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JUVINALL: Machine DesignFig. 1-1a W-1
JUVINALL: Machine DesignFig. 1-2 W-2
JUVINALL: Machine DesignFig. 1-3a W-3
JUVINALL: Machine DesignFig. 1-3b W-3
JUVINALL: Machine DesignFig. 1-3c W-3
JUVINALL: Machine DesignFig. 1-4 W-4
R
F
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
JUVINALL: Machine DesignFig. 1-6 W-6
n = 1000 rpm
T = 10 N • mm
�
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
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
JUVINALL: Machine DesignFig. 1-9 W-9
0.2d
Rim
Arm
Hub
0.8d d
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
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
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
JUVINALL: Machine DesignFig. 1-13 W-14
g = 9.81 m/s2
5 mm
30mm
1 N
m
JUVINALL: Machine DesignFig. P1.18 W-15
JUVINALL: Machine DesignFig. P1-23 W-16
a = 5 ft/s2
g = 32.2 ft/s2F
Pulley
JUVINALL: Machine DesignFig. P1-26 W-17
V = 5 ft /sm = 5 lb
R = 3 in.
JUVINALL: Machine DesignFig. P1-29 W-18
I = 10 A
Outputshaft
t = 2 hrn = 1000 rpmT = 9.5 N • m
V = 110 V +–
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
JUVINALL: Machine DesignFig. P1-49 W-19
55 mph
2.64 axle ratio
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
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
JUVINALL: Machine DesignFig. 2-3 W-22
A
X
X
RT
RT
RT
RT – T
RT – T
T
T
RTA
RTA
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
JUVINALL: Machine DesignFig. 2-5 W-24
A
AF F
(a) (b)
a
F
F
Fa
SectionAA plane
Fixedsupport
(bending moment)
JUVINALL: Machine DesignFig. 2-6 W-25
(a)
Fa
b
F
a
(b)
F
Fb (torque) F (shear force)
JUVINALL: Machine DesignFig. 2-7 W-26
F32 = 40 lb
H12
F42
V12
30°
1
1
in.12
2
1 in.
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
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
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
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
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
d
F
FF
F
JUVINALL: Machine DesignFig. 2-13 W-31
m
2b
b
b
d
a
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
7
JUVINALL: Machine DesignFig. 2-15 W-33
JUVINALL: Machine DesignFig. 2-16 W-34
w lb/ft
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)
JUVINALL: Machine DesignFig. 2-18 W-36
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
JUVINALL: Machine DesignFig. P2.2 W-38
gWall channel, C
2 in.
A
B
Density = �
Density = �r =
1.25 in.
r =1.25 in.
JUVINALL: Machine DesignFig. P2.3 W-40
1500 N 1500 N
1000 mm
45°
45° 45°
45°
B
D
C
A
JUVINALL: Machine DesignFig. P2.4 W-39
A
B
125 N
1000 N
JUVINALL: Machine DesignFig. P2.6 W-41
10 in.
Motor1 hp
1800 rpmGear box
Directionof rotation
Blower6000 rpm
JUVINALL: Machine DesignFig. P2.7 W-42
50 mm
50 mm
Clockwiserotation
Forwardair velocity
A
B
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
JUVINALL: Machine DesignFig. P2.9 W-44
Engine is attachedto aircraft structure here.
Engine
Reduction gear,ratio = 1.5
Propeller
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
600400
330 R330 R
40 R
100 R
800 N160
JUVINALL: Machine DesignFig. P2-11 W-46
Bevel gearreducer
Attachesto motor
Attachesto load
600 rpm1800 rpm
JUVINALL: Machine DesignFig. P2-12 W-47
100 mm
100 mmA
BC
D
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
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
Mixing paddle
g
JUVINALL: Machine DesignFig. P2-15 W-49
Motor
Radialflow
Directionof rotation
Mass of mixersystem = 50 kg
200 mm
A B
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
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°
300200
JUVINALL: Machine DesignFig. P2-18 W-53
100 N
A B
30050 N140
200
100 N
A B
12-in.pulley radius
JUVINALL: Machine DesignFig. P2-19 W-54
Cable
Cable
100 lb
100 lb
48 in. 12 in.
27 in.
Motorattaches
to this endof shaft
6040
50
JUVINALL: Machine DesignFig. P2-20 W-55
Fa = 1000 N
Ft = 2000 NFr = 600 N
A B
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
8020
40
20
30
JUVINALL: Machine DesignFig. P2-22 W-57
Fa = 200 N
200 N
Fr = 400 N
A B
Ft = 1000 N
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
L
Section on A-A
Key
JUVINALL: Machine DesignFig. P2.24 W-59
Rb
r
A
A
F
t
t/2
dD
F
JUVINALL: Machine DesignFig. P2-25 W-60
t
d
Total gas force = F
JUVINALL: Machine DesignFig. P2-26 W-61
a2aa
R
A B
L
F
L
A
L
ttf
JUVINALL: Machine DesignFig. P2-27 W-62
P Pd D
d D
JUVINALL: Machine DesignFig. P2-28 W-63
E
A
B
C
D
JUVINALL: Machine DesignFig. P2-29 W-64
k
k
kk
a
100 N
a
F F
JUVINALL: Machine DesignFig. P2-31 W-65
P
t '
t '
Rivet diameter = 10 mm
t
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
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
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
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
Se �f
E
JUVINALL: Machine DesignFig. 3-5 W-70
Str
ess
�
0
Strain �
Se
Sy
Su
F
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
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
JUVINALL: Machine DesignFig. 3-8 W-73
Distance fromquenched end
(b)
(a)
Roc
kwel
l C h
ardn
ess
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
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
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
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
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
JUVINALL: Machine DesignFig. 4-2 W-77
3
1
5
(b)(a) P
P
4
3
1
25
6
3
1
3
P
P
JUVINALL: Machine DesignFig. 4-3 W-78
2
PP
JUVINALL: Machine DesignFig. 4-4 W-79
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
(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
(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
(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
(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
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
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
JUVINALL: Machine DesignFig. 4-12 W-87
M
M M
M
h
b
h
h2
Centroidal axis
CGr = h
c =
dA = b d�
�
b
JUVINALL: Machine DesignFig. 4-13 W-88
(b)(a)
Loaded "curved beam"Unloaded "curved beam"
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
JUVINALL: Machine DesignFig. 4-15 W-90
(a)
Marked and unloaded
(b)
Loaded as a beam
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.
JUVINALL: Machine DesignFig. 4-17 W-92
M
V
M
V
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
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
�
� = 7.61 MPa0
� = 22.83 MPa
� = 32.61 MPa
JUVINALL: Machine DesignFig. 4-20 W-95
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
(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
2000 lb
JUVINALL: Machine DesignFig. 4-23 W-98
2 in.
1 in.
3 in. rad.
JUVINALL: Machine DesignFig. 4-24 W-99
"B" is at bottom of shaft, opposite "A"
Top of shaft
B
2 in.
A
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
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
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
y
y
xA
�1 = 57 ksi
�2 = –17 ksi
28°
x
JUVINALL: Machine DesignFig. 4-28 W-104
y
y
xA
� = 20 ksi
� = +37 ksi
� = –37 ksi
� = 20 ksi
17°
x
JUVINALL: Machine DesignFig. 4-29 W-105
–�
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
�1 + �22
�1 – �22
cos 2�
�1 – �22
sin 2�
0
2
JUVINALL: Machine DesignFig. 4-31 W-107
+�
+�
�2
�1
2�
1
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
JUVINALL: Machine DesignFig. 4-33 W-109
+�
�max = 37
Principal circle
123
(57, 0)(0, 0)(–17, 0)+�
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
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
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
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
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
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
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
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
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
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
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)
––
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
JUVINALL: Machine DesignFig. 4-61 W-142
60 mm
10 mm dia.
20 mm
P = 400 kN
P
JUVINALL: Machine DesignFig. P4-2 W-120
FEDCBA
JUVINALL: Machine DesignFig. P4-10 W-121
di = 20 mm
do = 24 mm
�max = 100 mm
T
JUVINALL: Machine DesignFig. P4-11 W-122
b
2rT
T
T
T
JUVINALL: Machine DesignFig. P4-18 W-123
M M
h
r
b
JUVINALL: Machine DesignFig. P4-19 W-124
4 in.200 lb
200lb
1-in.-dia round rod
3 in.
JUVINALL: Machine DesignFig. P4-21 W-125
A
P Q
A60
70,000 N
40 80
120
JUVINALL: Machine DesignFig. P4-23 W-126
h
X
b
a
c
F
JUVINALL: Machine DesignFig. P4-24 W-127
2 in.13
in.16
3in.16
3 in.4
3in.16
1 in.
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
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
JUVINALL: Machine DesignFig. P4-29 W-129
8 in.
in.3
in.
in.
12
12
in.12
38
JUVINALL: Machine DesignFig. P4-30 W-130
5
5 5
5 50
40
12 kN
L2
Cement L2
JUVINALL: Machine DesignFig. P4-34 W-132
100 mm
250 mm
200 mm
25-mm-dia. roundrod bent into crank
1000 N
1 in.
6-in. dia.
1-in. dia.shaft
Motor
1000-lbbelt tension
3000-lbbelt tension
JUVINALL: Machine DesignFig. P4-36 W-133
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
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
A
JUVINALL: Machine DesignFig. P4-41 W-135
JUVINALL: Machine DesignFig. P4-46 W-136
y x
18 45
30
JUVINALL: Machine DesignFig. P4-49 W-139
Free surface, �3 = 0
20 ksi
30 ksi
JUVINALL: Machine DesignFig. P4-52 W-140
100350
75
JUVINALL: Machine DesignFig. P4-52 W-141
5000 N5000 N 30 mm 200 mm
15 mm25 mm
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
JUVINALL: Machine DesignFig. P4-55 W-138
5000 N 5000 N50 mm 100 mm
15 mm
25 mm
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
JUVINALL: Machine DesignFig. 5-1 W-144
(a) (d) (e)(b) (c)
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
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
JUVINALL: Machine DesignFig. 5-4 W-147
+�/2
x
y
0+�
�2
�y
�x
�xy
�1
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
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)
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
JUVINALL: Machine DesignFig. 5-8 W-151
+� /2
120°
240°0°
34°
+0.00185–0.00075
+0.0004
�2 = –0.001 �1 = +0.0020
+�
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)
+�
+�
JUVINALL: Machine DesignFig. 5-10 W-153
+2600 �m/m
+450 �m/m
–200 �m/m
(a)
(b)
�0 = +2600
�90 = +450
�45 = –200
�0 = +2600
�90 = +450�2 = –510
�1 = +3560
�45 = –200
JUVINALL: Machine DesignFig. 5-11 W-154
29°
119°
JUVINALL: Machine DesignFig. 5-12 W-155
+� /2
0°
45°
90°
2600
–510 3560
+�–200
450058°
+�
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
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
0 ∆Deflection
Area = U'
Area = U
Area = dU
dQ
JUVINALL: Machine DesignFig. 5-15 W-160
QLoad
Area = dU'
JUVINALL: Machine DesignFig. 5-16 W-161
L/2 P/2P/2
x dx
L
P
b
h
JUVINALL: Machine DesignFig. 5-17 W-162
200 mm 2500 N2500 NL = 400 mm
P = 5000 N
b = 25 mm
h = 50 mm
JUVINALL: Machine DesignFig. 5-18 W-163
L
P
h
bx
c
a
y
Q
JUVINALL: Machine DesignFig. 5-19 W-164
F
h
b
V
F
F
P M
F
R
R
�
2R
�
�R – R cos �
(a) (b)
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
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)
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
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
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
F
JUVINALL: Machine DesignFig. 5-22 W-170
3 m
10 m
ya
Point of zerodeflection
1.2 m
500 kg mass
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
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.
Slenderness ration Le /�
10 1000.0001
0.001
0.010
ScrE
0.100
JUVINALL: Machine DesignFig. 5-25 W-173
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)
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.
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
JUVINALL: Machine DesignFig. 5-29 W-177
80,000 N 80,000 N
D
1 m
SF = 2.5Sy = 689 MPaE = 203 GPa (steel)
JUVINALL: Machine DesignFig. 5-30 W-178
80,000 N 80,000 N
D
200 m
SF = 2.5Sy = 496 MPaE = 71 GPa (aluminum)
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
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
JUVINALL: Machine DesignFig. 5-33 W-180A
Beam
Triangle
Quadrilateral
Tetrahedron
Pentahedron
Hexahedron
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)
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
JUVINALL: Machine DesignFig. 5-36 W-180D
�
3 3'
F (7)3x
�3x
F (7)
A, E
L
3y
F3
6
�
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
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
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
(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
JUVINALL: Machine DesignFig. P5-4 W-181
�120 = +625
�240 = +300
�0 = +950
JUVINALL: Machine DesignFig. P5-9 W-183
�0 = –300
�135 = –380
�270 = –200
�90 = –300
�45 = –380
�0 = –200
Gage readings Equivalent rosettes
JUVINALL: Machine DesignFig. P5-14 W-182
k = 5 N/mm
A
B
C
100 mm
100 mm
100 mm
F
F
F
JUVINALL: Machine DesignFig. P5-15 W-184
200 mm
25 mm-dia. steel
1000 N
100 mm
A
JUVINALL: Machine DesignFig. P5-16 W-185
d = 30d = 50 d = 40
4 kN
2 kN100 200 150
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.
JUVINALL: Machine DesignFig. P5-19 W-186a
w = 200 lb/in.
d
5 in. 15 in. 5 in.
0.75d 0.75d
JUVINALL: Machine DesignFig. P5-20 W-187
a
a F
F
b
JUVINALL: Machine DesignFig. P5-21 W-188
P
R
JUVINALL: Machine DesignFig. P5-22 W-189
F
b
h
2
b2
L
JUVINALL: Machine DesignFig. P05-23 W-190
5 kN
S
500 mm
300 mm
JUVINALL: Machine DesignFig. P5-27 W-191
2
1 1
2
1 m
0.7 m
1 m0.7 m
Boom
12 mm-dia. tie-rod
6 kN
JUVINALL: Machine DesignFig. P5-29 W-192
JUVINALL: Machine DesignFig. 6-2 W-194
2w
2c
t
P
P
(a) Center crack
w
t
P
P
(b) Edge crack
c
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.
JUVINALL: Machine DesignFig. 6-4 W-196
P
P
a2c
2w
t
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
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
+�
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
+�
+�
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
JUVINALL: Machine DesignFig. 6-9 W-201
Principal plane
Principal planes
Octahedral plane
+�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
+�
+�
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
JUVINALL: Machine DesignFig. 6-12 W-204
+�2
+�1SutSuc
Sut
Suc
0
Shear diagonal
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
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
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
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
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
Freq
uenc
y p(
x)
Quantity x0 � x1
�1
�1 < �2 < �3
�2
�3
x2
JUVINALL: Machine DesignFig. 6-18 W-210
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
% 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
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
JUVINALL: Machine DesignFig. P6-13 W-214
�1 = 200 MPa
�2 = 100 MPa
�2
�1 �1 = 150 MPa
�2 = –100 MPa
�2
�1 ba
JUVINALL: Machine DesignFig. P6-23 W-215
�x �x = 50 MPa
Sy = 500 MPa
�xy = 100 MPa
�xy
k
JUVINALL: Machine DesignFig. 7-1 W-216
c
k
m
(b)(a) (c)
k
m
m
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
�
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
d
L /2
L /2
2d
JUVINALL: Machine DesignFig. 7-4 W-219
(b)
d
L
(a)
�d2
4Area = A =
L
Bumper ofcross section A;volume = AL
h
JUVINALL: Machine DesignFig. 7-5 W-220
W
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
100-mmdia
120-mmdia
20-mmdia
JUVINALL: Machine DesignFig. 7-7 W-222
20 mm20 mm
250 mm
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
JUVINALL: Machine DesignFig. 7-8 W-224
Ki = 1.5
Ki = 1.5
d
JUVINALL: Machine DesignFig. 7-9 W-225
Ki = 1.5
Ki = 3
Ki = 1.5d
d2
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
JUVINALL: Machine DesignFig. 7-10 W-229
K = 1.55
K = 4
Dropweight
24 mm dia.
K = 1.4
30 mm dia.
JUVINALL: Machine DesignFig. 7-11 W-227
(a)
Axial hole
(b)
"Very long"
K = 2
K = 21-in dia.
JUVINALL: Machine DesignFig. 7-13 W-232
0.1-in dia. hole
Steel cableA = 2.5 in.2
E = 12 × 106
JUVINALL: Machine DesignFig. P7-2 W-228
JUVINALL: Machine DesignFig. P7-5 W-228
K = 5000 N/mmL = 5 m
v = 4 km/hr m = 1400 kg
Rope
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
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.
JUVINALL: Machine DesignFig. 8-2 W-234
Small region behaves plastically
Main body behaves elastically
0.300"
C
R
110-Volts AC
Flexiblecoupling
JUVINALL: Machine DesignFig. 8-3 W-235
Weights
Revolutioncounter
Test specimen
9 "78
Motor
++
++
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
++++++
++++++
++++
++
++
+++++++++++
++++++++++++
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
'
'
''
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
Actual maximum stressCalculated maximum
stress (Mc /I )
JUVINALL: Machine DesignFig. 8-7 W-239
MM
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
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'
'' '
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
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
–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
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
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)
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
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
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
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
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
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
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
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
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
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)
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'
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
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
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
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
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)
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
(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
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
JUVINALL: Machine DesignFig. P8-28 W-267
24 mm 24 mm20 mm
2-mm rad. 0.8-mm rad.
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.
JUVINALL: Machine DesignFig. P8-37 W-268a
1
0.050 in.
0.191-in. rad.
0.125-in. dia.
2 in.
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
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
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.
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
JUVINALL: Machine DesignFig. P8-46 W-268f
Tors
ion
stre
ss (
ksi)
0
–10
–20
–30
10
20
30
30 seconds
JUVINALL: Machine DesignFig. 9-1 W-269a
++
+
+
+
++
+
++
+
Electrolyte
Fe2+ ions in solution
Iron electrode with surplus of electrons
~ ~ ~ ~
~~
~~
~~~
~~ ~
JUVINALL: Machine DesignFig. 9-2 W-269b
Electrolyte
Exposed iron (anode or cathode)
Plating, as tin or zinc (cathode or anode)~ ~~ ~~~ ~
~~~~ ~~ ~ ~ ~
~~ ~
~~
JUVINALL: Machine DesignFig. 9-3 W-269d
Electrolyte
~~
~
~~ ~
~~
~~~~
~~
~
A B
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
JUVINALL: Machine DesignFig. 9-5 W-269f
Insulated copper wire
+–
Steel tank
Steel
Rust particles Rust particles
(a)
Rust begins at center of drop
(b)
"Crevice corrosion"
JUVINALL: Machine DesignFig. 9-6 W-269g
Steel Steel
Steel bolt and nut
Nonporous, pliableelectrical insulator
JUVINALL: Machine DesignFig. 9-7 W-270
Aluminum plates
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
JUVINALL: Machine DesignFig. 9-9 W-272
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
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
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
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
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
–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
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
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
JUVINALL: Machine DesignFig. 9-19 W-282
Hard-bronze bearingalloy spherical seat
10 mm
2000 N
Hardened-steel sphere
10.1 mm
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
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
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)
–
JUVINALL: Machine DesignProb. 9-1 W-269
RivetsTotal exposed area = 100 cm2
Metal platesTotal exposed area = 1 m2
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
Drain plug(steel)
Insert rod(magnesium)
Oil
Crankcase(steel)
JUVINALL: Machine DesignProb. 9-8d W-287
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
Locking plateArm
Geneva wheel
JUVINALL: Machine DesignProb. 9-20 W-288
100-mmradius
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
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�
Nut tolerance zone
Basic profile(as shown inFig. 10.2)
Screw
Basic profile
Screw tolerance zone
JUVINALL: Machine DesignFig. 10-3 W-291
Nut
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
a
JUVINALL: Machine DesignFig. 10-5 W-293
(c)(b)(a)
Force F
dc
Weight
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
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 ��
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
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
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
JUVINALL: Machine DesignFig. 10-12 W-300
Clamped member
BoltNut
JUVINALL: Machine DesignFig. 10-13 W-301
Pilot surfaceof bolt
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
Flat washer
(a) Screw (b) Bolt and nut (c) Stud and nut (d) Threaded rod and nuts
JUVINALL: Machine DesignFig. 10-15 W-303
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
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
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
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
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.)
JUVINALL: Machine DesignFig. 10-21 W-310
(b)(a)
(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.)
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
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
(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
(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
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 –
Conical effectiveclamped volume
(Hexagonal bolthead and nut)
30°
JUVINALL: Machine DesignFig. 10-28 W-317
d2
d3
d1
g
d
(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
JUVINALL: Machine DesignFig. 10-30 W-319
Pillow blockRotating
shaft
Metric(ISO) screw
9 kN
F
F2
F2
F2
F2
(a) (b)
Normal load, carried byfriction forces
Overload, causing shear failure
F
JUVINALL: Machine DesignFig. 10-31 W-320
150
150500
400
100
24 kN24 kN
150
D
A
D
E
JUVINALL: Machine DesignFig. 10-32 W-321
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
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
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
'
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
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
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
JUVINALL: Machine DesignFig. P10-09 W-330
5 in.
1/2 in. Acme threaddc = 5/8 in.
Fe = 0 to 8,000 lbkc = 6kb
Fe
Fe
JUVINALL: Machine DesignFig. P10-17 W-329
JUVINALL: Machine DesignFig. P10.26 W-331
(1)
1000 N
Springwasher
1000 N
(2)
1000 N1000 N
AA
Spring washer
JUVINALL: Machine DesignFig. P10-28 W-332
JUVINALL: Machine DesignFig. P10-39 W-333
280 mm
140 mm
230 mm
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
JUVINALL: Machine DesignFig. P10-44 W-335
22
22
22
22
22
22
22
22
22
22
22
22
22 222222
JUVINALL: Machine DesignTable 10-4 W-306
JUVINALL: Machine DesignFig. 11-1 W-336
Before setting
After setting
Full tubular
Bifurcated (split)
Metal-piercing
JUVINALL: Machine DesignFig. 11-2 W-337
(c)Compression
(a)Semitubular
(b)Self-piercing
JUVINALL: Machine DesignFig. 11-3 W-338
"Built-up" lightweight structure
Acute corner
Back (blind) sidenot accessible
Back (blind) side not accessible
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
(b) (c)(a)
JUVINALL: Machine DesignFig. 11-5 W-340
60�
JUVINALL: Machine DesignFig. 11-6 W-341
(a) (c) (d)(b)
45�60�
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
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
=
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
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
�a
(ksi
)
�m (ksi)190 50 62
13.6
JUVINALL: Machine DesignFig. 11-11 W-346
= = 0.5�a�m
3060
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
F
JUVINALL: Machine DesignFig. P11-4 W-348
15 mm
Weld length = 90 mmSy = 400 MPaSF = 3E70 series weld
F
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.
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
4 in.
3 in.
JUVINALL: Machine DesignFig. P11-12 W-351
4000lb
Note: There are two 4 in. welds.
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
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
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
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
JUVINALL: Machine DesignFig. 12-5 W-356
JUVINALL: Machine DesignFig. 12-6 W-357
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
JUVINALL: Machine DesignFig. 12-8 W-359
(a)Ls = (Nt + 1)d
(c)Ls = (Nt + 1)d
(b)Ls = Nt d
(d)Ls = Ntd
(b)(a)Contouredand plate
(d)(c)
JUVINALL: Machine DesignFig. 12-9 W-360
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
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.
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
� 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
� 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
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
� 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
JUVINALL: Machine DesignFig. 12-17 W-368
Without presetting
Load stress
Load stressplus residualstress
With presetting
–�
0
+�
�resid from presetting
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
� 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
=
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
F
JUVINALL: Machine DesignFig. 12-21 W-371
(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
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
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)
ClipsShackle (permitssmall fluctuationsin spring length)
Fixed pivot
Fixed pivot
JUVINALL: Machine DesignFig. 12-25 W-375
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
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
D
a
F
d
F
JUVINALL: Machine DesignFig. 12-28 W-378
Thickness = h
b
JUVINALL: Machine DesignFig. 12-29 W-379
FF
a
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
Belleville Wave Slotted Finger Curve Internally slotted(as used in automotive clutches)
JUVINALL: Machine DesignFig. 12-31 W-381
In series
JUVINALL: Machine DesignFig. 12-32 W-382
In parallel In series-parallel
JUVINALL: Machine DesignFig. 12-33 W-383
+ + + +
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
End attachedto door
Fixedend
Torsion bar
Center of gravityof 60-lb door
Door stop
JUVINALL: Machine DesignFig. P12-3 W-385
24 in.
110�
Deflection
Support
Spring
Retainer
Nut
Force
Forc
e
Threaded bolt
JUVINALL: Machine DesignFig. P12-11 W-386
Deflection
C
B
A
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
F
F = 45 to 90 lbDeflection = 0.5 in.D = 2 in.
JUVINALL: Machine DesignFig. P12-28 W-388
FSquared andground end
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
Key
Cam
Shaft
Stationary guide
Oscillating assembly
Roller follower
Spring
Adjusting nut
Cap screw
JUVINALL: Machine DesignFig. P12-35 W-390
Support
e
JUVINALL: Machine DesignFig. P12-37 W-392
F
Tire
Stationarysupport
Handle
Brakeshoe
Spring
Pin stops
Pivot A35 mm
Stationarysupport
JUVINALL: Machine DesignFig. P12-39 W-391
25 mm shaft
Torsion springs
Cable
Cable
110 mm dia.
110 mm dia.
JUVINALL: Machine DesignFig. P12-46 W-393
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
JUVINALL: Machine DesignFig. 13-2 W-396
(a) Hydrodynamic(surface separated)
(b) Mixed film(intermittent local contact)
(c) Boundary (continuousand extensive local contact)
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
�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)
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
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
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
JUVINALL: Machine DesignFig. 13-8 W-402
D
R
L
c
n
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
JUVINALL: Machine DesignFig. 13-10 W-404
Journal
Oil hole
W Partial bronzebearing
Oil level
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
JUVINALL: Machine DesignFig. 13-12 W-406
y
h Lubricant flow
Stationary bearing
Rotating journal
U
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
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
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
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
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
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
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
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
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.
JUVINALL: Machine DesignFig. 13-23 W-417
Oil hole
Steel backingBearing material
Axial groove
Oil
film
pre
ssur
e
JUVINALL: Machine DesignFig. 13-24 W-418
Groovedbearing
Oil inlet hole
Ungrooved bearing
2
Circumferentialgroove
L2L
D
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
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 = ?
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
JUVINALL: Machine DesignFig. 13-28 W-422
aa > b
bPads
RoRi
Runner
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.
JUVINALL: Machine DesignFig. P13-27 W-424
JUVINALL: Machine DesignFig. P13-29D W-425
4.5 kN
D = ? in.
R = ? in.n = 660 rpm
SAE ? OilTavg = ?°C
c = ? in.
L = ? L = ?
4
JUVINALL: Machine DesignFig. 14-1b W-426
3
(b)
Steps in assembly
21
(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)
Loadinggrooves
(a) Filling notch (loading groove) type
JUVINALL: Machine DesignFig. 14-3a W-428
(c) Double row
JUVINALL: Machine DesignFig. 14-3c W-428
(d) Internal self-aligning
JUVINALL: Machine DesignFig. 14-3d W-428
(e) External self-aligning
JUVINALL: Machine DesignFig. 14-3e W-428
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
JUVINALL: Machine DesignFig. 14-5 W-430
Addedstabilizing ring
(b) One-direction locating (c) Two-direction locating
JUVINALL: Machine DesignFig. 14-8 W-433
Bearing axis
Commonapex
Crowned roller body
Spherical roller head
Roller axis
(d) Idler sheave(unground bearing)
(e) Rod end bearing
JUVINALL: Machine DesignFig. 14-10 W-436
JUVINALL: Machine DesignFig. 14-10h W-437
(h) Integral spindle, shown with V-belt pulley
JUVINALL: Machine DesignFig. 14-11 W-438
dS dH
r
r
+
+
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
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
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
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
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%
Note spacers
JUVINALL: Machine DesignFig. 14-17 W-444
JUVINALL: Machine DesignFig. 14-18 W-445
F1
L1
JUVINALL: Machine DesignProb. 14-6 W-446
F2
2L1
F2
3L1
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
Gear Shaft Bearing
JUVINALL: Machine DesignProb. 14-19 W-449
JUVINALL: Machine DesignProb. 14-20 W-448
150-mm dia.
Gear120-mm dia.
1.2 kN
20°
B
A
300 mm
100mm
60mm
60mm
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
Right-angle gearing
Parallel gearing
JUVINALL: Machine DesignFig. 15-1 W-451
JUVINALL: Machine DesignFig. 15-2 W-452
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
JUVINALL: Machine DesignFig. 15-4 W-454
Involute curves
Base circle
Base pitch, pb
JUVINALL: Machine DesignFig. 15-5 W-455
�p
�g
Gearpitchcircle
Pinionpitchcircle
P (pitch point)c
dp
dp
JUVINALL: Machine DesignFig. 15-6 W-456
Pinionbasecircle
� (pressure angle)
�p
�g
Gearbasecircle
b
P
a
JUVINALL: Machine DesignFig. 15-7 W-457
Base circlePitch circle
Pitch circle
Pinion
a
Pc
fe
dg
b
�
�
Base circle
Gear
rp
rg
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
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
18
3632
30288064
4048
16
14
2022
2426
65
412
11
10
78
9
JUVINALL: Machine DesignFig. 15-10 W-460
Pinion
Rack
Circular pitch
p
JUVINALL: Machine DesignFig. 15-11 W-461
�
JUVINALL: Machine DesignFig. 15-12 W-462
Pitch circle
Base circle
�Base circle
Pitch circle Dedendumcircle
Addendumcircle
��
JUVINALL: Machine DesignFig. 15-14 W-464
Gear blank rotatesin this direction
Rack cutter reciprocates in a directionperpendicular to this page
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
P = 6 teeth/in.� = 20°�p�g
JUVINALL: Machine DesignFig. 15-16 W-466
= –3.0
rg
rp
c = 4 in.
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
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
rf
Fr
Ft
x
F
a
F
Constant-strenghparabola
JUVINALL: Machine DesignFig. 15-20 W-470
t
h
b
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
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
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
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
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
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
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
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
JUVINALL: Machine DesignFig. 15-29 W-478
Motor(input)
Driven machine(output)
p1
g1
g2
p2
a c
b
(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
(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 +
(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
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
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
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
JUVINALL: Machine DesignProb. 15-26 W-483
a
a
Motor
Driven machine
32T
24T To drivenmachine
1''
B
A
JUVINALL: Machine DesignProb. 15-27 W-484
90°2.0''
16T
1700-rpmmotor
100-lb.in.torque
(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
JUVINALL: Machine DesignProb. P15-47 W-485A
P2 P1
P2
S2
P1
S1
Input
Output
Arm
JUVINALL: Machine DesignProb. P15-50 W-485B
P1 P2
Input
S1 (100 teeth)
P2 (102 teeth)
P1 (101 teeth)
S2 (99 teeth)
Output
Arm
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
JUVINALL: Machine DesignFig. 16-1 W-487
(b) Rotated spur gear laminationsapproach a helical gear as laminationsapproach zero thickness.
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
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�
�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
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
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
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
Spiralangle
Circular pitch
Face advance
�
Meanradius
JUVINALL: Machine DesignFig. 16-10 W-496
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
�
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
JUVINALL: Machine DesignFig. 16-13 W-517
250 mm
Load
Motor
Rotation
140 mm
A
B
C
D140 mm
65mm
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
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
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
�S
JUVINALL: Machine DesignFig. 16-17 W-504
�R
A
P
P Fixed arm, A
RP (planet)
R (ring)
S (sun)
S
P
JUVINALL: Machine DesignFig. 16-18 W-505
Arm(input member)
Right axleLeft axle
P
P
RS
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
Fwt
Fwr
Fwa
Worm-drivingtorque
JUVINALL: Machine DesignFig. 16-20 W-507
Fgt
Fgr
Fga
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 �
�
JUVINALL: Machine DesignFig. 16-22 W-509
Vs
Vw
Vg Gearrotation
�
Worm
Gear
Worm rotation
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
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
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
c ≈ 6 in.
JUVINALL: Machine DesignFig. 16-27 W-514
Gear
Worm: hardened steelrpm =1200
Gear: Chill-cast bronze
Speed ratio, 11:1
Worm
JUVINALL: Machine DesignTable 16-1 W-501
p
b
JUVINALL: Machine DesignFig. P16-5 W-516
�
Pa
40 teeth 60 teeth
20 teethOutput
JUVINALL: Machine DesignFig. P16-08 W-515
24 teeth Input
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
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
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
Nw = 2Ng = 55
P = ?
JUVINALL: Machine DesignFig. P16-30 W-521
c = 8 in. Gear
Worm
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
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
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
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)
4-spline 6-spline 10-spline
(a) Straight-sided (b) Involute
16-spline
JUVINALL: Machine DesignFig. 17-4 W-526
JUVINALL: Machine DesignFig. 17-5a W-527
�stGravitationalforce, w
Mass, m
Shaft of spring rate k = w/�st
(a) Single mass
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
JUVINALL: Machine DesignFig. 17-5c W-527
�st
(c) Shaft mass only
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
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
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
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
JUVINALL: Machine DesignFig. 17-9 W-533
(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
JUVINALL: Machine DesignFig. 17-12 W-536
(a) Basic Oldham type (b) Modified type
JUVINALL: Machine DesignFig. 17-13 W-537
JUVINALL: Machine DesignFig. P17-1 W-538
20 in.
Flexible couplingMotor 0.25-in.-dia. shaft
JUVINALL: Machine DesignFig. P17-7 W-539
600 mm600 mm
50 kg
25-mm dia.
JUVINALL: Machine DesignFig. P17-11 W-540
40 in. 30 in.20 in.
120 lb80 lb
2-in.-dia. shaft
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
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
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.
Chain sprocket
JUVINALL: Machine DesignFig. P17-16 W-546
(a)
Stationary shaft
Clamping supports
Chain sprocket
(b)
Rotating shaft
Clamping supports
Drivingshaft
Drivenshaft
Provision foraxial movement
Ring elementsubjected to clamping
pressure, p
Friction liningmaterial
JUVINALL: Machine DesignFig. 18-1 W-547
dr
rri
ro
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
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
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
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
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
A'
�n
�
�
JUVINALL: Machine DesignFig. 18-8 W-554
O3
O3 O2
A
B
�'
�
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° – �
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
JUVINALL: Machine DesignFig. 18-10 W-556
O2
N
Pivot P
F
fN
�2
r f
r
�2
JUVINALL: Machine DesignFig. 18-12 W-557
P
f dN2 + f dN2
r
rf
f dN1
dN2
dN1
dN2
��
f dN2
f dN2
'
'
'
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
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
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
d�/2d�/2
P + dP P
Rotation
dNd�
JUVINALL: Machine DesignFig. 18-16 W-562
P1
s
P2
Band of width = b
Rotation
JUVINALL: Machine DesignFig. 18-17 W-563
�
a
F
c
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
Pads of diameter = 60 mm
125 mm
320 mmpmax = 500 kPaf = 0.30
JUVINALL: Machine DesignFig. P18-12 W-567
4m/s
1000 kg
JUVINALL: Machine DesignFig. P18-14 W-565
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
JUVINALL: Machine DesignFig. P18-17 W-569
Rotation
F = 1500 N
200 mm340 mm
400 mm 500 mm
JUVINALL: Machine DesignFig. P18-22 W-570
Rotation
A
F
240 mm
250 mm 320 mm
400 mm
150 mm
JUVINALL: Machine DesignFig. P18-23 W-571
500 mm
Spring
300 mm400 mm
350 mm
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
JUVINALL: Machine DesignFig. P18-31 W-573
Rotation
F = 300 N
500 mm
�
JUVINALL: Machine DesignProb. 18-33 W-574
55
258°
240
F
75
72
370
JUVINALL: Machine DesignProb. 18-34 W-575
Wt.
sa
c
270°
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
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.
JUVINALL: Machine DesignFig. 19-4 W-579
2�≈ 36°
dNdN2
dN/2sin �
(a) (b)
JUVINALL: Machine DesignFig. 19-5 W-581
Tension-carrying cords
Fabric cover
Rubber
JUVINALL: Machine DesignFig. 19-7 W-583
p
�r Pitchcircle
(a)
rc
p
(b)
A
B
AB
rc r
Chordal rise, r – rc
JUVINALL: Machine DesignFig. 19-9 W-584A
Pitch p
(a)
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
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
Turbine
Fluidcirculation
Inputshaft Output
shaft
Impeller
Reactor
JUVINALL: Machine DesignFig. 19-12 W-585
Turbine
Inputshaft Output
shaft
Impeller
One-wayclutchReactor
JUVINALL: Machine DesignFig. 19-13 W-586
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
JUVINALL: Machine DesignFig. P19-3 W-588
�
�
�
�
�2
c
�1r2
r1
JUVINALL: Machine DesignFig. P19-4 W-589
A
B
C
D
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
JUVINALL: Machine DesignFig. P19-15 W-591
Electric motorn = 1780 rpm
55% rated power
Fluid coupling—performance curves—
Fig. 19.11
Drivenmachine
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
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
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
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
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
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
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
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
JUVINALL: Machine DesignFig. B-1 W-601
h
h
b
d
b
Rectangle
Triangle
Circle
d
Hollow circle
y
y
di
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
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
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
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
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
–PL
P
P
�
�max
V = P
M = –PL
+
0
0
–
V
M
JUVINALL: Machine DesignFig. D-1(1) W-607
Lx
JUVINALL: Machine DesignFig. D-1(2) W-607
V = P
M = –Pa
+
0
0
–
V
M
–Pa
P
P
b
�
�max
xa
�max
M = –wL2/2
+
0
0
–
V
M
JUVINALL: Machine DesignFig. D-1(3) W-608
wLV = wL
wL2
2
w
x
L
JUVINALL: Machine DesignFig. D-1(4) W-608
0
0
–
V
M
–Mb
–Mb
Mb
P�
�max
xL
+
+
0
0
–V
M
JUVINALL: Machine DesignFig. D-2(1) W-609
�
Lx
P2
LP
2
P
P/2
–P/2
PL/4
2
+
+
0
0
–
V
M
JUVINALL: Machine DesignFig. D-2(2) W-609
�
Lx
b
PaL
PbL
P
Pb/L
Pab/L –Pa/L
a
+
+
0
0
– –
V
M
JUVINALL: Machine DesignFig. D-2(3) W-610
Lx
w
wL
wL /2
wL2
2
2wL2
wL2
+
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
+
+
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
0
–
–
0
V
M
JUVINALL: Machine DesignFig. D-2(6) W-611
a a
L
x
M0
M0
x'
b
�max
aM0
M0
aM0
�
–
JUVINALL: Machine DesignFig. D-3(1) W-612
�
+
+
0
0
–
–
V
M
PL8
Px
L
–
–
–
PL8
PL8
– PL8
PL8
P2
P2
P2
P2
L2
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)
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
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
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
JUVINALL: Machine Designp754 b1 W-???
JUVINALL: Machine Designp754b2 W-604