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Nov 03, 2014

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Mechanics of Machine Components
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Experience

Waste

Products

Humanresources

Productionsystem

Work experience and knowledge feedback

New products

Materialresources

JUVINALL: Machine DesignFig. 1-1a W-1

Page 914: Juvinall

JUVINALL: Machine DesignFig. 1-2 W-2

Page 915: Juvinall

JUVINALL: Machine DesignFig. 1-3a W-3

Page 916: Juvinall

JUVINALL: Machine DesignFig. 1-3b W-3

Page 917: Juvinall

JUVINALL: Machine DesignFig. 1-3c W-3

Page 918: Juvinall

JUVINALL: Machine DesignFig. 1-4 W-4

R

F

Page 919: Juvinall

Torq

ue (

N •

mm

)Cam rotation (rad)

(b)(a)

0.10

10

0

Forc

e (N

)

Followerdisplacement (mm)

(c)

10

1

0

JUVINALL: Machine DesignFig. 1-5 W-5

Page 920: Juvinall

JUVINALL: Machine DesignFig. 1-6 W-6

n = 1000 rpm

T = 10 N • mm

Page 921: Juvinall

3

Cra

nk t

orqu

e (k

N •

m)

Crank angle (rad)0

Actual torquerequirement

� 2�0

2

4

6

8

10

JUVINALL: Machine DesignFig. 1-7 W-7

Page 922: Juvinall

2�

Cra

nk t

orqu

e (k

N •

m)

Crank angle (rad)

Uniform torquesupplying equal

energy

Average torque

Actual torquerequirement

0 �0

2

4

6

8

10

JUVINALL: Machine DesignFig. 1-8 W-8

3

Page 923: Juvinall

JUVINALL: Machine DesignFig. 1-9 W-9

0.2d

Rim

Arm

Hub

0.8d d

Page 924: Juvinall

Vehi

cle

road

load

pow

er (

hp)

Vehicle speed (mph)0 20 40 60 80 100 120

0

40

80

120

160

JUVINALL: Machine DesignFig. 1-10 W-11

Page 925: Juvinall

Eng

ine

outp

ut p

ower

(hp

)

Engine speed (rpm)0 1000 2000 3000 4000 5000

0

40

80

120

160

JUVINALL: Machine DesignFig. 1-11 W-12

Page 926: Juvinall

Spe

cifi

c fu

el c

onsu

mpt

ion

of e

ngin

e (l

b/hp

• h)

Engine output power (hp)20 40 60

1000 rpm

1500 rpm

2000 rpm

2500 rpm

3000 rpm3500 rpm

4000 rpm

80 100 120 140 160 1800.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

JUVINALL: Machine DesignFig. 1-12 W-13

Page 927: Juvinall

JUVINALL: Machine DesignFig. 1-13 W-14

Page 928: Juvinall

g = 9.81 m/s2

5 mm

30mm

1 N

m

JUVINALL: Machine DesignFig. P1.18 W-15

Page 929: Juvinall

JUVINALL: Machine DesignFig. P1-23 W-16

a = 5 ft/s2

g = 32.2 ft/s2F

Page 930: Juvinall

Pulley

JUVINALL: Machine DesignFig. P1-26 W-17

V = 5 ft /sm = 5 lb

R = 3 in.

Page 931: Juvinall

JUVINALL: Machine DesignFig. P1-29 W-18

I = 10 A

Outputshaft

t = 2 hrn = 1000 rpmT = 9.5 N • m

V = 110 V +–

Page 932: Juvinall

0

T max

0.5

Crankshaft rotation, revolutions

Cra

nksh

aft

torq

ue

1.51.0 2.0

Curve A (linear variation)Curve B (half-wave rectified sinusoid)

JUVINALL: Machine DesignFig. P1-42 W-18A

Page 933: Juvinall

JUVINALL: Machine DesignFig. P1-49 W-19

55 mph

2.64 axle ratio

Page 934: Juvinall

JUVINALL: Machine DesignFig. 2-1 W-20

100 in.

V = 60 mph50 in.

CP

3000 lb

25 in.

Fd

Ft

Wr Wf

20 in.CG

Page 935: Juvinall

JUVINALL: Machine DesignFig. 2-2 W-21

Engine power, 96 hp

W = 3000 lb

Fd = 100 lb

Ft = 567.5 lb

Wr = 1618.5 lb Wf = 1381.5 lb

Fi = 467.5 lb

Page 936: Juvinall

JUVINALL: Machine DesignFig. 2-3 W-22

A

X

X

RT

RT

RT

RT – T

RT – T

T

T

RTA

RTA

Page 937: Juvinall

2 in.

3 in.

2 in.

5 in.

3000 lb.in.

T = 3000 lb.in.(input)RT – T = 5333 lb.in.

Transmissionin low gearR = 2.778RT = 8333 lb.in.

(output)

5333 lb.in.

8333 lb.in.

(b)

(a)

(d)

(c)

1087 lb

2864 lb

1087 lb

1087 lbII

IV

1087 lb

4444 lb

4444 lb

2864 lb

2864 lb

2667 lb

2667 lb

III

III

IV

I

I

II

B

D

A

C

JUVINALL: Machine DesignFig. 2-4 W-23

Page 938: Juvinall

JUVINALL: Machine DesignFig. 2-5 W-24

A

AF F

(a) (b)

a

F

F

Fa

Page 939: Juvinall

SectionAA plane

Fixedsupport

(bending moment)

JUVINALL: Machine DesignFig. 2-6 W-25

(a)

Fa

b

F

a

(b)

F

Fb (torque) F (shear force)

Page 940: Juvinall

JUVINALL: Machine DesignFig. 2-7 W-26

F32 = 40 lb

H12

F42

V12

30°

1

1

in.12

2

1 in.

Page 941: Juvinall

JUVINALL: Machine DesignFig. 2-8 W-27

F32 = 40 lb

F42

F42

F12

F32 = 40 lb

0

F12

1

Force polygon for link 2

2

Page 942: Juvinall

Ft = 60 lb

Fb = 55 lb

Fb (bonecompression force)

0.5 in.

0

Ft (tendonforce)

10 lbpinch

10 lb

3 in.

JUVINALL: Machine DesignFig. 2-9 W-28

Force polygon for finger

Page 943: Juvinall

b2

2L

wb2

2Lb2

4L

FaL

FbL

FbL

+

FaL

aL

b

F

V

MM

V

JUVINALL: Machine DesignFig. 2-10 W-29

M

a +

VV

R2R1

+

+

Positive shear force

Positive bendingmoment

wb (a + b/2 )L

w

wb (a + b/2 )L

+wb2/2L

wb 2

2La

Lb

R2R1

FabL

+

M

(b)(a)

Distributed loadSingle concentrated load

Page 944: Juvinall

JUVINALL: Machine DesignFig. 2-11 W-29A

2667 lb

2 in.

2864 lb

4444 lb

–2864 lb

–5728 in..lb

Torque

Moment

Shear

Loads

5000 lb.in.

2174 in..lb

2667 lb

IV

III

2 in.5 in.

+ 1580 lb

– 1087 lb

1087 lb

Critical section

C

V

M

T

B

1087 lb

4444 lb

2864 lb

III

IV

B

C

Page 945: Juvinall

IV

JUVINALL: Machine DesignFig. 2-12 W-30

2864 lb

4444 lb

T = 5000 lb.in.

V = 1580 lb

CM = 5728 lb.in.*

* Actually slightly less, dependingupon the width of gear C

Page 946: Juvinall

d

F

FF

F

JUVINALL: Machine DesignFig. 2-13 W-31

m

2b

b

b

d

a

Page 947: Juvinall

1

2

3

443

2

1

1

4'

4'

6

4'5

5

3

2

2

2 1

PinFork Blade

F

F

F

F4'

2

2

3

Page 948: Juvinall

7

JUVINALL: Machine DesignFig. 2-15 W-33

Page 949: Juvinall

JUVINALL: Machine DesignFig. 2-16 W-34

w lb/ft

Page 950: Juvinall

Spring in tensionk1 = 10 lb/in.

Spring incompressionk2 = 40 lb/in.

JUVINALL: Machine DesignFig. 2-17 W-35

100 lb

100 lb

10�

40�

(a)

(b)

Page 951: Juvinall

JUVINALL: Machine DesignFig. 2-18 W-36

Page 952: Juvinall

3

1strap

Topstrap

Rightplate

Bottomstrap

1 pitch

1 pitch

JUVINALL: Machine DesignFig. 2-19 W-37

Inner rowMiddle row

Outer row Inner rowOuter row

Area

Plate

Inner row

Topstrap

Bottomstrap

Leftplate

Outer row

(a)

(b)

(d)

(e)

( f )

(c)

Strap

Straps

Inner path

Middle path

Outer path Bearing with plate

Shear

Bearing with straps

Plate

2 straps

Bearing with strap

Bearing with plate

Shear

Plate

Strap

1 2

8

9

6

7

5

4

s bp

bs

Page 953: Juvinall

JUVINALL: Machine DesignFig. P2.2 W-38

gWall channel, C

2 in.

A

B

Density = �

Density = �r =

1.25 in.

r =1.25 in.

Page 954: Juvinall

JUVINALL: Machine DesignFig. P2.3 W-40

1500 N 1500 N

1000 mm

45°

45° 45°

45°

B

D

C

A

Page 955: Juvinall

JUVINALL: Machine DesignFig. P2.4 W-39

A

B

125 N

1000 N

Page 956: Juvinall

JUVINALL: Machine DesignFig. P2.6 W-41

10 in.

Motor1 hp

1800 rpmGear box

Directionof rotation

Blower6000 rpm

Page 957: Juvinall

JUVINALL: Machine DesignFig. P2.7 W-42

50 mm

50 mm

Clockwiserotation

Forwardair velocity

A

B

Page 958: Juvinall

A'

Pump450 rpm

Connectingtube

Directionof rotation

4:1 ratiogear reducer

C'

B

A

B'

Motor 1.5 kW1800 rpm

These unitsare attached toa fixed support.

JUVINALL: Machine DesignFig. P2.8 W-43

C

Page 959: Juvinall

JUVINALL: Machine DesignFig. P2.9 W-44

Engine is attachedto aircraft structure here.

Engine

Reduction gear,ratio = 1.5

Propeller

Page 960: Juvinall

Rotation

Verticaldriveshaft

Mountingflange

Propellerrotation

Y

X

Y

Z

Z

X

JUVINALL: Machine DesignFig. P2.10 W-45

2:1 ratio bevelgears are inside

this housingSuggested notation

for moments appliedto mounting flange

500 mm

Fowarddirection ofboat travel

Mx MyMz

150 mm

Page 961: Juvinall

600400

330 R330 R

40 R

100 R

800 N160

JUVINALL: Machine DesignFig. P2-11 W-46

Page 962: Juvinall

Bevel gearreducer

Attachesto motor

Attachesto load

600 rpm1800 rpm

JUVINALL: Machine DesignFig. P2-12 W-47

100 mm

100 mmA

BC

D

Page 963: Juvinall

8 in.

4 in.

6 in.

Output

Output shaft

Mountings

6 in. dia. gear

2 in. dia. pinion

Front bearings

Front bearings

Rearbearings

Motor input torque100 lb.ft

100 lb.ft

Reducer assembly

Housing andgear-shaft assembly

details

JUVINALL: Machine DesignFig. P2-13 W-48

Page 964: Juvinall

JUVINALL: Machine DesignFig. P2-14 W-51

X

Y

Y

X

B

D

A

C

12 in.

24 in.

Transmission2.0 ratio

Rear drive shaft–1200 rpm

Rear axle(not part offree body)

Front drive shaft–1200 rpm

Left-frontwheel axle

shaft–400 rpm

Engine2400 rpm

100 lb.ft torque

Right-front wheel axleshaft–400 rpm

Page 965: Juvinall

Mixing paddle

g

JUVINALL: Machine DesignFig. P2-15 W-49

Motor

Radialflow

Directionof rotation

Mass of mixersystem = 50 kg

200 mm

A B

Page 966: Juvinall

g

JUVINALL: Machine DesignFig. P2.16 W-50

B

Mountingwidth = 75 mm

to 150 mm

Fan

Radialair flow

Mass of blowersystem = 15 kg

A

Motor

Direction ofrotation

Page 967: Juvinall

JUVINALL: Machine DesignFig. P2-17 W-52

Y

FC

FA

Z

D

B

A

C

X

45 mm

30 mm

20 mm

Shaft

Gear 224-mm dia.

Gear 150-mm dia.

20°

20°

Page 968: Juvinall

300200

JUVINALL: Machine DesignFig. P2-18 W-53

100 N

A B

30050 N140

200

100 N

A B

Page 969: Juvinall

12-in.pulley radius

JUVINALL: Machine DesignFig. P2-19 W-54

Cable

Cable

100 lb

100 lb

48 in. 12 in.

27 in.

Page 970: Juvinall

Motorattaches

to this endof shaft

6040

50

JUVINALL: Machine DesignFig. P2-20 W-55

Fa = 1000 N

Ft = 2000 NFr = 600 N

A B

Page 971: Juvinall

JUVINALL: Machine DesignFig. P2-21 W-56

Pump shaft iscoupled to this

end of shaft

15050

100

Fa = 100 N

Ft = 1000 NFr = 200 N

A B

Page 972: Juvinall

8020

40

20

30

JUVINALL: Machine DesignFig. P2-22 W-57

Fa = 200 N

200 N

Fr = 400 N

A B

Ft = 1000 N

Page 973: Juvinall

JUVINALL: Machine DesignFig. P2.23 W-58

Fa = 150 N

Ft = 1500 NFr = 500 N

150

120

A B

250 N

100 N

200 300 140

Page 974: Juvinall

L

Section on A-A

Key

JUVINALL: Machine DesignFig. P2.24 W-59

Rb

r

A

A

F

t

t/2

Page 975: Juvinall

dD

F

JUVINALL: Machine DesignFig. P2-25 W-60

t

Page 976: Juvinall

d

Total gas force = F

JUVINALL: Machine DesignFig. P2-26 W-61

a2aa

Page 977: Juvinall

R

A B

L

F

L

A

L

ttf

JUVINALL: Machine DesignFig. P2-27 W-62

P Pd D

d D

Page 978: Juvinall

JUVINALL: Machine DesignFig. P2-28 W-63

E

A

B

C

D

Page 979: Juvinall

JUVINALL: Machine DesignFig. P2-29 W-64

k

k

kk

a

100 N

a

Page 980: Juvinall

F F

JUVINALL: Machine DesignFig. P2-31 W-65

P

t '

t '

Rivet diameter = 10 mm

t

Page 981: Juvinall

Str

ess

� (

ksi)

Strain � (arbitary nonlinear scale)

Slope = modulus of elasticity, E

F (Fracture)

Sy = 39

Su = 66

Se = 36

C

AB

0.2% offset0

20

40

60

JUVINALL: Machine DesignFig. 3-1 W-66

Page 982: Juvinall

Str

ess

� (

ksi)

Strain � (%)0 10 20 30 40 50 60 70 80 90 100 110

Hot-rolled 1020 steel

Su = 66 ksi

Sy = 39 ksi

Se = 36 ksi

G

AB

DC

F

H

120 130 140 150 160

Area ratio R

Area reduction Ar

0 1.1

0.1 0.2 0.3 0.4 0.5 0.6

1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6

0

20

40

60

JUVINALL: Machine DesignFig. 3-2 W-67

Page 983: Juvinall

True

str

ess

�T (

ksi (

log)

)

True strain �T (% (log))3 4 5 6 7 8 0.1 32 4 5 6 7 8 1.0 32 4 5 6 7 8 10 32 4 5 6 7 8100

10

20

30

40

60

80100

200

Elasticregion

Transitionregion

JUVINALL: Machine DesignFig. 3-3 W-68

Plastic strain-strengthening region

� T =

E� T

(E =

30

× 103 ks

i)�T = Sy = 39 ksi

F115

�Tf = 0.92

�T = �0 �T (�0 = 115 ksi, m = 0.22)

m

Page 984: Juvinall

True

str

ess

�T (

log)

True strain �T (log)

Elastic line (�T = E�T)

Curve II

Curve I (�T = Se ≈ Sy)

Plastic line (�T = �0�T )m

"Ideal" material

Se3

Se1

Se2

JUVINALL: Machine DesignFig. 3-4 W-69

Page 985: Juvinall

Se �f

E

JUVINALL: Machine DesignFig. 3-5 W-70

Str

ess

0

Strain �

Se

Sy

Su

F

Page 986: Juvinall

dD

KB,

rati

o S u

/HB

m, strain hardening exponent0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

300

400

500

600

700

800

900

1000

JUVINALL: Machine DesignFig. 3-6 W-71

Steel

d = indentation dia.D = ball dia.

0.2

0.3

0.4

0.5

0.6

Page 987: Juvinall

Dia

mon

d py

ram

id h

ardn

ess

(Vic

kers

)

Bri

nell

hard

ness

Ult

imat

e te

nsile

str

engt

h (k

si)

Rockwell C hardness

Shore hardness

Rockwell B hardness

(0)

72 80 90 100 (110)

(10) 20 30 40 50 60 70950

900

760

740

720

700

680

660640620600580560540520500480460440420400380360340320300280260240220200180160140120100

60

70

80

90

100110120

130

140

150160170180190200210220230240250260270280290300

9590807060504030

85756555464238343228262422

850

800

750

700

650

600

550

500

450

400

350

300

250

200

150

100

JUVINALL: Machine DesignFig. 3-7 W-72

Page 988: Juvinall

JUVINALL: Machine DesignFig. 3-8 W-73

Distance fromquenched end

(b)

(a)

Roc

kwel

l C h

ardn

ess

Page 989: Juvinall

Youn

gs M

odul

us,

E (

GP

a)

Strength S (MPa)0.1 1 10 100 1000 10,000

0.01

0.1

= 10–3

Woods

Polymersfoams

AshLead

W

WC

Si CCermets

Boron

Al203Beryllium

Cast irons

OakPine

PMMA

Porousceramics

1.0

10

100

1000

JUVINALL: Machine DesignFig. 3-11 W-74

Engineeringalloys

SE

= CSE

= CS3/2

E

= 10–4SE

= 10–2SE

Min. energystorage perunit volume

Yield beforebuckling

Max energystorage perunit volume

Bucklingbefore yield

Cork

Pu

Silicone

Hardbutyl

Softbutyl

= CS2

E

Elastomers

PP

II tograin

Mel

LDPE

PTFE

Pine

⊥ tograin

Balsa

HDPE

AshOak

Engineeringpolymers

PVC = 0.1SE

BalsaWood

products

Epoxies

PS

Nylons

Polyester

Designguidelines

CFRP

CFRPuniply

GFRP

LaminatesGFRP

Glasses

Sn

Concrete+

Al alloysCommon

rocksBrick etc

Zn alloysCu alloys Ti alloys

Mo alloys

SteelsNi alloys

Diamond

Si3N3Mg0

Be0

GeSilicon

Zr 02

Engineeringceramics

Engineeringcomposites

Mg alloysCement

Page 990: Juvinall

S1/2

Str

engt

h S

(MP

a)

Density � (Mg/m3)0.1 0.3 1

= CS2/3

�= C

3 10 300.1

1

10

Polymersfoams

100

1000

10,000

JUVINALL: Machine DesignFig. 3-12 W-74a

Guide linesfor minimumweight design

S�

= C

Cork

Balsa

Balsa

Woods

Softbutyl Elastomers

Engineeringpolymers

Porousceramics

Engineeringcomposites

Engineeringceramics

Engineeringalloys

KFRP

CFRP

Mg0

Diamond

SialonsSi3N4

Al203

Ge

GFRPUniplyKFRPCFRP

Glasses

AshOak

Pine

PineFir

Parallelto grain

Ash

Perpendicularto grain

Fir

Woodproducts

LDPE

PU

PTFE

MelPVC

EpoxiesPolyesters

NylonsPMMA

PS

Silicone

PP

OakHDPE

Leadalloys

Engineeringalloys

W alloys

Mo alloys

Ni alloys

Steels

Castirons

Znalloys

Al alloys

Tialloys

Stone,rock

Cu alloysMgalloys

Pottery

Si C

B

Si

GFRPLaminates

Be

Cementconcrete

CermetsZr02

Page 991: Juvinall

Str

engt

h at

tem

pera

ture

S (

T)

(MP

a)

Temperature T (C)0

Elastomers

T-IndependentYield strength

Upper limit on strength at temperature

Engineeringcomposites

Woods

100 200 300 400 600 800 1000 14000.1

1

10

100

1000

10,000

JUVINALL: Machine DesignFig. 3-13 W-74b

Engineeringalloys

Porousceramics

Engineeringceramics

Range typicalof alloy series

Polymerfoams

SiliconesButylsIce

LDPE

II tograin

Engineeringpolymers

PolyestersHDPE

PP

PC

PVCPF

Mg alloysNylons

⊥ tograin

⊥ tograin

PTFE

Epoxies

PMMAPolymides

Laminates

GFRP

CFRPUniply

KFRP

GFRP

CFRPZn alloys

Al alloys

Ti-alloys

Glasses

Bricketc.

Ni alloysSteels

SiC

Al203

Si3N4

Compression

Mullites

Mg0Zr02

Page 992: Juvinall

Har

dnes

s (R

ockw

ell C

)

Distance from quenched end (mm)0 10 20 30 40 50

10

20

30

40

50

60

70

JUVINALL: Machine DesignFig. P3-14 W-75

Page 993: Juvinall

P

JUVINALL: Machine DesignFig. 4-1 W-76

(c)

(a)

Isometric view of tensile linkloaded through a pin at oneend and a nut at the other.

(b)

(d)

� =

Equilibrium of left half showing uniform stress distribution at cutting plane

(e)

View showing "lines of force" through the link

Nut

P

EE

E

Direct view of element EEnlarged view of element E

+

+

DPA

�D2A =

4

P2

P2

Page 994: Juvinall

JUVINALL: Machine DesignFig. 4-2 W-77

3

1

5

(b)(a) P

P

4

3

1

25

6

Page 995: Juvinall

3

1

3

P

P

JUVINALL: Machine DesignFig. 4-3 W-78

2

Page 996: Juvinall

PP

JUVINALL: Machine DesignFig. 4-4 W-79

Page 997: Juvinall

JUVINALL: Machine DesignFig. 4-5 W-80

(a)

T

T

Isometric view

(b)

E

E

E E

Enlarged view ofelement

(c)

Direct view ofelement E

(d)Positive shear

Positive shear

Negativeshear

Negativeshear

Shear signconvention

Page 998: Juvinall

(a)

T

(b)

2

Torque axis

Zero shear stress existsalong all edges.

Maximum shear stress existsalong this line.

Enlarged view ofelement 2

JUVINALL: Machine DesignFig. 4-6 W-81

a

T

b

Line "A"

3

21

Top

Side Front

Page 999: Juvinall

(a)

�max

(b) (c)

Partial beam in equilibrium

Entire beam in equilibrium

Neutralsurface

Transversecutting plane

Neutralbendingaxis and

centroidalaxis Typical cross sections

M M

JUVINALL: Machine DesignFig. 4-7 W-82

Mc

cy

Neutral (bending) surface

Page 1000: Juvinall

(a)

�max

(b) (c)

Partial beam in equilibrium

Entire beam in equilibrium

Neutralsurface

CGCG CG CG

Typical cross sections

Neutral bending axisand centroidal axis

M M

JUVINALL: Machine DesignFig. 4-8 W-83

M

cy

Neutral (bending) surface

Page 1001: Juvinall

(a)

Initially straight beam segment

(b)

(c)

Initially curved beam segment

CG

Hyperbolic stress distribution withincreased stress at inner surface

M

e

Typical cross sectionCenter of

initial curvature

Neutral surface

JUVINALL: Machine DesignFig. 4-9 W-84

M

Centroidal surface

Neutral surfacedisplaced distance"e " toward inner

surface

co

ci

Page 1002: Juvinall

Centroidal surface

d�

b

ci

a d'

c'c

e

ey

d

M M

Neutral surface

Neutral axis

CG

Center of initial curvature

Centroidal axis

JUVINALL: Machine DesignFig. 4-10 W-85

c

cro

co y

rrnri

rrn

Page 1003: Juvinall

Mc I

Valu

es o

f K

in E

q. 4

.11

: �

= K

Ratio r /c1 2 3 4

Round, elliptical or trapezoidal

Values of Ko for outside fiber as at B

U or T

I or hollow rectangular

5 6 7 8 9 100

0.5

1.0

1.5

2.0

2.5

3.0

3.5

JUVINALL: Machine DesignFig. 4-11 W-86

Values of Ki for inside fiber as at A

I or hollow rectangular

Trapezoidal

b

B

B A B

B A

A

B A

b

bA

8

b2

b3b

6A

ABB b

bc

c

c

c

4

Round or elliptical

U or T

r

r

Page 1004: Juvinall

JUVINALL: Machine DesignFig. 4-12 W-87

M

M M

M

h

b

h

h2

Centroidal axis

CGr = h

c =

dA = b d�

b

Page 1005: Juvinall

JUVINALL: Machine DesignFig. 4-13 W-88

(b)(a)

Loaded "curved beam"Unloaded "curved beam"

Page 1006: Juvinall

JUVINALL: Machine DesignFig. 4-14 W-89

MN.A.

M

M + dM

Enlarged view of beam segment

V

V

dA dA

y

My/I (M + dM)y/I

dA

b

y0

y c

x dx

Neutral axis

Page 1007: Juvinall

JUVINALL: Machine DesignFig. 4-15 W-90

(a)

Marked and unloaded

(b)

Loaded as a beam

Page 1008: Juvinall

43

N.A.

�av = V/A

�max = V/A

JUVINALL: Machine DesignFig. 4-16 W-91

32

�av = V/A

�max = V/A

N.A.

Page 1009: Juvinall

JUVINALL: Machine DesignFig. 4-17 W-92

M

V

M

V

Page 1010: Juvinall

JUVINALL: Machine DesignFig. 4-18 W-93

M

V

X X

100

80

60

100

+40,000 N

–40,000 N

40,000 N

80,000 N

40,000 N

60

40

Page 1011: Juvinall

JUVINALL: Machine DesignFig. 4-19 W-94

(c)

b = 20

dA = 20dy

dA = 60dy

dx

40

(b)

b = 20

dA = 60dy

dx

10+

(a)

dA = 60dy

dx

10–

b = 60

Page 1012: Juvinall

� = 7.61 MPa0

� = 22.83 MPa

� = 32.61 MPa

JUVINALL: Machine DesignFig. 4-20 W-95

Page 1013: Juvinall

Oblique viewDirect view

�x

(a)

Marked eraser

(b)

(c)

Enlarged view of element

Oblique viewDirect view

(e)

Element subjected to �max

Loaded eraser

(d)

+�

+�

�max

x

S'

y0

S

Mohr's circle

JUVINALL: Machine DesignFig. 4-21 W-96

x

y

y

y

x xS'

S'SS

S'

S

yx

yx

Page 1014: Juvinall

(a)

Marked eraser (for twisting)

(b)

Enlarged element

(c)

+�

+�

�1�2

#1#2

x

y

Mohr's circle

JUVINALL: Machine DesignFig. 4-22 W-97

(d)

y

y

y

x

xTT

x#2 #1

0

Page 1015: Juvinall

2000 lb

JUVINALL: Machine DesignFig. 4-23 W-98

2 in.

1 in.

3 in. rad.

Page 1016: Juvinall

JUVINALL: Machine DesignFig. 4-24 W-99

"B" is at bottom of shaft, opposite "A"

Top of shaft

B

2 in.

A

Page 1017: Juvinall

JUVINALL: Machine DesignFig. 4-25 W-100

B

V = 2000 lb

2000 lb

M = 4000 in.lb2000 lb

4000 in.lbLoad diag.

2000 lb

Shear diag.

Moment diag.2000 lb

4000 lb

V

M

T = 6000 lb in.

A

Page 1018: Juvinall

y

y

xy

x

x

yA A x

JUVINALL: Machine DesignFig. 4-26 W-102

2 in.

(a)

Isometric view

(b)

Enlarged isometric view

(c)

Direct view

Calculated values: � = 40.8 ksi � = 30.6 ksi

(d)

Isometric view

A

�yx

�yx�yx

�yx

�xy

�x�x

�x

�x

�xy

�xy

�xy

A

x y

�yx�xy

Page 1019: Juvinall

y

y

x A x

JUVINALL: Machine DesignFig. 4-27 W-103

�yx = 30.6 ksi

�yx

�xy

�x = 40.8 ksi

Direct view ofelement A

y (0, +30.6)

x (40.8, –30.6)

�max = 37 ksi

�2 = –17 ksi

+�

+�

�xy

34°

56°0

�1 = 57 ksi

Page 1020: Juvinall

y

y

xA

�1 = 57 ksi

�2 = –17 ksi

28°

x

JUVINALL: Machine DesignFig. 4-28 W-104

Page 1021: Juvinall

y

y

xA

� = 20 ksi

� = +37 ksi

� = –37 ksi

� = 20 ksi

17°

x

JUVINALL: Machine DesignFig. 4-29 W-105

Page 1022: Juvinall

–�

JUVINALL: Machine DesignFig. 4-30 W-106

(�2, 0) (�1, 0)

(�y, �yx)

(�x, �xy)

�x + �y

2

�x – �y

2

0

2

+�

–�

+�2�

1

�xy2 +

2

2

�x – �y

Page 1023: Juvinall

�1 + �22

�1 – �22

cos 2�

�1 – �22

sin 2�

0

2

JUVINALL: Machine DesignFig. 4-31 W-107

+�

+�

�2

�1

2�

1

Page 1024: Juvinall

JUVINALL: Machine DesignFig. 4-32 W-108

z

x

y

A A

(2) (= z)

(a)Original element

(c)1-2 plane

(b)Principal element

(3)

(1) (2)

(1)

(d)1-3 plane

(3)

(1)

(e)2-3 plane

(3)

(2)A

Page 1025: Juvinall

JUVINALL: Machine DesignFig. 4-33 W-109

+�

�max = 37

Principal circle

123

(57, 0)(0, 0)(–17, 0)+�

Page 1026: Juvinall

JUVINALL: Machine DesignFig. 4-34 W-110

A

A �1 (tangential)

�2 (axial) �3 = 0 (radial)

+�

0 +��2 �1�3

Correct value of �max

Erroneous value of �max obtained if �3 is neglected

Page 1027: Juvinall

r/d0 0.1 0.2 0.3

1.0

1.2

1.4

1.6

1.8

2.0Kt (a)

2.2

2.4

2.6

2.8

3.0

JUVINALL: Machine DesignFig. 4-35 W-111

D d

r

M M

McI

32M

�d3�nom = =

D/d = 631.51.11.031.01

r/d0 0.1 0.2 0.3

1.0

1.2

1.4

1.6

1.8

2.0Kt

(b)

2.2

2.4

2.6

D d

rPP

PA

4P

�d2�nom = =

D/d = 21.51.21.051.01

r/d0 0.1 0.2 0.3

1.0

1.2

1.4

1.6

1.8

2.0Kt

(c)

2.2

2.4

2.6

D d

r

T T

TcJ

16T

�d3�nom = =

D/d = 21.21.09

Page 1028: Juvinall

r/d0 0.1 0.2 0.3

1.0

1.2

1.4

1.6

1.8

2.0Kt (a)

2.2

2.4

2.6

2.8

3.0

JUVINALL: Machine DesignFig. 4-36 W-112

M M

McI

32M

�d3�nom = =

D/d ≥ 21.11.031.01

0 0.1 0.2 0.31.0

1.2

1.4

1.6

1.8

2.0Kt

(c)

2.2

2.4

2.6

D/d ≥ 21.11.01

r/d

r/d

0 0.1 0.2 0.31.0

1.2

1.4

1.6

1.8

2.0Kt (b)

2.2

2.4

2.6

2.8

3.0

D/d ≥ 21.11.031.01

PP

PA

4P

�d2�nom = =

T T

D d

D d

D d

TcJ

16T

�d3�nom = =

r

r

r

Page 1029: Juvinall

d/D0 0.1 0.2 0.3

1.0

1.2

1.4

1.6

1.8

2.0

Kt

2.2

2.4

2.6

2.8

3.0

MMTT

PPD

d

Axial load:

Bending (in this plane):

�nom = ≈PA

P

(�D2/4) – Dd

�nom = ≈McI

M

(�D3/32) – (dD2/6)

Torsion:

�nom = ≈TcJ

T

(�D3/16) – (dD2/6)

JUVINALL: Machine DesignFig. 4-37 W-113

Page 1030: Juvinall

r/h(a)

0 0.05 0.10 0.15 0.20 0.25 0.301.0

1.2

1.4

1.6

1.8

2.0Kt

2.2

2.4

2.6

2.8

3.0

JUVINALL: Machine DesignFig. 4-38 W-113A

H/h = 621.21.051.01

M

r b

M

McI

6M

bh2�nom = =

r/h(b)

0 0.05 0.10 0.15 0.20 0.25 0.301.0

1.2

1.4

1.6

1.8

2.0Kt

2.2

2.4

2.6

2.8

3.0

H/h = 3

1.52

1.151.05

1.01

PA bh

P�nom = =

PP

hH

r b

hH

Page 1031: Juvinall

r/h(a)

0 0.05 0.10 0.15 0.20 0.25 0.301.0

1.2

1.4

1.6

1.8

2.0Kt

2.2

2.4

2.6

2.8

3.0

JUVINALL: Machine DesignFig. 4-39 W-114

H/h = ∞1.51.151.051.01

M

rb

h MH

McA

6M

bh2�nom = =

r/h(b)

0 0.05 0.10 0.15 0.20 0.25 0.301.0

1.2

1.4

1.6

1.8

2.0Kt

2.2

2.4

2.6

2.8

3.0

H/h = ∞1.51.15

1.05

1.01

r

bh H

PA bh

P�nom = =

PP

Page 1032: Juvinall

JUVINALL: Machine DesignFig. 4-40 W-114A

d/b(a)

0 0.1 0.2 0.3 0.4 0.5 0.6

d/b(b)

0 0.1 0.2 0.3 0.4 0.5 0.6

1.0

7

6

5

4

3

2

1

1.2

1.4

1.6

1.8

2.0Kt

Kt

2.2

2.4

2.6

2.8

3.0

d/h = 0

0.25

0.5

MM

PP

d bh

d bh

McI

6M

(b-d)h2�nom = =

PA (b-d)h

P�nom = =

2.0

1.0

Pinloadedhole

Unloadedhole

Page 1033: Juvinall

W/w1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.01

2

3

4

5

6

7

8

9Kt

10

11

12

13

14

15

16

17

18

JUVINALL: Machine DesignFig. 4-41 W-115

t

h

w

P

r

W

PA

�nom = = Pwt

r/w = 0.050r/w = 0.10r/w = 0.20

h/w = 0.5

0.5

0.75

0.5

0.751.0

0.751.0

1.03.0

3.0

3.0

Page 1034: Juvinall

F F

Sy

Su

JUVINALL: Machine DesignFig. 4-42 W-116

F F

(a) Unnotched

Stress

F = ASy

(c)

(e)

� = Sy

Stress

�max = Sy

�av = Sy /2

Stress con. factor = K = 2Same cross-section area = K

F =ASy

2

(d)

Stress

� = Sy

F

( f )

ab

cd

(b) Notched

Page 1035: Juvinall

JUVINALL: Machine DesignFig. 4-43 W-117

0

(a) Load causes no yielding

+ Sy

0

(b) Load causes partial yielding

+ Sy

0

(c) Load causes partial yielding

+ Sy

0

(d) Load causes total yielding

Load stress + =

+

+

+

+

+

=

=

=

=

Sy –2Sy –Sy

–Sy – 0

– 0

– 0

– 0

– 0 +

– 0 +

– 0 +

– 0 +

Load removalstress change

Residual stress

Page 1036: Juvinall

JUVINALL: Machine DesignFig. 4-44 W-118

F1

F2

M1 M1

F2

F110 mm

10 mm

50 mm

0

–300 MPa

300 mPa

25 mm

Z = bh2

6

Z =

Z = 1.042 × 10–5 m3

(0.025)(0.050)2

6

0 300 396 –396

–238

–96

62

Load stress

+

+

=

=

(a) Given information (see text)

(b)

––

0

Load removal stress change

––

0

Residual stress

––

0–96

62

62

62

–104

–62

–200

Residual stress

+

+

=

=(c)

––

0

Load stress

––

0

Total stress (straight beam)

––

0–96 300

Residual stress

+

+

=

=(d)

––

0 396

238

Load stress

––

0

Total stress (ready to yield)

––

0–96 –204

–122

–300

–60

Residual stress

+

+

=

=(e)

––

0

Load stress

––

0

Total stress (ready to yield)

––

Page 1037: Juvinall

JUVINALL: Machine DesignFig. 4-45 W-119

10.000 in.

T = 80°F

P = 0 lb P = 0 lb

10.008 in.

T = 480°F

P = 60,000 lb P = 60,000 lb

Page 1038: Juvinall

JUVINALL: Machine DesignFig. 4-61 W-142

60 mm

10 mm dia.

20 mm

P = 400 kN

P

Page 1039: Juvinall

JUVINALL: Machine DesignFig. P4-2 W-120

FEDCBA

Page 1040: Juvinall

JUVINALL: Machine DesignFig. P4-10 W-121

di = 20 mm

do = 24 mm

�max = 100 mm

T

Page 1041: Juvinall

JUVINALL: Machine DesignFig. P4-11 W-122

b

2rT

T

T

T

Page 1042: Juvinall

JUVINALL: Machine DesignFig. P4-18 W-123

M M

h

r

b

Page 1043: Juvinall

JUVINALL: Machine DesignFig. P4-19 W-124

4 in.200 lb

200lb

1-in.-dia round rod

3 in.

Page 1044: Juvinall

JUVINALL: Machine DesignFig. P4-21 W-125

A

P Q

A60

70,000 N

40 80

120

Page 1045: Juvinall

JUVINALL: Machine DesignFig. P4-23 W-126

h

X

b

a

c

Page 1046: Juvinall

F

JUVINALL: Machine DesignFig. P4-24 W-127

2 in.13

in.16

3in.16

3 in.4

3in.16

1 in.

Page 1047: Juvinall

JUVINALL: Machine DesignFig. P4-25 W-128

A

A

12,000 N

30 mm

24 mm

8 mm

5 mm

5 mm

Section AA

30 mm

Page 1048: Juvinall

400 N120-mm-dia.

sheave

Free endof shaft

1002000 N

JUVINALL: Machine DesignFig. P4-27 W-131

B

Connected toflexible coupling

and clutch

20-mm-dia. shaft

A

S

T

100

Page 1049: Juvinall

JUVINALL: Machine DesignFig. P4-29 W-129

8 in.

in.3

in.

in.

12

12

in.12

38

Page 1050: Juvinall

JUVINALL: Machine DesignFig. P4-30 W-130

5

5 5

5 50

40

12 kN

L2

Cement L2

Page 1051: Juvinall

JUVINALL: Machine DesignFig. P4-34 W-132

100 mm

250 mm

200 mm

25-mm-dia. roundrod bent into crank

1000 N

Page 1052: Juvinall

1 in.

6-in. dia.

1-in. dia.shaft

Motor

1000-lbbelt tension

3000-lbbelt tension

JUVINALL: Machine DesignFig. P4-36 W-133

Page 1053: Juvinall

50-mm dia.

100-mm dia.

30-mm dia.

JUVINALL: Machine DesignFig. P4-40 W-134

50 mm

100 mm

50 mm

4000 lb

F

B

A

Page 1054: Juvinall

500 lb

JUVINALL: Machine DesignFig. P4-38 W-134a

3 in.

4 in.

3 in.

2 in.

1000 lb

4 in.

1-in.-dia. shaft

A

B

Page 1055: Juvinall

A

JUVINALL: Machine DesignFig. P4-41 W-135

Page 1056: Juvinall

JUVINALL: Machine DesignFig. P4-46 W-136

y x

18 45

30

Page 1057: Juvinall

JUVINALL: Machine DesignFig. P4-49 W-139

Free surface, �3 = 0

20 ksi

30 ksi

Page 1058: Juvinall

JUVINALL: Machine DesignFig. P4-52 W-140

100350

75

Page 1059: Juvinall

JUVINALL: Machine DesignFig. P4-52 W-141

5000 N5000 N 30 mm 200 mm

15 mm25 mm

Page 1060: Juvinall

500 mm 250 mm

JUVINALL: Machine DesignFig. P4-54 W-137

d = 40 mm d = 40 mm

r = 5 mm

A

RA

B

RB

1000 N

D = 80 mm

Page 1061: Juvinall

JUVINALL: Machine DesignFig. P4-55 W-138

5000 N 5000 N50 mm 100 mm

15 mm

25 mm

Page 1062: Juvinall

Cal

cula

ted

elas

tic

stre

ss (

MP

a)

Time0 1 2 3 4 5 6 7 8 9 10 11 12

–200

0

200

400

JUVINALL: Machine DesignFig. P4-65 W-143

Page 1063: Juvinall

JUVINALL: Machine DesignFig. 5-1 W-144

(a) (d) (e)(b) (c)

Page 1064: Juvinall

Z

Y

Xx

y

z

dy (neg.)

dz (neg.)

dx

x → 0�x = lim dx

xy → 0

�y = limdyy

z → 0�z = lim dz

z

Unloaded elementElement loaded in uniaxialtension in X direction (withdeflections shown exaggerated)

JUVINALL: Machine DesignFig. 5-2 W-145

Page 1065: Juvinall

JUVINALL: Machine DesignFig. 5-3 W-146

dx

�yx

�xy

�xy (shown counterclockwise, hence negative)�yx (shown clockwise, hence positive)

y

xZ X

Y

y → 0absolute value = lim = tan � ≈ �dx

y

Page 1066: Juvinall

JUVINALL: Machine DesignFig. 5-4 W-147

+�/2

x

y

0+�

�2

�y

�x

�xy

�1

Page 1067: Juvinall

JUVINALL: Machine DesignFig. 5-5 W-148

(a)Single-element gages oriented

to sense horizontal strain

(b)Two-element rosettes oriented

to measure horizontal andvertical strain

(c)Three-element equiangular

rosettes

(d)Three-element rectangular

rosettes

Page 1068: Juvinall

JUVINALL: Machine DesignFig. 5-6 W-149

�2

�1

�240

�120

�0+�

+�

120°

240°

�2

�1

�120 �240

�0+�

+�

�2

�1

�240 �120

�0

+�

+�

(a) (b) (c)

Page 1069: Juvinall

JUVINALL: Machine DesignFig. 5-7 W-150

17°

240° gage(� = +0.00185)

120° gage (� = +0.0004)

0° gage (� = –0.00075)

�1 = +0.0020

�2 = –0.0010

Page 1070: Juvinall

JUVINALL: Machine DesignFig. 5-8 W-151

+� /2

120°

240°0°

34°

+0.00185–0.00075

+0.0004

�2 = –0.001 �1 = +0.0020

+�

Page 1071: Juvinall

JUVINALL: Machine DesignFig. 5-9 W-152

90°

�2

�1

�0

�90

(a)

45°

+�

+�

�2

�1

�90

�0

�45�45

(b)

+�

+�

�90

�2

�1

�0

�45

(c)

+�

+�

Page 1072: Juvinall

JUVINALL: Machine DesignFig. 5-10 W-153

+2600 �m/m

+450 �m/m

–200 �m/m

(a)

(b)

�0 = +2600

�90 = +450

�45 = –200

Page 1073: Juvinall

�0 = +2600

�90 = +450�2 = –510

�1 = +3560

�45 = –200

JUVINALL: Machine DesignFig. 5-11 W-154

29°

119°

Page 1074: Juvinall

JUVINALL: Machine DesignFig. 5-12 W-155

+� /2

45°

90°

2600

–510 3560

+�–200

450058°

Page 1075: Juvinall

+�

0+�

JUVINALL: Machine DesignFig. 5-13 W-156

�2 = –24

�3 = 0

�1 = 134 �1 = 0.002

(a)

+� /2

+�

�2 = –0.001 �3 = –0.0005

(b)

0

Page 1076: Juvinall

0

–0.04

–1.2

–0.8

–0.4

0

–0.8

–0.4

0

0.4

0.8

0.4

0.8

1.2

, (1

0–6

/mm

)M

, be

ndin

g m

omen

t (k

N•m

m)

V,

shea

r fo

rce

(kN

)

0

4

8

12

0

200

400

–2

–1

0

1

2

–0.08

–0.12

Def

lect

ion

(mm

)R

elat

ive

slop

e (m

illir

adia

ns)

JUVINALL: Machine DesignFig. 5-14 W-159

0.093

–0.677

–0.220

0.2700.835

0.838

0.0220.007

0.115

0.126

Tangent point

Parallel to true lineof zero deflection

True line ofzero deflectionLo

cati

on o

f ze

roab

solu

te s

lope

Init

ially

ass

umed

loca

tion

of

zero

slo

pe

0.119

+0.001

–1.109–1.096

A =0.093 mm

A = 0.011

A = 13 × 10–6

A = 11,000

A = 36,000

M EI

A = 3 × 10–6

A =0.457 × 10–3 A =

0.270 × 10–3

A = 0.565 × 10–30.220 × 10–30.419× 10–3

A = 0.120 mm

Abs

olut

e sl

ope

(mra

d)

0.852.67

8.46

220 255325 360

1822

9.80

5.12 5.670.69

1.94 2.47 0.28

Area = 58,000 kN•mm2

2.2

0.7Area =

220 kN•mmArea = 140 kN•mm

Area = 360 kN•mm

–1.8

d = 30

2.2 kN 1.8 kN

10

d = 40

1050 50100 200 200

d = 40

1.5 kN 2.5 kN

d = 50d = 60

Page 1077: Juvinall

0 ∆Deflection

Area = U'

Area = U

Area = dU

dQ

JUVINALL: Machine DesignFig. 5-15 W-160

QLoad

Area = dU'

Page 1078: Juvinall

JUVINALL: Machine DesignFig. 5-16 W-161

L/2 P/2P/2

x dx

L

P

b

h

Page 1079: Juvinall

JUVINALL: Machine DesignFig. 5-17 W-162

200 mm 2500 N2500 NL = 400 mm

P = 5000 N

b = 25 mm

h = 50 mm

Page 1080: Juvinall

JUVINALL: Machine DesignFig. 5-18 W-163

L

P

h

bx

c

a

y

Q

Page 1081: Juvinall

JUVINALL: Machine DesignFig. 5-19 W-164

F

h

b

V

F

F

P M

F

R

R

2R

�R – R cos �

(a) (b)

Page 1082: Juvinall

sin

–1.0

–0.5

0sin � d� = 1;

(From this, average value = can be determined)

�/2

0

0.5

1.0

2�

2�

2�

4�

2�

Avg value =

cos

–1.0

–0.5

0

0.5

1.02�Avg value =

sin

� c

os �

� (radians)0 �/2 � 3�/2 2�

–0.5

0

0.5

(0.707)(0.707) = 0.52�Avg value = 0.5 = 1

� = (Half of avg value shown in sin � plot)

cos2

0

0.5

1.0Avg value = 0.5

sin2

0

0.5

1.0Avg value = 0.5

∫ sin � d� = 02�

0∫sin � d� = 2;�

0∫

cos � d� = 1;�/2

0∫ cos � d� = 02�

0∫cos � d� = 0;�

0∫

sin2 � d� = (0.5) = ;�/2

0∫ sin2 � d� = �(0.5) =�

0∫sin2 � d� = �

2�

0∫

2�

4�

2�

cos2 � d� = (0.5) = ;�/2

0∫ cos2 � d� = �(0.5) =�

0∫cos2 � d� = �

2�

0∫

2�

�121

sin � cos � d� = = ;�/2

0∫ sin � cos � d� = 0�

0∫sin � cos � d� = 0

2�

0∫

JUVINALL: Machine DesignFig. 5-20 W-165

Page 1083: Juvinall

JUVINALL: Machine DesignFig. 5-21a W-166

F

h = 0.3 in.

b = 0.2 in.

E = 18 × 106 psiG = 7 × 106 psi

F

R = 2.0 in.

2R = 4 in.

(a)

Page 1084: Juvinall

CopperCast ironSteel

0.2 0.3Width, h (in.)

(b)

Def

lect

ion,

� (

in.)

0.4 0.50.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

JUVINALL: Machine DesignFig. 5-21b W-167

Page 1085: Juvinall

Def

lect

ion,

� (i

n.)

Radius, R (in.)1.0 1.5 2.0 2.5 3.0

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

JUVINALL: Machine DesignFig. 5-21c W-168

CopperCast ironSteel

Page 1086: Juvinall

0.06

0.05

0.04

0.03

Def

lect

ion,

� (

in.)

0.02

0.01

0.5

0.4

Thickness, b (in.)

0.3

0.2

0.3

Width, h (in.)

0.2

0.1

JUVINALL: Machine DesignFig. 5-21d W-169

Page 1087: Juvinall

F

JUVINALL: Machine DesignFig. 5-22 W-170

3 m

10 m

ya

Point of zerodeflection

1.2 m

500 kg mass

Page 1088: Juvinall

P/2

JUVINALL: Machine DesignFig. 5-23 W-171

a x

y

b2

a

3'

2'

1

2

3

b2

Pa/2

M0

P/2

P

P/2

P/2

M0

M0

Pa/2

M0

P/2M0

P/2

M0

(a)

(b)

P

Page 1089: Juvinall

JUVINALL: Machine DesignFig. 5-24 W-172

e

L or Le

P

P

P

P

x x

y

y

(b)Column cross section

(a)Two views of column

Axis of least I and � becomesneutral bending axis whenbuckling occurs. With columnformulas, always use I and �with respect to this axis.

Page 1090: Juvinall

Slenderness ration Le /�

10 1000.0001

0.001

0.010

ScrE

0.100

JUVINALL: Machine DesignFig. 5-25 W-173

Page 1091: Juvinall

Slenderness ratio Le /�20 40 60 80 100 120 140 1600

20

40

60

80

A

B

C

D

100

120

140

160

180

JUVINALL: Machine DesignFig. 5-26 W-174

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

Cri

tica

l uni

t lo

ad S

cr (

ksi)

Cri

tica

l uni

t lo

ad S

cr (

MP

a)

Sy = 689 MPa

Arbitrary valuesfor illustration

Sy = 496 MPa

Euler, E = 203 GPa (steel)

EF

Euler, E = 71 GPa (alum)

Page 1092: Juvinall

JUVINALL: Machine DesignFig. 5-27 W-175

L

Le

(b)

L Le

(c)

Le = L

(a)

(Buckledshape showndotted)

L Le

(d)

LLe2

(e)

Le = 0.707L Le = 0.5LLe = L Le = L Le = 2LTheoretical

Le = 0.80L Le = 0.65LLe = L Le = 1.2L Le = 2.1L

MinimumAISCRecommend

Source: From Manual of Steel Construction, 7th ed., American Institute of Steel Construction, Inc., New York, 1970, pp. 5–138.

Page 1093: Juvinall

Slenderness ratio Le /�20 40 60 80 100 120 140 1600

20

40

60

80

A

B

C

D

100

120

140

160

180

JUVINALL: Machine DesignFig. 5-28 W-176

0

100

200

300

400

500

600

700

800

900

1000

1100

1200

Cri

tica

l uni

t lo

ad S

cr (

ksi)

Cri

tica

l uni

t lo

ad S

cr (

MP

a)

Sy = 689 MPa

Johnson,E = 71 GPa,Sy = 496 MPa

Johnson, E = 203 GPa, Sy = 689 MPa

Euler, E = 203 GPaTangentpoints

Euler, E = 71 GPa

EF

Sy = 496 MPa

Page 1094: Juvinall

JUVINALL: Machine DesignFig. 5-29 W-177

80,000 N 80,000 N

D

1 m

SF = 2.5Sy = 689 MPaE = 203 GPa (steel)

Page 1095: Juvinall

JUVINALL: Machine DesignFig. 5-30 W-178

80,000 N 80,000 N

D

200 m

SF = 2.5Sy = 496 MPaE = 71 GPa (aluminum)

Page 1096: Juvinall

Cri

tica

l uni

t lo

ad S

cr (M

Pa)

Cri

tica

l uni

t lo

ad S

cr (

ksi)

Slenderness ratio Le/�20 40 60 80 100 120 140 160 180 2000

100

50

150

200

250

300

350

400

450

500

550

600

10

0

20

30

40

50

60

70

80

JUVINALL: Machine DesignFig. 5-31 W-179

ec/�2 = 1.0

ec/�2 = 0

0.6

0.3

0.1

Euler curve

0.05

Page 1097: Juvinall

JUVINALL: Machine DesignFig. 5-32 W-180

(a)Wrinkling, or "accordian

buckling" of thin-wall tube

(b)Typical local buckling ofan externally pressurized

thin-wall tube

(c)Wrinkling of thin, unsupportedflanges of a channel section

Page 1098: Juvinall

JUVINALL: Machine DesignFig. 5-33 W-180A

Beam

Triangle

Quadrilateral

Tetrahedron

Pentahedron

Hexahedron

Page 1099: Juvinall

JUVINALL: Machine DesignFig. 5-34 W-180B

(1)

(3)(6)

(7) (9)

(2) 31

2

5 7

W

4

6

(5) (10)

(4)

(8)

(11)

Page 1100: Juvinall

JUVINALL: Machine DesignFig. 5-35 W-180C

�3x

�3x

3'

3

F (7)3y F (7)

3x

6'

6

F (7)

L 6y

F (7)6x �6x

�6x

Page 1101: Juvinall

JUVINALL: Machine DesignFig. 5-36 W-180D

3 3'

F (7)3x

�3x

F (7)

A, E

L

3y

F3

6

Page 1102: Juvinall

2 m

22' (Constant A, E)

3 N

2 N

3.464 m

4 m

�2x

�2y

�3x

(3)

(2)

3 3'1

JUVINALL: Machine DesignFig. 5-37 W-180E

Page 1103: Juvinall

F (1)2y F (2)

2y

F (1)2x

F (1)1y

F (3)1y

F (3)1x

F (1)1x

F (2)3y

F (2)3x

F (2)2x

(1)

(2)

(3)

4 m

1

1

3

F (3)3y

F (3)3x

3

2 2

2 m

3.464 m

JUVINALL: Machine DesignFig. 5-38 W-180F

Page 1104: Juvinall

JUVINALL: Machine DesignTable 5-1 W-157

L

P

�� = PL

AE1. Tension or compression

Cross-section area = A

LT

2. Torsion

For solid round bar anddeflection in degrees,

K'a = section property. For solidround section, K' = J = �d4/32.

3. Bending (angular deflection)

I = moment of inertia aboutneutral bending axis

M

M

L

4. Bending (linear deflection)

I = moment of inertia aboutneutral bending axis

L

5. Cantilever beam loaded at end

I = moment of inertia aboutneutral bending axis

LP

� = TLK'G

� = MLEI

� = ML2

2EI

� = PL3

3EI

k = =P�

AEL

K = =T�

K'GL

K = =M�

EIL

k = =M�

2EI

L2

k = =P�

3EI

L3

�° = 584TL

d4G

Page 1105: Juvinall

(d4 – d4)

JUVINALL: Machine DesignTable 5-2 W-158

d

do

2b

2a

a

a

b

a

K' = J = �d4

32

di K' = J = o i�32

– 3.36 1 –K' = ab3

16b4

12a4163

ba

d

t

K' = �dt4

32

K' =

K' = 0.0216a4

K' = 2.69a4

�a3b3

a2 + b2

a

a

K' = 0.1406a4

Page 1106: Juvinall

JUVINALL: Machine DesignFig. P5-4 W-181

�120 = +625

�240 = +300

�0 = +950

Page 1107: Juvinall

JUVINALL: Machine DesignFig. P5-9 W-183

�0 = –300

�135 = –380

�270 = –200

�90 = –300

�45 = –380

�0 = –200

Gage readings Equivalent rosettes

Page 1108: Juvinall

JUVINALL: Machine DesignFig. P5-14 W-182

k = 5 N/mm

A

B

C

100 mm

100 mm

100 mm

F

F

F

Page 1109: Juvinall

JUVINALL: Machine DesignFig. P5-15 W-184

200 mm

25 mm-dia. steel

1000 N

100 mm

A

Page 1110: Juvinall

JUVINALL: Machine DesignFig. P5-16 W-185

d = 30d = 50 d = 40

4 kN

2 kN100 200 150

Page 1111: Juvinall

JUVINALL: Machine DesignFig. P5-17 W-186

a

Z

b

YX

F (used in Problem 5.17)

T (used in Problem 5.18)

Solid round rod ofproperties E, G, A,

I, and J.

Page 1112: Juvinall

JUVINALL: Machine DesignFig. P5-19 W-186a

w = 200 lb/in.

d

5 in. 15 in. 5 in.

0.75d 0.75d

Page 1113: Juvinall

JUVINALL: Machine DesignFig. P5-20 W-187

a

a F

F

b

Page 1114: Juvinall

JUVINALL: Machine DesignFig. P5-21 W-188

P

R

Page 1115: Juvinall

JUVINALL: Machine DesignFig. P5-22 W-189

F

b

h

2

b2

L

Page 1116: Juvinall

JUVINALL: Machine DesignFig. P05-23 W-190

5 kN

S

500 mm

300 mm

Page 1117: Juvinall

JUVINALL: Machine DesignFig. P5-27 W-191

2

1 1

2

Page 1118: Juvinall

1 m

0.7 m

1 m0.7 m

Boom

12 mm-dia. tie-rod

6 kN

JUVINALL: Machine DesignFig. P5-29 W-192

Page 1119: Juvinall

JUVINALL: Machine DesignFig. 6-2 W-194

2w

2c

t

P

P

(a) Center crack

w

t

P

P

(b) Edge crack

c

Page 1120: Juvinall

JUVINALL: Machine DesignFig. 6-3 W-195

2w = 6 in.

2c = 1 in.

t = 0.06 in.

7075–T651 Aluminum,Su = 78 ksi, Sy = 70 ksi,

Kic = 60 ksi

P

P

in.

Page 1121: Juvinall

JUVINALL: Machine DesignFig. 6-4 W-196

P

P

a2c

2w

t

Page 1122: Juvinall

JUVINALL: Machine DesignFig. 6-5 W-197

P

P

a2c

2w = 6 in.

t = 1 in.

�g = 0.73 Sy

a/2c = 0.25

Ti – 6Al – 4V (annealed)titanium plate

Page 1123: Juvinall

JUVINALL: Machine DesignFig. 6-6 W-198

+�

�2 = 40 ksi

(�max = 60)

�1 = 80 ksi

(a) Proposed application involving�1 = 80, �2 = –40, �3 = 0

+�

+�

(�max = 50)

�2 = �3 = 0�3 = 0

�1 = 100 ksi

(a) Standard tensile test of proposed material. Tensile

strength, S = 100 ksi

+�

Page 1124: Juvinall

JUVINALL: Machine DesignFig. 6-7 W-199

+�

+�

Uniaxialcompression Uniaxial

tension

Principal Mohr circlemust lie within thesebounds to avoid failure

For biaxial stresses (i.e., �3 = 0),�1 and �2 must plot within thisarea to avoid failure

0

+�2

+�10

Suc Sut Suc

Sut

Suc

Sut

(a) Mohr circle plot (b) �1 – �2 plot

Page 1125: Juvinall

+�

+�

JUVINALL: Machine DesignFig. 6-8 W-200

Principal Mohrcircle must liewithin thesebounds to avoidfailure

Uniaxial tension

Syt

+�2

+�1Syt

Syt

0

For biaxial stresses (i.e., �3 = 0),�1 and �2 must plot within thisarea to avoid failure

(a) Mohr circle plot (b) �1 – �2 plot

Page 1126: Juvinall

JUVINALL: Machine DesignFig. 6-9 W-201

Principal plane

Principal planes

Octahedral plane

Page 1127: Juvinall

+�2

(0, 100)(–100, 100) (100, 100)

(100, 0)(–100, 0)

(–100, –100)(0, –100)

(100, –100)

+�1

JUVINALL: Machine DesignFig. 6-10 W-202

(–58, 58)

(58, –58)

(50, –50)

0

Shear diagonal (�1 = –�2)

Distortion energy theory

Normal stress theory

Shear stresstheory

Note: �3 = 0

Page 1128: Juvinall

+�

+�

JUVINALL: Machine DesignFig. 6-11 W-203

Principal Mohr circle mustlie within these boundsto avoid failure

SutSuc

+�2

+�1Sut

Suc

Suc

+Sut

0

For biaxial stresses (i.e., �3 = 0),�1 and �2 must plot within thisarea to avoid failure

(a) Mohr circle plot (b) �1 – �2 plot

0

Page 1129: Juvinall

JUVINALL: Machine DesignFig. 6-12 W-204

+�2

+�1SutSuc

Sut

Suc

0

Shear diagonal

Page 1130: Juvinall

JUVINALL: Machine DesignFig. 6-13 W-205

�2 = –25 ksi

�2 = –25 ksi

�1 = 35 ksi �1 = 35 ksi

Note: �3 = 0

Steel,Sy = 100 ksi

Page 1131: Juvinall

JUVINALL: Machine DesignFig. 6-14 W-206

–25

–100

�2 (ksi)

�1 (ksi)35 58 66 100

(58, –58)

0

Normal loadpoint

Limitingpoints

� theory

D.E. theory

� theory

Load line

Shear diagonal

Page 1132: Juvinall

Str

ess

(% o

f ul

tim

ate

stre

ngth

)

Load (% of ultimate load)0 50

SF = 2 based onload, Eq. 6.10

SF = 2 based onstrength, Eq. 6.9

Fracture

100

50

100

JUVINALL: Machine DesignFig. 6-15 W-207

Page 1133: Juvinall

Freq

uenc

y p(

x) a

nd p

(y)

Strength (x), and stress (y) (MPa or ksi)0 40 70

JUVINALL: Machine DesignFig. 6-16 W-208

x (strength)y (stress)

�y �x

Page 1134: Juvinall

Freq

uenc

y p(

z)

Margin of safety, z, where z = x – y300

JUVINALL: Machine DesignFig. 6-17 W-209

z (margin of safety)

�z

Page 1135: Juvinall

Freq

uenc

y p(

x)

Quantity x0 � x1

�1

�1 < �2 < �3

�2

�3

x2

JUVINALL: Machine DesignFig. 6-18 W-210

Page 1136: Juvinall

Freq

uenc

y p(

x)

Quantity x

–3� –2� –1� � +1� +2� +3�

JUVINALL: Machine DesignFig. 6-19 W-211

0.13% 0.13%2.14% 2.14%

13.60% 13.60%

34.13% 34.13%of totalarea

Inflection point Inflection point

Page 1137: Juvinall

% r

elia

bilit

y(%

of

surv

ivor

s or

% c

umul

ativ

e pr

obab

ility

of

surv

ival

)

Number of standard deviations, k–4 –3 –2 –1 0 +1 +2 +3 +4

0.01

0.050.10.2

0.5

1

2

5

10

20

30

40

50

60

70

80

90

95

98

99

99.899.9

99.99

% o

f fa

ilure

s or

P,

% c

umul

ativ

e pr

obab

ility

of

failu

re

99.99

99.999.8

99

98

95

80

70

60

50

40

30

20

10

5

2

1

0.5

0.20.10.05

0.01

JUVINALL: Machine DesignFig. 6-20 W-212

–k�

% of failures

Fatigue life, strength, etc.

Extremevalues

k = –4, 99.99683% reliabilityk = –5, 99.9999713% reliabilityk = –6, 99.9999999013% reliability

% ofsurvivors

Page 1138: Juvinall

Freq

uenc

y p(

z)

Torque z (N • m)

(5.22)0

JUVINALL: Machine DesignFig. 6-21 W-213

z = x – y

�z

Freq

uenc

y p(

x) a

nd p

(y)

Torque x and y (N • m)

(a)

(b)

0 (14.8) 20.0

One bolt in500 twists off

x (bolt twist-off strength)

y (wrenchtwist-off torque)

�x�y

�x = 1 N • m�y = 1.5 N • m

k�z

One bolt in500 twists off

Page 1139: Juvinall

JUVINALL: Machine DesignFig. P6-13 W-214

�1 = 200 MPa

�2 = 100 MPa

�2

�1 �1 = 150 MPa

�2 = –100 MPa

�2

�1 ba

Page 1140: Juvinall

JUVINALL: Machine DesignFig. P6-23 W-215

�x �x = 50 MPa

Sy = 500 MPa

�xy = 100 MPa

�xy

Page 1141: Juvinall

k

JUVINALL: Machine DesignFig. 7-1 W-216

c

k

m

(b)(a) (c)

k

m

m

Page 1142: Juvinall

S u a

nd S

y (k

si)

Average strain rate (s–1)10–6 10–5 10– 4 10–3 10–2 10–1 1 101 102 1030

10

20

30

40

50

60

70

80

90

100

S y /

S u (%

)E

long

atio

n (%

)

0

10

20

30

40

50

60

70

80

90

100

JUVINALL: Machine DesignFig. 7-2 W-217

Yield strength Sy

Ultimate strength Su

Total elongation

Ratio Sy /Su

Page 1143: Juvinall

k

(a) (b) (c)

Elastic-strain energy stored

in structure = Fe�ForceFe

W O

hDeflection

Work of falling weight = W (h + �)

Guide rod

h

�st

12

JUVINALL: Machine DesignFig. 7-3a-c W-218

W

k

W

Page 1144: Juvinall

d

L /2

L /2

2d

JUVINALL: Machine DesignFig. 7-4 W-219

(b)

d

L

(a)

�d2

4Area = A =

Page 1145: Juvinall

L

Bumper ofcross section A;volume = AL

h

JUVINALL: Machine DesignFig. 7-5 W-220

W

Page 1146: Juvinall

1 in. × 3 in., I = bh3/12 = 6.46 in.4

2 × 4 white pineE = 106 psi

Mod. of rupture = 6 ksi

JUVINALL: Machine DesignFig. 7-6 W-221

30 in.

12 in.

60 in.

100 lb/in. 100 lb/in.58

58

Z = I/c = 3.56 in.3

100 lb

Page 1147: Juvinall

100-mmdia

120-mmdia

20-mmdia

JUVINALL: Machine DesignFig. 7-7 W-222

20 mm20 mm

250 mm

Page 1148: Juvinall

Tors

iona

l def

lect

ion

of s

haft

(de

g)

Shaft radius (mm)5.0 7.5 10.0 12.5 15.00

5

10

15

20

25

30

35

40

JUVINALL: Machine DesignFig. 7-7b W-223

Sha

ft s

hear

str

ess

(MP

a)

Shaft radius (mm)5.0 7.5 10.0 12.5 15.0

100

200

300

400

500

600

700

AluminumCast ironSteel

AluminumCast ironSteel

Page 1149: Juvinall

JUVINALL: Machine DesignFig. 7-8 W-224

Ki = 1.5

Ki = 1.5

d

Page 1150: Juvinall

JUVINALL: Machine DesignFig. 7-9 W-225

Ki = 1.5

Ki = 3

Ki = 1.5d

d2

Page 1151: Juvinall

Ki = 3.4

A = 700 mm2

JUVINALL: Machine DesignFig. 7-10 W-226

"Very long"(>10d)

"Negligible"

Ki = 3.5

A = 600 mm2

Shank

Head

Ki = 3.4

A = 300 mm2

Ki =1.5

Ki = 3.0

Ki = 1.5

A = 600 mm2

(a) Original design (b) Modified design

d

Page 1152: Juvinall

JUVINALL: Machine DesignFig. 7-10 W-229

K = 1.55

K = 4

Dropweight

24 mm dia.

K = 1.4

30 mm dia.

Page 1153: Juvinall

JUVINALL: Machine DesignFig. 7-11 W-227

(a)

Axial hole

(b)

Page 1154: Juvinall

"Very long"

K = 2

K = 21-in dia.

JUVINALL: Machine DesignFig. 7-13 W-232

0.1-in dia. hole

Page 1155: Juvinall

Steel cableA = 2.5 in.2

E = 12 × 106

JUVINALL: Machine DesignFig. P7-2 W-228

Page 1156: Juvinall

JUVINALL: Machine DesignFig. P7-5 W-228

K = 5000 N/mmL = 5 m

v = 4 km/hr m = 1400 kg

Rope

Page 1157: Juvinall

JUVINALL: Machine DesignFig. P7-11 W-230

(a)

Original design New design

(b)

Thread: Area = 600 mm2

K = 3.9

Thread:Area = A

K = 2.6

Area = AK = 2.6

"Very long"

A= 600 mm2

K = 3.9

K = 1.3

K = 1.3

Platform

Area = 800 mm2

Area = 800 mm2

Page 1158: Juvinall

dia. = 36 mm

K = 2.2

250 mm

(Fracturelocation)

3 mm(negligible)

JUVINALL: Machine DesignFig. P7-12 W-231

K = 1.5

Hole dia., d

A = 800 mm2

K = 3.8

(a)

Original design

(b)

Modified design

Assume that holedrilled to this depth,does not significantlychange the K = 3.8factor at the thread.

Page 1159: Juvinall

JUVINALL: Machine DesignFig. 8-2 W-234

Small region behaves plastically

Main body behaves elastically

Page 1160: Juvinall

0.300"

C

R

110-Volts AC

Flexiblecoupling

JUVINALL: Machine DesignFig. 8-3 W-235

Weights

Revolutioncounter

Test specimen

9 "78

Motor

Page 1161: Juvinall

++

++

Fati

gue

stre

ngth

, or

Pea

k al

tern

atin

g st

ress

S (

ksi (

log)

)

Life N (cycles (log))103 104 105 106 107 108

10

20

30

40

50607080

100

JUVINALL: Machine DesignFig. 8-4 W-236

(c) Log-log coordinates

Sn (endurance limit)'

'

'

"Knee" of curve

8:7 ratio

Not broken

7:1ratio

Life N (cycles (log))

(a) Linear coordinates (not used for obvious reasons)

(b) Semilog coordinates

Sn (endurance limit)

Fati

gue

stre

ngth

, or

Pea

k al

tern

atin

g st

ress

S (

ksi)

103 104 105 106 107 1080

10

20

30

40

50

Not broken

Life N (cycles � 106)

Sn (endurance limit)

Fati

gue

stre

ngth

, or

Pea

k al

tern

atin

g st

ress

S (

ksi)

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

Not broken

++++++

++++++

++++

++

++

+++++++++++

++++++++++++

Page 1162: Juvinall

S/S u

(log

)

Life N (cycles(log)) Sn = 0.5 Su(in ksi, Sn � 0.25 � Bhn;

in MPa, Sn � 1.73 � Bhn)

103 1042 4 6 1052 4 6 1062 4 6 1072

Not broken

4 60.4

0.5

0.6

0.8

0.9

1.0

0.7

JUVINALL: Machine DesignFig. 8-5 W-237

S = 0.9Su (in ksi, S � 0.45 � Bhn; in MPa, S � 3.10 � Bhn)

Sn

'

'

''

Page 1163: Juvinall

End

uran

ce li

mit

S

n (k

si)

' 'E

ndur

ance

lim

it

Sn

(MP

a)

Hardness (Rockwell C)0 10 20 30 40 50

0.25 Bhn

60

187 229 285

Hardness (HB)

375 477 653

700

20100

SAE 4063SAE 5150SAE 4052SAE 4140

200

300

400

500

600

700

800

900

40

60

80

100

120

140

JUVINALL: Machine DesignFig. 8-6 W-238

Page 1164: Juvinall

Actual maximum stressCalculated maximum

stress (Mc /I )

JUVINALL: Machine DesignFig. 8-7 W-239

MM

Page 1165: Juvinall

Pea

k al

tern

atin

g be

ndin

g st

ress

S (

ksi (

log)

S (M

Pa

(log

))

Life N (cycles (log))103 104 105 106 107

Wrought

Permanentmold cast

Sand cast

108 10956

78

10

12

14161820

30

35

25

40

50

60

7080

50

75

100

150

200

250

300

400

500

JUVINALL: Machine DesignFig. 8-8 W-240

Page 1166: Juvinall

Fati

gue

stre

ngth

at

5 �

10

8 c

ycle

sS

n (k

si)

Sn

(MP

a)

Tensile strength Su (ksi)

Su (MPa)

0 10 20 30

Alloys represented:1100-0, H12, H14, H16, H183003-0, H12, H14, H16, H185052-0, H32, H34, H36, H38

2014-0, T4, and T62024-T3, T36 and T46061-0, T4 and T6

6063-0, T42, T5, T67075-T6

40 50

0 50 100 150 200 250 300 350 400 450 500 550

60 700 0

50

100

150

10

20

30

JUVINALL: Machine DesignFig. 8-9 W-241

Sn = 19 ksi

Sn = 0.4Su'

'' '

Page 1167: Juvinall

Pea

k al

tern

atin

g st

ress

S (

ksi (

log)

)

S (

MP

a (l

og))

Life N (cycles (log))105 1062 4 6 8 1072 4 6 8 1082 4 6 85

6

50

75

100

150

200

7

89

10

12

14

161820

25

30

35

40

JUVINALL: Machine DesignFig. 8-10 W-242

Sand-cast

Extruded and forged

Page 1168: Juvinall

Rat

io,

(log

)pe

ak a

lter

nati

ng s

tres

s, S

or

S sS u

Life, N (cycles (log))103

Torsion

Axial (no eccentricity)

Bending

Sn = Sn = 0.5Su'

'

'

Sn = 0.9Sn = 0.45Su

Sn = 0.58Sn = 0.29Su

S103 = 0.9SuS103 = 0.75SuS103 = 0.9Sus (≈ 0.72Su)

104 105 106 1070.1

0.3

0.5

1.0

JUVINALL: Machine DesignFig. 8-11 W-243

Page 1169: Juvinall

–1.2Reversed bending

Reversed torsion

Reversed bending

DE theory

–0.8

–0.6

–0.4

–0.2

0.2

0.4

0.6

0.8

1.2

–1.2 –0.8 –0.4

Note: Dotted portion issuperfluous for completelyreversed stresses

0 0.4 0.8 1.2

�1Sn

JUVINALL: Machine DesignFig. 8-12 W-245

�1Sn

�2Sn

–1.0

1.0

Page 1170: Juvinall

Sur

face

fac

tor

Cs

Tensile strength Su (ksi)60 80 100 120 140 160

Su (GPa)

180 200 220 240 260

120 160 200 240 280 320

Hardness (HB)

360 400 440 480 520

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

JUVINALL: Machine DesignFig. 8-13 W-246

0.4 1.81.61.41.21.00.80.6

Mirror-polished

Fine-ground orcommerciallypolished

Machined or cold-drawn

Hot-rolled

As forged

Corroded in salt water

Corroded intap water

Page 1171: Juvinall

JUVINALL: Machine DesignFig. 8-14 W-247

Equalsurfacestresses

(a) d = (0.3" or 7.6 mm)

(b) d > (0.3" or 7.6 mm)

(c) d < (0.3" or 7.6 mm)

Page 1172: Juvinall

0

+

�min

�m = mean stress; �a = alternating stress (or stress amplitude)�max = maximum stress; �min = minimum stress�m = (�max + �min)/2�a = (�max – �min)/2

Str

ess

JUVINALL: Machine DesignFig. 8-15 W-248

�max

�max

�a

�m

�m �a

�a

�min

Page 1173: Juvinall

0 Sy–Sy

A' A

Sn

Sy

F

E

A"

D

C

G

H

106 ~

Values from S–N curve

105 ~

104 ~

10 3 ~

10 4 ~

10 5 ~10 6

~

103 ~

H'

B

�m (tension)–�m (compression) Su

JUVINALL: Machine DesignFig. 8-16 W-249

�a

Page 1174: Juvinall

Max

imum

str

ess

�m

ax (

% o

f S u

)

Minimum stress �min (% of Su)–100 –80 0 20 40 60 80 1000

10

20

30

40

50

60

70

80

90

100

JUVINALL: Machine DesignFig. 8-17 W-250

–60 –40 –20

–30

–20

40

50

Mea

n str

ess �

m (%

of S u

)

60

80

70

100

90

–10

10

30

20

60

50

40

Alternating stress �a (%

of Su ) 20

30

10

90

70

80

Su

103-cycle life

104

10610

5

107

3 × 103

3 × 104

Page 1175: Juvinall

JUVINALL: Machine DesignFig. 8-18 W-251

–20

–10

Max

imum

str

ess

�m

ax (

ksi)

Minimum stress �min (ksi)–80 –60 0 20 40 60 800

10

20

30

40

50

60

70

80

–20–40

50

40

Alternating stress �a (ksi) 20

30

10

70

60

103-cycle life

104

105

109

106

107

4 × 104

4 × 105

Su

40

50

60

70

80

10

30Mea

n str

ess �

m (k

si)

20

Page 1176: Juvinall

JUVINALL: Machine DesignFig. 8-19 W-252

Max

imum

str

ess

�m

ax (

ksi)

Minimum stress �min (ksi)–80 0 20 40 60 800

10

20

30

40

50

60

70

80

–40–60 –20

–30

–10

–20

40

50

60

70

80

10

30Mea

n str

ess �

m (k

si)

20

50

40

Alternating stress �a (ksi) 20

30

10

70

60

103 -cycle life

104

105

109

106 10

7

4 × 104

4 × 105

Page 1177: Juvinall

Sn

–Sn

Sy

Su

0

(a)

(b)

(c)

(d)

(e)

( f )

Cal

cula

ted

fluc

tuat

ing

axia

l str

ess

(ign

orin

g yi

eldi

ng)

JUVINALL: Machine DesignFig. 8-20 W-253

�a�m

�a

�a

�m

Page 1178: Juvinall

0

d < 2.0 in.

P(t)P(t)

P(t)

t

Commerciallypolished surface

Sy = 120 ksiSu = 150 ksi

JUVINALL: Machine DesignFig. 8-21 W-254

Page 1179: Juvinall

20 = 0.67

A10 3

~

10 4 ~

10 5 ~

10 6 ~

Axial loading stresses in ksi

Axial loading stresses in ksi

1�a

�a

Sy

�m

40

Point O

80

100

112 ksi

92 ksi

61 ksi

75 ksi

120

–120 –100 –80 –60 –40 –20 0 20 40

(used in Sample Problem 8.2)

60 80 100 120 150–�m (compression) +�m (tension) SySy Su

JUVINALL: Machine DesignFig. 8-22 W-255

Pea

k al

tern

atin

g st

ress

, S

(log

)

Life N (cycles (log))

S = 0.75Su = 0.75(150) = 112

'Sn = SnCLCGCS = (0.5 × 150)(1)(0.9)(0.9) = 61

103 104 105 106 107

61

75

92

112

3 2

Page 1180: Juvinall

Cal

cula

ted

nom

inal

str

ess

S

Life N (cycles)103 104 105

Unnotched specimensNotched specimens

106

(a) Unnotched specimen ("u")

(b) Notched specimen ("n") (c) Illustration of fatigue stress concentration factor, Kf

107

Kf = Sn(u)

Sn(u)

Sn(n) Sn(n)

JUVINALL: Machine DesignFig. 8-23 W-256

d

d

Page 1181: Juvinall

Notch radius r (in.)0 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16

Notch radius r (mm)0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

0

0.1

0.2

0.3

q

0.4

0.5

0.6

0.7

0.8

0.9

Use these values with bending and axial loads

Use these values with torsion

SteelSu (ksi) and Bhnas marked

1.0

JUVINALL: Machine DesignFig. 8-24 W-257

Aluminum alloy (based on 2024-T6 data)

200 (400 Bhn) 180 (360 Bhn)

120 (240 Bhn)

140 (280 Bhn)

100 (200 Bhn)

80 (160 Bhn)

80 (160 Bhn)

60 (120 Bhn)

60 (120 Bhn)

50 (100 Bhn)

Page 1182: Juvinall

100

200

d

cc'

b

a

b'

280300

0 100 200 300

106 ~ Life105 ~ Life

104 ~ Life

103 ~ Life

400 450�m, tension (MPa) Su

Sy

�a

(MP

a)

0

–300

300

300

600

0(a) (b) (c) (d)

(a) (b') (c') (d')

Calculatedstresses

Actualstresses

Constant-lifefatiguediagram

Cal

cula

ted

notc

h st

ress

(P/A

)Kf (

MP

a)A

ctua

l not

ch s

tres

s(P

/A)K

f + �

resi

dual

(M

Pa)

JUVINALL: Machine DesignFig. 8-25 W-258

d'

Page 1183: Juvinall

Commercial ground finishHeat-treated alloy steel,Su = 1.2 GPa, Sy = 1.0 GPa

T = 1000 ± 250 N • m

T = 1000 ± 250 N • m

D/d = 1.2 r/d = 0.05 SF = 2.0

JUVINALL: Machine DesignFig. 8-26 W-259

d

r

D

Page 1184: Juvinall

100

150

1200

B'

B

ANB

NB'

NA

(0.58)(0.9)(0.87) = 272 MPa

�max = Ssy106 ~ = ∞ life

Assuming 10 mm < d < 50 mm

2

116

200

300

–200 –100 0

0'

100 200

Sn = SnCLCGCS = '

300 400

Mean torsional stress �m (MPa)

500 600 700 800 900Ssy ≈ 0.58(1000) = 580 Sus ≈ 0.8(1200) = 960

Alt

erna

ting

tor

sion

al s

tres

s� a

(M

Pa)

JUVINALL: Machine DesignFig. 8-27 W-260

Page 1185: Juvinall

Alt

erna

ting

ben

ding

str

ess

�ea

(M

Pa)

Mean bending stress �em (MPa)0 100

(15.7, 65.0)"Operating point"

200 300 400 500 600 700 800 9000

100

200

300 "Failure point"

�max = Sy

Sy = 750

Su = 900

106 ~ = ∞ life

JUVINALL: Machine DesignFig. 8-28 W-261

900

r = 5 mm rad., machined surface

D = 18 mm (bearing bore)d = 16 mm (shaft dia.)

50 mm

f = 0.6 (between the objectand the disk)

T = 12 N • m (friction torque)

Su = 900 MPa

Sy = 750 MPa

' (1)(0.9)(0.72) = 291 MPa2

Sn = SnCLCGCS =

100 mm

Ft Fn

Page 1186: Juvinall

Str

ess

(ksi

)

(a)Stress-time plot

(b)S-N curve

–80

–40

0

40

80

JUVINALL: Machine DesignFig. 8-29 W-262

Rev

erse

d st

ress

S (

ksi (

log)

)

N (cycles (log))103 104 105 106 107

40

50

60

140

120

100

80

Representive 20-second test

1.6

× 1

04

3.8

× 1

04

10

5

Page 1187: Juvinall

0

–100

–200

–300

100

200

300

2~a

3~

(a)

Stress-time plot

2~ 1~

1~

Ben

ding

str

ess

(MP

a)σ a

(M

Pa)

Rev

erse

d st

ress

S (

MP

a)

�m (MPa)

�m – �a plot

(b)

Sy Su

N (cycles)

(c)

(d)

S-N plot

100 200 300 400 500

103 104 105 106 107 108

0

100

200

300

400

100

150

200

250

300

400

500

JUVINALL: Machine DesignFig. 8-30 W-263

b c

b d''

c

b'b

a'

a

c'd

d'

c''

d'

b''

d

Representative 6-sec test

c'

a' b'

2.5

× 1

03

3.5

× 1

06

2 ×

10

4Bending stress at

critical notch

Part

Aluminum alloySy = 410 MPaSu = 480 MPa

P(t)

Page 1188: Juvinall

0

Pmax

Pmax

T(d) Strength

(c) Total stress, (a) + (b)(a) Load stress

(b) Residual stress

Com

pres

sive

str

ess

(ksi

)Te

nsile

str

ess

and

stre

ngth

(ks

i)

JUVINALL: Machine DesignFig. 8-31 W-264

Axis of specimensymmetry andaxis of load

Page 1189: Juvinall

(1) (2)

P

JUVINALL: Machine DesignFig. P8-26 W-265

30 mm

30 mm

PP

P

30 mm

r = 2.5 mm

r = 2.5 mm

35 mm

30 mm

Page 1190: Juvinall

JUVINALL: Machine DesignFig. P8-27 W-266

3 in.3 in.

1 in. dia. 1 in. dia.14

2 in. 1 in.2 in.

F lb

1 in. dia.

1R8

1R8

1R16

Flb2

Flb2

Page 1191: Juvinall

JUVINALL: Machine DesignFig. P8-28 W-267

24 mm 24 mm20 mm

2-mm rad. 0.8-mm rad.

Page 1192: Juvinall

JUVINALL: Machine DesignFig. P8-30 W-268

High-carbonsteel, 490 Bhn,machined finish

1

0.1094 in.

3 in.4

8r = in.Kt = 1.7

F

4 in.

Page 1193: Juvinall

JUVINALL: Machine DesignFig. P8-37 W-268a

1

0.050 in.

0.191-in. rad.

0.125-in. dia.

2 in.

Page 1194: Juvinall

0

+80

–16Time

Nom

inal

str

ess

(MP

a)

JUVINALL: Machine DesignFig. P8-38 W-268b

60 mm50 mm

1.5 rad. 5-mm rad. 5-mm rad.

50 mm60 mm

Page 1195: Juvinall

JUVINALL: Machine DesignFig. P8-39 W-268c

-in. dia. hole116

1.0-in. dia.1.2-in. dia.

0.1-in. rad.

0.1-in. rad.

Torq

ue

7000 lb • in.

3000 lb • in.

Time

Page 1196: Juvinall

JUVINALL: Machine DesignFig. P8-44 W-268d

Helicalspur gear

Pump

Fillet

25-mm solidround shaft

500 N

750 N2000 N

Bending Kf = 2.0Torsional Kf = 1.5Axial Kf = 1.8

50 mm

250-mm dia.

Page 1197: Juvinall

Forces act at 500-mm dia.

Fx = 0.2625FyFz = 0.3675Fy

C

BAx

Forces act at 375-mm dia. (2)

120 dia. Keyway

(Kf = 1.6 for bend and torsion; 1.0for axial load. Use CS = 1 with these values.)

80 dia.

B

E

C D

A

(1)

Fx = 1.37 kN

Fz = 5.33 kN

Fy = 1.37 kN

Fy

D

y

z

JUVINALL: Machine DesignFig. P8-45 W-268e

550

400

450400

Page 1198: Juvinall

JUVINALL: Machine DesignFig. P8-46 W-268f

Tors

ion

stre

ss (

ksi)

0

–10

–20

–30

10

20

30

30 seconds

Page 1199: Juvinall

JUVINALL: Machine DesignFig. 9-1 W-269a

++

+

+

+

++

+

++

+

Electrolyte

Fe2+ ions in solution

Iron electrode with surplus of electrons

~ ~ ~ ~

~~

~~

~~~

~~ ~

Page 1200: Juvinall

JUVINALL: Machine DesignFig. 9-2 W-269b

Electrolyte

Exposed iron (anode or cathode)

Plating, as tin or zinc (cathode or anode)~ ~~ ~~~ ~

~~~~ ~~ ~ ~ ~

~~ ~

~~

Page 1201: Juvinall

JUVINALL: Machine DesignFig. 9-3 W-269d

Electrolyte

~~

~

~~ ~

~~

~~~~

~~

~

A B

Page 1202: Juvinall

JUVINALL: Machine DesignFig. 9-4 W-269e

Magnesiumanode

Zinc strips between steel spring leaves

Outlet

Inlet

(a) Water tank

(c) Leaf spring

(d) Ship

(b) Underground pipe

Magnesiumanode

Insulated copper wire

Zinc anodes

Page 1203: Juvinall

JUVINALL: Machine DesignFig. 9-5 W-269f

Insulated copper wire

+–

Steel tank

Page 1204: Juvinall

Steel

Rust particles Rust particles

(a)

Rust begins at center of drop

(b)

"Crevice corrosion"

JUVINALL: Machine DesignFig. 9-6 W-269g

Steel Steel

Page 1205: Juvinall

Steel bolt and nut

Nonporous, pliableelectrical insulator

JUVINALL: Machine DesignFig. 9-7 W-270

Aluminum plates

Page 1206: Juvinall

JUVINALL: Machine DesignFig. 9-8a W-271a

Salt water

Strongacids

Strongalkalis

Aeratedwater

U-Vradiation

A ExcellentB GoodC PoorD BadOrganic solvents

Ceramics,Glasses

KFRP

Polymers

PTFE, PP Epoxies, PS, PVC

HDPE, LDPE, PolyestersPhenolics

NylonsPMMA

CompositesGFRP

CFRP

A B C D D

Alloys

Alloys

CeramicsGlasses

Lead alloysSteels

Ti-alloys Cu-alloys

Al-alloys C-steels

Cast ironsNi-alloys

Ceramics,Glasses

KFRP

GFRPCFRP Polymers

Many elastomers

PTFE PVCPMMA

Nylons

LDPEEpoxies, HDPEpolyesters, PP,phenolics, PSFilled polymers

All

All

AlloysAllAll

All

Composites

KFRP

GFRPCFRP

Polymers

PSPVC

Mostelastomers

PhenomicsPolyesters

PULDPEHDPE

EpoxiesNylons

PP

PTFE

Composites

Polymers

PTFEEpoxies

LDPE/HDPEPP PS PVC

Nylons

PolyestersPhenolics

PMMAAlloys

Lead alloysNickel alloys

S-steelsCu-alloys

Al-alloys

Cast irons

Low alloysteels

C- steels

Ti-alloys CFRPKFRP

GFRPComposites Ceramics,

Glasses

All

Alloys

GoldLead

PTFEPVC

HDPE

Nylons

LDPE, EpoxiesElastomers

AlloysTi-alloys

Castirons

C-steel

Al-alloys

Ni-alloys

S-steels

PolyestersPhenolics

PSPMMA

PU Composites

CFRPCFRP

KFRPCeramics,Glasses

Glasses

Vitreousceramics

Mg 0 Zr02

Al203Si C

Si3N4Si02

Alloys

Al-alloys Cu-alloysZn-alloys

Ni-alloysSteels

S-steelsCast irons

Ti-alloys

C AB

Polymers Nylons

PMMA ElastomersPhenomics

Polyesters LDPE/HDPEP.V.,PS,PP,PTFEPVC,EpoxyComposites

GFRP

KFRP

CFRPCeramics,Glasses

Si02Glasses

Vitreous ceramics

Si C, Si3N4Al203

Zr02Graphites

Polymers

Page 1207: Juvinall

JUVINALL: Machine DesignFig. 9-9 W-272

Page 1208: Juvinall

Mo Cr Co Ni Fe Nb Pt Zr Ti Cu Au Ag Al Zn Mg Cd Sn Pb In

W

Mo

Cr

Two liquid phases

Increasingcompatibility;hence,increasingwear rate

One liquid phase, solidsolubility below 0.1%

Solid solubility between1 and 0.1%

Solid solubility above 1%

Identical metals

Co

Ni

Fe

Nb

Pt

Zr

Ti

Cu

Au

Ag

Al

Zn

Mg

Cd

Sn

Pb

In

JUVINALL: Machine DesignFig. 9-11 W-274

Page 1209: Juvinall

Wear coefficient, K10–2 10–3 10–4 10–5 10–6

Unlubed Poorlube

Goodlube Excellent lube

Unlubed Excellent lubePoorlube

Poorlube

Poorlube

Goodlube

Excellentlube

Goodlube

Unlubed

Unlubed Good lube Exc.lube

Unlubed Lubed

2-body 3-bodyHigh abr.concentr.

Low abr.concentr.

Unlubed LubedFretting

Abrasivewear

Adhesivewear

Nonmetal on metal or nonmetal

Incompatible metals

Partly compatible

Compatiblemetals

Identicalmetals

JUVINALL: Machine DesignFig. 9-12 W-275

Page 1210: Juvinall

r = 16 mm

F = 20 N

n = 80 rpm

Copper pin80 Vickers

Pin Pin

DiskDisk

Initial profiles Final profiles

t = 2 ht = 0 h

Disk volume lost

Pin volume lost = 2.7 mm3

= 0.65 mm3Steel disk210 Brinell

JUVINALL: Machine DesignFig. 9-13 W-276

Page 1211: Juvinall

Contact area

(a)

Two spheres

(b)

Two parallel cylinders

Contact area

x

z

y

JUVINALL: Machine DesignFig. 9-14 W-277

a

p

p

p0

R1

R2

z

xL

b

y

y

a

p0

Page 1212: Juvinall

Dis

tanc

e be

low

sur

face

–p0 –0.8p0 –0.4p0 0.4p00Stress

4a

(a)

Two spheres(a is defined in Fig. 9.13a)

3a

2a

a

0

JUVINALL: Machine DesignFig. 9-15 W-278

p0 = max. contactpressure

�z

�max

�x = �y

Dis

tanc

e be

low

sur

face

–p0 –0.8p0 –0.4p0 0.4p00Stress

7b

(b)

Two parallel cylinders(b is defined in Fig. 9.13b)

6b

5b

4b

3b

2b

b

0

�z

p0 = max. contactpressure

�y

�max

�x

Page 1213: Juvinall

–0.6p0 –0.4p0 –0.2p0 0 0.2p0

0

0.1p0

0.2p0

0.3p0

JUVINALL: Machine DesignFig. 9-16 W-279

�y ≈ –0.1p0

�max ≈ 0.3p0

�x ≈ –0.25p0

�z ≈ –0.7p0

One plane of maximum shear stress

�z ≈ –0.7p0

+�

+�

�y ≈ –0.1p0

�x ≈ –0.25p0

Page 1214: Juvinall

Str

ess

� yz

Distance y from load plane–4b –3b –2b –b 0 b 2b 3b 4b

–0.3p0

–0.2p0

–0.1p0

0

0.1p0

0.2p0

0.3p0

A

A B

F

F

b

B

�yz �yz

�z �z

�y �y

JUVINALL: Machine DesignFig. 9-17 W-280

p0 = max contact pressure

0.5b below surface

A B

A B

y

Page 1215: Juvinall

JUVINALL: Machine DesignFig. 9-18 W-281

�yt = 2fp0

�yt = 2fp0

�yzt = fp0

�yzt = fp0

�yt = –2fp0

�yt = –2fp0

p0 = maximum contact pressuref = coefficient of friction

Loaded cylinder(resists rotation to

cause some sliding)

Driving cylinder

y y

z

z

Direction of rotation

Direction of rotation

b b

Page 1216: Juvinall

JUVINALL: Machine DesignFig. 9-19 W-282

Hard-bronze bearingalloy spherical seat

10 mm

2000 N

Hardened-steel sphere

10.1 mm

Page 1217: Juvinall

Max

imum

con

tact

str

ess

p 0 (

MP

A)

Sphere radius, R1 (mm)5.00 5.01 5.02 5.03 5.04

50

100

150

200

250

JUVINALL: Machine DesignFig. 9-19b W-283

Cast ironCopperSteel

Page 1218: Juvinall

Com

pute

d m

axim

um e

last

ic c

onta

ct s

tres

sp 0

or

�z

(ksi

)

Life N (cycles (log))105 106 107 108 109 1010

100

150

200

300

400

500

600

700800

JUVINALL: Machine DesignFig. 9-21 W-285

Spur gears–high-qualitymanufacture, case-hardenedsteel, 60 Rockwell C (630 Bhn)

Roller bearings

Angular-contact ball bearings

Radial ball bearings

Parallel rollers

Page 1219: Juvinall

1

C

Protected ("noble", more cathodic)C

C

C

C

X

C

C

C

C

C

C

C

C

C

C

C

C

CC

JUVINALL: Machine DesignTab. 9-1 W-269c

2

10Key:

11

12

13

14

15

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

Gold, platinum, gold-platinum alloysC

C

C

X

X

X

X

X

X

X

C

X

X

X

F

F

X

X

F

C

C

C

C

C

C

X

X

X

C

X

X

X

F

F

X

X

F

C

C

C

C

C

C

X

X

C

X

X

X

F

F

X

X

F

C

C

C

C

C

C

C

C

C

C

C

F

F

C

C

F

C

C

C

C

C

C

C

P

P

X

F

F

P

X

F

C

C

C

C

C

C

X

X

X

F

F

X

X

F

C

C

C

C

C

C

P

X

F

F

P

P

F

C

C

C

C

C

X

X

F

F

X

X

F

C

C

C

C

C

X

F

F

X

X

F

C

C

C

C

C

F

F

X

X

F

C

C

C

C

F

F

P

X

F

C

C

C

F

F

C

P

F

C

C

F

F

X

X

F

C

F

F

C

P

F

F

F

C

C

F

F

F

F

F

F

F

F

C

FF

Rhodium, graphite, palladium

Silver, high-silver alloys

Titanium

Nickel, manel, cobalt, high-nickel andhigh-cobalt alloys

Nickel-copper alloys per QQ-N-281,QQ-N-286, and MIL-N-20184

Steel, AISI 301, 302, 303, 304, 316,321, 347*, A286

Copper, bronze, brass, copper alloys per QQ-C-551,QQ-B-671, MIL-C 20159, silver solder per QQ-5-561

Commercial yellow brass and bronze;QQ-B-611 brass

Leaded brass, naval brass, leaded bronze

Steel, AISI, 431, 440; AM 355; PH steels

Chromium plate, tungsten, molybdenum

Steel, AISI 410, 416, 420

Tin, indium, tin-lead solder

Lead, lead-tin solder

Aluminum , 2024, 2014, 7075

Steel, (except corrosion-resistant types), iron

Aluminum, 1100, 3003, 5052, 6063,6061, 356

Cadmium and zinc plate, galvanized steel,beryllium, cald aluminum

Magnesium

Legend:X – Not compatibleC – CompatibleP – Compatible if not exposed within two miles of a body of salt waterF – Compatible only when finished with at least one coat of primer*Applicable forms: 301, 302, 321, and 347 sheetand plate; 304 and 321 tubing; 302, 303, 316, 321,and 347 bar and forgings; 302 and 347 casting;and 302 and 316 wire. These materials must be finished with at leastone coat of primer.

C

+

Corroded ("active", more cathodic)

Page 1220: Juvinall

JUVINALL: Machine DesignProb. 9-1 W-269

RivetsTotal exposed area = 100 cm2

Metal platesTotal exposed area = 1 m2

Page 1221: Juvinall

Chromium-plated steel cap screwsTotal exposed area = 110 cm2

301 Stainless steel platesTotal exposed area = 1.5 m2

Electrolytic environment

JUVINALL: Machine DesignProb. 9-4 W-286

Page 1222: Juvinall

Drain plug(steel)

Insert rod(magnesium)

Oil

Crankcase(steel)

JUVINALL: Machine DesignProb. 9-8d W-287

Page 1223: Juvinall

100 N 100 N

Latchclosed

Latchopen

30 cycles/day, every day

Steel, 100 BhnSteel, 300 Bhn

JUVINALL: Machine DesignProb. 9-12 W-287a

30 mm

Page 1224: Juvinall

Locking plateArm

Geneva wheel

JUVINALL: Machine DesignProb. 9-20 W-288

100-mmradius

Page 1225: Juvinall

JUVINALL: Machine DesignFig. 10-1 W-289

Lp

End of thread

Lp

End of thread

End of thread

(a)Single thread–right hand

(b)Double thread–left hand

Page 1226: Juvinall

Pitch dia. dp

Crest

p

4

p

8

Root

Axis of thread

30�

p

JUVINALL: Machine DesignFig. 10-2 W-290

Major dia. d

Root (or minor) dia. dr

60�

Page 1227: Juvinall

Nut tolerance zone

Basic profile(as shown inFig. 10.2)

Screw

Basic profile

Screw tolerance zone

JUVINALL: Machine DesignFig. 10-3 W-291

Nut

Page 1228: Juvinall

p2

p2

JUVINALL: Machine DesignFig. 10-4 W-292

2� = 29�

5�45�

0.663p

0.163p

p

p

2

p

2

d

dr

p

22� = 29�

(a) Acme

(c) Square (d) Modified square (e) Buttress

(b) Acme stub

p

dmdr

0.3p

dm dr d

pp

2

p

2

dm dr d

p p

dmdr

� = 5�� = 7�

dm

d

d

Page 1229: Juvinall

a

JUVINALL: Machine DesignFig. 10-5 W-293

(c)(b)(a)

Force F

dc

Weight

Page 1230: Juvinall

A

A

L

q

JUVINALL: Machine DesignFig. 10-6 W-294

�dm

fn

w

nn cos �n

Section A A(normal to thread)

Scale 4:1

�n

�n

q fn

dm

Page 1231: Juvinall

JUVINALL: Machine DesignFig. 10-7 W-295

�n

h

h

b

A

A

B

B

Section B-B(normal to thread)

Section A-A(through screw axis)

tan �n =

Screw axis

bh

tan � = bh cos �

b/cos ��

Page 1232: Juvinall

Eff

icie

ncy,

e (%

)

Helix angle, �0� 10� 20� 30� 40� 50� 60� 70� 80� 90�

0

10

20

30

40

50

60

70

80

90

100

JUVINALL: Machine DesignFig. 10-8 W-296

e =cos �n – f tan � cos �n + f cos �

, where

�n = tan–1 (tan 14 � cos �)12

f = 0.01

f = 0.02

f = 0.05

f = 0.10

f = 0.15

f = 0.20

Page 1233: Juvinall

a

JUVINALL: Machine DesignFig. 10-10 W-298

Force F

f = 0.12

fc = 0.09

1-in. double-threadAcme screw

dc = 1.5 in.

Weight = 1000 lb

Page 1234: Juvinall

Forceflowlines

Nut

A - shear fracture line for nut thread stripping

B - shear fracture line for bolt thread stripping

B

A

JUVINALL: Machine DesignFig. 10 -11 W-299

dr

didp

d

1

Total = P

Total = P

Clampedmember

2

3

Bolt

t

Page 1235: Juvinall

JUVINALL: Machine DesignFig. 10-12 W-300

Clamped member

BoltNut

Page 1236: Juvinall

JUVINALL: Machine DesignFig. 10-13 W-301

Pilot surfaceof bolt

Page 1237: Juvinall

Materialbeing

compressed

JUVINALL: Machine DesignFig. 10-14 W-302

Motor

Materialbeing

compressed

Spur gears

Ball thrustbearings

Ball thrustbearings

Thrustwashers

(b) Screws in tension (good)(a) Screws in compression (poor)

Thrustwashers

Motor

Page 1238: Juvinall

Flat washer

(a) Screw (b) Bolt and nut (c) Stud and nut (d) Threaded rod and nuts

JUVINALL: Machine DesignFig. 10-15 W-303

Page 1239: Juvinall

0.65d

1.5d

d

(a) Hexagon head

(b) Square head

(d) Flat head (f ) Oval head

(h) Hex socket headless setscrew

(j) Round head with Phillips socket

(c) Round head

(e) Fillister head

(g) Hexagon socket head (i) Carriage bolt

JUVINALL: Machine DesignFig. 10-16 W-304

Page 1240: Juvinall

JUVINALL: Machine DesignFig. 10-17 W-305

(a)Conventional screwdriver

will tighten but notloosen the screw

(Plug in socket)

(b)Special tool required totighten or loosen screw

(5-sided head) ("Spanner head")

(c)Break-away heads

Page 1241: Juvinall

T4

T3

JUVINALL: Machine DesignFig. 10-18 W-307

y

Mohr circles

Fi

FiFi

Fi

y x

Fi

Fi

� +��

+�

�max = per max � theorySy

2Stresses with torques applied

Stresses aftertorques are relieved

x'

x (�, –�)

y'

y

T2

T1

Page 1242: Juvinall

Bol

t te

nsio

n

Bolt elongation

Torqued tension,galvanized

(high friction)

Torqued tension,galvanized and

lubricated

Torqued tension,black oxide

JUVINALL: Machine DesignFig. 10-19 W-308

Direct tension,black oxide

Direct tension,galvanized

Page 1243: Juvinall

JUVINALL: Machine DesignFig. 10-20 W-309

(a)Helical (split) type

(b)Twisted-tooth type

(Teeth may be external,as in this illustration,

or internal.)

Page 1244: Juvinall

JUVINALL: Machine DesignFig. 10-21 W-310

(b)(a)

Page 1245: Juvinall

(a)Insert nut (Nylon insert is compressed when

nut seats to provide both locking and sealing.)

(c)Single thread nut (Prongs pinch bolt threadwhen nut is tightened. This type of nut isquickly applied and used for light loads.)

JUVINALL: Machine DesignFig. 10-22 W-311

(b)Spring nut (Top of nut pinches

bolt thread when nut is tightened.)

Page 1246: Juvinall

Spring- top nut(Upper part of nut is tapered.

Segments press against bolt threads.)

Starting Fully locked

Nylon-insert nuts(Collar or plug of nylon exerts friction

grip on bolt threads.)Distorted nut (Portion of nut is distortedto provide friction grip on bolt threads.)

(a) (b) (c)

JUVINALL: Machine DesignFig. 10-23 W-312

Page 1247: Juvinall

JUVINALL: Machine DesignFig. 10-24 W-313

Fe

Fe Fe

(a)Complete joint

(b)Free body without

external load

Fb = Fi Fc = Fi

(c)Free body withexternal load

Fb Fc

Page 1248: Juvinall

(a) (b) (c)

(d)

g

JUVINALL: Machine DesignFig. 10-25 W-314

Fe Fb

Fc

Fb

Fb

Fc

Fc

Fc

F b a

nd F

c

Fc = Fi

F b =

F i and

F e

Fb

Softgasket

(Separating force per bolt)0 Fe

Fi

Page 1249: Juvinall

(a) (b) (c)

g

JUVINALL: Machine DesignFig. 10-26 W-315

Fe

Fb

Fc

Fb

Fb

Fc

Fb

"O-ring"gasket

(d)

F b a

nd F

c

Fb = Fi

Fc = Fi – Fe

Fc = 0

(Separating force per bolt)0

"Rubber"portion of

bolt

Fe

Fi

Page 1250: Juvinall

Forc

e

External load Fe

0

Fi

Fc

Fe

Fb

Fc = 0

Fb = Fe Fb = Fi +

JUVINALL: Machine DesignFig. 10-27 W-316

�Fb

�Fc

C A

Bkbkb + kc

Fekc

kb + kc

Fluctuationsin Fb and Fc

correspondingto fluctuationsin Fe between

0 and C

Fc = Fi –

Page 1251: Juvinall

Conical effectiveclamped volume

(Hexagonal bolthead and nut)

30°

JUVINALL: Machine DesignFig. 10-28 W-317

d2

d3

d1

g

d

Page 1252: Juvinall

(a)Bolt bending caused by nonparallelism

of mating surfaces. (Bolt will bendwhen nut is tightened.)

Connectingrod and cap

P

A

a

(b)Bolt bending caused by deflection

of loaded members. (Note tendencyto pivot about A; hence, bending is

reduced if dimension a is increased.)

a

AP

JUVINALL: Machine DesignFig. 10-29 W-318

Page 1253: Juvinall

JUVINALL: Machine DesignFig. 10-30 W-319

Pillow blockRotating

shaft

Metric(ISO) screw

9 kN

Page 1254: Juvinall

F

F2

F2

F2

F2

(a) (b)

Normal load, carried byfriction forces

Overload, causing shear failure

F

JUVINALL: Machine DesignFig. 10-31 W-320

Page 1255: Juvinall

150

150500

400

100

24 kN24 kN

150

D

A

D

E

JUVINALL: Machine DesignFig. 10-32 W-321

Page 1256: Juvinall

48

144-kN appliedoverload

JUVINALL: Machine DesignFig. 10-33 W-322

F

F

V

F

100

150

CG of bolt groupcross section

200180

4848

144 kN

144 kN (150 mm) =21.6 kN � m

200

180180

Page 1257: Juvinall

Su = 830

Str

ess,

� (M

Pa)

� = 0.0032 @ Sy = 660 on idealized curve

Strain, �0 0.01 0.02 0.03 0.04

Fluctuation in thread root stress – Case 2, Fi = 35.3 kN

Fluctuation in thread root stress – Case 1, Fi = 10 kN

12% elongation @ Su specified for class 8.8

0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.120

100

200

300

400

500

600

700

800

900

JUVINALL: Machine DesignFig. 10-34ab W-323

Sp = 660

Sp = 600

505

Forc

e (k

N)

Bolt tight,machine notyet turned on

38.3

35.3

Case 2 – Fi = 38.3 kN(bolt tightened to full

yield strength)

Bolt yields slightly, with noincrease in load or stress during

first application of Fe

29.3

4

0

10

20

30

40Fb

Machineoperating atnormal load

Machineturned off

Case 1 – Fi = 10 kN

Fc

Fb

Fe

Fc9

13

Time

(a) Fluctuation in Fb and Fc caused by fluctuations in Fe

(b) Idealized (not actual) stress–strain curve for class 8.8 bolt steel

Page 1258: Juvinall

Alt

erna

ting

str

ess,

�a

(MP

a)

Mean stress, �m (MPa)0

After initialtightening

After shut-downfollowing normal operation

(c) Mean stress-alternating stress diagram for plotting thread root stresses

130

77

200 400 600 8000

100

200

300

400

JUVINALL: Machine DesignFig. 10-34 W-324

� Life

Su = 830Sy = 660

4

2

1 3

During normaloperation

Operation at overload on vergeof causing eventual fatigue failure

Sn = SnCLCS CG = (1)(1)(0.9) = 373 MPa8302

'

Page 1259: Juvinall

Steel bolt, '' – 13 UNC,

grade 5 with cut threads

Ext

erna

l loa

d F e

Time

(b)Fluctuating separating

force versus time

(a)Simplified model of machine

members bolted together

g = 2''

Fmax

JUVINALL: Machine DesignFig. 10-35a-c W-325, 326a

0 to Fmax

Steelmember

0 to Fmax,fluctuating

external force

Fe

12

�a

(ksi

)

�m (ksi)0

�a = 37

�a = 23

�a = 22.7

20 40 60 80 100 1200

20

40

60

Limiting point for case a

Limiting point for case b

Sn = S 'nCLCGCS = (1)(0.9)(1) = 54 ksi1202

Sy = 120

Sy = 92

�a = 37

�a = 23

�a = 22.7

Limiting point for case a

Limiting point for case b

Sn = SnCLCGCS = (1)(0.9)(1) = 54 ksi'120

2

(c)Fatigue diagram for thread root

Su = 120

Sy = 92

Page 1260: Juvinall

Fe

"O-ring" gasket

250 mm

Aluminum cover plate,E = 70 GPa

Cast-iron cylinder,E = 100 GPa

Class 8.8steel bolt

350 mm

g/2

g/2

JUVINALL: Machine DesignFig. 10-36 W-327

Page 1261: Juvinall

JUVINALL: Machine DesignFig. P10-1 W-328

a

f = 0.13

fc = 0.10

1-in. double-threadAcme screw

dc = 2.0 in.

Weight = 10,000 lb

Force F

Page 1262: Juvinall

JUVINALL: Machine DesignFig. P10-09 W-330

5 in.

1/2 in. Acme threaddc = 5/8 in.

Page 1263: Juvinall

Fe = 0 to 8,000 lbkc = 6kb

Fe

Fe

JUVINALL: Machine DesignFig. P10-17 W-329

Page 1264: Juvinall

JUVINALL: Machine DesignFig. P10.26 W-331

(1)

1000 N

Springwasher

1000 N

(2)

1000 N1000 N

AA

Spring washer

Page 1265: Juvinall

JUVINALL: Machine DesignFig. P10-28 W-332

Page 1266: Juvinall

JUVINALL: Machine DesignFig. P10-39 W-333

280 mm

140 mm

230 mm

Page 1267: Juvinall

JUVINALL: Machine DesignFig. P10-41 W-334

Forc

e (k

N)

Time

15 kN 15 kN

30 kN

0

20

40

60

80 Fb and Fc

Fe

Light load Light load

Heavy load

Initialtighten

Page 1268: Juvinall

JUVINALL: Machine DesignFig. P10-44 W-335

22

22

22

22

22

22

22

22

22

22

22

22

22 222222

Page 1269: Juvinall

JUVINALL: Machine DesignTable 10-4 W-306

Page 1270: Juvinall

JUVINALL: Machine DesignFig. 11-1 W-336

Before setting

After setting

Page 1271: Juvinall

Full tubular

Bifurcated (split)

Metal-piercing

JUVINALL: Machine DesignFig. 11-2 W-337

(c)Compression

(a)Semitubular

(b)Self-piercing

Page 1272: Juvinall

JUVINALL: Machine DesignFig. 11-3 W-338

"Built-up" lightweight structure

Acute corner

Back (blind) sidenot accessible

Back (blind) side not accessible

Page 1273: Juvinall

Blindside upset

Blindside upset

Drive pinblind rivet

JUVINALL: Machine DesignFig. 11-4 W-339

Open-endbreak mandrelblind rivet

Blindside upset

Pull-throughblind rivet

Blindside upset

Closed-endbreak mandrelblind rivet

Blindside upset

Mandrel head collapsesas rivet is expanded

and pulled through rivet

Trim or grindmandrelPulling

head

Mandrel breaksafter seating andrivet expansion

Self-pluggingblind rivet

Page 1274: Juvinall

(b) (c)(a)

JUVINALL: Machine DesignFig. 11-5 W-340

Page 1275: Juvinall

60�

JUVINALL: Machine DesignFig. 11-6 W-341

(a) (c) (d)(b)

45�60�

Page 1276: Juvinall

FF

ht

t = 0.707

h

h

t

h

(a)

A

B

C

D

(b)

(d)Transverse loading

50 mm

(a' )Convex

weld bead

(a" )Concave weld

bead (poorpractice)

(c)Parallel loading

(e)Transverse loading

F

A

B

C

D

50 mm

F

JUVINALL: Machine DesignFig. 11-7 W-342

Page 1277: Juvinall

1052 + 202

J

T

802 + 452

JT

690.0t

525.8t

691.9t

131.4t690.0

t80t

674.1t

80t

5600 N • m

20 kN

295.7t

y

G

B A

JUVINALL: Machine DesignFig. 11-8 W-343

(a)

(b) (c)

100

x–

XX

C

B

Y

G

A

Y

150

300

20 kN

T (80)J

525.8t

105

8020

G

B

T=

T (105)J

=T (20)

J131.4

t=

T (45)J

295.7t

Torsional stresses Torsional plus direct shear stresses

=

Page 1278: Juvinall

B

C

A

B

A

X

X

120

16010 kN

60

70

(a) (b) Stresses on weld AB

121.2t

� =26.3t

� =

124tResultant stress =

JUVINALL: Machine DesignFig. 11-9 W-344

D

Page 1279: Juvinall

L /2

L /2

G (CG of total weld group)

G' (CG of this weld segment)

b

a

y

Y'

Y' Y

Y

X'X'

X

t

X

JUVINALL: Machine DesignFig. 11-10 W-345

Page 1280: Juvinall

�a

(ksi

)

�m (ksi)190 50 62

13.6

JUVINALL: Machine DesignFig. 11-11 W-346

= = 0.5�a�m

3060

Page 1281: Juvinall

JUVINALL: Machine DesignFig. 11-12 W-347

(a) Adhesive-bonded metal lap joint (b) Brazed tubing fittings (c) Glued wood joint

Removing thismaterial reduces

stress concentrationat bond edges

Page 1282: Juvinall

F

JUVINALL: Machine DesignFig. P11-4 W-348

15 mm

Weld length = 90 mmSy = 400 MPaSF = 3E70 series weld

F

Page 1283: Juvinall

3.0 in.

F

F

JUVINALL: Machine DesignFig. P11-07 W-349

E60 series welding rodsSy = 50 ksi (plates)h = 0.375 in.SF = 3

Note: There are two3 in. welds.

Page 1284: Juvinall

100 mm

Note: Each plate has two 75 mmwelds and one 100 mm weld.

60 kN

JUVINALL: Machine DesignFig. P11-11 W-350

75mm

55mm

Page 1285: Juvinall

4 in.

3 in.

JUVINALL: Machine DesignFig. P11-12 W-351

4000lb

Note: There are two 4 in. welds.

Page 1286: Juvinall

Fixedend

Spline

Spline

Generousradius

Bearing

Bearing

Torsion barportion

(a)Torsion bar with splined ends

(type used in auto suspensions, etc.)

(b)Rod with bent ends serving as torsion bar spring

(type used for auto hood and trunk counterbalancing, etc.)

JUVINALL: Machine DesignFig. 12-1 W-352

d

Page 1287: Juvinall

JUVINALL: Machine DesignFig. 12-2 W-353

D

F

End surfaceground flat (c)

Tension spring

(a)Compression spring

(ends squared and ground)

D

d

F

F

d

FD2

T =

FD2

T =

F

F

F

F

d

(d)Top portion of tensionspring shown as a freebody in equalibrium

D

F

F

Page 1288: Juvinall

JUVINALL: Machine DesignFig. 12-3 W-354

(a)Straight torsion bar

(b)Curved torsion bar

Pla

ne m

Pla

ne n

0

0

� =

� �

� �

TcJ

TcJ

TcJ

TcJ

� =

T

b

dc

a

T

T

T

Page 1289: Juvinall

Preferred range,ends ground

Kw

and

Ks

Spring index, C = D/d 2 4 6 8 10 12 14

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

2

4

6

8

10

12

14

16

18

JUVINALL: Machine DesignFig. 12-4 W-355

Kw

C a

nd K

sC

Preferred range, ends not ground

Ks

KwC

Kw

KsC

Ks = 1 + (shear correction only, use for static loading)

Kw = + (shear and curvature corrections, use for fatigue loading)

0.5C

0.615C

4C – 14C – 4

Page 1290: Juvinall

JUVINALL: Machine DesignFig. 12-5 W-356

Page 1291: Juvinall

JUVINALL: Machine DesignFig. 12-6 W-357

Page 1292: Juvinall

Min

imum

ult

imat

e te

nsile

str

engt

h (M

Pa)

Min

imum

ult

imat

e te

nsile

str

engt

h (k

si)

1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 1

Wire diameter (mm)

Wire diameter (in.)

1.00.10 10.0 100.02 3 4 5 6 7 8 9 1

0

50

100

150

200

250

300

350

400

450

500

0

1000

1500

2000

2500

3000

0.0400.0200.0080.004 0.080 0.200 0.400 0.800

JUVINALL: Machine DesignFig. 12-7 W-358

ASTM A229

ASTM A313(302)

ASTM A228 music wire (cold-drawn steel)

ASTM A401 (Cr-Si steel)

ASTM A230(oil-tempered carbon steel)

ASTM A232 (Cr-Va steel)

ASTM A229(oil-tempered carbon steel)

ASTM A227(cold-drawn carbon steel)

ASTM A313(302 stainless steel)

ASTM B159(phosphor bronze)

Inconel alloy X-750 (spring temper)

ASTM A227

Page 1293: Juvinall

JUVINALL: Machine DesignFig. 12-8 W-359

(a)Ls = (Nt + 1)d

(c)Ls = (Nt + 1)d

(b)Ls = Nt d

(d)Ls = Ntd

Page 1294: Juvinall

(b)(a)Contouredand plate

(d)(c)

JUVINALL: Machine DesignFig. 12-9 W-360

Page 1295: Juvinall

Rat

io,

defl

ecti

on–f

ree

leng

th,

�/L

f

Ratio, free length–mean diameter, Lf /D2 3 4 5 6

Unstable

Stable

7 8 9 10 110.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0.75

JUVINALL: Machine DesignFig. 12-10 W-361

A

A- end plates are constrained parallel (buckling pattern as in Fig. 5.27c)B- one end plate is free to tip (buckling pattern as in Fig. 5.27b )

B

Page 1296: Juvinall

12

JUVINALL: Machine DesignFig. 12-11 W-362

Lf

Ls

Fs

D + d � 1.5 in.

(Springfree) (Spring

withmin. load)

(Springwith

max. load)

105 lb

60 lb

(Springsolid)

Cashallowance

� 2.5 in.

in.

Page 1297: Juvinall

Life N (cycles (log))

JUVINALL: Machine DesignFig. 12-12 W-363

Str

ess

S (%

Su)

(log

)

103 104 105 106

30

20

40

50

60

70

800.9Sus � 0.72 Su

0.54 Su

0.395 Su

Su2

CLCSCGSn =

Su2

= (0.58)(1)(1)

= 0.29 Su

Page 1298: Juvinall

� a/S

u

�m /Su

0.1 0.2

(0.38, 0.38)

(0.325,0.325)

(0.265, 0.265)(0.215, 0.215)

0.72

0.3 0.4 0.5 0.6 0.7 0.80

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

JUVINALL: Machine DesignFig. 12-13 W-364

103�

104�

105�

106 + �

0.54

0.395

0.29

Region of interest

0

0

�m = 0= 1

�a�m

0� 1

�a�m

P

Static load

0= 0

�a�m

Page 1299: Juvinall

� max

/Su

�min /Su

0.20 0.40 0.60 0.800

0.20

0.40

0.60

0.80

JUVINALL: Machine DesignFig. 12-14 W-365

103 �

104 �

105 �

106 + �

P

0.76

0.65

0.53

0.43

Page 1300: Juvinall

Tors

iona

l str

ess

S s,

max

(%

Su)

Life N, (cycles)104

Shot-peened wire

103 105 106 107

30

40

50

60

80

70

JUVINALL: Machine DesignFig. 12-15 W-366

Design curves [1]Non-shot-peened wire

Calculated curve (from Fig. 12.14)

Note: For zero-to-max torsionalstress fluctuation

76

65

53

43

Page 1301: Juvinall

� max

(M

Pa)

�min (MPa)0 200 400

689

800

510

600 800

(965, 965)

(862, 862)

(Static load line)

(Load line, slope 600/300for Sample Problem 12.2)

1000

200

400

600

800

1000

JUVINALL: Machine DesignFig. 12-16 W-367

Infinite life withoutshot peening

Infinite life withshot peening

Page 1302: Juvinall

JUVINALL: Machine DesignFig. 12-17 W-368

Without presetting

Load stress

Load stressplus residualstress

With presetting

–�

0

+�

�resid from presetting

Page 1303: Juvinall

JUVINALL: Machine DesignFig. 12-18 W-369

25 mm

600 N

300 N

600 N

Squared andground ends,ASTM A232spring wire

300 N

Key

Cam

n =650rpm Shaft

�� + 25

Page 1304: Juvinall

� max

(M

Pa)

�min (MPa)0 200 400 600 800 1000 1200

200

400

600

800

975

750

540

1000

1200

JUVINALL: Machine DesignFig. 12-19 W-369A

�max�min

600300

=

Page 1305: Juvinall

D

r2r4 B

dd

F

D

A

F

r1

r3

JUVINALL: Machine DesignFig. 12-20 W-370

Bending stress at Sec. A:

� =16FD

�d3

r1r3

Torsional stress at Sec. B:

� =8FD

�d3

r4r2

Page 1306: Juvinall

F

JUVINALL: Machine DesignFig. 12-21 W-371

Page 1307: Juvinall

(b)Semi-elliptic

6FL

bh2

L L

� =

12FL3

Ebh3� =

(c)Full-elliptic

2F

2F

6FL

bh2

L L

� =

6FL3

Ebh3� =

2F

6FL

bh2� =

6FL3

Ebh3� =

(a)Quarter-elliptic

(simple cantilever)

L F F F

JUVINALL: Machine DesignFig. 12-22 W-372

Page 1308: Juvinall

F

L

x

JUVINALL: Machine DesignFig. 12-23 W-373

(a)

t

h

b

w

F

L

(b)t is constant; w varies linearly with L

(c)w is constant; t varies parabolically with L

L

h

b

If � and t areconstant, then x /wmust be constant.

If � and w areconstant, then x /t2

must be constant.

McI

6Fx

wt2� = =

F

b

h

Page 1309: Juvinall

Half of nth leaf

Half of nth leaf

n leaves

Half of 3rd leaf

Half of 3rd leaf

Half of 2nd leaf

Half of 2nd leaf

Main leafb

L L

h

F

JUVINALL: Machine DesignFig. 12-24 W-374

F

h

bn

(a) (b)

Page 1310: Juvinall

ClipsShackle (permitssmall fluctuationsin spring length)

Fixed pivot

Fixed pivot

JUVINALL: Machine DesignFig. 12-25 W-375

Page 1311: Juvinall

2F

Bolt, Kf = 1.3

�a�m

�a

(MP

a)

�m (MPa)

�a = 525

0

Design overload point

= 0.67

400 800 1200 1600

400

800

JUVINALL: Machine DesignFig. 12-26 W-376

� life, bendingSn

Sy Su

F = 1000 to 5000 N

(b)(a)

k = 30 N/mmh = 7 mm

F

Page 1312: Juvinall

6FL3

Ebh3

FL3

Eh3

L = 682

L = 682 L = 682

b = 416

b = 416 b = 333

L = 682

JUVINALL: Machine DesignFig. 12-27 W-377

� = = 0.0144 ; F�

Eh3

L3k = = 69.33

6FL3

Ebh3

FL3

Eh3�1 = = 0.0180

F�1

Eh3

L3k1 = = 55.55

Eh3

L3k = 76.30

4FL3

Ebh3

FL3

Eh3�2 = = 0.0482

Eh3

L3k2 = 20.75

(a) Triangular-plate solution to Sample Problem 12.4

(b) Trapezoidal plate solution to Sample Problem 12.5

+ =

k = k1 + k2

8383

Page 1313: Juvinall

D

a

F

d

F

JUVINALL: Machine DesignFig. 12-28 W-378

Page 1314: Juvinall

Thickness = h

b

JUVINALL: Machine DesignFig. 12-29 W-379

FF

a

Page 1315: Juvinall

Dd

Dh

Fact

ors

for

inne

r su

rfac

e st

ress

con

cent

rati

onK

i, ro

und

and

Ki,

rect

Spring index, C = or

2 4 6 8 10 121.0

1.1

1.2

1.3

1.4

1.5

1.6

JUVINALL: Machine DesignFig. 12-30 W-380

Ki, round

Ki, rect

Page 1316: Juvinall

Belleville Wave Slotted Finger Curve Internally slotted(as used in automotive clutches)

JUVINALL: Machine DesignFig. 12-31 W-381

Page 1317: Juvinall

In series

JUVINALL: Machine DesignFig. 12-32 W-382

In parallel In series-parallel

Page 1318: Juvinall

JUVINALL: Machine DesignFig. 12-33 W-383

Page 1319: Juvinall

+ + + +

Storage drum Output drum Storage drum Output drum

(a) Constant-force extension springs

(b) Electric motor brush spring

(c) Two forms of constant spring motors

JUVINALL: Machine DesignFig. 12-34 W-384

Page 1320: Juvinall

End attachedto door

Fixedend

Torsion bar

Center of gravityof 60-lb door

Door stop

JUVINALL: Machine DesignFig. P12-3 W-385

24 in.

110�

Page 1321: Juvinall

Deflection

Support

Spring

Retainer

Nut

Force

Forc

e

Threaded bolt

JUVINALL: Machine DesignFig. P12-11 W-386

Deflection

C

B

A

Page 1322: Juvinall

JUVINALL: Machine DesignFig. P12-15 W-387

F = 3.0 kN

DiDo

Do = 45 mm do = 8 mm No = 5

do

di

Di = 25 mm di = 5 mm Ni = 10

Page 1323: Juvinall

F

F = 45 to 90 lbDeflection = 0.5 in.D = 2 in.

JUVINALL: Machine DesignFig. P12-28 W-388

FSquared andground end

Page 1324: Juvinall

0

+

3600 engine rpm1800 camshaft rpm

"Reversal point"

Valve lift is 0.384 in.(maximum-on "nose" of cam)

"Reversal point"Valve lift is 0.201 in.

Valv

e ac

cele

rati

on

JUVINALL: Machine DesignFig. P12-34 W-389

Cam angle

Page 1325: Juvinall

Key

Cam

Shaft

Stationary guide

Oscillating assembly

Roller follower

Spring

Adjusting nut

Cap screw

JUVINALL: Machine DesignFig. P12-35 W-390

Support

Page 1326: Juvinall

e

JUVINALL: Machine DesignFig. P12-37 W-392

F

Page 1327: Juvinall

Tire

Stationarysupport

Handle

Brakeshoe

Spring

Pin stops

Pivot A35 mm

Stationarysupport

JUVINALL: Machine DesignFig. P12-39 W-391

Page 1328: Juvinall

25 mm shaft

Torsion springs

Cable

Cable

110 mm dia.

110 mm dia.

JUVINALL: Machine DesignFig. P12-46 W-393

Page 1329: Juvinall

JUVINALL: Machine DesignFig. 13-1 W-395

Main bearing

Connecting rod

Connecting rod bearing

Thrust bearing(flanged portion of main bearing)

Main bearing

Crankshaft

Main bearing cap

Connecting rod bearing cap

Page 1330: Juvinall

JUVINALL: Machine DesignFig. 13-2 W-396

(a) Hydrodynamic(surface separated)

(b) Mixed film(intermittent local contact)

(c) Boundary (continuousand extensive local contact)

Page 1331: Juvinall

JUVINALL: Machine DesignFig. 13-3 W-397

(a)At rest

W

Oil inlet

W

(b)Slow rotation

(boundary lubrication)

W

Bearing

Journal

Minimum filmthickness, h0

(c)Fast rotation

(hydrodynamic lubrication)

Oil flow

W

e

W

Resultant oilfilm force

W

Page 1332: Juvinall

�n/P

f

A

JUVINALL: Machine DesignFig. 13-4 W-398

Boundary lubrication

Mixed-film lubrication

Hydrodynamic lubrication

(viscosity × rps ÷ load per unit of projected bearing area)

Page 1333: Juvinall

JUVINALL: Machine DesignFig. 13-5 W-399

T

Cross-sectional area, A

where G = shear modulus

(b)

At equilibrium, torque Tproduces elastic displacement,�, across a solid element

F

h h

FhAG

� =

Surface velocity, U

where � = absolute viscosity

(c)

At equilibrium, torque Tproduces laminar flowvelocity, U, across a fluidelement

F

FhA�

U =

(a)

Rubber element

Fluid element

Page 1334: Juvinall

Abs

olut

e vi

scos

ity

(mP

a • s

)

Abs

olut

e vi

scos

ity

(�re

yn)

Temperature (°C)

Temperature (°F)

10 20 30 40 50 60 70 80 90 100 110 120 130 140

28026024022020018016014012010080

0.3

0.4

0.5

0.6

0.7

0.91.0

2

3

4

5

10

23

5

102

23

103

2

3

4

5

10

2

3

45

102

2

3

5

103

235

104

JUVINALL: Machine DesignFig. 13-6 W-400

SAE 70

20

40

5060

Page 1335: Juvinall

JUVINALL: Machine DesignFig. 13-7 W-401

Overflow rim

Oil

Level of liquidin bath

Saybolt viscometer

Kinematic viscosity,58 s at 100°C

Bottom of bath

Orifice

Bath

Page 1336: Juvinall

JUVINALL: Machine DesignFig. 13-8 W-402

D

R

L

c

n

Page 1337: Juvinall

JUVINALL: Machine DesignFig. 13-9 W-403

5000 N

D = 100 mm

R = 50 mmn = 600 rpm

Oil viscosity,50 mPa • s

c = 0.05 mm

L = 80 mm

Page 1338: Juvinall

JUVINALL: Machine DesignFig. 13-10 W-404

Journal

Oil hole

W Partial bronzebearing

Oil level

Page 1339: Juvinall

JUVINALL: Machine DesignFig. 13-11 W-405

Rotating journal

Fixed bearing

Lubricant

Lubricant flow

Coordinates:x = tangentialy = radialz = axial

W

dx

dy

(� + dy) dx dz

� dx dz

dx

dyp dy dz

∂�∂y

(p + dx) dy dzdpdx

Page 1340: Juvinall

JUVINALL: Machine DesignFig. 13-12 W-406

y

h Lubricant flow

Stationary bearing

Rotating journal

U

Page 1341: Juvinall

JUVINALL: Machine DesignFig. 13-13 W-407

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0 0.01 0.02 0.04 0.06 0.08 0.1 0.2 0.4 0.6 0.8 1.0 42 6 8 10

Min

imum

film

thi

ckne

ss v

aria

ble,

h 0 c0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Ecc

entr

icit

y ra

tio,

e/c

Bearing characteristic number, S =2R

c�nP

Optimum zone

Min. friction

Max.load

L /D = ∞

1

12

14

Page 1342: Juvinall

JUVINALL: Machine DesignFig. 13-14 W-408

1

2

3

45

10

20

30

4050

100

200

0 0.01 0.02 0.04 0.1 0.2 0.4 0.6 0.8 1.0 2 4 6 8 100.08

Coe

ffic

ient

of

fric

tion

var

iabl

e,f

R c

L /D =

Bearing characteristic number, S =2R

c�nP

14

12

1

Page 1343: Juvinall

JUVINALL: Machine DesignFig. 13-15 W-409

1.0

0.9

0.8

0.7

0.6

0.5

0.4

0.2

0.3

0.1

0 0.01 0.02 0.04 0.06 0.1 0.2 0.4 0.6 0.81.0 2 4 6 8 10

Min

imum

film

pre

ssur

e ra

tio,

Pp m

ax (

gage

)

L /D = ∞

1

Bearing characteristic number, S =2R

c�nP

12

14

Page 1344: Juvinall

JUVINALL: Machine DesignFig. 13-16 W-410

100

90

80

70

60

50

40

20

30

10

0 0.01 0.02 0.04

* Defined in Figure 13.20

0.06 0.1 0.2 0.4 0.6 0.8 1.0 2 4 6 8 10

Pos

itio

n of

min

imum

film

thi

ckne

ss,

� (

deg*

)

L /D = ∞

1

Bearing characteristic number, S =2R

c�nP

12

14

Page 1345: Juvinall

JUVINALL: Machine DesignFig. 13-17 W-411

100

90

80

70

60

50

40

30

20

10

0 0.01 0.02 0.04 0.06 0.08 0.1 0.2 0.4 0.6 0.8 1.0 42 6 8

Term

inat

ing

posi

tion

of

film

, �

p 0 (

deg*

)25

20

15

10

5

0

Pos

itio

n of

max

imum

film

pre

ssur

e, �

p max (

deg*

)

L /D = ∞ 1

1

�p0

�pmax

Bearing characteristic number, S =2R

c�nP

12

12

14

14

* Defined in Figure 13.20

Page 1346: Juvinall

JUVINALL: Machine DesignFig. 13-18 W-412

6

5

4

3

2

1

0 0.01 0.02 0.04 0.1 0.2 0.4 0.6 0.81.0 2 4 6 8 10

Flow

var

iabl

e,Q

Rcn

LL /D =

L /D =

L /D = 1

L /D = ∞

Bearing characteristic number, S =2R

c�nP

14

12

Page 1347: Juvinall

JUVINALL: Machine DesignFig. 13-19 W-413

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.01 0.02 0.04 0.1 0.2 0.4 0.6 1.0 2 4 6 8 10

Flow

rat

io,

Qs

QL /D =

L /D = ∞

1

Bearing characteristic number, S =2R

c�nP

14

12

Page 1348: Juvinall

JUVINALL: Machine DesignFig. 13-20 W-414

W

e

n

Oil of viscosity �and flow rate Q

R = D/2

Average film pressure = P =

Film pressure, p

WDL

h0

�p0

pmax

�pmax

Page 1349: Juvinall

JUVINALL: Machine DesignFig. 13-21 W-415

1000 lb

D = 2.0 in.

R = 1.0 in.n = 3000 rpm

SAE 20 OilTavg = 130°F

c = 0.0015 in.

L = 1.0 in.

Page 1350: Juvinall

JUVINALL: Machine DesignFig. 13-23 W-417

Oil hole

Steel backingBearing material

Axial groove

Page 1351: Juvinall

Oil

film

pre

ssur

e

JUVINALL: Machine DesignFig. 13-24 W-418

Groovedbearing

Oil inlet hole

Ungrooved bearing

2

Circumferentialgroove

L2L

D

Page 1352: Juvinall

JUVINALL: Machine DesignFig. 13-25 W-419

"Rifle drilled" passagein connecting rod*

Circumferential groovein main bearing

PistonPiston pin or wrist pin

Drilled passage in crankshaft

Circumferential groove in rod bearing

Circumferential groove in main bearing

*If omitted, piston pin bearing is splash lubricated.

Oil in Oil in

Page 1353: Juvinall

JUVINALL: Machine DesignFig. 13-26 W-420

W = 17 kN

D = 150 mm

R = 75 mmn = 1800 rpm

Force feed,SAE 10 oilTavg = 82°C

c = ? mm

L = ? mm

f = ?

Qs = ?

Power loss = ?

Oil temperature rise = ?

Page 1354: Juvinall

f, co

effi

cien

t of

fri

ctio

n

h 0,

min

imum

oil

film

thi

ckne

ss (

mm

)

Q a

nd Q

s, o

il fl

ow r

ate

(cm

3/s

)

c, radial clearance (mm)

*As defined in Fig. 13.13

0 0.05 0.10

Optimum band*

0.150

0.001

0

0.005

0.010

0.015

0.020

50

100

150

200

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.010

JUVINALL: Machine DesignFig. 13-27 W-421

Max

. lo

ad Min

. fr

icti

on

h0

Qs

Q

f

Page 1355: Juvinall

JUVINALL: Machine DesignFig. 13-28 W-422

aa > b

bPads

RoRi

Runner

Page 1356: Juvinall

JUVINALL: Machine DesignFig. P13-12 W-423

D = 4.0 in.

R = 2.0 in.n = 900 rpm

SAE 10 OilTavg = 150°F

c = 0.002 in.

L = 6.0 in.

Page 1357: Juvinall

JUVINALL: Machine DesignFig. P13-27 W-424

Page 1358: Juvinall

JUVINALL: Machine DesignFig. P13-29D W-425

4.5 kN

D = ? in.

R = ? in.n = 660 rpm

SAE ? OilTavg = ?°C

c = ? in.

L = ? L = ?

Page 1359: Juvinall

4

JUVINALL: Machine DesignFig. 14-1b W-426

3

(b)

Steps in assembly

21

Page 1360: Juvinall

(a)Relative proportions of bearings

with same bore dimension

(b)Relative proportions of bearings

with same outside diameter

JUVINALL: Machine DesignFig. 14-2 W-427

(LL00) (L00)

Lightseries

(200)

Mediumseries

(300)

Mediumseries

(300)

Extra-lightseries

(L00)

Extra-lightseries

Extra-extra-lightseries

(LL00)

Extra-extra-lightseries

Lightseries

(200)

Page 1361: Juvinall

Loadinggrooves

(a) Filling notch (loading groove) type

JUVINALL: Machine DesignFig. 14-3a W-428

Page 1362: Juvinall

(c) Double row

JUVINALL: Machine DesignFig. 14-3c W-428

Page 1363: Juvinall

(d) Internal self-aligning

JUVINALL: Machine DesignFig. 14-3d W-428

Page 1364: Juvinall

(e) External self-aligning

JUVINALL: Machine DesignFig. 14-3e W-428

Page 1365: Juvinall

JUVINALL: Machine DesignFig. 14-4 W-429

Oneshield

Twoshields

One seal Two seals Shieldand seal

Snap ring

Snap ringshield and

seal

Snap ringand twoshields

Snap ringand oneshield

Snap ringand two

seals

Snap ringand one

seal

Page 1366: Juvinall

JUVINALL: Machine DesignFig. 14-5 W-430

Addedstabilizing ring

(b) One-direction locating (c) Two-direction locating

Page 1367: Juvinall

JUVINALL: Machine DesignFig. 14-8 W-433

Bearing axis

Commonapex

Crowned roller body

Spherical roller head

Roller axis

Page 1368: Juvinall

(d) Idler sheave(unground bearing)

(e) Rod end bearing

JUVINALL: Machine DesignFig. 14-10 W-436

Page 1369: Juvinall

JUVINALL: Machine DesignFig. 14-10h W-437

(h) Integral spindle, shown with V-belt pulley

Page 1370: Juvinall

JUVINALL: Machine DesignFig. 14-11 W-438

dS dH

r

r

+

+

Page 1371: Juvinall

Per

cent

age

of f

ailu

res

Life1 2 3 4 5 6 7 8 9 10 11 12

2

4

6

8

10

12

14

16

18

20

22

24

JUVINALL: Machine DesignFig. 14-12 W-439

Median

Page 1372: Juvinall

Life

adj

ustm

ent

relia

bilit

y fa

ctor

Kr

Reliability r (%)90 91 92 93 94 95 96 97 98 99 100

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

JUVINALL: Machine DesignFig. 14-13 W-440

Page 1373: Juvinall

1800 rpm

Radial bearing

JUVINALL: Machine DesignFig. 14-14 W-441

1800 rpm

Angular bearing

Ft = 1.5 kN, Fr = 1.2 kNLight-to-moderate impactEight hours/day operation

Page 1374: Juvinall

1800 rpm

Case a: 90 percent reliability

JUVINALL: Machine DesignFig. 14-15 W-442

Case b: 30,000-hour life

No. 211 radial-contact bearing,C = 12.0 kN

Fr = 1.2 kNFt = 1.5 kN

Light-to-moderate impact,Ka = 1.5

21 mm

100 mm

55 mm

Page 1375: Juvinall

1000 rpm

Ka = 1.0 (uniform load)

Fr

No. 207 radial-contact bearing

JUVINALL: Machine DesignFig. 14-16 W-443

Rad

ial l

oad

(kN

)

01

1 2 3 1

Time

32

4567

20%100%

50% 30%

Page 1376: Juvinall

Note spacers

JUVINALL: Machine DesignFig. 14-17 W-444

Page 1377: Juvinall

JUVINALL: Machine DesignFig. 14-18 W-445

Page 1378: Juvinall

F1

L1

JUVINALL: Machine DesignProb. 14-6 W-446

F2

2L1

F2

3L1

Page 1379: Juvinall

3500 rpm

JUVINALL: Machine DesignProb. 14-10 W-447

No. 204 radial ball bearingFr = 1000 N, Ft = 250 N90% reliabilityLight-moderate shock loadingL = ? hr life

Page 1380: Juvinall

Gear Shaft Bearing

JUVINALL: Machine DesignProb. 14-19 W-449

Page 1381: Juvinall

JUVINALL: Machine DesignProb. 14-20 W-448

150-mm dia.

Gear120-mm dia.

1.2 kN

20°

B

A

300 mm

100mm

60mm

60mm

Page 1382: Juvinall

Clamping supportsChain sprocket

Rotating shaftChain

JUVINALL: Machine DesignProb. 14-21d W-450

1.75 ft 0.75 ft

600 lb 600 lb

2.25 ft

Page 1383: Juvinall

Right-angle gearing

Parallel gearing

JUVINALL: Machine DesignFig. 15-1 W-451

Page 1384: Juvinall

JUVINALL: Machine DesignFig. 15-2 W-452

Page 1385: Juvinall

JUVINALL: Machine DesignFig. 15-3 W-453

Line of centers

Point of contact

Pitch point

Common normal (to tooth surfacesat point of contact)

Driving gear

P

Driven gear

Page 1386: Juvinall

JUVINALL: Machine DesignFig. 15-4 W-454

Involute curves

Base circle

Base pitch, pb

Page 1387: Juvinall

JUVINALL: Machine DesignFig. 15-5 W-455

�p

�g

Gearpitchcircle

Pinionpitchcircle

P (pitch point)c

dp

dp

Page 1388: Juvinall

JUVINALL: Machine DesignFig. 15-6 W-456

Pinionbasecircle

� (pressure angle)

�p

�g

Gearbasecircle

b

P

a

Page 1389: Juvinall

JUVINALL: Machine DesignFig. 15-7 W-457

Base circlePitch circle

Pitch circle

Pinion

a

Pc

fe

dg

b

Base circle

Gear

rp

rg

Page 1390: Juvinall

JUVINALL: Machine DesignFig. 15-8 W-458

rg

Addendum circle

Dedendum

Angle ofapproach

p

Angle ofrecess

Position ofteeth leaving

contact

0g

0p

Pitch circle

Addendum

Addendum

Dedendum circle

Base circlePitch circle

Addendum circle

Angle ofapproach

Dedendum

Angle ofrecess

Pinion (driving)

Positionof teethenteringcontact

Base circleDedendum circle

Gear (driven)

c

b

a

n

n

rp

Page 1391: Juvinall

JUVINALL: Machine DesignFig. 15-9 W-459

Workingdepth

Wholedepth

Addendum

Dedendum

Clearance

Top

land

Face

Flan

kBo

ttom

land

Circular pitch p

Pitch circle

Filletradius

Dedendumcircle Clearance circle

(mating teeth extendto this circle)

Addendum circle

Tooththickness t

Face

width

b

t0

Width ofspace

Page 1392: Juvinall

18

3632

30288064

4048

16

14

2022

2426

65

412

11

10

78

9

JUVINALL: Machine DesignFig. 15-10 W-460

Page 1393: Juvinall

Pinion

Rack

Circular pitch

p

JUVINALL: Machine DesignFig. 15-11 W-461

Page 1394: Juvinall

JUVINALL: Machine DesignFig. 15-12 W-462

Pitch circle

Base circle

�Base circle

Pitch circle Dedendumcircle

Addendumcircle

��

Page 1395: Juvinall

JUVINALL: Machine DesignFig. 15-14 W-464

Gear blank rotatesin this direction

Rack cutter reciprocates in a directionperpendicular to this page

Page 1396: Juvinall

Driving gear

Driven gear

Base circle

Base circle

02

01

�2

�1

JUVINALL: Machine DesignFig. 15-15 W-465

Interference is on flankof driver during approach

(This portion of profileis not an involute)

(This portion of profileis not an involute)

Pitch point, P

Addendum circlesab

Page 1397: Juvinall

P = 6 teeth/in.� = 20°�p�g

JUVINALL: Machine DesignFig. 15-16 W-466

= –3.0

rg

rp

c = 4 in.

Page 1398: Juvinall

Pitch circle(gear)

JUVINALL: Machine DesignFig. 15-17 W-467

dg

dp

P

P

Fr

Fr

Pitch circle(pinion)

(Driving pinion rotates clockwise)

F

F

Ft

Ft

�g

�p

Page 1399: Juvinall

N = 12 teeth (input pinion)P = 3

600 rpm; 25 hp

(a)

(b)

JUVINALL: Machine DesignFig. 15-18 W-468

a

b cN = 36 teeth

(idler)N = 28 teeth(output gear)

Resultant force (applied by shaft to gear) = (1313 + 478) 2 = 2533 lb.

45°

Vab = 478 lb

Hab = 1313 lb

Vcb = 1313 lb

20°

20°

b

Hcb = 478 lb

c

a

Page 1400: Juvinall

rf

Fr

Ft

x

F

a

F

Constant-strenghparabola

JUVINALL: Machine DesignFig. 15-20 W-470

t

h

b

Page 1401: Juvinall

Lew

is f

orm

fac

tor

Y

Number of teeth N (Rack)12 15 17 20 24 30 35 40 4550 60 80 125 275 ∞

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

0.60

JUVINALL: Machine DesignFig. 15-21 W-471

� = 14 °1

2

� = 25°

� = 20°� = 20°, st

ub teeth

Page 1402: Juvinall

Load

Driving and driven gears0

F2

Time

Time

Fa = Fm =

Driving gear Idler gear Driven gear

0

(b) Stress fluctuation

Sn

�m

�a

Su

JUVINALL: Machine DesignFig. 15-22 W-472

1 revolution

F

Load

0

Idler gear

40% higher fat. strengthfor o-max loading(driver and driven)

Fat. strengthfor reversed

loading (idler)

Fa = FFm = 0

1 revolution

F

F

�a �m

�a

Page 1403: Juvinall

Geo

met

ry f

acto

r J

Number of teeth N

(b) 25° full-depth teeth

12 15 17 20 24 30 40 50 80 275 ∞0.15

0.20

0.25

Load applied attip of tooth(no sharing)

Load applied athighest point ofsingle-toothcontact(sharing)

851000

502517

0.30

0.35

0.40

0.45

0.50

0.55

0.60

JUVINALL: Machine DesignFig. 15-23 W-473

Geo

met

ry f

acto

r J

Number of teeth N

(b) 20° full-depth teeth

12 15 17 20 24 30 40 50 80 275 ∞0.15

0.20

0.25

Load applied attip of tooth(no sharing)

Load applied athighest point ofsingle-toothcontact(sharing)

8550

2535

17

0.30

0.35

0.40

0.45

0.50

0.55

0.60

Number of te

eth in matin

g gear

Number of te

eth in matin

g gear

1000

12545 6035

12545 6035

Page 1404: Juvinall

Velo

city

fac

tor

Kv

Pitch line velocity V (ft/min)* Limited to about 350 Bhn

E D

C

B

A

0 1000 2000 3000 4000 5000 6000 70001

2

3

4

5

0 10 20

Pitch line velocity V (m/s)

30

JUVINALL: Machine DesignFig. 15-24 W-474

Hobs, shaping cutters*

High precision, shaved and ground

Highest precision, shaved and ground

Hobs,

form

cutte

rs*

Precision, shaved and ground

Page 1405: Juvinall

Pinion

Gear

Steel, 290 Bhn

(manufacture of pinion and gear correspondsto curve D, Fig. 15.24)

P = 10

20° full-depth teethSteel, 330 Bhn

Np = 18 (teeth)

JUVINALL: Machine DesignFig. 15-25 W-475

Electricmotor1720 rpm

Conveyordrive(involvesmoderateshocktorsionalloading)860 rpm

Page 1406: Juvinall

Vgn = Vpn

Vgn = Vpn

Vp = VgVg

VpVgt Vpt = Vgt

Commonnormal

Commonnormal

Gear(driver)

Gear(driver)

Commontangent

(a) General contact position sliding velocity as shown

(b) Teeth in contact at pitch pointno sliding

Pinion(driven)

Pinion(driven)

Commontangent

Slidingvelocity

JUVINALL: Machine DesignFig. 15-26 W-476

Vpt

Page 1407: Juvinall

Surface fatigue life (cycles)104

CLi

105 106 107 108 109 1010 1011

0.6

0.8

1.0

1.2

1.41.61.82.0

JUVINALL: Machine DesignFig. 15-27 W-477

Page 1408: Juvinall

JUVINALL: Machine DesignFig. 15-28 W-477A

Win = 100 hp

3600 rpm

900 rpm

Negligible shock loadingLife: 5 years, 2000 hours/year Full power: 10 percent of time Half power: 90 percent of timeFailure in 5 years: 10 percent likely

Page 1409: Juvinall

JUVINALL: Machine DesignFig. 15-29 W-478

Motor(input)

Driven machine(output)

p1

g1

g2

p2

a c

b

Page 1410: Juvinall

(a)With three planets (typical)

JUVINALL: Machine DesignFig. 15-30 W-479

P

P

Ring

PlanetArmSun

R

A S

P

(b)With one planet (for analysis only)

P

R

A S

Page 1411: Juvinall

(R = input; A = output; S = fixed member)

JUVINALL: Machine DesignFig. 15-31 W-479A

R/2

2Ti

2Ti /3R

2Ti /3R

4Ti /3R 4Ti /3R

R + S4

Ti

R P

A

3R

R + S4

2Ti

3R

2Ti

3R4Ti

3RTo

Ti

�i

�o

SR

SR

4Ti

R

4Ti

3R

To =

= = 1 +

= Ti 1 +

Page 1412: Juvinall

(R = input; A = output; S = fixed member)

JUVINALL: Machine DesignFig. 15-32 W-480

P

R

V

S

�0

�0

�i

�i

A

R2 R + S

4

V2

VR/2V/2

=

SR�0

�i = 1 +

(R + S)/4

Page 1413: Juvinall

JUVINALL: Machine DesignFig. 15-33 W-481

P

P

R

S

90° = 17 teeth (ring)12

Planet willfit here

Planet willfit here 90° = 5 teeth (sun)

Planet willNOT fit here

Planet willNOT fit here

Page 1414: Juvinall

JUVINALL: Machine DesignProb. 15-21 W-482

Driven machinecoupled to this

shaft

45 teeth

P = 5, � = 25°15 teeth

45 teeth

25mm

100mm

25mm

1 kW, 1200-rpmmotor coupledto this shaft

c

B

b

A

a

Page 1415: Juvinall

JUVINALL: Machine DesignProb. P15-23 W-482A

A

B

36T

64T

24T, P = 6

18T, P = 9

2''

To drivenmachine

8''

2''

Coupled to 20 lb.in.torque motor

Page 1416: Juvinall

JUVINALL: Machine DesignProb. 15-26 W-483

a

a

Motor

Driven machine

Page 1417: Juvinall

32T

24T To drivenmachine

1''

B

A

JUVINALL: Machine DesignProb. 15-27 W-484

90°2.0''

16T

1700-rpmmotor

100-lb.in.torque

Page 1418: Juvinall

(b)(a)

JUVINALL: Machine DesignProb. 15-45 W-485

3

3

44

2

7

6

78

9

4

1

Low (L)

Neutral (N)

High (H)

3

2

Memberpushes here todisengage pawl

Hub can"overrun"in thisdirection

5

Page 1419: Juvinall

JUVINALL: Machine DesignProb. P15-47 W-485A

P2 P1

P2

S2

P1

S1

Input

Output

Arm

Page 1420: Juvinall

JUVINALL: Machine DesignProb. P15-50 W-485B

P1 P2

Input

S1 (100 teeth)

P2 (102 teeth)

P1 (101 teeth)

S2 (99 teeth)

Output

Arm

Page 1421: Juvinall

Reverse brake bandholds S2 fixed

Low brake bandholds S3 fixed

S3 (21 teeth)

P3 (33 teeth) P1 (27 teeth)

P2 (24 teeth)

S1 (27 teeth)S2 (30 teeth)

OutputInput

JUVINALL: Machine DesignProb. 15-51 W-486

Page 1422: Juvinall

JUVINALL: Machine DesignFig. 16-1 W-487

(b) Rotated spur gear laminationsapproach a helical gear as laminationsapproach zero thickness.

Page 1423: Juvinall

ppn

pn

pa

�n

p

�� Section NN

(normal plane)

Section RR(in plane of rotation)

JUVINALL: Machine DesignFig. 16-4 W-490

Rb

R

b

N

N

c

d

a�

e

Page 1424: Juvinall

Section NN(normal plane)

Section RR(plane of rotation)

d

2 cos2 �

JUVINALL: Machine DesignFig. 16-5 W-491

Re =

R

d

N

N

R�

Page 1425: Juvinall

�n

�F

Top of tooth

Pitchcylinder

Spur gear(helical gear with � = 0�)

d

JUVINALL: Machine DesignFig. 16-6 W-492

Fa

FrFt

Fr

Ft

Ft

Isometric viewshowing helical

gear forces

Top of tooth

Pitchcylinder

Helical gear

Section RR(plane of rotation)

Section NN(normal plane)

Fr

Ft

Ft

Fa

Fb

Fr

F

Fb

R

N

N

R

Page 1426: Juvinall

Np = 18 (teeth)Pn = 14�n = 20�

(a)

Electric motor hp 1800 rpm

(normalplane)

Input shaft ofdriven machine

600 rpm

� = 30�(right hand)

JUVINALL: Machine DesignFig. 16-07 W-493

Fr

FaFt

(b)Isometric view of

motor shaft and pinion

Direction ofrotation

� = 30�(left hand)

12

Page 1427: Juvinall

Geo

met

ry f

acto

r J

Helix angle �0� 5� 10� 15� 20� 25� 30� 35�

0.40

0.30

0.50

0.60

0.70

JUVINALL: Machine DesignFig. 16-8 W-494

J-fa

ctor

mul

tipl

ier

Num

ber

of t

eeth

Teet

h in

mat

ing

gear

Helix angle �0� 5� 10� 15� 20� 25� 30� 35�

0.95

0.90

1.00

5001507550

30

12141618203060150500

20

1.05

Page 1428: Juvinall

Developed backcone radius, rbg

rbp�p�p

b

Pitch conelength, L

Dedendum

Dedendum

Addendum

Pinion back cone Pitch cone

angles

Gearpitch cone

dp

JUVINALL: Machine DesignFig. 16-9 W-495

Gear pitchdia., dg

Gearbackcone

Pinionpitchcone

Page 1429: Juvinall

Spiralangle

Circular pitch

Face advance

Meanradius

JUVINALL: Machine DesignFig. 16-10 W-496

Page 1430: Juvinall

b

Ft

Ft

Fa

FrFn

Fn

F

Fr

Note: Fn is normalto the pitch cone.

d2

b2

dav

2

JUVINALL: Machine DesignFig. 16-12 W-498

Page 1431: Juvinall

JUVINALL: Machine DesignFig. 16-13 W-499

Geo

met

ry f

acto

r J

Number of teeth in gear for which geometry factor is desired0 10 20 30 40 50 60 70 80 90 100

0.16

0.18

0.20

0.22

0.24

0.26

0.28

0.30

0.32

0.34

0.36

0.38

15

20

40

30

50

80

Teeth in mating gear

60

100

0.40

Page 1432: Juvinall

JUVINALL: Machine DesignFig. 16-13 W-517

250 mm

Load

Motor

Rotation

140 mm

A

B

C

D140 mm

65mm

Page 1433: Juvinall

JUVINALL: Machine DesignFig. 16-14 W-500

Geo

met

ry f

acto

r J

Number of teeth in gear for which geometry factor is desired0 20 40

100

80

60

50

40

12

30

2520 15

60

Teeth in mating gear

80 1000.16

0.20

0.24

0.28

0.32

0.36

Page 1434: Juvinall

Geo

met

ry f

acto

r I

Number of teeth in pinion NP

0 10 20 30 40 500.05

0.06

0.07

0.08

0.09

0.10

0.11

JUVINALL: Machine DesignFig. 16-15 W-502

Ng = 100

Ng = 70

Ng = 50

15 Teeth in gear

90

80

60

4030

2520

Page 1435: Juvinall

Geo

met

ry f

acto

r I

Number of teeth in pinion NP

0 10 20 30 40 500.06

0.08

0.10

0.12

0.14

0.16

0.18

JUVINALL: Machine DesignFig. 16-16 W-503

Ng = 100

30 Teeth in gear

1520 25

5040

60

80

Page 1436: Juvinall

�S

JUVINALL: Machine DesignFig. 16-17 W-504

�R

A

P

P Fixed arm, A

RP (planet)

R (ring)

S (sun)

S

P

Page 1437: Juvinall

JUVINALL: Machine DesignFig. 16-18 W-505

Arm(input member)

Right axleLeft axle

P

P

RS

Page 1438: Juvinall

JUVINALL: Machine DesignFig. 16-19 W-506

Worm leadangle, �, and

gear helixangle, �

Centerdistance

c

Keyway

Axial pitch, P

Lead, L

Note: � and � aremeasured on pitchsurfaces.

Wormoutside dia.,

dw, out

Pitchdia., dw

Pitchdia., dg

Facewidth, b

Page 1439: Juvinall

Fwt

Fwr

Fwa

Worm-drivingtorque

JUVINALL: Machine DesignFig. 16-20 W-507

Fgt

Fgr

Fga

Page 1440: Juvinall

JUVINALL: Machine DesignFig. 16-21 W-508

fFn cos �

Fn sin �n

Fn cos �n

Fn cos �n cos �

Fn

Fn cos �n sin �

�n

Direction ofFga and Fwt

Direction of

Fgt and Fwa

Direction ofFgr and Fwr

(a) Worm driving (as in Fig. 16.20) (b) Gear driving (same direction of rotation)

�Fn

fFn sin ��

fFn cos �

Direction ofFga and Fwt

Direction ofFgr and Fwr

Direction of

Fgt and Fwa

fFn sin �

fFn

Fn cos �n sin �

�n

Fn cos �n

Fn sin �n

Fn cos �n

Fn

Fn cos �n cos �

Page 1441: Juvinall

JUVINALL: Machine DesignFig. 16-22 W-509

Vs

Vw

Vg Gearrotation

Worm

Gear

Worm rotation

Page 1442: Juvinall

Coe

ffic

ient

of

fric

tion

f

Sliding velocity Vs (ft /min)1 2 4 6 10 2 4 6 100 2 4 6 1000 2 4 6 10,0000

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0

JUVINALL: Machine DesignFig. 16-23 W-510

Page 1443: Juvinall

Worm: Steel, hardened and ground

Nw = 2, RH, p = in., �n =14 �

c = 5 in.

JUVINALL: Machine DesignFig. 16-24 W-511

Gear

60 rpm

Worm

Gear: Bronze

Motor2 hp., 1200 rpm

58

12

Page 1444: Juvinall

Worm rpm, nw

Coe

ffic

ient

C

0 400 800 1200 16000

10

20

30

40

50

60

70

80

JUVINALL: Machine DesignFig. 16-25 W-512

ft �

lb

min

� ft

2 �

�F

With fan (as in Fig. 16.26)

Without fan

Page 1445: Juvinall

c ≈ 6 in.

JUVINALL: Machine DesignFig. 16-27 W-514

Gear

Worm: hardened steelrpm =1200

Gear: Chill-cast bronze

Speed ratio, 11:1

Worm

Page 1446: Juvinall

JUVINALL: Machine DesignTable 16-1 W-501

Page 1447: Juvinall

p

b

JUVINALL: Machine DesignFig. P16-5 W-516

Pa

Page 1448: Juvinall

40 teeth 60 teeth

20 teethOutput

JUVINALL: Machine DesignFig. P16-08 W-515

24 teeth Input

Page 1449: Juvinall

JUVINALL: Machine DesignFig. P16-14 W-518

Motor

Output

50 teeth

20 teeth� = 0.50 rad

left hand

25 teeth� = 0.35 radright hand

A

B 125

100

20050 teeth

Page 1450: Juvinall

Gear

Pinion

1000 rpm

400 rpm

Bevel gears:35 hp

Np = 36Ng = ?

b = 2 in.� = 20�

P = 6

JUVINALL: Machine DesignFig. P16-19 W-519

Page 1451: Juvinall

Pinion

1500 rpm

Gear

A B

3 in. 3 in.

Bevel gears: 50 hp

Np = 30Ng = 60b = 3 in.� = 20�

P = 6

Flexiblecoupling tomachine

JUVINALL: Machine DesignFig. P16-23D W-520

Page 1452: Juvinall

Nw = 2Ng = 55

P = ?

JUVINALL: Machine DesignFig. P16-30 W-521

c = 8 in. Gear

Worm

Page 1453: Juvinall

Gear material: Chill-cast bronzeWorm material: Hardened steelNw = 3 p = 0.5 in. f = 0.029

Ng = 45 �n = 20�

c = 4.5 in.

b =1.0 in.

1200 rpm

JUVINALL: Machine DesignFig. P16-34 W-522

Page 1454: Juvinall

JUVINALL: Machine DesignFig. 17-1 W-523

(a) Square key

d

w

ww

2

(b) Flat key

w ≈ d/4 w ≈ d/4; h ≈ 3w/4

d

h

hw

2

(c) Round key

Key usually has drivefit; is often tapered

(d) Kennedy keys

Keys are tapered anddriven tightly; forheavy-duty service

(e) Woodruff key

Widely used in automotive andmachine tool industries

( f ) Gib-head key

Usually tapered, giving tightfit when driven into place;gib head facilitates removal

(g) Feather key

Key is screwed to shaft; hub is free toslide axially – easier sliding is obtained

with two keys spaced 180° apart

Page 1455: Juvinall

JUVINALL: Machine DesignFig. 17-2 W-524

d

D

(a) Straight round pin (b) Tapered round pin(c) Split tubular spring pin Grooves are produced by rolling,

and provide spring action toretain pin

(d) Grooved pin

Page 1456: Juvinall

JUVINALL: Machine DesignFig. 17-3 W-525

Basic Inverted

E-ring

External rings (fit on shaft)

(a) Conventional type, fitting in grooves

(b) Push-on type – no grooves required

Teeth deflect when installed to "bite in" and resist removal(less positive than conventional type)

Basic

Internal rings (fit in housing)

Inverted

I

I Section II

External ring (fit on shaft)

I

I Section II

Internal ring (fit in housing)

Page 1457: Juvinall

4-spline 6-spline 10-spline

(a) Straight-sided (b) Involute

16-spline

JUVINALL: Machine DesignFig. 17-4 W-526

Page 1458: Juvinall

JUVINALL: Machine DesignFig. 17-5a W-527

�stGravitationalforce, w

Mass, m

Shaft of spring rate k = w/�st

(a) Single mass

Page 1459: Juvinall

JUVINALL: Machine DesignFig. 17-5b W-527

m1

w1 w2w3

m2

�1 �2 �3

m3

w1 w2

w5

m1 m2m3

m4m5

w3w4

(b) Multiple masses

Page 1460: Juvinall

JUVINALL: Machine DesignFig. 17-5c W-527

�st

(c) Shaft mass only

Page 1461: Juvinall

50 300

Tracksprockets

Track

5060

T1

A BC

T2

Chain

30°

Chainsprocket100 diameter

Track sprocket250 diameter

Track

Fc (= 2500 N)

FT (= 1000 N)

(a) General arrangement

JUVINALL: Machine DesignFig. 17-6a W-528

d

Page 1462: Juvinall

JUVINALL: Machine DesignFig. 17-6b-d W-530

55 Small gap orspring washer

(b) Shaft layout

d

A

T1 T2

BC

S

A T1 S T2

2490Vertical forces

C

B325 2165

50245

Torque

62,500

55 50 60

95,800

125,000

(c) Loading diagrams

VV

MV

T1 S T2

Horizontal forces

B

CA

687.5 1250

937.5

VH

MH

500(Ft /2)

500(Ft /2)

80,30090,600

75,000

�ea

(M

Pa)

�em (MPa)

�ea�em

(d) Fatigue diagram

0 100 200

"Design overload" point

300 400 450

530

500

100= 2.9

200

165

Sn = S' CLCGCS = (0.5)(550)(1)(0.9)(0.78) = 186n

113,700 130,000

Page 1463: Juvinall

JUVINALL: Machine DesignFig. 17-7 W-531

d/4

d

(c) Shear failure of a tightly fitted key

d/4

d/8

d

(b) Key tightly fitted at top and bottom(a) Loosely fitted key

Page 1464: Juvinall

JUVINALL: Machine DesignFig. 17-8 W-532

Sled-runner keyway Profiled keyway

Fatigue stress concentration factor, Kf*Steel

Annealed(less than 200 Bhn)

Quenched and drawn(over 200 Bhn)

1.3

Bending

1.6

* Base nominal stress on total shaft section.

1.3

Torsion

1.6

1.6

Bending

2.0

1.3

Torsion

1.6

Page 1465: Juvinall

JUVINALL: Machine DesignFig. 17-9 W-533

Page 1466: Juvinall

(b) Constant-stress, constant strain shear coupling

JUVINALL: Machine DesignFig. 17-10 W-534

(a) Basic shear-type coupling

Bonded rubber element

(c) Tube form shear coupling

Page 1467: Juvinall

JUVINALL: Machine DesignFig. 17-12 W-536

(a) Basic Oldham type (b) Modified type

Page 1468: Juvinall

JUVINALL: Machine DesignFig. 17-13 W-537

Page 1469: Juvinall

JUVINALL: Machine DesignFig. P17-1 W-538

20 in.

Flexible couplingMotor 0.25-in.-dia. shaft

Page 1470: Juvinall

JUVINALL: Machine DesignFig. P17-7 W-539

600 mm600 mm

50 kg

25-mm dia.

Page 1471: Juvinall

JUVINALL: Machine DesignFig. P17-11 W-540

40 in. 30 in.20 in.

120 lb80 lb

2-in.-dia. shaft

Page 1472: Juvinall

JUVINALL: Machine DesignFig. P17-13a-f W-541,542,543

Driver56 kw

Bearing (2)

ShaftDriven28 kw

Driven28 kw

(b) Gear input shaft

(a) Connecting shaft

(c) Hydroelectric generator shaft

(d) Idler gear shaft

Bearings Shaft

Electricgenerator

rotor

Hydraulicturbine

DriverShaft

Bearing (2)

Driven

Idler

(e) Gear countershaft ( f ) Stationary countershaft

Shaft

Needle bearing (2)

Shaft

DriverDriven

Driver Driven

Coupling (2)Motor

Bearing (2)

Shaft

Driven machine

Page 1473: Juvinall

JUVINALL: Machine DesignFig. P17-14 W-544

5 in.

2 in.

Bearing ABearing B

Fr = 450 lb

Fa = 400 lb

Ft = 800 lb

3 in. rad

Page 1474: Juvinall

JUVINALL: Machine DesignFig. P17-15 W-545

125 mm

50 mm

B

A

Fr = 2.4 kN

Ft = 4.0 kN

Fa = 1.5 kN

Note: Gear forces actat a 75-mm radius

from shaft axis.

Page 1475: Juvinall

Chain sprocket

JUVINALL: Machine DesignFig. P17-16 W-546

(a)

Stationary shaft

Clamping supports

Chain sprocket

(b)

Rotating shaft

Clamping supports

Page 1476: Juvinall

Drivingshaft

Drivenshaft

Provision foraxial movement

Ring elementsubjected to clamping

pressure, p

Friction liningmaterial

JUVINALL: Machine DesignFig. 18-1 W-547

dr

rri

ro

Page 1477: Juvinall

Releaselever

To release

To transmission

Housing

Cover

Spring

Flywheel

Frictionplanes

Enginecrankshaft

Pressure plate

Clutch plate(driven disk)

Releasebearing

JUVINALL: Machine DesignFig. 18-2 W-548

Page 1478: Juvinall

Oil passage

Input

Oil passage

Piston

Oil chamber(pressurized toengage clutch)

Seals

Bushing

Key

Key

Output

Disks b – driven disks (3 disks, 6 friction surfaces)

Disks a – driving disks (4 disks, 6 friction surfaces)

JUVINALL: Machine DesignFig. 18-3 W-549

ri ro

Page 1479: Juvinall

dr

F

Cone

� Cone angle

Spline (sliding fit)

Shifting groove

Spring

Key

Cup

(a) (b)

drsin �

Local pressure = p

JUVINALL: Machine DesignFig. 18-5 W-551

r�

ri

ro

Page 1480: Juvinall

Lever

(a)Brake assembly

a A

F

Shoe(block)

O

Drum

Direction of rotation

JUVINALL: Machine DesignFig. 18-6 W-552

(b)Shoe and lever as a free body

(c)Drum as a free body

(d)Lever proportions for a

self-locking brake

F

OOv

Oh

A

r

bAv

fN

fN

N

N

Inertial and/orload torque, T

Ah

c

b

a

Page 1481: Juvinall

JUVINALL: Machine DesignFig. 18-7 W-553

6

23

1

8080

All dimensions in millimeters

1

4

6

(rotation)

23

4

400

300

250rad.

45°

300 Shoe width, 80 mmf = 0.20pmax = 0.40 N/mm2

400

120120

(a)

(b)

(c)

( f )

(d) (e)

5

5H25 = 4F

H52 = 4F

V26 = 1.41F

H54 = 4FH34 = 4FH43 = 4F

H62 = 7.07FH26 = 7.07F

V16 = 0.70F

H16 =3.46F

T = 880F

H36 = 10.53FH63 = 10.53F

V63 = 0.2H63

V36 = 2.11F

H13 = 6.53F

V13 = 2.11F

V12 = 2.41F

H12 = 3.07FO12

O16

O13

V62 = 0.2H62

V52 = F

H45 = 4F

V25 = FO25

F

45°

90° 90°

F

Page 1482: Juvinall

A'

�n

JUVINALL: Machine DesignFig. 18-8 W-554

O3

O3 O2

A

B

�'

Page 1483: Juvinall

JUVINALL: Machine DesignFig. 18-9 W-555

O3

d�

O2

A

dN

f dN

d cos (180° – �)= –d cos �

d sin (1

80° – �)

= d sin �

Drum rotationNote: d = O2O3 b = width of shoe

B

r �1

�2

c

F

180° – �

Page 1484: Juvinall

JUVINALL: Machine DesignFig. 18-10 W-558

300 rpm

C = 500

200

Springcompressedto force F

Force torelease brake

Cast-iron drumMolded composite

shoe lining ofwidth b = 50

All dimensions in millimeters

(a) Complete brake

(b)Drum and right shoe

F

150

150 150

300

200

150

O2

O3

�1

�15045°

45°�2

d

Page 1485: Juvinall

JUVINALL: Machine DesignFig. 18-10 W-556

O2

N

Pivot P

F

fN

�2

r f

r

�2

Page 1486: Juvinall

JUVINALL: Machine DesignFig. 18-12 W-557

P

f dN2 + f dN2

r

rf

f dN1

dN2

dN1

dN2

��

f dN2

f dN2

'

'

'

Page 1487: Juvinall

Drum

Rotation

Adjustingcam

Brake lining

Anchor pins

Hydraulic wheel cylinder

Return spring

O2

O3

JUVINALL: Machine DesignFig. 18-13 W-559

C

r

d �1

�2

Page 1488: Juvinall

Anchor pin

Hydraulic wheel cylinder

Forwardrotation

Adjusting camand guide

Brake shoe

Brake liningAnchor pin

Hydraulic wheel cylinder

Brake drum

Adjusting camand guide

JUVINALL: Machine DesignFig. 18-14 W-560

Returnspring

Page 1489: Juvinall

P1

P1

P2

F

P2

a

Band of width = b

Rotation

Cutting plane forfree-body diagrams

JUVINALL: Machine DesignFig. 18-15 W-561

c

r

Page 1490: Juvinall

d�/2d�/2

P + dP P

Rotation

dNd�

JUVINALL: Machine DesignFig. 18-16 W-562

Page 1491: Juvinall

P1

s

P2

Band of width = b

Rotation

JUVINALL: Machine DesignFig. 18-17 W-563

a

F

c

Page 1492: Juvinall

P1

P2

Band width, b = 80 mm

Rotation

JUVINALL: Machine DesignFig. 18-18 W-564

� = 270° Friction coefficient, f = 0.20

Maximum lining pressure,pmax = 0.5 MPa

a = 150 mm

F

c = 700 mms = 35 mm

r = 250 mm

Page 1493: Juvinall

Pads of diameter = 60 mm

125 mm

320 mmpmax = 500 kPaf = 0.30

JUVINALL: Machine DesignFig. P18-12 W-567

Page 1494: Juvinall

4m/s

1000 kg

JUVINALL: Machine DesignFig. P18-14 W-565

Page 1495: Juvinall

JUVINALL: Machine DesignFig. P18-17 W-568

Electricmotor

Gearreducer

Friction clutch

T = 6 N • m, 600 rpm

Rotary inertial load,I = 0.7 N • m • s2

Page 1496: Juvinall

JUVINALL: Machine DesignFig. P18-17 W-569

Rotation

F = 1500 N

200 mm340 mm

400 mm 500 mm

Page 1497: Juvinall

JUVINALL: Machine DesignFig. P18-22 W-570

Rotation

A

F

240 mm

250 mm 320 mm

400 mm

150 mm

Page 1498: Juvinall

JUVINALL: Machine DesignFig. P18-23 W-571

500 mm

Spring

300 mm400 mm

350 mm

Page 1499: Juvinall

Woven lining

Cast- irondrum

JUVINALL: Machine DesignFig. P18-24 W-572

2

5

3

4

61

18 in.

25 in.

150

5 in.

5 in.

23 in.

18 in.

30 in.

Rotation5

Page 1500: Juvinall

JUVINALL: Machine DesignFig. P18-31 W-573

Rotation

F = 300 N

500 mm

Page 1501: Juvinall

JUVINALL: Machine DesignProb. 18-33 W-574

55

258°

240

F

75

72

370

Page 1502: Juvinall

JUVINALL: Machine DesignProb. 18-34 W-575

Wt.

sa

c

270°

Page 1503: Juvinall

JUVINALL: Machine DesignFig. 19-1 W-576

Motorrotation

(a) Manual adjustment

(b) Pivoted, overhung motor

(c) Weighted idler pulley

Adjustment

Tightside

Pivot

Pivot

Overhang

Idler

Weight

Tightside

Page 1504: Juvinall

JUVINALL: Machine DesignFig. 19-2 W-577

0.50 in.

0.31 in.

0.66 in.

0.41 in. 0.53 in.

0.75 in.0.91 in.

A

0.38 in.

0.32 in.3 V

0.62 in.

0.54 in.0.88 in.

5 V

8 V

DE

C

B

(a) Standard sizes A, B, C, D, and E

(b) High-capacity sizes 3V, 5V, and 8V

0.88 in.

1.25 in.1.50 in.

1.0 in.

Page 1505: Juvinall

JUVINALL: Machine DesignFig. 19-4 W-579

2�≈ 36°

dNdN2

dN/2sin �

(a) (b)

Page 1506: Juvinall

JUVINALL: Machine DesignFig. 19-5 W-581

Tension-carrying cords

Fabric cover

Rubber

Page 1507: Juvinall

JUVINALL: Machine DesignFig. 19-7 W-583

p

�r Pitchcircle

(a)

rc

p

(b)

A

B

AB

rc r

Chordal rise, r – rc

Page 1508: Juvinall

JUVINALL: Machine DesignFig. 19-9 W-584A

Pitch p

(a)

Page 1509: Juvinall

JUVINALL: Machine DesignFig. 19-10 W-584B

A

A

r

r4(D/2)

r3

D

Ti

�i �o

To

Inputshaft

Oil particle

Impeller

Gasket

Case

Turbine

Fluidcirculation

Oil seal

Output shaft

Core or innershroud

r2

r1

�i

Blades

Section AA

Page 1510: Juvinall

Per

cent

rat

ed t

orqu

e

Input speed �i (rpm)0 200 400 600 800 1,000 1,200 1,400 1,600 1,800

0

40

80

120

160

200

240

280

320

360

JUVINALL: Machine DesignFig. 19-11 W-584C

12 8

7

5

20

100

16 14

10

6

4

3

2

Percent slip

Maximumcouplingtorque

Electric motortorque curve

Page 1511: Juvinall

Turbine

Fluidcirculation

Inputshaft Output

shaft

Impeller

Reactor

JUVINALL: Machine DesignFig. 19-12 W-585

Page 1512: Juvinall

Turbine

Inputshaft Output

shaft

Impeller

One-wayclutchReactor

JUVINALL: Machine DesignFig. 19-13 W-586

Page 1513: Juvinall

Torq

ue r

atio

Speed ratio0 0.2 0.4 0.6 0.8 1.0

0.8

1.2

1.6

2.0

2.4

2.8

3.2

Eff

icie

ncy

(%)

0

20

40

60

80

100

JUVINALL: Machine DesignFig. 19-14 W-587

Converter efficiency

Couplingefficiency

Convertertorque ratio

Coupling torque ratio

Page 1514: Juvinall

JUVINALL: Machine DesignFig. P19-3 W-588

�2

c

�1r2

r1

Page 1515: Juvinall

JUVINALL: Machine DesignFig. P19-4 W-589

A

B

C

D

Page 1516: Juvinall

JUVINALL: Machine DesignFig. P19-8 W-590

V-belt� = 18°f = 0.20

Belt maximum tension = 1300 NBelt unit weight = 1.75 N/m

r = 100 mmPulley radius� = 170°

n = 4000 rpm

Page 1517: Juvinall

JUVINALL: Machine DesignFig. P19-15 W-591

Electric motorn = 1780 rpm

55% rated power

Fluid coupling—performance curves—

Fig. 19.11

Drivenmachine

Page 1518: Juvinall

JUVINALL: Machine DesignFig. U19-1 W-580

Multiple V-belt, � = 18°, size 5VUnit weight = 0.012 lb/in.Power input = 25 hpPmax = P1 = 150 lbf = 0.20

3.7 in. dia.

Drivingpulley

Number of belts = ?

Drivenpulley

n = 1750 rpm

165° angle of wrap

Page 1519: Juvinall

1.44 –2.99

B1 engaged

–4.31Reverse

B3 engaged

1.00 1.00

C1 engaged

1.004

C2 engaged

1.44 1.00

B1 engaged

39%

61%

39%

61%

1.443

C2 engaged

1.00

(b) Power flow block diagram

(c) Gear shift pattern(a) Internal power flow diagram

2.53

C1 engaged

2.532

B2 engaged

1.44 2.53

B1 engaged

3.661

–Neutral

Torqueratio

Tout/Tin

Frontplanetary

train

Fluidcoupling

Rearplanetary

trainGear

No clutches or brakes engaged

B2 engaged

Gear Ratio

Neutral –

1 3.66

2 2.53

3 1.44

4 1

Reverse –4.31

C1 B1 C2 B2 B3

S1, P1, R1 S2, P2, R2 S3, P3, R3

B3

B2B1

C2C1Neutral

S1, P1, R1 S2, P2, R2 S3, P3, R3

B2B1

C2 B3C11

S1, P1, R1 S2, P2, R2 S3, P3, R3

B3

B2B1

C2C12

S1, P1, R1 S2, P2, R2 S3, P3, R3

B3

B2B1

C2C13

S1, P1, R1 S2, P2, R2 S3, P3, R3

B3

B2B1

C2C14

S1, P1, R1 S2, P2, R2 S3, P3, R3

B3

B2B1

C2C1Reverse

Fluidcoupling

Gearinterface

Bearing

JUVINALL: Machine DesignFig. 20-2 W-594

Page 1520: Juvinall

JUVINALL: Machine DesignFig. 20-3 W-595

Input torqueTi

54-tooth ring

R1

×Ti3

TiP

81TiP

81

TiP

81

TiP

81

TiP

81

TiP

81

TiP

81

TiP

40.5

P1

S1

TiP

40.5

TiP

40.5

TiP

40.5A1

TiP

81

P

2715-tooth planet

12-tooth sun

P

27

P12

P19.5

P12

P

7.5

Torque from B1:

TB1 =

TB1 = 0.44Ti

(3)

TiP

40.5 P19.5

Output torque:

To =

To = 1.44Ti

(3)

Arm

To

Page 1521: Juvinall

JUVINALL: Machine DesignFig. 20-4 W-596

TiP

67.5

TiP

67.5

TiP

67.5

Ti3

P

22.5

TiP

Ti

67.5

TiP

67.5

S2

6P

TiP

33.75

TiP

67.5

R2

34.5P

TiP

33.75

TiP

33.75

TiP

33.75A2

P28.5

TiP

33.75 P28.5

Output torque:

To = (3)

To = 2.53Ti

Arm

22.5

45-tooth sun

69-tooth ring

P

TiP

67.5 P34.5

TB2 = (3)

TB2 = 1.53Ti

P2

12-tooth planet

Page 1522: Juvinall

JUVINALL: Machine DesignFig. 20-5 W-597

TiP

67.5

34.5TiP

675

69TiP

675

TiP

67.5

34.5TiP

67.5

34.5TiP

675

TiP

67.5

TiP

67.5

TiP

67.5TiP

67.5

TiP

Ti

67.5

S2

TiP

33.75

34.5P

10P

34.5

10•

TiP

33.7569TiP

675

A2, A3

P28.5

P18

TiP

33.7569TiP

675P28.5

Output torque:

To = – 3

To = –2.99Ti

P18

Arms

22.5

45-tooth sun

P

P2

12-tooth planet

P3

16-tooth planet

R2, S3

69-tooth ringand 20-tooth sun

Page 1523: Juvinall

JUVINALL: Machine DesignFig. 20-5 W-598

34.5TiP

675

34.5TiP

675

34.5TiP

675

34.5TiP

675

P26

Torque from reverse lock, B3

TB3 = (3)

TB3 = 3.99Ti

26 R3

52-tooth ring

P

Page 1524: Juvinall

JUVINALL: Machine DesignFig. 20-6 W-599

To

TiP

40.5

TiP

81

S1

24-tooth sun

TiP

81

TiP

81 19.5P

TiP

40.5

TiP

40.5

Output torque:To = 1.00Ti

TiP

81 P12

Torque from C1:

TC1 = 3

TC1 = 0.44Ti

A1

TC1

TC1

Arm

12P

Page 1525: Juvinall

0.0117Ti P

Tf

Tf P

67.5

TC2P

Clutchtorque

TC2

103.5

P28.5

Arm

A222.5

45-tooth sun

P 34.5P

P2

12-toothplanet

69-tooth ring

R2S2

To

P28.5

Output torque:

To = 0.117Ti P (3)

To = 1.00Ti

Tf P

67.5

TC2P

103.5

For equilibrium of P2:

∴ Planet pin force = 0.0117Ti P

=

Tf + TC2 = Ti

Tf = 0.39Ti

TC2 = 0.61Ti

JUVINALL: Machine DesignFig. 20-7 W-600

Page 1526: Juvinall

JUVINALL: Machine DesignFig. B-1 W-601

h

h

b

d

b

Rectangle

Triangle

Circle

d

Hollow circle

y

y

di

Page 1527: Juvinall

Rod

Disk

Rectangular prism

Cylinder

y

d

d

b

x

xz

z

y

y

t

JUVINALL: Machine DesignFig. B-2 W-602

L

c

L

a

z

y

d

xz

Hollow cylinder

L

y

do

di

xz

Page 1528: Juvinall

Tempering temperature (°F)

Reduction of area

400

%

ksi

600 800 1000 12000

20

40

60

60

80

100

120

140

160

180

200

220

240

JUVINALL: Machine DesignFig. C-5a W-603

4130

4130 1095

1050

1095

1050

1095

1030, 1040

1095, 4130

1040

1040

1030

1030

1050

1030, 1040, 4130

1050

Elongation

Ultimate strength

Yield strength

Page 1529: Juvinall

Tempering temperature (°F)

Reduction of area

400

%

ksi

600 800 1000 12000

20

40

60

60

80

100

120

140

160

180

200

JUVINALL: Machine DesignFig. C-5b W-604

Elongation

Ultimate strength

Yield strength

1095

1050

1040

1050

1040

1040

1040

1050

1095

10951050

1095

Page 1530: Juvinall

Tempering temperature (°F)

Reduction of area

400

%

ksi

600 800 1000 12000

20

40

60

100

140

120

160

200

180

220

260

240

280

300

JUVINALL: Machine DesignFig. C-5c W-605

Elongation

Ultimate strength

Yield strength

4340

9255

4140

43409255

4340

4140

9255

9255

4140

4140, 4340

Page 1531: Juvinall

Diameter of test specimen (in.)

Diameter of test specimen (mm)

0 1 2 3 450

60

70

80

90

ksi MPa

100

110

120

130

140

150

160

170

180

190 1300

1200

4340

4340

4140

3140

4140

3140

1040

1040

1100

1000

900

800

700

600

500

400

0 200 400 600 800

Su

Sy

1000

JUVINALL: Machine DesignFig. C-6 W-606

Page 1532: Juvinall

–PL

P

P

�max

V = P

M = –PL

+

0

0

V

M

JUVINALL: Machine DesignFig. D-1(1) W-607

Lx

Page 1533: Juvinall

JUVINALL: Machine DesignFig. D-1(2) W-607

V = P

M = –Pa

+

0

0

V

M

–Pa

P

P

b

�max

xa

Page 1534: Juvinall

�max

M = –wL2/2

+

0

0

V

M

JUVINALL: Machine DesignFig. D-1(3) W-608

wLV = wL

wL2

2

w

x

L

Page 1535: Juvinall

JUVINALL: Machine DesignFig. D-1(4) W-608

0

0

V

M

–Mb

–Mb

Mb

P�

�max

xL

Page 1536: Juvinall

+

+

0

0

–V

M

JUVINALL: Machine DesignFig. D-2(1) W-609

Lx

P2

LP

2

P

P/2

–P/2

PL/4

2

Page 1537: Juvinall

+

+

0

0

V

M

JUVINALL: Machine DesignFig. D-2(2) W-609

Lx

b

PaL

PbL

P

Pb/L

Pab/L –Pa/L

a

Page 1538: Juvinall

+

+

0

0

– –

V

M

JUVINALL: Machine DesignFig. D-2(3) W-610

Lx

w

wL

wL /2

wL2

2

2wL2

wL2

Page 1539: Juvinall

+

0

0

V

M

JUVINALL: Machine DesignFig. D-2(4) W-610

L

x

a

PL

P

PPba

a

–Pb/a

–Pb

b�

�max

z

Page 1540: Juvinall

+

+

0

0

– –

V

M

JUVINALL: Machine DesignFig. D-2(5) W-611

a

L

x

M0

M0

Lb

M0

L

M0

L

M0a

L

M0b

L

Page 1541: Juvinall

0

0

V

M

JUVINALL: Machine DesignFig. D-2(6) W-611

a a

L

x

M0

M0

x'

b

�max

aM0

M0

aM0

Page 1542: Juvinall

JUVINALL: Machine DesignFig. D-3(1) W-612

+

+

0

0

V

M

PL8

Px

L

PL8

PL8

– PL8

PL8

P2

P2

P2

P2

L2

Page 1543: Juvinall

JUVINALL: Machine DesignFig. D-3(2) W-612

+

+

0

0

– –

V

M

Pb2

L3

P

xa b

L

Pab2

L2Pa2b

L2

(3a + b)

Pb2

L3

2Pa2b2

L3

Pab2

L2

(3a + b)

Pb2

L3 (a + 3b)

Pb2

L3

– Pa2b

L2

(a + 3b)

Page 1544: Juvinall

JUVINALL: Machine DesignFig. D-3(3) W-612

+

+

0

0

V

M

xw

L

wL2

12

– wL2

12– wL2

12

wL2

24

wL2

12wL2

wL2

wL2

wL2

Page 1545: Juvinall

JUVINALL: Machine DesignFig. D-4 W-613

107

95

.00

12

2.1

7

14

4.8

1 R

OO

T1

75

.84

PIT

CH

20

6.8

8 O

.D.

25

82

.21

N •

m

10

1.6

85

.00

82

.63

152

276

400

530

646

680

716

1060

A shaft with integral worm, dimensions in millimeters.

RB

RA

8.68 kN

10

98

7654

32

1

Page 1546: Juvinall

1

h hole

s shaft

Classof fit

Bargraph(basichole

system)

2 3 4 5 6 7 8

Loose fit Free fit Medium fit Snug fit Wringing fit Tight fitMediumforce fit

Heavyforce andshrink fit

.0216 (.0025) .0112 (.0013) .0069 (.0008) .0052 (.0006) .0052 (.0006) .0052 (.0006) .0052 (.0006) .0052 (.0006)

.0216 (.0025) .0112 (.0013) .0069 (.0008) .0035 (.0004) .0035 (.0004) .0052 (.0006) .0052 (.0006) .0052 (.0006)

.0073 (.0025)

Note: Numbers in the table are for use with all dimensions in millimeters, except for those in parentheses, which are for use with inches.

.0041 (.0014) .0026 (.0009) 0 (0)

Cb

Cs

Ca

Ci 0 (0) .00025 (.00025) .0005 (.0005) .0010 (.0010)

JUVINALL: Machine DesignFig. E-1 W-614

aa

hh h h s h h h

s ss

sa

ss

Page 1547: Juvinall

JUVINALL: Machine Designp754 b1 W-???

Page 1548: Juvinall

JUVINALL: Machine Designp754b2 W-604