œ r s ia
aka%*W&&*& &B
<af t b # r$g9&a%BW8#k# :#&& t b »
BWWÜWMP(&f
I&y^bWMKR&Gg
# t # #
*%aaiMM#R%La
3 # I% *M ü K k9 &
%r
M b a # *% # w g
mm#
lo
%9g%)
% p ro v
# m # i# jW y lB W
B#m # 0 f
ProQuest Number: 27591595
All rights reserved
INFORMATION TO ALL USERS
The q u a lity of this re p ro d u ctio n is d e p e n d e n t upon the q u a lity of the copy subm itted.
In the unlikely e v e n t that the a u th o r did not send a c o m p le te m anuscript
and there are missing pages, these will be n o te d . Also, if m aterial had to be rem oved,
a n o te will in d ica te the d e le tio n .
uest
ProQuest 27591595
Published by ProQuest LLO (2019). C o p yrig h t of the Dissertation is held by the Author.
All rights reserved.
This work is protected against unauthorized copying under Title 17, United States C o d e
M icroform Edition © ProQuest LLO.
ProQuest LLO.
789 East Eisenhower Parkway
P.Q. Box 1346
Ann Arbor, Ml 4 8 1 0 6 - 1346
3 m
Ibe i* * # b e # #
Fa&r&a#y I# %p@l*
O b ia a < B k
g&om *ampl#t&o& &f h i# *%#&&*# *#
Qb&#0 Two# Qniveralty# @b*a#&al* China, he reaeived $h#
D##### of Daohalo# of $ol*noo In laab&nioal Ja IneariBg
ia3
h
B
*1
9
b
g
,
8
#*
&
#t
b
a
m
*
0
#
l
e
y
*
a%
y
9
m
8
a
&
*
C
%
B
8
&
H
i
#
h
#
8
yT
y
a
a
e
p
o
r
t
,a
h
&
n
^
h
a
l
*C
h
i
n
a
*a
#*
#
&
&
*
&
$#
a
#
i
n
#
*
f
@8& &8*i@taB& agpervlmap o f amaiatanawa»
Da
19^6, ho wa# #all*d haak to th* National High*#?
%
i
l
3
G
d
l
*
;
t
E
p
y
a
d
&
j
L
c
H
n
L
4
%
a
*
Da»€H*e]L en;;i]rua#*
iBditaaMGa* <Kf
4
»
n
;
l
r
w
»
a
%
p
a
a
a
d
:
&
3
a
a
;
1
%
m
a
*
*
t
;
c
c
rc
m
EkkjCozi* #üOüB*#%»ijoy& t&s#* :%ag%sr%w*<dboajLi*
3kw# tyaw» 4#Q%Q3a**<;i%&d&
iBkta* (3%&jkcu&saGp**
a
k
t
%
W
8
&
3
B
b
K
9
P
3
4
g
9
&
i
;
3
L
6
9
&
(
%
o
a
a
%
*
*
K
a
q
r<
&
*
&
%
a
g
k
%
*
&
à
â
a
k
*
9
a
a
;
i
j
E
w
;
s
*
%
'
,
S&o jla; n o w @i <*«WKKljLdka/&#» :(t>3p bisa* jGkeggasBo t i f î&awBl;***» tadP
aB8Mdbu8ü3dL<w&]L :
8
&
3
a
&
*
J
3
w
»
<
*
a
<
&
%
%
#
&
#
s
a
b
*
»
%%@3k<kaap<dkk <»%% ib&&* ibkwtadl#* f%%» b&ii.* <Sa%s3P*#4» ifai* ;;tü98P*ê#M#
ladlnoe 2%al%Ry*%*p IkSdjg) jauadt i*%k# 4
&
c
G
%
g
s
]
L
#
i
b
*
k
d
L
jlsk ,
3
%
K
%
B
a
#
%
%
*
r3kPî;(>#
3%wk <
*
a
Q
p
^
»
3
*
a
a
8
*
*
o
d
&
;
&
l?
m
G
M
P
&
c
i
w
w
&
a
(
S
c
R
c
w
»
iii t
&
%
*v
&
c
B
n
w
»
<
a
iI
j
N
ü
&
c
M
P
i
&
l
&
o
w
p
g
r«
o
d
f
i
a
@
%
a
b
w
B
3
%
9
U
B
W
&
lj
l
B
W
%
]
k
9
%
&
3
L
*4
K
B
K
Ï]
W
%
*
(
a
a
a
&
z
d
l
a
B
8
%
,B
5
»
(
a
3
j
%
%
l
l
4
Ü
B
&
DO'&rt#@nt* Folytochalo Inatitmt* of Droo^Syn*
wWwi# to
to Pmfmmmop
him
wrmoimtlom
H. Mmodaft fo r to® aoggmmtioiB o f # 1 #
mitt tcs>ie maâ fo r Mm d lrootloa AWmg #@ oours® o f i t *
iisrom tigfttioa.
&® m # e r Mmo M #m #
#
Mm iia^btméamms to Mp» & R, O orrari -m& Mr. R. f« &)«#*
# o h@%#d in t&# aimoammiom o f m i# w o M *# W l: to
a>* J* to o # fo r h is #o#go#tionm taxlL assiatmnos In m#
ocmstrueMon o f #*» mê»l # # tm *
A IT
The Oüjeot of t^ la t&aela la ta Inveatlg&ta & snetbod
a f doter&lnlm^ th * toyalaa#!
abaft ayatama hy marna# o f & modal*
algoed *8#
ab&â&Gtaela&loa &f
A uodal ayatam 1# de*
to almBlmtévarloa# type# &f ab&ft
ayatm#*
ISsw* idW»1&8üpGK%33*LtdL<%0L <%('TWkw»
irjKbgp@i1%&<%%i <*%w%3p@
wa«*
<&i* #Boqr aSiawflb jwgrarteai jTooa&a dboi «wiy%lQa%e#3bQyg jpspawo*»
tla # 1# eonalé&pa&ly alm p iiflad by *#aBolng tb# aetoal aya*
tw%& t%} a <%yiMB8lawCll3r a&wl alawmtlaellgr aKpilsMClaiüb agn*ta*%,
]&} /fw&anüL# ta*# #w%üjbfal*R%t *%r#t%N& 1# a sagltdkamauR* adkagla»
abawPt SMP #üCLtl«4#*âfM& b*%ü%G&wkï àgn»t#«&i*bjüdk aKMaaiaib# <wf a
a#rl#a o f m&s*## eoaaaoted by aeatioa# o f #l& #tlo ab&ft#*
Tb# coayo&tloa&l No&aer tabu&atioa method la oommoaly #*#&
fo r oaloul&tlag the toralooal vlbr& tloa Gh&rmoterlatia#
and la fa n llla r to the #yer&## engineer*
% # modal te a t 1# oommoaly mead la aolvlOR enrlaaarln#
problem#* eapecl&lly problem* 1& dyaamlo*»
^eaBaremant*
a&abe mad# o f the performaaoa of the modal end the bdha*
i f j lo r < )f ttaa; 3)r(»t%>«"1%y3M& j*9i*lb4KQ& fsaigr %*#& *xKte<3jl<)ti#(% ta%4*%4#8]gr*
I&W» j83%Bt%jy%*jL* <%f l5orqajL<%EB&3L #i&%»%%edkjkcw* 3%r%>1>leaaat 4&*&ai lb** <3w&%vdl*di
#uK& aw3wqpia»t:#,:l3r# #;3kcwM» #&3L3L <&f 1%**#
«W&
j&*%*%%üH9%3w%3r
jliif^ogpGsejbdLcoi, jMawdh
<%f iydLlBP*&tsl<*Kk lodf a
lyr^ iiE ;# (DjZ -tlia i^ o c le l*
S2biq ci&oiiarekcgr
o f tlila nov.:oJ lo p rL ;3arlly dopoiideat upon tlio oaro In de*
el. ;]}, œid c
w tio n o f tho modol ayotom*
of
O W pW r
1*1
md M et#»
1»
W o p E M W tlm
WLnolpl# Of
1
Karwnio Vltw etlon*» - ^* * • $*»* * «*#*#*.# »* #* * $* *
^
IW I# #
6
Toraional VlbratlOM#***,#*#*#****#$*#*#$#»*#
Chapter
%pe# % w lo m l V ibration
0#%
0 *0
######*# #$ * # * # * « * # # # * * # # * # * # # * * # * # # # *
,
1%
* * # # * # * * # :#* * # # # # # * * * # $ * * # * # * * ill-
0# 3
* # $ * * * # * # * # * * # # # . * * * # # * # # * #»#* 20
2*î{.
ayatem*#*»*#***#*#.. # ** * * # * , * * # . * * ^
0*S
8altl*% a#* Syatoss#: # * # * * $ # * ■*•#,# *- # # * * * * * $ # # ♦ * » # 20
2#6
G#mW
&#?
CWpWr
*##* #* ,* *# .. . #. #* * * .* # )1
Omered
3*
37
#KW m l Pr@##My (W Lm latlm i
3*1
W w a l * * . *###$..,4#.#,.#####$##*.*#*####*.*. Ii3
3#2
#»####,*** !Â
3*3
% rw W W p le d D#0* (W erm tlng àet##*###.*##* $2
% rlA# Inatall&tloa*#®***#.*###..#..#**#**#** 61
ÎA B Œ
OP S O îM - lf S
( e o n tla a sâ }
P «S »
I#
Bwery of IMel ï««t
* # $ # # # * * * * * # * #' # * * * * * * * # * * * # * # * #
. 66
o£ a » B otel
h *‘
6?
% a tr@ l în fo * ^ à flîjm tio a * « **» •» .*.»
5»
69
Qonatrmotlwi of Eorslooal 7iib»% lw i
Moâol Systom
5*3.
ïtofesere o f ïte le l S
5 .2
GommWrntion o f laas-ûsartia»..* . . * . » » . * . , * » » 80
5*3
Oolootlom -@ f-%af%* *
$»h
toporfeîijg of % # Oonsîs»i0tlm of '
y
s
.
m
.
a
,
.
«
.
.
#
#5
*
85
%aol SystM StOBâ,*.**,» pO
5*6
MoWr Drlvo
^
5*7
Csœ and % llo % r
91
% # to r
6,
o f &W@1 SyStea
6 ,1
D o to m iim tio n o f % #a îleœwnt o f
6,2
OeiîoW itettMcai, o f S ffO o tif® £®ngm o f
Oooücasdi o f Ohoffe, * #* , , t
^08i o f
7*
7*1
4, n l|.
PrOï|OO30<^»4 « * 44 4 *4 4 « * * • • 4 • *# ,1 ^ 6
OiBeaBsiœas oaâ %gg##ioms
Poifonaanoo of ïh« Itodsl SysWm,,.,#.,.,,,,,,
page
7 *0
A p p r o p id a te
7 *3
P ro p o M d r i a n
e f % # IJ b d e l
o f T o rq u e O o n tr o l f o r
J o d e l % e t# a ,
* * * * * * # * « # * # * * * * * # * * «. :# # #: m* * '* * '# # $ # « *t * # '♦ # *' * # #3 ^ 0
F ig u r e
F ig u r e
T it le
N W )e r
%.
& # F w # m m t« a
% e tw * # * #
2
2*
!%%%x%uic l o t i o n * #»♦s#%♦*■«##f:f t # * * f # # # * # ♦ * t » * # « f *
S
3*
% # Torsion o f a %#f%* #-#*## #* ## *#* #-* ##* #* * * #* ♦*
T
1$^
% # Torelmml Ow»D#gre#H)f*%wWom %"#$#%* ##**# %1
6*
Defleoti# j^imgrmm of T#o^%#s
7#
Thro<h#M œ #
3*
gquiValeut Teo* and %r0###w#
*###**** 0)
# :* # * # # # * # * # # * # » * , # # # * * * * * $ * # * # #
**###**## 29
9*
Owred ^^tem#**##**#**#*#**##* 3S
10#
Thrw##Aft 3y#tm and it# équivalent %mtem###* gg
11.
%uivelent Brenohed %#tem of
The GenoMLl
12#
ayetmm*.#*#***#***#.,#** W
3evon^Naoa 5yetW and It# équivalent
Teo#% L#e
W
13#
M j a o m t ]%àè#e# I n
O e z w ra l S y e t e m # # * . * * . # # * # * * # *
lî|..
Behavior of The Remainder Torque*#.#*#*.#*#**#** $1
1^#
Direet#Ooupled D.G. ^meratlng ^#t end it#
é q u iv a lu t $ y # t e m e # # . # . # # * * , # . # * * , . # # # # # . # * * * # * *
l6,
W
$1
NOMaal élmetlo Ourvea of
OlreoWWpled Generating det######*#**##*##.»## g9
17#
équivalent ByeWs WP Marine ln#tall#ti<m***#*,*# 60
OF F io o m s A m
(
F ig u r #
13*
P iA m a
}
T it le
pa#
Bwmltant %# and 3^erWa Foroe# o f
% w # U y llM e r #
iF ^ O y e le # a in g le W lo t in g 8ag& 3## * * * $
19*
ih e rti#
Ourvw fo r 1, 0, 3#!:
20 #
% # < W Tor(%ue of One Pyllndor of I|.«*Oyole
71
71
Eh#ne md lt$ F lra t % re# %momlo (km#<monta** 73
21*
CWnwlrnAm
22#
M alt % l^ t 8#*
23*
A # # 4 # # # iy * * * * # * * * # * # # # * * * #, # * * * * * * # * .:# 0%
2l|4
iWLt o f m>d#l ayatam#******#**##**.## @3
2g*
Bearing
Bemrlmg Rapport»*#********#*#,****** 89
26#
Btruotur# o f ^ d o l ayetem Stand#****#*##*##**#** 92
27*
motor Drive Arrangement#*.#***.***.#**####*#*###*#
.23*
Sjbaple ikmaonio Woti(m Diagram###*#****###*$#### 99
23*
0#r% P r o f il# # # # * * * # # * # * * * #. #. * * # .* * .* * # * * # * # * .#* * # * * # # 9 9
30#
B arellelo^am
31*
83Q>#rimenWL Wtermixmtion of Mment of
********#***##*.##**#*#.*$101
Inertim of Botnting Body#*#*.,,#***,##.**#..*##,lOg
32#
Experimental Determination of MoBwat of
In e rtia o f (%mnnel«'ArM Aaaambly*# *###**#********106
33#
Determination o f Mcment o f In e rtia o f
m e i ^ t a * * . * * * * # * # * ® # # # # * # * * . . . # * * # * # # * # * * # *1 0 9
m m a w Fiom m mo piATss
( o o R t lm d
)
T itle
pa#
m rn W r
3l$4. % # w m # of Bolt and
3g*
% a f t in g
o f V a r y in g D i a m m t w * * # # * # # . * # * # * * * * # # * $ :
3o*
Engine Cylinder %## o f MWel # Te#t
37*
Generator Am&ture dm@# o f Model ^ Teet 1##.#*##119
38#
iW e l ByeWn
39*
#)gin# Cylinder %%ee o f Mod<^ ^ Teet 2*#*#*.****!%>
1|0#
% u lv e lm t Byetem o f Prepellm r-* % # t 2*****#*,*129
L l#
f r o p e llw
1(2#
M o d e l B y e tm
k3*
Beemmno# Diagrem o f %ro#d
I3ire##Co%#led (W #r#t&i% Bet* **#123
% # # o f M o d el ^ Tem t 0 * * * * # * * * * * * # * * * * 1 0 9
*
M a r in e l m t e l l e t i m * * # * # * * * # * * * * * l 3 ^
e lth
V ie o o u e B e iq p in g # * * * # * # * # # # # * * * * # # * * # # * * # - * * * * * # # #,
B#eme of CmmDriving BWmnlem**.#.* * * ** *******:
mmm » m m m
a» m »s
# « #
WssÉme
1#
â t e t t s t iw » « e % !& » 1
I M s B a d » ..* .» . * . » • • • • » • •
2,
3*
9 )
#
9m w #
N W rn W L 'm ,# ,# ,**,,,*.*.# # # .*# **!#
% # # » o f Sis-C ÿlJjM **
U*
, *# , » . # # : * * , # , # * $» , # # 1 %
g*
# # %
% »#m
o f
S a g fc »
1 *1
P r in o ip l#
o f
o n e la a t i e
g y a ta m 1#
dlatwxbed fr<m it # poaltloa o f equilibrium by tW aud#m
p llo a tlo n end removal o f $### external foroee, en e lw tle
reetorlng foroe #111 tend 1x> bring #w eyetem be<^ to Ite
o rig in e l oonflguretlon#
The In e rtie o f the moving mmWr
eoted upon eeueee I t to m>v# peet It# o rig in e l p oeltlm i eW
wneequontly #et up the reetorlng fore# In tb# o ^ ^ e lt# dl^»
reotlon*
&e#e e lte rn e tlv e mmw&ent# or vlbretlon# #111
follow therefrom*
Oonelder e myetem o(m#l#tlng o f e me## euapmaded to 1h#
fre e end o f e aprlng ahldh 1# rig id ly held # t the other end#
% dls^laoing # # %m## in the ac^dlreetlon mad thmi relee#^
ing I t (Fig* D * vlb retlo n o f the ayet@m eon be pro&ioed by
the e le e tlo energy mtored In the eprlng*
Thl# w ill oontl«#^
nue tiro u ^ r^radumlly deor#a#lng m #lltu d e u n til I t fin a lly
ooime to ro#t a t It # o rig in a l poeitlon of equilibrium *
The gradual deoreaelng o f the # # lltu d # o f mteh a k lM o f
v ib ratio n reau lt# from the frio ti< n m l w elatanoe exietlng
in the eyatmi during the motion*
I f none o f the eneiw Df
vibraW ey ##t#n ##p aM d o #m #)#% lm W E W #^ frlo tio n # the
1*2
la it e gm#T#l am##
la # perlodia
#%Wi $4agp##W It a a lf la #11 It# pmptl^
m lay# a fte r # eerW la la te rv a l o f
##H#d tw period*
T *
% # #l3%l##t klad of porlodio motloa 1# # barmalo w #
ti< m #
m i# i a # th e w t i o m
r e p r o a o n to d h y # ie
# la # fo m o tlo n *
Gonold#' tbo ow# o f oa##d#gpo#*of*fr#W(m mymtmm ##
#om i la F Is* 1 *
%### % #m#WL#d w rW ,o#l% tqr #
aprlns o f a aprlng eoaatant k * la oonatralaod to mv# im
#,e
d lro etlo a oiOqT*
aprlns la wel htlo## aM the
I t la aammod th a t #i#
body 1# #prln$l##a la It^
a o lf.
«
/ / / / / / / / /
m
X
# 1 ^
Üh# % A d # m # n t# l O no^D # r # # - * o f,'F r w d ( m
l^y e te m *
% e fro # or natural e ib ra tlo a oaa be maintained by ^ao
#le#tl(Kl% ' o f #%e oprlng a fte r a mWdenly extemml force 1$
applied and roloaaed#
%e mathematloal ^Mipreaalon o f #ie##
3
vlbraticm a çan be dOriymd from Bewtw*# aeetmd la # *
Â#
d iffe re n tia l egwtl^m o f m tlm Wme the fern
am = #' k%
o r
m g e im — 0
(1 )
& e #em#ra% eolmtlem o f tb l# e^etlom
n r
% = C% e ln t /
be w lt W i ee
7k
+ Gg GO# t
m
Af m
eW re 0% md % ere erbltRpery eonetente#
A e ib r a t o r y m o tio n r $ # r e e e n te d b y e q u a t io n
e d a h a r m m le v lb r e t l< m #
In
# ile
(2 ) le
em ee #%e v i b r a t i o n
e lete o f tw parte* One le proportlmWL to
e e ll^
eon#^
elm t V ^ & "
having the mmdmm dlaplgw^mmt o f 0% # the othw la ppopo*^*
tlo im l to
B la e e
ooe t^ /l^ F end dapmWln^: <m the amplitude o f
e la t i / 3 ^
end
eoe tV k /%
ow
b o t h p e x d o d le fa m e #
tlone vhloh reoeat thew elvee eeo^i time a fte r an In te rv a l o f
time
T * the period# eu(h th at
f /“
- = 2TT
N m
or
T=27n—
(3)
V k
In o r ^ r to determine ihe oonetante o f Integration
aM
%
O2 * tW problem ehould be fu lly etaW d to # e e lfy de^
f lia lt e iy
at W
th e W
lt ia i
f o r ln # t@ m e e # W i t
in ltl(d mommt# W
o f eqolllhrlam W
BObatltatlng
m
t = 0
ma## la palled oat o f It # poaltlm i
and It# In it ia l velo city 1#
Im aqoatlon {2) glv##
%= %
dz
A# the velo o lty
% * ------# a t
t » 0 *
#
Baao#*
dMk
^
0 .=
aoabtltuting o f W # a raaalt# In equation (2 ) lead# to tb#
a i^ r o a a l w
^
/|g '
m = — — gift t r — # % 00# t4'uM
V% &
V m
*
(W
Otherwl##; I f the maa# i# palled out of It# poaltlom o f
aqulllhplam to
%» %
and W m mleamod wlthoat W L tla l v#;^
lool% # the fo llo # l% 03q>ro##lon fo r tW vlIxMitory w tlo n o f
the maas v l l l bo obtained a#
X a %0 oo# t / —
^
t$)
m
iEhl# apoolflo iB^latiom repreaonta am amda*##d free vlbratlom#
o f Vhloh Iho period# maplltade and It# natur# o f movawnt are
a h ovm I n
F l^
2#
7
X.
*2^A
Period ^ #
m d % e jW k liW d #
%o *
It 1# mwtomory to denote
4% * e$%loh 1# W m m
me tw nmWamI e lrm la r freqnenoy #md 1# memewed In rmdlmne
& # reolproeml of T le defined me # e naW»
per eeoond#
r#l freqi^eaoÿ^,
In eyole# per eeeoM# end ^ivem by
% n r
if
|îT / / m
ü
h
e
m
m
x
i
m
m
d
l
^
I
m
o
e
m
e
m
t a
i
^i
e
% e w o l-^ a t o f t w
nm ee
m
im %
m
a
p
l
l
t
u
d
eo
fv
i
b
r
m
t
i
O
R
#
# m@d $ h e m tm tle dm #
flo c tio n of the eprl% under # # metlmi o f the w e i# t ie
%
cT»
mt
k
W im m
k
s
m
cfl
R
r
In
mt
In e h e e a n d
g *
3 ^
ln * / e e e * ' $ # ie
m l fm q u e n ty # 1 1 1 b #
1
jê
f
^
or
2T
2
T Tr V:/cc Q
C j;t
fn = 3 # m V î7 3 T Z
<?}
SMm mlmtloR#dLp ie very uaeful fo r <^ek em tlaating
tk e m t u m l fm q u e m y o f e v l b m t lw
a ym te m # ie n
o f the vlb m tin g ma## 1# kiimim# and
tw
# e l# t
a ta tio defleotlon oan
b e e a lo u lm te d f
1*3 Bevi## o f Tomlon % am oteri#tlo#*^':'*#% e e la a tio aefor#
tm tlon in toreiom of a #haft m y be derlvea frcm # tr# i^ # i b f
mmteriài#*
Oommiaer à o ireu lar ahaft of aim^eter a
g#% Z # being WLated by a torqu# exiled at m e
* lenr
It
earn be ehoim tb at the e ire u la r meetion o f the ehaft remain#
m#mn^:5ed In #11 It# dlmenalem darlRg the t# l# t; provided
tim t the anr^le o f W l# t 1# very # m ll#
ta&e dia ram ^o#a in Fir;# 3# #ie etmln 1# given
1)3^ th e f o llo w in g
e q u a tio n #
« ---- ss I*<p
dx
i^ere 4^ Im a eoietont denoting the m le of WLot per unit
l%zth of #ié #mft*
dx
U -rdB
% # 3
%0 etroaa
a =
Wiere
% e T o rs io n o f & S h a ft*
# # In Ibe# per aq* In# # la f;lven by
G /T
G 1# t3:ie *m)dulue o f rig id ity In lb@* per aq. In* o f
the im to rla l o f shaft#
a: = 0 r 4G «
At the aurfeoe o f the eaoft#
Or
dx
Gd
—
2
m
(—
dx
•3
Wm? Wm s i f f l e t em&
£m?m i»
sââ »
#m@ taj® top#» aeting «pon t W #afI ts$
=J Q p f^ ê M . = 0 ^
T
Itoting # #
J m .polap wm@R% of ia«pfela of oposs-ssettca»!
« *» » 1 » Ia J * ‘
Ve^m
For
a -eipoBlajp abaft
a
n
â
32,
f »0
«
>
J»e
<
0
(
T
T
#
/
3
SÎ
T h e r e fo r # t h e r e l m t l m
W W em
th e
e t r a ln
#md # #
e tm e e
o f e W letlx;^ Shaft w lih in the lim it o f p ro portionality o f
#w m aterial la #ven by #ko follow ing eapreeal<m#$^
T
«
#40
m
OP
S
J
2s
= — -
(3)
&
&
®
f
e
o
p
a
i
e
œ
a
S
.s
p
p
l
i
j
g
o
o
n
a
t
a
s
f
e
o
pt
f
e
o
t
o
r
s
l
o
i
m
lp
l
g
i
-
9
a i% o f tâîO Wmf# Is
«a # * to *# ®
Is weesm -
sgy to ppoâoc® as aaagl© o f tw is t o f # a s h a ft @#ml to oas
» a ia a .
Hiwj®* i f i t I# d s n o t# b f k% » I t fo llo w s # * t
f
m
ss
@
F w
m e ir m l a r s h a ft#
I
J
=
7T ^32$
ird A a
mmmmt o f im ertla o f a ro tatln ^ body 1# a mwsmm»
o f It» propm*ty to ro s la t m y oWmgo In Its moMon proaioed
by mtomal aotlom*
It la# im ^'onorol# e x p m m W by th#
Integral#
V
Where
g
dm = me## of eleiw ntary p m ### in the body#
r = dietonoe of t^ie portlolo from an azlo about
# lo h I t 1» rotating#
3h m m ln a tin ," th e aW vo In te g ra l# I t 1$ u m m lly o w v e n le n t
to met
I 5
g
^
in 3b##min*.©»ee''
#tere r^ Im ealled the radium o f gyration end Im defined am
the dlmtanoe from the mxlm o f ro tatio n a t ehlsh the en tire
mmmm o f a body %my be e o n e m tre te d and e t l l l have th e mam#
mment o f Iw r t la a# I t ham Im It# omtnmliy dlm trlbnted fowm.
10
If
aadLm#
mozmnt o f In e rtia o f a body# # o u t a oentroldal
%o # i# knmm* it# mmwit o f im r tia # o u t
#%i#
p a ra lle l to the oontroidal #%i# m y W oal<m latM from #m
p rin o ip le o f p a r# ll# l*# x i# thoormm*
I
idler#
=
%
*
I t a ta tw that#
« 2
(n )
d i# # « dietano# wwm m thee# Wo axw#
%>r#i<mal Vihration*^*^% #a a shaft# fixed a t w # md#
ia W i#ted by applying an
torque a t #ie fre e end#
e tra in mergy i# fb#arted in the # a ft#
# ith ln We lim it
o f proportionality# only a very m m ll amount o f a tra in enM
orgy ia abaorbed by frioti<nmO. reaietanow during the motion
a fte r the load ie rm ored*
ed in
The greater propw tion ie etorw^
shaft ae en#pgy o f vibration*
Thi# energy ie av'*
a ila b ^ fo r expenditure shorn the torque ie remove4^ wad tW
torelcm al vibration# o f the ^ W t w ill be produeed thereby*
Oonelder a #l3g#le torsional pendulum# eonaieting o f a
length o f i^m ft fixed a t o%%# end and earryiiag a heavy disk
a t me fre e end (Pig^
i f # e d i^ i# dieturbed fr<m it#
position o f 0(p%ilibrium by the application o f an axtem al
to%*que and then releaaed# toraional vib ratio n o f the shaft
and the di#c w ill be produeed*
In m i# oaae the equation o f motion o f the ayetem
11
b#
by
# #
m m w t o f tW
r e a c t in g f o r ^
00# acting %»<m the # m ft to the re sis tin g torque owlns to
tW In e rtia o f the dlgdc#^
Por w angle o f tw ist
9
dur#
Ing vibration# W# m w m t w M ng on tw #haft 1$ #
hm:%e# tho oquatlm o f motion boo^mms
I ê
I
«
»*
<W
1# t w mms mmmt o f In e rtia o f th# ai#e # #
rospoot to mo axle o f ro ta tio n and #
c o lo r a t i o n o f # o
d is k #
1# the ang^ilar #o^
T h l# e q u a tio n r # r o a e n t i n g
th e
to r ^
olonal vib ratio n Is soon to bo the onalogno o f mo llw a r
% $ * I|.
1#
T h # % n * # lo n a l Om M Do r e o * o f % o o d < m % o t # L
B o # T lm o # m k o # # b o o k *^ T flo % ^ tlo n P rb b l^ a s # * *
MuKhers re fe r to m# Bibliography a t m# end o f the paper*
12
B qm W Lon (1 2 ) h a # th e
IW
e o ln t io n h m
9%) s
0
wW n
m#
###
t » 9 ;
9
»
#w a# fe r n : a #
fo r m
a # e c p m tic m
( 1 ) * hem e#
(ÿ)*
% ## I f
m # d l# p l# # # m m t 1 # *
#0 eo# t
/W
—
(3 3 )
m tM sW Llar wy# # # period o f tm w lom l vib ratio n w ill
b e g iv e n b y
2TT
f = 7 - ......
V %
II
. -
= 2TT /
/ i'
a
n
d
m
#f
r
o
q
u
o
n
o
yi
#g
i
v
e
n
b
y
^ ._ L _ /5 :
s rr J
I
( ill. )
®sis # 6 « 8 # ta t Ap@qwen@y o f t» s is a ia î rlb ra M o n is
independent o f the m p lltW k» but a fu n o tiim o f the to M io m l
s tiffo o a o #
I *
k$; # and th# mmont o f in o rti#
v ib ra tin g m###
I t i# tmderstood from provloua review , th a t the tor^^
sim m l e tiffm e # o f a o iro a lo r s h a ft i# d ire c tly proper*
tlo im l to the diam eter to the fo u rth power end invm m oly
p ro p c rtio n e l to the
o c
o f the a W ft* l# e *
# /
I
(9)
The me## moment o f in e rt!# o f the di#^ i# d ire c tly proper»
tio n e l to both the w#i n t end me square o f me M diu# o f
13
grratlon; l.o,
I o c
Benee I t
^
(1 0 )
be o&nG%#&od th& t & ayatea. cem &latlng o f &!be@vy
d lak attached to a lon$ aTondor ab& ft a l l l ea&eate v lb ra *
tlo n a o f #uob low er froqueaoy; g b lle & ll^ b t dlak G arrled
& abort a t& ff a b a ft w ill v ib ra te w ith & h i-h o r freg aew y*
a
8*1
v z m & T io iB ,
1$ $# g#a**#to#a that
imay be
eae#wüwKS ial#% G % t «aadW üby&dPeree bg& % B U ürb& b& ed o a & y tg r 18%*
*&&*%&* fo ro * ladaeed &n t&# eyataa*
%be y lb r*tia & #%&#
a&w&tadknedl le :ped&&r%H&& 4%> ae .f%q&e cnp %#ü&83#& IWf t&w* iSdleM»
i%io%w&I 3M&8l8taaa&e 4K%aj*Sli%5 dkapiiyg t&wa
jU * eàwPuBW&& 1%>
ba ae& llg lb le,
1% or&er te mtgay toreioaei vib#*tl&&e# I t la advladbl#
to
r& a & e e tb #
a & tu & l a y e te m i a t e
« & e q u iv a le n t a y e te m #
la
general# any &##&BgemeBt o f rotary maoblBery found la eagl»
nearing praetl&e eaa be reaeonably traaaforma# In to a alar la *
ma#8 o r maiti-ma&e torelonel vib ratio n ayetem#
%be#e ala»
p llf le i eyetema eaa be tboroa0Hy an&e&eto&&
to r iiy worked oat on the b&al# of the theory o f vibration*
IQy ualBg the an alytle method baaed on the theory ooWblned
sdUWb IjWb&rajx&ry 03> fladül eagwarlBWHBta# i8%e ao]bitl<8& o f id#
%HPGbl«aa ean %»* a&w#a#aa#%fliy (^ytalüw&â*
:8a the ]pre8H8%t obwg>*
tw&r# ia%8 jhm dkLaeadb& la <%f tamaatdbyg t&wa iMH&asMwl agnateoa; alJÜL
%M& dé3pi9i&& @a%& <%L8e%w@*edLk
2#2
Oae*aaa8 ayetem,*##! ayatem eonalatlag o f a alagle dldk
attaebed to a abaft* aa mentioned In the prevlona a rti& le o f
Ig
reprement* the simple
sya&ma
i3JL*%r^Kps;%%*dLgCl gM##LtjL«Ka t&L&adbi llet **%%4K%gp%*aM*#*ia)%t
Î&) *
iab*k
3WWB*#
lagr <%aaa IbM»
( 1%)
][ it 4» 1&%4» s; 0
/ / y / '// ./ ' / / / / / f / /
&#
IBkwe iBogp*»
3/atem*
I0a* ir&b#rbloKi la j& tuap#
aacw&le laotdkaa* Bbw; a#%dll4MLtl(m odP t&w# aK&dbaB%&@#& iBg&adka&**
%aat&w»& 1K&11 fc&sa a lyargr BKM*gGd%&I 4boo& ftor asKlviays t&%» idtbn*»
iüLoa 3pro&>l8BüB*
%dyb tcwa irl&aMktos*r
%w*
#%a #w##&l&a
# # #a a la 4 )a t
I t fo lia * * th at
e
#
at
4%*4A a a la *>%it
# 2
t%y
16
tÈ^ss ia te
(13)» I t glvaa
«■ 2 Éü^ 0 <*■
= 0
ï t la aw n th a t a fta r
i'sS)
usa o f &##»'
Oaaeo smiWd# # » <Siffs»aotial a#mM.oa o f rastlon Woœwm a
sfepla algabrai# © ip ati*» léiidh ®an bo soïw d by m M i m m »
tio a l troaim m i#*
BVom équation (Ig )
a>B -
mâ
fL
*
ï
----- " /——
2 T%/ I
ghow&ng tb# value o f k% * tb# êprlag @#8#%#at la tgeai&a 4%f
thé eb&ft an#
I # tbe maa* momeat @f la e rtla q f tbe dlak#
ta%» %%&tw3%& iSpeqpa&nagF éawi be fowBid jüpom 4&guwK&&c&i (3dS).
3#
ta# BW&aa <%f @8&aft :i@ %%>t sgag&j^&ibika* ia%* i%t#ua%c& a&M&gpKM%ey
edüLl IBban (ïGgH&Qd aamriüky cm t&w* aww&6 swamwM&t <%& iiüKPtdUk oüT
18%& a&kKft*
*%xp tÈw) B8U&* sdT düu&ft %a%y T&e aww&e !%y
iwükli%s laübo aw%B#%8%t 4Èw& mBw&a 3#%m9&rt od* laaMrtlaL iof lQae <&l8k
tG%9&tkwKP %dU8& %8&* 8KW*8 BBameKdb o f iQ#B4&i& <&f tÈwe s&wift jb%
SMülTdbyg t&w»
ilt baw* bewüB aüü&ted 3%reidb#w833r thadb
aeuM&ed au* t&w*
magr l&e 1M&»
<%f d&aw&&p#tjüog i&M* *t8%&&a <w%argQr bap**»
t%> &# aau&GtdUa aysüWKB
au* dljTbarbedb
It# &or^KLtlo& <%P cKpalIl&Bü&Bm
3BT #&&3w&t&<8& il* aawnamedL ibD b#3&&r8K#dl*, law*
jbüKiüOKKgr 3B&y i%& fü%8%& l& *t *lB@du&]M@%#BKr ftü&a enar y oooudi#
4&e**U%&08ab
3h iWba ftüLlasdayg awü&egüü&blc# 18%»
<#P tb#
SB&&8 dur aTàil: w lIl tH) ta&dU&g i%ü%> meaKmant#
3A&P afiiüngie <%f todU&t
b&eqww» &m
tgr d#
<t%r%%y2ipih%Mdk&@& 18%»
* %B%& t%w*i9or& <&%&& (%i :LQAB%ww»&8# 18%» tmdUft
i# *&%&&
%&%*&
#
%b# %%»G#atdW&l eowBnsy &%%the a&w&ft
*w& @«w0ü» *
F.S» - J
k$e. m
a»: klastie ®ne?®r .#
&#
= - ^ k ^
âmstmmt la
K*B* s —— iJtl?
2
#%p@
la the
w lo o lty
Aaaaja® ta » r» tio n ts b»
as
# ■ ô® s in a)
tb «
^
#
“ i r
“ ®o^n®o»«dj,t
d#
a
»potanîstîkl m
a
r
g
yt n
s tra in a w % y la
iS m
& xM v«m
poalM on oj? #
»m a d m &
i
.g
f.B ,)
H
2
h
©
k
im
t
iem
e
r
g
yis
n
m
t
m
lp
o
s
l
t
t
®
»
t
h
ev
o
l
o
*
e
l
t
yiss
a
s
t
e
a
a
m
o
s
i
as
m
a
l
s
to
f#
i
@
k
i
n
e
M
.
®
m
m
r
g
yo
f#
#
a
b
a
f
ta
n
a#
m
to
ft
b
sa
iA
, 1*
0*
1
2
L
2
IB&e
% 4 a) I
ad»
*&t aagr
<%f t&w* #hadM&
iWbrqwygi liw* le%yÿB& 1# ipro%KMPt&dRMüI $e 8b* dL&ate&ww* f^xsa t&wk
jr&%*d 4##d# 18&* a&yg&lar TM&lowdkty *&
% jRpomlBa#
md m wt b#
=
Urn
I
IBs* Idüa&tjüB 4*G*#%gy o f aw& *]k8a#at <%f lÆQ%ÿ8b (be , cLKataad) %
j&pom i&y& fljB&d dw%&* dkBw&tliyg I@ i&a t&w* iB88a&T8 of in@%MKL&
o f 18%a VÈWÜL* a&w&ft* 3U»
2c,»3s» ==
jk% )
2
6
^
6
jawod IB&we iBCUbatl, ïdjOK&i&&<& ewGSKpggar <>jr 8*%* adbu&jrt; 31» IBbwami
E*B*îïÉîa«s *
2
6 *' o
^
m
IBbdLa;
IBbwadk ta%@» aaawKa saKaaBBi&t <%f jüo*%%»%aiai <%f lïkw» «GaawEMk la*
iagrGMBBs&iaak&jLar #*qpajL#%*]Le&%$k ibot <*QM»**tl%3Lp*& 49#
awüzaa jWBX%taod&
4&%k jESfdw» aaacl oüT tW sGbwajrtk*
]&%
%
%
» (l iG<>KU@4Ke"*SktK%1P# *%yi»t%8S0# 1ÜÜW99P4KZ%%ee%,
aL\,» "
3&#3%4i )di8%s
% erefor$j
à .j= _ 3 *
%D * V 3
&
* - T = - /—------- — r
(%o*QSM83xÊjaag G&K&a; iwdLiaai tas*» 8Kfw&t;&9& (3k6)*
(17)
31» (üGMfjLoRaa* lü&iajb
ib&ü» «Kfyr&olb ûdT 6&%e aseuBB; (OüT a&aauEMb aawssr t%k IbadkBBCk jLK*t%> i&oqpo%*idb*f
iWr laahBw&Nwsfirgr, isgr atdkSjbcys (:%/\)) I*, 4%o 3^% jESap I jka é*&*
oulatlon*
As a g eiw m î r a ie , soggeatM ï f Wilaom,^ the ma## o f
:2*
2kBM) laym&CB&t# 1)€W3&E*
20
i&C tb@ l88g#&(ür
the a&wd^k 3bi fe a t aaajd#üUb&& Tby th# i%%N#WMagy la vi%#mddkN&*
p e r a a e o n d ê o e # a e t &%&&&&
2*3
1 *0 0 0
*
TgowObae ayatam#**» & almpl# tmowme##
ijL j* !> * (K%B#jU*t#
eaw&i oüüL
9L SLangÿWb odT
dbeaa &&
idlth #&]ba*Rry cULak «dk
]&& t&UL* 4WW&G* akf tÈM» ai«8aa @&%» a#üf@a 4t&ap]WM#**f
m08&8 &n o#ro&&to dlreotlon* eaah othar ma& th*& rel*a@#&*
th# ayetem w&ll b# pot la ta & #%&%* o f t#r@&8&al ?ibp*tlo&*
# lg t # ^ 3*0 ^b*o 3y#t#m*
equatloB# @f m&t&o& for th* ma$#e@ 1 &#& 2 #ft*% thay
are glvem a ai8pl8aom#n& o f
6% «ad #2 * roapoot&voly* &*a
b * g& lttea a&*#
% ®2
*
Ô% » ■#2 î * 3 bÈmc O t
♦
%
*
ftj. > » 0
25,
üaiïsg fcô
fowa#
2
f
3 = 0
S w matüpal fr@#iomo% mmy_ %» fmmd ft*®a
(13)
â é ts m te a a ta l
swpatieaî»
k% •
% ui ^
• %
» Ig
'- %
(19)
anâ solving ît j
1^ IgiW ^
*
kjjÇ ïj^ *
Ig 3 ® Ô
(19a)
5
M
al
at
o
©
m
m
#
@
f
v
a
g
w
m
m
a
y
e
#
m
M
o
n
*
$
i#
, Im
#%
@
$
W
root fo r
î i.a .
%
u)
*
%
w
Paa*/»oo,
% %
# fte â lîy » the ” atarisl
1#
h
=
•sfcerè
k<- *
gIT.f
(20)
*
I,
Ig
'
(21)
J 0 / 2 = te»lomî riflcllty of tfea atoaffc.
At
In a ta at tb * dlak# &t aaeb
*111 move tbpewab
d iffe re n t en&Ml&r dlaplaeementa In eppealte dlreetlane to
@eab other* ao th a t tb er* aeat b# a point on the ehaft a t
Wbidb no tw le t ooour#*
Sble point 1* #&lle& the node o f
torelon&l vibratio n *
&b# leoatlon of the node ean Tbe deter*
Blaad by &8#wnln$ two almple one ^oaea aymteme o#
ta ra i fr#g#88&l#a v ib ratin g with reepeet to the aame flB#&
point*
I f the dleteaw# frem eaOb end to #%**%%&& 1&* 3^^
an# &2 * reopeotlvely* the relatlonaulo ia rea& lly dbtaln*
e& &e foiiow a#*
%
%
<22 )
%
kt
0
% a) ^
#
% 6)
0
%
*
or
%
a
X
.
i g
c A
j L
^ ,
% 4
4*
#2
^bl# equation ebo## th a t the ra tio la independent o f th#
e&tero&l torque*
If on& #&ak has very large
of l&opt&a o&mp*###
%ltb tb&t of tbe otb#e* Ik aoted from botb eguakloo# (22)
8B& (&3)# tbok tbe Bode e l l l be eltaated very elo## ko o r #
even &k the lo rje #&#k*
Ibe oï&gtlG Gurve, ahoen la 3i&* 6 , giv*8 #&&
cuda d la trlb u tlo a &&& the loo& tlon o f the Bod##
Tble 1#
Iknoüa && tbo f lr e t modo or on&»nodo vlbratlom *
± Op
te.
yi%# 6 # Defiootion Diagram of IWo-maae dyetem*
T^o oorreot^o? for the maa# of ab&ft oaalbe :r&&Glby
addlnj ono*thlrd of tbc naoe no .ont of In&rtià of the eor*
rogpondln, »ortlon of mh&ft on each aléa of the node to the
m&&8 moment of &Q@rti& of tba dlak at eaob en# reonGetlvoly*
1 ,0 ,* ewbBtltutl&g
1% + I* &%,/ 3 2^ for
$
beoomoo#
aa#
3b8B tb# natural frequeney
oh
l
o
+
%
2*%. 2hroo~ ^
o lü t ln ^
of
a b o r t in g
lo
do^o^od b y
T
I-
%
■a
%• I
^ almplo throo^^aao gyaton oon*
30 c t o 2 ^
show n I n
1% j
%2
c o n n o c to d t o o o t u o r b y tw o o o o t lo n #
y,
Tho m om onto o f I n o r t l a
a n d Sho t o o
s h a ft have to r s io n a l r l o l d lt io a
k t%
p o r tio n s
# k %2 a n d
'O o t l v o l y *
7 * Tbroo- aoG 2ygto%:.
a ro
o f th e
of
âiatei W glwem m m # « # 1 » ■âiaplao^wnfcii e#
fg
SÎMÎ
#3 ,
M le m e a #
tsm b# p m & w W
*
v lh m t im *
@m ««pm tis*» o f
mig" b#
wdfcten #8 milmst^
%
* ^ jIC ®j. •
& «2
♦
î j ®3
*
«2
#2 )
*
0
» % 3 +
( ®j.. ■• ®g )
%
-
) » #
*■
0
#® tapWomm# fom##
•
~
-
*2
)
*
0
®2 * A ^4 *2 - *1 ) *
®2
s 0
-
®3 l t
-%2< %
■• ®2 3
0
i
sa
;
?
:
a
i
n
‘
«m
f
eo
fW
m
o
g
m
r
n
o
n
s
e
q
w
a
M
m
m
t
u%
»t
g
0j
asd # 0 a a t« 2*al fregm eaalam «% bîiosa # il# . W #
o
fe
o
a
i
f
i
o
i
o
a
t
av
W
.
#
*
#
*
0
’* # " % 2 **
0
* lc*«
«©
26
5tee fr@qu8B#' equation
h
h
% %
h.
H
la %
h h
oi,2
2 ^ Ij
%
.%
%3
4*:
2
J& (>093%p(%ndl<k3%t tssgr (sf* dBtt&Rpgrjkny» (%urb tabdli* lEq&ao&i&Gi jl** jpap()t#a)3Ly
ika t%aà8üCLf&t%» taoK) 3jidI3k9^l(&BWi3L tasâNt
fTiiajbjLo#
4%Gdbü;i%ljb&:tdli%8; jla&t*;
haa IBaeo %»ow&iL ]p<keK&a*fj&#wo&i <%jridk&iJQ&i 3P*»#
33%*Gi8(Knr&2* (1 4&Ulj%E%*sN3#%|; iacw3a*
ifaübqsaLtdlcas*
SSs*» :lcMgR»3* jPsm#**
cguw&rwgr (S^Liho# 83%*» jTSjcqat; <>3* jriünaîap2*;**t4&3: sacnaa» <)ir
9abjll.e tab# ]bdlë#bw;3*
igjLv%Sf; Ib&k# aMNKMadl smcwa# lad* 9dLt%%qi1&*x%Ki
spjWB&t ki90 aaodb&g* <)%i Lrio <>las.g;t:i<> csaafVi»,
C%&«w88?srija3g %%
&&
iGdL<& <3&&eir4&*, tabus fyL%*sHb awx&it <)f ir3wb9P&t:lOBi ()<%c8a%%e %dbw&& <]&adk
Ü&ké
jbBi sKoa*
sdGdLILadk %%&#
Bmama# %#*# la tb c oppoait* aireatlG n*
1ÿ*R*
%b*
eWB#* %b#a tb# 4%#4m0 88aam# a#*# la #8# &&**##
t%l#a tdbiülftt taba» cw&a&wms* saaww* 3aN9iN&& :%
&& t%2w* og;%%)j&jLtK& 4aülaM*<f%dla%Bbp
10&M» tnec» <&]L
<%W0P1F#N& aaesk g&bkoiaa $ü8 #31%: 1F& awcKl ?%%; tabw» :&#*
# f %h# B&é# Im e&db #&#& ##& b@ &&t#aRta*&jRm#& iWa»
ex#w###l#a f w tb * ra tio o f aa^ular ai*plao@m&8& * t # ##****
,
m 1—
*^3
.
% w »:
..o,
ai
%
■ %
%i
Jeta
+û)J^ ( - I f i J k - )
%
(2P3
fctl
B
®
t
a
j
_*
1 t
t
t
i
*â
i
B
Î
M
t
e
e
®
0f»
ô
oA
s
at
e
»a
t
a
s
a Ï3
{ï
?
l
g
»f
a
)l
a
ï.% m
Ip I
^ --- 5
«3 -
(30)
«a
Pbr tAo t#&*#84# viby&tkiR* tb# dlstaamo of go# of $b# god##
from #b8 #&#B Z% 1#
by
* i^i—
^
«1 -
3
&2
th#
of
oth&r godé from %h# m&## %g la
l. s lp (--------- ^ ------- )
^
&3 - %
32,S BkûLt#fdgaaB&
(30b)
%%w» é4B&&tdkB& <&f
j
%
%
p
a
w
a
y
a
%
r
a
t
#
&
b
a
m
r
t
B
#
i
9
0
3
%
*t
b
a
w
a
%
w
&
*
G
*
w
;o
a
w
a
l
b
#
*
&
@
t%
%
p
by jB&3Jk&8dk%s $8%» %*yBbà%& jtw&G dk&*aaüKb#d* t&w» fSM&gwawaéy 4Hgwa^»
tleo B tb&8 obtain## w ill be very #gWbe##aa&*
& good epproa&m&tiga to tb# fwBdameat&l fr#gB#n#&##
o f vibe&t&aa o f tb#
*yat#m ##& be obt&&Bed by ip#»
daolgg tb# a o tu ai eyatem to am eq u ivalen t t# o * o# tb##e«m&9#
a y a tw *
Aoeordlng to tbe et&tememt 1& Wileaa*8 book# I t la %#* dw&tood that# #be& the magee# form & ayatam&tl# ayraagemeBt#
#uob &8 #&»&# found la maelB# i&at&llatio&a# a le e trio a l goa*
erati& g eat and auto*tran#a&e#iOB myetem#* i t may be treated
In the follow ing #ay$«
A) OomblB# the eloaely grouped e^lne
to form & aim#
g l# heavy ^ a a th ig h lo loe&ted in the m lddl# o f the grogp*
B) 3bka thla re#ult&nt m&es. or
to*,0taor with the or&#
glnal heavy m&#&#8 Which are #ep#r&t0d from the engin# gragp
t
of
o
r
m
&
r
e
d
u
c
e
d
t
h
r
e
c
M
m
a
#
#a
y
e
t
e
m
,
g
h
##
p
p
r
o
%
l
m
&
t
#V
#
h
&
*
*
o
ft
h
eflr
e
ta
n
d
.e
e
o
o
n
d
d
e
g
r
e
ef
r
e
q
u
e
n
o
l
e
ae
o
n
b
ed
e
t
e
r
m
i
n
e
d
aa already daeerlbed#
G)
Doing th# game way to reduoe th# equivalent thr8#«m&&8
ayat&m to a
gy&t&m* the fundamental frequa&ey may
t&GLlOuJL tecL#
(^aiaaipgililgr, <&aa*e aiuuai/ Tbi& jt@dk%%B 1>ct
ft)**
the d iffe re n t* in the mas# momenta o f ia a r tla o f two u n lik e
maasGB Which are transformed*
In determlnlBg the equiva*
le n t len gth o f a h a ft fo r the two-m&a# #yet#%, I t la adviea*
v ie to onauro
fo llo v ln - ro ln tlo je h lp { P is* 3 )$#
o
à
I,
o
o
0
h O
1^
L
Ô
i'i
,
3 -
%
»
%
/j
« /
E q u i v a l e n t Two*» a.-ul Æ ir s o - îla a s S y s ts m ,
♦
%
1
h. *
D)
I)
)
(31)
%2
quote from & ll#o n*3 book, itu a a y be concluded th a t**
I& oaoo o f a d l^ c t*c o u p le d e*oobilcm l
e r e r a tli» &et#
are several equally epaoed minor m&a#e@ connected
30
thpou h a dhort length
ah afttn g
aa# la rg e
imaga#
torglonal rlg ld ltle # o f varlooa aeotlon# o f üb&ftiBg &a
the Foduoed ayatom la iBoroamod du# te tbo laoeoamod effoo#
tiv » len g th o f the gpaeing#*
& *lo #e# OppeoËiB&t&o# to tb #
fuo%&i#*&alMkl jh»ocpH%o#%r <M8& tw* cüytüjUmBd 1%y
OdT t&w» SKMP*
iE4&3Etdl<wa aSowstKMp; tübw&i; :&#&,
f * . #
#t0*c
t /
(3S)
z
jf
#* ju3L '{&*; 3r%*QKaiACM%(;3r (talcBWlaitw)# l&gr tswckdsaawaw# sagaSÊSodK
jp*
** 4BK>3*Pl)€rtW»ll jP3L3M@t; jp%*cpT%%#*Bwogr
2E
i#F<%0QpimEWBi%%ja2& jPawfto*» mdbdlid&L dk8%*G8nw&** taBwama t&agt
]Q%%8db*K%» (sar sadbcK)** aaauawKM* #w*
BmW r o f
# m r %eee#
1
2
1#00 0#93
:!][)
3
o*m
0*91
$
6
oo
0,91
0#91
0#90
Ill 3%&F%G$»an, j&jf "Bbwe t;2%&i&8%sl@afi.4&%% i&tBBüPt; lietiBgHBBs ;& sasiSltjb*»*) i~*rfk0 fLTKl t&io ^&2^l*ren aaauo&iSjBd» jla* veKpgr sawoe#* 38K%Pi&'
flLsKxjlbCle ib&waaa ib&%8 <xnwf3j&*) i03%a&i&:8ii&j?i%# @n&<db aw# t&io #%3n6i%8M&(püP
dL r*a:p^hfW3
tJ#* :2ï%ji]fU3K>rtütTL jp%M@w3%B9a**%y (waai 1b<) (p#»*r
tüajbnodt jp%%%2& iBbwe %%&<%
ww&GK&
much orror»
ib&ac%Mh,B%8j&@ a*3n*i&#a
Wb&n the etlffo a## o f the traBemlaalon. Wbmft
la tneroaae# in e#mp8ri#o& e lth
eh&f&f a* in the oaee o f diroet*oo#pled eleetp lo al geBermt*
eet# the erro r introdueoa by reduelng tho aotu&l eyetem
to a
or
system i&
3n&I)
;&& @8gr. QaMp&na&B8#&t (%f
Tdübrâdü&on agratWB& tbanp*
are 08 many pr&Beip&l mod** of vibration &* there are epaee#
beteeea m%*»eo,
Thorofbro, the tBD*no#e frequency ean not
be obtslnod by the
methodz ##& & th#8#Mm&#8 &y#t*A
will ]&ot enàblG the fr^ tenqy wltb:m&re t^on two node# to be
Bhe tcbnl&tlon rvtLod o f dealing w ith tho:multl^&a#8
#
l8 ocn&ldored to be & b e tte r w#y o f &az^yl&g out the
frequency eaieulm tlon fo r eyéteme w ith many maeeee*
Beelde#
tb# Bbre e&aet eolutlaa o f tb# frequ#B#&e#* I t give# the re *
la tlv a amplitude# o f vibretloB a t varlou# ma#@e#* on Wbldb
the determlnatlom o f the vibratory etreaao* o f the abaft
ayatem eaa bo baaed#
*>.<5 ChEKaamBwl Z&jnBtowsL******
ojp
,*f>diPodl agrartKxaa <%c%Gj83u8tw& (%f si aw&s+jüaa;
3üt1;w&ea%&(%-1*5 tp**9 »<%
%
* tagwe aGüusjPtaaH# %dbjL<aki
~a#3*od i&L%reiBbk@9r a&& ISkwadk gHSjpiivLlai oum^rwl*#' T*%»]uGH3dLt%3r <%f 1%
hwB asaw*"»
Yfecisi 1M5 afsaugMba) g%
%
%
%Ibt; o1>i&GLi238M& l%& l&qaa&BGÜlt; ip<&cBajl%*3%& txaipqguw»,»
93k%& d&8rb<*3%BKliiiLtdl<%Bi <%f IS&kO i9c%Ky%3Lo9aa&]L
câïSKeq&<%1&80P"»
jtetüloa odP 8iw&% (I lagrartaBs !L<& 0K)%%8dl<&c^pt&bl3r 8:lB%puljLl'l4#dl itjp t&&(k
jaot%%&l iagretBBai ilas iq5%»]LadB<&& Tagr a d^ysssGBdli&BLlJlsr 49<&uiliF;kl,49%%*% jggratKMBi
<>f j&ab%g)l8 f-QORQ* aiet
I&3L3L as&w&jPI;# aaodl saaawgww* ]p<>tw&i;@r
tdbü» @
w&8%# GPgH&ewdl $&# dlKt labwe «%&##* <xf
#*%» 4B&%%%B3K@
8awB#* adLtwrpLok
38
(Kg' <%o%%9M$iPl%&:ag% 18%wa
j*gn*1b«aML
jkadbo jll&B abrujbM&ten^ i&gnel&aRa 1,8 gwRSMpdLawS cw&t tlet T8%l3ü*8MüL*a* 1#Ma#R#
3Lts i&IJLl laet (%uw&tB#d ;aa% !)«klja%F$*f
awh*8âiB@» tl%&
tR8H&ta& tNB %%; aHbjkrap 48830%a/#i I8aw%t ailJl t&%@i ibogp**
8&<%CW&3L :P3j»3KiÜbdLI:Êj%y 31$ iLÊ3B3LtW*d& I# tgsa) j8&%ëifi&6i <%B&3F*
39bw# ;&#(»*
p e rtle # &f the dya#ml@8l%y eqolvaiaGt 8y#t#m #*& 1b* &##&#*&#
Aj
B^givm iaat
Goswsld&üp t&w# %dbG*idL* sRserir <wP m apotaWktPL laadw#* %%otdb%& $&%&#
:: ** BKB&eiüb odT i%Maptdk& cdP %Kü&8tdüag samaw*
JTZ 4# r*>an f&nrriiaa* vgdloodUby <%P 4&%& adbaiMb
j# 3P p 38 GdP t%w& a&kaft
«bac
E *B * #
3 /g
{
in ^
Î
fl c*e s
m
£1%
iig
%
93hw& %s&0KSl;&& (%r*8qr gr
Ix& 6K)*»2;tkir*; jlsi ci
i;%t3bSH9&i%y <*%» iB%&à 3?çy%ü&i;3üB%5 sppüsawGl# tdüwea&odftxssa^#
^
h
. (-5 -1 =
%
%f %&gp&3;e3&]L0üRd% 4k>3MNJL<XBW%3L jbüLggi/aiigy «W» 2%byadPtw##
<}3r t&aa& «mgulmp
33
3h# a tm in mmfgy ©f #
1
f., B$ * —
t
la&waape
issftas* W .# .Is
a#
%
»— kt
2
Té
tP
** aaswaaa
In laüuB isbwajptt
<>
**' 8j382üüLâ&i» (13uà%%]Lad93«5&8Cït; OjP iBSüé ia&w3jPl&
3&I; ** iL<%k:3]lcd3wi]L SfjLdl&Uhgr 43dP &&%
8k aGtit*Mb*
aBck (>i%i4K*p to
tBsdlsi
#*f%S3«g; iMB&aüLijgkdl <&eROSilBa%%*t #*#&
(ajL#E%ü&*g8%; ;s:)#a]Ls%p imeflfrpdljbijeH*# j&$; jPstSjlc»*** $8aw&t;$'*
.(-5 -)=
gtlaae#
4*2^
®2
XI2
i m
^2
0)
%
Oqulvolo % 3org&&,
ihe power tran aaltted la shaft# la
fewer
iv#a by
# .f jTl
Od M
Bmm.
“
%
m. *,
mi
A
3&W& «übgpl*
g3N&&#Gt #&& 3ba a
geagp r$M&A@*»
tâW%& $ü*pa%y&88%8%&* (&@a T&* <w&8i33F 2<w&2<w%& t%» #& (&gqjhf&lde%&
1&ïi2'CH&;"8aGW8w&
gdt aatwGfv*)*
l33r
iï/wGHB# :B4BdltrtdL()%ied3d*i}a jÿs&att aaaoodbuLcKBt*
33bw» #hg9a3Lif*L&3KKit sEgBsisgesy» jüB, tgKü&jBkt t&wGt ïaskawaw&i* laaadi
383uajM%& aüp<* %%>t%dbJL 4g
ta%e ;84%B*& sgposedL, (waaa 1&4» taps&GdBw&dl 1%gr
t8ba :2*&iskw%&&; 48*%au8a»3Jb4&(%ipaFSüw^&CBBwajLgr aicwa i^aa* Kwaiguwpstil jpsmBkgsüBaa;#
cdl4&6 <&a8& %wB (üBüL&nJÜL(ii%}(I jPa&oaBi 4Hgt%@L%dlG&3*i (SSIT) aüàd (32**)*
ï9%Lg&* gt 48bK3i%* <k i*]ü%*)3U& ëpNKr&d i&9PQh*adsw&3rt (gfatweai jaikdl 3Ltw*
$k3iajbf3i5j&%it iab8*e<s*4sw&j&st ag;i*i>8gs :&%
%isawsK» j&]LI aüSw&f't** ià%B& «smaBaww*
ara :p<rpLl&eKM2 Tbgr (3wuna%Lil<%aLLi;y
g03aa%üb3Ltdl4k8#
lll& a te à tla g ^bampï#* # B e fe rrir# to J l/* 9# a#Bua# tb#
a&CUgsü&Bg ir&l&wN#**»
-«
38#b& t08#*&a# #&&**
%
-
19*80 t# 8 # "ia * ##&*^
h
*
%
#
h
'
% i «
0*26 &an$~&a* 8ee*&
21#60
18*000 to n #*lm */*aa*
S
7*000
%
•
800 w *
]%
#
600 rpm
&
t 2
800#^
%%%» Q%K&cli%&l asy&tKBB la*
3%Bai3%&lo#d5 egnGtg&i &bKH*o. iuu
%MK#&a#K%& %gr t&wa dgnaamüUBallgf
SMb#jU&
Wb# tgcwMl odP
9&1 aG&aflM* aewl üa&maaw* la* aawmwBwwl ta b# 2200 ippoi#
35
Pig* 9 - Simple 'rv/o-Sliaft Geared System.
(a)
tb
(b)
Pig. 10 • Zbree-Shaft System and
Its Equivalent System.
C
■B
ilT.
d
r
-'tb
*
■tc
II
■D
O
1:
(a )
ta
(b)
I.
Ï
« If.
C— i - | ' >
# ;? t,(-
i ----- — ) 2
200
#:
toro-^iri* OU'.:.'*
* lo
I*
# %/+2 + 0*26 ( -------- }^
+ Is
s n i*5 *f
t%i 3B
&6K&,^
*# 1LG*0.JD
; ,,
“tb • “ta
#
Ac381y
!
^ 5® • Taw
!h
— )*'
200
6':#800 to»#-*!:;*/??#!*
oc^i&%dk%3 ( 28)
:v . *"
, :-----: t b 4,»—'— —#,
I
24
4^, # —
1 -"---^ . -------"
- , —:--- -—
3
tn
#
i%g i%T_, » 2. - > m •;
IA *0 %
*
72.'
% ♦ % + Ig
21*W
7s
»
:n..-'
'"X)
1 9 2 .6
?
777,6 X 1
s 0 1 , ; T JÎ 1 9 2 .6
#
» 32.!; 4. 2l.':Si * 192,6
13: » * .’•■>
„
Sïiô»A-
îa-'xto
U)
1
m—x 7 3 0 7
** jK36 <%*
1 /.
.2
’ . 777,-' y. log
* — ji 7307 r ----------- ^ ---- :— ( 2 ! 6*6! )
aJ
ij:--> 3
37
a#
2*7
#
<%)4a/ 8TT at IB )
9#
s%>8 <8a&,
gb%MM&»3b*wrt aaai iuH%L"d%w%f% Gk*&e*&
*0badM& 83M#k@m i&ofWKletdb&a
t&QN*#
t&WM** aa&afl8* a f 4&13y%er*8i& txgp*
j&ldkw&l a#igjkiltl4&8 sdUdb adbt@w#%ea !8&aww&8 aim tw» r%w&&QWM& $«» iaa
*KB%&9%L&a%db &%%w8#kw&& #gr»%%w8 las Wbdkdb idtl idbadM&e @aa& aakeesM#
lelt&i t&w& 9@aa# *g»e<H&»
:Plr\» 3# ( %>* 3K> ) #0&cmM* t&w»
lp%ae*g& 3%>#m <*f t&w* 18%pa#&**&wwft aoratWRa G&wa 14%» *Kpal*%dkeBd;
(qretwaa#
$bw& 3pa%%}&%4KL*8 <%f 4&%&
agnetem jWbCMBa *&&
B^Lg# 3W)bt Bblidb 3U; awwfW2aH& 4%> ]&#%%» t&M&
odf
%
a%
&3r !)3> <%l)i&8L&*30Mai *kat
:(%. 4* :!&
H
•
% (
%
#
%c (
%
#
%
f
♦
% c % /% f
*
% { Mo/% y
^Ss
3&i%& **
*5(83 (
kibjt I"
asiba (
*%
&%
#* 4»qfou&4K%JB33*i ()**
iBiiy, ]bsr6t%%jQ(g
j#
xawgpF 1>a
la& t3ba* lawaeadl
# *&]> **%%& #%, 1b<& t&adt j%%&ggl#e
&t% <%c%piPG&9g3*%BM3jLi%# B%aw*w%Gk# * :e<#«gp4;dytK&iy€CK3r*
-
©I 4*
®3_- i|^ }
«0
-
«2 ♦
®2 " %
)
*®
®3 * ®Î4- ^
•®
• iEg*)^ ©2 *
A\ + % l( % ” ®1 ) +
*» #2 %
®î|. * % )
#0
(36)
g&# %#fbu3W& #%M&ga@Kw»l@*i #&3UL be j&OM&wa ftwaa#
k^ •
0
0
0
k^g • IgA)
0
0
0
-
‘
#
- k^
• k$g
’
Q
gSkwa j%ey&(%G%&%&egr
%
8a%
3P laat <)*)t%&jbE%9wï
% Σ % %
- [2 lî# t3 » 3 + % J ♦
*
♦ Z g l3 k tl(Il+ ;i))*)a ^
% 1 % 2 k%3 ( % * % ♦ % •♦ % :)
# 0
w a
li»W
A» 2 ,
'
§
1:
m
g
8
*
*
-
^ %
*
h *' % ♦ % ,
I -------- *
3
^ £t) L {■..% * % , .h * % ^ I b J I B l ï
4*
« ) f a )|
C û^ i
a ) |û ) î
3 L /4 > |4 3 |a > |
# » M éDj_ # 43 g # 4)3
4 3 r .............
.
^
î
#
0
am maWml #*#i«m *âé8 o f @a#
b
m
w
#m
#
«
#
@
a
#f
t
a
s
t
û
«
f
e
#
@
W
#
\
f1
,
#
, #
/ Il
# k# / %
43| *
k$3 / %
S
h
i
sa
q
u
i
A
&
a
a
g
l
#
M
#
e
@
e
»
a
lm
o
W
#
»
#
ep
o
*
s
t
&
l
®
,m
e
#
#o
fw & m M m h t
S
»(S s m v tû Â w o à g
m
w
ai
^
a
t
a
ai
a
b
ya
m
a
.
%
1
-
j
f
t
a
f
®
s
y
a
î
»t
o#
&
#
%m
m
#
*
aa
s
p
#
e
o
m
w
e
t
o
#b
y» #
m
#
W
to a « a » » g tor-îw ï#
#
«
m
t
oa
s
*1
1
#
#w a # lv m lW ; W W w A s y s t« 1#
%
».
f
w
g
w
m
m
â
w
o
ft
o
l
at
a
w
w
f
e
s
âe
y
a
t
o
»
o
a
«W
t
o
u
r
n
a
t
o
o
st
b
®
t
o
l
l
w
t
o
gm
m
l
y
a
t
o( a m
M M m *a
b
®
»
l
*
î
#
3J&;"
]Bbp%siac&%*dl i3gr8itwKB& <3dT
(%EWOK**%Gi%jLiBeMaL %
& * SSbuaJCIbB (Zsteweq**! ahysttwaaak
lEbbe 2aGit%%3»«& je%*GMg;a#KE%ojl**at <%l* i& #*3jny&ï<k (*%*BüP4& %&**>#*;%&*##& lagreG#:* &#*
<)*>twajLzw&dl jPapGGsi *&qguu#d&jl<MB& (3»0)
% ig
2So3;9^L%%8: ;(%>%» :Eg* #
%
#
S iia lla rly * fy p &■
&
«
&>a
syatœ j
H / h
ISGwnwBd»
ta^ea
:0L «*
6).
8)
8%)<&CÜ&4&]L #&dU8M& CNXMKP# B&K&l
Ir
k.
li; jP()]Llo%f8 IKbwadb
«KM»**
^
^
:lToa
*
or
* (s :
3? •
or
1
Î% y )/I
ijt 2
SacMsne tSasit sdüwBKi
n » l;
* iBbw» awaocBodl apcxpib 1$ vaa
V0ry
eo#p<
b# fl:
a f tb# number o f abaft#.
tom 1# &# abomn 1# Pig* 11*
of
n
2L+ 1
;:'bratlcnc
h&Yo &3
t;c n ; ayo
found from equation (30)*
modoB o f n a tu ra l
oa:y bo
3,
]&%#%&&& ]PR8QK8;oi o&&aa&A%ic
3*1
GOB#*#!**"- Tb* tb # # r*tl*a l **lcul&t&&n o f o a te r*! fe»*
guanal*8 o f
tbe
a&opl* ayatem ha# &##a alaoua»## &a
dbapter#
However* tb# o e a lll& tla # eyetem*
o f aotual lA B tallatloB a *ro oeBAlly laAdbsaore
a# e ffe o tiv e method o f atteok &a aeeeaaary*
&m&
3b f*@ llita $ #
B atural frequonoy ooleulatlOB#* 1% la aeoeaaary to red&e#
tbe oogplea eyatema to aiq p ler ags&ae&emt ayatema#
I t la reqo&ped th a t the #g&lvaleBt eyatem eetalaa a*
oloaely a* poaalbl# the el& atlo and dyn&mlo dbaeaoterlatlaa
o f the o rig in a l ayatam#
E&pa#l#ne# and jud emant In fl# *
e&oe the aeouragy w ith ablob th# egolvalont ayatma
duo#* the v ib ratio n al obaraoterletloa o f the o rig in a l ay*#
tern*
%bor# are three type* o f equivalent myatema being go*
n e ra lly followed*
One type o f equivalent ayetem la obtain*
ed by eonalderlng the moving maaao* a t eaah onmln# oyllnder*
flyw heel* altern ato r* propeller and other la r # oomp&et
p a rt* && eonoantrated ma*#ea ooBneoted by el& etlo Ohaft* o f
n eg lig ib le ma**#**
Rhl* cono*ntr&ted*n&8* ayetem la e%*
texalvaly dlaeuaeed In W lleon** book# the explanation and
m
the preeedwre me&tloaed la tb la hook w ill h* folio####
3*2
Pbeghamey 3bhul&t&&D*~~* I t 1# tb a e re tlg a lly po*#&ble
to fla d am many natural frequan&&e* a# tba auWber o f *p&a*a
1b&t%&&8%k :mau&8#& of i& 3&iltdU48Kw&e agratwaa tqr t&%& 3w&th#M& odT awrt*
&$%%& %#) a jgrosgp c%f &K%aogp&a«K%&8 <&gwKKtl<8%*
aK>tlam jhwam
tkw* f%M&qu*B&Ggr i*qpwKtiaH& awwa t#» dwKP&iM&&#
3S%&$ jü* 4nr&*
&aatüür tB%&8«üLeg&db& a&rom IGh# ipr3w&t&«M& %K>&Eds ef
gpMs$3%(%* iWbo
f%xr l&t
c%f viübrmdslooi glidLog <&in&ry ia&g&t
eoa%poa%M&odULBg larltlaMCl a%w&4H& smdLl «dboiN» t&w& %%yr8#& ogwor***
t&on p&u o w ill not aaually he inveatlgat##*
A good
pro%lm&tlo& to the B##t Imnortaat a a ta ra l fregueael## o f
t&%&
i%#o pGK&oel&w&l BKM&ee cwf vll%rat3ü8a gww& he <*btadha»&
iby iMaduadbsg t&w& egpü&yaldw&t
or threemmams ayetema#
*Qr&t@@& to (ühapldMP tm#**
However* eoaaiderahle e rro r may he
Introdueed &a h&adllBg gome ape&lal oaaea* and the tahul&tloa
imothod o f G&rrylag out the frequency oaloul&tio'@ hoeome* d
daelrehle*
Ihe jhMK&B&agy tahul*tdk%i%a&tb&d la haaw^ltoxaa the thee*
r%*1&&eail
IShw&ls iG&ie iiaLtussaul -ESpGMgiagKBHBgr (%jr l&cxpi&loaa*
&3L iflbipatdlOKi <%9^p]MB3%BMG%a(l8 iso <& &(xow3jLtdLon (tf <*gp&3L313)i*&t:B* ttort*»
TBSHBKi ta%e 4&]Uaü&t»l4& f%*rew»a*
#*i%d t&aaa l%%eKPi;lj&
jpi'CBa t3&#
(OdT t&&«» tKkuBdTi;*
(*f thw@ CN*4&i]L]La1b3kBy& isw&ewee*#
%>%*&##:&(%& <%f tx)%*gp&ek iii; auQF OBd*
«iloiyg t&a#>
][f fua <%%&*
(%
ww@to
tüsa* <)g&odl3LlaitdL<%OL <%f tab*» zawt#:»#»# (W& ggaak ladUB*» oik ibbwads ]po3j&i; i&ika
the eqeatlGB* o f torqw# &&& b* **$igp4%B Wa#
gbd&e th# egBdltiea tb&t tb*e#
i# a& torgw* a t tb»
o f tb * gb&ft# the ##&*&&&& i#w&
bo eolved fo r tba fregwmagy
<j , dbi#& la &nalw##& È& tb#
eaproaa&on o f torque*
Tbla w ill eoreogpond to oae o f tb#
BOtuaml frequeaole#*
The method o f oaloulatlon due to flolee# a ta rt# tb# e e l*
oualtlo& w ith & rough g&e#* &t the freguanay*
The
t&OB o f aJ fa r the fle e t t r ia l eaa be made from the ealeu#
tiom baaed on
3W&A&@&& two# or thre&4m&ma eyetem#
Aaegm* the ayetem ahewa ia Pig* I# ( #* L6 ) to be
vih r& tia# w ith the freqwenoy o f a ^ i *
If
w#r# a a&~
IbaawCl j%peqBB&n*gp çwp $&%& agratMom* ai f%*@# iribs%atdkx& 4&@u3UÊ cnaww»
leltaiotU; @*gr dUEtagRoai t%%pqww» awr&i%%& (8& t&w» dgratWRa#
&edb t&w&
ads oew&b laaa# be tha* fogaa <wP
ftüLlÆMsa iBbedb t&w& awBoeOUergd&lcwi w rill Tbe
#&&6uyjb; jit
a
* 4> <<A% i*ia
idüPüWBB awdbllkraadlly iGhadb %&&& %Bg;üUltwK&& odf t&w> i^kead; amw** %%»
1 3&adUhKB» i*<&* #
4%. s* 1 ; t&%& TK&b*%&to%gr tKxrq&w* odT tbdb#
maaa ie #%m
1* «* 3&l
or
aiba «kJitt
tÈw» a&k&oObat# Tp*3a*e#
%
•
%
a in u)g $
Te
t2
E
t3
E
■A
■B
^Ige 12 - Seven-îvlass System and
Its équivalent Two-Mass System.
"r+1
k tr
k
o
r+1
Fig* 13 - Adjacent liasses in General System.
w
4# a
fîteeati» is amemWA, #1@ l»i?epe & m
tsm
:#W% to mo plsjht of B*#8
m m
(Figt. Wim
If
#m# aWtloa of #mft îias a topaloml rigidity o f
#
its mglo of telat for # o wedasm ralu® of W r # @ 1#
h
aaîS fâse seçllta^ a t
.
Ig «mat tea
1
%I
IBbjj* bax&ggp# o&fk ta%» idBb%y%&o$Mr txMpgmw* adt 3%
% <xf ea& aagfljb
Wé0
to
%2
#2 #
Ig
g&dL* t%>rqpw@ awükliyf t&w# aa&m# I&
{ 1 .
viW&rad#
^ ^
}
Aa #f35#e3f jPw8&*
nW%0d bgr $&%* dWLffGoMBoaw» edT the a%w&f% 4boü%Bà*#t ladft @
w%&
jKla&w# o f
:&g
!0b### e*I&tia%m3*Qrlbe
dblah sam t*
to *pblt&*#y awwddkBB* 10BM&%db89& tb#
idb&l* ayateob)
!^5) ;#&#*# t#& 9a8aww8ddb#aKUMMW&
aod tb# iaüMBnMKübys
]*#
foam
SkGH* SBlspakaBoL#;* %*&*&&*
!2%>%»#jL<aaw,aL l93Lt%%%&1kla%K& *
î|8
M
o
ft
o
r
#
@
#â
m
ûtrnom ûW
% 9 m#
%
*
®W i *
s
a
e
t
i
o
s
i
so
f#
m
f
%
t
e
#
%.%
î
*
S to lla p ly ,
mi
»
#
%
.■a*test£tutî«g into
m m rn
% 4)2
* 1^-g «J® f j
•
- % }
(#)# it foîlowB
w. C % -
M
- ( is^i - ^
/ î^ î
M
%» /
^
Xatroâuaiî^ # m aot»tlcœ»: * 1 & may tes omUed tte® #lasti«»
jyasrtia coimtmiW#
s
teaseo
%. (
%■
* te, , cj® î
* «,
ïtels raâatloa giv## # # to%#m is
^
(W )
ga«tiœ sf tte® «feaft
of m e aystea in term# of tt» topqw# ia tfe® Mjmoeat see»
tlons of #aft#
A ^tln from (39)
4 :r(
' ( ®r * * r « i ^
®j
0)2
®r » ®3P-1 • —
^ h H * ^2®2 * —
% ( r - l)
or
®_ •
® p.i
o)2
r» l
----------- ( 2 1 ,
♦ W *r*l )
% % )
g&KaWB 3Mgt*a&tkl#ak aaJLlei;# 1B&%
» *%%%&%& <%f 1fSf3wBl& lad; eaigr %8w&aw iRGr %**
jBgwaikdl t#bwB%i BSae ssBkuJLe
4SR%la1%
%y;meMFjLcM&*k aaawEWaw»* ;&%*& tab*
iBe%pg*akoü%GLl ;?ljgjLdWLt%y <%f taawk SMpgpwrldPigB 4N94*1%&g)%t <%f
#&3%&
already knew#*
l!i ]K*lgS, 3L8 ( ip* !&aS
j9w*sRa%QdkBgg
«» 31
4aw%& la# jREMi3%Gl j&i40%% G&&& la&womr# «atBOw&tdlçMQi*
jlik jBkuajTt;
SBrwoiKljGg; IBkw* iBooptpa**
# *&%*' t%(kP(%uw» las js&kauPi; Ic^,; **GGF
:gy*G8m tàbeaw» t&sa* (&%i
fig
48%>i%ajLE%&&»
<%f Ibmr&iét; <>f $*kw&3*t Ikq&g awsdl
*ib<k,
:B%%3r Tbê* <saLl4%uülcL$%»c%*
I>3r
t&i& f&Ggaat
tb# GBplltwdm e&
be
t9aw*
<>f l&sdli&t jLoi
iHy&iB&GiKibratoBy torque a& 3^ 4#Bi
#Bd *0 on tbyeug&o&t tb# Whole eyatem*
F in a lly , arr&v&BG &t the la a t m&&8 1* , the y&b&atayy &#p*
que le expreeeed by
*
3b order to have the eyetem v l*
brating* i t la n#@eee&ry to apply a t
ly
* * #%ter&al to r*
go
qua#
Dut Wbaa
happen# to be & natural freq##B#y*
tWL# remainder torq#* *9#I& besom* aero and no eater&ai
torque vou&d be required fo r the deeoribed vib ratio n *
I t l8 neoeaaary to aeeume a valu* o f
#o th a t
the remainder torque beeome# aero; he&ee* the magnitude an!
eign o f the remainder torque might be taken a# & refereno#
fo r Ohooalng
in the eut and tryiproee###
o f the remainder torque
i * ehown In Fig*
As^bbt
9^%% verau# the natural frequeaey
( P# #1
%b* behavior o f the
remainder torque 1# u#ed a# a guide in eatim ating the ear*
root value o f
<0 fg# the eubaequeot t r ia l*
ObaerviBg the diagram* When
must be alao aero#
ia taken aero#
Belo* the f lr a t natural fregueney
f@%t
la poaltivo# between the f ir a t and the aoGOBd frequeQ&lea
i t la negative* and ao on*
a t adjoining
Bbe Interoeptlona o f the eurve
natural frequen&iea *111 beaom# fa r apart a#
I t @08# to higher degree mode#*
In order to lllu a tra te the eourae o f o&leulatlon in
building up the frequeney tab le#, nomerieal example# d ie*
ouaaed in Wilaon*# book are reproduged in the follow ing*
3k*e I%#n IB&rtK%&#ar Iboc&cs *^8e@&wKnidH&l TNlbr*Ltlo%#
51
ext O
Natural
Frequency
Fig, ll|. - Behavior of The Remainder Torque,
_Gen,
Fngine
I
a)
27
165
27
27
165
27
165
27
32
l(S5
b)
Fig, l5 - Direct-Coupled D.G, Gen, and Its Equivalent Sys,
3,3
i W tlsw »* W #
D, c, Seawatlag Set#
page Si, Voi, I }
%e aqalWLant ayatea o f
wtmAl Imotmllatlom 1@ whom
ia H g , IS { p . S i ),
A)
#
« s t i m h i p o u # a y # o fiwit ï» im m â . f r » # w w 3 ' # w * -
oMe*»
syatom m whom to F ig . 1 S0 ,
M W # @@m*
Ig
« 1<% % 6
# 990 lb « ,» in * »oe»^
&
» 38 - S? X 2 1/2
# 99,5 iam.
Tfâ^ 0
#'
38 L
TT 3*25^ X It S 10^
32 X ms
X 10^
lb s ,-îa */î? a â .
Shoïi trùBL ospftMoa ( i l )
I
fn
k 99a ♦ 23SOO ) 5lj* 3S X 10^
» —— / ----------------------
2TT^
Ihtaoâueins # 0
990 % 23500
ooawootioa faetesa a# meaAiomW ta S*S
( P* 3 0 )t top aSx m tm a «a«s«8j
H obos
%
# <2290 0 λ
#
2290 / 0,91
K # 0 ,91
* 2,SS0
53
21)
mmmi mWWl
m w W- «htaiasâ
«& #% ' % w la g m
tm Iή * îSb »«*
Ï4
# Ïq
# 16S
X3 * W
Ï0
*
:3 #500
%
*
a?* 3 m 81 im ,
%
*
27 38: « 59 te»#
fsS5 * la *, #
, .
A
fi%# # ------ ——-------------- # 67#% 3629 ,:'
w*
31
'
W5 % 12 X 10^
^
tetg # ----- -- ------
e 92.5 % 1 #
^
59
% l
6 ? .t »
TT3
&
*
.
» 13^#100
-
^
Mta
Ig
-
k#
I,
# 186,7W
92*5 s 10^
—
W .8 3 5
.
« 136100 X 1367#
I . I,
it
*3
“f
# 2g #W X
# $35*5 %
e
,# _# 1361 # X 3935
o )|
* 2 3 lla 7
67#1M
iùn
X
J
2 3 1 I 1I 7
i
f
» 535.5 z 10^
•
2 6 Î 1.71 X 10^
or ^ # 6 #
m 259
OP 629 ?a<
fn * 60 o3
»
2*&72
OP
6, 0a
IPOX3
% #0 &&0#
^ Ê&2*5 #
.###
ill)
gb*
Gqlwm 3*
per
& FOÜgb gu@88
; i*e ** && t& l* o*#**
fe r
I I , 1% * Ig * 3^ * %g * %6 * *%& 2àS00*)a #%» ly ,
Ib * ?&&#& o f o) &$ amegm&d *& f& e *t g a tn is y ü#bül#ê%&
aamb#
tb& igmodbabMp
&> become a&ro*
{küiBmaa tk» * jl&emBB&oy: t&w» «wtjl*» <&r 1bw3j&t <%f # # 3%&diaw& @ü>
3%** 1 laaaw», 18&&
adb **%#& agis# ;%r@ 4dbtw%&8aw& à#
ta%& cK&ld*ûL&%dkXB %HpooGw%&&
amü&Q&am&etdbag 18&&
iat
db&ri6<y&Icwi eg%d%&l%w&& 3a% ao]A8@& 8 fk%%& tÈw* 6Cw%P083w%od&a%g
imaiy# i&f 4» #
(kü&BBKi j>* 4# 3&W* tüQpgü# *&%& te ta&e tw&Gl3JL8tdk8& a#T lomaw# I *
18%& l%POdk%$S <%e t&w# tcMpgu# ta&%&l*d&&a iaa CbCbaaa ;) a%w& t&w*
dbNPle<d%&oai i& <%&3agm& tk
Cküb&BRï 45# 4* S&w* *3U2e%9M&&e *aam <%f t&w» tKKpqpwN» @%n&*iâM*â aMP#*»
Tdk&üaiüF *J& (k^&ubBi 5 fÿlvsw* t&M& teibel ibo%%pw» tg> tx; t&w» 8*826
fo&lew&Bg :#&#&*
CoIum& 7# * gbe tar&lOBal e& gldltiçe e f th * r@#p#é%&ve »*##
tion# o f abaft*
k% * *&& be @#l@wlatea by the ea&rae8lo&
o f (9 ), ii* * #
hS$ X 12 X 10^
A
^1,2,3.4,5 • - --------^
• ^ '7 * 10
S1,D$ % ÎO'^
_
k%6----------- # 17 % 10' îbs-teA«â»
3i
-6
Column 8* - The
in d&riootion through t
^tlon
of Duaft up to tho U8%t folleælng maao Is obtalmod from
1
fié a — —
Z(
I aj - è Î rad.
-4;
Thu fin a l tables fo r ta& oao^nodu and tuo-aade froquoneloa
ui*o %)ros-,.. :tcd on the fo l'P o u lu p %>agqG,
57
CD
p
o
•H
©
P
t.o
p p ü
c5 «H ©
rH
rP
O
4-1
O
A
M
vO
CJ
Oj
f-i
Q
+0
-P
»H
F:4
r-i
p
o
FH
C"
P
O
FH
#
-
o
N
.s
X
5
H
-?
1
f4
V
O
CM
•H
-P
d
O
%
C
V\
w
H
N
Q
N
IA
fs
N
CD
N
Q
«0
■>,
1
N
<â
N
O
S
*o
V.
X
H
W
O
<v
Q
N
«V
K
O
X
$
X
Q
1—1
Q
K
a
Os
X
43
N
Os
's
ÿ
‘'C
O
%
N
O
"o
X
Q
5
«Â
NC3
<3
'v.
K
N
N
N
O
CO
P
G "P ra
p ci cj
O
[4
VO
<x
,
’—
, -V
<3
O
Q
P:
3
N
©
P
Ü
tn
H
X
«h
r.O
VO
o
00
%
'0
•H
1—!
cj
>
O
D-
%Q
Q
M
K
a)
•H
(D
K
M
-P
S «aPi
II
O
♦H
O
0
W
K
O
o
m
r«k
C\
CD
N.
0
X
II1
a
Ci
SI
N
<3
«0
I
o
oIdPo
o
g
g
&
o
u
fn
0\
c! or 3
©*H
Q -P
'§
&
C3
c
co
I
O
CM
\A
«t
PO
0 fî-P
c70 o
o
© «H «H
ro
rH
II
cj
•r4
P
P
P
© 44 P
n o ©
P
0
u
M
Q
?
'O
ô
O
%»
Ô
CM
'3
X
K
I
Q
X
Q
$
N
«a
43
X
Q
C3
>
;
"V
HI
y>
(A
'O
V©
o
Q
'o
vfi
lo
I
<n
N
4
ü
m
Ü1
â
Vn
%
»
F->
iH
«0
ô
2
O 44
P, O
O
fa CM
Va
N
rn
O
r4
hs
r~i
~ü~
&
î>
i po
ü
ro
,
lA
vO
d
U
O
O
H
i~!
ü
&■
CM
O
Ü
,
O
©
c©b
58
C
O
»—
Ql)
00
C e ©
3 .Z *
-C
—'
"
O
O
o
On
<0
c
o
r -
VO
m
P
q>
-w
S
uo
Z o
-rs
c <
o
TJ
u
C»
G
P
N
s
û
C
N
O
6
43
0
!§
N
43
%
43
1
1
h'
o
N
Q
'X
Ps
o
IN
0
fx
c
fx
K
X
M
K
N
?
N
N
6
N
ô
N
U
^
N
ô
N
V \
o
3
V»
c r v *1
Q «
(2
H
O
1 1
?
J3
^
N
d
$
<3
X*
00
'À
W
Q>
N
U_
Jd"
—. C 0
M- o r
ta P -p
r
-w 0
M • «»
3 C V
V 3 V
E
QU
lr\
CA
OJ
rf\
o
K
ta **.
CL o
u;
S
1
H
-S
-s .
C
a
®
6
<0
6
PL
"o
et
L
Q
Q
Q
Q
K.
N.
Q
K
O
rx
H
K
O
VO
Q
.H
Q
N
«6
O
r i
1
1
1
1
Q
Os
'««
O
\
o
S
Q
fV
4»
1
<o
<3
»
o
VQ
VO
43
o
co
rs
i>
6
1
<0
ex
43
O
Ô
h.
43
S.
o
M
*%
fs.
O
(X
S 4
^S
N
X
Q
rx
(4)
1
%
K
M
1
fx
o
X.
»<
S
M
X
K
|S
Q
Xs
X
<3
CO
Tv
W\
X
c
y
«3
h
VO
'•
P
N
Xy
II
vp
K
)
Q
1 -w
u es (/>
9
CJV
w
43
N
II
?
c
n
K
5
N
#:
43
k
|N^
N
j
j3û
VO
K
%
f
-
s
c
<4-
H.
a
R
d
Q
(%
-O
U)
1
II
1C CM
2 9
M
s
IN
-
«0
-5 »
O
Os
N
VO
O
'v .
3
H
CM
.?
c
-M
<WL*_ L
E O V
\
2
VO
H
U
k
NO
's.
VO
VO
■X.
c'
h
VO
VO
•X
If 3
rrs
N
X
—
0
«0
1
%
>%
o
o
—
N
ô
*2
ô
2
o
>s
V
>>
o
Vû
-= t
O
2
ô
%
>\
O
o
2
o
2
L
O
-V*
d
L
d
£
ta
a
29
el&etlG gurea# o f tha## two mode# o f fy@# vlb#&tlo& a##
ahowB In 21g* %6f tbo vmrloya valu## oT 9 Obtained la tb *
tablea aroTwaod la p lo ttin g tbe dl&gram*
#lnoo tb# mm$8e#
àr& aaeumed ooiovrSr&ted &t d é fin it# pointa la t&# ay&tom
and âro oonoooted by welgbtloGe abafting* tbo ourvo# e#& b#
eogploted by & a&rloa o f atr& lgbt lln o a*
3bo nodo# o f vl#
bratlon oan be loeatod la &ho noæwal o laatlo ourv## wboro
tbo ourvoB oroao the noutral lin # *
16 ~ normal B iaatio Our*## o f
, Dlreot-Goüpled D. 0* Gwnaratlag 8#%$
e e-
■ef e
#
r4
H
M
•H
M
©= .
m
•H
-P
■P
OJ
P
•H
P
•O
H"©
"Ü
PO
r"4'^
P ^ 1/
H ro
/
V\
m
m.
•H
M
M
m
#V\
r4
H
om
3#4
Im W lla tia m *
%a
s fu is m
{ Wilson.’ » bool., psgo %
# 1 . ÏÎ
of tfa« aoiwl installation 1» W # m
in Fig. 17 (î># 6o },
I ) 2®o»Sa»»
Ig
% s#m (% g, 170 ) .
« 1,635 g !| ♦ 0.3175 * 2 « 8*175 % « » # # . ssc.2
» 2 # , 000 lb#-i&«»8S0*®
%
# 1.970 toas-ffe, 880.2
53,000 Ibs-ia-sôo,^
£
* # 0 4*0,3333)* 3,75 # 6lO ,éî66 f t .
# 7,325 ins*
1 7 1 6 .7 # X 12 X 104
» ---------------------------------- # 12.7 X 1 # Ib s -in /ï-a â ,
32 m 7325
%
%om «quation (21)
/ ( 220000 ♦ 53000 )12.7 x Io4 '
/ -----------------:-------------- ------------- * 17,32 raâ/m
V
220000 X53000
n /#
ana
II)
t„m - 60 «5/ Stt
# I6g #«*
%r®«-Maga a y a t« ( iPii?. i?b ),
I.% »
Ig
#
110,000 lbs*:i»*s«e*®
Ip
*
53,000 Ibn-ltw w e,'^'
»
170 in# ,
1% #
7 ,# 0 in a,
k ti ,
775G a ri2 , % 10! .
% 10^ ibg^n^m a.
A lsa,
Sîî.?*S *
%
*
%:
m oow
*
12 ,39 m 10®
■
110000 .
%
ïp
ê
_
12* )9 * 10®
*
93000
s
116#3
10,309,3
% &
^
^
% h
# W 9 ». ^ « ,9
.« » # tii,0 ô o
m # 7 9 » 116.. 3 *
%%
3,:OOi|,0QO
S&gmgqpaü&aa (28)
d )^ m 9 1 ^ ,6
s j i 9 lA *6 î® - 3O0W # '
# glglwé t:
V399
%t@no0
#
f*
17*32
0r
100
» 6o*J / 2TT # 169,5
or
999 «pste
aW # ###
M s saw bo#L tee
mms metwam #?@ sle#@
ÎIÎ)
«M #m se*
to #@ f ir s t
fo r # ie f i r s t %»■ zW s# tmq^mse-
% )lm r
clos is shown In #%@ f 1 m l t # le s roooW W «s W lw ,
#&3W
3 tp}:M&3jG0B*&3. :pdL"aUdjllkSwQwB of" ibbwat
aw»**!;!*)*;** oiP
aBwaJEl; aa*%ar lb## a\3%%%%dl *%*# jpo]Lïd938f$<*
3Ro9* igdLILdl %*t%8w&l
i&
twao&i» 33* 2* i*s&# 3l%&*
t t C 1,3951
)^
}.
# # ----------------------- •0 * 3 T 3
32
amo#
ffe >
??2000 % 0,373
♦ ---------3 t m f ~
;
m
36,500 tm s -ft/m a .
m o m X 0 ,37 3 .
% 3 » --------- —----------- * 3l»ti00
7720» X 0,373
fct6 • ---------- :--------------•
600
Wo
# # m m a l e la s tic m rm ê # r the f i r s t two pvim-P*
p a l jaoéss c f w itesM an a » p lo tte d In
1 7 **
64
N
w
<o
Cu
« .Z
(V
Q
H
Q
H
O
N
<1
O
S'
A
s-
o
h-
«
- I^
9
9
ty
4
C
II
Q
9
O
N
9\
9
Q
«9
00
o
‘A
'A
c
-c
<
0
ç
Q
9
N
o
6
♦J
<
y
o
9
V
vû
<0
v6
«0
<A
%
s
Vû
«0
W
N
2
Q
X5-*
5
H
-t.
4
L
O
\ù
N
00
Vo
o
-4
00
9\
o
%
00
Vû
V
-4
-4
N
9\
L
.
ty
o
Q
<
y
3
-a
<A
S.
%
Q\
«A
N
N
<
rr\
|2
V
(y
g
«
y
3
Va
J
O
r s |
o
^
F
U
-J
CÛ
N
N
3
_o
I
ü <J *3
9
9
<
y
9
9
-dHW
li.
Q) -S
'9
9\
<
Os
9
9
-S*
\
A
î'
c
E
c
tl
3
<r
w
W
U-
3y3
c -M
<
u
VJ
u
ÿ
9
9
9
Os
O
Q\
N
<*
Z)
N
h
I
i2\
k.
5>
9
es %
M-
II
t+-
VO
9
04
« H- »£ O «
>
H
VÛ
9
Z
Os
V\
9
§
?
Z\
U
?
9
9
9
9
f^
Os
M
?
?
N
fA
9
O
9
%
%
SO
9
~ z
9.
9
CL
65
C
w
CO
N
|.5 ^
U
Q
(h
N fA
W
*A O' A N
Ô
N
/»
N
w
A
9
0\
)
.V
C
%
U
0
«
J
L
•K. 9
C
N
-^1c
tf
N
LJ
u
OQ
'cg
o
V
V
<0
9w-*
ID
Q
F
9
«0
«0
<
K
)
(A
o
o
O
N
A
9
9
H
|c0
9
9
î;'
<o
O'
N
9
9
9
‘a
•a
«0
<0
9
o
0\
9
'9
VO
N.
VQ
A
N
o
^
II'
F
<y-r .2
3 c ,H
(r 3 u
V
(A ,o ^
. *
—
cy
o
00
5)
o\
Q
> S
9
9
9
9
00
VO
%
N,
O
K
(A
0
N
Vû
Os
h-
os
I I
1
O
N.
-3
t
9
9
9
9
<A
O'
-il
N
9
9
I
c
î
'
c 1
<r-
9\
Q\
'-i
I
3
9
9
00
9
V0W
-9
3
h |
h
I
VO
<n
h
N
I
% qr
.3
u
IL
(û
3
'9
o
o
9
Q
S
"q
q
?
K
9
.-2
Q
9
os
O
N
H L
o
Qs
zt
O
O'
<Vi
O'
-il
c
9
U
H-
<VI
|tl
i
^
•0
V
»
9
;i
&
sO
c
h
%
9
S'
II
S'
cr\
S'
o
9
o
*2
■2
2
S'
M
9
9
9
N
Os
S' cy
k\
9
2
Vû
(L
o
66
ST ::
ibdfï
sscanKsi, çpfTgKe
2E%%twp(%3baw>l;lJ3%&#4***«' 29r%%3Li%0M%%*dbayg i;spo4bn&e*8s* tâüa&t; laamet l&cw» #*9*af*
%»3jl<%ap&4*dl 38#*%» %aeKta%4%aB8ü3dL«k83L awaÜüof&dlcBQi *ka%& g98MS*K;%*]L33f **l&uK&aw#w& Ggp
3&K>c&e»l ipQwaiik;#
93baisk ]p:P()CHGMau2%8 Sis* 4B3Et*a@3a*3;9T»]L:r iiaKwa jbei
<538 @
üla^%*3w9%%GBBb* 3ü3dL3)gt
SK*r #&%* 8ü&3p%tiia%sa» %8K)<&8&,,*
3b#g&#IB&wGt i#dkn*% 1%a3%%*Qr% iBswadk
liksawaowKrcaTweaat;* )83»8 %
%
8%
db&
3Bw%Bdwa *%%/ !B$%e %mcHak»iL# aaaadi #%
%
%
%W
3&%&B@
dL<*%* SMT
!&&&*& ]p4%%*a%&ap#p
3le T&j&cle l&c> 3#p(H5&(>t; IS&wBt
ariC%JL*p*K&3&e* 3P%T9dB%*#»t3f$%8k&
3Eit
<&%*»#*# #t
sa&gkaüL &** <*oaaapt%pqaw&tw*i& Mgajlaüa3L$*ii%fuuaLL1k3r ;3€K0WQK&1%pdL<WBil]L3r adLBK&f»
]L#w» @3* 4a3PEM0BajLaw*2l]ky #»4g#dk*KaLlas3it; i&c; 4B&%gi 38Kt3^&»*#iÊj#a& dbaaülügpo»
3Ea #&gkQûUl%qg; scHBkt ;pop<*b(&aKB%8 !L%i (SgrKuaaajbea#*, ik&aat sagMakaï i@
d%
%
wgW
##»
ti(%Kw# aai4%u&(l
i&a* &:L&#<&33p, ,&;*
iB%*» 4%9m&aBaa&** iwaadl
e3k@4»1%l<9 (düwa3%êw9d&€Kpd&j&%%%jp** <}jT %&%#<38*jL82&*&aLl argnBlbsBGWi
ISkw» {>abGül]L3LàdbjL%%g a*3n@1%%a& <%f aaaa iBw&lBwuaOl 3üRu5l%aC&]LaLtdl<>BL *#@w&
t>& 3»€g)]Ltw8H&<l Ibgr 4i a;3jBdL]L6KP 4&qp&jliR8LL<%E%& *%9i&ibeG8k, «W3&%8&i)t,lJaaS *>jp
#&
<3dT %a*i2W
9H&G& <scKK8Qw&Gr%*M& lagT j;4&edbjLoa&** edP aBiaiflb# 4&%
# 43k9Rtj;
&#dU&MBa j&ik t&ad# ]p3%8My&CMuw& aap4&3L@:&(&Qb,
3533» t<>3%&jL<%88a]L 3*dL%8P*;jkgja%i 38K)j&#]L agrarawBK Jlai laawdL* ja& taaw»
<%f #1 38WCli;3f**Bgw&f* iBSfstt*»**
jl8 SfiwadLSgr a&3w%BMS4&#d&3L@ i%» awSas**»
ILaktw»
35a#» 3aai*R%3m*:l 2%p«hqpi*MrH;jLej* lOdf $&%#»
*&%sp#w8ygMMBH**&tM**
6?
BWGi&GÏ oa%R
€k&1b8:PSBi33aM& tsgr ifi1b3*80biüry& ü&%e *rfiBl%8:a* #BBé&
G&& ralatlonablp o f s&m&laÿ&ty bot*@«a tbe m&dal aad tb# pre*
to#%ypa# the naturel fraque&ela# o f the la tte r oan be dbtalB*
#&*
3b& ehar&otar&GtlGB of the for@#& vib ratio n o*& #1*0
tx* iSiGudjltwdl Ibgr
*t3Farb3*B&*
S3M» eyi%*3A*/bdL(%Kk idbuawaçwsBBoaai i«dl]Ll
%>& 4&1>**(}3qr<*cl ii% tdbwB aaodk&l t%aw#4b iNdbeti la (iSLalbtiadbdLitg; t%>3Pt(Ww* 31** jag»*»
p ile# *
I# doaJlAR w ith t&o tupeinnal vlbratlona In tbe
oraak ah&ft o f a raolprooatln# en&ln#* tbe e xitin g torga*
la not aimplo harmonic* oonaequently very elaborate oalou*
lationB are required*
I f tbe tangential d ffo rt o f #& an*
glne &&& rGpr*&e#te& by eoma impulaefproduclng deyioe# aueb
a* & caa moGhanla™* v iirh gommunleatea torque to the model
ayatem# the performan&e o f the model may then Tbe regarded
#8 foreed vibration*
^*2
O baraeterletloo o f %be ^bdel System#*** In order to
have the performance o f the model gyatem e im lla r to th at o f
tho proto*type* I t 1& neoeae&ry to determine the condition*
under which the model eyetam re ta in * the aame dynamlo and
e la s tic eh arao terietic* o f the orl^ln & l ayetem*
$he baaic equation expreea&Bg the eem&nti&l <%f a3%&r*
monio torelonal vib ratio n la repreeented by equation
&
•
1 / 2-n-y k% / I
68
where
I
*
m&aar moment o f In e rtia o f the vibr&tl&g
body*
#
tGrala&&l
?rom equation (9 )*
«
rig id ity o f tba ayatam.
la given l&y
J & / Z
Bet the edb&er&pte p $#%&
as
gondltlon# on the
protowtype &nd model* reapeatlv&ly#3be i&WWLo <%f 10%* jhw*»
quenelAB eaa be obt&ine& a# fo lio # *;
^
tl*2)
Por e clld olronl&r abaft*
iTdA
J
m -----------------
32
and #&&& both of the dbafta are mode o f &gme m aterial#*
tb la equation boeomea;
( fp / & )
s %
/% )^ ( 4 //p )
/Ip )
%bl& abowa th at the ra tio between the freguenaie# o f t*o
alm lla r ayateme depe&da up&m the relatio n # between tbe;0by*
e le a l dtmeaalona o f the two arrangement#*
I f tbe d é fin it#
r& tle# era aot up between the oêrreaponüng item# o f tb# two
ayatem# reapeetlvely, the fraqweBGl#* # f #b* proto~typ$ %*&
69
b# predlotçd from th# result# q f the model tee&m*
^#3
Jerque Control In rorned V ib ratio n #*** I f an applied
torque
gin * ) t . la acting on the aya&em * tb#
foroed vlb retlaaa o f the applied frequa&ey
It* prodm##*
%be eaar&et&r&atiea o f the f&reed vlbr&tlG& depends igpoa #&*
aroporty o f
&)
ap^llod torquu*
Ppcpmty 3f
#la# D riving TOrque*
gb# toraiwB&l vibration# Im the arankabaft o f a roolproeat*
ILn,; iBn&G&B#. aa%* ea&sltM*! tgr t&w» 233BF4&8lj5&rBd&tiaw& 3b&
IjsKS
jL# <i%üoa;ldb&ZH8Ml #& ai <:cxc&>l:]akt%&<%ai <&f3P(M8l& ladT
IWhue iLGw&Bf&jlgi {)3* ibfie
part# ecnKl t&adk ipeedlCMajla iy%K%d&a*&dl<%BL.
din (33<Ij&a%db8%' (;,&* vysHowszaajp*,
%&ce3&yuu8i:&j3%%
dtpiiGwadlc; latpwagr <038 üüt#*
cTwysra l%jw» garaeaSs a&i&TI; -toiq&ua (%@83*&l#%IKIbQ6» <%j8
taaj&guD <K3B%p\3îï€9%t;o <xf cllje:\).?P9%ib
tü&<% tü'itglio <3%
%
@
3^e(:3^p%p<>G%&1bi33gs %8e&aw»oe, 3b3d*x*tt@L Ikc/Agui* dkuw*
<3c%BWüa>crbjü3(:«'%%3(l f%i%i 12%* .gpaat
]i)
is&aaKtSjFi, j&agôp*»
1%e%p<guw9%k
15k)%%g%%e '
I?t Q<)%rwMa3»tïî%9S at 'jiea%)T.e3& crgreitfpa Sjwdbo *%
%
%
iBkwe s%gii3/9%aa.#%%1; %ajicu34»3 (8P%) ëOB%'itwxl 1G%
> 1b%
&&B8i Oiaapo <&f (&11 t&k#»
:B*3iFlJ%t2 ]33i%Ttat <>f 18bd& ggpdüà&c jaü&caaâKüjlsBübk
ISasKZS) iPSNSMsjbMW*
**pp*
pljledk #%:gp%2Gw* (%(» {)(%Ek9dld&Boe%k%tl/» TFâü&3L9Ltül*%Ei <9&i#epqad»$&@8pdLaktdl4*ai 4a%
%
#k
1b<) 1B&k@
k
]33*&:3U#L%%%> 483K% %&iO i33g%KP&a.4k 3*g#qw; i8wBl%l33gS <39& t&%*t ]pl*"'
(I
laagElKWf# **& <**a*BqpC&dk <ad8
tabw* 8%%%* %%%M9M»8Muwp**f aj8**%*BdL*t #*%%& # # ]p**aMa3L1%**%$& j8QW%WN* #ap*» T&Sbùdb*
ta»a Aga tm t BS&ê (%*q%%dk&»aaag;I** aa# 8&woMK& âl%&ZP&jB#; 3W3 ( a#**»
]B\, la*, (ScMQüadkB^isi l)GW3&E* **Ikea*ljBa <»&* laSkgft
t%&(8k iSeysjliwBW**# C%]w%pdb4aB» 32
:%k%$w*$iQ*&3L i&8gdi%BW*"»
iEkw* <%*dL9&a§E 1b*%m%wwk <%& tüaw*
i&xMBwa&E iBKiadgi; j&j* %a*&db» wqp %%f igbw» pq&gnu&tkeaai: jPcwyw* 4a@c%d*t%*a%gs ladk
jaagr jLEwaiaaatt, ILii IBkwa agysaSkek»
]DEi #%%%ak&3F2K&n@
; IB&w» {%%dli#j8#g ibKKÿhgsaak <)dT 4%
%
%(ezagglsa*** t9bw& $%&*»
iüaZL :PN9<%îj)ï!GW3aktKÎjo@; saakaua aa^pg^g* * iKhLi<)&i ]âqp(%a*&<w8w» IGaw* |jad%p4kaL*i
t%)3*qp*8 iQd;t%Ia%(g <%
%
% GBwe» txEqsiiïE 4*&wadP1% ila;
laws t&i*» leoBBi <*f IBbwe
iBEkaw&G*; <3d8 G&ie ipdL#rl%B% aa;4»#a&)3ir #*%*& <t i>awft <Kf tübw» SMoaaaaGHBl&jkB***
iPcdl.
93aa» igWLiP3.adl()%& <%*»
lOdT j&c%%iEW9wod;3jn*3«'%*3K3 laoi;* jUki* ip*»*»
3Kl2)39CHBwi1%%jG|g ewoKl :e<)1%gK&3k8ig ixwfba* «w*%%law» ]p8P*k@Ktdl<%*Ç&]l3r i&d&CHsaap»
jpljlaüMkdl Tbgr ip&ato&ng; IB&we secHi tkOQp^lsBBüïl&aL&SLar <9&i 1%*#G i#<%*dLakai*
!Z5%@ 3L%%eapi%IL& twoüpqpa# awaai Iw»
jPsposa t&aw» ipdl**tx%% jftnwBW* d&%#k
i%& tü&MB 3j3aM"tdL& *&(%tjLoa <%f IK&w» ifSosjLSKPt&akaiKSjBg; lüKW&a* TbgT isailtül'»
ipjüÿiaag t&kG
aübjajrtu*
sabL#
(%0R&9W&a*4* Tbcxdk*
5*
izKaB&eadb
4d&HGR*i& taie» j&asjUB» (%f IW&w* tpxMiaa&c
jf<%p tabw» ljo4*%ytaL$k
<3huar)i&ear
Se# Bibliography Im tba back o f the pepw*
jl* |%l3p<*a jlit
71
(xas Pro s a tire
R e s u lta n t F o rc e
I n e r t i a F o rc e
120°
0°
2i).0°
360°
1^.80°
600°
720*
F ig * 18 - R e s u lt a n t Gas and I n e r t i a F o rc e s o f
O n e -C y lin d e r» F o u r-C y c le » S in g le - A c t in g E n g in e*
360*
One
Two C y l
F ig *
19 -
I n e r t i a To rq ue C urves f o r 1» 2
, 3 , I4. C y l*
78
1
%
• — «rro
#mp#
(%
* gPg
* 3F| s W #
1% *
# * aemak an#!#
# e a a j& l& r v e lo c ity o f the araak Wb&ft *
8B&
a#e e#B&t*&ts*
a»0 g*pre#aea &» fwaetloaa o f
q #
Rj/&
%&*** a@a*%ma$#
# W%& amWÉk»
o f waakwp&aiu# to lea&th o f tb# @oBa&otbge*&&&,
!Rw%r%mgr
%%& <&ctv<)%3BKl%%aH3l jCï'CPi @
L lejfwwaar odp i#9w* dGrtssBadltw* (xlT iB&wit (8%%a%i&e aaWksüap
(KB&jRBi lOdP sKBi (azii^Lno#
!3&*e Ijow&aftdlai twoecgQa» <aaa*%F(&a j%BRp #& 3e4*<&#/»
jpseocwajbjlisg 4a%%8ÿl%%a& i*dLt8i 3. ,» 3%,* j* j* && (sgrlJ&BdbMP*» laapc* aaasyaga jkck
iPaiaB* 3.5» ( Sk# TTl ) ,
^ISbd) gpaa# p:Ey&g**B83P%* tKsssgguw» 318 t%a*wu*Ol]kaF j»iB%&ddL4&dt Tbgr ai tk*K%*aN»«*
a la gaalyeia*
F&g* $& { p# 7 3 ) dhow# the g#8 torg## o f
008 gylloaor o f & fouz*ayalo Dl##oi eogloe ##& it # f l* # t
throe hirmoolo eompoBootB ( aao D#& Hartog*# hook )#
%h#
Irre & h la rlty o f the torqoe throwghoy# the oyole la evldaat#
jod the avoraco torque delivered hy the oyllader ie only &
# ml l ;Eyp%&@Ptjlc%Bi
tacw) 3k&jpdL%%g;
G&io aBKaasIjgaaaa tK>%*epjw& BrijLcti <&gw3U3*@f <3%%%%l3i(g
]Et 3La* iakl#M& s%
<&@
ü%tawajb t&3w8 tasjp*»#» SawsaaawaaajLa
OuuMfswBt <%c&db»d tKsgertkier agjbma#) ai %"CRiagbi **a%gwp<)ic2j3Bkt%#wà%% <3d* igaat @a&*
tawaal, <giieif*wk* tmutt awaaagr zaw&ape %wBUf9BK%Qdla oàaBgpüàsâaa&is** 4*3*8 3peq%*jl%#d&
ibo srqgpKreawBR&lb tïie ibcxEtgu** lO&EXMre laa (%lf%a;e dlelba&jLlH#
iltt jL#k i@Ki3;y'
ikci iZbke j;<Ma3P*"aqF4S3L«» laiygZlss*» IBbweKt ISkwBrs* 31** 3Sd*]üES"<%3%à**ap 33a&am:;9&&&d8w*;
73
F ir in g
In t a k e
C om pression
F u ll- L o a d
H a lf - L o a d
Id lin g
A v e ra g e
360'
To rq u e
720 '
— o rd e r
1 o rd e r
1— o r d e r
2 r e v o lu t i o n s
F ig * 20 - The Gas Torque o f o n e -o y lim d e r o f a F o u r C y c le D ie s e l E n g in e and i t s F i r s t T h ree H arm onic Components<
Td&llat #0# m t*&*oydle# mingle * aat&ag eng&na# übawe tba
working eye&e la p#rl&#le * ltb #8* revolution e f tb# emwdk
abaft# tbere are a# harmonie oomponent# of the h&lf*or##*#
3ba m&thematloal theory dhowa that any perlodlo ourv# oan
b* apllt gp Into a aarle# of almpl# harmOBlo 08rve&$
Bb*
torque eure* o&a therefore b* repre#*mt#& by a oonataBt term
aa& a aerte# of harmo8le#&ly varyla# term»*
Zhe general
eK&re&alon of the Fourier aerie» take# the form#*
f( # )
*#*%} + 4 ^ (d b i# + *^ aim 2# + *$ #&& 3# * * * *
+ b% 00# # * b# 60# 2# + b^ ooa 3# # * * *
%here a#
la the oOBateBt mean torque* and &% # #2 # * * *
and &1 * &2 *
**# eonatenta lndl&*&lB& the amplitude#
<%f ^a%<» lysaarlosM» jbu&rBxoGsdLo iGxsagpHOqo&xBdba**, «&ijL<aa isaaai %>#wgb8db<k%s%dL%*#wai
jEypcKKk *%n eBM&3.;p!9jLaf <&2T t&i** txaopquwa owaaeiMak#
][][)
IwaapBacMOdlo jla&sLIarsKSwe <%f tBgKays*ki%tdLs&l
jToz» .ïlüygOL#*
(?3r%jL%&gb8a* <}jp 35i#k jSbigEln**
%agtt9bodL <%É* :li%*pea#1%ijsaktKl<>%&
])#%cg34*3T&dL*&»
jüGwg: t%)3r(%wws ]bu&*& ]b<*<*n <&gr#q)]Ucg%4»cl tsgr #C* 3%,
o fioot (%f jLzBGrtAla
4%%ia
3L%i %*Kil<8&k iB%*e
<}a& tK»%*qKW» j&a* 4k#k&a&%& 3L%ttx>
(w)ip%*eH&t:3Joy% IB&ie l&eoPBacMajLe <*cw9dr*^lj%#^B8*1&8 cdtitsLinaNl
edla# là** kÈ&g* i&ew* %%r&&aHi3P%* <3%*pir4» jBüLowsw»*
tKgr
4K*i **i%eû%3P**
72
In
(aawspdb*** (S** TRgüL 3[# lab*» jPt9%GBdL#*%» #M#9PdLaw*
at#» iBÊWagpeaadülbaai
(aagpqn* jLa T%%dltAM*& *%*;
9f i*»
or
4" Z { jlgi «sSja n^ <» 33%i iBK*#; a*» )
3! ,, tEo* 4» :E
.a io re
,,aLn ( a,*» -* 0%%% )
3*Q^ # osKEWBlsaBod; ;%**#& ItauoygeBilbdLBLl ilBfjpcwig jSzi :ll)ak*3)#K%p
**S%# 3üOk, <Kf p&a*l%aa aapekok#
$1
$B <)ipdb3g» aoKtaJx**»,
#
3* 483M8Bo&e jaaaggle# #*_ja%%p:ljL1%w%34k <)*? 1B%%& lodNBi <%*€&#» 3P%&aB%]Li%aa3t% iaaoesac»*
III# 40H3B%2M3;s*Bi1& (OdT GwKEygGBRktaLaCl SKfSf<xei&,
(C)(
** idkuaaw* i&rkgSL*»* *BOK%
J&%a* 13%^* (KBg&]Ll1b%&dk*s; 43I ' iBt#
lOLlBkt <>;Makwr )**K**acwQjL<* isaes**
p o a a a ta *
33a# 1FGLl3#%& <}f iSkWD
#*%%&
j3%% <&%%& cb9db*M0;#jÜBM**K
BaGdkdlBy? ai 3iauc%&c%ajL<} «sKkOLlgrBulB odT t&i<& 1kcuQtS(%Bdb3.a]L @dE2%3ri; iBtiBir#»*
j&3%c& :Li; <5#n Ik# (dkwORwn IGgr 'pOGlboz*
GBaett
a
(SX'ak *f Z3%
%/f
95&& aagwazi ib4%rw3<Mai>l.ja]l (adf'osMGgp
equatlcn #
% b %a
%
#
2 ac a X B
awaaa Ibe (%«Ct4âüdL8Lt&&dl jf*# ** ik&w»
of platan a&ewb
&
# ta t& l #%eok&* fdatb
B
a* mp*ak dh&ft rpm*
a
e aaadbmr a f iwarklB# ayal## par ad&wte*
B
* B&adk &*&&&#* foot#
liGRBae, jCtKE» jftMULptm^RgneCtak, i*3Jc%s]L«h*jaw&t;lj33; «Q9w%&oa@i** iw&%aBP%*
%
%1* Ê*,/ S& sucwl IL #*
%
«
% / 2 TT
Wov #eabl»#m ettag o r feso-<^el®
«bar®
H« M,
%
»
&
%
«
» a /- n -
3&W* iWBpr&Gtloal%%p1#%*
1* than m&d# ta tb*
a f the jba&ptlm am
harma&la aogpaaent#
* 1%r
& dyBamla etudy a f the vmr&as# inovlag ipapt# ragpeetlve^y*
I t jb&* b*#& Dot*a th a t tb * iB é p ti* &*a aomparatlvely anail
Ita a w ia a ffa e t b#&
:b%&4##üMüükl1# t&m ia t* %n&# and 3rd ar&MMb
A
tb# raaultm ot haMmaBlg aompaBaBta a f taagontlmi e ffo rt #%?*#
77
fo r 08# eyllndêp 1# abown la Blleaa*# book# wbldb la ôoâ"
p lie d from pr& etleal #*&& rel& tlag to the variosa typ## o f
eng&neg* and I t may be waod a# a good approximation im a&#&#
Tdhere & epeelal h&rmonio analyala ha# not been made*
III)
GGüblB&tion of Harmonic# fo r h b ltl*G *llB d #r Shrine*,
In & m altl-O yllnder engine the torga# exerted on the drank»
#h&ft a t e&dh eyllader imay be ##pre#eat#d by a éompoalto to r*
quo curve a# thonn prevlonaly In Fig* 13 and 20 * whloh eaa
be s p lit up in to It# harmonie eompononta reapeetivoly*
In
order to obt In the reault&nt h&rmoBlé I t beeomea necemeary
to eonblné the jroup* o f harmonie# o f equal order but In d if­
feren t ph&ae*
Thla can he don# e ith e r by adding together
&# vaetora the reau ltaat harmonie component# o f varlou# cy­
lin d e r* or# by adding a ll the #ln# component# and the eo#ln*
component# reapeotlvely* and then eaWbinlng tb# two resul­
tant#*
The ybaae re la tio n b'twoen v&riou# torque harmonie a t
reapeotlve cylinder# *111 depend on the type# o f engine# and
the fir in g order o f the engine*
According to Oouain*# aba­
tement* a convenient method o f analysing the torque harmonio
o f e o ita in type# o f eajinoa i * to regard the engine a# eona latln g o f a number of t*o *o ylin d er lenlt# #o th a t ;for eadh
ipajj* o f 4%yiia%ler# i*# gpyt g%8k eagKloadUan fVn* e$wd% r*MPOlBdKlo&
<%P the er#Kd( a&wwft*
I t 31# alaw» #dhdL#&b]k& to <ira* IBbe
dbjUdh 9WM» 113aw»tr#d%*a &%k l&llaKKi*# tKwok#
3&)
SB&rqg# <3o%d%xXl asWl :DrlTdk%5 AasM*B$#g*%Q# i%KP
I t %%&& bew&a a&KBBB t&w&t tba&
SysMbwa#
o f iBb# (gnsll# lâ&p&ajdkoB cdE
borgu# o& #& oaclllatlm g
earn be found th e o re tic a lly
from tb# harmon&e analy#!# o f tb# torgg# ewve#
jRowever*
el&ber&t# @#l#ulatio& *a& oombeream# work on analytic and
graphic method can not avoided*
I t i# * therefore* o f great
In to ro et to Inveetlget# % proper way o f oontrolll&g the appdUkxl torque OKtsëWWüi ieyateok
t&eu0bt#%wMM& ]L&d to the IdkMicdrtiaing & oaaM
d rive eyatem to put tbo torque curve in to the model system*
d&noo the e ffe c t o f the eimultanaou# application o f a num­
ber o f external torque# to & torsional vib ratin g aystom i *
equal to the sum Of the effect# o f the various torques ap­
p lie d in d ivid u ally* the p rinciple o f lin e a r superposition
eon be applied*
P ig, 13 shows the resu ltan t ta n g e n ti*!
e ffo rt acting on the crank shaft being made up o f the in e rtia
force and the gas preaeure#
The disturbing torque may be
introduced in to the model system by usine two groups o f camdriving; one 1# made to give the in e rtia torque and the other
i# made to exert the ga# pressure*
Othcrwi##* both the in e r­
tia fo»cc and the gas pressure o f each cylinder may be put
;#&& single cam-driving medhanlam*
Per m u lti-cylin d er en­
gine model aystaa* due regard should be given to t^e phase
W W w ##
# w .ft'ad&s oȉ9T
te te te m m
te# vmelmtim ot tnwik te a ft #PMmge*
S® «©aftjssl tea âtttetfeias teg#m$ te® meter #teteg «#«
hm
t
#a
@
#
#
%
m
»
a«
#m e s m ^ ià
W mk t
e
e#
#
@
6
#
m
b
®
a& »
j
g
m
t
e
atm n f & e
e
w
W
e
m
b
t
er
w
@
@
«
n
â
t
e
ew
#
â
t
e
## #
#
teteP * #m te te m ^ a te M « # i tee ew H teilener a tte ^
80
GCLKKZBGRXKia#
:K83BGr 2BB8T5a(
!>#1 B*a%wpg (WP Bkkb&I
:Et %ww& %*w%& awüitidGMWl t&w%&
tb * o s c illa tin g system o f an aetaml In a ta lla tlo n earn b# re­
placed by on equivalent ayetom* oonaletlng o f a eerie * o f
m&eeea eonnaoted by eeetlon* o f ebeftln #, wbldb re ta in *
oloeely tba dynamlo and e la e tlo dbaraotGrletloB o f tbe o ri­
g in al arranjonent#
I f & model eyetem la oonatr&oted thldb
la geomatr&eally s im ila r to I t * and Id e n tic a l m aterial# are
uaed fo r oorreepondlng e la e tlo part»* tb e lr natural fr e quenole# w ill then b# almply related to eaob other*
I t la noted th a t* In the free torsional vib ratio n #y#*
tom* three fbBdamontal item» are o f gro&t importanae* namely*
the m aao-tnertia* the torBlonal rig id ity o f the abaft and
the dynamic arrangement o f them*
Therefore* i f the model
ayate# 1* to perform & & tl8f& otorlly In the experlment&l work*
i t l8 evident th at a#*y and rapid ehange o f :m&»#-&narti* and
e f ootive abaft length 1» neeeaaary*
The oonatruetion o f
the model ayatam henee involve» a oomblnatlon o f the theo­
re tic a l oonaldoration and the p ra e tla a l work*
*>*2 CkB&atBN&etjkxn
1&&# %B&*# laoawmt
1%%*
2
SBdkla 31# «Mfalaw&teii f%%B& %
2 rg; * <%r <K%3V<Ri&e%d%ly (SK-icaawMi »a#
T*
as *
o f i&ysHüklcmu* %
%
%# 3L* & jfuzwyblOBt
o f lin e a r dim#8#&#B# and can b@ ooaeldered *a proportional
to tb# diataB## from tb# axis of ra ta tio n to tbo loeat&oa
o f ama@*
H#n## tb# m & *»-in#rtia o*a b# put uad## OOBtrol
o f & oonatant weight by moving i t toward of away from tb#
##&* o f tb# dbaft#
&W»
*%&& @dttaa&%#d 4&& *B& #&%& t&dkdb j&# awwÊ# <%f 1a*9
sbaBaaedUB %H&dk&Mbob#w*^#
aam* #%$& %g>
tae tkwKB**
aaaüu;# #» t&wat a& gxdbd# 31» a%%rBWM& f%%r t#%& aK#y#&dL#
ifbdk #b4wma#3d* aaa* t&wm& aClGBgwRi 1%%g#i&w*r *#t t&w&ir
t6%* a&w&ft
j& tdkght jf lt ,
t#k
S8L { 3%
% 8%& ) a&woe# 4k
a&à&tdb 40f t8&# 38&&Q%wüi-«G*a aawmBB&Ckr*
2&Dt# to 3%L&* <&$-
:&) j&lBBdüBüm #0b@8KB*l# <%f
at 3/^&2* *up# <8fb iid&o
djkCfeaNMot ]U&a :ta%8 3* * jr%r Tn&rlotw; raa^p» (WT ad^M&8tB*B&t edf
Ifi# %8&»8*dJaartdüa»
8)
<5 podkma*
%, * <**
2 paijMB*
3a # !P*
2 p air#;
& # Ig *
3%a& a%%ao*r T^logao# *o*» awk&e o f aklgBdkaum
%%### *&f »a&OBt 0*277*
G&dta 8t%raia&d&,
t&wair iB&io&o»
au# tadüamed I&0 &a&»p l&w> 8Pdk&# j&ür twdl»
82
— 1
— ,--------------------------------------,—
T- t- ~......- .....................
1
--------!— ^
---------- .
-1 .
r r ..................................
I
1
'
)— —
-1—0 ____--------1
—1
-------------------------------------1
— —
T Î ± _________________T .‘
'
M l
*
L
—t 1
—1r—
=
End S p a c e r
C e n tra l Spacer
0 .1 7 ^ " h o fa s
1_
-o ^
i"
1r^
t
/^2
■—r1t
Vr
1I__ (1[
:11
^
1
■/a" —
holz
1
1N
11
11
( n o t i n s c a le
" if :
)
Eig<;^ 21 — Ch.annel~Arm A ssem bly*
^
11
11
I1
11
iJ!}
igpaaWBf
3^#y**
sSjwgplzgg ]p#r$%M»e#
l&etmMWBB iBwMdbk
It)
mwM* madk* i&f %%%&#* %NBP # f
%&*%%&%# <xf 3U(32*
at
ile dbdLIladl
<>f jsibasegpi; adPlb*# #*d*sMB«d*>3;y%,
33Bw* <*3u#4#ar*a9w*#*
<%**
#&3&B (33%t%]L#w& jpawp 4B%&#
J&3L3k@B jhw&Bkdl (Bacp a;$#q%*PBH#
%;) II&jB&E: g&odLgfhrb,»,
%%)4» iNmsai8@3d&#* iBGcq* sBW
&g&e <%jP BwaâLdl apctSjliBdl* jp%Maw@*»4Badb
o f :&**
(%*D* iPeMOBGKÏ
4»*r
(%** (SaLZyPeKXHB***; 1Wtk&4a&C%B9W*a*
SL/jB** (1EB& 1*,» ]P4w;%>(H0MBdL?xB3L3r# j*ar@ <;%%& lee ggeHb TraapjUoR**# TiM»jL89i1&*
(
:&%>* %wyg*» (5lt
4Bkk#gr *%%%» iBM9#»ka*dL <)*&% <%st taba» aiaamGt&àw»
j rl odl % 3aew#3jlT# t%o (%,3!3K5** * {)+ILS>6**
3L*08db^* frB&ertOLar#
33bw# «K%3%BN»$gpw%K*dül*%g; %8»&§{bdbs* j*a&* C^tS&G!»
<%%*&
OftOG?;* :%%>ab»# ]p«%Rgpa»edki;*%>]gy^t
33BW* #m#dLggilbai #**%* a*OKBw&3;r j%au*t%*B*Ma t%s the (@%gwc8a4»3/**%**a#*
t>3r twalLta sgow& lowttwe,» aa j9&w3M%& jlxk IfSjgk» 3%3t ( :P* 3It )*»
3&%*k
moviag y&88* o f the weight* o& veaioua length* o f dha8n#&»
888* @88 eetim&t#a a t tb# cantor o f the wel&bt to the can*
to r o f the dhaft&
Ô& 6* lo a
# # %i/% 2*
to
8 3 /8 *
On p* long dhaanoi#*#**
r * 1 %/38*
to
3 %/8*
On Ig * ie&g dbaanolm&rm,
r # i i/3 8 *
to
6 %/&*
au
c e n te r h o le
d r i l l e d f o r l / k ”rt -2 0 screw
( f u l l s c a le
P ig . 22 -
)
D is k W e i # i t s .
f a s t e n in g b o l t
and n u t
6
P ig *
23 -
o h a n n e l-a rm
lÆ a s s -In e r tîa A ssem bly o f Model System .
j&a3U&otl<8i odP jBbadPk#*"** S&w» to]n*lo@üül *dL;gldjJ%r o f #&wüft
%&k # :&8 <H%ls&üL&t4M& f&<8B t&w& ft%sa8jU& (9)# #%kl i t I#
&&k t&K) ]pa%MMc%w& a&wsptwBP* i%> %w* ]p%<n%o*4%&o%ϟL t#
d ,/ / #
Izi (BPdkBP tx> gajja saw#* dba aww&BQüdkQg <%f t&wa gw&pfossaaBKW» o f Bb#
23cdk>l* jit %%%# (k&oick&d 1%> g*N) aOU&ndkMr rcwS <%p a&t&io
of
8BK1I I
<%P @&K)ü& %/^WS* #
SCbo <&p*]Ll %%%& oqr $&w*
48%%M* %dbp*
f%a%&&9&k3Bad&e%d@ûL <%f 3%w&*Q%w*bl3r oo%w*t@a%B dWba*
BB&tKM* azwS la radaie# :lo%%s aM&oak ]L*By2#hk
%B&8# <&f ta%& BK>da]l
SkarfyUBloaab adstfSS»
<xf %M&apdb%8# #*pe %%o<#N*aeB%r ##> t&w%&
drlidLnf 18%%%R%0b 4&*m%@&@ru&&&aBa ftgp aad&eyswül txxpqiw»
tdloa jLf& ]pd*3s%dla*3K&Tb]Let»,
3E&W
E* %awi8a^*dL3W88p4sdla a&apo 4o]L*sB%M*dl <%;& tSaw* e&w&ft i&e* j8üaeM8& jbck
ZPyLgp* i&J)*
SZkbG <;(xr%ta?0i]L
<3wf tGsw» <dbwaa3rkail4*a*%g;& laa*#! 43a*3»ljL#"
odl ladLiBb j& agawkiLIL laKtlksw* Iso %;<%ww8nBBat <)%i tiaa* a&iaft aft#» ibSLapadb a%jk*
With tb la mrraa ement tbe a ffeo tlve lon&tba o f aeotloa# o f
shaft 8#o o&aily db#B%&*&le*
IB the f lr a t aotwgp* *
fo o t la loagtb #a# used*
l/lô *
*&**% wire o f about 6
I t dbould be a*ted th at tb le
round rod 1* fa ir ly uniform tbrougbout It# #bol* le&gtb,
3b# shaft o f the model ayatom may b# mad# o f two rod# o f dlf«
foro&t diameter# by joining together w ith rig id eonaegtl&a
to give the deaired ra ria tlo a o f th# toralon&l rlg ld ltl# # o f
varloua Beotlon# o f tb# ahaft*
5»^
Supporting o f 3b@ Madel Syatem#**- Itl& aa already Tboea
86
ebowa th at f&#@
are *a*out*d vltbaB t any external
&&6&&la8^torgw# aating on the ay&tam*
3h@refGr#, tb# p r l*
38#ry point o f aqpportlng the iM&del ey&tem 1# to latro d o **
I l t t I * or *e goaatealBt at all && the j%yeb#mjnMx&<ngF4Bé*
to m a l Bowree* mo th a t It# natural fregaenole# w ill be tb#
#@8# a* th a t of a fre e noasopad vib ratin g *y#tem*
3bl# baale Idea Im pll## tb&t theiBoàol ayataa jdhmiW
e itb o r be eypported on a very fre e upper bearing or an##
a eery t&im long wire*
3b# e rlte rio n o f the
la tte r method lie # in the fa s t th at the toraïonal r ig ld l*
ty o f the th in long w ire le a a a ll oompared with th at o f the
abaft o f the model eyetem*
I t 1# then aeewmed th at tb#
model eyetem ie In e ffe o t & fre # v ib ratin g ay&tem#
jl)
(ïcüoooü&ortjLcxBL !3%»tw%tSKQL 33bu& ZBbwajfii jaaadl SE&ae
-
]Ctt jig* :p%%&u:l3*3M& i%> 3%0c*i* 4t irdLg;i<l <K>;#%eoi%io8& Ibw&tBW
MBKSBi IB&i# fWbwadEI;
jawad IL&ie TPdLre #o taiait: iiot ipetlj&i&life 3SKy%R*%a*MQd& w ill (%cHa%8* ati; iBbw*
loiaslb*
1 «BBwaJljL 3so]b& jL* <%s%il3bew& 4#pEjL#Ll3L3r s&t; <*%
%
*%<*%%& <%f tdbwe
*032*3*1; <&f blae iggadlGCl a%F%*i&GRab» taadLa; l&&]ke auoMS tësw* snüwa%><HGa:3Loga
Tpdls*# 4K%
%
& 4L IQW&BLtt
#B3Wi t2:a)3r STO ISjH/fe*' i)K»3Ld&Bgp@Hl 1)0 qktaSMM*
(it iBbie jftoaetzuaps*#
33bjls; jodbadb la» anagpi>cH#4kdL ibc) be cwa&HBüül# %>j»
<n%%%p,r3jag 4& ]U0N&(i 4&jT jal)CMa1b tüijLiMbgr 3pOLWQK%a
#3r#lt6az%»
ib&ie idbuoCle lactdbalL
jl **l9&e]L TwdLzq** 3&*%âp& %k>* 25* 3Lat t%8W
9w& fo r a&ygp%>cHPl3l33ëS
tdh# %BK>dk»3L aggralbaMOb»
8?
3%) @Naa*pN8â%@dLcBà
TBbw» BKKvGhk
33bü» iwg&gwBüP 498%dl (&f 1Bbw& sdlsM* edbKyw&d 1b<* Jflaw»dt apmkljLaübCLy" #%o 1834**%
18bw» iBwod&éCl aqrs&t%9%a 3W
K%
&%>«* i*üw8%)3BGM#4Ha4*
SBbdl*; jl%%Blbai3^Iaktdl<%ck «la #*
Tdsw)3L& die ia%aa laGMwawt&edl îO%
& j& 1%#:13.
Ibc» i%kUl<&bL tibw» ]s*)1%a%p*
**BB dbPdL%M8 j*ai*wmdb&3r la&liL 1b<t i*$rt*&(aw*dL,
la #lg *
33bw» ft^llosRÊaig #ük%»t%8&i
( p* 33 )* àbe*# tba aeaetruatl## o f the *wgp#&*
8lOB amaembly,
Mbte to Pig,
:&j
3bw» 8pdknd3j& la* iaedb» odf
:P8w%%& twKP cüf t&w» a&WKp#
j&a @ü%&ta%; t&w» %qppSB~ a&M3B3j&&r *#&*%# <%& t&w* t%%> «RaefSwG* <xf tS%*
$&%pua1k tüwæiatg 1%> i%d&& IBb# loawl cdf a%u%pea%8l(m azwl t&w» 3XM*9%»
4W%& CK%BBKM>t8 ibo t l *
T&irS#
l&OÜd* Of ()*C#&*
iUe dadCllakl w d e lly sdb tiw» twyttOGa ftop t&w* e&üspgaaeldwi %düP»*
%&M» tB3%#*Rf#%yw* %w>le <%f
4&ia8%8tdu ie dsdLllakl 2%%r tâ *
gC&Bg iko ixiBKai t&wa wdbpe 3b% ai *l80Ld <B%BK8&etixwa#
;2) Ji aBBalJl ipïays ojP t&w» sijB* t%> gjbpe 48%ug jf lt ibo ta&e %w)l#
dbdlilawl <83 t&w» agdkadüU* iat i&awKi t%> 4&K8&# tgp t&%* sdüp* idbie&k
jla twqo&BMi <81 t&M8 @%dLBd3U@ tgr ]paw&@l%g& tbaHeuggi t&w» hole #ük t%w#
lowSMr 8ZW& ,
À 1F*notdb <l8 <%it <«& t&%& awwefaww» oj» tha ]p3&yi
!Eb# IBbytü&t
%K%rt <%f tâwG
3U& a%wi& odT aamB&l lüp&mM» ftop t&w» 8%g%#
3%; le laouzübed *B& aijPpsmw* *#&»
Ik&a&w&d adk t&w* tcg» o f IKbe %@od&dl agnateek *t*8a&.
88
S p in d le & T h ru s t B e a rin g Assem bly
Top fro m e o f
Model s ta n d
S p in d le
T h ru s t B e a rin g
©
k iA " -2 0
ta p p e d h o le s
on 1 7/ 8 "
c ir c le
fiin
l/If ." ro u n d p lu g
w it h V ^n o tch
5^^
Vh
( h a l f s c a le
F ig #
)
Q-
I
Ho# 7I4- d r i l l f o r
s u s p e n s io n w ir e
( h a l f s c a le
2l|. - S u sp en sio n U n it o f M odel System#
39
0}
The model #y8tem aboulé not awing to and fro In tbo air,
and tho abaft nuat be guidod to ollslnato lateral vibration,
'OoaLO, of b
eond
i it la nocoaaarg to uao aomo boar*
ings to keep sag oh&f^ In placo *
Tbooo boarin s should
bring no frictional ro&lat&ncc to the shaft*
apaelnjs bocwucn tÊio maoa-"l
Since the
may hcve to be oh&njod*
and the shaft might be replaced for different aot~up. It
Implioa that t'.o bocringo %mas D€ easily adjustable and
quickly removable*
Split notches milled on t^o sliding
plates can make a slip-in combination for thla purposo*
L the bearing supports can bo
ovod. alon: the upr
tao stand or removed acoa&laniy.
vj of
Pig* 2$ shows the con­
struction of the bearing sup orts and they are mounted cross­
ing the dl&gonalD on the stand#
© 4—
-
m
h%:
W
_ i_
c
lo
.c
trC
fn
G
<
i )tolcs
■f«)r U "'Jboi£s O -f
Vu
'/s
ihrQo<Js
- '•o’x v t i ; a»d .'oai’ln
;>u,) orta.
1j
1
jjL
2Sl»
% ï/S * # *p# !&##& te
m
bol
<m tbe
bole# are al## t@a&ed arouad tbe #«#tral # l# t fo r
a)
A V*notdb
% &He4at 08# en*
0#B#tr&Gt&#& # f ^b#
tiom
A b a il
fo r #mm#8#l#8«
mat fo r
b]
along
#0
r point
91
%ba SKWBWKW&aaof
ta%e
#&#%#& 1* fla#& gp @&
Amm# md tw W # rl% im ppo#*
pip&ag trea&a*
W rnmW <m # &
Tb* #tr&otu%# probably ibma
to t&msRda*
%&#&&## or ##m&31*Aio& o f the Ataaâ
&m orld ep tly ua&**&r#&I##
3b Plgb 86 ( p# 9& )* tbe #tr&o»
to r# o f %&# model eye##* #$*&& &# eba*#*
Bote to Fig# 86%*
1)
gba f*#B#e are made o f
8* x 3* x 3/16* ateel eagle*#
%b#y are beet to Wbap# *a& welded a t tb# joiate#
Tbe
era#* member* are meed fo r atlffeB lB # *&& fo r tbe eoapea*
adamof tb# model ayatem oa tbe top pleee#
are braeed o& the #*&1 by le g b o lt**
Botb:freme*
Wbodea bleak# are ##t
up fo r etraigbtenla# iwp tbe *$#&&#
&j
Ibe atmad baa e lx pomt* wbldb are made o f 3 /k * bl&tk
a te el pipe*#
g&tbrea&ed tea# ar# ##*& fo r tbe driving
platform # aad the adjoatabl# @ro#**meWb#r* #o tbeyiaaylb*
moved along tbe upright*#
%&# platform * o@n be aeogred
&a plaee by aet aerew# i& eo llar# Ibramad to e&diiMOB&Ugs
3)
fb * #eldlBg»n*ok fl&agea are #*#& aa& braeed a t e&eb
end o f the poet#*
la jf&oadUky
The eomplete etreetar# o f th i* etand
afN&ar %x>ltjbq& tkmma l&ie jnuKaapH* to ibot&i
-frame» <xa #&%» t%%> aaaS bottoBb
cZie cv&tuwdl adkB* cdT t&w» etam&otsure ôd» tba» îBodkül arrête**
*t8w%& jü* aÊKMsa ab% Bik&te IL ( 3&# 9C> )#
92
w a lls
2 X )
-j. wooden b lo c k
c ro s s
member '
m o to r d r iv e
p la t f o r m
flo o r
%
flo o r
Pig* 26 - Structure of îvîodel System Stand.
93
B la to
1 “ i> t v u 0 v \iT B o f Uodol Systom Stand,
Motop W lw A aartilar*—— 2 » t s s m m m m % qS «tes* «Warn
%6
is %M@a
# w a ®3»fe?ol,
ifSS
^
iê m «£ p%«#iaia@ & w % ^ vm>m #
m cmles* to a% m # *m # o moto# apwd o f
& l«gr a iw ft aosd a
wed*
p o ll# «TO
In %g* 27# #m steateSi Shows # e mshmmtlo a$wm#**
aajst o f ti» drivlmg syst«a»
ttjs f t # m *
# # i #@ #m@msiow itoow ta
Ml# œ raiîatol* @p@@d rmtm «W %» estlamWÉ # *
PKsstm toly*
A)
low %BOd fe s ta H a tio a .
H o tO P
HK!
#
TfZ$
Hetofcioa %%ttor=thp(w# Vmri#lo-'%e@d«Rpl?#
ftiiissr
# a./ a*(%
R oâ«ctii.a Hafilo #w o u #i S to p -P a tt^ s
#
1 / 3,75
MaiiitiB Spooâ at Casa % a f t
1?2S
“ ------71— :— — *
2 ,6 5 X 8,75
B> E l#
.
w-
Iw ta lla tlo a ,
I
t
e
b
s
e
a%
o
e
d
a
tG
a
m
a w ft
#
1 7 2 5 x 2 ,6 5 3: 3,75
âetttalty #@ s lip oa«ild mot mwotawi im
.
# ,0 0 0
V -W lt # t# s ,
■also tba spO'M m tio w ill a # # W c lo sed %#oa # e mWo
9$
c a m -s h a ft, 1/ 2 " d l a
U "
X 1/ 2 " V - b e l t
2 " ~ 5 " O .D .
lt-- 8te p V - b e l t p u l l e y
2 8 " X 1/ 2 " V - b e l t
39 " X 1/ 2 " V - b e l t
^ 7 " O .D .
V"#belt p u l l e y
V a r ia b le * * s p e e d -d r lv e p u l l e y
{ speed r a t i o o f tr a n s m is s io n 7 : 1
M o to r
(
lA HP, 17 25 RPM )
P'igp 27 " M o to r D r iv e A rran g e m e n t
Siiowing Iiow-Spe©d P o s it io n *
)
96
§
•P
CO
>
î!
A
h
0
P
1
OJ
<D
P
csS
H
Pk
# # plW k
of
W
A
iW #m ##@4 m % # #
f3motlo&3.3y
#gr
60
la M ttla load w WW
#
3S#000
henee#
#m ao lw tlo n o f #%# a im o f #mf%# Wmrlmg# W it md
loy eta# W a w t takm # e atrsmcth of m aW rlaia Imto am»»
al4er#M^(m#
a a y w # # # W i#
m 4 fo r eommnlmee o f Im W lia tlw *
W p e rw m i
aatuel ploturo
o f OrWLog #y#W% la aW m la M #t0 2 ( p# 96 )#
ÿ*7
0am aad
&% mwrmlnlDg the a#»
twpoi fro q u ^ g ^ a o f tbe model i^naWm# a drive o f Wrmoalo
motlom mgr W a
@^W&#
llo d w atl^julmte # o oeG lH atloo o f tba
%ea tW w p lle d
oolnolde# laltb %o
n&tmmi fW#e%x>3r o f # # model ayatm% % pWaommoa o f
rommmw W ill W oteorved la tbé perfo%mmoe o f # e modal*
Bw dnv# fo r $W model ^ te m m y W omrrled oot ty
# o erefu lly # a lg m d mm eWLOb prodoma a almg>io W rm nlo
motion*
Om# m e t W token to avoid # e poaaltle lo te r*
fOrmme to # e motion o f #%e mm W ilie trm m m lttlng # e drive
toem r^ # e model eyatem#
A)
Dmlgn Of Cam#
% # p re tlm o f mm dealgn in t&Kle oe#e w nela#* In fW tlr^
p8
Vmrlom
ü f tw
m $ t ooweapoWL to
oértWba m ^u lw pom lM ow of # e em#
& # q#a la aaqpeeW
^ ^Ivo tbe fe llm m r & W m W W
I)
oÿ
Motiom
I t 1$ im #r#tood th a t I f a point la W 9 l% in a o lro u lw
path# it# projection on % dlw w tor o f the o iro le w ill hm#
# ei$#lo hemonio
A hm^mmio motl<m dlagrm im
prodneed in th i#
1# Wiow in Fig# 28*
fs
c
bz
'&/
28
II)
uii3)ple Barmonlo Hotlon
Ib# O eoillating ^ ll e r Follower#
3h order to prwemt the oai^lesdty o f a erWWmd m ilder
zmohenim owing to the e ffe c t o f the m n rn lari^ o f the eon*^^
neotlng*rod# I t 1$ odvleeble to me# a e^dLng follow er to tran#'
m it pure a% ular aaotion#
On #ie other ha## tlm déviation
99
P la t o Cam w it h O s o i l l a t l n s R o l l e r F o llo w e r
E q u iv a le n t l i n e a r d is p la c e m e n t o f sw ing f o l l o w e r
a 1 In #
H o l l e r d ia m e te r
« 1 /2
in #
D ia m e te r o f b a s e c i r c l e
« 7 /8 in #
O s c i l l a t i n g f o l l o w e r arm le n g t h
■ 2 in *
C e n te r d is ta n c e b etw een c a m -s h a ft and p i v o t o f f o l l o w e r
8 2 3 /8 i n .
X
F ig *
29 - S im p le H arm onic M o tio n Cam P r o f i l e #
o f motlom #
point o f mlia&og
#20
do# to
pmper ##ommo# o f JKKt m y a im b# d W M A W #
I# )
%4yoot o f f l « ^ %m
lo
%Ilo#m%
oat to# mmi p ro fil# # #w $^m#r#I m thod %%##d $a
A ln m
m
t l#
d W
e ln g
i$
f o iim
m
d #
% g »
##m p ro file m ii tb#
Bj
%>
(
p $
9 9
)
# m
m
dW ew iow o f # 1 # m t^
Of f r m m i m i m L cf OmwiWlv#*
A pmr#II#%o##m lix^kmgg# #»# <W#i^n#d fo r trmnamitting # #
r o W % m t i < m prodaood by # # # w m d it# f>Ho##r m w A m
#nl#m to tw mmmmitm o m m tly o f # # model #y#tw%
%#
pmWLlel rod 1# ommooted tgr pim #d jo i# # to IW W m#
folloow # W
a m z ^ #%l#h 1# keyed <m % e # W C l # of the
#a;^powio%i imit oC the model ayatem*
%
the natar#
tk i# IW m ^ both tb# oraok md tb# f ellmmr hare # # ####
em^pOar d i m l o o w # # # #t t w # # w angular reOmity#
# e W i ia made in ?i$# #
got# to % g* ^
1)
A
to a W # # # #rr#n@;m#ent*
( p# 101 )
% # m in j follom m r i# mWbe o f
5/3*^ %
«Umdmm bar#
# groove la m illed mt on# end to #da#t # e W### #e&l#r*
& bole la d r lllM a t a dlateme# o f
ro lim and a brom# aleov# o f
2^
Aws the om t#r o f
to r# la tw o pre##f
101
cam
fo llo w e r
s p ln c jle o f th e
m odel s u sp e n s io n
p a r a l l e l ro d
P ig # 30 -
P a r a lle lo g r a m L in k a g e *
mm
M In fox* m #
pont*
pmmlWL ïo â is
'sdM # _ # a jo in ti a t a atstaja»® od! i î/2 " fw m # » <m#@p
a f ma ptsot*
g>
m# memk ia aad» <xf %" x ï/s * al« to x a tes?* a # # * a
ta « tlta a a t ona m t # geaatva a « m il «#«% : W r @mm
W#»d m m e apWQL#*
a âtatœ ee e f
Sba p a m lla l voâ ta a m w a ta t a t
Ê 1 /2 ” Axm ma @<wtay o f m@ # tw i@ a fta r
.& #:#& % 80 m a t iarnm ta a l* # « ma #ma m tÈ m
# tn # a .as # # # llm w Ottainaâ Amm #w m m
ma em plata sem$# off ma wm* Ittlo w ap .« à W t
togoa ta m e m tn ï l a t * 3# { p». 103 )
ma
I
Ih
I
H
o
®
•P
aj
H
Pk
oi&rnm
6#
GT MODHL mnsm
6*1 DoterminAtlon <>f BW# Wmm* <>f
%# #»##
of ixmrtlm my b# divided imW Wo ]gwt#*
m* ) cm»*
#t*nt mmmb ôf Inerti# #f tW chmnel"*WTt ####d>%y# md
b* ) v m 4 # l e « m a t of iwrtim of #w> m W ) l # welg^it#*
à)
%»# rnmoat
Inertlm of Owawl^^m
S3b# Oq^oimd P#adbi&lW ^5ma;py^ ^ # l« le method of deWm
#W33g tW moMont of
of rot&tln^ body mwer&am#
ta lly 1# aeed la tblo w##*
%1# meiWd ###%#»
th»
following taoorotloal oonsldaratlona*
la % g # 31 t w rotmtlag bodf 1# m m p e a d W by W e lt*t
wlroa $0 #a to b# frw W oaolllaW la
Lot
ü%# hmd#mtal pim#*
# # ##!::#% of #%# body la IW*
L # l#%th of the mwpomlm#1%%# la Inohe*
R # Wdlal dlmtm## of #%#i
OBelllatlon la la###
a vopy m m ll m gl# o f W la t
% a$
à la , ex ^
ex
^ ^ #
& Oc
$ #
fwm #&e ml# of
/ ^ / L Z
%q rm W ri% fw ee
P #
wm
w aln or # ---------#
I,
She mmtxarlAg toTqw
m #
y %m
W fi2
% a spKtag ®M3®taat in toaraioa is â®fin®a as
M
Mow
f
«
W R®
YIT^
2 V i / ^ t ' « a y -— ^
W-H®"
3®e*
W b2
I
2 ttJ
Bene#
I
#'
X L
W r2
It.TT''- Ï, f®
mae We
ik$)
ae$W )ly le mie^emzed by
We th la wires am show la P I# 32# wiW
B # 1/^** *
M ffo z w t aeWo;) in oxperimeaW #yo o b ta iiW by varying
tW lo n jth o f We aaepezwloa wires#
ZZZJ[ / / / /
+
+
+
+
-^ Ij* 32 ^ %perlmeàWL r^tewinm tlcm
o f ...wont o f In e rtia o f
AaaWbly#
s)
6*
W #
o,ai3T
Wrem
: «
% m 3 f % o $ # * 3600
#
%& %
0,2137 * 0 . 2 S X 3600
• --------------------------s—^
— #
s II %
là (# 8 * )
, ^
4*37 / Il
f Wm)
'5 1/ 8 *
2 7 ,5 0 0
0,001251j.
5 iV # "
.2 7 ,0 0 0
0,0 03 25 0
% 6 1 /# »
.28,125
0 ,# 1 # 8
k i5 /W
28,000
0,001253
I
V #
*
»
0.001250
ÎÎJS-1»-S«S,2
0,2355 a * ,
0 ,2 8 5 5 M 0 ,2 5 X
*
X
t
6 ,5 1 /
El
X f®
taeta mm*-
«#»#&# w w # o foiai»a iB
àW
t
*
19*25
sbâob gW»#
I
» --------------— ---------- «
k f i m jt 19*15®
0 ,0 # 1 9
■
?f ■*
I
0,1}
0*W 9 * 0*25 X 3500
«— —
-----------^
39 ,5 X t X r
_ .
*
9 ,7 9 5 /1 .
%;et rw u lt*#
B@w#
f
# 10^1 #pm # W w I,
I
, ^
# P*?9g / L#93?y %1%3^
B)
# # # r!owm%i: a f
I)
^10 êl#m am fa » W # d
# 1|:
e
# % 0I7
e f Wel^gi#
mm» a# A o w la
b (,lte
m te to tW c&wmal«»
i t Im pm vM M #m t tw dlmtaw#
WWe#a Wo contera o f # # 4isW W l #m «W fk W m lÿw W )!#*
% i# wrlmMm vmlm e f m#s mommt c f
la tm%m
c f Wc distance r
i^ lll h# #a#p##'
(
^ 3 ^ p# %0p )#
Applyia^ tbe p riW lp ie o f parall@l?'*a%iç Weor#%
1^ 1*3 * P* 1^# r # # ite
I
#
%
equatlca ( i l ) )
4^
g
ïja t M s
«sas#
l.
«
J
#——
(-
■+
g
d®
—
%
/
IW
- ih
F ig , 33 «9 Détermina"»
t î o n o f Moment o f I n e r t i a
o f D ia k W eig h ts
D #
d
(a) B o lt Head
*
2"
,
0 266
"
(b) Nut
(o ) Screw Body
D:
-
1
}
MM) T
_L'
T
a
a
m0 .4 3 "
o ■ 0 .1 7 1 "
Lg 5 le n g t h o f shank
g le n g t h o f th re a d s
D g p i t c h d ia m e te r
a 0 , 2175 "
D-, g mean d ia m e te r
a 0,2175"- 0.0026"
Dp a m a jo r d ia m e te r
a 0. 2Î17"
F i g . 3L - E le m e n ts o f B o l t and N u t.
a a 0 ,1 ^ 8 "
c»a 0,173"
D .i 0.2175»+
0.0026
# 0 , 22"
a
a
2 »B
m
m
m
m
m
to
f
o
f#
od
î
a
î
a
.o
fd
J
f
f
w
o
a
tt
M
t
f
e
*
S
Ô
S
8 o
a
a
b
o
o
b
t
o
t
m
a%
s
a
b
a
t
t
t
e
t
t
i
s
st
t
o
»
i
W
l
o
w
w
l#
t#in
#
oc
a
î
o
a
l
a
t
s
î
î
m
»
* .)
m ekâieÊ rn t' %
%
b, )
*
0,a05 lb s .
{ 0,509 *
tM s k disiss,
%
) -«'0,0002? *
*
0,1+3® IW ,
0,432
* " ^, ( 0 ,5 # -f 3?^ I
0* î
! • ttilcS -iisîsa,
%
"
# ——
396
3
2
} a
»m m
%
* 0,
#
0,993
( 0*509 *•
î
s U.OOH77 *
s m m ^ t o f È m r tls . o f t
t
i
©
I m lim
W w lcm latW from
m sâ m t e
s
a
g
r
o f dlfâPmMmt wiüPlgmwtlom#
tW W it M M # W lt Wdy aM m t#
3l^ ( P* 109 ) w # M fw w eé W
A il d jW w lq w
lÆ ^ * %
Im
sm w #*
tee
m m eotlons to #@
w«1ae8 obtai»A iv m . p m a t l e ^ *@ams#% has?» b®e» »i® ta
#ie ftml mlmlattwa.
W
Bom a«i *
W m 0*8(56 % 0.43“ X 0,1?1 x 0,383 # O.W77g »«♦
*{5 /3 6 } 0.*43® ♦ *3 « 0*02563
Ï
0*.00?75
336
# -------- — ( 0*02568 +
*
}
* 0.0300)0515 * o,w(m Qo6 #
@emO ïte a ^ ia l
W
s
»
I
0,366 X 0,488® X 0,1.73 x 0,283 * 0,007# IW,
( S /# ) 0.W3® *
0,007#
#—
• 0.0251:4 ♦ ^
-( 0 ,0 8 % ♦ a® >
« 0,006000511 * o .o o rw al a®
loliew tad C iw m laa Com t*
• • (Tr/4 } 0*88® X 0,173 X 0,283 # 0,0019 lbs.
3, ^
(0,22^ /
3p2 « 0,
0,0019
# — — — ( 0,00605 * #
I
g
)
# 0,0000000298 * 0,moodf98 %®
W l# sBp® » t tWeméW
IW «W l# le iig tti, #W
1% # 1 1 W fepaatad aspopotely # p
##8W®a aM #@ tmtfe»
parta,
àwaaaw ,#«#**
a&aa # # » t ^
* o.ai# • o,o#6 * o.âis*
VoX ^ fe par IW i
m ( 7T/% } 0,215® x 0.233
# 0,0.1## Ib » ,
:
. 0.01028 ^ 0..215®
g
»■---- —-----( --------- ♦ # )
336
8
ÿ
« o .o o m m # 0 : #
% jop ûltffwmr # 0, 21+7"
# e i# t par inm 1@%@% * C'n’/lj, } 0, 247® x 0.213
# 0,01355 îb a ,
I
s '■
336
( 0, 247® / 8 * #
« 0,OOWO#675 * 0.0000351 r®
)
She t@ ia î mma a m # # o f is te rtia o f # -* W IW anâ m W a t#
.mstelmâ. fop vwlawsi aSsoB**'
Cl)
%* tmg bol# ^
I
m
1*
O.OCKWUS +
1 lA " l»as WL% o f
I
m
*
©#00006139
l/2 * A m # md
0 ,0 0 0 0 0 1 ^
2* l88$ bd&tiBf
I
W «#d#
*
0 ,0 (m # 7 9
<aw8#&a&# 3^
o,ow ooiT&
Cÿ) !|." 3«af b o lt o f
1 #
w ft
+
3 |4 î-* stbanfa
0,00000198 *
la
3A " W #'8ds,
OmOcmAd*
3/%* W e^a#»
0,:i
g&wB tadBüI edr#e@tdbn& BBw&m %KB8#a&
<%f 1&M&&
tb#e*a#*
Otoooomîîis +. o,ooo(W99 ^
3* lomg w i t o f S l^ j."
I '#
%%" 'W e # # ,
irw&rtijk &B 1@&* a&B*
iWk) $B*& ( 3# # aa*& d8%Mam&# tg&oa
%db%&&&G%i *%f t#%& 8&w8%aal#%8%88 swai t&K& imsigBHb**
ga***
<)*2
o f IBffagddbP# IdH%g#b <%f 3#HM&&888 <&f a&wwf&*
j&)
tSie @#%%9etdbn& laæyzGb <%r & awM&ticKi (&f a&u&f&i%y& TB&jU&% 00%*»
#80%$ BDotbor eeatlan by abaft &3#pll%a& la &&8um#& to t#
greate# tba& the aotoal leagtb owlog to tb# lo c al é&fçrma*
tloB o f tbo abaft Mboio I t ontora tbo coupling*
I t la luo*
d#B8tood tia t* #bere I t enter# the cagpll&g* the abaft tw iata
IndapoBdontI* o f the oow#ll&g fo r & certain la&ctb and th a t
abaft and coupling have agu&l an lea o f ta la t fo r the re *
aalB&or o f the dlat&oçe throujL the coupling*
10 quote from tlla o n *# book* *ln the caae o f member#
th&t are ahruok on to the ab aft, &###&# that the abaft #0*
tK&e# ia%& *ütt*dÈw&& saem&wür i\%r a ILeag^Si
Ibo çw%e~qpwK*t*QP
4bo CK%&*hwCLf t&M» dUU*mei%&r edf t%K> #hadft* 18&e @R&all4Mr vsdba#
applying to tig h tly &hrynk*om mewher»*
In th la oaae* too
bra&e plate# w ith a half-round notch are clamped on to the
ehaft# and the tlsatnea# o f the f i t can not be egpected a#
what o f & 8hruBk-#& member#
I t #111 be aeeumed* therefor*#
tL*av t&K) ehod^b ontBMp# t&wk attw&ghed %3&mbc%* fo r fi lIor^ÿBb egpwül
Sx) th3%&&-gt#8ftcr (%r @#%M& moa%> -of t&&& dla%a&t03* <%f t&%& abadMb*
:B) j&t 1# Ib&ljhMn&d tiw&t t&w& atlhSfeoia^g efl%h&t of alecMRW* d&w*
jXxaJa (%B th# lbljbja%»#a cwf the jM t* tÈw» leegÿWh o f tie aCU&ev*
In re la tio n to the abaft diameter and the m aterial o f the
eleeve*
In th l# arrangement* the a tlffe n ln g e ffe c t on the
abaft may &i#o be neglected*
G)
*& daallBg w&tb tb * trgB*8È**lo& myatem o f a iQ*r&a* &B##
ta lla tla & ahep* tbe prgpëll## la separated from the englae
T%y a long length o f Intoraedia*» ahaftl##* the aodel aya&em
m&^bt be too long to be able to handle by th is model ayatem
ataad*
Ih la lead* to the Idem o f replae&ag the model 0baf#
by another shaft o f a&aMao&form dlmmetef#
%be e tiffa * * * o f
ead\ section require# aepmrata oonBld&ratlon; hoaever, th l*
a lte ra tio n fa c ilita te # the adjustment o f the o v e r-a ll length
o f the model ayatem#
She a ffe c tiv e length o f ahaftlng nhleh jolne another
aaotlon o f large dlau&t&r 1$ greater than the actual length
oolng to the lo c a l deformation a t the junoturo*
^h* email
Shaft* In e ffe c t* b u rle* It s e lf la the larg er 4BB# ;*& dbomi
36*
t£^
r— '<iS3î»
P
i
g
.3
5- #
m
f
to
f
Varg-lag M aM teys.
S
h
®
allowmo®
\
d
e
p
e
n
d
®
-apon
r
a
t
i
oo
f@
i
@
shaft
didBBBtdWMB#
3xwR&%g& taaül*#
f%*am t&%#
( ***#
%&k $b*
l%&Q&c# pmyps 34%>, IR&l* :% )
3Sa%C%»<f&lip%» ]j<8Bygidbk {Kir zakkoufls odP TKargriagE 33dL#8%w»t;*ap*,
mt#io s I /
Istio 1 % / I>2
1.35
0*055
1*50
2,1)0
0,095
0,100
3.00
0.107
Infinity
0,125
<>#3 SS&a*#; ipjp
3Ei; ha* i&]L%48i&d%y S&aw8a&
ai%w3M%& :&& b&kd* spstsMfjbcpyw* oasakaytwaape iK&wMit #& StisJM; g#%;agrjLng #k i#****
rdLSk# (@3^
SBBtgr lawKSMG *##p*q»**éLK iae3M&**#k (saT :%%?<*# iFl3b9P#ttdl<%%%ayf
*&&jLo&& «BBS» iaa*i%0Lll3r i8%l*f$ül3i;3wjL(&tw8MS
i9GLi&*;tdL<> swgàPsmawBkt
ISgr
;& aitRawSy ()j» aaK%:%%9*3L
19&%# %a(>d*3L aqpTBlbsMBK, tdBw* *K*d&%%gf
jES&asaa edp t8i# i0^ll%%qa;t3l(XA 43<>%qp%&ifrH08oeiaLKy3 ta&
zaswabRw* ]B*aw#ib
bo observed#
31 dbpdliro aOTZüuadbodt jfypCMSs IBkig» iaf>i%CRP' *%%M8L iGbwa
m#@b#Rl8* &# tr8n8m ltt#& to th# model ayatom tbroudh I t *
eugpooiion#
%b& model system Im tbsa acted Tby tb&*
n#l tarqu# thidh serve* to
system*
the o8oill% tlo& o f the
I t la eased upon the prim cipl# o f re&on&na# dh&db
oooure shem tbo applied freqoaBay oo&&&lae* e lth aay #B# # f
117
the aa&w al fp#guaae&e# o f the o*e&il*t&ag system*
3b tb#
08# naturel freguaaay* o # e lll& tlo a o f #er*
te&B mode 1# #b#epv#d*
3b# de&vimg speed *&11 eorreepoDd
to o0#lMùNWUBfü8r ]&&tu&el fteqpBKKgr <xP iBapsaodel system o@m#
# e msxlmm jmg^L&tode o f o e o llle tlo a is roadbed*
^KBSpl#* llla e tp s te d &a Chapter 3 3br aat%G#&
gwaOy <w&l(KCLatdW%a %gr twâMÆ3gd%&0BL3aet&K%& edlll 1w* redBersNMl in
Bbe jPol3x%*ioy; t&adk#*
<& e&wwdk #& tb# oa3UB&ai%*& imdkG*##
$i eo8*&&%dÜ&9@i3B*y Tbs loadbr *14#% t&w* tèw»t %4w*w8j&*#
3%kK *grlia%aa&q** 3%9ü$*N&yeüke* i&iBgÿ&e**w&tia%& «By&i&a» d&aM&eü»*
be a 2inZ 38^ <%$ #&* %9&ne3%&tgo&$
5B%8 «K$wiin&3aa%t (gr*tRB& 3U% 8&w&#& 3k& 3%L$, :Kg*4& * laag** güL *
C&w%pt4KP jk*
jC)
3ba* oaCLeuüU&takl fïq&güKB&Glawa maa*:-
3L*t laodk»
2#620
,&pBi
8%wi BKwa#
y#3K%F i*pm
<%p
#1#
(WP 3U&2
2&et*4)p <%f 3&W# Jkwlel 2%ysü8*a*
4%%p33r to #»q%w%ti(8& (1^))
^^ / %
«
<4P / % * (Va //p ) (% / i ^ j
ma»t.
la
m Q»2S*
%
HsfflW
#
(dp / % A * { 3,35 / 0 ,0 ^ A
*
313*51 X 10®
,
JS
/« •
Z„
X
— -------
® ' 313.51 * WP x % X % 2
(m)
OjrUoâap % w ma
C^Uaâar Maaa*»
Ip. »
\
iw»in'»a®e.?
( m.s* 3K5k p . 13j» ) I
1 - 6*
2 * 1/%" ttîlBfc dlsîoi
t • 1 'VI}.* 1@% W l# sœa «Ht*
% *
0,00125
0,000%
0,0000085
+
*
O.OOW
0,00Q;ik56
0,001193
♦
0.00120^
\ # 0,001793 ♦
„
rg
0,0013055 X 1,1® * 0,(
Sîgla# &flSæâmr % « !% * (1)
# ® flM Kt îüod® o f
fp «. W m» t ‘ P •
119
1
6" diannel-arm
2
l/iî." thick disks
2
—
j»-»
--- L— 1
^,...11
r ■ 1.1"
bz;._L.. .
1
36 — E n g in e C y lin d e r Mass
Model System
-
Test
1
1*
- 1 5 ohaimol-arm
2 . 1" thick disks
i|. - 1/2” thick disks
2
r » 6 *8 6 6 "
^ lg +
37
- 3 ’* bolts and n u ts
r
m6 .8 6 6 "
G e n e ra to r A rm a tu re Mass
Model System
-
Test
1.
120
kZ^ X 27 X 165
7*708
tJ
2Si>.iîi
itr- X
X u,uuj5H^a
x %“
313.51 X 10®
0,003252 X
%'
/ ^ may be
If fjn la xariod, the ooprftspoading raltiea of t
oalculateds-
ops
cpm
2
®
1 .0 0
60
1 ,0 0 0 0
7 .7 08
1.25
75
1,5625
4.933
_
Inehos
■p « 122 ope#
122^ X 27 X 165
,
“
313,51 X 10^ X 0,003252 X
65.05
'
Beep the a@m# 8*t-up as calculated In ( l ) ^ above*
%
2
in c h e s
66*0#
7+708
44933
(b)
1*000
8*%40
13+180
Generator Armature Mass and ëpaolne.
Generator Armature Mass*Ip
#
23#600 Ibs-in-sec#^
ops
cpa
1.000
2*906
174*3
3+630
60.0
218*0
3^ (
38*
119 ) ! •
1 » 15* lAaaml-mmm
t « 1" ' #l@ k # # »
4 • %/t” W # ôl:itea
2
^
«
3* lm% bol-fc* mad nwfes
0% W 3&
0,00228 ,
0.000003&28
♦ 0,00462
* 0 ,0 0 1 #
* 0.0m%'32l{.
0 *# 1 6 3 7 W
♦ 0,00936824
r§
jg
Sf^
Ch*8dWH&#%Wf a%M%8i3%g**»
3B& <%éa#Q» $# i&aüM* i8%è *w*a# j8#<as#tBKi*#& adbaHj&rllgr
t&w*
48%* :#%p#adLQg ae&tdb&. gWT 3B&&81F %MMb*#Mwa i@&# #&%*
(SliMk <gdL!aM&#%* )%pww%&zy& a%w& 4&w*
e ^&eaays %*&at 1%*
&W&*
Cl)
#8# tb#
a f vib#*&iaB#
#
<#%% /& * 38*#
* 7 # 7 08 3C-- ,» SbjLSS!»*
27
u im
epB
apa
l.W
1.25
60
76
■
—m
1,0000
1,5625
/a # 9,13^5"
X 32 *
^
i# 0»Vi3l62
313.51 m 10® X 9,1355
.
‘m
InaW *
m
i
##62
-
#
47.1312
.2
313+41 % 1
0.W3162 X
.
1*
1
È M
3# %
13.1'
y
3.630
»'tl
*
fa®
174.3
213*0
# P*
%&%
1*##*
0*062* *
apm # th@
6%'%#* ^
( P#- 18). )#
1*8 #p&atn% *
7*?08 » 0*06$ % %
#
9,136# - 0*068 % 8
#
9#'
123
suspension wire
(0*02^ dla# about 10'' long)
^ ^ 1
l/I'p" bolt and nut
l/L" thick disk
6” channel-^arm'
model shaft of 0.062" dla
gen.
3 " bolt and nut
l" thick disk ^
l5
channel*arm-
l/2" thick dis
FI ;> 38
Ilodel System
- Direct-coupled Generating Set.
.
fla to g. - Fodel System
6 - G y lln ü e r E n g in e D lr o c t-C o u n lo d to G e n e r a to r.
Ill)
%b# model ayatem eee&llm### wl%b * l l t t i * aeekla# mad teea*
bl&Rg &R $&# vewtieml plaa# «&#& t&* motor 1# &e&v&og*
torelOQal pead&iwa
A
]a*f%*gwaBgy 1*
4 * ABBd&er o f 2&et# t&a Wbol#
olBdlng the aweponalon # lr# ie potmtlng *b#& the vibr&tlon
the model la peogream&B#* however# i t la dlmlalah## Wbll#
the drlvlB # epeed 1» iBeroemea*
%h# ataod 1# ahakea too#
but I t la believed to give no ef#e#t o f r#a&a#ae**
fhe applied frequenelea are o&t&laea by meaaorlng the
roaalBg epeed o f the earn abaft*
8he& the maxlmm @%pll*
tud# of v ib ra tlo a o f the model ayatem la obaerved# the ap*
p lie d fregueaey la taken a t th at instant to give the natoràl
freqaenay o f the eorreapondlng mod* o f vib ratio n o f the
model eyatam*
(a j
#br onawnode v ib ra tio n ,
oounted fo r
10 eeoonda* or*
fg& #
(b)
33*# opm
For t*o*nod* vib ratio n *
counted fo r
9*7^ revolatiOB# iha# been
27*2 revolgtioa* Ihaa been
10 a&oond*; or
f+2
»
16#*0 spm
Wî
(a i
6oiva*4«w»
mS. 3«leu3.«fe»4 BmWwO,
o w m a # TlWàtÊom**
(W.,milm$ed %e«p9aey#
# 60 eyo
#w t
# gS.g #m
;»
Bm #
e— —
60
0#W
<» 2*5 #
Cbî ■Wo» WMWd@ vlbmmWlem*:»
O gtm laW l Wmmaam-t,
$ 1 # *3 @m
# #
# 1 # *0 #pm
H fflE » ©
m
—----- -— » 0fC^32
i? lt*3
ov &.3 #
i%7
rated &,T#0 BB# a# 138 rpm emgla* ea#»
neoted t# tba pro p eller throagb a long leagtb o f tr&n*&&#*
elon ehaft#
lb# egulvmieat eyetam 1# eh@w& l&3%ak 17*## P*aP do# Oba#*
te r
1)
3 *
3b# oalawlated frequeaolea are*#
Satagdt
lAsLb epm or 2*7#8 spa
Bad MBd#
1#0%1*O epm or 17*3# ep#
$etW8p o f 3b# Bbdel
1& order to elmülate tb# long leostb #eot&o& o f tbeipr»»
p e lle r abaft# two wire# o f d iffe re o t
diameter are aolder*
ed together to m@k# the model ebaft*
G*re ha# beaa taken
a t joaotloa to #Bewr# the torelom al rig id ity *
"(i&)
ijR flja*% <]%r3JLiuakKr laawwt #ki%d 2%>aiojLb%o*
:Ea IKkLlsk i&gLae,
## 3L6.TH?*
d^ #
Shew#
( d^ /d ^
0*06àg*
a ( 16*7$ / 0*062#
# k»nuz3 X i(#
( l)
Mae* aod üpaGlna# fo r #o,
3L *
1 , g*
^6*000 l&**inM&#e^8
6
BOgia* O yl***
X28
^
im#
m# m
) *
1 • 6*
2 * 3/%" # i« a ; mrnW
2 <* I" 1#% botis* aial m ta
0.0012S
.
O.OOOS&
* 0.00106
pg
,_A.0000C^3 * ... O..OOQlg3l9 .if...,
^ #
0 ,0 # 7 # 3
♦ . 0,00113378
'
■* 1*03125*
m ,
Ig, #
0,0011923 *
*
0.00305125
@ b#
f î» # %
m e *# ©
&
t w
0,00113373 X 1 .
lb m
M
m
,
%
«
2 ,7 5 3
#pm
#
# W iw ,
/
2,753® X W X W^OW
0.39813
dg « — —----------- y------------------------%-#
:*23 X IC^ X 0,00305125 X fa®
%®
#
*
a 1
#
v
a
r
i
e
d
,@
m
@
e
m
e
#
e
m
d
l
»
g
v
a
l
a
o
B
o
f /« m
m
y
toe o alcalated i"
*1.
«P*
&m
1,0
"
^
5Î1-
im he#
1,00
0,31
oJP
1
6 " channe l- a r î! î
1 - 6 "
2
1 /Il"
2 • 1" b o lt s
2
1" b o lt s and n u ts
r :
t h i c k d is k s
o h a n n e l-à m
and n u ts
r s l.i|8 6 ”
1 . 03125 "
f —*H- - - - - - - - Il
lï
(a )
iïo .
F l g . 39
1 ,3 ,1 ;., 6
c y l.
(b )
No.
i
I
1
1
2 ,5
o y l.
d n g in e C y lin d e r lias s ^ îk>del System - T e s t
2
OL
Ô
I
j* 0.0625
F i g , i|.0 - é q u iv a le n t System o f P r o p e l le r w it h
r « 1.7 2
F i g . ij.1 IJodel System
1
9" c h a n n e l-a rm
2
l/I|."
2
1 l/I|"
P r o p e l le r lias s
•
Test
2.
t h i c k d is k s
b o lts
and n u ts
fo r m e aeomd m # - o f v lW a ti» #
.
.
■
ip # 3,f«35 # » *
17.35® X W X WW#
^ 3 5,A #
® * i|335,23 z 10& % 0 .(X )3 0 a # x
/.
%®
;
35,5%&00
1,10363
0.39313
Mam
*
.
'
opa
.
1*0000
32*0S%1
39*5500
1*0000
5,66 i 5.
6,2700
aaft % « ln g »
3^ a
3g
4.
# ,
8# 5»
60*00
335*63
376*50
% l.lm #r$*
22*000 Ibm-lmf#*#*®
( Fi*;,
p. 129 ) I
a ■**■ i * i«Bg b o lt# aisi ïsîts
1 ♦ 6* <Siafflael»a»
0.00125
■0.0000021
^
# 0,0012523
&
#
,
5
or
♦ 0.00012378
* 0.00012373 r®
0,00305125 / 2 *
0,001525625
0,001525625 * 0,0012523
w -------------------------- :-------------#
0,00012373
#
%aeiMg WW##m HO, 3 e y l. an# Bo,
Ip S 90»
oyl, i-
2*20315
% w W » # # m m 'mMî» «g Wm
i*e#* g# **
a* M # *
*
0 ,% )% .
Cb)
fp o p o lls r %«m mâ a p # # % ,
(ï3
a # â m lW i % # # « fo r
Ss km p «ts9
êm
8#mo3
%#@
o»W
A
a » * b#»
90
g*.
# o«oô2S*
C % # W# #*
m W ïw à ty , tfa® p ro p e lle r spastog
% # l#® # # # # # .
gp » 5& W # « a /g # 1 » o *i
780®
le # 0 . # m f—
W
) # Ml##**
a#7S-3® X 7800 X 53000
0 ,0 0 3 6 1 *.
W@g*&3 m 10^ * i5 l* # jÉ i m %® *
& * Ê»
%
#
% 9 6"« «
/g
»
M l.6 6 * /0 # .T 1
#
199#51"
3efe-% o f %*© p ropeller mam m a «>ftotoî fe r
%
# 0.*f*#
%®
p
-
.
< % / A , .A # {
# 3 *ia
##
0*9®* 199,53 * 0*ooM?5i
3*136 X 32 X 0,
( F ig , 111» p* 1 # ) I
1 *" 9'
2 •* l / I l
3 # 1 1
O.OOli
0 ,0 0 C *
♦
0*0000023. . »
.ar0,00li.7325
♦
0.00106
0*0,001I{S58 r®.
0.W120553
0.0)7333 • 0,® t7325
w
#
# 2,93
a*
m
0,
o,o6®5
-------- — s 1*33
—
Dg
«fame#
O .C % 7
I
—
%
m
/
0, 0S
'
*
0 ,c 4 7
*
0 ,0 8
#
0 ,0 0 3 7 6 "
ït o r e f o r e , f la a l i y
'
7a
•
3S » 0*003#
#
* .9 9 6 # '
Fbe f * # 1 ap*
**& *
//
* 0*#8 * tb * .g&Bdl j%p&&ü%s3ü*
/#
H)
f& ator
# ( 3& a 0,81 ) « 0,90376 # ag#390&k*
9@afl8U##&l#& o f %b# Bba*& 8y#tam*
( Bl&t# #* P#13# )
j&aawae tbo dbaft ontere the Ol&ap by a leogtb ogwal to the
diameter o f the ab aft,
j%B*
3be model eyatem Im thu# jwetsgp
;&&<#%& * ae eboaa && Fig*
Im Wbieb#
Bbgiae oyliadar maea apa&inge ou the dbaft of
0*933?“ fo r Mo*
.to *
2*3695" fo r »o*
0*06&$*
&&*#
1# ani 2| So, 2 , asA
3;
k a M $t Ho*
6 eyltoa«ps,
3
m6
$ «aâ
h eyllwïora»
su sp e n s io n w ir e
( 0 .0 2 " d i a . , 10 1 /2 " lo n g )
1#
l"
m odel s h a f t e x te n s io n
(0 .0 6 2 5 " d i a . , 20" lo n g )
lo n g b o i t and n u t
l/k "
t h i c k d is k
6 " d ia n n e l - arm
1 . 03125 "No# 1 o y l .
Jl
1.L86"
T
Ko# 2 c y l#
No# 3 o y l .
f
m odel s h a f t
(0 .0 6 2 # " d i a . )
No.
i
r
c y l.
Il
l#k86"
No. # c y l .
No. 6 c y l .
m odel s h a f t
(0 # 0 l|7 " d i a . )
V)
o
o\
1 l/Ii"
l/L "
b o i t and n u t
th ic k d ls k - - ^
9 " c h a n n e l-a r m y
r ro p ♦
/
/
1 .. H
^
1 . 723 "
1
P ig . 1l 2 - Model System
1
-
1
■
M a rin e I n s t a l l a t i o n
135
Plate $ - Model System
6- C y lin d e r E ng ine M a rin e
P r o p u ls io n I n s t a l l a t i o n .
BWü*a
ozi Bb# idbaZMk o f
<)*Olür* dWü*m#1%Kr *«*
2Kl*j;H;%58dü, «» OtCtpl;. *
3:I:[)
Sfewdb aktsPULll»;*,
3&3<>
jlat %a«wG&* jbci lb&&a «taaawb iB%
8%
%
%
%
@
op #u* !&%
& i3«w#d& (J&) *
9Bbw» ;wBqp3r<yr*a*KBWGw» c%f tdbdlj# ]OBON&#*3. adbkOVH» 3j#@# j*<*sw:dLt;i;yjLts3r, gpri*"#
jgsBB&aJblLar Tbd&tkmKzg;* tt*** 4a8ar»iawa «sgCljLi&dksür ]8***»d*@w# #%%%» aMBrt" tggt spsk**
Bkta#» (BSloiBw*
a»* IB&k* #*%%pC&jl4waLjfa^gwsf&awowsgr goo# SadLggbp*
4*%» jToz* <a%>aw»3PiP%3nyg %&%** i#4#ecMQ*% law)#*# <*dF
*gyi%1bG8& gwBo&jtlJLàkiBiM* sdlidbi sa##» i%pq%Bdbu*jbBy8&*
düLj%(%l4*üLl,1& t%> €8RÜ&8@m $gbwB
be**» %0K>dba]L
]&%; i*%k# i& IMltctZl#*
3&%& t&iO l@3KM>I%dl %a(M3k» 4&df
irlib]p«kt;lon «odT Sgaa* %âè)d&qüL
(j&jt JBcxr
jE%%* 310 #*#cHnKl8*
2),7!> ipereqauLurkjLcgcNB «ups» <#;%%%%%*#
jkt*** *
{%}) 25c%» i39R3w"%w3Ha#
jSw&#!> %q#irc}3A3d&&<)%ie; i*3P<*
&a jpt»* IlO i8$>4B%%&e* &,*<»* jf
a%%Bi
m
Gmvmlwm W W #m # ©
FF#gR#B#&e**
më
w
^1»
Grnlmmwd WvmpmkBS'f
#
a , ■m
#
##»#: * -------
(te)
. 5 2 ,5
-% 0,0278
#
«w»
52*5 #m
or
2,78 5
# r #m *#o #
SalosüyitMni
f jg
Emma
mm» #
^
m
'' '
339.7
#
339*7 ep®
#
323*5 m a
m 0* 077% Or 7*71 #
130
7*1
o f Tb# *!odol
I t ha# alreaây Tb##a
###&#& la Chapter ^ how engineering problem# may be atadlad
by m&GB# o f the method o f model te a t*
In deelgnlng a model,
condition# maat be o a re fu lly determined In order to retain#
in every re#pe@tf the ehar&eterl&tle# o f the o rig in a l ayatam*
Fredlotlan 1# then made fo r the behavior o f the o rig in a l
ayatem from the perform&nGo o f the model*
Ihe model need in th la inveatig ating work la oonmtruet*
ed In geomotrioal a lm ila rlty to the proto*type* 1*0+, the
id ealieed or egwiv&lent aymtam o f the o rig in a l eyatam*
!IS3d#%»j?cree# Ib&we» j&cwORiapswagr iBdltâki tdbwGJlhL the las&cUsl lagratKMBi 3p**prpg*'
cbaeera tasw* tKsiTac&cxKüaül
agjLcwaJL logrartëKBi
43%k9UP*%<Mbi&;Kia;i%i*&* (sdT ithie cirdL#*
lugpon l&ort&i &&ie 4*iLtdLgKf%&a;tK)3"y <;oo33re:pi;i33y&
<%f IsbwB c»rdLa»3jQW&3L iKacEq&zsgpBagaKcyt Sandso jits* 4»cpwjLin8Ll<*i%t (%yat%ew& *ücw&
t&w& @
kGH8%ü%Qd&g» <34%Bw&t%%Ri<)tkia*%k
%B(%3ü»3L #%3rart*KB&#
jfiKB* #&**
tag** ]%K>d@l *%F%&1538a jla (>cKBw&{%%99d*dL, dit, jits :r<)<&ùjlapaMl tüsu&i; t&*#» 3%K>dbeCl
*%gT8l&G83i 1%
G* joOLoaw&lgr (3gBwkiTfai3jGG3t; jLii <33f%%B&adLo jaa&dL Bulastjio ipMPCPSM&if,*
tdLest i&c> tSaat <)4p3L%jLitgCl
ICI; laR&g* 403};;3Krnr4»dl !&%
%ae%rs%%q&3L tea&tm isbwadb tübw» iMBgpüroisaatiüO**
OjT t&%* tü&3mG*l(%%%aL& Trijb3PgitdL<*%% sactclGl aqF%%1%8W
& aw#Bi* be* Ibw» dLij*1&u8E4&"»
48W
& tKgr eamftwajkn
Shy» jftKKftkw***
t&sd*#*#»
1#
:rGiot%33*3; tadLggkitt 1)4» q*)3*%49üBd&8Mgi#
3S& twba* %>fq»4S#*dk&]ag;
ggbwgalbo:*», «i iG**BqBM*apaLaw8*%Slat 3a*%d&* 3L%i TbestgbL iboartw* teo 4#%iOMNr 1düwa cle*
]Ewaa*taaap# cwf tahwa tkewai; :p%a4fUL%jb*; j(ïP(XG& IbBwa <)*ü%xo%%3ja;bw»dl ifajjuwax*»
J&Z1 @a8g&3;y9%jL8 o f IG&W
S# 4&I*WW9*W%<>3r 4aWl**48Pq%S>«8B*%3UaH* 1bel2*P6H8Kl t&k#k 43Wk]k*
aoGM# t@
3w&
:(yp4&cpüK)i&<%&d%i* j&a* iBwaw&*» <3:%taaa* jg%>]L3Womidk%&g
page##*»
jL) 3&Bwa4>c83WP#wQdL<*a* i& lütxdWkï a%f%*t%é*a#
SS#* %üK>db»]L i@grarG**Bi31%; 3*<*t t%p spiibti ;aa&jhaw#4&*%>]Le%aBU*a;-dl%%8Kr4%|j&j&
igadl 3&%%8Ma*&1%03%o;&jow»cl j*i}&odL%%dp* #wb tdbe {w&]l<Ri]LiK4M»d 'piaJkuw&ak*
5&a**
(>f 4&4%ERaaM9W33r ]0*»(Msi*8Maapgr jftxp ^p8H»tüb%gr iBkk&
i#%k3juw**f
<801 30W
&1; 1%t <)%>tw%inadl lagr a#M%#%%p3L%yg *dlt8b ik <)gM5Ul%wBWP3r <KW#3L#t*
35e%t&% t&%8 aaewmst 23*38%aikl& (%g» jkaw»&*tdL*& (&2* iskw* %r%&K%M&i%3jaG&)Bs&aü* agodl
IBbwB
<%2' 18bw& aweetElcwa <%f aGbwwfMb sawagr Siaoys* :&a%(%&3'rq#otr %#&%%#**
(Main, tap t W» ;&%%awxnjüp«it* **<*#>«%%%%*
3*p<%&t ISkwa ;2%%i%3i%s*aG%$%&3L jfamaw*
guanéy equ&tioa# the torglon&l v lb r*tlo & ay*t@m ba# tb#
j%>l]an%i%y& eaüU&tdUa&e&ü^pa,*
f lK
V
Tübaoa»
I x/
<1 **i&&a88*t<wp oj* tb# labadft#
!I 1* MaosasQodb<3:^ i3M*i4%i)aL €%f tdba*pdLtopSktKlasa; %a«Law#,
/ # SLswoystai <%f tab*» i#&wadPt:*
Ih i# e&preaelo# ah#»» that both tb# m&ea 3Bom#Bt o f
and tbo epaolng b&tmeea ma&a#* a ffa o t the fregwanay o f tb *
vibratin g ayatam inveraoly && the aqpmr* root of the lio e w
diw aaion*
%)
BoB^Ualformity e f %&» 0&d@& ^b&ft*
I t l8 ahawA ia the above am reaalon th at the freguanoy v*#
rie a w ith the #@#are o f the abaft diameter While the leogtb
o f the 2&wü^i#^4#*%BW#2Km*#tof ia a rtla remain wnabaDged*
3ba model abaft i& aaawmed to b* o f oaiform eiae tbe8#0&e#t
it# Vbol# length*
I f the model abaft i& not n a ifo r# in
ol&e, tb# frequency may b# changed conaiderahly,
II)
gffo o tive Length o f #he 8#@tio& of Wbdel Shaft*
I t %R%& gaw&UBBwi t&y%t* 2b& 0w&tt3j%g
tba* aàck&ai aQnete&&# t&w;
abadft awatea#; the cldwgp# <&f t&wB Bü&ae#düB#3d&i& set eawdb 48%& (dp
IB# 2H»otdk*& tor an imaotait (KB&al ibo t&w* dWLem*M&ar
t&w& abaüft#
BkM*G9%%p# i t 1# IbeajLevqwi t&wwt t&w* cdSfecüüive SLexk^Wb cdP t%w*
@w»cti4w% cdP a&wwft BB%y ta» gaMwataop t&uw% t&w» «og&eclB&d vTüiwe (iae
t<> the i%BKM%pt#üüati4%e cüP tiw» tijgitoKW*# <%P iik t bartaewm t&w*
%aa3W&#iiKM*ti#t elaegp aaai t&w* a&w&ft*
3^%%a 1&w@ cQQprgwNRio&k i*besm&
4ab<nn», t&# ibM&gwwKtey <%f t&w» aKM&el sgratKBR 411 t&WKP*j%%P# tw*
lower*
A# & m atter o f f&ot* vh#n the epaeing 1# not ##t
igp very oloae# the e ffe c t on the frequency o f the model "*y»#
tarn duo to th i* uncertain condition m&at be neg lig ib ly
am&ll*
^hen the anaclng# bet*e#a the m&*8#iB*iti&8 are
fa ir ly am allf a# in the te e t o f a marine in a ta lla tlo B * the
4&KP0#
III)
th# Clagpiaa @ff#e$ imcy b#
Corroctiaa fo r #**# o f Shaft o f tb * Mb&el System*
Ibe abaft &# ageum*# to b# weljbtlaas#
I& @a#e a Il^ b t
ayatam la aet ep * ltb am&Il maa#*loert*a amâ long aaetlon#
o f ah âft, aa la tb * a*#a o f aooond te a t o f tba maria# &B#*
ta lla tlo n # oorraetloa fo r tb# maaa of abaft may b# taken
in to aooount by follow ing tbe ru i# d#aorib#& prevlooaly ia
Gbaptér 2 *
B)
DampiBj Bffaot#
Ib * model ayatem la aaawmad to vlbrat# &a jaaiæm&mgww&j&MW*
torelonal ayatem*
I f damping la introdwoed in to tb# :mod#l
ayatom from any aooro#, fo ria a ta n c # , tb * frla tlo n a l re#!#*
tane# ealatlng in tbe a&zportlag bearing## tb# natorai ;fr#*
gw&Boy *111 be radBood#
lag
3bla may be verled from tbe fo lio *»
l&wt
email damping or
1
gbere
& < #_ # % ItuL*
n&L
0^
f_ # damped natural freq&en@y
M
I
# maae moment o f In e rtia
#
e
tormlOBal rig id ity of tb# dbaft
# damping oo&ataAt Wbidb produoe* tb# damp*
jby; i&Em#&*1&&lA&]pr^portlon#l to tb * v l*
bra&loaal velo o lty
*2
#
o rltl(# & damplB#, tb@ valu* o f damping ooa#»
toad; W iloh 3KnMP*#%waa*#k i&& $&w* *g%w&ltaaH& ojP
t8M8**lidbaa 4a% frswk irl%8Nktloa i*it%kirl*4KBw*
dmplag
IhdüB a&wBPB t&u&t $&H& darngpod %%&twGMdl f%MW%#e%wgr &# iloasBr tbaaa
iWb* %HB&a8%M%& %w&tw3NCL fïNwaoaw&gy*
g&WM* odP 4&
A&#K»* t&w» r#aK%oaB%&* édU**
id ltb irl*<xM&$ dbaqpiay; ahoam* tba*
tWCfsw^b odP daBgplay2 <%% t&u& fymaqwww&egr raddLo *%t %q&@o%wKBawk
3&l
( I%$ 3i&) )# id; 1# B04H& tÜWKt tai* *N*#0&WKBgW#
a&ülftM* to t&wk idWPt #w* (K%9B%wp*d i#it&k t&w» %8%aam%>o& aPorirad
ifib*%%tl(%&#
]8#*w&# t&w& «gwpliawâ f%M*gwa8&#y *kt %%M&oiww&8* iK&Il
be Bldk^itlar IcwM*# l&wa# IBao %%at%wMkI d%M»q%ww&oy <>f t&w» i%H»$
m%%aa&H»a TdW%r*ddW%B agfatamk»
jlIt&M5ua)& t&M» daegplayg bw&* *K%aa s&fÊüw&t <*& t&w» $HWpf%m39à*B*a
4)f lBbo lacKb&I agFeiMM#*
la» %&> o<%38l(&&r%d*lo i&r%%%r 3ba twde*
i*y& t&w& agypllak# iüreg%w%nagr to
t&se xw&tgom&l jRpoqpw&Bdgr
o f iBbo zaodaül agnGt#@& Wbwan ta%# {&B9pdba& jka twüllaMnea l&o t%* vsnry
m aall*
ïBbo dam%pl%y& iai twMBb tOie la&dCIl agn&t%H& *o&& lib * %%&&$%&»%%%%»
1^3
OO
OsZ
o .ll
0 ,6
0 .Ô
o)
=
h o
/.2
hU
F r < z c j^ U (2 n c j
I G
/8
R o i i o
h-3 • Resonance D iagram o f
F o rc e d V i b r a t i o n w i t l i V is c o u s Damping » Showing The
iï,f f e c t o f Damping on F re q u e n c y R a tio a t R esonance,
-2.0
jUf aagr#
iBbawi auwsBBWül 4w>
p*%%po3r&loa&#l*
]Ct #a%o%jU& %w*
Beta# th a t p##&iotia& fo r #b# behavior o f tb * proto»typ*
fro # tb# p«rfor#*B@* o f tb * BB&*I »yotm& a#n iab%ylx*aww&*
QBdor tb l# çoBâltloB#
A ll th&#« feotorm j%#% ao&t&omod «blob & ff#ot tb * per#
formanoe o f th6 modal ayetem may bo p a rtia lly or fa ily
:a3&dlBKlj»@kâ 6dl*89wB%* tpgr iabw>ggp#*t%i<>#Cl (N)ii@üldleü*aLtjLo*% os* Ibgr ]***&:&%%&
jK*qBMKM3iP#*gM8K%l%8 31%
% b3%@ cwaciBrLüPuicrbjLf):! (>jT tJi* lakatlal agsrartwiBt f%K#»
j&BOpiÜ&wawp taaad&ljGf; Bmaiplc#
?#»2! ikgnPOPcypGPdLedb**
IBB;** S%k>dbB3L i8grarbOB&, *«"# &jba&*» 1G%w*
dPa&GHgfaaKowogr if*%r4E*k*; iedL#& t8%*& #K%WBaaMt <adf t&%#» jdbuauft: 43jL#a%*1&#r* jtik
%%111 jdtkGHiF #w9q?*%eH)jLaLb1L<» (S&waaaggMk <3üT
3&#8pgf%y%#s9LBw&4t ocP tiaa» %ac*dbB3L
at,f3tM3%& jPoa* *& aijLr&it» ja&waamge* (%f Sasw* aübawlMb djlaB#1ber*
SDOOM»;» iodf gpsibolasaE ikdMOB&dLtdLifljbgr aawadt
JBtmr
i>€oeüRc%e#88ücw8*p <owf i8%(*
3aK>dbB& agr(;1&8*a, jit: la* dksaiiiPtadl t%c> **€)loot% tb l# i#dl3%& jPo:r tdbw)
G@aw*l*t
iB&aat 8%ewà&3l ja3F%rG%*B%*
!%(*%%) f%8üP(Kr#kb:l4> (K):%d&t;loa sasggr dk3u*& Tb<& (OWbtwodlzmk* *%>%* ik&k#*
lacwckal i&#*9r& %%y gtei&i%%jai% %
%
%
> iL%&@a&gkdb&3L a&yaikwBt iKlGki %awtGU*4"lj54*%*kjl<&*
ftBP 4%&>@rt*
aüboü&xl Ibi» luww&dl
jgatt; ]L#Bp%s<* #BWwGdl8y&##* «BawadLl aaauBW&*<la3aMp4bjl@w*
*1 a&a&BkdbMP 2%K>db&l
][t jla %%#HOk&*%sH*apgr jl%%
tao»
41 (BGHawl ]pqp<y%%3G?t%l<%%i iOGwl
ei
jLxi
ITiu) 2%P()&W)8€M& 2»3j;*& 4&af IPomgti* <%cK0d%i'O&
JMk&dk*! i98r#ibM#B&#4*"""
3L& *& i%>%3rjLi%3 tdbM* torqp**» Into tab*» ]%K)dbB& ocP ai adbw&j*# gqsnadMWOkt
jLt iLe 3*0Hgti*jp<»dl l&o» zagdkB» ljadl#apdLdb**k3L
f%*%* ip&%<legw* $%]#%#%**#*
*%EW
& og?:33jF tab*» c*>a***»«qpM@%w3Wl*%g laogpqpoK* t%> ây&cai aaaw»#;
jia t&se
<%** 4&
]P4Hp]p8i9(Mnd:iJcy5
aKpgr#üDy»8%a%%Bdb*
Bk&a»jLrw;aftjl& (wowl %&*** ag*w& tx>*qp%#w* oof 4*%%cyln*
<%yCULcw&e%' a%üw#t 1b<» xasid#iNdltab #i ikeqpâkSNad&e» <%SB& ftnr *&awB&& agrlia"»
j&asp*
Ï15%*ü*<» iBWKBà* 3%8%3r i%#k BioMatM&di *9%k *k ladkcysl# dbpdltMext la&uBJpl;
abb %%r<%gHa** ip&WBw*** %%)]L*jbloa t&o awaudbi *»#%*%%*
rtuuBt; Is*»
tw&ioGws jlii isetl&ijQa; tag* iWbw» <B*a&at aw* laba&t 18%* 0&&eüp*&gM&e%ÿdL#ibjL<H# (OdP
taba*
awB&jLcM* aaeKgrTb*» 3*<*tw*jba*»d «&# IGo labw* jC^Li'lng; <)#&#»**
$HB& tdbe* ]p*s*4&aLa%i3b&3P i&3*%q%ii@p*B%e334* <%f 1Kbu&4; <%EygjLcw»*
Sg&w& awBB* la&iawgl; lowKzipgrijQi; iPLll iakw» 1%09&qpwaf*gpopcN3b&ekl%%gE <s*Baw#
ij* 48apdùoM&&Tbgr 8%%*» %aot*>%*-<33*lif4&a*3rart@Bi*
2&**l3ig; :fo3J&epRR%3P# i#3ÜLl
Tbo TWj*€Ha 3Ü& idbu&a* lawtcdb&a&aBi Ibo1s%*@aiaRtlttibkia» asDtdLcMa (%f tdbx» eg***
teo tabd* eaoasljQ*» i8gr3L&%3dW@3&]8Bw;@HN* ja*#py&]p#Kt*»3;y#
tw) TuusGd aw# #L jpdLvoti jpoarb oüT tabeaw*
3P#Ke*%3Llj&3L TsdLtBi tab** a*%BkadkiadM;*
]L(XE%s %%)& iNdLIl
isa&dl %acM8i;tw»(K :&%)
3?1L*BKjlthI**
tab** :fo]Llo%f#p8 (wcwi tObo laasgrlas** (sgKljli&db&x* aaai******
ipSPorvildkBKi#
!%%&*; ILaaog; ILjlggbls *#%xe3Liyg** aàp*k
Ibe
lb**
indH**
ipjLdbaailJXar b&%** jflUeacjlblL** <&<>%Da**<&tiL<%EW» 1b4*t9*N**M& t%ba 3%@:l3cw(KW* aaadl
tbw* 4%33vyN&*g;Ma%wajLEy& anasija** cgrljlztdbBa* laa&aw;**# dka tab** %9E>t&e3L
3B& zswagr %%$
tabw*
(OKkXBaakcdkjlcwaai leawak» *adF
3109812 iLjlght; iggMPdkoy;*; i*3J&3L 1b4k (d%ül4& 1&%
> #&%p3Ly t%o laba* %ag>db*I 1*91*#
tmmtha drivlag tarqp* elollar to the Imput obtained fraa
the
m e # a n lm *
%b* #*me and tb#&# folio#**#
ah#u&a be adjuetable to handi# varlou# aprangemoBt ef the
#&&*& ay&te#*
& eketeh *hê%ln& the Id#* of tbl# erB&Rge#
amB&l# provided &&$%$* kk ( P* 34? *&& IbS )*
BOt# to F ij,
iaamde o f at##l rod la reaaoaebi# *1%#
o f appro&lm&t# leagth egeel to the lbe&ght o f the etand*
2b# #*1& b e a rln j* fo r th la ehaft a*y be eeoured on top
#Bd bottom frame# o f the «tend#
Interm ediate ibeae&n* ##*
ppo&t# a r* **qpir#& fo r e tlffn eea and adjustment*
2be pivo t poet 1# mounted In a lin e w ith the model
aymtem*
Follower# mn#t b* lin ed up along the ;plvot ]po#t
and In p a ra lle l w ith the m a*8»lB #rtl* ObannelmarB# of the
model eyetem before engaging the cam#*
2h&# lanm&re# the
proper pha#e re la tio n met up la 3he earn# on the cam dbaft*
(3)
Figure#
a* b, c dbo# the aaeeWbly o f the cam shaft
and the p ivo t poet o f the emlng follow ere*
Flgwr* d the*#
the fle x ib le connection between #&* fciio w er and the &&##*
In e rtia channel-arm o f the model ayatem#
Oi)
2%B»i%B3%w#cf b#l#B#la& the model When the eammdrlv*
1 kl
d r iv i n g
s h a ft
follower
pivot post
a
. s h a ft /
bearing
(b )
model
system
/Stand
i’ ig * i|l|, - Scheme o f Cam—S h a f t A rran gem ent*
3J4S
follow er
sw ing f o l l o w e r
m a s s - in e r t ia c h a n n e l
arm o f m odel system
s h a f t o f th e
m odel system
F ig * [li!. -
d
-
Scheme o f The F l e x i b l e
C o n n e c tio n b etw een The C a m -F o llo w e r and The M a s i n e r t i a
C h a n n e l-a rm o f Ih e M odel S ystem .
iW
(jg IbwadLBys
lyjldkBd <%ki iBkw$
Tugpcwakp agF%aBW#d&*»là***l f%%qp*%ryap#B*eo&1& iiwqsr I}#» %)3*o*»
atiaS** iOdP t&ie BGCNga»! **3rat#Ba#
4» ibdb#*"
ipod Bgggr Tbt* TaaKkd 1%) <%;%%%%*<*%staws&i jpailar ,83* ;ft>]LIo*p*3p* 1*0 iBbaadb
iKkuagr laape <%pH&]p*Lt*tdL a*jü%aa3^SüKf**<)üL83i3r
a ada&sli* aw #
1,
s.
* rn h m U im fn M m m te te g im » te s *»
B. %m m #w w a. % .» » * % # :, »#%.#
2»
»,
êâXtim,
1937.
Wil#€®î
“
Solbatlem. o f tewlom&l
Pro&lmm “* V ol. I ,
smrn m m
& &MM* m # te rn , ».%, #
Sooom eaittem , 2St|^.
3,
», A,
^ * tewlm wa. VlW *#cm " ,
amn m i^ a &%#, i* » iw k , R .i,, 1 9 * .
%#
J, P* B » Hartogi
• itecîMBBieal Vlbrntltm #
W e ^ v m m il Do#: Go,, Mm ïo ife, M .ï,
te W o a itlw , Wk%
S,
F* M. Gousteai
* te # ly # W . Boaigs o f R l# %«##
teWmW. C tatestitm tegtm a " ,
M te m Piibltehts^ Co*s»„ v m %«%,.
I9l4i«