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Fundamentals of Machine Elements, 3rded.

Schmid, Hamrock and Jacobson 2014 CRC Press

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Fundamentals of Machine Elements, 3rded.Schmid, Hamrock and Jacobson

2014 CRC Press

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Edge view

(a) (b)

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2014 CRC Press

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2014 CRC Press

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2014 CRC Press

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2014 CRC Press

3$4' ,'

,&0C&%'1

F@D4'& )*:P+ J#5@= 5$4' D'D&0C&%'1:

Tooth profile

Pitch circle

Whole depth, ht

Addendum, a

Dedendum, b

Root (tooth)Fillet

Topland

Pitch circleBase circle

Pressureangle,

Line ofaction

Circular pitch, pc

Working

depth, hkClearance, cr

Circular tooththickness

Chordal tooththickness

Gear

Pinion

Centerdistance, cd

Pitc

hd

iam

eter

,dg

Rootdiameter

rbp

rp

rop

Outside

diameter,dop

rbg

rg

rog

Base diameter, dbg

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2014 CRC Press

,' /00%" Q0C&-=.#%4'&

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radius Clearancecircle

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2014 CRC Press

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2014 CRC Press

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Diametral pitch,Class pd, in

1

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Medium coarse 12, 14, 16, 18Fine 20, 24, 32, 48, 64

72, 80, 96, 120, 128e 150, 180, 200

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2014 CRC Press

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0 600 1200 1800 2400 3000 3600

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100

50

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mitted,

kW

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0in. (m=2;d=50mm)

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;d=4.00in.(m=4;d=100mm)

3 pitch; d = 8.00 in.

(m= 8; d= 200 mm)

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2014 CRC Press

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B

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Outside circle(gear)

Lab(Length of action)

Line of action

Pitch point

(a) (b)

L1

L2

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2014 CRC Press

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Parameter Symbol (pd < 20 in. 1 ) (pd 20 in.

1 ) system

Addendum

a 1

/p d 1

/p d 1.00

mDedendum b 1.25/p d 1.200/p d + 0.002 1.25mClearance c 0.25/p d 0.200/p d + 0.002 0.25m

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2014 CRC Press

L-G0.4%& !4'G&

F@D4'& )*:)Y+ !0-5%'4=%@0- 0? @-G0.4%& =4'G&:

A4A3

A2

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B1

B2

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C4

C3

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0

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2014 CRC Press

B'= 0? B$$'0#="

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Fundamentals of Machine Elements, 3rd

ed.Schmid, Hamrock and Jacobson

2014 CRC Press

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Diametralpitch Center distance,cd , in.

pd , in. 1 2 4 8 16 32

18 0.005 0.006

12 0.006 0.007 0.009

8 0.007 0.008 0.010 0.014

5 0.010 0.012 0.016 3 0.014 0.016 0.020 0.028

2 0.021 0.025 0.033

1.25 0.034 0.042

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2014 CRC Press

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2014 CRC Press

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Shaft 2

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Shaft 5

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2014 CRC Press

;

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2014 CRC Press

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P

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2014 CRC Press

,' !05% G5: E4#.@%1

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16

AGMA quality index

Rela

tivecost 10

100

1

0.5

468101214

Special methods

Productiongrinding

Shaving

Dimensional tolerance (in.)

PowderMetal

Shaping &Hobbing

10-4 10-210-310-5

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2014 CRC Press

E4#.@%1 L-9& 4000 > 20 12-14

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2014 CRC Press

F0'C !4W@-D 0? ,'5

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Gearblank

Formcutter

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ed.Schmid, Hamrock and Jacobson 2014 CRC Press

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M0AA@-D

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(a)

Hob

Helical gear

Hob rotation

(b)

(b)

Gearblank

Gearblank

Hob

Top view

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,'F@-@5"@-D

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(a)

(b)

15 or 20 position 0 position

Grinding wheels

Gear

Gear

Single-ribbed

grinding wheel

Multiribbed

grinding wheel

Two grinding

wheels

Grinding

wheel

Worm

gear

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M#'9-&55 ;h&=%5 0- J&-9@-D3%'&-D%"

F@D4'& )*:N*+ ;h&=% 0? J'@-&.. "#'9-&55 0- #..08#A.& A&-9@-D 5%'&55 ?0' 5%&&. D'5: H#I/"'04D"c"#'9&-&9 5%&&.52 HAI F.#C& 0' @-94=%@0- "#'9&-&9 -@%'@9@-D 5%&&.5: Q0%& %"#%J'@-&.. "#'9-&55 '&?&'5 %0 =#5& "#'9-&55 ?0' %"&5& D'5: !"#$%&'BQ3LiB,[B 3%#-9#'9N)Y)c`Y* \NYY*]:

10150120 200 250 300 350 400 450

20

100

150

200

250

300

350

400

30

40

50

60

Bendingstren

gth,

Sb,

MPa

k

si

Brinell hardness, HB

Grade 1

Throu

gh-ha

rdened

Throug

h-ha

rdene

d

Grade 2

Nitrid

ed

Nitride

d

Grade1-Nitr

alloy

250 300 350275 325

100

200

300

400

500

Bendingstre

ngth,

Sb,

MPa


Grade3-2.5%

Chrome

Grade2-2.5%

Chrome

Grade2-N

itralloy

Grade1-2.5%

Chrome

70

20

30

40

50

60

ksi

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F@D4'& )*:NP+ ;h&=% 0? J'@-&.. "#'9-&55 0- #..08#A.& =0-%#=% 5%'&55 -4CA&' ?0' %80D'#9&5 0? %"'04D"c"#'9&-&9 5%&&.: !"#$%&'BQ3LiB,[B 3%#-9#'9 N)Y)c`Y* \NYY*]

75150 200 250 300 350 400 450

100

600

700

800

900

1000

1100

1200

1300

125

150

175

Contactstrength,

Sc,

MPa

ksi


Grad

e1

Grad

e2

1400

2.22 HB +200 (MPa)

0.322 HB + 29.1 (ksi)

Sc={

Grade 2:

2.41 HB +237 (MPa)

0.349 HB + 34.3 (ksi)S

c={

Grade 1:

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3%'&-D%" 0? ,' [#%&'@#.5

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Material designation Grade Typical Bending strength,S b Contact strength,S cHardness

alb/in.

2

MPa ksi MPaSteel

Through-hardenedb 1 180-400 HB 0.0773 HB + 12.8 0.533 HB + 88.3 0.349 HB + 34.3 2.41 HB + 2372 180- 400 HB 0.102 HB + 16.4 0.703 HB + 11.3 0 .322 HB + 29.1 2.22 HB + 200

Carburized & hardened 1 55-64 HRC 55.0 380 180.0 12402 58-64 HRC 65.0c 450c 225.0 15503 58-64 HRC 75.0 515 275.0 1895

Nitrided and through- 1 83.5 HR15N 0.0823 HB +12.15 0.568 HB + 83.8 150,000 1035hardenedb 2 0.1086 HB + 15.89 0.749 HB + 110 163,000 1125

Nitralloy 135M and 1 87.5 HR15N 0.0862 HB + 12.73 0.594 HB + 87.76 170,000 1170Nitralloy N, nitridedb 2 87.5 HR15N 0.1138 HB + 16.65 0.784 HB + 114.81 183,000 1260

2.5% Chrome, nitridedb 1 87.5 HR15N 0.1052 HB + 9.28 0.7255 HB + 63.89 155,000 1070

2 87.5 HR15N 0.1052 HB + 22.28 0.7255 HB + 153.63 172,000 11853 87.5 HR15N 0.1052 HB + 29.28 0.7255 HB + 201.81 189,000 1305Cast Iron

ASTM A48 gray cast Class 20 5.00 34.5 50.0-60.0 345-415iron, as-cast Class 30 174 HB 8.50 59 65.0-75.0 450-520

Class 40 201 HB 13.0 90 75.0-85.0 520-585ASTM A536 ductile 60-40-18 140 HB 22.0-33. 150-230 77.0-92.0 530-635

(nodular) iron 80-55-06 179 HB 22.0-33.0 150-230 77.0-92.0 530-635100-70-03 229 HB 27.0-40.0 185-275 92.0-112.0 635-770120-90-02 269 HB 31.0-44.0 215-305 103.0-126.0 710-870

BronzeSut > 40,000 5020.035.9307.5isp

(Sut > 275 GPa)Sut > 90,000 0540.565616.32isp

(Sut > 620 GPa)Powder Metal

FL-4405, = 7.30 g/cm3 80 HRB 49.0 340 282.0 1945FLN2-4405, = 7.35 g/cm3 90 HRB 60.0 410 180.0 1240FLC-4608, = 7.30 g/cm3 65 HRB 95.72 660 210.0 1450FN-0205, = 7.10 g/cm3 69 HRB 30.0 210 180.0 1240

a Hardness refers to case hardness unless through-hardened.b See Figs. 14.24 and/or 14.25.c 70,000 psi (485 MPa) may be used if bainite and microcracks are limited to grade 3 levels.

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,' 3%'&-D%" [09@a=#%@0- F#=%0'5#-9 d&.@#A@.@%1 F#=%0'

/#A.& )*:R+ d&.@#A@.@%1 ?#=%0'> ,$:!"#$%&'F'0C BQ3LiB,[B N)Y)c`Y* \NYY*]:

Probability ofsurvival, percent

Reliability factora

Kr

509099

99.999.99

0.70b

0.85b

1.00

1.251.50

a Based on surface pitting. If tooth breakage isconsidered a greater hazard, a larger value may

be required.bAt this value, plastic flow may occur ratherthan pitting.

B..08#A.& A&-9@-D 5%'&55+

B..08#A.& =0-%#=% 5%'&55+

b,all =Sb

ns

YN

KtKr

c,all =Sc

ns

ZNCH

KtKr

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J&-9@-D 3%'&55 !1=.& F#=%0'

F@D4'& )*:NR+ 3%'&55 =1=.& ?#=%0': H#I J&-9@-D 5%'&-D%" 5%'&55 =1=.& ?#=%0' 2*2 !"#$%&'BQ3LiB,[B 3%#-9#'9 N)Y)c`Y* \NYY*]:

Number of load cycles, N

102 103 104 105 106 107 108 109 1010

Stresscycle

factor,Y

n

2.0

1.00.9

0.8

0.7

0.6

0.5

3.0

4.0400 HB:Y

N= 9.4518 N -0.148

Case Carb.: YN= 6.1514N -0.1192

250 HB: YN= 4.9404 N -0.1045

Nitrided: YN= 3.517 N -0.0817

160 HB: YN= 2.3194 N -0.0538

YN= 1.3558 N -0.0178

YN= 1.6831 N -0.0323

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U@W@-D d&5@5%#-=& !1=.& F#=%0'

Stressc

ycle

factor,Z

n

2.0

1.1

1.0

0.9

0.8

0.7

0.6

0.5

Number of load cycles, N

102 103 104 105 106 107 108 109 1010

Zn= 1.249 N-0.0138

Hydrodynamic: Zn= 2.466 N -0.056

Zn= 1.4488 N -0.023

1.5

Mixed:Zn=3.834N

-0.094,N

>105

Boundary: Zn= 7.821 N-0.156, N > 105

Zn = 1.47, N < 104

Zn = 1.10, N < 104

Grade 1 & 2Nitrided

F@D4'& )*:NR+ 3%'&55 =1=.& ?#=%0': HAI U@W@-D '&5@5%#-=& 5%'&55 =1=.& ?#=%0' 3*: !"#$%&'BQ3LiB,[B 3%#-9#'9 N)Y)c`Y* \NYY*]:

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^0#95 0- ,' /00%"

F@D4'& )*:NT+ ^0#95 #=%@-D 0- #- @-9@G@94#. D'%00%":

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Wr

Wt

W

/#-D&-%@#. .0#9+

L? 4+@5 @- "0'5&$08&'+

Q0'C#. .0#9+

d#9@#. .0#9+

Wt =hp

u =

60hp

dNa

Wt =

126, 050hp

dNa

W =t

cos

r = t tan

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F@D4'& )*:NV+ B ='#=K %"#% "#5 9&G&.0$&9 #%%"& '00% 0? # D' %00%" 94& %0 &

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3$4' ,' ,&0C&%'1 F#=%0'5

F@D4'& )*:OY+ 3$4' D' D&0C&%'1 ?#=%0'5 ?0' ?4..c9&$%" @-G0.4%& $'0a.&: H#I-XNYZ2 HAI-XNPZ: !"#$%&' B,[B 3%#-9#'9 _YVcJV_ \)_V_]:

01512 20 25 30 40 60 80 275

0.10

0.20

0.30

0.40

0.50

Geometryfactor,Yj

Number of teeth, N

Number ofteeth inmating gear.Load consideredapplied athighest pointof single-toothcontact.

125

1000170

8550352517

Load applied at

tip of tooth

1512 20 25 30 40 60 80 275

Geometry

factor,Yj

Number of teeth, N

1250.20

0.30

0.40

0.50

0.60

Load applied at

tip of tooth

Number ofteeth inmating gear.Load consideredapplied athighest pointof single-toothcontact.

100085502517

(a) (b)

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B,[B J&-9@-D 3%'&55 ;e4#%@0-

b =WtpdKoKsKmKvKb

bwYj

8"&'&56X %'#-5C@W&9 .0#9> Q+7X 9@#C&%'#. $@%="> C

c)

,0X 0G&'.0#9 ?#=%0',8X 5@S& ?#=%0',9X .0#9 9@5%'@A4%@0- ?#=%0'

,1X 91-#C@= ?#=%0',/X '@C %"@=K-&55 ?#=%0'

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ed.


jG&'.0#9 #-9 3@S& F#=%0'5

F@D4'& )*:V+ jG&'.0#9 ?#=%0'> ,"> #5?4-=%@0- 0? 9'@G@-D $08&' 504'=& #-99'@G&- C#="@-&:

!"#$%& '()*#&%+

,#-*. '/0%"(.% 1%($23/4%" +/5")% 6/"8 +*/)9 +*/)9 +*/)9

!"#$%&' ()** ()+, (),* ()-,.#/01 20%34 ()+* ()5* ()-, +)+,6%78&918 20%34 ():* ()-* +)** +)-,

Diametral pitch,pd , Module,m ,in. 1 mm Size factor,Ks 5 5 1.00

4 6 1.053 8 1.15

3 12 1.25

1.25 20 1.40

/#A.& )*:_+ d&=0CC&-9&9 G#.4&5

0? 5@S& ?#=%0'> ,8:

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ed.


^0#9 9@5%'@A@%@0- ?#=%0'+

8"&'&:9%X . =0''&=%@0- ?#=%0':+;X $@-@0- $'0$0'%@0- ?#=%0':+9X $@-@0- $'0$0'%@0- C09@a&':9.X C&5" #.@D-C&-% ?#=%0':&X C&5" #.@D-C&-% =0''&=%@0- ?#=%0'

^ =0''&=%@0- ?#=%0'+

^0#9 `@5%'@A4%@0- F#=%0'

Km= 1.0 + Cmc(CpfCpm+ CmaCe)

Cmc =

1.0 for uncrowned teeth

0.8 for crowned teeth

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ed.


U@-@0- U'0$0'%@0- F#=%0'

F@D4'& )*:O)+ U@-@0- $'0$0'%@0- ?#=%0'> :+;:!"#$%&'BQ3LiB,[B 3%#-9#'9 N)Y)c`Y* \NYY*]:

0.60

0.50

0.40

0.30

0.20

0.10

0.00

bw/dp

=2.00

1.50

1.00

0.50

For bw/dp< 0.5 use

curve for bw/dp= 0.5

Pinion

proportion

factor,Cpf

0.70

0 200 400 600 800 1000

Face width, bw(mm)

400 10 20 30

Face width, bw(in.)

U@-@0- $'0$0'%@0- ?#=%0'+L? /

F0' NP CC k A8 k *ON CC>

F0' *ON CC k A8 l )YNY CC>

H5&& %&

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ed.


[&5" B.@D-C&-% F#=%0'

F@D4'& )*:OO+ [&5" #.@D-C&-% ?#=%0': !"#$%&'BQ3LiB,[B 3%#-9#'9 N)Y)c`Y* \NYY*]:

C ma = A+ Bb w + Cb 2w

Ifbwis in inches:

Condition A B C

Open gearing 0.247 0.0167 0.765 ! 10 4

Commercial enclosed gears 0.127 0.158 1.095 ! 10 4

Precision enclosed gears 0.0675 0.0128

0.926

!

10 4

Extraprecision enclosed gears 0.000380 0.0102 0.822 ! 10 4

Ifbw is in mm:

Condition A B C

Open gearing 0.247 6.57 ! 104 1.186 ! 10 7

Commercial enclosed gears 0.127 6.22 ! 104 1.69 ! 10 7

Precision enclosed gears 0.0675 5.04 ! 104 1.44 ! 10 7

Extraprecision enclosed gears 0.000380 4.02 ! 104 1.27 ! 10 7

0 200 400 600 800 1000

Face width, bw(mm)

0.80

0.70

0.60

0.50

0.40

0.30

0.20

0.10

0.00

Meshalignmentfactor,Cma

Face width, bw(in)

403020100

Openge

aring

Comm

ercia

lenclose

dgea

runit

s

Precis

ionen

closed

gearun

its

Extra-pr

ecision

enclose

dgearu

nits

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ed.


U@-@0- U'0$0'%@0- #-9 [&5" B.@D-C&-%[09@a&'5

F@D4'& )*:ON+ ;G#.4#%@0- 0? !#-9!):!"#$%&'BQ3LiB,[B 3%#-9#'9 N)Y)c`Y*\NYY*]:

S

S/2S1

U@-@0- $'0$0'%@0- C09@a&'+

[&5" #.@D-C&-% =0''&=%@0- ?#=%0'+

Cpm= 1.0, (S1/S)< 0.175

1.1, (S1

/S)

0.175

Ce =

0.80 when gearing is adjusted at assembly

0.80 when compatibility between gear teeth is

improved by lapping

1.0 for all other conditions

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ed.


`1-#C@= ?#=%0'+

7"&'&

[#

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ed.


`&5@D- U'0=&94'& )*:N+ [&%"095 %0L-='& J&-9@-D U&'?0'C#-=& 0? ,'5L? # D' 90&5 -0% $'094=& # 5#%@5?#=%0'1 9&5@D- A#5&9 0- A&-9@-D'&e4@'&C&-%5> # 9&5@D- #.%&'#%@0- C#1 A& -&&9&9: /"@5 @5 -0% #.8#155%'#@D"%?0'8#'9> 5@-=& 54=" #.%&'#%@0-5 C#1 "&.$ @- 0-& #' #-9 "4'% @-#-0%"&'> #-9 C#1 #h&=% #550=@#%&9 C#="@-& &.&C&-%5 54=" #5 A'@-D5:M08&G&'> 50C& ?#=%0'5 %"#% @C$'0G& A&-9@-D $&'?0'C#-=& #'& %"& ?0..08@-D+

): d&94=%@0- @- %"& .0#9> 54=" #5 A1 @-='@-D =0-%#=% '#%@0> 0' #.%&'@-D

0%"&' #5$&=%5 0? %"& 515%&C:N: L-='& %"& =&-%&' 9@5%#-=&:O: B$$.1 D'5 8@%" # =0#'5&' $@%=":*: m5& # "@D"&' $'&554'& #-D.&:P: m5& # "&.@=#. D' @-5% 0? # 5$4' D':R: m5& # =#'A4'@S&9 C#%&'@#.:T:

LC$'0G& %"& D' #==4'#=1 %"'04D" C#-4?#=%4'@-D $'0=&55 5&.&=%@0-:V: 3&.&=% # A&W&' H5%'0-D&'I D' C#%&'@#.:_: m5& # 8@9&' &h&=%@G& ?#=& 8@9%":)Y: B$$.1 5"0% $&&-@-D %0 %"& %&&%":

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ed.


U@W@-D

F@D4'& )*:OP+ B D' 5"08@-D &

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ed.


B,[B !0-%#=% 3%'&55 ;e4#%@0-

c = E

WKoKsKmKv

2

12

= pH(KoKsKmKv)1

2

[# g5> gC> #-9 gG #'& 9&a-&9 #5 8@%" %"& B,[B J&-9@-D 3%'&55;e4#%@0-:

pH= E

W

2

12

E

= effective elastic modulus = 2

1 2a

Ea+

1 2b

Eb

W

= dimensionless load = w

ERx=

W

ERxbw

1

Rx= 1rp

+1

rg

1sin

= 1dp

+1

dg

2sin

b= Rx

8W

1/2

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ed.


`&5@D- U'0=&94'& )*:O+ [&%"095 %0L-='& U@W@-D d&5@5%#-=&

L? # D' 90&5 -0% $'094=& # 5#%@5?#=%0'1 9&5@D- A#5&9 0- 54'?#=& $@W@-D'&e4@'&C&-%5> # 9&5@D- #.%&'#%@0- C#1 A& -&&9&9: /"@5 @5 -0% #.8#155%'#@D"%?0'8#'9> 5@-=& 54=" #.%&'#%@0-5 C#1 "&.$ @- 0-& #' #-9 "4'% @-#-0%"&'> #-9 C#1 #h&=% #550=@#%&9 C#="@-& &.&C&-%5 54=" #5 A'@-D5:M08&G&'> 50C& ?#=%0'5 %"#% @C$'0G& $@W@-D $&'?0'C#-=& #'& %"& ?0..08@-D+

): d&94=%@0- @- %"& .0#9> 54=" #5 A1 @-='@-D =0-%#=% '#%@0> 0' #.%&'@-D0%"&' #5$&=%5 0? %"& 515%&C:

N: L-='& %"& =&-%&' 9@5%#-=&:O: B$$.1 D'5 8@%" # a-&' $@%=":*: m5& # "@D"&' $'&554'& #-D.&:P: m5& # "&.@=#. D' @-5% 0? # 5$4' D':R: m5& # =#'A4'@S&9 C#%&'@#.:T:

L-='& %"& 54'?#=& "#'9-&55 A1 C#%&'@#. 5&.&=%@0-> 0' A1 $&'?0'C@-D #54'?#=& "#'9&-@-D 0$&'#%@0-:

V: LC$'0G& %"& D' #==4'#=1 %"'04D" C#-4?#=%4'@-D $'0=&55 5&.&=%@0-:_: m5& # 8@9&' &h&=%@G& ?#=& 8@9%":)Y: L-='& %"& .4A'@=#-% a.C %"@=K-&55:

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`&5@D- U'0=&94'& )*:*+ ^4A'@=#-%[email protected] /"@=K-&55

L% 8@.. A& #554C&9 %"#% %"& $08&' %'#-5C@W&9> D' #-9 $@-@0- #-D4.#' G&.0=@%1> -4CA&'0? %&&%" @- $@-@0- #-9 D'> D' C#%&'@#.5> .4A'@=#-% $'0$&'%@&5> #-9 D&0C&%'1 0? %"&$@-@0- #-9 D' #'& K-08- 0' =#- A& 9&%&'C@-&9 ?'0C 9&5@D- =0-5%'#@-%5: j? %"&5&> %"&.4A'@=#-% $'0$&'%@&5> &5$&=@#..1 %"& $'&554'& & #'& C05% .@K&.1 %0 A&4-K-08- 0' 8@.. "#G& %"& .#'D&5% 4-=&'%#@-%1: d&D#'9.&55> %"&5& $'0$&'%@&5 5"04.9 A&

#W#@-#A.& ?'0C %"& .4A'@=#-% 54$$.@&':/"& -0'C#. ?0'=& #=%@-D 0- %"& D' %&&%" =#- A& 0A%#@-&9 ?'0C ;e: H)*:PYI #5+

/"& .4A'@=#%@0- G&.0=@%1 ?0' %"& $@-@0- #-9 D'5 @5 0A%#@-&9 ?'0C ;e5: H)*:N_I #-9 H)*:OYI#5

/"& &h&=%@G& '#9@45 @5 0A%#@-&9 ?'0C ;e: H)*:T*I #5

u =up + ug

2=prpsin + grgsin

2

W =Wt

cos

1

Rx=

1

rp+

1

rg

1

sin

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Fundamentals of Machine Elements, 3

rd

ed.


`&5@D- U'0=&94'& )*:* H=0-=.49&9I

P: /"& &h&=%@G& C094.45 0? &.#5%@=@%1 @5 0A%#@-&9 ?'0C ;e: HV:)RI+

R:

F0' 5%&&.c0-c5%&&.> =oX NNT:Pp ,U# HON:_T [$5@I:T: ;e4#%@0-5 H)O:RVI> H)O:R_I> #-9 H)O:TNI 1@&.9 %"& 9@C&-5@0-.&55 .0#9> 5$&&9>

#-9 C#%&'@#.5 $#'#C&%&'5 #5+

V: /"& .4A'@=#-% a.C %"@=K-&55 @5 %"&- 0A%#@-&9 ?'0C %"& M#C'0=Kc`0850-

&e4#%@0- ?0' '&=%#-D4.#' =0-%#=%5 D@G&- A1 ;e:qH)O:T)I+

E =

2

(1 2a)

Ea+(1 2

b)

Eb

W =

W

bwERz

; U=ou

ERx; G =E

Hmin = hmin

Rx= 1.714(W)0.128U0.694G0.568

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rd

ed.


`&5@D- U'0=&94'& )*:P+ ,'`&5@D- 31-%"&5@5

): F'0C 9&5@D- '&e4@'&C&-%5> 9&%&'C@-& %"& $08&' %'#-5?&'> %0%#. .@?&'&e4@'&9> #-9 $@-@0- #-9 D' 5$&&9:

N: /"& D' '#%@0>)$> C45% A& K-08- ?'0C 9&5@D- '&e4@'&C&-%5: L? %"@5 G#.4& @5-' 0' @- & # 5&=0-9 5%#D& @5 #9G@5#A.&:

O:

L? %"& $@-@0- ?#=&c%0c9@#C&%&' '#%@0 @5 -0% # 9&5@D- '&e4@'&C&-%> @% =#- A&&5%@C#%&9 ?'0C %"& ?0..08@-D &e4#%@0- ?0' 5$4' D'5+

7"&'&)$X*)i*+@5 %"& D' '#%@0:

*:

;5%@C#%& ,0?'0C /#A.& )*:V:

bw

dp=

gr

gr + 1,

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rd

ed.


`&5@D- U'0=&94'& )*:P H=0-%@-4&9I

P: /"& .0#9 9@5%'@A4%@0- ?#=%0'> ,9> =#--0% A& 9&%&'C@-&9 4-%@. K-08.&9D& 0?%"& 9&5@D-> C#-4?#=%4'@-D #$$'0#="> #-9 C04-%@-D @5 &5%#A.@5"&9: B'04D" #$$'0

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rd

ed.


`&5@D- U'0=&94'& )*:P H=0-%@-4&9I

T:

/"& $'&554'& #-D.&> @> @5 D&-&'#..1 ="05&- #5 NYZ> 5@-=& %"&5& D'5 #'& 8@9&.1#G#@.#A.&: M08&G&'> %"& $'&554'& #-D.& =#- A& '&94=&9 %0 0A%#@- "@D"&'=0-%#=% '#%@05> 0' @-='&9 8"&- $'&=@5@0- #-9 -0@5& #'& -0% @554&5:d&D#'9.&55> @% @5 '&=0CC&-9&9 %"#% 5%#-9#'9 G#.4&5 0? )*:PZ> )T:PZ> NN:PZ> 0'NPZ A& 45&9:

V: B D&0C&%'1 ?#=%0' ?0' 5$4' D'5 @5 D@G&- A1+

7"&'&)$@5 %"& D' '#%@0: Q0%& %"#% %"& $.45 5@D- @- %"& 9&-0C@-#%0' 0? ;e:qH)*:T_I #$$.@&5 ?0' & %"& -&D#%@G& 5@D- ?0' @-%&'-#. D'5&%5:

AB

2C=#- A& =0-5&'G#%@G&.1 &5%@C#%&9 #5 #$$'0

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rd

ed.


`&5@D- U'0=&94'& )*:P H=0-%@-4&9I

)N:

B- &5%@C#%& ?0' %"& $'&?&''&9 -4CA&' 0? $@-@0- %&&%" @5 %"&-+

F0' %"& 5$&=@#. =#5& 0? 5%&&. D'5 H;o X NNT ,U#I # $'&554'& #-D.& 0? @XNYZ>

,/X)> D8%XD8/XD8> #-9 2CXY:*P> %"& $'&?&''&9 -4CA&' 0? $@-@0- %&&%" A&=0C&5

)O: jA%#@- %"& $@W@-D '&5@5%#-=& =0-5%#-%+

)*: /"& $@-@0- $@%=" 9@#C&%&' @5 %"&- &5%@C#%&9 #5

Np =1

Kb

Yj

I

b

2c

E

2

n2

sc

nsb

Np = (101.17 GPa)gr+ 1

gr

b

2c

ns

Kc =0.3183E

hpKoKmKv

Ip

nsc

c

2

dp =

Kcbw/dp

1/3

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rd

ed.


`&5@D- U'0=&94'& )*:P H=0-=.49&9I

)P: /"& ?#=& 8@9%" =#- A& =#.=4.#%&9 ?'0C %"& '#%@0 0? / @% @5-&=&55#'1 %0 #-#.1S& %"& 9&5@D- C0'& =.05&.1 @- #==0'9#-=& 8@%" %"$$'0#="&5 9&5='@A&9 @- 3&=%@0-5 )*:)) #-9 )*:)N: /"@5 @5 =.'.1 '&e4@'&9

5@-=& # -4CA&' 0? #$$'0

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U[ 3$4' ,'[#-4?#=%4'&

F@D4'& )*:OR+ U'094=%@0- 0? D'5 %"'04D" %"& $089&' =0C$#=%@0- $'0=&55: H#I 3%&$5'&e4@'&9 %0 $'094=& # $#'%2 HAI @..45%'#%@0- 0? %00.@-D '&e4@'&9 ?0' # 5@C$.& 5$4' D':!"#$%&'B?%&' g#.$#Kf@#- #-9 3="C@9 \NY)Y]:

Compacted

shape

(green)

Upper punch

Lower punch

Powder

Feed

Shoe

(b)

Ejector

Lower punch

PM spur gear

(green)

Core rod

Upper punch

(a)

Die

1. 2. 3. 4.

Die

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S 14 CRC P

34'?#=& `&-5@a&9 U[ ,'5

F@D4'& )*:OT+ LC#D& 0? #U[ C#%&'@#. #?%&' '0..

9&-5@a=#%@0-: Q0%& %"&.08 $0'05@%1 -' %"&54'?#=&> '&54.%@-D @- "@D"#..08#A.& =0-%#=% 5%'&55&5:!"#$%&'!04'%&51 !#$5%#-B%.#-%@= !0'$:

Subsurface porosity

Densified surface

100 m

F@D4'& )*:OV+ B 5%&$$&9D' $'094=&9 %"'04D"

%"& C&%#. @-f&=%@0-C0.9@-D $'0=&55: !"#$%&'!04'%&51 U&''1 /00. bd&5'="> L-=:

F@D4'& )*:O_+ B =0..&=%@0-

0? U[ D'5 45&9 @-#4%0C0%@G& #$$.@=#%@0-5:!"#$%&'!04'%&51 !#$5%#-B%.#-%@= !0'$:

Date post:	02-Jun-2018
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