Design of Transmission Elements

460 Pages·0139.232 MB·English

by  T J Prabhu

D E S ıG N O F
TR A N S M ıS S IO N E LE M E N TS
T J P R A B H U
. .
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C O N T E N T S
Forew ord
Preface
Ļckn ow ledgem en
C haptcr
Spur G em s
H elical Geĺ s
B evel G e ars
4 W orn ı G ears
5 Speed R educef s
6 M ultispeed G ear B ox
7 G ear D esign u sin g L ew is and B u ckin gham
E qu atio ns
8 L u brication and Journal B earings
9 R o lling C o n tact B earings
B eıt D riv es
C hain D riv es
łJ u tches
B rakes
p ow er screw s
c
am s
16 G en ev a M ech anism
17 R atchet an d Paw l M echanism
18 W ire R opes
19 A ddiūon al Inform ation / Problem s
20 E x ercise Problem s
21 Short Q u estion s
22 0 bjectiv e T y \ Qu estion s 22 1 22 7
R eferenc s
Su pplem eiıţ A (1 47)
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A C K N O W L E D G E M E N T
co n suTltheids bwohoikle gwrerwiti nogu tt Mosf bm oyo kle catnudre I n wq tieshs tAo nthuamn bk e rt hoe f abuotho okrs s waenrcĺ
pu blishers o f tho se bo o ks
w ish to e xp re ss m y de e p gratitu de to o u r be lo v e d Ľ iıa irm ar
D r S Jagathraksha gan fo r his en co u ragenae n t an d fo r the su p p o rt a n c
fa cilitie s giv en to m e a t B IST w hile w ritin g this bo o k
I am gra te fu l to D r In g p V ajrav elu , o u r P rin cip a l, fo r his c o n side ratio n
a n d u n de rstan din g to w ards m y e ffo rt
i b
w ish to sta te tha t the se e d fo r w ritin g, w a s so w ı1 n m e y
M r T S S annbaiıda n ı o f p re n tice H all o f In dia (P ) L td , w ho m I re m e m ber
w ith gratitu de
I ex pre ss m y sin ce re tha n ks to D r M A V elu sw am i, P rin cip a l, Je ru sa le m
C o lle ge o f E n gin e e rin g M a dra s (F o rm er P ro fe sso r o f M e c ha n ic a l E n gg ,
,
IW M a dra s) m y m e n to r an d w e llw ishe r fo r 20 ye ars, fo r h is e n c o u ra ge m e n t
, ,
a n d fo r w ritin g a F o rew o rd to this bo o k
Sp e cial thm ıks are du e to m y co lle agu e s aiıd stu de n ts fo r th e su gge stio n s
a n d fo r pro o f re a din g
L a stly I w ish to a ppre cia te the patien c e an d u n de rsta n din g sho w n by m y
fam ily m e m be rs du rin g the w ritin g o f this bo o k
T J P R A R H U
P A C E T RD T ıU ￡ W T H E D W O N
S U P P L E M E N T A ha s be en ex p a n de d to in clu de
,
N E W P R O B L E M S in this e ilitio n
T J P R A B Æ
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1 SP U R G E A R S
.
1. 1. Spur. Helical an d bev el gears co m e m tıer too thett *oarln* W o rm and
w o rm w hee l m ake a " scre w an d too thed gear' drive an d can ıw v i*\ıłııi*ı*l łı*
a screw an d n u t pair
1. 2. A dvan tages of T oothed G eariııg
Pmoawcheirn Gep leûaaoırıot lsds r,e itvaçuest,o amdrueoe b witloeid set, hlyme iatrıt see(ńad)a ilnc ho vamnaprdialoicnutg s ıakeyqinouduipal mo(eRf nemtfa, cTmhainıhleitnolı * · ımmIie)ltıa»,(l bııï)\ ııłıthtrillnnhae
e friciency, (c) reliability in o peratio n and (d) conatan t ve ıoolly nıılo (,u n like th*
belt drives, there is n o slip the dńve is positive)
T a bıe 1. 1 C om pa rison of T5 kw D rlvee
D i \
r ve N2ı W # '"t %
di i
n
1 3 E fticien cy
T able 1 2
1 4 T ran sm itted P ow er
. .
T o o thed gea rs tran sm it greatest pow er G ear reducers in m arine turblneB
hav e capacity upto 50, 000 kw In w o rn ı gear Č ive the capacity ie ıim ited tc
Io ss and hence luw
e fficien cy)
T bı 1 3
a e
.
里
团
团
ĮH łļ
1 5 Periphera l V elo city
T abıe 1 4
. i
D rives M ax v eıocEÐ ïn m
Ħat belts 25
V belt w ith steel w ire co re 50
" łw d
T oothed gears 150 180 (hence find applications
ţņ a
1 6 R eliability
. .
A u to n ıo tiv e difrentials run m o na than 160 000 km befo re they need to
be replaced T his in dicates that too thed gears ha, v e long ıife and »1« W hly
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1 2
ï1eliabıe
d
1 N oisie r oper*tio tı at higher spee s
2 C ost (R ef T able 1 1)
lm portu ıt coıısideratio ns in choosing the m ate ria l fo r gea rs
] łh
im po rtıunst ııdallye ar coan ıp nn»omnisme etıasl li m amdaet erinia lsm ceaeıtıi nbge ltıhsee d v ario us c onflictinge
tw m m eM s
1 & 1 C ast Iro n
go od n oLioswe · bcaotsetn ııennatt epńraolp, erhtays gCoIo hda sm tahceh dinisaabdiıvitayn,t aMgeg ho f wloewa r t ernessiilset asntrceen gatnhd
1 & ıS*eels
s hav e M gher sngth W ear resistan ce u = ıl u c ııııya ı Lw oy neat
treatm iefn tthe Csuarrfbaocne hoarr cahlleosys sotfe ethıse swe iuthnotutr sepae cniaĮal tehreiaalts trmeaeetmt ethnet rceaqnu iarlesmo ebnet
,
o f the Saptepellisc awtioitnh B H N < 35o are used in night aııd m editu ıı du ty dńves
U sua lly heat tnıeııt is giv en to the blanks befo re the te e th are cu t Ħnion
surface shou ld be hafder tha n thiıt o f gear, because pin io n ııas to run fo r greater
ııu ıııber o f cycles than \ The difrerence hı hardn ess sho u ld be atleast 20
B H N
steels w ith B H N > 35o are used in heavy du ty č iv es an d also w here
co m pacıııess is requ ired A fter cu ttin g the teeth hea t trea tm en t is done and
gro *m d to elim in a te disto rtio n s etc T here is n o n to pro v ide a d fïerence in
sw lace halldlıess be tw een pin io n an d gear
A U gears o v er 150 m m diam eter are m ade fro m e ither c astin gs, fo rsings
o r w ełdm en ts G ears o f siæ ıno re than 500 m m in dia n ıete r a re difficult to heat
treat W Den C I o r steel castin gs afe used fo r gear, pin io n is o f fo rged steel
1 8 3 N on M etalıic G ears
.
N ylon Fibre rein fo rced plastics (FRP)
,
A dvan tages
1 Q uiet opera tio n 2 D am pin g o f shock an d v ibratio n 3 M arıu facturing
心じ口口o 1ııy
D isa dvan tages
1 L ow lo ad carryin g capacity 2 L ow heat co n đu ctiv ity
1 9 Iiailıłres in G ears
. .
岗 1 9 ıT ooth B reakage
. . .
哨
Ħıe periodical efrect o f this lo ad m ay lead to the deve lo pıııe«ıt o f fatigue
d
To oth can a lso be fractu red by a co nside rable sılo tt tnimgee tohve r(lFoiıg
S ° ry peak lo ad) w hen in «lu ced stress exceeds the ultim a bĵ
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1 3
LO AD DISTR 旧 UTION A LO N G T H E
PA TH OF CO NTA CT FO R A P A IR
O F TE ETH
tla T im e fo r one R e v o lu tion
) tt22ss ıTıiimm ee bbïf eenn ggaa ggeemm eenn tt
.
.
。
.
一
一
。
、
。
。
1 9 2 Surfa ce Faihıres G etıera lly called w r
. . .
习 旅 tin g
Surface fa tigue faiıure m eurs due to m atıy rep etitio n s o f high con tact
stresses (Fig 1 3 c)
b) A brasion (Fig 1 3 d)
It is due to abrasio a o f le eţh su rlaces by m e ta l pa rtic ıes an d fo re ign
mthaetier rsieacl teionnte, riinncgr ethasee os odnıtea cwt ozrokıiıteıg sTtrhe sis s ews eaaıtrd w ctaemakseesn sb rtheaek itneegt ho,f dtheec rteeaes?e s
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ıı园
1 4
戸
F IG 13 c F ıG 13d F IG 1 3 e
FIG 13o FIG 1 3 b
G EA R FA ILU R ES
c) Seim e / Scońn g (Fig 1 3 e)
U n der heavy lo ad the tem peratu re o f the lubricatin g o il rapidly rises and
oittsh evri scsnousigtyiy fallTshenA s aas rtheseu lgte, atrhse rooitla tfeı lnsoı fbterre akpas rtaincdle st haer ete etothm e nagwaagye feraocshn
e t h ıeav in g scores , aııd scratches on su rfaces
1 93 ,0 pen dfiv es fail by w ear an d fracture o f teeth w herea s clo sed dïives fail
m o s ◆ y by pittin g
1 10 B eam Słreiıgth C alcu la tion s
.
It is assum ed that the too th is a cu ıtilever w ith tip lo ad (Fig ı4) ]n
the actual case m axim iın ı load occurs in the m iM le It is also a ssu m ed that om】y
a sin gle pair takes the lo ad A ctu ally a secon d pair w ill a lso be sha rin g the load
R efe r to Fig 1 4 G ear three F is resolved in to tan gen ūal com ponent
n
F an d radiaı co m poneiıt F
t ,
B en din g m om ent M = F h
, t
B en ding stress at the base , c'b - M / Z ,
w he re Z = (1 / 6) bt2 (M odu lus o f section )
F gives direct com pressiv e sh ess pailu re in the fo rm o f fracture o11
L H sider is caused by tensiıe stress c' H en ce ,u sualıy the e ffect of direct
, t ,
co m pre ssiv e stress is neglected
F h ￠
t b
N o w , Đb = (1 / 6) bt? or F, = a'b
M u ltiply aiıd div ide F by p
t c
2
bt p
.
ľ t - 66 p cíb , - _ ic Pc - c ircu lar pitch
c
- [t 2 / 6hp. J bpcĐ b - ybpce'b ļ i
T he te rm w ithin the squa re brackets is kn oiw n as fo rm factor , 四国醒园田
Fo m ı fac to r is a dlrııen sia ıless qw ￠ity If the ge ar ıs
dim en sio n s \ h, aiıd pc w ill e ach be inereaseq pa\opo rtioa a te ıy H ence
o f y w ill iem ain unchang ŁE qł
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1 6
F 1
r
ď I t
op t i h th
IS
B en ding str · sı
吲
哚 crz
吲
D iiiiiiiiii rrrrrrrrrr e ctttttttttt c o mm prrrrrrrrrr e ssssllllllllllve
stre ss
Te n s iıe
島
} . i
G eo r } P i tch clrcıe
Line of G eo r 2
a ct ion
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T T
d l
m m o u e
1 13 D esign Ben din g Stress [o b】
The tooth breakage is caused by fatigue du e to repeated ben din g stresses
Therefo re, allow able stresses m ust be determ ined on the basis o f en du n m ce lim it
[o b ] = cr 1 fo r ro tatio n in o n e direc tio n (1 1)
fo f ro tation in bo th directio n s (1 2)
l life factor Table 1 6
,
fiılet stress co*ıceııtratios factor T able 1 7
n? 1facetnodr uorafn scaef eltiym, itT ainb lere v1e9rsed ben, din g, Table 1 8
T a bıe 1. 6 L ife Factor for Ben din g K
, bı
M ateriaı SurfatY
K
bl
ś 350
7
10
< 107 Ų
Steel * > 350 io7 1 N
25 × 107 0 7
Cast lron « 25 × 107
c*o eIff ftichiem cta skeb ıh airsd noebstsa inHeBd f>o r 3H50B an<d 3th5e0 co re ha rdn ess H B < Y3w50 /thNen the
,
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nq«= inr
1 7
T * hb \. 7 Sıress C o ı o n pactnr for Fiıı￠* K
. o
M ahw laı ılm 1«ııï nıt K
.
Sled . m \ m w lis«x\ su rli« ų h a n ıc I 5
Sïe«ł. Ta se h a n h ţ\\\w m tthų\ stcls ) I 2
C ast ıtriw I 2
T a 1. 8 E n du raï« e L im it, o ı
M « æ ial or 1 \ E ndıırance u nıit in R ew rsed
ı
B endlııg N /m m
ı
Forged S
0 25 (Đ + Đ ) + 50
. y
C ast s l s
0 22 ((T + cr ) + 50
. y
A llo y sıee ıs 0 35 (r + 120
u
Ca st lroıı 0 45 ar
U
ıw *ie ar u u ltim ate stn H ısth, N / m n ı2 , cr y yieıd stress, N / m m 2
T ıbıe 1 9 M etar of Safety n
,
M ıite riaı ì e of T H eıt T Ħ*tın m t Factor of
L ına n u fattııre Saf« y n
,
Steel m :- N o hent treatm ent 2 5
C nst tron Tcm pçrod o r no rm alised 2 0
w #
Sıceı Forged han i cd 2 0
w wı gw Surfıce haïdcned 2 5
N o rm alis«xl 2 0
1 ıDesign C o n ta ct Stn ess [ a' ]
. c
Su rface stre qgth is proportion al to the su rface harh ess Therefo re
,
allo w able ca ıtact stre ss is o e d by m ultiplying the hardn ess nun ıber by
,
suitıble co effic ien ts an d life fscıo rs
m n R
w w w
,
C B o r C R co effic ien t dependin g o n the su rface hardn ess, Table I 10
H B o r H R C B rin elı o r Rackw eıı hardness n uıııber
Ķ life facto r T abłe 1 11
l ,
1 1 & In du ced C on ta ct Sıress a
T be tee th are co n sidered as tw o co ntıctin g cyıin de rs T he rad i o f these
cylĖıdem are equ al to the rıdii o f cu rv atu re o f the too th Ħo files at
pitch po in t O n bısis o f tlıis assuınptio n , it has beco m e po ssiM e to calcu lałe
the co nbıct su e ss u sinıg dıe resu ıls o f itıvestigati«m s o f co n taM ïeııgth o f
.
cyıinČ icıı w iııaeķ (F ig I 6)
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