Chapter 1 Lecturer - Gear Drive

8/19/2019 Chapter 1 Lecturer - Gear Drive

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Universiti Tun HusseinOnn Malaysia

Mechanical Engineering

Mechanics of Machine (DAM31703)

Presented by

Tuan Mohd Hafeez bin TuanIbrahim

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CHAPTER 1POWER TRANSMISSIONGEAR DRIVE

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LEARNING OUTCOMES

DEFINE THE TERMINOLOGIES OF GEAR-BASED TRANSMISSION SYSTEM.

SOLVE GEAR TRAIN PROBLEMS.

INTERPRET AND APPLY THE CONCEPT OFGEAR TRANSMISSION SYSTEM IN THE REAL

WORLD APPLICATIONS.

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CONTENTS

• GEAR TERMINOLOGY• CLASSIFICATION OF GEAR

• GEAR RATIO

• GEAR TRAINS

• PLANETARY/EPICYCLIC GEAR• SIMPLE PLANETARY GEAR

• GEAR POWER

• GEAR EFFICIENCY

• POWER TRANSMISSION EFFICIENCY• EQUIVALENT MOMENT OF INERTIA

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GEAR TERMINOLOGY

The driver is usua! "aed#he pinion$ %hie #he drive&is usua! "aed #he gear'

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GEAR TERMINOLOGY

Spur gear teeth features

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GEAR TERMINOLOGY

piniongear;

diameters pitchteeth;of numberwhere

per teeth]mm[,mm][ ;

inch] perteeth[,inch][ ;

4.25unit),SIModue!in

inches), pitch!in"iametra

pitch,#ircuar

==

==

=

=

===

==

==

P G

d t

m pm p

P p pP

P t d t d m

d t d t P

t d t d p

d d

d P P GG

P P GGd

P P GG

π

π

π π

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GEAR TERMINOLOGY

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GEAR TERMINOLOGY

PRESSURE ANGLE$ φ ( #he a&)e *e#%ee& #he i&e #a&)e #+*+#h ,i#"h "ir"es +- .a#i&) )ears a&d a i&e ,er,e&di"uar #+#he sur-a"es +- #he #ee#h a# #he "+a"# ,+i'

φ cosdiameter,circe$ase d d

b =

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GEAR TERMINOLOGY

• INTERFERENCE ETWEEN MATING SPUR GEAR TEET01

– F+r "er#ai& "+.*i&a#i+&s +- &u.*ers +- #ee#h i& a )ear ,air$ #here is ier-ere&"e *e#%ee& #he #i, +- #he #ee#h +& #he ,i&i+& a&d #he 2e# +rr++# +- #he #ee#h +& #he )ear'

– Ier-ere&"e %i +""urs %he& a s.a ,i&i+& drives a ar)e )ear'

– I# is desi)&er3s res,+&si*ii#! #+ e&sure #ha# ier-ere&"e d+es &+# +""ur i& a )ive& a,,i"a#i+&'

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CLASSIFICATION OF GEARS

Parallel axes – transmit power from 2 parallel shafts.

Eg:spur gear,helical gear and herringbone gear.

Intersecting axes – transmit power between 2perpendicular shafts that intersect. Eg:bevel gear,angular gear and miter gear.

Crossed axes/Non Intersecting Axes – transmit power between 2 perpendicular shafts which does notintersect. Eg:crossed gear, worm gear, hypoid gear.

Perpandicular Axes Shaft/Rotary to translation –Theshaft axes between deriver and driven gear are perpendicular to each other and do not intersect to eachother. Eg. Rack gear , Pinion ger

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CLASSIFICATION OF GEARS

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S,ur Gears

Are used in transmitting torque between parallel sa!ts


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0ei"a Gears

Are used in transmitting torques between parallel or non

parallel sa!ts" te# are not as nois# as spur gears


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$ig% 13%2


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eve Gears• Are used #+

#ra&s.i# r+#ar!.+#i+& *e#%ee&ierse"#i&) sha-#s

&eet are !ormed on 'oni'al

sur!a'es" te teet 'ould be

straigt or spiral%


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W+r. Gears

Are used !or transmitting motion between non parallel

and non transmitting sa!ts" (epending on te number o!

teet engaged 'alled single or double% )orm gear mostl#

used wen speed ratio is quiet ig" 3 or more


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N+.e&"a#ure

*maller +ear is ,inion and -arger one is te gear

.n most appli'ation te pinion is te dri/er" &is redu'es

speed but it in'reases torque%


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Ier&a S,ur Gear S!s#e.


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GEAR RATIO

2

%

2

%

%

2

%

2

ocit&dri'er 'e

ocit&dri'en 'e

t

t

d

d

N

N n =====

ω

ω

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• A# "+a"# ,+i A$ #he ve+"i#ies$ v +- *+#h )ear aree4ua'

• Gear ra#i+ "a& *e s!.*+i5ed %i#h + (positive) -+r #hesa.e dire"#i+& a&d – (negative) -+r +,,+si#e dire"#i+&'

O O’

OO’OO’ (( C C ( center distance( center distance

(( r r %% r r 22


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GEAR TRAINS

directionopposite**

+

+

+

>

−=

−

−

−=

=

=∴

−=

−=

−=

D

A

D

C

C

B

B

A

C

D

B

C

A

B

A

D

D

C

C

D

C

B

B

C

B

A

A

B

t

t

t

t

t

t

t

t

n

t

t

DC

t

t C B

t

t

B A

ω

ω

ω

ω

ω

ω

ω

ω

ω

ω

ξ

ω

ω ξ

ω

ω

ξ

22

Simple gear train


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GEAR TRAINS

Compound gear train dri'enonteethof roduct

dri'er onteethof roduct

directionsame

;

+

+

=

>−−

−

−=

=

=

=∴

−=

−=

D

C

B

A

C B

C

D

A

B

A

D

D

C

C

D

B

A

A

B

t

t

t

t

n

t

t DC

t

t B A

ω ω ω

ω

ω

ω

ω

ω ω

ω ξ

ω

ω ξ

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EXAMPLE 1.1EXAMPLE 1.1

http://problem%20example/gear%20drive/EXAMPLE%201.1.dochttp://problem%20example/gear%20drive/EXAMPLE%201.1.dochttp://problem%20example/gear%20drive/EXAMPLE%201.1.doc


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GEAR TRAINS

2222

and

D D AC B B A A

DC B A

t mt mt mt m

r r r r

=+

+=+

25

directionsame

;

+

+

>−−

−

−=

=

=

=∴

−=

−=

D

C

B

A

C B

C

D

A

B

A

D

D

C

C

D

B

A

A

B

t

t

t

t

n

t

t DC

t

t B A

ω ω

ω

ω

ω

ω

ω

ω

ω

ω ξ

ω

ω ξ

$ecause of the shaft % and shaft 2 are parae, so+$ecause of the shaft % and shaft 2 are parae, so+

Reverted/coaxial gear trainReverted/coaxial gear train


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GEAR POWER

• T+ sa#is-! #he a% +- e&er)! "+&serva#i+&$ %he&)ear #ra&s.i# ,+%er$ #he ,+%er +- drive& )ear ise4ua #+ #he ,+%er -r+. #he drivi&) )ear'

• T+r4ue "a& *e derived -r+. #he Ne%#+&3s

se"+&d La%$ #ha# is su. +- #+r4ue is e4ua #+,r+du"# +- .+.e +- i&er#ia$ I +- #he )ear a&d#he a&)uar a""eera#i+&$ α +- #he )ear'

α τ I =∑27

( ) ( ) DRIVEN DRIVER

DRIVEN DRIVER P P

τω τω ==


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GEAR EFFICIENCY

n P

P

DRIVER

DRIVEN G

%

2

%%

22

τ

τ

ω τ

ω τ η ===

28

τ %

τ 2

ω %ω 2


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POWER TRANSMISSIONEFFICIENCY

29

P M ( -./0 -1 M--0

P D ( -./0 -1 "03M

I ( I/0I5 -1 /5#6 S651

X = $/50I7

P M P 1

P 2

P 3

P 4

P D

I M

I D

I T

X


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30

τ M

τ 2

α M ; ω M

α T ; ω T

α D ; ω D

τ 8

τ 4

τ D

τ X

τ %


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498

498

844

29%

29%

%282

%

and )!In

and )!In

)!In

G D D D X

GT T

M M M

n I c

n I b

I a

η τ

τ α τ τ τ

η τ

τ α τ τ

α τ τ

==−−

==−

=−

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( ) ( )

( )

( ) D D D X G DGG X D D D

G

T T T GT T T T

G

M M M M M M M M M

M M M

I n

I P

P P

I n

I P

P P

I P I P

P

ω α τ η τ

ω α τ τ ω τ

η

ω α η τ

ω α τ ω τ

η

ω α ω α τ ω τ

ω τ

−−=−−==

=

−=−==

= −=−==

=

498

498

84

49884

29%

29%

%288

29%%2

%%

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he power e:uation for the motor, gears and drum+he power e:uation for the motor, gears and drum+


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M

DO

P

P ==

input

outputη

49829% η η η ×=O

33

he efficienc& of the s&stem+he efficienc& of the s&stem+

If the friction tor:ue,If the friction tor:ue, τ τ X X is negected and the s&stem run withis negected and the s&stem run with

constant 'eocit&, the efficienc& of the s&stem+constant 'eocit&, the efficienc& of the s&stem+


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EQUIVALENT MOMENT OF INERTIA

I& #he ,revi+us #+,i"$ )ears are assu.ed #+ &+# havi&).+.e +- i&er#ia' I& rea "ases$ )ears d+' I& +rder #+r+#a#e a )ear$ "er#ai& a.+u +- #+r4ue is &eeded #++ver"+.e #his .+.e +- i&er#ia' Si&"e )ear A is"+&&e"#ed #+ )ear $ ar)er #+r4ue is &eeded' We "a&si.,i-! +ur "a"ua#i+& *! 2&di&) #he e4uivae.+.e +- i&er#ia'

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T+r4ue a# )ear #+ a""eera#e1 I1

A B B B B n I I α α τ ==

n A

B

A A

B BG

τ τ

ω τ ω τ η ==

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+ear e!!i'ien'#+ear e!!i'ien'#

&orque at gear&orque at gear A A to a''elerateto a''elerate I I BB

( ) ( )[ ] AG

B

G

A B

G

B B

G

B An I nn I n I n α

η η α

η α

η τ τ

==== 2


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+=

G

B A EQ

n I I I

η

2

A A A I α τ =

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&orque at gear&orque at gear A A to a''elerateto a''elerate I I A A

&otal o! torque at gear A to a''elerate&otal o! torque at gear A to a''elerate I I A A andand I I BB

A

G

B

A A

G

B

A A

n I I

n I I α

η α

η α τ

+=

+=

22

&ere!ore" te equi/alent moment o! inertia re!er to A o!&ere!ore" te equi/alent moment o! inertia re!er to A o!

te s#stemte s#stem


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PLANETARY/EPICYCLICGEAR6#a*e7e8,ai&9

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PLANETARY/EPICYCLIC GEAR

Type of tooth cut

GEAR NAME TOOTH CUT

** &A-&A-

,-A&,-A& &A-&A-

A-*.+ A-*.+ .&A-.&A-

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PLANETARY/EPICYCLIC GEAR

• E8#er&a )ear drives a&+#her e8#er&a )ear$ +u#,u#dire"#i+& is reversed

• E8#er&a )ear is i& .esh %i#h a& ier&a )ear$dire"#i+& is sa!e

GEAR NAME SUN PLANET ANNULUS

SUNpposite :pposite :

/e/e

pposite :pposite :

/e/e

PLANETpposite :pposite :

/e/e*ame;/e*ame;/e

ANNULUSpposite :pposite :

/e/e*ame;/e*ame;/e

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Direction of rotationDirection of rotation


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SIMPLE PLANETARY GEAR

• Su,,+se i# is re4uired #+ 2&d #he )ear ra#i+ +- S #+ L%he& A is hed 28ed/+":ed' The ,r+"edure is as-++%s1

6a9 Give a )ears ;< r+#a#i+& 6"+":%ise9

6*9 0+d #he ar. L 28ed a&d r+#a#e #he a&&uus A =<r+#a#i+& 6ai"+":%ise9$ #hus re#ur&i&) i# #+ i#s-+r.er ,+si#i+&'

6"9 Su. u, #he &u.*er +- r+#a#i+&'

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SIMPLE PLANETARY GEAR

*tep*tepumber o! rotationumber o! rotation

-- A A **

a +i/e all gears ;1 rotationa +i/e all gears ;1 rotation ;1;1 ;1;1 ;1;1

b ?a;b@ ;1;1 00 1;1;t t A At t **

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SIMPLE PLANETARY GEAR• I& s#e, 6*91

( )

=−

−=∴

−=

−=

×

−=

×=

S

A

S

AS

S

A

P

A

S

P

A

P

P

S

A

S

t

t

t

t N

N

t

t

t

t

t

t

N

N

N

N

N

N

%

;%since

5

S

AS

t

t N +=%of motionresutingha'eweup,Summing

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.n step '.n step '

&e gear ratio o! * to - wen&e gear ratio o! * to - wen A1 is locked

%

%

+

== S A

L

S t

t

N

N n


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SIMPLE PLANETARY GEAR• I- a #he )ears are r+#a#i&) a&d &+ )ears are

+":ed$ #he ,r+"edure is as -++%s1

6a9 Give a )ears ;a r+#a#i+&

6*9 0+d #he ar. L 28ed a&d r+#a#e a&!

a&&uus A ;* r+#a#i+&'6"9 Su. u, #he &u.*er +- r+#a#i+&'

*tep*tepumber o! rotationumber o! rotation

-- A A **

a +i/e all gears ;a rotationa +i/e all gears ;a rotation ;a;a ;a;a ;a;a

b ?stepa;stepb@ ;a;a a;ba;b a;a;t t A At t **bb

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EXAMPLE 1.EXAMPLE 1.44



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T0AN> YOU

Chapter 1 Lecturer - Gear Drive

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