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GOVT ENGINEERING COLLEGEAURANGABAD
GUIDED BY : DR.S.B. CHIKALTHANKAR
INTRODUCTION TO BEVEL GEARS
PRESENTED BY:
PRASAD PARGAONKAR ANSARI ABDUL BARI SHASHANK DATTATRYWASGI[BE10F02F005] [BE10F02F006] [BE10F02F007]
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CONTENTS
Int!"#$t%!n
H%&t!' !( G)*&
T'+)& !( B),)- G)*&
T).%n!-!/%)&
F!$)& *n*-'&%& !n B),)- G)*&
W)* &t)n/t "'n*.%$ &t)n/t
A++-%$*t%!n&
N#.)%$*-
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Introduction
G)*& *) ))-& !
$'-%n")& %t t))t t*t
.)& %t t) t))t !( !t)
/)*& t! t*n&.%t .!t%!n
G)*& *) #&)" %n
),)'t%n/ (!. *#t!.!3%-)&
t! &.*-- t!'&
What are Gears?
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GEAR TERMINOLOGY
PIT4H DIAETER
ROOT DIAETER
4ENTER
DISTAN4E
OUTSIDE DIAETER
DIAETRAL PIT4H TOOTH SIE
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GEARS
SPURGEAR
WORGEAR BE8EL
GEAR
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Functions of Gears
T*n&() !t%!n 4*n/) D%)$t%!n
In$)*&)9D)$)*&) S+))" In$)*&)9D)$)*&) T!#)
T!#) %& t#n%n/ ! t%&t%n/ (!$); E
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Transmt m!t!n "et#een sha$ts
Gear t%&esS&'r (ears ) &ara**e* sha$ts ) m!st +!mm!n
Be,e* (ears) &er&en-+'*ar sha$ts
W!rm (ears &er&en-+'*ar !,er*a&&n( sha$ts
Ra+/ an- &n!n (ears) +!n,ert +r+'*ar
m!t!n t! *near m!t!n
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History of GearsThe G*eas!n W!r/s
B!n A+%- >? 1@6? W%--%*. G-)*&!n $*.) t! A.)%$*
(!. B!%&!=*n)? 4!#nt' T%++)*'? I)-*n"? %t %&
.!t) *n" 3!t) )n ) *& * -*" !( (%(t))n;
H) *$#%)" %& t*%n%n/ t!#/ *++)nt%$)&%+ *& *
.)$*n%$ %n t) R!$)&t) .*$%n) &!+& !( A&* R;
S%(t *n" I;
An/)-- S!n& *n" "#%n/ t) 4%,%- W* !=)" *t
4!-t& A.!' %n H*t(!"? 4!nn)$t%$#t.
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R)t#n%n/ t! R!$)&t) %n 1@65? W%--%*.
G-)*&!n 3)/*n %& !n .*$%n) &!+? %$
),!-,)" %nt! T) G-)*&!n W!=& *n" #-t%.*t)-'
%nt! t) +#3-%$-' )-" G-)*&!n 4!+!*t%!n;
O%/%n*--' %& (%. .*n#(*$t#)" * /)n)*- -%n)
!( .)t*- !=%n/ t!!-& *n" .*$%n)&? %t
&+)$%*- ).+*&%& !n )n/%n) -*t)& *n" +-*n)&
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In 1@7>? W%--%*. G-)*&!n %n,)nt)" t) (%&t 3),)- /)* +-*n);
T%& "),)-!+.)nt +!,)" t! 3) t) 3)/%nn%n/ !( * n)
%n"#&t' C t) 3),)- /)* %n"#&t' C *n" !+)n)" ,*&t n)
+!&&%3%-%t%)& (! t) t*n&.%&&%!n !( .!t%,) +!);
A .*&t) $*(t&.*n )n"!)" %t *n %n"!.%t*3-) %--
* &+%%t !( %n")+)n")n$) *n" 3!*" ,%&%!n ! $)*t)" * n)
t'+) !( .*$%n) t!!- *n" (!#n")" t%& 3#&%n)&& !n %")*-& !(
&),%$) *n" (*% ")*-%n/;
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Deveo!"enta History T)) *) .*n' $-*%.& t! t) %n,)nt%!n !( t) "%(())nt%*- /)* 3#t
%t %& +!&&%3-) t*t %t *& =n!n? *t -)*&t %n &!.) +-*$)&? %n *n$%)nt
t%.)&; S!.) %&t!%$*- .%-)&t!n)& !( t) "%(())nt%*- %n$-#"):
1050 B4771 B4: T) Book of Song%$ %t&)-( *& %tt)n
3)t))n 502 *n" 557 A;D; .*=)& t) *&&)t%!n t*t t) S!#t
P!%nt%n/ 4*%!t? %$ .*' *,) #&)" * "%(())nt%*- /)*? *&
%n,)nt)" "#%n/ t) W)&t)n !# D'n*&t' %n 4%n*;
150 C 100 B4: H'+!t)&%)" #&)? n! "%&$)"%t)"? %n t) G))=
Ant%='t)* .)$*n%&.
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S!#t P!%nt%n/ 4*%!t .!")-;
2272 AD: D)&+%t) "!#3t& (!. ()--! .%n%&t)& *t $!#t? * #n (!. t)
K%n/"!. !( W)% %n 4%n* %n,)nt& t) (%&t %&t!%$*--' ,)%(%*3-) S!#t P!%nt%n/
4*%!t? %$ +!,%")" $*"%n*- "%)$t%!n *& * n!nC.*/n)t%$? .)$*n%)"
$!.+*&&; S!.) $ $*%!t& .*' *,) #&)" "%(())nt%*- /)*&;
65@? 666 AD: t! 4%n)&) B#""%&t .!n=& *n" )n/%n))& $)*t) S!#t
P!%nt%n/ 4*%!t& (! E.+)! T)nJ% !( *+*n;
1027? 1107 AD: D!$#.)nt)" 4%n)&) )+!"#$t%!n& !( t) S!#t P!%nt%n/
4*%!t 3' Y*n S# *n" t)n W# D))n? %$ ")&$%3)" %n ")t*%- t)
.)$*n%$*- (#n$t%!n& *n" /)* *t%!& !( t) "),%$) .#$ .!) &! t*n )*-%)
4%n)&) )$!"&;
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1720: !&)+ W%--%*.&!n #&)& * "%(())nt%*- /)* %n * $-!$=;
1@10: R#"!-+ A$=).*nn !( G).*n' %n,)nt& * (!#C))-
&t))%n/ &'&t). (! $*%*/)&? %$ &!.) -*t) %t)&
.%&t*=)n-' )+!t *& * "%(())nt%*-;
1@27: .!")n *#t!.!t%,) "%(())nt%*- +*t)nt)" 3'
*t$.*=) On&%+!) P)$#)#;
1721@52 !( t) 4!n&),*t!%) ")& At& )t t%)& %n
F*n$) (! #&) !n* * &t)*. $*t; S!#$)&: B%t*nn%$*
On-%n) *n"
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1@2: R%$*" R!3)t& !( En/-*n" +*t)nt& /)* !( $!.+)n&*t%!n? *
"%(())nt%*- (! !*" -!$!.!t%,)&;
1@7>: A,)-%n/ *n" P!t) !( R!$)&t)? K)nt -%&t * $*n) -!$!.!t%,) %n t)%
$*t*-!/#) (%tt)" %t t)% +*t)nt "%(())nt%*- /)* !n t) )* *
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1@7: (%&t #&) !( "%(())nt%*- !n *n A#&t*-%*n &t)*. $* 3'
D*,%" S)*);
15@: 8)n!n G-)*&.*n +*t)nt& t) T!&)n "#*-C"%,)
"%(())nt%*-? * t'+) !( -%.%t)" &-%+ "%(())nt%*- t*t )-%)&
&!-)-' !n t) *$t%!n !( /)*%n/ %n&t)*" !( * $!.3%n*t%!n !(
$-#t$)& *n" /)*&
0 B4 C 20 B4: D%(())nt%*- /)* &'&t).& +!&&%3-' #&)" %n
4%n*
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INTRODUCTION TO BEVEL
GEAR#B),)- /)*& t*n&.%t +!) 3)t))nt! %nt)&)$t%n/ &*(t& *t *n' *n/-) !
3)t))n n!nC %nt)&)$t%n/ &*(t&; T)'
*) $-*&&%(%)" *& &t*%/t *n" &+%*-
t!!t 3),)- *n" '+!%" /)*&
Bevel gearsare $ears%&ere t&e
a'es of t&e t%o s&afts intersect
and t&e toot&()earin$ faces of t&e
$ears t&e"seves are conicay
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Beve $ears are "ost often
"ounted on s&afts t&at are +,
de$rees a!art- )ut can )e
desi$ned to %or. at ot&er an$es
as %e* T&e !itc& surface of
)eve $ears is a cone*
Beve $ear in
roer s&utter door*
http://en.wikipedia.org/wiki/Cone_(geometry)http://en.wikipedia.org/wiki/Cone_(geometry)7/23/2019 Abdul Bari (Dome)
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Inde!endenty fro" t&e o!eratin$ an$e- t&e $ear a'es "ust
intersect
/at t&e !oint O0
B),)- /)* -%(t& (-!!"/*t)3' .)*n& !( $)nt*- &$);
http://en.wikipedia.org/wiki/Floodgatehttp://en.wikipedia.org/wiki/Floodgate7/23/2019 Abdul Bari (Dome)
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BEVEL RING GEAR ON THEREAR WHEEL OF ASHAFT-DRIVEN BICYCLE
#!ira )eve $ear ( 1F
Friedric&s&afen
http://en.wikipedia.org/wiki/Shaft-driven_bicyclehttp://en.wikipedia.org/wiki/Shaft-driven_bicycle7/23/2019 Abdul Bari (Dome)
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GEOETRY AND TERINOLOGY
Fi$(2
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W)n %nt)&)$t%n/ &*(t& *) $!nn)$t)" 3' /)*&? t) +%t$ $!n)&
*n*-!/!#& t! t) +%t$ $'-%n")& !( &+# *n" )-%$*- /)*& *)
t*n/)nt *-!n/ *n )-).)nt? %t t)% *+)
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Fi$(3 Beve $ear no"encature
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%&ere 1v is caed t&e virtua nu")er of teet&- !
is t&e circuar !itc& of )ot& t&e i"a$inary s!ur
$ears and t&e )eve $ears* 12 and 13 are t&e
nu")er of teet& on t&e !inion and $ear- 42 and
43 are t&e !itc& cone an$es of !inion and $ears*
It is a !ractice to c&aracteri5e t&e si5e and s&a!e
of )eve $ear teet& as t&ose of an i"a$inary s!ur
$ear a!!earin$ on t&e deveo!ed )ac. cone
corres!ondin$ to Tred$od6s a!!ro'i"ation*
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B),)- /)* t))t *) %n))nt-' n!n C %nt)$*n/)*3-);
T) !=%n/ ")+t !( t) t))t %& #*--' 2.? t) &*.) *&
(! &t*n"*" &+# *n" )-%$*- /)*&? 3#t t) 3),)- +%n%!n %&
")&%/n)" %t t) -*/) *"")n"#. 0;7 !=%n/ ")+t;
T%& *,!%"& %nt)())n$) *n" )-t& %n &t!n/) +%n%!n t))t;
It *-&! %n$)*&)& t) $!nt*$t *t%!;
T) /)* *"")n"#. ,*%)& (!. 1. (! * /)* *t%! !( 1? t!
0;5> . (! *t%!& !( 6;@ *n" /)*t);
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NOTESMT%o i"!ortant conce!ts in $earin$ are pit!
s"r#aeand pit! a$gle* T&e !itc& surface of a$ear is t&e i"a$inary toot&ess surface t&at you%oud &ave )y avera$in$ out t&e !ea.s andvaeys of t&e individua teet&* T&e !itc& surface
of an ordinary $ear is t&e s&a!e of a cyinder* T&e!itc& an$e of a $ear is t&e an$e )et%een t&eface of t&e !itc& surface and t&e a'is*MT&e "ost fa"iiar.inds of )eve $ears &ave !itc& an$es
of ess t&an +, de$rees and t&erefore are cone(s&a!ed*T&is ty!e of )eve $ear is caed e%ter$al)ecause t&e$ear teet& !oint out%ard* T&e !itc& surfaces of "es&ede'terna )eve $ears are coa'ia %it& t&e $ear s&afts7 t&e
a!e'es of t&e t%o surfaces are at t&e !oint of intersectionof t&e s&aft a'es*
M eve $ears t at ave ! tc an$ es o
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M eve $ears t at ave ! tc an$ es o$reater t&an ninety de$rees &ave teet&t&at !oint in%ard and are caed i$ter$al
)eve $ears*MBeve $ears t&at &ave !itc& an$es ofe'acty +, de$rees &ave teet& t&at !oint
out%ard !arae %it& t&e a'is and rese")et&e !oints on a cro%n* T&at8s %&y t&is ty!eof )eve $ear is caed a r&'$$ear*M9iter $earsare "atin$ )eve $ears %it&
e:ua nu")ers of teet& and %it& a'es atri$&t an$es*M#.e% )eve $earsare t&ose for %&ic& t&e
corres!ondin$ cro%n $ear&as teet& t&at
http://en.wikipedia.org/w/index.php?title=Miter_gears&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Skew_bevel_gears&action=edit&redlink=1http://en.wikipedia.org/wiki/Crown_gearhttp://en.wiktionary.org/wiki/obliquehttp://en.wikipedia.org/wiki/Crown_gearhttp://en.wikipedia.org/w/index.php?title=Skew_bevel_gears&action=edit&redlink=1http://en.wikipedia.org/w/index.php?title=Miter_gears&action=edit&redlink=17/23/2019 Abdul Bari (Dome)
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T(pes
Beve $ears are cassi;ed in di
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Straig!t )evel gears &ave conica !itc&surface and teet& are strai$&t and ta!erin$
to%ards a!e'*Spiral )evel gears &ave curved teet& at anan$e ao%in$ toot& contact to )e $radua ands"oot&*
*er&l )evel gears are very si"iar to a )eve$ear ony e'ce!tion is t&e teet& are curved= t&eends of eac& toot& are co!anar %it& t&e a'is- )utt&e "idde of eac& toot& is s%e!t
circu"ferentiay around t&e $ear* 1ero )eve$ears can )e t&ou$&t of as s!ira )eve $ears/%&ic& aso &ave curved teet&0 )ut %it& a s!iraan$e of 5ero /so t&e ends of t&e teet& ai$n %it&t&e a'is0*
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H(p&i+ )evel gearsare si"iar to s!ira )eve )ut t&e!itc& surfaces are &y!er)oicand not conica* >inion can
)e o
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Stra(ht "e,e* (ears
T)&) *) /)*& $#t (!. $!n%$*- 3-*n=& *n" $!nn)$t
%nt)&)$t%n/ &*(t *:1;
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Straig!t Bevel Gear
Ter,i$&l&g( Straig!t Bevel Gear F&re e"ati&$s
N&,e$lat"re
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N&,e$lat"re
5! Nu")er of teet& on !inion
5$ Nu")er of teet& on !inion
>ressure An$e of Teet&*
! >itc& An$e /!inion0**** tan(2/5
! 5
$0
$ >itc& An$e /$ear0**** tan(2/5
$ 5
!0
> ! >o%er at >inion s&aft /.0
n! Rotationa s!eed of !inion s&aft /revs"in0
d! >inion >itc& Circe dia"eter /""0
9! tor:ue on !inion s&aft /N"0
Fs #e!aratin$ Force /N0
F! >inion T&rust /N0
F$ Gear T&rust /N0
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0ORCE ANALYSIS
0(. 12.3 Gear t!!th $!r+es
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*er&l Bevel Gears
T&e advanta$e of 1ero )eve $ears co"!ared to strai$&t )eve
$ears is t&at t&ey o!erate %it& a s"oot& ocaised !oint contact as
o!!osed to a ine contact ena)in$ s"oot&er o!eration %it& o%
vi)ration eves and &i$&er s!eeds* Because t&ere is no s!ira an$e
and no additiona deveo!ed t&rust t&ese $ears can )e used as
direct re!ace"ents for strai$&t )eve $ears* T&ese $ears nor"ay
&ave a !ressure an$e of 3, o* T&e "ini"u" nu")er of teet& on
t&e !inion is 2* T&e desi$n of 1ero $ears is reativey s!eciaised
and t&ey are "anufactured usin$ s!ecia Geason "ac&ine toos**
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#!ira Beve Gear
T)&) *) +!"#$)" #&%n/ *
&+%*- /)* (!. %$ )-t& %n
* &.!!t) "%,) %t*3-) (!
%/) &+))" %/) -!*")"
*++-%$*t%!n&; A/*%n &*t%&(*$t!'
+)(!.*n$) !( t%& t'+) !( /)*
%& -*/)-' ")+)n")nt #+!n t)
%/%"%t' !( t) 3)*%n/& *n"
.!#nt%n/&;
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n Nor"a >ressure an$e** !itc& cone an$e4 Hei' an$e
inion T&rust F! F
t /tan
nsin cos 4 0 J tan cos K
Note= / 0 if &ei' an$e is as s&o%n and / (0 if &ei' an$e iso!!osite to t&at s&o%n
Hy!oid $ears are )est for t&e a!!ications re:uirin$ ar$e s!eed
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Hy!oid $ears are )est for t&e a!!ications re:uirin$ ar$e s!eed
reductions %it& non intersectin$ s&afts and t&ose a!!ications
re:uirin$ s"oot& and :uiet o!eration* Hy!oid $ears are $eneray
used for auto"otive a!!ications* T&e "ini"u" nu")er of teet& for
s!eed ratios $reater t&an ? =2 is ei$&t at&ou$& ? teet& !inions can )e
used for ratios )eo% ?=2* Hy!oid $ears &ave !ressure an$es
)et%een 2+ and 33o* T&e desi$n of &y!oid $ears is reativey
s!eciaised and t&ey are "anufactured usin$ s!ecia Geason
"ac&ine toos**
i i ) i d i d i &
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Desi$nin$ )eve $ears is nor"ay done in accordance %it&
standards as isted under s!eci;cations a)ove= T&e notes )eo%
reate to a!!ro'i"ate "et&ods for esti"atin$ $ear stren$t&s*
T&e "et&ods are reay ony usefu for ;rst a!!ro'i"ations
andor seection of stoc. $ears /ref in.s )eo%0* M Detaied
desi$n of )eve $ears s&oud ony )e co"!eted usin$ t&e
reevant standards* Boo.s are avaia)e !rovidin$ t&enecessary $uidance* #oft%are is aso avaia)e "a.in$ t&e
!rocess very easy*
T&e e:uations are )asicay "odi;ed s!ur $ears e:uations usin$
a s!ur $ear e:uivaent nu")er of teet& 5e
E:uivaent Nu")er of teet& on $ear 5 e$ 5 $ cos $
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*er& )evel gears
T) F%/; %--#&t*t)& )! 3),)- /)*&? %$ *) *,%n/
$#,)" t))t -%=) &+%*- 3),)-&; B#t t)' *,) * )!
&+%*- *n/-);
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Co"!arison of intersectin$ and o
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Miter gears
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"*, " C 3 &%n
,*, "*,n 96000
Ft 10009 8*,
W)) 8*,%& %n .)t)& +) &)$!n"? "*,%& %n .)t)&? n
%& %n ),!-#t%!n& +) .%n#t)? Ft %& %n N *n" W %& +!)
%n =W;
Fn Ft 9 $!&4
F Fn $!&4
F* Fn &%n .
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TOOTH BENDING STRESS =(
T) )#*t%!n (! 3),)- /)* 3)n"%n/ &t)&& %& t) &*.) *& (!
&+# /)*&;
53 FtK,K!K.9 3.J
W))?
FtT*n/)nt%*- -!*" %n N
..!"#-) *t t) -*/) )n" !( t) t!!t %n ..
3 F*$) %"t %n ..
G)!.)t' (!. (*$t! 3*&)" !n ,%t#*- n#.3) !(t))t;
K, 8)-!$%t' (*$t!
K! O,)-!*" (*$t!
K. !#nt%n/ (*$t! ;
N",)er teet! i$ gear #&r '!i!
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gge&,etr( #at&r. is +esire+/ press"re a$gle 01& a$+ s!a#ta$gle 21&
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K, 8)-!$%t' (*$t!
K! O,)-!*" (*$t!
K. !#nt%n/ (*$t!
")+)n"%n/ !n )t) /)*& *) &t*""-) .!#nt)" 3)t))n t! 3)*%n/& ! !,)#n/
!#t3!*" !( 3!t 3)*%n/&? *n" !n t) ")/)) !( .!#nt%n/ %/%"%t' *& &!n %n *3!,)
t*3-)
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N",)er teet! i$ gear #&r '!i! ge&,etr( #at&r.
is +esire+/ press"re a$gle 01&/ spiral a$gle 34& a$+
s!a#t a$gle 21
&
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Nu"erica
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Nu"erica E'(2
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E'(3
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A !air of )eve $ears is trans"ittin$ 2, . fro" a !inion rotatin$ at ?,,r!" to $ear
d & f &i & i & i i & f f ?,
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"ounted on a s&aft %&ic& intersects t&e !inion s&aft at an an$e of ?,o*T&e !inion &asan outside !itc& dia"eter of 3,, ""- a !ressure an$e of 3,o and aface %idt& of ,""- and t&e $ear s&aft is rotatin$ at 3,, r!"* Deter"ine / a 0 t&e !itc&an$es for t&e$ears- / ) 0 t&e forces on t&e $ear- and / c 0 t&e tor:ue !roduced a)outt&e s&aft a'is
Data= 2, .- n2 ?,, r!"- n3 3,, r!" -#&aft an$e= 42 43?,o
- T&e se"i !itc& cone an$es are s&o%n in Fi$*2*2* -d2 3,, ""- P 3,o
and ) ,""*
r2 ,*Q d2 ,*Q'3,, 2,, ""r3 , Q d3 , Q'?,, ,, ""
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r3 ,*Q d3 ,*Q'?,, ,, ""42 ( 43 ?, ?*2 2*+o
r3av r3 ,*Q)sin 43 ,, ( ,*Q',' sin?*2 3@Q*Q+""
r2av r2 ,*Q)sin 42 2,, ( ,*Q',' sin2*+ +Q*3 "" &0 & & 0 si$ si$51 ta$6 7 7 7891320 8 8 :&s:&s51 i 3 6 7;598 S&l"ti&$< =)>V2 Sd2avn2 ?,,,, S ' /3'+Q*30'?,, ?,,,,
Q*+@ "sF3a Fnsin Psin43 2@,' sin3,o sin?*2o + NF3r Fnsin Pcos43 2@,' sin3,o cos?*2o 33 NS&l"ti&$< =>Tor:ue Ft ' /,*Qd3av 0 ' 2,(
2? ' /,*Q' 3@Q*Q+0 ' 2,(
3@*+ N"
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THAN OU
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