft
aperangl
e
I
nt
er
nal
t
apermeasur
ement
:
Pl
aceoneendoft
het
aper
edr
i
nggaugeont
hesur
f
acepl
at
e.Pl
acesui
t
abl
esl
i
p
gaugecombi
nat
i
ons(
M1)i
nbet
weent
wobal
l
ssucht
hatbot
hbal
l
sar
ci
ncont
act
wi
t
hi
nt
er
nalsi
deoft
her
i
nggauge.Pl
acet
her
ev
er
seendoft
het
aper
edr
i
nggauge
ont
hesur
f
acepl
at
eandr
epeatt
heabov
epr
ocedur
ef
orr
eadi
ngM2.Measur
et
he
hei
ght(
H)ofr
i
nggaugewi
t
haVer
ni
erhei
ghtgauge.Measur
et
hedi
amet
erofbal
l
s
(
d)wi
t
hami
cr
omet
er
.
Then,
t
anα=(
M 2M1)/
2(
H-d)
M1=Di
st
ancebet
weent
wobal
l
satupr
i
ghtposi
t
i
on
M2=Di
st
ancebet
weent
wobal
l
satupsi
dedownposi
t
i
on
H=Hei
ghtoft
het
aper
edpar
t
d=Di
amet
eroft
hebal
l
α=Hal
ft
aperangl
e
STUDYMATERI
ALPage51
METROLOGY
2.
17
Gauges:
Bef
or
eaccept
i
nganycomponentt
hati
smanuf
act
ur
ed,needt
obei
nspect
edf
orhi
gh
accur
acy
.I
nmasspr
oduct
i
onsev
er
alcomponent
swi
l
lbemanuf
act
ur
edchecki
ngeach
par
tr
equi
r
eshi
ghcostandt
i
me.Conf
or
mat
i
onsf
ort
hepar
t
scanbedoneeasi
l
y
,by
measur
i
ngt
her
equi
r
edt
ol
er
ancesofpar
t
susi
nggauges.Gaugesar
escal
el
essr
i
gi
d
i
nst
r
ument
s,t
hesegaugesar
emadet
ospeci
f
yt
hel
i
mi
t
soft
hecomponent
.Unski
l
l
ed
per
sonscancheckt
hewor
kpi
ece.Noneedt
odocal
cul
at
i
onsf
ormeasur
ement
.They
gi
v
equi
ckr
esul
t
.
Gaugesar
eoft
wot
y
pes:
AGoNogauge(
orGo/
nogo)r
ef
er
st
oani
nspect
i
ont
oolusedt
ocheckawor
kpi
ece
agai
nsti
t
sal
l
owedt
ol
er
ances.I
t
snameder
i
v
esf
r
om i
t
s use:t
he gauge has t
wo
STUDYMATERI
ALPage52
METROLOGY
t
est
s;
t
hechecki
nv
ol
v
est
hewor
kpi
ecehav
i
ng
t
opassonet
est(
Go)andf
ai
l
t
he
ot
her(
NoGo)
.
I
ti
sani
nt
egr
alpar
toft
hequal
i
t
ypr
ocesst
hati
susedi
nt
hemanuf
act
ur
i
ngi
ndust
r
y
t
oensur
ei
nt
er
changeabi
l
i
t
yofpar
t
sbet
weenpr
ocesses,orev
enbet
weendi
f
f
er
ent
manuf
act
ur
er
s.
Ty
pesofgauges:
a.
)
PLUGGAUGE
i
.SOLI
DTYPEDOUBLEENDED
STUDYMATERI
ALPage53
METROLOGY
i
i
.TAPERI
NSERTEDTYPE
i
i
i
.
FASTENEDTYPEDOUBLEENDED
i
v
.PROGRESSI
VETYPEPLUGGAUGE
STUDYMATERI
ALPage54
METROLOGY
b.
)
SNAPGAUGE
c.
)
RI
NGGAUGE
STUDYMATERI
ALPage55
METROLOGY
d.
)THREADSNAPGAUGE
Mat
er
i
al
f
orgauge:
• Har
dnesst
or
esi
stwear
,Shoul
dbemadewi
t
hhi
ghcar
bonst
eelandheat
t
r
eat
edt
oi
mpar
thar
dness
• St
abi
l
i
t
ysot
hatt
heywon’
tchangesi
zeandshape
• Cor
r
osi
onr
esi
st
ant
• Hi
ghdegr
eeofaccur
acy
• Lowcoef
f
i
ci
entoft
her
mal
expansi
on
• Lowt
her
mal
conduct
i
v
i
t
y
• Coat
edpr
oduct
swi
l
l
bebenef
i
ci
ar
y
STUDYMATERI
ALPage56
METROLOGY
2.
18
Tay
l
or
sPr
i
nci
pl
eofGaugeDesi
gn:
1.GOGaugeshoul
dbedesi
gnedf
orMMC,
NOGOGaugef
orLMC
I
ft
hepl
uggaugei
scheckt
hehol
e,
si
z
eofGoshoul
dbet
ol
owerl
i
mi
tandNOGOt
oUpperl
i
mi
t
.
Si
mi
l
ar
l
yi
fsnapgaugei
susedt
ocheckt
heshaf
t
,si
zeofGOshoul
dbet
o
upperl
i
mi
tofshaf
tandNOGOt
ol
owerl
i
mi
t
.
2.Tay
l
or
’
spr
i
nci
pl
est
at
est
hatt
he“
GO”gaugeshoul
dcheckal
lt
hepossi
bl
e
el
ement
sofdi
mensi
onsatat
i
me(
Roundness,si
ze,l
ocat
i
on,et
c.
)t
heno
gaugeshoul
dcheckonl
yoneel
ementoft
hedi
mensi
onatat
i
me.
STUDYMATERI
ALPage57
METROLOGY
3.Hol
est
hatneedt
obei
nspect
edwi
l
li
nov
alshapeusual
l
y.SoNOGOwi
l
l
notent
erandwewr
ongl
ypr
ospectt
hatNOGOi
snotent
er
i
ngi
nhol
eso
i
t
sper
f
ect
.
ASSI
GNMENT-I
I
Q1) Expl
ai
nt
heconst
r
uct
i
onandusesofi
)Ver
ni
erbev
elpr
ot
r
act
or
.i
i
)Opt
i
calbev
el
pr
ot
r
act
or
.
Q2) Der
i
v
eanexpr
essi
onf
ordi
spl
acementofbubbl
ei
nt
er
msofr
adi
usofcur
v
at
ur
e,
basel
engt
hofl
ev
el
anddi
spl
acementhei
ght
.
1.
2.
3.
4.
5.
QUESTI
ONBANK:
a)Def
i
nel
i
nearmeasur
ement
.Li
stt
hel
i
nearmeasur
i
ngi
nst
r
umentaaccor
di
ng
t
ot
hei
raccur
acy
.
b)St
at
et
heusesof
:
i
)Tool
maker
sf
l
ati
i
)Angl
epl
at
ei
i
i
)Vbl
ocki
v
)St
r
ai
ght
edge.
a)Expl
ai
nt
heconst
r
uct
i
onandusesofi
)Ver
ni
erbev
elpr
ot
r
act
or
.i
i
)Opt
i
cal
bev
el
pr
ot
r
act
or
.
b)Cal
cul
at
et
heangl
eoft
aperandmi
ni
mum di
amet
erofani
nt
er
nalt
aperf
r
om
t
hef
ol
l
owi
ngr
eadi
ngs:Di
amet
erofbi
ggerbal
l–10.
25mm,Di
amet
erofsmal
l
er
bal
l–6.
07mm ,Hei
ghtoft
opofbi
ggerbal
lf
r
om dat
um –30.
13mm ,Hei
ghtof
t
opofsmal
l
erbal
l
f
r
om dat
um –10.
08mm
a)St
at
et
hepr
i
nci
pl
eofami
cr
omet
er
.Sket
chout
si
demi
cr
omet
erandnamei
t
s
v
ar
i
ouspar
t
s.
b)Whatar
et
hev
ar
i
ousi
nst
r
ument
susedf
ormeasur
i
ngf
l
at
nessofasur
f
ace
pl
at
e?Descr
i
bet
het
estpr
ocedur
ebyusi
ngoneofsuchi
nst
r
ument
.
a)Namet
hev
ar
i
ousi
nst
r
ument
susedf
ormeasur
i
ngangl
es.
0
b)A200mm si
nebari
st
obesetupt
oanangl
eof25.Det
er
mi
net
hesl
i
p
gaugesneededf
r
om87pi
ecesset
.
(
a)Whatdoy
ouunder
st
andbyamar
ki
ng“
1Di
v=0.
005mm i
n100mm”f
oundon
apr
eci
si
onspi
r
i
tl
ev
el
.Al
sodescr
i
behowt
heaccur
acyoft
hegr
aduat
i
onsona
spi
r
i
tl
ev
el
canbechecked.
(
b)Der
i
v
eanexpr
essi
onf
ordi
spl
acementofbubbl
ei
n
t
er
msofr
adi
usofcur
v
at
ur
e,
basel
engt
hofl
ev
el
anddi
spl
acementhei
ght
.
STUDYMATERI
ALPage58
METROLOGY
6.
Expl
ai
nt
hecl
assi
f
i
cat
i
onofpl
ai
nl
i
mi
tgauges?Sket
chandexpl
ai
nanyf
ourt
y
pes
ofpl
uggauges?
7. (
a)Towhataccur
acyt
heangl
escanbegener
at
edwi
t
hangl
ebl
ocks?Whyt
her
e
i
sal
i
mi
t
at
i
onont
hi
saccur
acy
.
(
b)Showt
hear
r
angementofangl
egaugeswi
t
hneatsket
chest
omeasur
ei
.11020’
andi
i
.240i
i
i
.280-52”i
v
.54.
260wi
t
hmi
ni
mum numberofgaugesf
r
om aset
of[
10,
30,
90,
270,
410][
1’
,
3’
,
9’
,
27’
,
]and[
3”
,
6”
,
18”
,
38”
]
8. Expl
ai
nwi
t
hneatsket
ches,
t
heconst
r
uct
i
onandappl
i
cat
i
onof
(
a)Ver
ni
erbev
el
pr
ot
r
act
or(
b)Opt
i
cal
bev
el
pr
ot
r
act
or
.
9. Expl
ai
nandi
l
l
ust
r
at
et
wosi
mpl
et
est
sonanopt
i
cal
f
l
atwhi
chwi
l
l
r
ev
eal
whet
her
asur
f
acei
sconv
exorconcav
ewi
t
haneatsket
ch.
10. (
a)Whatdoy
ouunder
st
andbyamar
ki
ng“
1Di
v=0.
005mm i
n100mm”f
oundon
apr
eci
si
onspi
r
i
tl
ev
el
.Al
sodescr
i
behowt
heaccur
acyoft
hegr
aduat
i
onsona
spi
r
i
tl
ev
el
canbechecked.
(
b)Der
i
v
e an expr
essi
on f
ordi
spl
acementofbubbl
ei
nt
er
msofr
adi
usof
cur
v
at
ur
e,
basel
engt
hofl
ev
el
anddi
spl
acementhei
ght
.
12. Expl
ai
nt
heTay
l
or
’
spr
i
nci
pl
eofl
i
mi
tgaugi
ng,
wi
t
hr
ef
er
encet
ogaugi
ngofr
ect
an
gul
arhol
es.Di
scusst
heef
f
ectofv
i
ol
at
i
ngt
heTay
l
or
’
spr
i
nci
pl
e?
STUDYMATERI
ALPage59
METROLOGY
CHAPTER3
OPTI
CALMEASURI
NGI
NSTRUMENTS
FLATSURFACEMEASUREMENT
I
NTRODUCTI
ON
Today
,
i
ti
sanaccept
edf
actt
hatl
i
ghtwav
espr
ov
i
det
hebestst
andar
df
orl
engt
h.
Thesi
gni
f
i
canceofl
i
ghtwav
esast
hel
engt
hst
andar
dwasf
i
r
stexpl
or
edby
Al
ber
tA.Mi
chel
sonandW.
L.Wor
l
ey
,al
t
houghi
ndi
r
ect
l
y
.Theywer
eusi
ngan
i
nt
er
f
er
omet
ert
omeasur
et
hepat
hdi
f
f
er
enceofl
i
ghtt
hatpassedt
hr
ougha
t
r
emendous di
st
ance i
n space.I
nt
hei
r exper
i
ment
,t
hey measur
ed t
he
wav
el
engt
hofl
i
ghti
nt
er
msofmet
r
e,t
heknownst
andar
dt
hen.Theysoon
r
eal
i
zedt
hatt
her
ev
er
sewasmor
emeani
ngf
ul
—i
tmademor
esenset
odef
i
nea
met
r
ei
nt
er
msofwav
el
engt
hsofl
i
ght
.Thi
saspectwassoonr
ecogni
zed,as
sci
ent
i
st
sbegant
ounder
st
andt
hatt
hewav
el
engt
hofl
i
ghtwasst
abl
ebey
ond
anymat
er
i
alt
hathad hi
t
her
t
o been used f
ort
he st
andar
d.Mor
eov
er
,t
hey
r
eal
i
zedt
hatl
i
ghtwasr
el
at
i
v
el
yeasyt
or
epr
oduceany
wher
e.
Opt
i
calmeasur
ementpr
ov
i
desasi
mpl
e,easy
,accur
at
e,andr
el
i
abl
emeansof
car
r
y
i
ngouti
nspect
i
onandmeasur
ement
si
nt
hei
ndust
r
y
.Thi
schapt
erpr
ov
i
des
i
nsi
ght
si
nt
osomeoft
hei
mpor
t
anti
nst
r
ument
sandt
echni
quest
hatar
ewi
del
y
used.Al
t
houghanaut
ocol
l
i
mat
ori
sani
mpor
t
antopt
i
cali
nst
r
umentt
hati
sused
f
ormeasur
i
ngsmal
l
angl
es,
i
ti
snotdi
scussedher
e.
.
Si
nceopt
i
cali
nst
r
ument
sar
eusedf
orpr
eci
si
onmeasur
ement
,t
hepr
oj
ect
ed
i
mage shoul
d be cl
ear
,shar
p,and di
mensi
onal
l
y accur
at
e.The desi
gn of
mechani
cal
el
ement
sandel
ect
r
oni
ccont
r
ol
sshoul
dbecompat
i
bl
ewi
t
ht
hemai
n
opt
i
calsy
st
em.I
n gener
al
,an opt
i
cali
nst
r
umentshoul
d hav
et
hef
ol
l
owi
ng
essent
i
al
f
eat
ur
es:
1.Al
i
ghtsour
ce
2.Acondensi
ngorcol
l
i
mat
i
ngl
enssy
st
em t
odi
r
ectl
i
ghtpastt
hewor
kpar
tand
i
nt
ot
heopt
i
cal
sy
st
em
3.Asui
t
abl
est
ageort
abl
et
oposi
t
i
ont
hewor
kpar
t
,t
het
abl
epr
ef
er
abl
yhav
i
ng
STUDYMATERI
ALPage60
METROLOGY
pr
ov
i
si
onsf
ormov
ementi
nt
wo di
r
ect
i
onsand possi
bl
yr
ot
at
i
on abouta
v
er
t
i
cal
axi
s
4.Thepr
oj
ect
i
onopt
i
cscompr
i
si
ngl
ensesandmi
r
r
or
s
5.Av
i
ewi
ngscr
eenorey
epi
ecet
or
ecei
v
et
hepr
oj
ect
edi
mage
6.Measur
i
ngandr
ecor
di
ngdev
i
ceswher
ev
err
equi
r
ed
Whent
wo l
i
ghtwav
esi
nt
er
actwi
t
heachot
her
,t
hewav
eef
f
ectl
eadst
oa
phenomenoncal
l
edi
nt
er
f
er
enceofl
i
ght
.I
nst
r
ument
sdesi
gnedt
omeasur
ei
nt
er
f
er
ence
ar
eknown as i
nt
er
f
er
omet
er
s.Appl
i
cat
i
on ofi
nt
er
f
er
encei
sofut
mosti
nt
er
esti
n
met
r
ol
ogy
.I
nt
er
f
er
encemakesi
tpossi
bl
et
oaccur
at
el
ycompar
esur
f
acegeomet
r
ywi
t
h
amast
er
,
asi
nt
hecaseofopt
i
calf
l
at
s.Mi
cr
oscopi
cmagni
f
i
cat
i
onenabl
esmi
cr
onl
ev
el
r
esol
ut
i
onf
orcar
r
y
i
ngouti
nspect
i
onorcal
i
br
at
i
onofmast
er
sandgauges.Laser
sar
e
al
soi
ncr
easi
ngl
ybei
ngusedi
ni
nt
er
f
er
omet
er
sf
orpr
eci
si
onmeasur
ement
.Thef
i
r
st
par
toft
hi
schapt
erdeal
swi
t
haf
ew pr
omi
nentopt
i
cali
nst
r
ument
ssuchast
het
ool
maker
’
smi
cr
oscopeandopt
i
calpr
oj
ect
or
.Thel
at
t
erpar
tdeal
swi
t
ht
hepr
i
nci
pl
eof
i
nt
er
f
er
omet
r
yandr
el
at
edi
nst
r
ument
at
i
oni
ndet
ai
l
.
3.
1
Tool
Maker
’
sMi
cr
oscope
Weassoci
at
emi
cr
oscopeswi
t
hsci
enceandmedi
ci
ne.I
ti
sal
soamet
r
ol
ogi
calt
oolof
t
hemostf
undament
ali
mpor
t
anceandgr
eat
esti
nt
egr
i
t
y
.I
naddi
t
i
ont
opr
ov
i
di
ngahi
gh
degr
eeofmagni
f
i
cat
i
on,ami
cr
oscopeal
sopr
ov
i
desasi
mpl
eandconv
eni
entmeans
f
ort
aki
ngr
eadi
ngs.Thi
senabl
esbot
habsol
ut
eandcompar
at
i
v
emeasur
ement
s.Letus
f
i
r
stunder
st
andt
hebasi
cpr
i
nci
pl
eofmi
cr
oscopy
,
whi
chi
si
l
l
ust
r
at
edi
nFi
g.3.
1.
STUDYMATERI
ALPage61
METROLOGY
Fi
g.3.
1Pr
i
nci
pl
eofmi
cr
oscopy
Ami
cr
oscopecoupl
est
wost
agesofmagni
f
i
cat
i
on.Theobj
ect
i
v
el
ensf
or
msani
mage
oft
hewor
kpi
eceatI
1att
hest
op.Thest
op,
f
r
amest
hei
magesot
hat
,
i
tcanbeenl
ar
ged
byt
heey
epi
ece.Vi
ewedt
hr
ought
heey
epi
ece,anenl
ar
gedv
i
r
t
uali
mageI
2i
sobt
ai
ned.
Magni
f
i
cat
i
onateachst
agemul
t
i
pl
i
es.Thus,ahi
ghl
yef
f
ect
i
v
emagni
f
i
cat
i
oncanbe
achi
ev
edwi
t
honl
ymoder
at
emagni
f
i
cat
i
onateachst
age.
Amongt
hemi
cr
oscopesusedi
nmet
r
ol
ogy
,wear
emostf
ami
l
i
arwi
t
ht
het
oolmaker
’
s
mi
cr
oscope.I
ti
samul
t
i
f
unct
i
onaldev
i
cet
hati
spr
i
mar
i
l
yusedf
ormeasur
ementon
f
act
or
yshop f
l
oor
s.Desi
gned wi
t
ht
he measur
ementofwor
kpi
ece cont
our
s and
i
nspect
i
onofsur
f
acef
eat
ur
esi
nmi
nd,at
oolmaker
’
smi
cr
oscopesuppor
t
sawi
de
r
ange ofappl
i
cat
i
onsf
r
om shop f
l
oori
nspect
i
on,and measur
ementoft
ool
sand
machi
nedpar
t
st
opr
eci
si
onmeasur
ementoft
estt
ool
si
nameasur
i
ngr
oom.Themai
n
useofat
oolmaker
’
smi
cr
oscopei
st
omeasur
et
heshape,si
ze,angl
e,andposi
t
i
onof
smal
lcomponent
st
hatf
al
lundert
he mi
cr
oscope’
s measur
i
ng r
ange.Fi
gur
e 3.
2
i
l
l
ust
r
at
est
hef
eat
ur
esofat
y
pi
cal
t
ool
maker
’
smi
cr
oscope.
Fi
g.3.
2Tool
maker
’
smi
cr
oscope
I
tf
eat
ur
esav
er
t
i
calsuppor
t
i
ngcol
umn,whi
chi
sr
obustandcar
r
i
est
hewei
ghtofal
l
ot
herpar
t
s oft
he mi
cr
oscope.I
tpr
ov
i
des a l
ong v
er
t
i
calwor
ki
ng di
st
ance.The
wor
kpi
ecei
sl
oadedonanXYst
age,
whi
chhasapr
ov
i
si
onf
ort
r
ansl
at
or
ymot
i
oni
nt
wo
pr
i
nci
paldi
r
ect
i
onsi
nt
hehor
i
zont
alpl
ane.Mi
cr
omet
er
sar
epr
ov
i
dedf
orbot
hXandY
STUDYMATERI
ALPage62
METROLOGY
axest
of
aci
l
i
t
at
el
i
nearmeasur
ementt
oahi
ghdegr
eeofaccur
acy
.Theent
i
r
eopt
i
cal
sy
st
em i
shousedi
nt
hemeasur
i
nghead.Themeasur
i
ngheadcanbemov
edupand
downal
ongt
hesuppor
t
i
ngcol
umnandt
hei
magecanbef
ocusedusi
ngt
hef
ocusi
ng
knob.Themeasur
i
ngheadcanbel
ockedi
nt
oposi
t
i
onbyoper
at
i
ngt
hecl
ampi
ngscr
ew.
Anangl
edi
albui
l
ti
nt
ot
heey
epi
ecepor
t
i
onoft
heopt
i
calt
ubeal
l
owseasyangl
e
measur
ement
.Asur
f
acei
l
l
umi
nat
orpr
ov
i
dest
her
equi
r
edi
l
l
umi
nat
i
onoft
heobj
ect
,so
t
hatashar
pandcl
eari
magecanbeobt
ai
ned.
Theel
ementt
hatmakesami
cr
oscopeameasur
i
ngi
nst
r
umenti
st
her
et
i
cl
e.Whent
he
i
magei
sv
i
ewedt
hr
ought
heey
epi
ece,t
her
et
i
cl
epr
ov
i
desar
ef
er
enceordat
um t
o
f
aci
l
i
t
at
emeasur
ement
.Speci
al
i
zedr
et
i
cl
eshav
ebeendev
el
opedf
orpr
eci
seset
t
i
ng.A
t
y
pi
calr
et
i
cl
ehast
wo‘
cr
osswi
r
es’
,whi
chcanbeal
i
gnedwi
t
har
ef
er
encel
i
neont
he
i
mageoft
hewor
kpi
ece.I
nf
act
,t
het
er
m‘
cr
osswi
r
e’i
sami
snomer
,becausemoder
n
mi
cr
oscopeshav
ecr
osswi
r
eset
chedongl
ass.Fi
gur
e3.
3i
l
l
ust
r
at
est
hepr
ocedur
ef
or
l
i
nearmeasur
ement
.
Fi
g.3.
3Al
i
gnmentofcr
osswi
r
eswi
t
ht
hemeasur
i
ngpoi
nt(
a)Readi
ngR1(
b)Readi
ng
R2
Ameasur
i
ngpoi
ntont
hewor
kpi
ecei
sal
i
gnedwi
t
honeoft
hecr
osswi
r
esandt
he
r
eadi
ngR1ont
hemi
cr
oscopei
snot
eddown.Now,
t
heXYt
abl
ei
smov
edbyt
ur
ni
ngt
he
mi
cr
omet
erhead,
andanot
hermeasur
i
ngpoi
nti
sal
i
gnedwi
t
ht
hesamecr
osswi
r
e.The
r
eadi
ng,R2i
snot
eddown.Thedi
f
f
er
encebet
weent
het
wor
eadi
ngsr
epr
esent
st
he
di
mensi
onbet
weent
het
womeasur
i
ngpoi
nt
s.Si
ncet
het
abl
ecanbemov
edi
nt
wo
mut
ual
l
y per
pendi
cul
ardi
r
ect
i
ons (
bot
hi
nt
he l
ongi
t
udi
nalas wel
las t
r
ansv
er
se
di
r
ect
i
ons)usi
ngt
hemi
cr
omet
er
s,apr
eci
semeasur
ementcanbeobt
ai
ned.I
nsome
t
oolmaker
’
smi
cr
oscopes,
i
nst
eadofami
cr
omet
erhead,
v
er
ni
erscal
esar
epr
ov
i
dedf
or
STUDYMATERI
ALPage63
METROLOGY
t
aki
ngr
eadi
ngs.
Tabl
e7.
1Lensesusedi
nt
heMi
t
ut
oy
ot
ool
maker
’
smi
cr
oscope
Tabl
e3.
1gi
v
est
hedet
ai
l
sofl
ensesav
ai
l
abl
ei
na‘
Mi
t
ut
oy
o’t
oolmaker
’
smi
cr
oscope.
Whi
l
et
heey
epi
ecei
si
nser
t
edi
naney
epi
ecemount
,t
heobj
ect
i
v
el
enscanbescr
ewed
i
nt
ot
heopt
i
cal
t
ube.Forex
ampl
e,
anobj
ect
i
v
el
ensofmagni
f
i
cat
i
on2×andaney
epi
ece
ofmagni
f
i
cat
i
on20×wi
l
l
t
oget
herpr
ov
i
deamagni
f
i
cat
i
onof40×.
Ther
et
i
cl
ei
sal
soi
nser
t
edi
nt
heey
epi
ecemount
.A posi
t
i
oni
ngpi
ni
spr
ov
i
dedt
o
posi
t
i
ont
her
et
i
cl
eaccur
at
el
y
.Adi
opt
r
eadj
ust
mentr
i
ngi
spr
ov
i
dedi
nt
heey
epi
ece
mountt
obr
i
ngt
hecr
osswi
r
esoft
her
et
i
cl
ei
nt
oshar
pf
ocus.Themeasur
i
ngsur
f
acei
s
br
oughti
nt
of
ocusbymov
i
ngt
heopt
i
calt
ubeupanddown,wi
t
ht
heai
dofaf
ocusi
ng
knob.Looki
ngi
nt
ot
heey
epi
ece,t
heusershoul
dmakesur
et
hatt
hecr
osswi
r
esar
e
kepti
nocul
arf
ocusdur
i
ngt
hef
ocusi
ngoper
at
i
on.
Posi
t
i
oni
ngoft
hewor
kpi
eceont
het
abl
ei
sext
r
emel
yi
mpor
t
antt
oensur
eaccur
acyi
n
measur
ement
.Themeasur
i
ngdi
r
ect
i
onoft
hewor
kpi
eceshoul
dbeal
i
gnedwi
t
ht
he
t
r
av
er
si
ngdi
r
ect
i
onoft
het
abl
e.Whi
l
el
ooki
ngi
nt
ot
heey
epi
ece,t
heposi
t
i
onoft
he
ey
epi
ecemountshoul
dbeadj
ust
edsot
hatt
hehor
i
zont
alcr
osswi
r
ei
sor
i
ent
edt
o
coi
nci
dewi
t
ht
hedi
r
ect
i
onoft
het
abl
emov
ement
.Now,t
heey
epi
ecemounti
sf
i
r
ml
y
secur
edbyt
i
ght
eni
ngt
hef
i
xi
ngscr
ews.Thewor
kpi
ecei
spl
aced/
cl
ampedont
het
abl
e
andt
hemi
cr
omet
erheadt
ur
nedt
oal
i
gnanedgeoft
hewor
kpi
ecewi
t
ht
hecent
r
eoft
he
cr
osswi
r
es.Then,t
hemi
cr
omet
eri
soper
at
edandt
hemov
i
ngi
magei
sobser
v
edt
o
v
er
i
f
ywhet
hert
hewor
kpi
ecepav
ementi
spar
al
l
elt
ot
hemeasur
i
ngdi
r
ect
i
on.Byt
r
i
al
ander
r
or
,
t
heusershoul
densur
et
hatt
het
womat
chper
f
ect
l
y
.
Mostt
oolmaker
’
smi
cr
oscopesar
epr
ov
i
dedwi
t
hasur
f
acei
l
l
umi
nat
or
.Thi
senabl
es
t
hecr
eat
i
onofacl
earandshar
pi
mage.Outoft
hef
ol
l
owi
ngt
hr
eet
y
pesofi
l
l
umi
nat
i
on
modest
hatar
eav
ai
l
abl
e,
anappr
opr
i
at
emodecanbesel
ect
edbasedont
heappl
i
cat
i
on:
STUDYMATERI
ALPage64
METROLOGY
Cont
ouri
l
l
umi
nat
i
on Thi
st
y
pe ofi
l
l
umi
nat
i
on gener
at
es t
he cont
ouri
mage ofa
wor
kpi
ece,andi
ssui
t
edf
ormeasur
ementandi
nspect
i
onofwor
kpi
ececont
our
s.The
i
l
l
umi
nat
ori
sequi
ppedwi
t
hagr
eenf
i
l
t
er
.
Sur
f
acei
l
l
umi
nat
i
onThi
st
y
peofi
l
l
umi
nat
i
onshowst
hesur
f
aceofawor
kpi
ece,andi
s
usedi
nt
heobser
v
at
i
onandi
nspect
i
onofwor
kpi
ecesur
f
aces.Theangl
eandor
i
ent
at
i
on
oft
hei
l
l
umi
nat
orshoul
dbeadj
ust
edsot
hatt
hewor
kpi
ecesur
f
acecanbeobser
v
ed
underopt
i
mum condi
t
i
ons.
Si
mul
t
aneous cont
ourand sur
f
ace i
l
l
umi
nat
i
ons Bot
h cont
ourand sur
f
ace ofa
wor
kpi
ececanbeobser
v
edsi
mul
t
aneousl
y
.
Someoft
hel
at
estmi
cr
oscopesar
eal
sopr
ov
i
dedwi
t
hangl
edi
al
st
oenabl
eangl
e
measur
ement
s.Measur
ementi
sdonebyal
i
gni
ngt
hesamecr
osswi
r
ewi
t
ht
woedges
oft
hewor
kpi
ece,oneaf
t
ert
heot
her
.Anangul
arv
er
ni
erscal
e,gener
al
l
ywi
t
hal
east
countof61,
i
susedt
ot
aket
her
eadi
ngs.
Appl
i
cat
i
onsofToolMaker
’
sMi
cr
oscope
1.I
ti
susedi
nshopf
l
oori
nspect
i
onofscr
ewt
hr
eads,gear
s,andot
hersmal
lmachi
ne
par
t
s.
2.I
t
sappl
i
cat
i
oni
ncl
udespr
eci
si
onmeasur
ementoft
estt
ool
si
nt
ool
r
ooms.
3.I
thel
psdet
er
mi
net
hedi
mensi
onsofsmal
lhol
es,whi
chcannotbemeasur
edwi
t
h
mi
cr
om¬et
er
sandcal
l
i
per
s.
4.I
tf
aci
l
i
t
at
est
empl
at
emat
chi
ngi
nspect
i
on.Smal
lscr
ew t
hr
eadsandi
nv
ol
ut
egear
t
eet
hcanbei
nspect
edusi
ngt
heopt
i
onal
t
empl
at
er
et
i
cl
es.
5.I
tenabl
esi
nspect
i
onoft
aper
sonsmal
l
component
supt
oanaccur
acyof61.
3.
2
Pr
of
i
l
ePr
oj
ect
or
:
Thepr
of
i
l
epr
oj
ect
or
,
al
socal
l
edt
heopt
i
cal
pr
oj
ect
or
,
i
sav
er
sat
i
l
ecompar
at
or
,
whi
chi
s
wi
del
yusedf
ort
hepur
poseofi
nspect
i
on.I
ti
sespeci
al
l
yusedi
nt
ool
r
oom appl
i
cat
i
ons.
I
tpr
oj
ect
sat
wodi
mensi
onalmagni
f
i
edi
mageoft
hewor
kpi
eceont
oav
i
ewi
ngscr
een
t
of
aci
l
i
t
at
emeasur
ement
.Apr
of
i
l
epr
oj
ect
ori
smadeupoft
hr
eemai
nel
ement
s:t
he
pr
oj
ect
orcompr
i
si
ngal
i
ghtsour
ceandasetofl
enshousedi
nsi
deanencl
osur
e,
awor
k
t
abl
et
ohol
dt
hewor
kpi
ecei
npl
ace,andat
r
anspar
entscr
eenwi
t
horwi
t
houtachar
t
gaugef
orcompar
i
sonormeasur
ementofpar
t
s.
STUDYMATERI
ALPage65
METROLOGY
3.
2.
1Opt
i
cal
Squar
es
Anopt
i
calsquar
ei
susef
uli
nt
ur
ni
ngt
hel
i
neofsi
ghtby90°f
r
om i
t
sor
i
gi
nalpat
h.Many
opt
i
cali
nst
r
ument
s,
especi
al
l
ymi
cr
oscopes,
hav
et
hi
sr
equi
r
ement
.Anopt
i
calsquar
ei
s
essent
i
al
l
yapent
agonalpr
i
sm (
pent
apr
i
sm)
.Regar
dl
essoft
heangl
eatwhi
cht
he
i
nci
dentbeam st
r
i
kest
hef
aceoft
hepr
i
sm,
i
ti
st
ur
nedt
hr
ough90°byi
nt
er
nal
r
ef
l
ect
i
on.
Unl
i
keaf
l
atmi
r
r
or
,
t
heaccur
acyofapent
apr
i
sm i
snotaf
f
ect
edbyt
heer
r
or
spr
esenti
n
t
hemount
i
ngar
r
angement
.Thi
saspecti
si
l
l
ust
r
at
edi
nFi
gs3.
4and3.
5.I
tcanbeseen
f
r
om Fi
g.3.
4t
hatami
r
r
ori
skeptatanangl
eof45°wi
t
hr
espectt
ot
hei
nci
dentr
ayof
l
i
ght
,
sot
hatt
her
ef
l
ect
edr
aywi
l
l
beatanangl
eof90°wi
t
hr
espectt
ot
hei
nci
dentr
ay
.I
t
i
sobser
v
edt
hatanyer
r
ori
nt
hemount
i
ngoft
hemi
r
r
orori
nmai
nt
ai
ni
ngi
t
sbase
par
al
l
el
,
i
naf
i
xedr
ef
er
ence,
t
ot
hebeam i
sgr
eat
l
ymagni
f
i
edbyt
heopt
i
call
ev
eref
f
ect
.
Theset
woer
r
or
si
ncombi
nat
i
onmayev
enbegr
eat
ert
hant
hewor
kpi
ecesquar
eness
er
r
or
.
1—Ref
l
ect
edr
aywi
t
houter
r
or
s
2—Ref
l
ect
edr
ayduet
omount
i
nger
r
or
3 —Ref
l
ect
edr
ayduet
obaseer
r
or
Fi
g.3.
4Mi
r
r
orr
ef
l
ect
i
ngl
i
ghtby90°
STUDYMATERI
ALPage66
METROLOGY
Fi
g.3.
5Opt
i
cal
squar
e
Fi
g.3.
6Useofanopt
i
cal
squar
et
ot
estsquar
eness
Thi
spr
obl
em maybeov
er
comebyusi
nganopt
i
calsquar
e.Fi
gur
e3.
5i
l
l
ust
r
at
est
he
opt
i
calpat
ht
hr
oughanopt
i
calsquar
e.Thei
nci
dentr
ayi
sr
ef
l
ect
edi
nt
er
nal
l
yf
r
om t
wo
f
acesandemer
gesf
r
om t
hesquar
eatexact
l
y90°t
ot
hei
nci
dentl
i
ght
.Thi
si
sa
r
emar
kabl
epr
oper
t
y
.Anysl
i
ghtdev
i
at
i
onormi
sal
i
gnmentoft
hepr
i
sm doesnotaf
f
ect
t
her
i
ghtangl
emov
ementoft
hel
i
ghtr
ay
.
Opt
i
calsquar
esar
eoft
wot
y
pes.Onet
y
pei
sf
i
t
t
edi
nt
oi
nst
r
ument
sl
i
ket
el
escopes,
wher
ei
n an opt
i
calsquar
ei
sf
act
or
y
f
i
t
t
ed t
o ensur
et
hatt
he l
i
ne ofsi
ghti
s
per
pendi
cul
art
ot
hev
er
t
ex
.Thesecondt
y
pecomeswi
t
ht
henecessar
yat
t
achment
sf
or
maki
ngadj
ust
ment
st
ot
hel
i
neofsi
ght
.Thi
sf
l
exi
bi
l
i
t
yal
l
owsopt
i
calsquar
est
obe
usedi
nanumberofappl
i
cat
i
onsi
nmet
r
ol
ogy
.Fi
gur
e3.
6i
l
l
ust
r
at
est
heuseofan
opt
i
cal
squar
et
ot
estt
hesquar
enessofmachi
nesl
i
deway
s.
Squar
enessoft
hev
er
t
i
calsl
i
dewaywi
t
hr
espectt
oahor
i
zont
alsl
i
dewayorbedi
sof
ut
mosti
mpor
t
ancei
nmachi
net
ool
s.Thet
estset
upr
equi
r
esanaut
ocol
l
i
mat
or
,pl
ane
r
ef
l
ect
or
s,
andanopt
i
calsquar
e.I
ti
snecessar
yt
ot
akeonl
yt
wor
eadi
ngs,
onewi
t
ht
he
r
ef
l
ect
oratposi
t
i
onAandasecondatposi
t
i
onB,t
heopt
i
calsquar
ebei
ngsetdownat
t
hei
nt
er
sect
i
onoft
het
wosur
f
aceswhent
her
eadi
ngatBi
st
aken.Thedi
f
f
er
ence
bet
weent
het
wor
eadi
ngsi
st
hesquar
enesser
r
or
.
7.
3OPTI
CALI
NTERFERENCE
Ar
ayofl
i
ghti
scomposedofani
nf
i
ni
t
enumberofwav
esofequal
wav
el
engt
h.Weknow
t
hatt
hev
al
ueoft
hewav
el
engt
h det
er
mi
nest
hecol
ourofl
i
ght
.Fort
hesakeof
si
mpl
i
ci
t
y
,
l
etusconsi
dert
wowav
es,
hav
i
ngsi
nusoi
dal
pr
oper
t
y
,
f
r
om t
wodi
f
f
er
entl
i
ght
r
ay
s.Fi
gur
e3.
7i
l
l
ust
r
at
est
hecombi
nedef
f
ectoft
het
wowav
esofl
i
ght
.
STUDYMATERI
ALPage67
METROLOGY
Fi
g.3.
7Twowav
esofdi
f
f
er
entampl
i
t
udest
hatar
ei
nphase
Thet
wor
ay
s,AandB,ar
ei
nphaseatt
heor
i
gi
nO,andwi
l
lr
emai
nsoast
her
ay
s
pr
opagat
et
hr
oughal
ar
gedi
st
ance.
Supposet
het
wor
ay
shav
eampl
i
t
udesy
Aandy
B,t
hent
her
esul
t
antwav
ewi
l
lhav
ean
ampl
i
t
udey
R=y
A+y
B.Thus,
whent
het
wor
ay
sar
ei
nphase,
t
her
esul
t
antampl
i
t
udei
s
maxi
mum andt
hei
nt
ensi
t
yofl
i
ghti
sal
somaxi
mum.Howev
er
,
i
ft
het
wor
ay
sar
eoutof
phase,
saybyanamountd,
t
hent
her
esul
t
antwav
ewi
l
l
hav
eanampl
i
t
udey
R=(
y
A+y
B)
cosd/
2.I
ti
scl
eart
hatt
hecombi
nat
i
onoft
het
wowav
esnol
ongerpr
oducesmaxi
mum
i
l
l
umi
nat
i
on.
Consi
dert
hecasewher
et
hephasedi
f
f
er
encebet
weent
het
wowav
esi
s180°
.The
ampl
i
t
udeoft
her
esul
t
i
ngwav
e,whi
chi
sshowni
nFi
g.3.
8,i
st
heal
gebr
ai
csum ofy
A
andy
B.Thecor
ol
l
ar
yi
st
hati
fy
Aandy
Bar
eequal
,
t
heny
Rwi
l
l
bezer
osi
ncecos(
180/
2)
i
szer
o.Thi
smeanst
hatcompl
et
ei
nt
er
f
er
encebet
weent
wowav
eshav
i
ngt
hesame
wav
el
engt
handampl
i
t
udepr
oducesdar
kness.
STUDYMATERI
ALPage68
METROLOGY
Fi
g.3.
8Twowav
esofdi
f
f
er
entampl
i
t
udes,
outofphaseby180°
Oneoft
hepr
oper
t
i
esofl
i
ghti
st
hatl
i
ghtf
r
om asi
ngl
esour
cecanbespl
i
ti
nt
ot
wo
componentr
ay
s.Obser
v
i
ngt
hewayi
nwhi
cht
hesecomponent
sr
ecombi
neshowsus
t
hatt
he wav
el
engt
h ofl
i
ghtcan be used f
orl
i
nearmeasur
ement
.The l
i
near
di
spl
acementdbet
weent
hewav
el
engt
hsoft
het
wol
i
ghtr
ay
sr
esul
t
si
nmax
i
mum
i
nt
er
f
er
encewhend=λ/
2,
wher
eλi
st
hewav
el
engt
hofl
i
ght
.
Fi
g.3.
9For
mat
i
onoff
r
i
nges
Nowi
nwhatwayi
st
hi
spr
oper
t
ygoi
ngt
ohel
pusi
nt
aki
ngl
i
nearmeasur
ement
s?Fi
gur
e
3.
9i
l
l
ust
r
at
es how t
he pr
oper
t
y ofi
nt
er
f
er
ence ofl
i
ghtcan be used f
orl
i
near
measur
ement
.Letusconsi
dert
womonochr
omat
i
cl
i
ghtr
ay
sf
r
om t
wopoi
ntsour
ces,
A
andB,
whi
chhav
et
hesameor
i
gi
n.Thel
i
ghtr
ay
sar
emadet
of
al
l
onaf
l
atscr
eent
hati
s
pl
acedper
pendi
cul
art
ot
heaxi
sOO1.Theaxi
sOO1i
si
nt
ur
nper
pendi
cul
art
ot
hel
i
ne
j
oi
ni
ngt
het
wopoi
ntsour
ces,AandB.Si
ncebot
hr
ay
sor
i
gi
nat
ef
r
om t
hesamel
i
ght
sour
ce,
t
heyar
eoft
hesamewav
el
engt
h.Letusal
soassumet
hatt
hedi
st
ancesOAand
STUDYMATERI
ALPage69
METROLOGY
OBar
eequal
.
Now,consi
derconv
er
genceoft
wor
ay
satpoi
ntO1ont
hescr
een.Si
ncet
hedi
st
ances
AO1andBO1ar
eequal
,
t
het
wor
ay
sar
ei
nphase,
r
esul
t
i
ngi
nmaxi
mum i
l
l
umi
nat
i
onat
poi
ntO1.Ont
heot
herhand,atpoi
ntO2,t
hedi
st
anceBO2i
sl
ongert
hant
hedi
st
ance
AO2.Ther
ef
or
e,byt
het
i
met
het
wor
ay
sar
r
i
v
eatpoi
ntO2,t
heyar
eoutofphase.
Assumi
ng t
hatt
hephasedi
f
f
er
ence d = λ/
2,wher
eλ i
st
hewav
el
engt
h ofl
i
ght
,
compl
et
ei
nt
er
f
er
enceoccur
s,
f
or
mi
ngadar
kspot
.
Atpoi
ntO3ont
hescr
een,t
hedi
st
anceBO3i
sl
ongert
hanAO3.I
ft
hedi
f
f
er
ence
bet
weent
het
wodi
st
ances,t
hati
s,BO3−AO3,i
sequalt
oanev
ennumberofhal
f
wav
el
engt
hs,
t
het
wo
l
i
ghtr
ay
sar
r
i
v
i
ngatO3wi
l
lbei
nphase,l
eadi
ngt
ot
hef
or
mat
i
onofabr
i
ghtspot
.Thi
s
pr
ocessr
epeat
sonei
t
hersi
deofO1ont
hescr
een,r
esul
t
i
ngi
nt
hef
or
mat
i
onof
al
t
er
nat
edar
kandbr
i
ghtar
eas.Thi
spat
t
er
nofal
t
er
nat
ebr
i
ghtanddar
kar
easi
s
popul
ar
l
yknownasf
r
i
nges.Thedar
kar
easwi
l
loccurwhenev
ert
hepat
hdi
f
f
er
enceofA
andBamount
st
oanoddnumberofhal
fwav
el
engt
hs,andt
hebr
i
ghtar
easwi
l
loccur
whent
hepat
hdi
f
f
er
enceamount
st
oanev
ennumberofhal
fwav
el
engt
hs.
3.
4I
NTERFEROMETRY
I
ti
snowqui
t
eobv
i
oust
ot
her
eadert
hatt
henumberoff
r
i
ngest
hatappeari
nagi
v
en
l
engt
hont
hescr
eeni
sameasur
eoft
hedi
st
ancebet
weent
het
wopoi
ntl
i
ghtsour
ces
andf
or
mst
hebasi
sf
orl
i
nearmeasur
ement
.Thi
sphenomenoni
sappl
i
edf
orcar
r
y
i
ng
outpr
eci
semeasur
ement
sofv
er
ysmal
ll
i
neardi
mensi
ons,and t
hemeasur
ement
t
echni
quei
spopul
ar
l
yknownasi
nt
er
f
er
omet
r
y
.Thi
st
echni
quei
susedi
nav
ar
i
et
yof
met
r
ol
ogi
calappl
i
cat
i
ons such as i
nspect
i
on ofmachi
ne par
t
sf
orst
r
ai
ght
ness,
par
al
l
el
i
sm,andf
l
at
ness,andmeasur
ementofv
er
ysmal
ldi
amet
er
s,amongot
her
s.
Cal
i
br
at
i
onandr
ef
er
encegr
adesl
i
pgaugesar
ev
er
i
f
i
edbyt
hei
nt
er
f
er
omet
r
yt
echni
que.
Thei
nst
r
umentusedf
ormaki
ngmeasur
ement
susi
ngi
nt
er
f
er
omet
r
yt
echni
quei
scal
l
ed
ani
nt
er
f
er
omet
er
.
Av
ar
i
et
yofl
i
ghtsour
cesar
er
ecommendedf
ordi
f
f
er
entmeasur
ementappl
i
cat
i
ons,
dependi
ngonconv
eni
enceofuseandcost
.Themostpr
ef
er
r
edl
i
ghtsour
cei
sa
t
ungst
enl
ampwi
t
haf
i
l
t
ert
hatt
r
ansmi
t
smonochr
omat
i
cl
i
ght
.Ot
hercommonl
yused
STUDYMATERI
ALPage70
METROLOGY
l
i
ghtsour
cesar
emer
cur
y
,
mer
cur
y198,
cadmi
um,
kr
y
pt
on86,
t
hal
l
i
um,
sodi
um,
hel
i
um,
neon,
andgasl
aser
s.Amongal
lt
hei
sot
opesofmer
cur
y
,
mer
cur
y198i
soneoft
hebest
l
i
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ces,pr
oduci
ngr
ay
sofshar
pl
ydef
i
nedwav
el
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nf
act
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el
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hof
mer
cur
y198i
st
hei
nt
er
nat
i
onal
secondar
yst
andar
dofl
engt
h.
Kr
y
pt
on86l
i
ghti
st
hebasi
sf
ort
henew basi
ci
nt
er
nat
i
onalst
andar
dofl
engt
h.The
met
r
ei
s def
i
ned as bei
ng exact
l
y1,
650,
763.
73 wav
el
engt
hs oft
hi
sl
i
ghtsour
ce,
measur
edi
nv
acuum.Gasl
aser
scompr
i
si
ngami
xt
ur
eofneonandhel
i
um pr
oducel
i
ght
t
hati
sf
armor
emonochr
omat
i
ct
hanal
lt
heaf
or
ement
i
onedsour
ces.I
nt
er
f
er
ence
f
r
i
ngescanbeobt
ai
nedwi
t
henor
mouspat
hdi
f
f
er
ences,
upt
o100mi
l
l
i
onwav
el
engt
hs.
Whi
l
eopt
i
calf
l
at
scont
i
nuet
o bet
hepopul
archoi
cef
ormeasur
ementusi
ng t
he
i
nt
er
f
er
omet
r
y t
echni
que, a host of ot
her i
nst
r
ument
s, popul
ar
l
y known as
i
nt
er
f
er
omet
er
s,
ar
eal
soav
ai
l
abl
e.Ani
nt
er
f
er
omet
er
,
i
not
herwor
ds,
i
st
heext
ensi
onof
t
he opt
i
calf
l
atmet
hod.Whi
l
ei
nt
er
f
er
omet
er
s hav
el
ong been t
he mai
nst
ay of
di
mensi
onalmeasur
ementi
nphy
si
calsci
ences,
t
heyar
eal
sobecomi
ngqui
t
epopul
ari
n
met
r
ol
ogyappl
i
cat
i
ons.Whi
l
et
heywor
kaccor
di
ngt
ot
hebasi
cpr
i
nci
pl
eofanopt
i
cal
f
l
at
,whi
chi
sexpl
ai
nedi
nt
heSect
i
on7.
4.
1t
heypr
ov
i
deaddi
t
i
onalconv
eni
encest
ot
he
user
.Themechani
caldesi
gnmi
ni
mi
zest
i
meconsumi
ngmani
pul
at
i
on.Thei
nst
r
ument
can be f
i
t
t
ed wi
t
h addi
t
i
onalopt
i
caldev
i
ces f
ormagni
f
i
cat
i
on,st
abi
l
i
t
y
,and hi
gh
r
esol
ut
i
on.I
nr
ecentt
i
mes,t
heuseofl
aser
shasgr
eat
l
yext
endedt
hepot
ent
i
alr
ange
andr
esol
ut
i
onofi
nt
er
f
er
omet
er
s.
3.
4.
1Opt
i
cal
Fl
at
s
Themostcommoni
nt
er
f
er
enceef
f
ect
sar
eassoci
at
edwi
t
ht
hi
nt
r
anspar
entf
i
l
msor
wedgesboundedonatl
eastonesi
debyat
r
anspar
entsur
f
ace.Soapbubbl
es,oi
lf
i
l
ms
onwat
er
,andopt
i
calf
l
at
sf
al
li
nt
hi
scat
egor
y
.Thephenomenonbywhi
chi
nt
er
f
er
ence
t
akespl
acei
sr
eadi
l
ydescr
i
bedi
nt
er
msofanopt
i
cal
f
l
at
,
asshowni
nFi
g.3.
10.
STUDYMATERI
ALPage71
METROLOGY
Fi
g.3.
10Fr
i
ngef
or
mat
i
oni
nanopt
i
cal
f
l
at
Anopt
i
calf
l
ati
sadi
skofhi
ghqual
i
t
ygl
assorquar
t
z
.Thesur
f
aceoft
hedi
ski
sgr
ound
andl
appedt
oahi
ghdegr
eeoff
l
at
ness.Si
zesofopt
i
calf
l
at
sv
ar
yf
r
om 25t
o300mm i
n
di
amet
er
,
wi
t
hat
hi
cknessr
angi
ngf
r
om 25t
o50mm.Whenanopt
i
calf
l
ati
sl
ai
dov
era
f
l
atr
ef
l
ect
i
ngsur
f
ace,
i
tor
i
ent
satasmal
langl
eθ,
duet
ot
hepr
esenceofanai
rcushi
on
bet
weent
het
wosur
f
aces.Thi
si
si
l
l
ust
r
at
edi
nFi
g.3.
10.Consi
derar
ayofl
i
ghtf
r
om a
monochr
omat
i
cl
i
ghtsour
cef
al
l
i
ngont
heuppersur
f
aceoft
heopt
i
calf
l
atatanangl
e.
Thi
sl
i
ghtr
ayi
spar
t
i
al
l
yr
ef
l
ect
edatpoi
nt‘
a’
.Ther
emai
ni
ngpar
toft
hel
i
ghtr
aypasses
t
hr
ought
het
r
anspar
entgl
assmat
er
i
alacr
osst
heai
rgapandi
sr
ef
l
ect
edatpoi
nt‘
b’
on
t
hef
l
atwor
ksur
f
ace.Thet
wor
ef
l
ect
edcomponent
soft
hel
i
ghtr
ayar
ecol
l
ect
edand
r
ecombi
nedbyt
heey
e,hav
i
ngt
r
av
el
l
edt
wodi
f
f
er
entpat
hswhosel
engt
hdi
f
f
er
sbyan
amount‘
abc’
.
I
f‘
abc’=λ/
2,wher
eλi
st
hewav
el
engt
hoft
hemonochr
omat
i
cl
i
ghtsour
ce,t
hent
he
condi
t
i
onf
orcompl
et
ei
nt
er
f
er
encehasbeensat
i
sf
i
ed.Thedi
f
f
er
encei
npat
hl
engt
hi
s
onehal
ft
hewav
el
engt
h,aper
f
ectcondi
t
i
onf
ort
ot
ali
nt
er
f
er
ence,asexpl
ai
ned i
n
Sect
i
on3.
3.Theey
ei
snow abl
et
oseeadi
st
i
nctpat
chofdar
knesst
er
medaf
r
i
nge.
Next
,consi
deranot
herl
i
ghtr
ayf
r
om t
hesamesour
cef
al
l
i
ngont
heopt
i
calf
l
atata
smal
ldi
st
ancef
r
om t
hef
i
r
stone.Thi
sr
ayget
sr
ef
l
ect
edatpoi
nt
s‘
d’and‘
e’
.I
ft
he
l
engt
h‘
def
’
equal
s3λ/
2,
t
hent
ot
ali
nt
er
f
er
enceoccur
sagai
nandasi
mi
l
arf
r
i
ngei
sseen
byt
heobser
v
er
.Howev
er
,atani
nt
er
medi
at
epoi
ntbet
weent
het
wof
r
i
nges,t
hepat
h
di
f
f
er
encebet
weent
wor
ef
l
ect
edpor
t
i
onsoft
hel
i
ghtr
aywi
l
lbeanev
ennumberofhal
f
STUDYMATERI
ALPage72
METROLOGY
wav
el
engt
hs.Thus,
t
het
wocomponent
sofl
i
ghtwi
l
l
bei
nphase,
andal
i
ghtbandwi
l
l
be
seenatt
hi
spoi
nt
.
Tosummar
i
ze,whenl
i
ghtf
r
om amonochr
omat
i
cl
i
ghtsour
cei
smadet
of
al
lonan
opt
i
calf
l
at
,whi
chi
sor
i
ent
edatav
er
ysmal
langl
ewi
t
hr
espectt
oaf
l
atr
ef
l
ect
i
ng
sur
f
ace,abandofal
t
er
nat
el
i
ghtanddar
kpat
chesi
sseenbyt
heey
e.Fi
gur
e3.
11
i
l
l
ust
r
at
est
het
y
pi
calf
r
i
ngepat
t
er
nseenonaf
l
atsur
f
acev
i
ewedunderanopt
i
calf
l
at
.
I
ncaseofaper
f
ect
l
yf
l
atsur
f
ace,t
hef
r
i
ngepat
t
er
ni
sr
egul
ar
,par
al
l
el
,anduni
f
or
ml
y
spaced.Anydev
i
at
i
onf
r
om t
hi
spat
t
er
ni
sameasur
eofer
r
ori
nt
hef
l
at
nessoft
he
sur
f
acebei
ngmeasur
ed.
Fi
g.3.
11I
nt
er
f
er
encef
r
i
nges
Fr
i
ngepat
t
er
nspr
ov
i
dei
nt
er
est
i
ngi
nsi
ght
si
nt
ot
hesur
f
acebei
ngi
nspect
ed.They
r
ev
ealsur
f
acecondi
t
i
onsl
i
kecont
ourl
i
nesonamap.Fi
gur
e3.
12i
l
l
ust
r
at
est
y
pi
cal
f
r
i
nge pat
t
er
ns,and Tabl
e 3.
2 of
f
er
s usef
ulhi
nt
s aboutt
he nat
ur
e ofsur
f
aces
cor
r
espondi
ngt
ot
hepat
t
er
ns.Oncewer
ecogni
zesur
f
aceconf
i
gur
at
i
onsf
r
om t
hei
r
f
r
i
ngepat
t
er
ns,
i
ti
smucheasi
ert
omeasur
et
heconf
i
gur
at
i
ons.
Fi
g.7.
12Fr
i
ngepat
t
er
nsr
ev
eal
sur
f
acecondi
t
i
ons
Compar
at
i
v
eMeasur
ementwi
t
hOpt
i
calFl
at
s
Oneoft
heobv
i
oususesofanopt
i
calf
l
ati
st
ocheckt
hehei
ght
sofsl
i
pgaugebl
ocks.
STUDYMATERI
ALPage73
METROLOGY
Thesl
i
pgauget
hati
st
obecheckedi
skeptal
ongsi
det
her
ef
er
encegaugeonaf
l
at
t
abl
e.Anopt
i
calf
l
ati
st
henpl
acedont
opofbot
hgauges,
asshowni
nFi
g.3.
13.Letus
assumet
hatAi
st
hest
andar
dr
ef
er
encegaugebl
ockwhi
l
eBi
st
hegaugebl
ockt
hati
s
bei
ngi
nspect
ed.
Fi
g.3.
13Hei
ghtmeasur
ementusi
nganopt
i
cal
f
l
at
Amonochr
omat
i
cl
i
ghtsour
cei
susedandt
hef
r
i
ngepat
t
er
nsar
eobser
v
edwi
t
ht
he
hel
pofamagni
f
y
i
nggl
ass.I
tcanbeseenf
r
om t
hef
i
gur
et
hatt
heopt
i
calf
l
atmakes
i
ncl
i
nat
i
onsofqandq'wi
t
ht
het
opsur
f
acesoft
het
wosl
i
pgauges.I
deal
l
y
,t
het
wo
angl
esshoul
dbet
hesame.Howev
er
,
i
nmostcases,
t
heangl
esar
edi
f
f
er
entbyv
i
r
t
ueof
wearandt
earoft
hesur
f
aceoft
hesl
i
pgauget
hati
sbei
ngi
nspect
ed.Thi
scaneasi
l
ybe
seenbyl
ooki
ngatt
hef
r
i
ngepat
t
er
nt
hati
sf
or
medont
het
wogauges,
asseenf
r
om t
he
magni
f
i
edi
mages.Thef
r
i
ngesseenonbot
ht
hegaugesar
epar
al
l
elandsamei
n
numberi
fbot
ht
hesur
f
acesar
eper
f
ect
l
yf
l
at
;ot
her
wi
se,t
henumberoff
r
i
ngesf
or
med
ont
het
wogaugesdi
f
f
er
s,
basedont
her
el
at
i
onshi
pbet
weenqandq'
.
Now,l
ett
henumberoff
r
i
ngesont
her
ef
er
encebl
ockbeNov
erawi
dt
hoflmm.I
ft
he
di
st
ance bet
ween t
he t
wo sl
i
p gauges i
s L and λ i
st
he wav
el
engt
h oft
he
STUDYMATERI
ALPage74
METROLOGY
monochr
omat
i
cl
i
ghtsour
ce,t
hent
hedi
f
f
er
encei
nhei
ghthi
sgi
v
enbyt
hef
ol
l
owi
ng
r
el
at
i
on:
h=l
LN2l
Thi
ssi
mpl
epr
ocedur
ecanbeempl
oy
edt
omeasur
ev
er
ysmal
lhei
ghtdi
f
f
er
encesi
nt
he
r
angeof0.
01–0.
1mm.Howev
er
,
t
heaccur
acyoft
hi
smet
hoddependsont
heaccur
acy
oft
hesur
f
acepl
at
eandcondi
t
i
onoft
hesur
f
acesoft
hespeci
menonwhi
cht
heopt
i
cal
f
l
ati
sr
est
i
ng.I
ti
sdi
f
f
i
cul
tt
ocont
r
olt
he‘
l
ay
’oft
heopt
i
calf
l
atandt
husor
i
entt
he
f
r
i
ngest
ot
hebestadv
ant
age.Thef
r
i
ngepat
t
er
ni
snotv
i
ewedf
r
om di
r
ect
l
yabov
e,
and
t
her
esul
t
i
ngobl
i
qui
t
ycancausedi
st
or
t
i
onander
r
or
si
nv
i
ewi
ng.A bet
t
erwayof
conduct
i
ng accur
at
emeasur
ementi
st
o usean i
nt
er
f
er
omet
er
.Whi
l
eav
ar
i
et
yof
i
nt
er
f
er
omet
er
sar
eusedi
nmet
r
ol
ogyandphy
si
cal
sci
ences,
t
wot
y
pesar
edi
scussedi
n
t
he f
ol
l
owi
ng sect
i
on:t
he NPL f
l
at
ness i
nt
er
f
er
omet
erand t
he Pi
t
t
er
–NPL gauge
i
nt
er
f
er
omet
er
.
Tabl
e3.
2Fr
i
ngepat
t
er
nsandt
her
esul
t
i
ngsur
f
acecondi
t
i
ons
3.
5I
NTERFEROMETERS
I
nt
er
f
er
omet
er
s ar
e opt
i
cal i
nst
r
ument
s t
hat ar
e used f
or v
er
y smal
ll
i
near
measur
ement
s.Theyar
eusedf
orv
er
i
f
y
i
ngt
heaccur
acyofsl
i
pgaugesandmeasur
i
ng
f
l
at
nesser
r
or
s.Thoughani
nt
er
f
er
omet
erwor
ksont
hesamebasi
cpr
i
nci
pl
east
hatof
anopt
i
cal
f
l
at
,
i
ti
spr
ov
i
dedwi
t
har
r
angement
si
nor
dert
ocont
r
ol
t
hel
ayandor
i
ent
at
i
on
off
r
i
nges.I
ti
sal
sopr
ov
i
dedwi
t
hav
i
ewi
ngorr
ecor
di
ngsy
st
em,whi
chel
i
mi
nat
es
measur
ementer
r
or
s.
STUDYMATERI
ALPage75
METROLOGY
3.
5.
1NPLFl
at
nessI
nt
er
f
er
omet
er
Thi
si
nt
er
f
er
omet
erwasdesi
gnedanddev
el
opedbyt
heNat
i
onalPhy
si
calLabor
at
or
yof
t
heUni
t
edKi
ngdom.I
tcompr
i
sesasi
mpl
eopt
i
calsy
st
em,whi
chpr
ov
i
desashar
p
i
mageoft
hef
r
i
ngessot
hati
ti
sconv
eni
entf
ort
heusert
ov
i
ewt
hem.Thel
i
ghtf
r
om a
mer
cur
yv
apourl
ampi
scondensedandpassedt
hr
oughagr
eenf
i
l
t
er
,r
esul
t
i
ngi
na
gr
eenmonochr
omat
i
cl
i
ghtsour
ce.Thel
i
ghtwi
l
lnowpasst
hr
oughapi
nhol
e,gi
v
i
ngan
i
nt
ensepoi
ntsour
ceofmonochr
omat
i
cl
i
ght
.Thepi
nhol
ei
sposi
t
i
onedsucht
hati
ti
si
n
t
hef
ocalpl
aneofacol
l
i
mat
i
ngl
ens.Ther
ef
or
e,t
hecol
l
i
mat
i
ngl
enspr
oj
ect
sapar
al
l
el
beam ofl
i
ghtont
ot
hef
aceoft
hegauget
obet
est
edv
i
aanopt
i
calf
l
at
.Thi
sr
esul
t
si
n
t
hef
or
mat
i
onofi
nt
er
f
er
encef
r
i
nges.Thel
i
ghtbeam,whi
chcar
r
i
esani
mageoft
he
f
r
i
nges,
i
sr
ef
l
ect
edbackanddi
r
ect
edby90°usi
ngagl
asspl
at
er
ef
l
ect
or
.
Theent
i
r
eopt
i
calsy
st
em i
sencl
osedi
namet
alorf
i
br
egl
assbody
.I
ti
spr
ov
i
dedwi
t
h
adj
ust
ment
st
ov
ar
yt
heangl
eoft
heopt
i
calf
l
at
,whi
chi
smount
edonanadj
ust
abl
e
t
r
i
pod.I
naddi
t
i
on,t
hebasepl
at
ei
sdesi
gnedt
ober
ot
at
edsot
hatt
hef
r
i
ngescanbe
or
i
ent
edt
ot
hebestadv
ant
age(
Fi
g.3.
14)
.
STUDYMATERI
ALPage76
METROLOGY
Fi
g.3.
14Opt
i
cal
sy
st
em ofanNPLf
l
at
nessi
nt
er
f
er
omet
er
Fi
gur
e3.
15i
l
l
ust
r
at
est
hef
r
i
ngepat
t
er
nt
hati
st
y
pi
cal
l
yobser
v
edont
hegaugesur
f
ace
aswel
last
hebasepl
at
e.I
nFi
g.3.
15(
a)
,
t
hef
r
i
ngesar
epar
al
l
elandequali
nnumberon
t
het
wosur
f
aces.Obv
i
ousl
y
,t
het
wosur
f
acesar
epar
al
l
el
,whi
chmeanst
hatt
hegauge
sur
f
acei
sper
f
ect
l
yf
l
at
.Ont
heot
herhand,i
nFi
g.3.
15(
b)
,t
henumberoff
r
i
ngesi
s
unequaland,si
ncet
hebasepl
at
esur
f
acei
sensur
edt
obeper
f
ect
l
yf
l
at
,t
hewor
kpi
ece
sur
f
acehasaf
l
at
nesser
r
or
.Duet
ot
hef
l
at
nesser
r
or
,t
heopt
i
calf
l
atmakesunequal
angl
eswi
t
ht
hewor
kpi
eceandt
hebasepl
at
e,
r
esul
t
i
ngi
nanunequalnumberoff
r
i
nges.
Mostoft
het
i
mesf
r
i
ngeswi
l
lnotbepar
al
l
ell
i
nes,butwi
l
lcur
v
eouti
napar
t
i
cul
ar
STUDYMATERI
ALPage77
METROLOGY
f
ashi
ondependi
ngont
heext
entofwearandt
earoft
heuppersur
f
aceoft
hewor
kpi
ece.
I
nsuchcases,
t
hef
r
i
ngepat
t
er
ngi
v
esacl
ueaboutt
henat
ur
eanddi
r
ect
i
onofwear
.
Fi
g.3.
15Exampl
eoff
r
i
ngepat
t
er
ns
Fi
g.3.
16 Test
i
ng par
al
l
el
i
sm i
n
gauges
(
a)Equal
f
r
i
ngesonpar
al
l
el
sur
f
aces
(
b)Unequal
f
r
i
ngesduet
of
l
at
nesser
r
or
Measur
i
ngEr
r
ori
nPar
al
l
el
i
sm
TheNPLf
l
at
nessi
nt
er
f
er
omet
eri
susedf
orchecki
ngf
l
at
nessbet
weengaugesur
f
aces.
Thegauget
obecheckedi
spl
acedonabasepl
at
et
hathasahi
ghdegr
eeoff
l
at
ness.I
f
t
hegaugel
engt
hi
ssmal
l
ert
han25mm,t
hegaugei
spl
acedont
hebasepl
at
eandt
he
f
r
i
ngepat
t
er
ni
sobser
v
ed.I
ft
hegaugebei
ngi
nspect
edi
sf
r
eef
r
om f
l
at
nesser
r
or
,
t
hen
t
hef
r
i
ngesf
or
medonbot
ht
hegaugesur
f
aceandt
hebasepl
at
ear
eequal
l
yspaced.
Forgaugesl
ongert
han25mm,f
r
i
ngepat
t
er
nont
hebasepl
at
ei
sdi
f
f
i
cul
tt
oobser
v
e.
Ther
ef
or
e,t
hegaugei
spl
acedonar
ot
ar
yt
abl
e,asshowni
nFi
g.3.
16.Supposet
he
gaugesur
f
acehasf
l
at
nesser
r
or
,becauseoft
heangl
ei
tmakeswi
t
ht
heopt
i
calf
l
at
,a
numberoff
r
i
ngesar
eseenont
hegaugesur
f
ace.Nowt
het
abl
ei
sr
ot
at
edt
hr
ough180°
,
andt
hesur
f
aceoft
hegaugebecomesev
enl
esspar
al
l
elt
ot
heopt
i
calf
l
at
.Thi
sr
esul
t
s
i
nmor
enumberoff
r
i
ngesappear
i
ngont
hegaugesur
f
ace.
Letusconsi
deragauget
hatshowsn1f
r
i
ngesal
ongi
t
sl
engt
hi
nt
hef
i
r
stposi
t
i
onand
n2i
nt
hesecondposi
t
i
on.Asseeni
nFi
g.3.
16,
t
hedi
st
ancebet
weent
hegaugeandt
he
opt
i
calf
l
ati
nt
hef
i
r
stposi
t
i
onhasi
ncr
easedbyadi
st
anced1,ov
ert
hel
engt
hoft
he
STUDYMATERI
ALPage78
METROLOGY
gauge,
andi
nt
hesecondposi
t
i
onbyadi
st
anced2.I
ti
scl
eart
hatt
hedi
st
ancebet
ween
t
hegaugeandt
heopt
i
cal
f
l
atchangesbyλ/
2,
bet
weenadj
acentf
r
i
nges.
Ther
ef
or
e,
d1=n1×λ/
2andd2=n2×λ/
2.
Thechangei
nangul
arr
el
at
i
onshi
pi
s(
d2−d1)
,
t
hati
s,
(
d2−d1)=(
n1−n2)×λ/
2.
3.
5.
2Pi
t
t
er
–NPLGaugeI
nt
er
f
er
omet
er
Thi
si
nt
er
f
er
omet
eri
susedf
ordet
er
mi
ni
ngact
uall
engt
hsofsl
i
pgauges.Si
ncet
he
measur
ementcal
l
sf
orahi
ghdegr
eeofaccur
acyandpr
eci
si
on,t
hei
nst
r
umentshoul
d
beusedunderhi
ghl
ycont
r
ol
l
edphy
si
calcondi
t
i
ons.I
ti
sr
ecommendedt
hatt
hesy
st
em
bemai
nt
ai
nedatanambi
entt
emper
at
ur
eof20°
C,andabar
omet
r
i
cpr
essur
eof760
mmHgwi
t
hawat
erv
apourpr
essur
eof7mm,andcont
ai
n0.
33%byv
ol
umeofcar
bon
di
oxi
de.
Theopt
i
calsy
st
em oft
hePi
t
t
er
–NPLi
nt
er
f
er
omet
eri
sshowni
nFi
g.3.
17.Li
ghtf
r
om a
monochr
omat
i
csour
ce(
t
hepr
ef
er
r
edl
i
ghtsour
cei
sacadmi
um l
amp)i
scondensedby
a condensi
ng l
ens and f
ocused ont
o an i
l
l
umi
nat
i
ng aper
t
ur
e.Thi
s pr
ov
i
des a
concent
r
at
edl
i
ghtsour
ceatt
hef
ocalpoi
ntofacol
l
i
mat
i
ngl
ens.Thus,apar
al
l
elbeam
ofl
i
ghtf
al
l
sonaconst
antdev
i
at
i
onpr
i
sm.Thi
spr
i
sm spl
i
t
st
hei
nci
dentl
i
ghti
nt
ol
i
ght
r
ay
sofdi
f
f
er
entwav
el
engt
hsandhencedi
f
f
er
entcol
our
s.Theusercansel
ectadesi
r
ed
col
ourbyv
ar
y
i
ngt
heangl
eoft
her
ef
l
ect
i
ngf
acesoft
hepr
i
sm r
el
at
i
v
et
ot
hepl
aneof
t
hebasepl
at
e.
STUDYMATERI
ALPage79
METROLOGY
Fi
g.3.
17Opt
i
cal
sy
st
em oft
hePi
t
t
er
–NPLgaugei
nt
er
f
er
omet
er
Thepr
i
sm t
ur
nst
hel
i
ghtby90°anddi
r
ect
si
tont
ot
heopt
i
calf
l
at
.Theopt
i
calf
l
atcan
beposi
t
i
onedatadesi
r
edangl
ebymeansofasi
mpl
ear
r
angement
.Thesl
i
pgauget
hat
i
st
obecheckedi
skeptr
i
ghtbel
owt
heopt
i
calf
l
atont
opoft
hehi
ghl
yf
l
atsur
f
aceof
t
hebasepl
at
e.Thel
owerpor
t
i
onoft
heopt
i
calf
l
ati
scoat
edwi
t
haf
i
l
m ofal
umi
ni
um,
whi
ch t
r
ansmi
t
s and r
ef
l
ect
s equalpr
opor
t
i
ons oft
he i
nci
dentl
i
ght
.The l
i
ghti
s
r
ef
l
ect
edf
r
om t
hr
eesur
f
aces,namel
yt
hesur
f
aceoft
heopt
i
calf
l
at
,t
heuppersur
f
ace
oft
hesl
i
pgauge,andt
hesur
f
aceoft
hebasepl
at
e.Li
ghtr
ay
sr
ef
l
ect
edf
r
om al
lt
he
t
hr
eesur
f
acespasst
hr
ought
heopt
i
calsy
st
em agai
n;howev
er
,t
heaxi
si
ssl
i
ght
l
y
dev
i
at
edduet
ot
hei
ncl
i
nat
i
onoft
heopt
i
cal
f
l
at
.Thi
ssl
i
ght
l
yshi
f
t
edl
i
ghti
scapt
ur
edby
anot
herpr
i
sm andt
ur
nedby90°
,sot
hatt
hef
r
i
ngepat
t
er
ncanbeobser
v
edand
r
ecor
dedbyt
heuser
.
Fi
g.7.
18Fi
el
dofv
i
ewoff
r
i
ngepat
t
er
n
Thet
y
pi
calf
r
i
ngepat
t
er
nobser
v
edi
sshowni
nFi
g.3.
18.Super
i
mposi
t
i
onoft
hef
r
i
nges
cor
r
espondi
ngt
ot
heuppersur
f
aceoft
hesl
i
pgaugeupont
hosecor
r
espondi
ngt
ot
he
sur
f
aceoft
hebasepl
at
ei
sshowni
nFi
g.7.
18.I
tcanbeseent
hatt
het
woset
sof
f
r
i
ngesar
edi
spl
acedbyanamountawi
t
hr
espectt
oeachot
her
.Thev
al
ueofav
ar
i
es
dependi
ngont
hecol
ouroft
hei
nci
dentl
i
ght
.Thedi
spl
acementai
sexpr
essedasa
f
r
act
i
onoft
hef
r
i
ngespaci
ngb,
whi
chi
sasf
ol
l
ows:
f=a/
b
Thehei
ghtoft
hesl
i
pgaugewi
l
lbeequalt
oawhol
enumberofhal
fwav
el
engt
hs,
n,
pl
us
STUDYMATERI
ALPage80
METROLOGY
t
hef
r
act
i
on a/
b oft
hehal
fwav
el
engt
hsoft
her
adi
at
i
oni
nwhi
cht
hef
r
i
ngesar
e
obser
v
ed.
Ther
ef
or
e,
t
hehei
ghtoft
hesl
i
pgauge,
H=n(
λ/
2)+(
a/
b)×(
λ/
2)
,
wher
eni
st
henumber
off
r
i
ngesont
hesl
i
pgaugesur
f
ace,
λi
st
hewav
el
engt
hofl
i
ght
,
anda/
bi
st
heobser
v
ed
f
r
act
i
on.Howev
er
,pr
act
i
t
i
oner
sofi
ndust
r
i
almet
r
ol
ogyar
enothappywi
t
ht
hev
al
ues
t
husobt
ai
ned.Thef
r
act
i
onr
eadi
ngsar
eobt
ai
nedf
oral
lt
het
hr
eecol
our
sofcadmi
um,
namel
yr
ed,gr
een,andv
i
ol
et
.Foreachoft
hewav
el
engt
hs,f
r
act
i
onsa/
bar
er
ecor
ded.
Usi
ngt
hesef
r
act
i
ons,aser
i
esofexpr
essi
onsar
eobt
ai
nedf
ort
hehei
ghtoft
hesl
i
p
gauge.Theseexpr
essi
onsar
ecombi
nedt
ogetagener
alexpr
essi
onf
orgaugehei
ght
.
The Pi
t
t
er
–NPL gauge i
nt
er
f
er
omet
eri
s pr
ov
i
ded wi
t
h a sl
i
de r
ul
e,i
n whi
ch t
he
wav
el
engt
hsofr
ed,gr
een,andv
i
ol
etar
esett
oscal
e,f
r
om acommonzer
o.Thi
s
pr
ov
i
desar
eadyr
eckonert
ospeedupcal
cul
at
i
ons.
3.
6
Fl
at
nessMeasur
ement
3.
6.
1
Rubbi
ngoft
wosur
f
acesbyusi
ngPer
si
anbl
ue
Spr
ead on y
oursur
f
ace pl
at
ea t
hi
nl
ay
erofHi
gh SpotBl
ue orot
hermar
ki
ng
medi
um,
l
ayon i
tt
hewor
kpi
ecet
o bescr
aped,and sl
i
dei
taf
ew t
i
mes,wi
t
h
moder
at
eandev
enpr
essur
e,i
naci
r
cul
arorf
i
gur
eei
ghtpat
t
er
noneort
woi
nches
acr
oss.Remov
et
hewor
kpi
ece.I
t
shi
gherar
easr
ubbedont
hesur
f
acepl
at
e,
became
mar
kedi
nbl
ue,andar
ecl
ear
l
yv
i
si
bl
e.Nowwi
t
hy
ourscr
apershav
eawayt
hemet
al
att
hosemar
kedspot
s.Thesur
f
acewi
l
lhav
ebecomeal
i
t
t
l
ebi
tf
l
at
t
er
,andy
ouwi
l
l
hav
ej
ustmadey
ourf
i
r
stscr
api
ngpass.
Fi
gur
eshowsascr
apedpr
oduct
3.
6.
2
Usi
ngst
r
ai
ghtedges/kni
f
eedge
STUDYMATERI
ALPage81
METROLOGY
Thesur
f
acet
obecheckedi
smar
kedoutwi
t
hasof
tl
eadpenci
l
,soasnott
o
damaget
he
sur
f
ace,
i
nt
oaser
i
esofpar
al
l
el
bandsasshowni
nFi
g.2.
26.I
ti
st
hencheckedusi
ng
abev
eledgest
r
ai
ghtedgeandusi
ngal
i
ghtboxorf
eel
ergauges,dependi
ngupon
t
hesi
zeoft
hesur
f
aceandt
her
equi
r
edaccur
acyofmeasur
ement
.I
ti
si
mpor
t
antt
o
not
et
hatt
hought
hesur
f
acemayappearf
l
ati
fmeasur
edpar
al
l
elt
ot
hesi
des,but
addi
t
i
onalchecksneedt
obemadeacr
osst
hedi
agonal
st
odet
ecter
r
or
soff
l
at
ness
duet
o‘
wi
ndi
ng1oft
hesur
f
ace.
Measur
i
ngf
l
at
nessusi
ngSt
r
ai
ghtedgesandf
i
l
l
ergauges
3.
6.
3
Di
al
gauge
3.
6.
4
I
nt
er
f
er
omet
er
3.
6.
5
Beam compar
at
or
Thi
smet
hodi
spar
t
i
cul
ar
l
yconv
eni
entf
ort
est
i
ngt
hef
l
at
nessofsur
f
acedur
i
ng
manuf
act
ur
e.
Thi
smet
hodi
sbasedont
hepr
i
nci
pl
eofcompar
i
ngt
hest
r
ai
ght
nessofasuccessi
on
ofgener
at
or
si
nt
hesur
f
aceundert
estwi
t
ht
hatofaknownr
ef
er
encest
r
ai
ghtedge.
Thecompar
i
soni
scar
r
i
edoutbyt
heBeam Compar
at
or
,asor
tofsensi
t
i
v
edi
al
i
ndi
cat
orwhi
ch,
i
nef
f
ect
,
measur
est
hev
er
t
i
caldi
spl
acementoft
hemi
dpoi
ntofany
STUDYMATERI
ALPage82
METROLOGY
par
t
i
cul
argener
at
orwi
t
hr
espectt
oat
heor
et
i
calst
r
ai
ghtl
i
nej
oi
ni
ngi
t
sends.Fr
om
t
hesemeasur
ement
s,t
hei
deaoft
heappar
entconv
exi
t
yorconcav
i
t
yofgener
at
or
canbehad,whi
chmaybeusedt
odet
er
mi
net
hegener
aldepar
t
ur
es,oft
hesur
f
ace
f
r
om meant
r
uepl
aneasexpl
ai
nedl
at
er
.
Thebodyoft
hecompar
at
orconsi
st
sofar
obustbutl
i
ghtbeam hav
i
ngt
hr
ee
suppor
t
i
ngf
eet
madeofhar
denedst
eelandspher
i
cal
l
yended,onef
i
xedatt
hecent
r
eofbeam but
of
f
setf
r
om t
hei
nej
oi
ni
ngt
heot
hert
wo.Thet
wosuppor
t
i
ngf
eetatt
heendsmaybe
cl
ampedt
ot
hebeam i
nsy
mmet
r
i
cal
l
ydi
sposedposi
t
i
onswi
t
hr
espectt
ot
hecent
r
al
f
ootandatadi
st
anceapar
tdependi
ngupont
hesi
zeoft
hesur
f
aceundert
est
.By
hav
i
ngonl
yt
hr
eesuppor
t
i
ngf
eet
,t
hebeam i
sacci
dent
l
yl
i
abl
et
ober
ol
l
edov
eron
t
hesi
denotsuppor
t
edbyt
heof
f
setf
oot
.I
nor
dert
oav
oi
dt
hi
s,af
our
t
hf
ooti
nt
he
f
or
m ofaspher
i
cal
l
yendedspr
i
ngpl
ungeri
spr
ov
i
dedataposi
t
i
onsy
mmet
r
i
cal
l
y
opposi
t
et
hef
i
xedof
f
setf
oot
.Thef
our
t
hf
ooti
snor
mal
l
yar
r
angedt
ober
easonabl
y
cl
earoft
hesur
f
acepl
at
eandcomesi
nt
ooper
at
i
ononl
yi
ft
hebeam t
endst
of
al
l
.A
v
er
ysensi
t
i
v
edi
ali
ndi
cat
orsuppor
t
edi
nt
hecent
r
alweboft
hebeam andt
heaxi
sof
i
t
sspher
i
cal
l
yendedcont
actpl
ungerl
i
esi
nt
hepl
anet
hr
ought
heaxi
soft
het
wo
adj
ust
abl
ef
eet
.Fort
est
i
ng pur
poses a r
ef
er
ence sur
f
ace i
s empl
oy
ed whose
st
r
ai
ght
nesshasal
r
eadybeencheckedbyot
hermet
hodsandt
hust
heer
r
or
sofi
t
s
st
r
ai
ght
nessar
eknown.Thecompar
at
ori
ssuppor
t
eduponequalsl
i
pgaugesor
l
appedpadsonbot
ht
her
ef
er
enceandt
het
estsur
f
acessot
hatt
hef
eetoft
hebeam
compar
at
ordonotacci
dent
l
yl
ocat
ei
nt
hehol
l
owsoft
hescr
apedsur
f
ace,andt
he
r
eadi
ngsar
et
akenwi
t
hr
espectt
ot
hehi
ghspot
soft
hesur
f
aces
1.Di
al
gauge,
2.Mov
abl
ecol
umn,
2.3.Robustandl
i
ghtbeam,
4.
Fi
xedcol
umn
STUDYMATERI
ALPage83
METROLOGY
3.
6.
6
Aut
ocol
l
i
mat
or
Thi
si
sanopt
i
cal
i
nst
r
umentusedf
ort
hemeasur
ementofsmal
l
angul
ardi
f
f
er
ences.
Forsmal
langul
armeasur
ement
s,aut
ocol
l
i
mat
orpr
ov
i
desa v
er
ysensi
t
i
v
e and
accur
at
e appr
oach.Aut
ocol
l
i
mat
ori
s essent
i
al
l
y an i
nf
i
ni
t
yt
el
escope and a
col
l
i
mat
orcombi
nedi
nt
oonei
nst
r
ument
.Thepr
i
nci
pl
eonwhi
cht
hi
si
nst
r
ument
wor
ksi
sgi
v
enbel
ow.Oi
sapoi
ntsour
ceofl
i
ghtpl
acedatt
hepr
i
nci
palf
ocusofa
col
l
i
mat
i
ngl
ensi
nFi
g.
.Ther
ay
sofl
i
ghtf
r
om Oi
nci
dentont
hel
enswi
l
lnowt
r
av
el
asapar
al
l
elbeam ofl
i
ght
.I
ft
hi
sbeam nowst
r
i
kesapl
aner
ef
l
ect
orwhi
chi
snor
mal
t
ot
heopt
i
calaxi
s,i
twi
l
lber
ef
l
ect
edbackal
ongi
t
sownpat
handf
ocussedatt
he
samepoi
ntO.I
ft
hepl
aner
ef
l
ect
orbenowt
i
l
t
edt
hr
oughasmal
langl
e9,
[
Ref
erFi
g.
8.
31]t
henpar
al
l
elbeam wi
l
lbedef
l
ect
edt
hr
ought
wi
cet
hi
sangl
e,andwi
l
lbe
br
oughtt
of
ocusatO’i
nt
hesamepl
aneatadi
st
ancexf
r
om O.Obv
i
ousl
y00′
=x=
26.f
,wher
ef
’
\
st
hef
ocall
engt
hoft
hel
ens.Ther
ear
ecer
t
ai
ni
mpor
t
antpoi
nt
st
o
appr
eci
at
eher
e:
Theposi
t
i
onoft
hef
i
nali
magedoesnotdependupont
hedi
st
anceofr
ef
l
ect
orf
r
om
t
hel
ens,i
.
e.separ
at
i
onxi
si
ndependentoft
heposi
t
i
onofr
ef
l
ect
orf
r
om t
hel
ens.
Buti
fr
ef
l
ect
orsmov
edt
oomuchbackt
henr
ef
l
ect
edr
ay
swi
l
lcompl
et
el
ymi
sst
he
l
ensandnoi
magewi
l
l
be
f
or
med.Thusf
orf
ul
lr
angeofr
eadi
ngsofi
nst
r
umentt
obeused,t
hemax
i
mum
r
emot
enessof
t
her
ef
l
ect
ori
sl
i
mi
t
ed.Forhi
ghsensi
t
i
v
i
t
y
,i
.
e.f
orl
ar
gev
al
ueofa;f
orasmal
l
angul
ardev
i
at
i
on8,
al
ongf
ocal
l
engt
hi
sr
equi
r
ed.
STUDYMATERI
ALPage84
METROLOGY
3.
6.
6
Angl
edeccor
Thi
si
sal
soat
y
peofanaut
ocol
l
i
mat
or
.I
tcont
ai
nsasmal
li
l
l
umi
nat
edscal
ei
nt
he
f
ocalpl
aneoft
heobj
ect
i
v
el
ens(
col
l
i
mat
i
ngl
ens)
.Thi
sscal
ei
nnor
malposi
t
i
oni
s
out
si
det
hev
i
ewoft
hemi
cr
oscopeey
epi
eceasshowni
nFi
g.Thei
l
l
umi
nat
edscal
e
i
spr
oj
ect
edasapar
al
l
elbeam byt
hecol
l
i
mat
i
ngl
enswhi
chaf
t
erst
r
i
ki
ngar
ef
l
ect
or
bel
owt
hei
nst
r
umenti
sr
ef
ocusedbyt
hel
ensi
nt
hef
i
el
dofv
i
ewoft
heey
epi
ece.I
n
t
hef
i
el
dofv
i
ewofmi
cr
oscopet
her
ei
sanot
herdat
um scal
ef
i
xedacr
osst
hecent
r
e
ofscr
eenandt
her
ef
l
ect
edi
mageoft
hei
l
l
umi
nat
edscal
ei
sr
ecei
v
edatr
i
ghtangl
e
t
ot
hi
sf
i
xedscal
easshowni
nandt
het
woscal
es,i
nt
hi
sposi
t
i
oni
nt
er
secteach
ot
her
.Thust
her
eadi
ngont
hei
l
l
umi
nat
edscal
emeasur
esangul
ardev
i
at
i
onsf
r
om
oneaxi
sat90°t
ot
heopt
i
calaxi
sand t
her
eadi
ng on t
hef
i
xed dat
um scal
e
measur
est
hedev
i
at
i
onaboutanaxi
smut
ual
l
yper
pendi
cul
art
ot
heot
hert
wo.I
n
ot
herwor
ds,
changesi
nangul
arposi
t
i
onoft
her
ef
l
ect
ori
nt
wopl
anesar
ei
ndi
cat
ed
bychangesi
nt
hepoi
ntofi
nt
er
sect
i
onoft
het
woscal
es.Readi
ngsf
r
om scal
ear
e
r
eaddi
r
ectt
o1′
wi
t
houtt
heuseofami
cr
omet
er
.
Angl
edecor
REVI
EW QUESTI
ONS(
Quest
i
onbank)
1.Whatar
et
heessent
i
al
f
eat
ur
esofanopt
i
cal
sy
st
em?
2.Expl
ai
nt
hepr
i
nci
pl
eofmi
cr
oscopy
.
3.Wi
t
ht
hehel
pofaneatsket
ch,expl
ai
nt
heconst
r
uct
i
ondet
ai
l
sofat
oolmaker
’
s
mi
cr
oscope.
4.Wr
i
t
eanot
eonsur
f
acei
l
l
umi
nat
i
onmodesav
ai
l
abl
ei
nat
ool
maker
’
smi
cr
oscope.
5.Di
scusst
hei
mpor
t
antappl
i
cat
i
onsofat
ool
maker
’
smi
cr
oscope.
STUDYMATERI
ALPage85
METROLOGY
6.Expl
ai
nt
heopt
i
cal
sy
st
em andwor
ki
ngpr
i
nci
pl
eofapr
of
i
l
epr
oj
ect
or
.
7.Whatar
et
he adv
ant
ages ofopt
i
calsquar
es when used i
n opt
i
calmeasur
i
ng
i
nst
r
ument
s?
8.Wi
t
ht
hehel
pofasi
mpl
esket
ch,expl
ai
nhow opt
i
calsquar
esar
emadeuseofi
n
t
est
i
ngt
hesquar
enessofmachi
nepar
t
s.
9.Expl
ai
nt
hephenomenonofopt
i
cal
i
nt
er
f
er
ence.
10.Expl
ai
nt
hemeasur
ementmet
hodol
ogyi
nv
ol
v
edi
nt
heuseofopt
i
cal
f
l
at
s.
11.Br
i
ef
l
ydescr
i
bet
hepr
ocedur
ei
nv
ol
v
edi
nchecki
ngsl
i
pgaugesusi
ngopt
i
calf
l
at
s.
Whatar
et
hel
i
mi
t
at
i
onsoft
hi
smet
hod?
12.Wi
t
ht
hehel
pofaneatsket
ch,expl
ai
nt
heopt
i
calsy
st
em usedi
nanNPLf
l
at
ness
i
nt
er
f
er
omet
er
.Di
scusst
hepr
ocedur
eofmeasur
i
nger
r
ori
npar
al
l
el
i
sm usi
ngt
hesame.
13.Wr
i
t
eanot
eont
hePi
t
t
er
–NPLgaugei
nt
er
f
er
omet
er
.
14.Whatar
et
headv
ant
agesandl
i
mi
t
at
i
onsofl
aseri
nt
er
f
er
omet
r
y
?
15.Expl
ai
nt
hewor
ki
ngpr
i
nci
pl
eofal
aseri
nt
er
f
er
omet
er
.
Assi
gnmentI
I
I
Q1) Expl
ai
nt
heTool
maker
’
smi
cr
oscopeandi
t
suses
Q2) whati
sopt
i
cal
f
l
at
?Whatt
hei
rt
y
pes?St
at
et
hel
i
mi
t
at
i
onsofopt
i
cal
f
l
at
Q3) Expl
ai
nt
hei
nt
er
f
er
omet
eri
nmeasur
i
ngf
l
at
nessofsur
f
aces.
CHAPTER4
SURFACEROUGNHESSMEASUREMENT
4.
1
Sur
f
acet
ext
ur
eandi
t
si
mpor
t
ant
:
Whati
ssur
f
acet
ext
ur
eorsur
f
acef
i
ni
sh?
?
 Sur
f
acef
i
ni
sh,al
soknownassur
f
acet
ext
ur
e,i
st
hechar
act
er
i
st
i
csofasur
f
ace.
I
thast
hr
eecomponent
s:
l
ay
,
sur
f
acer
oughness,
andwav
i
ness.
.
Whyt
ost
udyaboutsur
f
acet
ext
ur
e?
?
 Pr
oper
t
i
essuchasappear
ance,cor
r
osi
onr
esi
st
ance,wearr
esi
st
ance,f
at
i
gue
r
esi
st
ance,l
ubr
i
cat
i
on,
abi
l
i
t
yt
ohol
dpr
essur
e,
l
oadcar
r
y
i
ngcapaci
t
yet
c.
,ar
e
i
nf
l
uencedbysur
f
acet
ext
ur
eorsur
f
ace.
.
4.
2
Fact
or
sAf
f
ect
i
ngSur
f
aceRoughness
1.Vi
br
at
i
ons
2.Mat
er
i
al
ofwor
kpi
ece
3.Ty
peofmachi
ni
ng
STUDYMATERI
ALPage86
METROLOGY
4.Ri
gi
di
t
yoft
hesy
st
em consi
st
i
ngofmachi
net
ool
,f
i
xt
ur
ecut
t
i
ngt
ool&
wor
k
5.Ty
pe,
f
or
m,
mat
er
i
al
andshar
pnessofcut
t
i
ngt
ool
6.Cut
t
i
ngcondi
t
i
ons(
speed,
f
eedanddept
hofcut
)
7.Ty
peofcool
antused.
4.
3
I
sHi
ghSur
f
aceFi
ni
shAl
way
sDesi
r
abl
e?
?
• Heatexchangert
ubest
r
ansf
erheatbet
t
erwhent
hei
rsur
f
acesar
esl
i
ght
l
y
r
oughsoher
er
oughnessi
ssl
i
ght
l
ypr
ef
er
r
ed.
• Br
akedr
umsandcl
ut
chpl
at
eset
c.wor
kbestwi
t
hsomedegr
eeofsur
f
ace
r
oughness.
• I
nI
.
C engi
nessmoot
hsur
f
acesar
edesi
r
edso ast
or
educet
hef
r
i
ct
i
on
bet
weent
hemat
i
ngpar
t
s
• Forqui
t
t
eroper
at
i
onst
hesur
f
acesmustbesmoot
h.
4.
4
Pr
i
nci
pal
Reasonsf
orCont
r
ol
l
i
ngSur
f
aceText
ur
e
 Toi
mpr
ov
eser
v
i
cel
i
f
e
 Toi
mpr
ov
ef
at
i
guer
esi
st
ance
 Tor
educei
ni
t
i
al
wearofpar
t
s
 t
or
educef
r
i
ct
i
onal
wear
 Tor
educecor
r
osi
onbymi
ni
mi
z
i
ngdept
hofi
r
r
egul
ar
i
t
i
es
 Forgoodappear
ance
4.
5
Or
der
sofGeomet
r
i
cal
I
r
r
egul
ar
i
t
i
es.
Thei
r
r
egul
ar
i
t
i
escanbecl
assi
f
i
edi
nt
o4t
y
pesoror
der
st
heyar
e:
a.Fi
r
stor
der
b.Secondor
der
c.Thi
r
dor
der
d.Four
t
hor
der
a.Fi
r
stor
der
:
Thei
r
r
egul
ar
i
t
i
escausedbyi
naccur
aci
esi
nt
hemachi
net
ool i
t
sel
far
ecl
assi
f
i
ed
undert
hi
sor
der.
Thesei
ncl
ude:
I
. I
r
r
egul
ar
i
t
i
escausedduet
ol
ackofst
r
ai
ght
nessofgui
deway
sonwhi
ch
t
ool
mustmov
e.
STUDYMATERI
ALPage87
METROLOGY
I
I
. Sur
f
acei
r
r
egul
ar
i
t
i
esar
i
si
ngduet
odef
or
mat
i
onofwor
kundert
heact
i
on
ofcut
t
i
ngf
or
cesandduet
ot
hewei
ghtoft
hemat
er
i
al
i
t
sel
f
.
b.Secondor
der:
Thei
r
r
egul
ar
i
t
i
escausedduet
ov
i
br
at
i
onsofanyki
ndar
e
cal
l
edsecondor
der
i
r
r
egul
ar
i
t
i
es.Thesei
ncl
udechat
t
er mar
ksont
hesur
f
aceoft
hepar
t
s.
c.Thi
r
dor
der:
Ev
eni
ft
hemachi
newer
eper
f
ectandcompl
et
el
yf
r
eef
r
om
v
i
br
at
i
ons
some
i
r
r
egul
ar
i
t
i
esar
ecausedbymachi
nei
t
sel
fduet
o char
act
er
i
st
i
cs of t
he pr
ocess.
Thi
si
ncl
udesf
eedmar
koft
hecut
t
i
ngt
ool
.
d.Four
t
hor
der:
Thef
our
t
hor
deri
r
r
egul
ar
i
t
i
esi
ncl
udet
hosear
i
si
ngf
r
om t
he
r
upt
ur
e
of
t
he
mat
er
i
al
dur
i
ngt
hesepar
at
i
onoft
hechi
p.
Thei
r
r
egul
ar
i
t
i
esont
hesur
f
aceoft
hepar
tpr
oducedcanal
sobegr
oupedi
nt
ot
wo
cat
egor
i
es.Theyar
e:
i
.Roughnessorpr
i
mar
yt
ext
ur
e:
The sur
f
ace i
r
r
egul
ar
i
t
i
es ofsmal
lwav
el
engt
h ar
e cal
l
ed pr
i
mar
yt
ext
ur
e or
r
oughness.Thesear
ecaused bydi
r
ectact
i
on oft
he cut
t
i
ng el
ement
son t
he
mat
er
i
ali
.
e.cut
t
i
ngt
oolshape;t
oolf
eedr
at
e,f
r
i
ct
i
on,wearet
c.Thesei
ncl
udet
hi
r
d
andf
our
t
hor
der
.
i
i
.Secondar
yt
ext
ur
eorwav
i
ness:
Thesur
f
acei
r
r
egul
ar
i
t
i
esofconsi
der
abl
ewav
el
engt
hofper
i
odi
cchar
act
erar
ecal
l
ed
secondar
yt
ext
ur
eorwav
i
ness.Thi
si
sduet
owearofgui
des,mi
sal
i
gnmentof
cent
er
s,
v
i
br
at
i
onsofanyki
ndet
c.Thesei
ncl
udef
i
r
standsecondor
der
.
4.
6Sy
mbol
sUsedt
oI
dent
i
f
ySur
f
aceFi
ni
shesandChar
act
er
i
st
i
cs
STUDYMATERI
ALPage88
METROLOGY
4.
7
Sur
f
aceFi
ni
shTer
mi
nol
ogy
• Sur
f
ace dev
i
at
i
ons:depar
t
ur
es f
r
om nomi
nalsur
f
ace i
nf
or
m ofwav
i
ness,
r
oughness,
f
l
aws,
l
ay
,
andpr
of
i
l
e
• Wav
i
ness:
sur
f
acei
r
r
egul
ar
i
t
i
est
hatdev
i
at
ef
r
om meansur
f
acei
nf
or
m ofwav
es
• Wav
i
nesshei
ght
:
peakt
ov
al
l
eydi
st
ancei
ni
nchesormi
l
l
i
met
er
s
• Wav
i
nesswi
dt
h:di
st
ancebet
ween successi
v
ewav
i
nesspeaksorv
al
l
ey
si
n
i
nchesormi
l
l
i
met
er
s
• Roughness:r
el
at
i
v
el
yf
i
nel
yspaced i
r
r
egul
ar
i
t
i
es super
i
mposed on wav
i
ness
pat
t
er
n
• Causedbycut
t
i
ngt
ool
orabr
asi
v
egr
ai
nact
i
on
• I
r
r
egul
ar
i
t
i
esnar
r
owert
hanwav
i
nesspat
t
er
n
• Roughnesshei
ght
:Radev
i
at
i
onmeasur
ednor
malt
ocent
er
l
i
nei
nmi
cr
o
i
nchesorµm
• Roughnesswi
dt
h:di
st
ancebet
weensuccessi
v
er
oughnesspeakspar
al
l
elt
o
nomi
nal
sur
f
acei
ni
nchesormi
l
l
i
met
er
s
• Pr
of
i
l
e:
cont
ourofspeci
f
i
edsect
i
ont
hr
oughasur
f
ace
• Roughnesswi
dt
h cut
of
f
:gr
eat
estspaci
ng ofr
epet
i
t
i
v
e sur
f
ace i
r
r
egul
ar
i
t
i
es
i
ncl
udedi
nmeasur
ementofr
oughnesshei
ghtmustbegr
eat
ert
hanr
oughness
wi
dt
h
• Fl
aws:i
r
r
egul
ar
i
t
i
essuchasscr
at
ches,hol
es,cr
acks,r
i
dges,orhol
l
owst
hatdo
STUDYMATERI
ALPage89
METROLOGY
notf
ol
l
owr
egul
arpat
t
er
n
• Lay
:
di
r
ect
i
onofpr
edomi
nantsur
f
acepat
t
er
ncausedbymachi
ni
ngpr
ocess
4.
8
Sy
mbol
st
hatI
ndi
cat
eDi
r
ect
i
onofLay
STUDYMATERI
ALPage90
METROLOGY
STUDYMATERI
ALPage91
METROLOGY
4.
9
Av
er
agesur
f
acer
oughnesspr
oducedbyst
andar
dmachi
ni
ngpr
ocesses
Mi
cr
oi
nchesMi
cr
omet
er
s
Tur
ni
ng
100–250
2.
5–6.
3
Dr
i
l
l
i
ng
100–200
2.
5–5.
1
Reami
ng
50–150
1.
3–3.
8
Gr
i
ndi
ng
20–100
0.
5–2.
5
Honi
ng
5–20
0.
13–0.
5
Lappi
ng
1–10
0.
025–0.
254
STUDYMATERI
ALPage92
METROLOGY
4.
10 Met
hodsofEv
al
uat
i
ngSur
f
aceFi
ni
sh
a.Peakt
ov
al
l
eyhei
ghtmet
hod
b.Av
er
ager
oughnessmet
hod
c.For
mf
act
ormet
hod
a.Peakt
oVal
l
eyHei
ghtMet
hod:
• Measur
es maxi
mum dept
h ofsur
f
ace i
r
r
egul
ar
i
t
yf
orgi
v
en sampl
i
ng
l
engt
h
• Lar
gestv
al
ueofdept
hi
sconsi
der
edasr
oughnessv
al
ue
• Thev
al
ueobt
ai
nedwoul
dnotgi
v
eaper
f
ectassessmentofr
oughness
• ThePeakt
oVal
l
eymet
hodcut
st
hepeaksof
ft
hewav
e,
andt
henusest
he
bandbet
weent
odet
er
mi
net
her
oughness.Thi
smet
hodi
snotcommonl
y
usedi
nCanada.
STUDYMATERI
ALPage93
METROLOGY
b.Av
er
ageRoughnessMet
hod
I
. CLAMet
hod
I
I
. RMSmet
hod
I
I
I
. Tenpoi
ntmet
hod
ARI
THMETI
CAL MEAN ROUGHNESS /
CENTRE LI
NE AVERAGE (
CLA)
, OR
ARI
THMETI
CAVERAGE(
RA)
STUDYMATERI
ALPage94
METROLOGY
RMSMet
hod
• I
ti
sdef
i
ned ast
hesquar
er
ootofar
i
t
hmet
i
cmean oft
hesquar
esoft
he
or
di
nat
esoft
hemeasur
edf
r
om t
hemeanv
al
ues.
2
2
2
2
2
RMSAv
er
age=√(
y
y
y
y
….
+y
n)
1+
2+
3+
4+
n/
TENPOI
NTMet
hod
FORM FACTORMETHOD
STUDYMATERI
ALPage95
METROLOGY
• I
ti
sobt
ai
nedbymeasur
i
ngt
hear
eaofmat
er
i
alabov
et
hear
bi
t
r
ar
i
l
ychosenbase
l
i
nei
nt
hesect
i
onandt
hear
eaoft
heenv
el
opi
ngr
ect
angl
e
Degr
eeoff
ul
l
ness(
K)
=Ar
eaoft
hemet
al
/
Ar
eaofenv
el
opi
ngr
ect
angl
e
Degr
eeofempt
i
ness(
Kp)
=1K
4.
11Roughnesssy
mbol
STUDYMATERI
ALPage96
METROLOGY
4.
12Sy
mbol
sr
epr
esent
i
ngt
hechar
act
er
i
st
i
cst
obet
ol
er
anced
STUDYMATERI
ALPage97
METROLOGY
STUDYMATERI
ALPage98
METROLOGY
STUDYMATERI
ALPage99
METROLOGY
4.
13
4.
14
Met
hodsf
ormeasur
i
ngsur
f
acer
oughness

TouchI
nspect
i
on

Vi
sual
I
nspect
i
on

Scr
at
chI
nspect
i
on

Mi
cr
oscopeI
nspect
i
on

Sur
f
acePhot
ogr
aphs

Mi
cr
oI
nt
er
f
er
omet
er

Wal
l
aceSur
f
aceDy
namomet
er

Ref
l
ect
edLi
ghtI
nt
ensi
t
y
Di
r
ectI
nst
r
umentMeasur
ement
St
y
l
usPr
obeI
nst
r
ument
–Aski
dorshoei
sdr
awnsl
owl
yov
ert
hesur
f
ace.
–Ast
y
l
usmov
eov
ert
hesur
f
acewi
t
ht
heski
d.
–Anampl
i
f
y
i
ng dev
i
cef
ormagni
f
y
i
ng t
hest
y
l
usmov
ementand
i
ndi
cat
or
.
–Ar
ecor
di
ngdev
i
cet
opr
oducet
r
aceoft
hesur
f
acepr
of
i
l
e.
–Ameanofanal
y
zi
ngt
het
r
ace
STUDYMATERI
ALPage100
METROLOGY
4.
14.
1 PROFI
LOMETER
I
ti
sani
ndi
cat
i
ngandr
ecor
di
ngi
nst
r
umentt
omeasur
er
oughnessi
nmi
cr
ons.The
mai
npar
t
soft
hei
nst
r
umentar
et
r
acerandanampl
i
f
i
er
.Thest
y
l
usi
smount
edi
n
t
hepi
ckupandi
tconsi
st
sofi
nduct
i
onoi
ll
ocat
edi
nt
hemagnet
.Whent
hest
y
l
us
i
smov
ed on t
hesur
f
acet
o bet
est
ed,i
ti
sdi
spl
aced up and down duet
o
i
r
r
egul
ar
i
t
i
esi
nt
hesur
f
ace.
Thi
smov
ementi
nducest
hei
nduct
i
oncoi
lt
omov
ei
nt
hedi
r
ect
i
onofper
manent
magnetandpr
oducesav
ol
t
age.Thi
si
sampl
i
f
i
edandr
ecor
ded
STUDYMATERI
ALPage101
METROLOGY
4.
13.
2 Toml
i
nsonSur
f
aceMet
er
:
Thi
si
nst
r
umentusesmechani
cal
cumopt
i
cal
meansf
ormagni
f
i
cat
i
on.
Const
r
uct
i
on
I
nt
hi
st
hedi
amondst
y
l
usont
hesur
f
acef
i
ni
shr
ecor
deri
shel
dbyspr
i
ngpr
essur
e
agai
nstt
hesur
f
aceofal
appedcy
l
i
nder
.Thel
appedcy
l
i
nderi
ssuppor
t
edone
si
debypr
obeandot
hersi
debyr
ol
l
er
s.Thest
y
l
usi
sal
soat
t
achedt
ot
hebodyof
t
hei
nst
r
umentbyal
eafspr
i
ngandi
t
shei
ghti
sadj
ust
abl
et
oenabl
et
hedi
amond
t
obeposi
t
i
onedandt
hel
i
ghtspr
i
ngst
eelar
mi
sat
t
achedt
ot
hel
appedcy
l
i
nder
.
Thespr
i
ngar
m hasadi
amondscr
i
beratt
heendandsmokedgl
assi
sr
estont
he
ar
m
STUDYMATERI
ALPage102
METROLOGY
Wor
ki
ng:
Whenmeasur
i
ngsur
f
acef
i
ni
sht
hebodyoft
hei
nst
r
umenti
smov
edacr
osst
he
sur
f
acebyascr
ew r
ot
at
i
ont
hev
er
t
i
calmov
ementoft
hepr
obecausedbyt
he
sur
f
acei
r
r
egul
ar
i
t
i
esmakest
hehor
i
zont
all
appedcy
l
i
ndert
or
ol
l
.Thi
sr
ol
l
i
ngof
l
appedcy
l
i
ndercausest
hemov
ementoft
hear
m.Sot
hi
smov
ementi
si
nduces
t
hedi
amondscr
i
beronsmokedgl
ass.
Fi
nal
l
yt
hemov
ementofscr
i
bert
oget
herwi
t
hhor
i
zont
almov
ementpr
oducesa
t
r
aceont
hesmokedgl
asspl
at
eandt
hi
st
r
acei
smagni
f
i
edbyanopt
i
cal
4.
13.
3 TAYLOR–HOBSON-TALYSURF
STYLUSPROBEI
NSTRUMENT
TheTay
l
or
HobsonTal
y
sur
f
–Ast
hepr
obemov
es,
Ar
mat
ur
epi
v
ot
sar
oundaEshapedst
ampi
ngs.
–Anymov
ementont
hest
y
l
uscausest
heai
rgapt
ov
ar
y
.
–Ampl
i
t
udeofA.
C.cur
r
enti
smodul
at
ed.
–Si
gnal
i
sdemodul
at
edt
ogett
hev
er
t
i
cal
di
spl
acementofst
y
l
us.
I
ti
swor
ki
ngonacar
r
i
ermodul
at
i
ngpr
i
nci
pl
eandi
ti
sanaccur
at
emet
hod
compar
i
ng wi
t
ht
he ot
hermet
hods.The mai
n par
t
s oft
hi
si
nst
r
umentar
e
di
amondst
y
l
us(
0.
002mm r
adi
us)andski
d.
STUDYMATERI
ALPage103
METROLOGY
Pr
i
nci
pl
e
Thei
r
r
egul
ar
i
t
i
esoft
hesur
f
acear
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STUDYMATERI
ALPage104
METROLOGY
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STUDYMATERI
ALPage105
METROLOGY
CHAPTER 4 (second part)
COMPARATORS
Comparators can give precision measurements, with consistent accuracy by eliminating human
error. They are employed to find out, by how much the dimensions of the given component differ
from that of a known datum. If the indicated difference is small, a suitable magnification device
is selected to obtain the desired accuracy of measurements. It is an indirect type of instrument
and used for linear measurement. If the dimension is less or greater, than the standard, difference
will be shown on the dial. It gives only the difference between actual and standard dimension of
the workpiece.
5.1
Characteristic’s of Comparators:
1. It should be compact.
2. It should be easy to handle.
3. It should give quick response or quick result.
4. It should be reliable, while in use.
5. There should be no effects of environment on the comparator.
6. Its weight must be less.
7. It must be cheaper.
8. It must be easily available in the market.
9. It should be sensitive as per the requirement.
10. The design should be robust.
11. It should be linear in scale so that it is easy to read and get uniform response.
12. It should have less maintenance.
13. It should have hard contact point, with long life.
14. It should be free from backlash and wear.
5.2
Classifications of Comparators:
1. Mechanical Comparator: It works on gears pinions, linkages, levers, springs etc.
2. Pneumatic Comparator: Pneumatic comparator works by using high pressure air,
valves, back pressure etc.
3. Optical Comparator: Optical comparator works by using lens, mirrors, light source etc.
4. Electrical Comparator: Works by using step up, step down transformers.
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5. Electronic Comparator: It works by using amplifier, digital signal etc.
6. Combined Comparator: The combination of any two of the above types can give the
best result.
5.2.1 Mechanical Comparator
Types of mechanical comparators
a) Dial gauge
b) Johansson Mikrokator
c) Reed type mechanical comparator
d) Sigma comparator
a) Dial gauge
It operates on the principle, that a very slight upward pressure on the spindle at the
contact point is multiplied through a system of gears and levers. It is indicated on the face
of the dial by a dial finger. Dial indicators basically consists of a body with a round
graduated dial and a contact point connected with a spiral or gear train so that hand on the
dial face indicates the amount of movement of the contact point. They are designed for
use on a wide range of standard measuring devices such as dial box gauges, portal dial,
hand gauges, dial depth gauges, diameter gauges and dial indicator snap gauge.
Figure shows dial gauge for comparison measurement
Corresponds to a spindle movement of 1 mm. The movement mechanism of the
instrument is housed in a metal case for it's protection. The large dial scale is graduated
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into 100 divisions. The indicator is set to zero by the use of slip gauges representing the
basic size of part.
Requirements of Good Dial Indicator:
1. It should give trouble free and dependable readings over a long period.
2. The pressure required on measuring head to obtain zero reading must remain constant
over the whole range.
3. The pointer should indicate the direction of movement of the measuring plunger.
4. The accuracy of the readings should be within close limits of the various sizes and
ranges
5. The movement of the measuring plunger should be in either direction without affecting
the accuracy.
6. The pointer movement should be damped, so that it will not oscillate when the
readings are being taken.
Applications:
1. Comparing two heights or distances between narrow limits.
2. To determine the errors in geometrical form such as ovality, roundness and taper.
3. for taking accurate measurement of deformation such as intension and compression.
4. To determine positional errors of surfaces such as parallelism, squareness and
alignment.
5. To check the alignment of lathe centers by using suitable accurate bar between the
centers.
6. To check trueness of milling machine arbours and to check the parallelism of shaper
arm with table surface or vice.
b) Johansson Mikrokator:
This comparator was developed by C.F. Johansson.
Principle:
It works on the principle of a Button spring, spinning on a loop of string like in the case
of Children’s toys.
Construction:
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The method of mechanical magnification is shown in Figure. It employs a twisted metal
strip. Any pull on the strip causes the centre of the strip to rotate. A very light pointer
made of glass tube is attached to the centre of the twisted metal strip. The measuring
plunger is on the slit washer and transmits its motion through the bell crank lever to the
twisted metal strip. The other end of the twisted metal strip is fastened to the cantilever
strip. The overhanging length of the cantilever strip can be varied to adjust the
magnification of the instrument. The longer the length of the cantilever, the more it will
deflect under the pull of the twisted metal strip and less rotation of the pointer is
obtained.
Figure shows Johansson Mikrokator
When the plunger moves by a small distance in upward direction the bell crank lever
turns to the right hand side. This exerts a force on the twisted strip and it causes a change
in its length by making it further twist or untwist. Hence the pointer at the centre rotates
by some amount. Magnification up to 5000X can be obtained by this comparator.
Advantages of Mechanical Comparator:
1. They do not require any external source of energy.
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2. These are cheaper and portable.
3. These are of robust construction and compact design.
4. The simple linear scales are easy to read.
5. These are unaffected by variations due to external source of energy such air, electricity
etc.
Disadvantages:
1. Range is limited as the pointer moves over a fixed scale.
2. Pointer scale system used can cause parallax error.
3. There are number of moving parts which create problems due to friction, and
ultimately the accuracy is less.
4. The instrument may become sensitive to vibration due to high inertia.
c.
Reed type mechanical comparator
Figure shows Reed type comparator
d.
Sigma comparator
The plunger is attached to a bar which is supported between the bending plates at the top
and bottom portion as shown in Figure. The bar is restricted to move in the vertical
direction. A knife edge is fixed to the bar. The knife edge is attached to the sapphire plate
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which is attached to the moving block. The knife edge extorts a force on the moving
block through sapphire plate.
Figure shows Sigma comparator
Moving block is attached to the fixed block with the help of crossed strips as shown in
Figure (b). When the force is applied on the moving block, it will give an angular
deflection. A Y-arm which is attached to the moving block transmits the rotary motion to
the driving drum of radius r. This deflects the pointer and then the reading is noted.
If l = Distance from hinge pivot to the knife edge
L = Length of y-arm
R = Driving drum radius
D Length of the pointer
Then the total magnification = (L/l) *(D/R)
2. Optical comparators:
a)
Crookes Optical Comparator
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Principle:
In mechanical optical comparator, small variation in the plunger movement is magnified:
first by mechanical system and then by optical system.
Construction:
The movement of the plunger is magnified by the mechanical system using a
pivoted lever. From the Figure the mechanical magnification = x2 / x1. High optical
magnification is possible with a small movement of the mirror. The important factor is
that the mirror used is of front reflection type only.
The back reflection type mirror will give two reflected images as shown in Figure, hence
the exact reflected image cannot be identified.
Advantages:
1. These Comparators are almost weightless and have less number of moving parts, due
to this there is less wear and hence lessfriction.70
2. Higher range even at high magnification is possible as the scale moves past the index.
3. The scale can be made to move past a datum line and without having any parallax
errors.
4. They are used to magnify parts of very small size and of complex configuration such
as intricate grooves, radii or steps.
Disadvantages:
1. The accuracy of measurement is limited to 0.001 mm
2. They have their own built in illuminating device which tends to heat the instrument.
3. Electrical supply is required.
4. Eyepiece type instrument may cause strain on the operator.
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5. Projection type instruments occupy large space and they are expensive.
6. When the scale is projected on a screen, then it is essential to take the instrument to a
dark room in order to take the readings easily.
b.
ZEISS ULTRA OPTIMETER
C.
Zeiss optotest comparator
Electrical Comparators:
Electrical comparators give a wide range of advantages. As we know, components like levers,
gears, racks and pinions, activate mechanical devices. The accuracy and life of the instruments
are affected as they are subjected to wear and friction Electrical comparators have no moving
parts. Thus a high degree of reliability is expected from these instruments. Generally there are
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two important applications of electrical comparators:1. Used as measuring heads2. Used for
electrical gauging heads, to provide usual indication to check the dimensions within the limits
laid down.
The first application is very important when there is a requirement for precise measurement for
e.g. Checking or comparison of workshop slip gauges against inspection slip gauges. The second
application is used to indicate with a green light if a dimension is within the limits. A red lamp
indicates an undersize dimension; a yellow lamp indicates an oversize dimension. So the
operator is not required to be aware of the actual tolerances on the dimension. After setting the
instrument correctly, all that needs to be done is to place the component under the plunger of the
gauging head. The signal lamps provide in standard positive indication of the acceptability of the
dimension under test
Advantages:
1. Measuring units can be remote from indicating units.
2. Variable sensitivity which can be adjusted as per requirement.
3. No moving parts, hence it can retain accuracy over long periods.
4. Higher magnification is possible as compared to mechanical comparator.
5. Compact sizes of probes arc available.
Disadvantages:
1. The accuracy of working of these comparators is likely to be affecting due to temperature and
humidity.
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2. It is not a self contained unit; it needs stabilized power supply for its operation.
3. Heating of coils can cause zero drifts and it may alter calibration.
4. It is more expensive than mechanical comparator
Pneumatic Comparators (Solex Gauge):
Principle:
It works on the principle of pressure difference generated by the air flow. Air is supplied at
constant pressure through the orifice and the air escapes in the form of jets through a restricted
space which exerts a back pressure. The variation in the back pressure is then used to find the
dimensions of a component.
Working:
As shown in Figure (a) the air is compressed in the compressor at high pressure which is equal to
Water head H. The excess air escapes in the form of bubbles. Then the metric amount of air is
passed through the orifice at the constant pressure. Due to restricted area, at A1 position, the
back pressure is generated by the head of water displaced in the manometer tube. To determine
the roundness of the job, the job is rotated along the jet axis, if no variation in the pressure
reading is obtained then we can say that the job is perfectly circular at position A1. Then the
same procedure is repeated at various positions A2, A3, A4, position and variation in the
pressure reading is found out. Also the diameter is measured at position A1 corresponding to the
portion against two jets and diameter is also measured at various position along the length of the
bore
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Any variation in the dimension changes the value of h, e.g. Change in dimension of 0.002 mm
changes the value of h from 3 to 20 mm. Moderate and constant supply pressure is required to
have the high sensitivity of the instrument.
Advantages:
1. It is cheaper, simple to operate and the cost is low.
2. It is free from mechanical hysteresis and wear.
3. The magnification can be obtained as high as 10,000 X.
4. The gauging member is not in direct contact with the work.
5. Indicating and measuring is done at two different places.
6. Tapers and ovality can be easily detected.
7. The method is self cleaning due to continuous flow of air through the jets and this makes the
method ideal to be used on shop floor for online controls.
Disadvantages:
1. They are very sensitive to temperature and humidity changes.
2. The accuracy may be influenced by the surface roughness of the component being checked.
3. Different gauging heads are needed for different jobs.
4. Auxiliary equipments such as air filters, pressure gauges and regulators are needed.
5. Non-uniformity of scale is a peculiar aspect of air gauging as the variation of back pressure is
linear, over only a small range of the orifice size variation.
CHAPTER 5
SCREW THREADS
6.1
Terminology of Screw Threads:
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1. Screw thread. A screw thread is the helical ridge produced by forming a continuous helical
groove of uniform section on the external or internal surface of a cylinder or cone. A screw
thread formed on a cylinder is known as straight or parallel screw thread, while the one formed
on a cone or frustum of a cone is known as tapered screw thread.
2. External thread. A thread formed on the outside of a workpiece is called external thread e.g.,
on bolts or studs etc.
3. Internal thread. A thread formed on the inside of a workpiece is called internal thread e.g. on
a nut or female screw gauge.
4. Multiple-start screw thread. This is produced by forming two or more helical grooves,
equally spaced and similarly formed in an axial section on a cylinder. This gives a ‘quick
traverse’ without sacrificing core strength.
5. Axis of a thread. This is imaginary line running longitudinally through the centre of the
screw.
6. Hand (Right or left hand threads). Suppose a screw is held such that the observer is looking
along the axis. If a point moves along the thread in clockwise direction and thus moves away
from the observer, the thread is right hand ; and if it moves towards the observer, the thread is
left hand.
7. Form, of thread. This is the shape of the contour of one- complete thread as seen in axial
section.
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8. Crest of thread. This is defined as the prominent part of thread, whether it is external or
internal.
9. Root of thread. This is defined as the bottom of the groove between the two flanks of the
thread, whether it be external or internal.
10. Flanks of thread. These are straight edges which connect the crest with the root.
11. Angle of thread {Included angle). This is the angle between the flanks or slope of the
thread measured in an axial plane.
12. Flank angle. The flank angles are the angles between individual flanks and the perpendicular
to the axis of the thread which passes through the vertex of the fundamental triangle. The flank
angle of a symmetrical thread is commonly termed as the half- angle of thread.
13. Pitch. The pitch of a thread is the distance, measured parallel to the axis of the thread,
between corresponding points on adjacent thread forms in the same axial plane and on the same
side of axis. The basic pitch is equal to the lead divided by the number of thread starts. On
drawings of thread sections, the pitch is shown as the distance from the centre of one thread crest
to the centre of the next, and this representation is correct for single start as well as multi-start
threads.
14. Lead. Lead is the axial distance moved by the threaded part, when it is given one complete
revolution about its axis with respect to a fixed mating thread. It is necessary to distinguish
between measurements of lead from measurement of pitch, as uniformity of pitch measurement
does not assure uniformity of lead. Variations in either lead or pitch cause the functional or
virtual diameter of thread to differ from the pitch diameter.
15. Thread per inch. This is the reciprocal of the pitch in inches.
16. Lead angle. On a straight thread, lead angle is the angle made by the helix of the thread at
the pitch line with plane perpendicular to the axis. The angle is measured in an axial plane.
17. Helix angle. On straight thread, the helix angle is the angle made by the helix of the thread at
the pitch line with the axis. The angle is measured in an axial plane.
18. Depth of thread. This is the distance from the crest or tip of the thread to the root of the
thread measured perpendicular to the longitudinal axis or this could be defined as the distance
measured radially between the major and minor cylinders.
19. Axial thickness. This is the distance between the opposite faces of the same thread measured
on the pitch cylinder in a direction parallel to the axis of thread.
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20. Fundamental triangle. This is found by extending the flanks and joining the points B and C.
Thus in Fig. 13.2, triangle ABC is referred to as fundamental triangle. Here BC=pitch and the
vertical height of the triangle is called the angular or theoretical depth. The point A is the apex of
the triangle ABC.
21. Truncation. A thread is sometimes truncated at the crest or at the root or at both crest and
root. The truncation at the crest is the radial distance from the crest to the nearest apex of the
fundamental triangle. Similarly the truncation at the root is the radial distance from the root to
the nearest apex.
22. Addendum. For an external thread, this is defined as the radial distance between the major
and pitch cylinders. For an internal thread this is the radial distance between the minor and pitch
cylinders.
23. Dedendum. This is the radial distance between the pitch and minor cylinder for external
thread, and for internal thread, this is the radial distance between the major and pitch cylinders.
24. Major diameter. In case of a straight thread, this is the diameter of the major cylinder
(imaginary cylinder, co-axial with the screw, which just touches the crests of an external thread
or the root of an internal thread). It is often referred to as the outside diameter, crest diameter or
full diameter of external threads.
25. Minor diameter. In case of straight thread, this is the diameter of the minor cylinder (an
imaginary cylinder, co-axial with the screw Which just touches the roots of an external thread or
the crest of an internal thread). It is often referred to as the root diameter or cone diameter of
external threads.
26. Effective diameter or pitch diameter. In case of straight thread, this is the diameter of the
pitch cylinder (the imaginary’ cylinder which is co-axial with the axis of the screw, and
intersects the flank of the threads in such a way as to make the width of threads and width of the
spaces between the threads equal). If the pitch cylinder be imagined as generated by a straight
line parallel to the axis of screw that straight line is then referred to as the pitch line. Along the
pitch line, the widths of the threads and the widths of the spaces are equal on a perfect thread.
This is the most important dimension at it decides the quality of the fit between the screw and the
nut.
27. Functional (virtual) diameter. For an external or internal thread, this is the pitch diameter
of the enveloping thread of perfect pitch, lead and flank angles having full depth of engagement
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but clear at crests and roots. This is defined over a specified length of thread. This may be greater
than the simple effective diameter by an amount due to errors in pitch and angle of thread. The
virtual diameter being the modified effective diameter by pitch and angle errors, is the most
important single dimension of a screw thread gauge.
6.2.
ERRORS IN THREADS
•
In the case of plain shafts and holes, there is only one dimension(i.e. diameter), which
has to be considered
•
While in the case of screw threads there are at least five important elements, Major
Diameter, Minor Diameter, Effective Diameter, Pitch And Angle Of The Thread Form
•
Errors on the major and minor diameters will cause interference with the mating thread.
Similarly pitch and angle errors are also not desirable as they cause a progressive
tightening and interference on assembly.
PITCH ERRORS IN SCREW THREADS:
Generally the threads are generated by a point cutting tool.
The ratio of the linear velocity of tool and angular velocity of the work must be correct and
constant, otherwise pitch errors will occur.
If there is some error in pitch, then the total length of thread engaged will be either too great
or too small, the total pitch error in overall length of the thread being called the cumulative
pitch error.
Various pitch errors can be classified as:
Progressive
Periodic
Irregular
Eratic.
(i)
PROGRESSIVE PITCH ERROR.
This error occurs when the tool work velocity ratio is incorrect.
May caused due to pitch errors in the lead screw of the lathe or other generating machine.
The other possibility is by using an incorrect gear or an approximate gear train between work
and lead screw e.g.,
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II.
PERIODIC PITCH ERROR
This repeats itself at regular intervals.
Successive portions of the thread are either longer or shorter than the mean.
Error occurs when the tool work velocity ratio is not constant.
Results when a thread is cut from a leadscrew which lacks squareness causing leadscrew to
move backward and forward once in each revolution.
Errors are cyclic and pitch increases to a maximum, and then reduces through normal value
to a minimum and so on. The graph between the cumulative pitch error and length of threads
for this error will, therefore, be of sinusoidal form.
iii) Irregular Errors. These arise from disturbances in the machining set-up, variations in
the cutting properties of material etc. Thus they have no specific causes and correspondingly
no specific characteristics also.
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Erratic Pitch. This is the irregular error in pitch and varies irregularly in magnitude over
different lengths of thread.
iv) Drunken error:
– Error occurs when thread is not cut to the true helix angle.
–
6.3
Measurement of various elements in screw threads:
Most important six elements
a) Major Diameter
b) Minor Diameter
c) Effective Diameter
d) Pitch
e) Thread Angle
f) Thread Form.
a) Major Diameter:
Major Diameter is usually measured by
 MICROMETER
 BENCH MICROMETER
A good quality hand micrometer is quite suitable. In taking readings, a light pressure must be
used as the anvils make contact with the gauge at points only and otherwise the errors due to
compression can be introduced. It is, however, also desirable to check the micrometer reading on
a cylindrical standard of approximately the same size, so that the zero error etc., might not come
into picture.
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For greater accuracy and convenience, the major diameter is measured by bench micrometer.
This instrument was designed by N.P.L. to estimate some deficiencies inherent in the normal
hand micrometer. It uses constant measuring pressure and with this machine the error due to
pitch error in the micrometer thread is avoided. In order that all measurements are made at the
same pressure, a fiducial indicator is used in place of the fixed anvil. In this machine there is no
provision for mounting the workpiece between the centres and it is to be held in hand. This is so,
because, generally the centres of the workpiece are not true with its diameter. This machine is
used as a comparator in order to avoid any pitch errors of micrometers, zero error setting etc. A
calibrated setting cylinder is used as the setting standard.
Measurement of Major Dia for Internal Screw Thread:
Stylus probe instrument is used for MEASURING Major diameter of internal screw thread as
shown
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b) Measurement of Minor Diameter:
This is also measured by a comparative process using small Vee-pieces which make contact with a
root of the thread. The Vee-pieces are available in several sizes having suitable radii at the edges.
The included angle of Vee-pieces is less than the angle of the thread to be checked so that it can
easily probe to the root of the thread. To measure the minor diameter by Vee-pieces is suitable for
only Whitworth and B.A. threads which have a definite radius at the root of the thread. For other
threads, the minor diameter is measured by the projector or microscope.
The measurement is carried out on a floating carriage diameter measuring machine in which
the threaded work-piece is mounted between centres and a bench micrometer is constrained
to move at right angles to the axis of the centre by a Vee-ball slide. The method of the
application of Vee-pieces in the machine is shown diagrammatically in Fig.. The dimensions
of Vee-pieces play no important function as they are interposed between the micrometer
faces and the cylindrical standard when standard reading is taken. It is important while taking
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readings, to ensure that the micrometer be located at right angles to the axis of the screw
being measured. The selected Vees are placed on each side of the screw with their bases
against the micrometer faces. The micrometer head is then advanced until the pointer of the
indicator is opposite the zero mark, and note being made of the reading. The screw is then
replaced by standard reference disc or a plain cylindrical standard plug gauge of
approximately the core diameter of the screw to be measured and second reading of the
micrometer is taken.
c)
Effective Diameter Measurements.
The effective diameter or the pitch diameter can be measured by . any one of the following
methods :
(i) The micrometer method
ii) The one wire, two wire, or three wire or rod method.
Two Wire Method.
The effective diameter of a screw thread may be ascertained by placing two wires or rods
of identical diameter between the flanks of the thread, as shown in Fig. 13.15, and
measuring the distance over the outside of these wires. The effective diameter E I s then
calculated as
E=T+P
Where T= Dimension under the wires =M—2d
M=dimension over the wires, d= diameter of each wire
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The wires used are made of hardened steel to sustain the wear and tear in use. These are given a
high degree of accuracy and finish by lapping to suit different pitches. Dimension T can also be
determined by placing wires over a standard cylinder of diameter greater than the diameter under
the wires and noting the reading R1 and then taking reading with over the gauge, say R2.
Then T=S—(R1—R2).
P=It is a value which depends upon the dia of wire and pitch of the thread.
If P= pitch of the thread, then
P= 0.9605p−1.1657d (for Whitworth thread).
P= 0.866p—d (for metric thread).
Actually P is a constant Value which has to be added to the diameter under the wires to give the
effective diameter. The expression for the value of P in terms of p (pitch), d (diameter of wire)
and x (thread angle) can be derived as follows :
In Fig (b), since BC lies on the effective diameter line
BC= ½ pitch=½ p
OP=d cosec x/2∕2
PA=d (cosecx∕2−1)∕2
PQ=QC cot x∕2=p∕4 cot x∕2
AQ=PQ−AP=p cot x∕2∕4 – d(cosec x∕2 −1)∕2
AQ is half the value of P
.’. P value=2AQ
=p∕2 cot x∕2 −d (cosecx∕2−1)
Two wire method can be carried out only on the diameter measuring machine described for
measuring the minor diameter, because alignment is not possible by 2 wires and can be provided
only by the floating carriage machine. In the case of three wire method, 2 wire, on one side help
in aligning the micrometer square to the thread while the third placed on the other side permits
taking of readings.
Three Wire Method.
This method of measuring the effective diameter is an accurate method. In this three wires or
rods of known diameter are used ; one on one side and two on the other side {Fig. (a) and (b)].
This method ensures the alignment of micrometer anvil faces parallel to the thread axis. The
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wires may be either held in hand or hung from a stand so as to ensure freedom to the wires to
adjust them under micrometer pressure.
M=distance over wires E=effective diameter
r=radius of the wires d=diameter of wires
h =height of the centre or the wire or rod from the effective
x=angle of thread.
From fig.(b),
AD = AB cosec x∕2 = r cosec x∕2
H = DE cot x∕2 = p∕2 cot x∕2
CD = ½H = p∕4 cot x∕2
H = AD−CD
r = cosec x∕2− p∕4 cot x∕2
Distance over wires=M = E+2h+2r
= E+2(r cosec x∕2 – p∕4 cot x∕2)+2r
= E+2r (l+cosec x∕2 )− p∕2 cot x∕2
or M = E+d (1+cosec x∕2) − p∕2 cot x∕2
(since 2r = 0 )
(i) In case of Whitworth thread:
X = 55°, depth of thread = 0.64 p, so that
E= D—0.64 p and cosec x∕2 = 2.1657
Cot x∕2 = 1.921
M = E+d(1l+cosec x∕2) — p∕2 cot x∕2
= D−0.64p+d(1+2.1657)−p∕2(1.921)
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= D+3.1657d−1.6005p
M = D+3.1657d—1.6p
where D=outside dia.
(ii) In case of metric threads:
Depth of thread=0.6495p
so, E = D-0.6495p.
x = 60°, cosec x∕2 = 2 ; cot x∕2 = 1.732
M = D−0.6495 p+d(l+2)—p∕2 (1.732)
= D+3d−(0.6495+0.866)p
= D+3d—1.5155p.
We can measure the value of M practically and then compare with the theoretical values with the
help of formulae derived above. After finding the correct value of M and knowing d, E can be
found out.
If the theoretical and practical values of M (i.e. measured over wires) differ, then this error is due
to one or more of the quantities appearing in the formula.
Effect of lead angle on measurement by 3- wire method. If the lead angle is large (as with
worms; quick traversing lead screw,etc .) then error in measurement is about 0’0125 mm when
lead angle is 41° for 60° single thread series. For lead angles above 4£°, the compensation for
rake and compression must also be taken into account. There is no recommendation for B.S.W.
threads.
Rake Correction in U.S. Standard :
E = M + cot x∕2∕2n—- − x(1 +cosec x∕2+s2 ∕2 cos x∕2 cot x∕2)
where
x∕2 =half the included angle of threads.
E = effective diameter
M = actually measured diameter over wires:
n = number of threads/inch.
d = diameter of wire.
S = tangent of the helix angle in thread.
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Best size wire Method.
This wire is of such diameter that it makes contact with the flanks of the thread on the effective
diameter or pitch line. The effective diameter can be measured with any diameter wire which
makes contact on the true flank of the thread, but the values so obtained will differ from those
obtained with ‘best size’ wires if there is any error in angle or form of thread. t is recommended
that for measuring the effective diameter, always the best size wire should be used and for this
condition the wire touches the flank at mean diameter line within ±1/5 of flank length
Let the thread angle be θ/2
Assignment -VI
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Q1)
Q2)
Q3)
Describe with neat sketches two-wire method of measuring the effective diameter of a
screw threads.
with the help of sketch describe how tool maker’s microscope can be used to measure the
elements of screw threads.
what are the different elements of a screw thread? What are the instruments used for the
measurement of the elements of the screw thread
Question bank-VI
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
a) Name and describe the various methods of measuring the minor diameter of the thread.
b) Describe the effects of pitch errors on the effective diameter of a screw thread.
a) Describe any one method of measuring effective diameter of internal threads.
b) Describe the following pitch errors of thread in brief: i) Periodic ii) Drunken error.
a) Describe with neat sketches two-wire method of measuring the effective diameter of a
screw threads.
b) Name the important elements of thread which are required to be measured in order to
determine the accuracy of screw threads. Describe in brief how the errors in these
elements affect the working of the threaded elements.
a) Name the various types of pitch errors found in screw. State their causes.
b) Describe the method of measuring the pitch of the screw by using the pitch measuring
machine.
Draw an illustrative line diagram of a pitch measuring machine and describe its working
principle?
With the help of sketch describe how tool maker’s microscope can be used to measure
the elements of screw threads. [16]
(a) What do you understand by the term ‘the best wire’ in connection with screw thread
measurement? Derive an expression for the size of the best wire.
(b) List the different types of pitch errors of screw threads.
(a) Explain the working of a differential screw type micrometer with the help of neat
sketches.
(b) Describe the method of checking flatness and square ness with the axis of spindle end
of an external micrometer
(a) State clearly the way in which the micrometer dials used for different thread pitches
are graduated.
(b) Explain how thread micrometer can be used to measure effective diameter of the
screw thread.
With the help of sketch describe how tool maker’s microscope can be used to
measure the elements of screw threads.
(a) What are the different elements of a screw thread? What are the instruments used for
the measurement of the elements of the screw thread.
(b) Can you apply Taylor’s principle of limit gauging to gauging of screw threads? If so,
how?
(a) How is Taylor’s principle of limit gauging applicable to gauging of screw threads.
(b) What are the elements required to be measured for determination of the accuracy of
screw threads? Explain.
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CHAPTER 5(second part)
Gear Measurement
Gears are a mechanical drive which transmits power through toothed wheel. In this gear drive, the
driving wheel is in direct contact with driven wheel. The accuracy of gearing is the very important
factor when gears are manufactured. The transmission efficiency is almost 99 in gears. So it is very
important to test and measure the gears precisely. For proper inspection of gear, it is very important
to concentrate on the raw materials, which are used to manufacture the gears, also very important to
check the machining the blanks, heat treatment and the finishing of teeth. The gear blank should be
tested for dimensional accuracy (face width, bore, hub, length, and outside diameter), and
eccentricity. As outside diameter forms the datum from where the tooth thickness is measured, it
forms an important item to be controlled. Concentricity of the blanks is also essential and the side
faces should be true to the bore. On very precise gears details like tip radius, shape of root provided
and surface finish are also measured.
The most commonly used forms of gear teeth are
1. Involute
2. Cycloidal
 The involute gears also called as straight tooth or spur gears.
 The cycloidal gears are used in heavy and impact loads.
 The involute rack has straight teeth.
 The involute pressure angle is either 20° or 14.5°
Types of gears
1. Spur gear:Cylindrical gear whose tooth traces is straight line.
These are used for transmitting power between parallel shafts.
2. Spiral gear :The tooth of the gear traces curved lines.
3. Helical gears:These gears used to transmit the power between parallel shafts as well as non-parallel and
non-intersecting shafts.
It is a cylindrical gear whose tooth traces is straight line.
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4. Bevel gears:The tooth traces are straight-line generators of cone.
The teeth are cut on the conical surface. It is used to connect the shafts at right angles.
5. Worm and Worm wheel :
It is used to connect the shafts whose axes are non-parallel and non-intersecting.
6. Rack and Pinion:Rack gears are straight spur gears with infinite radius.
Terminology of gears:
1. Tooth profile:
 It is the shape of any side of gear tooth in its cross section.
2. Base circle:
 It is the circle of gear from which the involute profile is derived.
 Base circle diameter Pitch circle diameter x Cosine of pressure angle of gear
3. Pitch circle diameter (PCD):
 The diameter of a circle which will produce the same motion as the toothed gear wheel
4. Pitch circle
 It is the imaginary circle of gear that rolls without slipping over the circle of its mating
gear.
5. Addendum circle:
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 The circle coincides with the crests (or) tops of teeth.
6. Dedendum circle (or) Root circle:
 This circle coincides with the roots (or) bottom on teeth.
7. Pressure angle (a):
 It is the angle making by the line of action with the common tangent to the pitch circles
of mating gears.
8. Module(m):
 It is the ratio of pitch circle diameter to the total number of teeth.
9. Circular pitch
 It is the distance along the pitch circle between corresponding points of adjacent teeth
10. Addendum:
 Radial distance between tip circle and pitch circle. Addendum value = 1 module.
11. Dedendum:
 Radial distance between itch circle and root circle, Dedendum value = 1 .25 module.
12. Clearance (C):
 A mount of distance made by the tip of one gear with the root of mating gear.
Clearance = Difference between Dedendum and addendum values
13. Blank diameter:
 The diameter of the blank from which gear is out. Blank diameter = PCD + 2m
14. Face:
 Part of the tooth in the axial plane lying between tip circle and pitch circle.
15. Flank:
 Part of the tooth lying between pitch circle and root circle.
16. Top land:
 Top surface of a tooth
17. Lead angle:
 The angle between the tangent to the helix and plane perpendicular to the axis
of cylinder.
18. Backlash:
 The difference between the tooth thickness and the space into which it meshes.
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Gear Tooth Caliper
In gear tooth vernier method the thickness is measured at the pitch line. Gear tooth
thickness varies from the tip of the base circle of the tooth, and the instrument is capable of
measuring the thickness at a specified position on the tooth. The tooth vernier caliper consists of
vernier scale and two perpendicular arms. In the two perpendicular arms one arm is used to
measure the thickness and other arm is used to measure the depth. Horizontal vernier scale
reading gives chordal thickness (W) and vertical vernier scale gives the chordal addendum.
Finally the two values e compared. The theoretical values of ‘W’ and‘d’ can be found out by
considering one tooth in the gear and it can be verified.
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In fig note that w is a chord ADB and tooth thickness is specified by AEB. The distance d is
noted and adjusted on instrument and it is slightly greater than addendum CE Therefore, ‘W’ is
chordal thickness and‘d’ is named as chordal addendum.
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Vernier method like the chordal thickness and chordal addendum are depends upon the number
of teeth. Due to this for measuring large number of gears different calculations are to be made for
each gear. So these difficulties are avoided by this constant chord method.
Assignment-VII
Describe briefly the following method of tooth thickness measurement.
Q1)
i) Constant chord method. ii) Base tangent method.
Q2) Describe the method of checking of involute shape of gear?
Question bank VII:
1. Describe a gear tooth vernier calliper and explain its use for checking tooth thickness and
depth of teeth.
2. a) Explain the method used for checking pitch of the gear.
b) Name the various elements of the spur gear which are checked for accuracy of the
gear.
3. (a) Describe the method of checking of involute shape of gear?
(b) Explain the importance of Base pitch measuring instrument.
4. Explain Multi-Dimension Automatic Gauging and Sorting machines.
5. Explain
in
detail
the
following
methods
of
inspecting
gear
(a) Concentricity & cylindricity (b) Run out and axial slip.
6. (a) What are various errors in gears? Explain, with neat figures.
(b) State the various sources of errors in manufacturing gears.
7. Explain with the help of sketches the working principles of the instruments used in
checking of profile and base pitch of the gear
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CHAPTER 6
MACHINE TOOL ALIGNMENT TEST
INTRODUCTION
The quality and accuracy of work piece depends on machine tools
Alignment is tested while assembly, after assembly, erection, repairs or overhauls as per
accuracy test chart.
The acceptance tests are
Alignment /Geometric tests
Performance / Practical tests
Working accuracy also influenced by following factors:
Cutting tool geometry
Materials of work piece and tool
Shape and size of work piece
Cutting parameters
Work holding
Skill of labour
Working conditions
Alignment tests:
Straightness of guide ways and slide ways
Flatness of bed ways
WRT to standard planes parallesim of slide ways and axes
True running
Pitch errors of lead screw
Pitch errors of gears
Axial slip
Eccentricity
Roundness
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Equipment required for alignment
Dial gauge
Test mandrel
Straight edges and squares
Sprit level
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Autocollimator
Waviness meter
8.1 Alignment Test on Lathe
A. Test for level of installation
B. True Running of Locating Cylinder of Main Spindle
C. Axial Slip of Main Spindle
D. True Running of Headstock Centre.
E. Parallelism of the Main Spindle to Saddle Movement
F. True running of taper socket in main spindle.
G. Parallelism of tailstock sleeve taper socket to saddle movement.
H. Alignment of both the centre's in vertical plane.
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a. Test for level of installation;
Measuring instruments required:
Sprit level
Gauge Blocks
Procedure:
The level of the machine bed in longitudinal and transverse directions is generally tested
by a sensitive spirit level. The saddle is kept approximately in the centre of the bed
support feet. The spirit level is then placed at a-a (Fig. above), ensure the level in the
longitudinal direction. It is then traversed along the length of bed and readings at various
places noted down. For test in transverse direction the level is placed on a bridge piece to
span the front and rear guide ways and then reading is noted. It is preferable to take two
readings in longitudinal and transverse directions simultaneously so that the effect of
adjustments in one direction may also be observed in the other. The readings in
transverse direction reveal any twist or wind in the bed.
Permissible Error:
Front guide ways: 0.02 mm/Meter convex only
Rare guide way: 0.01-0.02 convexity
Bed level in cross wise direction: ± 0.02/Meter
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b. True Running of Locating Cylinder of Main Spindle
Measuring instruments required:
Dial Gauge
Procedure:
Locating cylinder is provided to locate the chuck or face plate. The dial indicator is fixed
to the carriage (or any other fixed member) and the feeler of the indicator touches the
locating surface. The surface is then rotated on its axis and indictor should not show any
movement of needle.
Permissible Error:
0.01mm/one Rotation
c. Axial Slip of Main Spindle :
Measuring instruments required:
 Dial Gauge
Procedure:
To test this, the feeler of the dial gauge rests on the face of the locating spindle shoulder
and the dial gauge holder is clamped to the bed (Fig below). The locating cylinder is then
rotated and the change in reading noted down. The readings are taken at two
diametrically opposite points.
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Permissible Error:
0.01mm/one Rotation
d. True Running of Headstock Centre.
Measuring instruments required:
Dial Gauge
Procedure:
Headstock centre and the workpiece have to rotate with this centre. If it is not true with
the axis of movement of the spindle, eccentricity will be caused while turning a work, as
the job axis would not coincide with the axis of rotation of main spindle. For testing this
error, the feeler of the dial indicator is pressed perpendicular to the taper surface of the
centre (Fig.), and the spindle is rotated. The deviation indicated by the dial gauge gives
the trueness of the centre.
Permissible Error:
0.01mm/one Rotation
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e. Parallelism of the Main Spindle to Saddle Movement
Measuring instruments required:
 Dial Gauge
 Taper Shank Test Mandrel of 300mm length
Procedure:
This has to be checked in both vertical and horizontal planes.
a mandrel is fitted in the taper socket of the spindle. Mandrel has a concentric taper shank
which is close fit to the spindle nose taper. The feeler of the dial indicator is pressed on
the mandrel and the carriage is moved. The indication in horizontal plane is given by dial
(b) and in vertical plane by dial (a) (Fig.).
Permissible Error:
(a)0.02mm/300 mm mandrel rising towards free end
(b) 0.02mm/300 mm mandrel inclined at free end towards tool pressure
f. True running of taper socket in main spindle.
Measuring instruments required:
 Dial Gauge
 Taper Shank Test Mandrel of 300mm length
Procedure:
If the axis of tapered hole of the socket is not concentric with the main spindle axis,
eccentric and tapered jobs will be produced. To test it, a mandrel is fitted into the tapered
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hole and readings at two extremes of the mandrel are taken by means of a dial indicator
as shown
Permissible Error:
Position A 0.01 mm, Position B 0.02 mm.
g. Parallelism of tailstock sleeve taper socket to saddle movement.
Measuring instruments required:
 Dial Indicator
Procedure:
Sometimes the job is held between head-stock and tail stock centre for turning. If the
tailstock guide ways are not parallel with the carriage movement there will be some offset
results in taper turning. The test is carried out by fixing the dial indicator on the tool post
and pressing the plunger against the sleeves first in vertical and then in horizontal plane
(Fig. 16.9). The carriage is moved along the full length of the sleeve and deviations as
indicated by dial indicator.
Permissible Error
(a) 0.01/100 mm(tailstock sleeve inclined towards tool pressure )
(b) 0.01/100 mm(tailstock sleeve rising towards free end only)
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h. Alignment of both the centre's in vertical plane.
Measuring instruments required:
 Dial Indicator
Procedure:
This test is to be carried out in vertical plane only. A mandrel is fitted between the two
centres and dial gauge on the carriage. The feeler of the dial gauge is pressed against the
mandrel in vertical plane as shown
Permissible Error
0.02mm over 600mm length of mandrel
8.2
Alignment Tests on Pillar Type Drilling Machine:
a) Flatness of clamping surface of base.
b) Flatness of clamping surface of table.
c) Perpendicularity of drill head guide to the base plate.
d) Perpendicularity of drill head guide with table.
e) Perpendicularity of spindle sleeve with base plate.
f) True running of spindle taper.
g) Parallelism of the spindle axis with its vertical movement.
h) Squareness of clamping surface of table to its axis.
i) Squareness of spindle axis with table.
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a) Flatness of clamping surface of base.
The test is performed by placing a straight edge on two gauge blocks on the base plate in
various positions and the error is noted down by inserting the feeler gauges. This error should
not exceed 0.1/1000 mm clamping surface and the surface should be concave only.
b) Flatness of clamping surface of table.
This test is performed in the same manner as test (1), but on the table. The permissible
error is also same.
c) Perpendicularity of drill head guide to the base plate.
The squareness (perpendicularity) of drill head guide to the base plate is tested :
(a) in a vertical plane passing through the axes of both spindle and column, and
(b) in a plane at 90° to the plane at (a).
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The test is performed by placing the frame level (with graduations from 0.03 to 0.05
mm/m) on guidecolumn and base plate and the error is noted by noting the difference
between the readings of the two levels. This error should not exceed 0.25/1000 mm guide
column for (a) and the guide column should be inclined at the upper end towards the front
only,
and
0.15/1000
mm
for
(b).
(Please note that Fig. 16.18 shows the similar test for the squareness of drill head guide
with table, the only difference being that the frame level is to be placed on the base
instead of table).
d) Perpendicularity of drill head guide with table.
e) Perpendicularity of spindle sleeve with base plate.
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f) True running of spindle taper.
g) Parallelism of the spindle axis with its vertical movement.
h) Squareness of clamping surface of table to its axis.
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i) Squareness of spindle axis with table.
Assignment -VIII
Q1) what is meant by alignment tests on machine tools? Why they are necessary? Explain.
Q2) Distinguish between ‘geometrical’ and ‘practical’ tests on a machine tool
Q3) Describe alignment test of a milling machine with neat sketches
Question bank:
1.
2.
3.
4.
5.
a) What is meant by alignment tests on machine tools? Why they are necessary? Explain.
b) Distinguish between ‘geometrical’ and ‘practical’ tests on a machine tool
a) Describe with neatly drawn sketches the following tests on Lathe:
i) Spindle centre runout. ii) Spindle taper bore run out. iii) Chuck runout.
b) Name the different alignment tests to be performed on a drilling machine and explain
any two of them in detail.
a) Describe the following alignment tests on a milling machine with neat sketches.
i) Squareness of the centre J-slot of work table with main spindle. ii) Parallelism of main
spindle of Lathe to saddle movement.
b) Describe the followings alignment tests on a pillar drilling machine.
i) Flatness of claming surface of table. ii) Perpendicularity of drill guide to the label
a) Distinguish between ‘geometrical’ and ‘practical’ tests on a machine tool.
b) Describe the followings alignment tests on a pillar drilling machine.
i) Flatness of clamping surface of table.
ii) Perpendicularity of drill guide to the label.
What is meant by alignment tests on machine tools? Why they are necessary?Explain.
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6.
7.
8.
9.
10.
11.
12.
(a) Distinguish between geometrical and practical tests on machine tools.
(b) Explain various instruments required for performing the alignment tests on machine
tools.
Describe the following alignment tests on a pillar drilling machine.
(a) Square ness of the spindle axis with table. (b) Perpendicularity of drill guide to the
table.
Specify with the diagrams how the following tests would be carried out on a center lathe:
(a) The straight ness of the bed, horizontally and vertically. (b) The spindle axis parallel
to the bed in both the horizontal and vertical planes. State also the permissible degree of
accuracy in each case.
State and explain with sketches the various geometrical tests made on lathe machine tool
before acceptance.
(a) Distinguish between geometrical and practical tests on machine tools.
(b) Explain various instruments required for performing the alignment tests on machine
tools.
Explain with neat sketch the method of checking the following in the acceptability test of
drilling machine.
(a) If the spindle is running true (b) If the table and pillar are mutually perpendicular
(c) If the spindle perpendicular to the table.
Describe the following alignment tests on a pillar drilling machine.
(a) Square ness of the spindle axis with table.
(b) Perpendicularity of drill guide to the table
STUDY MATERIAL
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