Report September

7/25/2019 Report September

1/28

A PROJECT ON

BALANCING OF SEVERAL MASSES AS BLADES ON A SINGLE AXIS AS IMPELLER

Submitted by:

AASHUTOSH VYAS (090460119007)

SARTHAK PATEL (090460119013)

DEPARTMENT OF MECHANICAL ENGINEERING

GUIDED BY

Mr!ITENDRAKUMAR PATEL

M"#$%&'#% E&'&""r'& D"*%r+,"&+

U&'-"r.% #/"" / E& A& T"#$

G%&$'&%%r

A Project Report Submitte to

Guj!r!t "ec#$o%o&ic!% U$i'er(it)

I$ P!rticu%!r Fu%*i%% o* t#e Re+uireme$t( *or

"#e De&ree o* E$&i$eeri$&

I$ Mec#!$ic!%

UNIVERSAL COLLEGE OF ENGINEERING AND TECHNOLOGY

9+$N/-",2"r 01


2/28

Acknowledgement

"o!) i$ e'er) *ie%, pr!ctic!% tr!i$i$& i( !$ import!$t ro%e i$ m!r-i$& ! tr!i$ee ! per*ect per(o$

i$ #i( .or- !$ !%(o m!-e( #im pu$ctu!%/

/

0e e1te$ our (i$cere t#!$-( to Mr !ITENDRAKUMAR PATEL (L"#+r"r) 5 Mr HITESH

PATEL (E+"r&% G'") *or t#eir -i$ (u&&e(tio$( .#i%e .or-i$& !t C B DOC"OR

VEN"ILA"ORS PV"/ L"D/ !$ *or &uii$& uri$& t#e cour(e o* t#i( .or-/

0e !re t#!$-*u% to Mr. MITTAL PATEL HOD o* Mec#!$ic!% Dep!rtme$t !$Pr''*%

Dr N K SHERSIA /rt#eir -i$ (upport/

M) (peci!% t#!$-( to m) *!mi%) member(, *or t#eir u$i+ue (upport i$ (ucce((*u% comp%etio$ o*

Project/ Fi$!%%) I .ou% %i-e to t#!$- e!c# !$ e'er) per(o$ .#o #!( irect%) or i$irect%) #e%pe

i$ t#i( project/

AAS2U"OS2 VYAS 3454674885449:

SAR"2A; PA"EL 345467488548


3/28

ABS"RAC"

"#rouout t#e more e$terpri(i$& cou$trie( o* t#e .or%, t#e be$e*it( to i$u(tr) o* u$ert!-i$&

o$ (ite, t#e comp%ete (er'ici$& !$ rep!ir o* (tr!te&ic rot!ti$& m!c#i$e( #!'e %o$& bee$

reco&$i=e !$ !pp%ie .it# co$(ier!b%e re.!r/ "#e #ier t#e c!p!cit) o* t#e m!c#i$e( !$

t#e more (tr!te&ic t#eir $!ture o* oper!tio$ to prouctio$ em!$(, t#e &re!ter !re t#e be$e*it( to

be re!%i=e i$ term( o* reuce o'er!%% co(t( !$ m!c#i$e o.$time/ Fi$!% m!c#i$i$& !$

b!%!$ci$& o* m!$) t)pe( o* rotor !((emb%ie( #!'e !%.!)( bee$ percei'e !( bei$& !mo$&(t t#e

mo(t i**icu%t proceure( to u$ert!-e o$ (ite, p!rticu%!r%) .it# %!r&er rotor( !$ t#e #ier (pee

>F%e1ib%e? rotor(/

Virtu!%%) !%% rot!ti$& compo$e$t( e1perie$ce (i&$i*ic!$t impro'eme$t( .#e$ b!%!$ce/

Co$(umer( t#rouout t#e &%ob!% m!r-et co$ti$ue to em!$ '!%ue i$ t#e prouct( t#e)

purc#!(e/ "#e) em!$ per*orm!$ce @ (m!%%er, %iter, more e**icie$t, more po.er*u%, +uieter,

(moot#er ru$$i$& !$ %o$&er %!(ti$&/ B!%!$ci$& c!$ co$tribute to e!c# o* t#e(e !$ i( o$e o* t#e

mo(t co(t e**ecti'e me!$( o* pro'ii$& '!%ue to t#e co$(umer/


4/28

UNIVERSAL COLLEGE OF ENGINEERING 5 TECHNOLOGY

Department of Mechanical Engineering

CERTIFICATE

Date:

09/11/2012

"#i( i( to certi*) t#!t t#e [email protected] e$tit%e >BALANCING OF SEVERAL MASSES AS

BLADES ON SINGLE AXIS AS IMPELLER? #!( bee$ c!rrie out b) AAS2U"OS2 VYAS

3454674885449: !$ SAR"2A; PA"EL 345467488548


5/28

"ABLE OF CON"EN"S

"I"LE PAGE

AC;NO0LEDGEMEN"

ABS"RAC"

CER"IFICA"E

1 I&+r/#+'/&888888888888888888888888886

D".#r'*+'/&888888888888888888888888887

3 L'+"r%+r" R"-'"8888888888888888888888819

4 R"%':%+'/& *%& /r +$" *r/2",888888888888888881; Pr/


6/28

8/ IN"RODUC"ION

U$b!%!$ce occur( i$ ! rot!ti$& m!c#i$e .#e$ t#e m!(( ce$ter%i$e !$ t#e &eometric ce$ter o* t#e

rot!ti$& p!rt o $ot coi$cie o$ e!c# ot#er/ U$b!%!$ce rotor( &e$er!te 'ibr!tio$ .#ic# m!)

!m!&e t#eir compo$e$t(/ I$ orer to e1te$ t#e %i*e o* t#e m!c#i$e, 'ibr!tio$ ue to u$b!%!$ce

mu(t be reuce to !ccept!b%e %e'e%/ De(pite t#e !bi%it) to reuce u$b!%!$ce to %o. %e'e%(, t#e(e

%e'e%( or %imit( mu(t be e*i$e/ It .ou% be u$eco$omic!% to e1!&&er!te b!%!$ci$& +u!%it)

re+uireme$t(/ 2o.e'er, i* t#e b!%!$ci$& +u!%it) i( u$ere(tim!te, it .ou% reuce m!c#i$e

re%i!bi%it) !$ !'!i%!bi%it)/ Moreo'er, (ometime( em!$i$& o'er+u!%i*ie b!%!$ci$& reuce(

m!c#i$e !'!i%!bi%it) b) co$(umi$& $ece((!r) time i$ u$$ece((!r) b!%!$ci$&/ 2e$ce it i(

$ece((!r) to b!%!$ce rotor( i$ ! .!) t#!t it (tri-e b!%!$ce bet.ee$ eco$omic!%%) preci(e !$

tec#$ic!%%) (ou$ .!)/

"#e purpo(e o* b!%!$ci$& ! rotor i( to #e%p e$(ure t#!t t#e m!c#i$er) i( (!*e !$ re%i!b%e/ "#i( i(!c#ie'e .#e$ t#e rotor m!(( !$ rot!tio$!% ce$tre%i$e !re !( c%o(e to e+u!% !( po((ib%e/

E1ce((i'e u$b!%!$ce c!$ c!u(e 'ibr!tio$ !$ (tre(( i$ t#e (#!*t or !tt!c#e piece(/ For e1!mp%e,

! &e$er!tor .it# #i (#!*t 'ibr!tio$ c!$ c!u(e t#e o'er#u$& e1citer to %oo(e$ !$ *!i%/ D)$!mic

*orce( c!$ !%(o be tr!$(mitte to (upporti$& (tructure(, (uc# !( t#e be!ri$& #ou(i$& or e+uipme$t

c!(e/ A$ u$b!%!$ce ce$tri*u&e o$ ! commo$ ec- c!$ c!u(e 'ibr!tio$ i$ !j!ce$t piece( o*

e+uipme$t/ I* oper!tor( #!'e to .!%- o$ 'ibr!ti$& &r!ti$&, t#i( c!$ c!u(e !$$o)!$ce !$ *!ti&ue/

E1ce((i'e 'ibr!tio$ c!$ c!u(e .e!r i$ be!ri$&(, (e!%(, &e!r(, etc/ !$ reuce t#e %i*e e1pect!$c)

o* t#e(e p!rt(/


7/28

0e !re .or-i$& i$ C B DOC"OR VEN"ILA"ORS PV" L"D/ For !$!%)=i$& it( u$b!%!$ce

prob%em i$ t#eir impe%%er !$ rotor(/ Our !ppro!c# i( to !re(( t#e i((ue o* u$b!%!$ce o* rotor(

*rom it( core .#ic# me!$( .e !re tr)i$& to (o%'e t#e prob%em .#i%e !%% m!$u*!cturi$& proce((e(

!re bei$& o$e o$ rotor( *rom be&i$$i$&/ "#i( !ppro!c# .i%% pro'e to be u(e*u% to reuce t#e

+u!$tit) o* u$b!%!$ce to %e'e%( o* to%er!b%e %imit(/ I* it i( o$e .it# c!re u(i$& !%% t#e -$o.%e&e

o* !t! !'!i%!b%e, po((ibi%it) o* mi$imum b!%!$ci$& time or $o b!%!$ci$& time c!$t be ru%e out/

"#i( report pro'ie( brie* o* i**ere$t u$b!%!$ce co$itio$( .it# it( t)pe, !$ criteri! u(e .#e$

b!%!$ci$& rot!ti$& e+uipme$t/


8/28

/ DESCRIP"ION

A( ! rotor (pi$(, ce$tri*u&!% *orce( !ct upo$ it/ "#e (ur*!ce !rou$ t#e perip#er) i( (tre((e !(

p!rtic%e( !re pu%%e out.!r *rom t#e !1i( o* rot!tio$/ I* !%% o* t#e(e r!i!% *orce( !re e+u!%, t#e

rotor i( (!i to be b!%!$ce !$ (#ou% $ot 'ibr!te/ 2o.e'er, i* t#e rotor co$t!i$( ! #e!') (pot to

o$e (ie, t#e(e r!i!% *orce( .i%% $ot c!$ce% !$ t#e u$b!%!$ce *orce .i%% te$ to pu%% t#e rotor

*rom t#e ce$tre o* rot!tio$

/

"#e %oc!tio$ o* t#e m!(( ce$ter !$ t#e pri$cip!% i$erti! !1e( !re etermi$e b) t#e i(tributio$

o* m!(( .it#i$ t#e p!rt/ U$b!%!$ce e1i(t( .#e$ t#e !1i( o* rot!tio$ i( $ot coi$cie$t .it# !

pri$cip!% i$erti! !1i(/ It i( import!$t to r!. ! i(ti$ctio$ bet.ee$ u$b!%!$ce !$ b!%!$cecorrectio$/ U$b!%!$ce i( ! m!(( propert)/ It become( ! c#!r!cteri(tic o* t#e p!rt .#e$ !$ !1i( o*

rot!tio$ i( e*i$e/ B!%!$ce correctio$ i( ! me!$( to !%ter t#e m!(( propertie( to impro'e t#e

!%i&$me$t o* t#e !1i( o* rot!tio$ .it# t#e m!(( ce$ter !$or t#e ce$tr!% pri$cip!% !1i(/ Bot# c!$

be e1pre((e !( .eit( !$ r!ii !$ #!'e (#!re termi$o%o&)/

B!%!$ci$& i( t#e proce(( b) .#ic# .e %e!r$ t#e !mou$t !$ po(itio$ o* t#e #e!') (pot (o .e c!$

eit#er ! !$ e+u!% !mou$t o* .eit to t#e oppo(ite (ie o* t#e rotor or remo'e !t t#e #e!')

(pot/ 0e -$o. t#!t t#e more u$b!%!$ce .e #!'e, t#e &re!ter *orce, !$ t#u(, t#e &re!ter t#e

'ibr!tio$ !mp%itue/ For t#i( re!(o$, .e u(e !mp%itue o* 'ibr!tio$ to #e%p u( to etermi$e t#e

!mou$t o* u$b!%!$ce .e #!'e/

At t#e (t!rt o* ! b!%!$ci$& prob%em .e #!'e $o ie! #o. %!r&e t#e #e!') (pot i( $or o .e -$o.

.#ere t#e p!rt i( %oc!te/


9/28

I* !$ u$b!%!$ce .eit i( !e to ! per*ect%) b!%!$ce rotor, t#e p!rt .i%% 'ibr!te !t ! *re+ue$c)

e+u!% to it( rot!ti$& (pee/ "#e p!rt .i%% 'ibr!te .it# cert!i$ !mp%itue, !$ ! re*ere$ce m!r- o$

t#e p!r- .i%% !ppe!r/

B) !i$& ! tri!% .eit to t#e u$b!%!$ce p!rt, o$e o* t#e t#ree t#i$&( mit #!ppe$

8: Fir(t, .e mit ! t#e tri!% .eit o$ t#e #e!') (pot/ I* .e o, t#e 'ibr!tio$ .i%%

i$cre!(e, but t#e re*ere$ce m!r- .i%% !ppe!r i$ t#e (!me po(itio$ i$ t#e it i o$ t#e

ori&i$!% ru$/ "o b!%!$ce t#e p!rt !%% .e #!'e to o i( mo'e t#e tri!% .eit irect%)

oppo(ite to it( i$iti!% po(itio$ !$ !ju(t t#e !mou$t o* .eit u$ti% .e !c#ie'e !

(!ti(*!ctor) b!%!$ce/

: "#e (eco$ t#i$& t#!t cou% #!ppe$ i( t#!t .e cou% ! t#e tri!% .eit i$ e1!ct%) t#e

rit %oc!tio$ oppo(ite t#e #e!') (pot/ I* t#e tri!% .eit .ere %e(( t#!$ t#e u$b!%!$ce, .e

.ou% (ee ! ecre!(e i$ 'ibr!tio$/ "o b!%!$ce t#e p!rt !%% .e #!'e to o i( to i$cre!(e t#e

.eit u$ti% .e !c#ie'e ! (!ti(*!ctor) %e'e%/

I* t#e tri!% .eit .ere %!r&er t#!$ t#e u$b!%!$ce, t#e$ it( po(itio$ $o. be t#e #e!') (pot/

I$ t#i( c!(e, !%% .e .ou% #!'e to o to b!%!$ce t#e p!rt i( reuce t#e !mou$t o* tri!%

.eit u$ti% .e !c#ie'e ! (!ti(*!ctor) %e'e%/


10/28

! b!%!$ci$& m!c#i$e, irect re!i$& o* u$b!%!$ce m!) be !'!i%!b%e !$ c!%ibr!tio$ ru$( m!) $ot

be re+uire/

/8: S"A"IC UNBALANCE:

A co$itio$ o* (t!tic u$b!%!$ce e1i(t( .#e$ t#e m!(( ce$ter oe( $ot %ie o$ t#e !1i( o*

rot!tio$/ St!tic u$b!%!$ce i( !%(o -$o.$ !( Force Unbalance/ A( e*i$e, (t!tic u$b!%!$ce i( !$

ie!% co$itio$, it #!( t#e !itio$!% co$itio$ t#!t t#e !1i( o* rot!tio$ be p!r!%%e% to t#e ce$tr!%

pri$cip!% !1i( / No coup%e u$b!%!$ce/

Fi&/ $o/ /8/8

St!tic u$b!%!$ce #!( t#e u$it( o* "'$+="&+$ or ,%..>"&+$ !$ i( e1pre((e

U./r

.#ere i( .eit 3or , i( m!((: !$ r i( t#e e**ecti'e r!iu( o* t#e .eit/

/: DYNAMIC UNBALANCE

"#e mo(t &e$er!% c!(e o* u$b!%!$ce i$ .#ic# t#e ce$tr!% pri$cip!% !1i( i( $ot p!r!%%e% to !$ oe(

$ot i$ter(ect t#e !1i( o* rot!tio$/


11/28

Fi&/ $o/ //8

/.obb%e?/ Coup%e u$b!%!$ce i( t.o e+u!% .eit( i$ t.o i**ere$t p%!$e( 84 e&ree( *rom

e!c# ot#er/

Fi&/ $o/ /


12/28

!e or remo'e: i$ ! p%!$e (ome i(t!$ce *rom t#e m!(( ce$tre/ "#e !%ter!tio$ cre!te( ! (t!tic

u$b!%!$ce !( .e%% !( ! coup%e u$b!%!$ce/ Co$'er(e%), ! rotor .it# +u!(i@(t!tic u$b!%!$ce c!$ be

b!%!$ce .it# ! (i$&%e correctio$ o* t#e rit m!&$itue i$ t#e !ppropri!te p%!$e/

Fi&/ $o/ /6/8

I$ t#e c!(e o* (t!tic u$b!%!$ce, !( %o$& !( t#e i(t!$ce *rom t#e ce$ter o* &r!'it) time( t#e r!iu(

!t .#ic# t#e .eit i( !e time( t#e !mou$t o* .eit i( e+u!%, t.o or more i**ere$t .eit(

c!$ be u(e/ I$ Fi&ure , i* t#e i(t!$ce to t#e p%!$e co$t!i$i$& o$e .eit i( t.ice t#e i(t!$ce

!( to t#e ot#er .eit !$ t#e r!iu( !t .#ic# t#e .eit( !re p%!ce !re t#e (!me, t#e$ o$%) #!%*

!( muc# .eit i( re+uire i$ t#!t p%!$e/

Coup%e u$b!%!$ce i( ! %itt%e e!(ier (i$ce t#e i(t!$ce *rom t#e CG i( $ot import!$t/ A( %o$& !( t#e

.eit time( t#e r!iu( *or bot# .eit( !re e+u!%, t#e$ bot# portio$( o* t#e coup%e !re e+u!%/

For e1!mp%e, i* t#e r!iu( !t .#ic# o$e .eit i( !e i( t.ice t#e r!iu( o* t#e ot#er, t#e$ o$%)

#!%* !( muc# .eit i( re+uire/ I* t#e r!iu( c!$ rem!i$ t#e (!me, t#e po(itio$ o* t#e coup%e

.eit( !%o$& t#e !1i( o* t#e rotor c!$ be !ju(te b) t#e i(t!$ce bet.ee$ t#e .eit(/ For

e1!mp%e, coup%e .eit( t#!t .ei &r!m( !$ !re 4 i$c#e( !p!rt.ou% be e+u!% to coup%e

.eit( t#!t .ei 84 &r!m( !$ !re 84 i$c#e( !p!rt/D)$!mic u$b!%!$ce i( !%(o re*erre to !(

t.o p%!$e u$b!%!$ce, i$ic!ti$& t#!t correctio$ i( Re+uire i$ t.o p%!$e( to *u%%) e%imi$!te

)$!mic u$b!%!$ce/ A t.o p%!$e b!%!$ce (peci*ic!tio$ i( $orm!%%) e1pre((e i$ term( o* =rper

p%!$e !$ mu(t i$c%ue t#e !1i!% %oc!tio$ o* t#e correctio$ p%!$e( to be comp%ete/ D)$!mic


13/28

u$b!%!$ce c!pture( !%% t#e u$b!%!$ce .#ic# e1i(t( i$ ! rotor/ "#i( t)pe o* u$b!%!$ce c!$ o$%) be

me!(ure o$ ! rot!ti$& b!%!$cer (i$ce it i$c%ue( coup%e u$b!%!$ce/

A$) ri&i rotor c!$ be b!%!$ce i$ !$) t.o p%!$e( o$ t#e rotor/ For co$'e$ie$ce, mo(t rotor( !re

b!%!$ce i$ t#e t.o p%!$e( $e!re(t t#e be!ri$& jour$!%(, (i$ce !cce(( to ! .eit i( u(u!%%)

co$'e$ie$t !$ t#e .eit( #!'e t#e &re!te(t e**ect o$ t#e 'ibr!tio$ %e'e%/ "#i( !ppro!c# to

b!%!$ci$& i( re*erre to !( t#e i$*%ue$ce coe**icie$t met#o o* b!%!$ci$&/ It i$'o%'e( ob(er'i$&

t#e ori&i$!% 'ibr!tio$ occurri$& i$ ! rotor, t#e$ !i$& c!%ibr!tio$ 3tri!%: .eit( i$ e!c# o* t#e

t.o (e%ecte b!%!$ci$& p%!$e(/ "#e re(u%t o* t#e(e re!i$&( !re c!%cu%!te i$ t#e i$(trume$t to

&i'e ! b!%!$ce .eit to be !e i$ e!c# o* t#e t.o p%!$e(/ 0#e$ t#e rotor i( bei$& b!%!$ce i$

! b!%!$ci$& m!c#i$e, irect re!i$& o* u$b!%!$ce m!) be !'!i%!b%e !$ c!%ibr!tio$ ru$( m!) $otbe re+uire/ "#ere !re (e'er!% t)pe rotor(, #o.e'er, t#!t #!'e c#!r!cteri(tic( t#!t %e$ t#em(e%'e(

to ! i**ere$t t)pe o* .eit correctio$/ Rotor( t#!t !re omi$!te b) (t!tic u$b!%!$ce m!) be

better correcte b) (p!ci$& t#e (t!tic correctio$( i$ (e'er!% 3or $umerou(: p%!$e( !%o$& t#e rotor

%e$&t#/ N!rro. p%!$e rotor( $orm!%%) re(po$ better b) b!%!$ci$& t#e (t!tic u$b!%!$ce *ir(t !$

t#e$ reuci$& t#e coup%e u$b!%!$ce to !$ !ccept!b%e %e'e%/ A rotor i( co$(iere !( ! $!rro.

p%!$e rotor i* t#e i(t!$ce bet.ee$ t#e correctio$ p%!$e( i( %e(( t#!$ 8< o* t#e i(t!$ce bet.ee$

t#e be!ri$& jour$!%(/

A$) rotor .it# !$ u$e'e$ i(tributio$ o* m!(( !bout it( !1i( o* rot!tio$ #!( !$ u$b!%!$ce/ Fi&ure

(#o.( ! rotor .it# !$ u$b!%!$ce c!u(e b) !$ e1tr! m!(( Jm/ A (imi%!r e**ect i( cre!te b)

out o* ce$tre m!c#i$i$&, $o$ u$i*orm .i$i$&( i$ !rm!ture(, b%!e( o* i**ere$t (i=e( o$ rotor(,

i$ter$!% *%!.( i$ c!(ti$&, u$e'e$ e$(it) o* m!teri!% etc/

0#e$ rotor rot!te(, t#e e1tr! m!(( Jm e1ert( ! ce$tri*u&!% *orce/ "#i( ce$tri*u&!% *orce mo'e(

!rou$ .it# t#e rot!ti$& m!(( !$ c!u(e( e*orm!tio$ to t#e (#!*t !$ 'ibr!tio$ to t#e ()(tem/

Si$ce e1ce((i'e 'ibr!tio$( !re objectio$!b%e, .e tr) to reuce t#em !$ !re o$e b) reuci$&

U$b!%!$ce/


14/28

"#e u$b!%!$ce JU o* t#e rotor i( &i'e$ b)

U mKr

m u$b!%!$ce m!((/

r R!iu( !t .#ic# t#i( m!(( i( %oc!te/

It i( (ee$ t#!t u$b!%!$ce JU i( i$epe$e$t o* (pee !$ it e1i(t( e'e$ .#e$ t#e rotor i(

(t!tio$!r)/ 0#e$ t#e u$b!%!$ce rotor rot!te(, t#e ce$tri*u&!% *orce i( &i'e$ b)

F m' mr U

' Li$e!r 'e%ocit)

A$&u%!r Ve%ocit)

"#i( i( c%e!r t#!t t#e ce$tri*u&!% *orce JF i( irect%) proportio$!% to t#e u$b!%!$ce JU #e$ce .ec!$ reuce t#i( *orce !$ t#ere*ore 'ibr!tio$ b) reuci$& u$b!%!$ce/

0#!t i( t#e e**ect o* u$b!%!$ce o$ ! rot!ti$& p!rt At o$e e1treme, i* t#e rotor mou$t( !re ri&i,

t#e *orce( e1erte !t t#e be!ri$& (upport( c!$ be 'er) #i !$ pote$ti!%%) !m!&i$&/ "#e *orce(

!re ! *u$ctio$ o* t#e u$b!%!$ce/ "#e) !re t#e ce$tri*u&!% *orce( e(cribe e!r%ier/ At t#e ot#er

e1treme, .it# *%e1ib%e mou$t(, t#e p!rt i( %oo(e%) co$(tr!i$e !$ m!) e1#ibit %!r&e !mp%itue(

o* i(p%!ceme$t/ "#e !mp%itue o* 'ibr!tio$ i( proportio$!% to u$b!%!$ce !$ %imite b) t#e

i(t!$ce bet.ee$ t#e m!(( ce$ter !$ t#e !1i( o* rot!tio$/ Mo(t !pp%ic!tio$( !re ! combi$!tio$ o*

bot#/

Amp%itue R!tio !$ Fre+ue$c) R!tio !re $o$@ime$(io$!% me!(ure( o* i(p%!ceme$t !$ (pee

re(pecti'e%)/ Fre+ue$c) R!tio i( (pee .it# re(pect to t#e ()(tem( $!tur!% *re+ue$c), bot#

e1pre((e i$ (imi%!r u$it( i/e/ rpm, 2=, r!(ec/ Amp%itue R!tio i( i(p%!ceme$t, 1, .it# re(pect

to t#e u$b!%!$ce m!(( ecce$tricit), e *rom U me/ At %o. (pee(, i(p%!ceme$t i( (m!%% .it#

re(pect to t#e m!(( ce$ter o**(et/ It i$cre!(e( (%o.%) !( t#e ce$tri*u&!% *orce i$cre!(e(/ At #ier

(pee(, more t#!$ t.ice t#e $!tur!% *re+ue$c), i(p%!ceme$t '!rie( %itt%e .it# (pee or !mpi$&


15/28

!$ !ppro!c#e( ! %imit o* t#e u$b!%!$ce m!(( ecce$tricit)/ At (pee( $e!r re(o$!$ce 3$ 8:

i(p%!ceme$t c!$ be 'er) %!r&e !$ '!rie( &re!t%) .it# t#e !mpi$& r!tio, ccc/

"#e re%!tio$(#ip o* t#e %oc!tio$ o* t#e u$b!%!$ce *orce .it# re(pect to t#e (#!*t ce$ter !$

rot!tio$!% !1i( i( &re!t%) !**ecte b) t#e pro1imit) o* t#e (#!*t (pee to t#e %!ter!% $!tur!%

*re+ue$c)/ Rec!%% t#!t t#e !mou$t o* u$b!%!$ce i( e*i$e !( t#e m!(( o* t#e i(c time( t#e

ecce$tricit) o* t#e ce$ter@o*@&r!'it) 3CG:/ 0e%% be%o. t#e critic!% (pee, t#e #i (ie o* t#e

.#ir%i$& (#!*t coi$cie( .it# t#e !$&u%!r %oc!tio$ o* t#e CG / A( t#e ru$$i$& (pee o* t#e rotor

!ppro!c#e( t#e critic!% (pee, t#e ce$ter o* rot!tio$ be&i$( to (#i*t to.!r t#e CG / At re(o$!$ce,

t#e p#!(e !$&%e bet.ee$ t#e e1citi$& *orce 3irectio$ o* t#e u$b!%!$ce: !$ t#e !ctu!% 'ibr!tio$

3#i (ie: .i%% be 54Q/A*ter &etti$& t#e brie* o* t#e t)pe( o* b!%!$ci$&, .e t!-e ! %oo- !t .#!t -i$ o* m!c#i$e i( u(e

i$ t#e i$u(tr) !$ u$er(t!$ it( *u$!me$t!%(/

I$ C B DOC"OR VEN"ILA"ORS PV"/ L"D/ "#e) u(e ! #ori=o$t!% b!%!$ci$& m!c#i$e/ 2ere

.e t!-e ! (umm!r) o* t)pe( o* b!%!$ci$& m!c#i$e( !'!i%!b%e/

C%!((i*ic!tio$ o* B!%!$ci$& M!c#i$e

Balancing Machine

HardSoft

Combin

ed beltand end

EndBelt

Two

planes

Single

plane

Vertical Horizonta


16/28

H%r ?"%r'& ?%%'&

M%#$'&"

S/+ ?"%r'& ?%%'&

M%#$'&"

O+'&" D)$!mic b!%!$ci$& m!c#i$et#!t etect( u$b!%!$ci$& !( !ce$tri*u&!% *orce b) u(i$&(o%i (upporti$& ()(tem( *orbe!ri$&

D)$!mic b!%!$ci$& m!c#i$et#!t etect( u$b!%!$ci$& !( !'ibr!tio$ b) u(i$& *%e1ib%e(upporti$& ()(tem( *or be!ri$&

M"+$/ / D"+"#+'/& Detect( ce$tri*u&!% *orce t#!t!ct( o$ be!ri$&

!/ Me!(ure( ! (m!%%i(p%!ceme$t bet.ee$be!ri$& be$c#e( .#e$

be!ri$& !re (upporteb) #!r (pri$&(/

b/ A *orce etector i(!tt!c#e to t#ep!((!&e.!) o* ! *orcebet.ee$ *r!me !$be!ri$&/

Detect( 'ibr!tio$ o* t#ebe!ri$&/ A 'e%ocit) etector i(!tt!c#e to t#e p!((!&e.!) o*! *orce bet.ee$ *r!me !$be!ri$&/

N%+r% r"@" /

2"%r'& .**/r+'& ..+",

%& +".+ r"-/+'/& .*""

"#e $!tur!% *re+ue$c) o*be!ri$& i( #ier t#!$ t#ere'o%utio$ $ (pee/

"#e $!tur!% *re+ue$c) o*be!ri$& i( %o.er t#!$ t#ere'o%utio$ $ (pee/

S'+%2" r/+/r. Rotor( t#!t !re m!$u*!cturei$ mu%ti (m!%%@item %otprouctio$, t#u( t#ec!%cu%!ti$& circuit (etti$& #!(to be c#!$&e *re+ue$t%)/Rotor( t#!t (pe$ more time i$(t!rti$& !$ (toppi$&

re!ctio$(, t#u( it t!-e time to(et circuit c!%cu%!tio$/ Rotor(#!'e %!r&e i$iti!% u$b!%!$ce/

Rotor( t#!t !re m!$u*!cturei$ mu%ti (m!%%@item %otprouctio$, t#u( t#ec!%cu%!ti$& circuit (etti$& mu(t$ot be c#!$&e *re+ue$t%)/Lit .eit rotor(/ Ver) #i(pee rotor(/

"!b%e No/ 8


17/28

/: CORREC"IONS

0#e$ u$b!%!$ce #!( bee$ ie$ti*ie !$ +u!$ti*ie, t#e correctio$ i( (tr!it *or.!r/ 0eit

#!( to be eit#er !e or remo'e *rom t#e rot!ti$& e%eme$t/ "#e u%tim!te !im bei$& to reuce

t#e u$e'e$ m!(( i(tributio$ (o t#!t t#e ce$tri*u&!% *orce( !$ #e$ce t#e 'ibr!tio$( i$uce i$t#e (upporti$& (tructure( !re !t !$ !ccept!b%e %e'e%/

;1) F'" ?%%'&

M!$) rotor( c!$ o*te$ be b!%!$ce i$ p%!ce, ru$$i$& !t t#eir o.$ oper!ti$& (pee, .it# mi$imum

i(!((emb%)/ "o b!%!$ce i$ p%!ce, o* cour(e, ! b!(ic re+uireme$t i( t#!t t#e rotor #!( to be

!cce((ib%e to m!-e correctio$(/ M!c#i$e( (uc# !( *!$( !$ b%o.er( !re &oo c!$i!te(/ "ot!%%)

e$c%o(e motor !rm!ture( !$ pump impe%%er( !re $ot/ "#e tec#$i+ue o* b!%!$ci$& i$ p%!ce i(

re*erre to !( Fie% B!%!$ci$& !$ it o**er( (ome i(ti$ct !'!$t!&e( i$c%ui$&

B!%!$ci$& i( per*orme o$ t#e comp%ete !((emb%e m!c#i$e !$ compe$(!te( *or t#e

!((emb%) to%er!$ce( i(cu((e e!r%ier/ Co(t%) !$ time@co$(umi$& i(!((emb%) to remo'e t#e rotor to ! b!%!$ci$& m!c#i$e i(

e%imi$!te/ "#e e**ect( o* temper!ture, pre((ure, i(tortio$ !$ ot#er e$'iro$me$t!% i$*%ue$ce( c!$ be

i$corpor!te/ "#e re(u%t!$t 'ibr!tio$ c!$ be t#e to%er!$ce !pp%ie to t#e rotor, r!t#er t#!$ t#e pub%i(#e

b!%!$ce to%er!$ce( $orm!%%) u(e i$ ! b!%!$ci$& m!c#i$e/

"#i( i( p!rticu%!r%) !'!$t!&eou( i* t#e (upporti$& (tructure i( c%o(e to ! re(o$!$ce/ "#e

u$b!%!$ce i$ t#e rotor m!) #!'e to be !ju(te to !b$orm!%%) *i$e %e'e%( to mi$imi=e t#e

re(u%t!$t re(o$!$t (tructur!% 'ibr!tio$ Moer$ i$(trume$t( (uc# !( 'ibr!tio$ !$!%)=er(, !t!

co%%ector( !$ port!b%e b!%!$cer( pro'ie !ccur!te i$*orm!tio$ to !((i(t i$ t#e b!%!$ci$& proce((/"#e 'ibr!tio$ %e'e% me!(ure !t t#e rot!ti$& (pee *re+ue$c) i( u(e !( !$ i$ic!tor o* t#e

!mou$t o* u$b!%!$ce/ "#e %oc!tio$ i( etermi$e b) me!(uri$& t#e p#!(e/ P#!(e, 3t#e re%!ti'e

motio$ o* o$e p!rt o* ! m!c#i$e to !$ot#er: i( me!(ure b) me!$( o* ! (trobo(copic %it or b)

!$ i$ic!tor i$ t#e i$(trume$t, tri&&ere b) ! p#otoce%%/


18/28

It i( imper!ti'e t#!t t#e 'ibr!tio$ me!(ure i( ! re(u%t o* t#e u$b!%!$ce !$ $ot (ome ot#er

e1iti$& *orce/ O$%) ! et!i%e, t#orou, !$!%)(i( c!$ ie$ti*) .#ere t#e 'ibr!tio$ me!(ure i(

comi$& *rom/ M!$) (ource( o* 'ibr!tio$ c!$ occur !t t#e rot!ti$& (pee *re+ue$c)/ 38: 0#e$

*ie% b!%!$ci$&, tri!% .eit( *or b!%!$ce comput!tio$ !$ perm!$e$t .eit( *or *i$!% correctio$

!re $orm!%%) !e to t#e rotor/ C!re (#ou% be t!-e$ .#e$ !tt!c#i$& .eit(/ "#e) (#ou% be

!tt!c#e (ecure%) (o t#!t t#e) c!$$ot J*%) o** .#e$ t#e m!c#i$e i( oper!ti$&/ "#e) $ot o$%)

co$(titute ! per(o$$e% (!*et) #!=!r but !%(o c!$ c!u(e !m!&e/ Loo(e b!%!$ce .eit( r!tt%i$&

!rou$ i$(ie ! turbi$e *or e1!mp%e c!$ .rec- t#e m!c#i$e/


19/28


20/28

84 RO"A"ING MAC2INERYVIBRA"IONANALYSIS AND ENGINEERINGAPPLICA"IONS

/G/ YANG

88 VIBRA"ION AND ACCIDEN" OF

"URBOGENERA"OR

0/ X/ S2I, / B/ S2I/

8 OURNAL OF VIBRA"ION P/GNIL;A

"!b%e $o/

A*ter re'ie.i$& t#e(e !$ *e. more p!&e( .e u$er(too t#e b!(ic o* b!%!$ci$& !$ *ou$ !

.#o%e $e. irectio$ to e1p%ore i$ orer to (o%'e t#e prob%em/


21/28

6/ REALIA"ION PLAN OF "2E PROBLEM

A*ter (tu)i$& tec#$ic!% p!per( .e re!%i=e t#!t .e #!'e to (top u$b!%!$ce i$ rotor( *rom it(ori&i$/ So .e #! to i& eep to *i$ t#e c!u(e( o* u$b!%!$ce o* rotor( !$ t#e proceure .e #!'e

to u$er&o to reuce t#e u$b!%!$ce to t#e permi((ib%e %imit/ C!u(e( *or u$b!%!$ce c!$ be

c%!((i*ie i$ *o%%o.i$& t)pe(

1 M%&%#+r'& #%.".

M!$) c!u(e( !re %i(te !( co$tributi$& to !$ u$b!%!$ce co$itio$, i$c%ui$& m!teri!%prob%em( (uc# !( e$(it), poro(it), 'oi( !$ b%o.#o%e(/ F!bric!tio$ prob%em( (uc# !(

mi((#!pe$ c!(ti$&(, ecce$tric m!c#i$i$& !$ poor !((emb%)/ Di(tortio$ prob%em( (uc# !(

rot!tio$!% (tre((e(, !ero)$!mic( !$ temper!ture c#!$&e(/ E'e$ i$#ere$t rotor e(i&$

criteri! t#!t c!$$ot be !'oie/ M!$) o* t#e(e occur uri$& m!$u*!cture, ot#er( uri$& t#e

oper!tio$!% %i*e o* t#e m!c#i$e/ 0#i%(t (ome correctio$( *or ecce$tricit) c!$ be cou$ter!cte

b) b!%!$ci$&, it i( ! compromi(e/ D)$!mic b!%!$ci$& (#ou% $ot be ! (ub(titute *or poor

m!c#i$i$& or ot#er compromi(e m!$u*!cturi$& pr!ctice(/ I$ t#e m!$u*!cturi$& proce((, i*

proper c!re i( t!-e$ to e$(ure t#!t c!(ti$&( !re (ou$ !$ m!c#i$i$& i( co$ce$tric, t#e$ it

*o%%o.( t#!t t#e t.o !1i( .i%% coi$cie !$ t#e !((emb%e rotor .i%% be i$ ! (t!te o* b!%!$ce/

A..",2 #%.".

"#ere !re m!$) re!(o$( .#) u$b!%!$ce occur( .#e$ ! rotor i( bei$& *!bric!te/ Pri$cip%e

!mo$& t#e(e i( ! (t!c- up o* to%er!$ce(/ 0#e$ ! .e%%@b!%!$ce (#!*t !$ ! .e%%@b!%!$ce

rotor !re u$ite, t#e $ece((!r) !((emb%) to%er!$ce( c!$ permit r!i!% i(p%!ceme$t, .#ic#

.i%% prouce !$ out o* b!%!$ce co$itio$/ "#e !itio$ o* -e)( !$ -e).!)( !( to t#e

prob%em/ A%t#ou !$ ISO (t!$!r oe( e1i(t *or S#!*t !$ Fitme$t ;e) Co$'e$tio$(, i$

pr!ctice, i**ere$t m!$u*!cturer( *o%%o. t#eir o.$ proceure(/ Some u(e ! *u%% -e), (ome !

#!%* -e), !$ (ome $o -e) !t !%%/ "#u(, .#e$ ! u$it i( !((emb%e !$ t#e perm!$e$t -e) i(


22/28

!e, u$b!%!$ce .i%% o*te$ be t#e re(u%t/F!i%ure to o (o .i%% me!$ t#!t t#e %o.@%e'e% b!%!$ce

to%er!$ce( (peci*ie i$ t#e(e (t!$!r( .i%% be impo((ib%e to !c#ie'e/

3 I&.+%" ,%#$'&" #%."

0#e$ ! rotor #!( bee$ i$ (er'ice *or (ome time, '!riou( ot#er *!ctor( c!$ co$tribute to t#e

b!%!$ce co$itio$/ "#e(e i$c%ue corro(io$, .e!r, i(tortio$, !$ epo(it bui% up/ Depo(it(

c!$ !%(o bre!- o** u$e'e$%), .#ic# c!$ %e! to (e'ere u$b!%!$ce/ "#i( p!rticu%!r%) !pp%ie( to

*!$(, b%o.er(, compre((or( !$ ot#er rot!ti$& e'ice( #!$%i$& proce(( '!ri!b%e(/ Routi$e

i$(pectio$ !$ c%e!$i$& c!$ mi$imi=e t#e e**ect, but e'e$tu!%%) t#e m!c#i$e( .i%% #!'e to be

remo'e *rom (er'ice *or b!%!$ci$&/ L!r&e u$b!%!$ce( .i%% o* cour(e re+uire %!r&e .eit

correctio$( !$ u$%e(( c!re i( t!-e$, t#i( c!$ #!'e ! etrime$t!% e**ect o$ t#e i$te&rit) o* t#e

rotor/ Co$ce$tr!ti$& ! .eit !ju(tme$t 3.#et#er !i$& or t!-i$& !.!): !t ! &i'e$ poi$t

c!$ .e!-e$ t#e rotor/ For e1!mp%e p!per ro%%( !re *!bric!te *rom tubi$& !$ %!r&e !itio$(

or remo'!% o* .eit c!$ e**ect t#e (tre$&t# o* t#e .!%%( o* t#e ro%%/ "#i( m!) c!u(e it to

e*%ect .#e$ (pi$$i$& !t oper!ti$& (pee !$ t#u( i$uce #!rm*u% 'ibr!tio$( o$ t#e be!ri$&(

!$ p!per m!c#i$e *r!me/

6/ O+$"r C%.".

A$ot#er c!u(e o* u$b!%!$ce t#!t i( $ot re!i%) !pp!re$t, i( t#e i**ere$ce bet.ee$ t)pe( o*

rotor(/ "#ere !re t.o i(ti$ct t)pe( @ ri&i !$ *%e1ib%e/ I* ! rotor i( oper!ti$& .it#i$ 94 @

9 o* it( critic!% (pee 3t#e (pee !t .#ic# re(o$!$ce occur(, i/e/ it( $!tur!% *re+ue$c): it

c!$ be co$(iere to be ! *%e1ib%e rotor/ I* it i( oper!ti$& be%o. t#!t (pee it i( co$(iere

ri&i/ A ri&i rotor c!$ be b!%!$ce !t t#e t.o e$ p%!$e( !$ .i%% (t!) i$ b!%!$ce .#e$ i$

(er'ice/ A *%e1ib%e rotor .i%% re+uire mu%ti@p%!$e b!%!$ci$&/ I* ! rotor i( b!%!$ce o$ ! %o.

(pee b!%!$ci$& m!c#i$e !((umi$& it i( ri&i !$ t#e$ i$ (er'ice become( *%e1ib%e, t#e$

u$b!%!$ce !$ t#u( #i 'ibr!tio$, .i%% be t#e re(u%t/ ")pic!% m!c#i$e(, .#ic# *it t#i(

c!te&or), i$c%ue (te!m !$ &!( turbi$e(, mu%ti(t!&e ce$tri*u&!% pump(, compre((or( !$

p!per ro%%(/ I$ t#e p!per i$u(tr) p!rticu%!r%), u(e o* ro%% b!%!$ci$& met#o( t#!t .ere

(!ti(*!ctor) .#e$ p!per m!c#i$e( .ere ru$$i$& !t %o. (pee, !re $o. i$!e+u!te/ A( o%er

m!c#i$e( (pee up !$ $e. #i@(pee m!c#i$e( !re i$(t!%%e, preci(io$ ro%% b!%!$ci$& i(


23/28

m!$!tor)/ F!i%ure to o (o .i%% re(u%t i$ ro%% e*%ectio$( .#ic# c!$ e**ect prouct +u!%it) !$

e'e$ c!u(e (tructur!% !m!&e/

A*ter ecii$& t#e e**ect o* t#e c!u(e( .e #!'e to e'!%u!te t#e '!%ue o* permi((ib%e u$b!%!$ce

!ccori$& to t#e oper!ti$& co$itio$ o* it( u(e/ It c!$ be o$e *o%%o.i$& t#i( met#o/ "#e

'ibr!tio$ (t!$!r( commo$%) u(e i$ i$u(tr) put t#eir criteri! b!(e o$ t#e U$b!%!$ce

re(po$(e 3'ibr!tio$ !mp%itue: irre(pecti'e o* rotor !$ *ou$!tio$ (ti**$e((/ A%(o, t#e m!&$itue

o* t#e *orce &e$er!te ue to u$b!%!$ce !$ rotor m!(( !re $ot !re((e/ I$ b!%!$ci$&, t#e m!((,

(ti**$e(( !$ 'ibr!tio$ o* !$ u$b!%!$ce rotor !re re%!te t#rou ! p!r!meter c!%%e i$*%ue$ce

'ector/

6/8: U$b!%!$ce E1i(ti$& !$ Limit

"#e term u$b!%!$ce i( re*erre to t.o +u!$titie(/ Fir(t i( t#e b!%!$ci$& !ccept!$c limit o* !

rotor !$ i( u(u!%%) c!%%e 'ermi((ible or allo)able unbalance/ Seco$ I Determi$!tio$ o*

B!%!$ci$& Hu!%it) Limit t#e e*i(tin+ or re(idual unbalance i$ ! rotor/ I$ !ccept!$ce te(t(, t#e

*o%%o.i$& %o&ic i(imp%icit%) !pp%ie

ULimit W UE1i(ti$& t#i( B!%!$ci$& Hu!%it) .it#i$ "o%er!$ce 3Accepte:

ULimit UE1i(ti$& t#i( B!%!$ci$& Hu!%it) out o* "o%er!$ce 3Rejecte:

0#e$ Fie% B!%!$ci$&, !ccept!b%e b!%!$ci$& i( re%!te to t#e 'ibr!tio$ %e'e%/ I* t#e 'ibr!tio$ %e'e%

i( !ccept!b%e, t#e b!%!$ce %e'e% i( !ccept!b%e/ 0#e$ b!%!$ci$& i$ ! b!%!$ci$& m!c#i$e, ! &uie i(

re+uire t#!t e+u!te( t#e %e'e% o* u$b!%!$ce i$ t#e rotor to .#!t .i%% be !$ !ccept!b%e 'ibr!tio$

%e'e% .#e$ t#e rotor i( i$(t!%%e !$ oper!ti$& i$ it( o.$ e$'iro$me$t/ "#e mo(t .ie%) u(e

&uie i( t#e ISO St!$!r re*ere$ce e!r%ier/ It i( import!$t to re'ie. ISO St!$!r 85648 *or !$

u$b!%!$ce to%er!$ce .#e$ u(i$& t#e (t!ticcoup%e met#o o* b!%!$ci$& i$ ! b!%!$ci$& m!c#i$e/

"#e (#!pe o* ! rotor ict!te( t#e u$b!%!$ce to%er!$ce !$ become( ! %!r&e *!ctor !t t#e e1treme(

o* rotor ime$(io$(/ For e1!mp%e, i* t#e $orm!% u$b!%!$ce to%er!$ce *or ! ()mmetric!% rotor i(


24/28

!pp%ie to ! $!rro. p%!$e rotor, t#e re(u%ti$& coup%e u$b!%!$ce m!) be to 7 time( better t#!$

re+uire/ "#i( c!$ re(u%t i$ e1ce((i'e remo'!% o* met!% or !itio$ o* more .eit t#!$ i(

re+uire to !c#ie'e !ccept!b%e *orce( !t t#e be!ri$&( ue to t#e coup%e u$b!%!$ce/ I$ t#e (!me

m!$$er, t#e (t!tic u$b!%!$ce i$ !$ o'er#u$& rotor re+uire( t#e u$b!%!$ce to%er!$ce be reuce !t

t#e m!jor %o! c!rr)i$& be!ri$& to !c#ie'e !ccept!b%e *orce( o$ t#e be!ri$&(/


25/28

/ PROEC" PLAN

7/ CONCLUSION


26/28

"#e u(e o* t#e (t!ticcoup%e met#o o* b!%!$ci$& i$ *ie% b!%!$ci$& (#ou% be u(e .it# (ome

t)pe rotor(, e(peci!%%) rotor( omi$!te b) (t!tic u$b!%!$ce, $!rro. p%!$e rotor( !$ o'er#u$&

rotor( to reuce b!%!$ci$& time !$ impro'e t#e re(u%t(/ Ot#er !pp%ic!tio$( i$c%ue reuci$& t#e

*%e1 or bo. i$ rotor( !$ reuci$& t#e 'ibr!tio$ %e'e% !t re(o$!$ce *re+ue$cie(, e(peci!%%) t#o(e

!((oci!te .it# (t!tic u$b!%!$ce/ 0#e$ u(i$& t#e (t!ticcoup%e met#o o* b!%!$ci$& i$ !

b!%!$ci$& m!c#i$e, it i(import!$t to !pp%) ISO St!$!r( proper%) to e(t!b%i(# re!%i(tic

to%er!$ce( *or bot# t#e (t!tic !$ t#e coup%e u$b!%!$ce/

Mo(t o* to!)( i$(trume$t!tio$ i$c%ue( t#e !bi%it) to i(p%!) bot# t#e correctio$ !( .e%% !( t#e

'ibr!tio$ %e'e% i$ ! (t!ticcoup%e moe/ I* $ot, computer pro&r!m( !$ c!%cu%!tor( !re !'!i%!b%e to

per*orm t#i( *u$ctio$/ P%!ci$& correctio$ .eit( .it# or !&!i$(t rot!tio$ i**er( *rom i$(trume$tto i$(trume$t/ Speci*ic proceure( to (o%'e *or (t!ticcoup%e u$b!%!$ce !re !'!i%!b%e *or cert!i$

i$(trume$t(/

0#e$ u$b!%!$ce #!( bee$ ie$ti*ie !$ +u!$ti*ie, t#e correctio$ i( (tr!it*or.!r/ 0eit #!(

to be eit#er !e or remo'e *rom t#e rot!ti$& e%eme$t/ "#e u%tim!te !im bei$& to reuce t#e

u$e'e$ m!(( i(tributio$ (o t#!t t#e ce$tri*u&!% *orce( !$ #e$ce t#e 'ibr!tio$( i$uce i$ t#e

(upporti$& (tructure( !re !t !$ !ccept!b%e %e'e%/ E'er)t#i$& t#!t rot!te( $ee( to be i$ ! (t!te o*

b!%!$ce to e$(ure (moot# ru$$i$& .#e$ i$ oper!tio$/ Preci(io$ b!%!$ci$& i( e((e$ti!% to t#e

m!$u*!cture o* rot!ti$& e+uipme$t !$ to t#e rep!ir !$ re$o'!tio$ o* i$(t!%%e m!c#i$e(/ A(

m!c#i$e (pee( i$cre!(e, t#e e**ect( o* u$b!%!$ce become more etrime$t!%/ Moer$ tec#$o%o&)

!%%o.( *or !ccur!te b!%!$ci$& to be per*orme bot# i$ t#e *ie% !$ i$ t#e .or-(#op/ I$cre!(e

time bet.ee$ out!&e( !$ !'!i%!bi%it) *or prouctio$ i( t#e prime be$e*it/


27/28

9/ REFENRECE

8/ D)$!mic b!%!$ci$& o* rotor( b) Dr/ R!ji' "i.!ri

Dep!rtme$t o* Mec#!$ic!% E$&i$eeri$&

I$i!$ I$(titute o* "ec#$o%o&) Gu.!#!ti 984


28/28

86/ B!1ter, N/ L/ !$ 0#!%e), "/, 855, A'e$ture( i$ B!%!$ci$&, b!%!$ci$& tec#$i+ue(,

c!(e #i(torie(, ot#er co$(ier!tio$(/8/ Y/C/ 2!$, A$ Optimi=!tio$ Met#o *or B!%!$ci$& Rotor(/4roceedin+( o t/e 5SEE.87/ /B IA, L// YU, C!%cu%!tio$ o* Reuci$& Vibr!tio$ V!%ue o$ Rotor( .it# Le!(t

S+u!re Met#o,3ournal o Nort/)e(t Uni6er(ity7Natural Science Edition889/ 0/ ;e%%e$bur&er 859 "r!$(!ctio$( o* t#e Americ!$ Societ) o* Mec#!$ic!% E$&i$eer(,

our$!% o* E$&i$eeri$& *or I$u(tr) 56, 6@74/8/ / Drec#(%er 854 I$(titutio$ o* Mec#!$ic!% E$&i$eer( Co$*ere$ce o$ Vibr!tio$( i$

Rot!ti$& M!c#i$er), C!mbri&e, U;, 7@94/ Proce((i$& (urp%u( i$*orm!tio$ i$

computer !ie b!%!$ci$& o* %!r&e *%e1ib%e rotor(/

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