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Gear Design and Analysis

Kinematics of gear teeth and gear trains.Force analysis.Design based on tooth bendingstrength.Design based on tooth surfacestrength.

Dr.Hamdy Ebaied 1

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Force Analysis Helical Gears

Dr.Hamdy Ebaied 2

t= pressure angle (20oor 25o)

= helix angle (10, 20, 30, or 0o

)

n= normal pressure angle

= helix angle

t= tangential pressure angle

tann= tan

tcos

Wr= W sinnW

t

= W cosn

cos

Wa= W cosnsin

!here W= "o"al #or$e

Wr= radial $omponen"

Wt = "angen"ial $omponen" ("ransmi""ed load)

Wa= axial $omponen" ("hrus" load)

Wr= Wttant

Wa= Wt tan

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Dr.Hamdy Ebaied 3

Gear Strength(Stress Analysis):

Design o# Heli$al %ears mus" &i"h s"and "hebasi$ "hree s"resses

a)'"a"i$ #ailure due "o bending.

b)a"igue #ailure due "o bending s"ress.$)'ur#a$e #a"igue #ailure ('ur#a$e !ear).

ll $al$ula"ion pro$edure as in spur gear ex$ep"

"he #ollo&ings*

1+ -

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Gears: Stresses

Dr.Hamdy Ebaied

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Dynamic Factor kv

Dr.Hamdy Ebaied 5

1200

1200 vkv

+=

British Unit SI units

Cast profile

Cut or milled

Hobbed or shaped

Shaved or ground

Formula of Bendingstress

00

00 vkv

+=

1200

1200 vk

v

+=

50

50 vkv

+=

/0/0 vkv

+=

05.3

05.3 vkv

+=

1.

1. vk

v

+=

5.3

5.3 vkv

+=

5.55.5 vkv +=

FY

PWktv

= FmY

Wktv

=

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Dr.Hamdy Ebaied

2+ hegeome"ry #a$"or #or ex"ernal spur and heli$al gears (sur#a$e #a"igue)

pn* normal $ir$ular pi"$h

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Dr.Hamdy Ebaied /

* leng"h o# "he line o# a$"ion in "he "rans-erse plane

m% * %ear ra"io (ne-er less "han 1)

m4 * oad+sharing ra"io

&here *

r6and r%are "he pi"$h radii andrb6and rb%"he base+$ir$le radii o# "he pinion and gear, respe$"i-ely.

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Dr.Hamdy Ebaied

a * addendum

3+ 7 * geome"ry #a$"or #or %8

# 4% 9 /5 7 = 7 ig (a)

4%: /5 7 = ; 7

; * #rom ig(b)

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Dr.Hamdy Ebaied