spur design

8/11/2019 SPUR Design

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M E C H A N I C A L E Q U I P M E N T D E S I G N

G E A R S

Classification:

1) According to the position of axis of shafts :

a)Parallel:Spur gears

Helical gears (teeth are inclined to the axis)

b) Non parallel or intersecting(coplanar): Bevel gears

c) Non parallel and non intersecting(spatial):Ske bevel gears or spiral gears

!or" gears are also classified as spiral gears in hich shafts are usuall#

perpendicular$

%) According to the peripheral velocit#:a) &o velocit#: &ess than ' "s

b) ediu" velocit#: Beteen '"s and 1* "sc) High velocit#: +reater than 1* "s

') According to t#pe of gears:

a) ,xternal gears: +ears "esh externall#b) -nternal gears: +ears "esh internall#

c) .ack and Pinion: +ear "esh internall# and externall# in a straight line

/) According to the position of teeth on the gear surface:

a) Straight: Spurb) -nclined: Helical

c) 0urved: Spiral

Beam strent! of ear toot!" Le#is e$%ation:

he strength of gear is deter"ined b# &eis b# taking the tooth as a bea"2 shon

in the figure$1$ he e3uation given b# &eis is used for deter"ining the si4e andproportions of gears$


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t 5 xpc and h 5 kpc

TW 5 6bpcx

% 7k

# 5 x% 7k

Here # is knon as &eis for" factor or tooth for" factor$ 8 and k are constants$

# depends on nu"ber of teeth and s#ste" of teeth$

# 5 9$1%/ 9$7;/ ( for 1/


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!-5T

T

WbCv

WbCv

++

+

%1

)(%1

!here ! 5 otal d#na"ic load in Netons$ !5 Stead# trans"itted load in Netons

v5 Pich line velocit# in "s b5 face idth in ""2 and

05efor"ation or d#na"ic factor in N""

he defor"ation factor depends on error in action beteen teeth2 the class of cut of the

gears2 the tooth for" and the "aterial of gears$

he value of 0 depends upon the error "a# be deter"ined b# the relation:

GP EE

eKC

11

$

+

=

,P 5 odulus of elasticit# for the "aterial of pinion in Pa,+ 5 odulus of elasticit# for the "aterial of gear in Pa

e 5 ooth error in action

k 5load stress factor

he "axi"u" alloable tooth error in action depends upon the pitch line velocit# andthe class of cut of the gears$

STATIC T''TH L'AD:

he static tooth load2 hich is also called bea" strength or endurance strength is obtainedb# &eis for"ula b# substituting flexural endurance li"it or elastic li"it stress 6cin

place of per"issible orking stress 6$

Static tooth load !S5 6e bpc #

@or safet# against tooth breakage2 the static tooth load should be grater than the d#na"ic

load$

*EAR T''TH L'AD:


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he "axi"u" load that gear teeth can carr# ithout pre"ature ear depends upon the

radii of curvature of tooth profiles and on the elastic and surface fatigue li"its of the

"aterials$ he "axi"u" or the li"iting load for satisfactor# ear of gear tooth isobtained b# the e3uation2

bQKDW Pw =

!5 axi"u" or li"iting load for ear in Netons

P5 Pitch circle dia"eter of the pinion in ""

b 5 face idth of the pinion in ""D 5 .atio factor

51

%

VR

VR5

PG

G

TT

T

%2 C for external gears

E for internal gears

F 5 &oad stress factor

+ )11

(/$1

sin)( %

GP

es

EE+

6es 5 Surface endurance li"it in Pa or N""%$

5 Pressure angle

,P5 Goungs "odulus for the "aterial of the pinion in N""%

,+ 5 Goungs "odulus for the "aterial of the gear in N""%

Note:1$ he surface endurance li"it for the steel "a# be obtained fro" the folloing

e3uation: 6es 5 (%$; B$H$N$>9) N""%

%$ he "axi"u" li"iting ear load "ust be greater than the d#na"ic load$


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P R ' B L E M S

1$ A bron4e spur pinion rotating at 799 rp" drives a cast iron spur gear at a

trans"ission ratio of /:1$ he alloable static stresses for the bron4e pinion andcast iron gear are ;/ Pa and 19* Pa respectivel#$ he pinion has 17 standard

%99full depth involute teeth of "odule ; ""$ he face idth of both the gears is

=9 ""$@ind the poer that can be trans"itted fro" the stand point of strength$

he service factor is e3ual to one$ he tooth for" factor can be taken as

# 5 9$1*/ 9$=1% and the velocit# factor as

0v 5v+'

'

%$ A pair of straight teeth spur gears is to trans"it %= F hen the pinion rotates at'99 rp"$ he velocit# ratio is 1:'$ he alloable static stresses for the pinion and

gear "aterials are 1%9 Pa and 199 Pa respectivel#$ he pinion has 1* teeth

and its face idth is 1/ ti"es the "odule$ eter"ine "odule2 face idth and pitch

circle dia"eters fro" the stand point of strength onl#2 taking into considerationthe effect of d#na"ic loading$

he service factor is e3ual to one$ he tooth for" factor can be taken as

# 5 9$1*/ 9$=1% and the velocit# factor as

0v 5v+'

'

'$ A gear drive is re3uired to trans"it a "axi"u" poer of %%$* F$ he velocit#ratio is 1:% and speed of pinion is %99 rp"$ he approxi"ate centre distance

beteen the shafts "a# be taken as 799 ""$ he teeth has %99stub involute

profiles$ he static stress for the gear "aterial2 hich is cast iron "a# be taken as

799 Pa and face idth as 19 ti"es the "odule$ @ind the "odule2 face idth andnu"ber of teeth on each gear$

0heck the design for d#na"ic and ear loads$ he defor"ation factor and loadstress factors "a# be taken as ;9 and 1$/ respectivel#$

/$ 0alculate the poer that can be trans"itted safel# b# a pair of spur gears ith the

data given belo: /Ta0e 1elocit2 factor + 34/35.66 Nu"ber of teeth on pinion 5 %9

Nu"ber of teeth on gear 5 ;9

odule 5 / ""

@ace idth 5 79 "" ooth profile 5 %99 involute

Alloable bending strength of the "aterial 5 %99 Pa2 for pinion 5 179 Pa2 for gear

Speed of the pinion 5 /99 rp"

Service factor 5 9$; &eis for" factor 5 9$1*/ 9$=1%

Desin Proce,%re for S7%r Gears


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Ste7 8: @ist of all2 the design tangential tooth load is obtained fro" the poer trans"itted

and the pitch line velocit# b# using the relation:

v

PCW

s

T =

!5 Per"issible tangential tooth load in Netons$P 5 Poer trans"itted in !atts$

? 5 Pitch line velocit# in "s$

0S5 Service factor$

1al%es of Ser.ice factor

T27e of loa, 3 !rs4,a2 9"8 !rs4,a2 ;< !rs4,a2

Stead# 9$; 1$99 8=;>

&ight shock 1$99 1$%* 8=>

spur design

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