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JUVINALL: Machine Design Fig. 1-1a W-1
JUVINALL: Machine Design Fig. 1-2 W-2
JUVINALL: Machine Design Fig. 1-3a W-3
JUVINALL: Machine Design Fig. 1-3b W-3
JUVINALL: Machine Design Fig. 1-3c W-3
F
R
JUVINALL: Machine Design Fig. 1-4 W-4
0
(a)
1 Force (N)
Torque (N • mm)
10
0
0.1
0
Cam rotation (rad)
1 Follower displacement (mm)
(b)
(c)
JUVINALL: Machine Design Fig. 1-5 W-5
0
n = 1000 rpm
T = 10 N • mm
JUVINALL: Machine Design Fig. 1-6 W-6
10
Actual torque requirement
Crank torque (kN • m)
8
6
4
2 3 0 0
Crank angle (rad)
JUVINALL: Machine Design Fig. 1-7 W-7
2
10
Crank torque (kN • m)
Actual torque requirement 8 Average torque 6
4 2 0 0
3
Uniform torque supplying equal energy
Crank angle (rad)
2
JUVINALL: Machine Design Fig. 1-8 W-8
Hub
Rim
0.8d d
Arm 0.2d
JUVINALL: Machine Design Fig. 1-9 W-9
Vehicle road load power (hp)
160
120
80
40
0 0
20
40
60 80 Vehicle speed (mph)
JUVINALL: Machine Design Fig. 1-10 W-11
100
120
Engine output power (hp)
160
120
80
40
0 0
1000
2000 3000 Engine speed (rpm)
JUVINALL: Machine Design Fig. 1-11 W-12
4000
5000
1.3 Specific fuel consumption of engine (lb/hp • h)
1000 rpm 1.2 1.1
1500 rpm
1.0 2000 rpm 0.9
2500 rpm 3000 rpm 3500 rpm
0.8
4000 rpm
0.7 0.6 0.5 0.4 20
40
60
80 100 120 Engine output power (hp)
JUVINALL: Machine Design Fig. 1-12 W-13
140
160
180
JUVINALL: Machine Design Fig. 1-13 W-14
5 mm 1N
30 mm
g = 9.81 m /s 2 m
JUVINALL: Machine Design Fig. P1.18 W-15
a = 5 ft/s2
F
g = 32.2 ft/s2
JUVINALL: Machine Design Fig. P1-23 W-16
Pulley R = 3 in.
V = 5 ft /s m = 5 lb
JUVINALL: Machine Design Fig. P1-26 W-17
I = 10 A V = 110 V
Output shaft
+ –
n = 1000 rpm T = 9.5 N • m
t = 2 hr
JUVINALL: Machine Design Fig. P1-29 W-18
Crankshaft torque
Curve B (half-wave rectified sinusoid) Curve A (linear variation) T max
0
0.5 1.0 1.5 Crankshaft rotation, revolutions
JUVINALL: Machine Design Fig. P1-42 W-18A
2.0
55 mph
2.64 axle ratio
JUVINALL: Machine Design Fig. P1-49 W-19
3000 lb
50 in.
V = 60 mph CP
CG
20 in.
25 in.
Ft
Wr
100 in.
JUVINALL: Machine Design Fig. 2-1 W-20
Fd
Wf
W = 3000 lb Engine power, 96 hp Fi = 467.5 lb
Fd = 100 lb
Ft = 567.5 lb Wr = 1618.5 lb
JUVINALL: Machine Design Fig. 2-2 W-21
Wf = 1381.5 lb
RT A
X
RT – T T
RT – T
T A
RT RT RT
X
JUVINALL: Machine Design Fig. 2-3 W-22
RT A
T = 3000 lb.in. (input)
RT – T = 5333 lb.in.
Transmission in low gear R = 2.778
RT = 8333 lb.in. (output) 3 in.
5333 lb.in. (a)
I 3000 lb.in.
2 in. 5 in. 2 in.
1087 lb
I
1087 lb II
A 1087 lb
D
(b)
IV
II
2667 lb 2864 lb
2667 lb 8333 lb.in.
2864 lb 4444 lb
III (d)
B
4444 lb 1087 lb
2864 lb
C
(c) IV
JUVINALL: Machine Design Fig. 2-4 W-23
III
F
F
F
A a F Fa A (a)
(b)
JUVINALL: Machine Design Fig. 2-5 W-24
a b F Section AA plane Fixed support
(a) F Fa (bending moment)
Fb (torque) F (shear force)
(b)
JUVINALL: Machine Design Fig. 2-6 W-25
F32 = 40 lb
1
2
1 in. 2
1 H12 V12 1 in.
30°
F42
JUVINALL: Machine Design Fig. 2-7 W-26
F32 = 40 lb 0
2 1 F32 = 40 lb F12
F42 F12 F42
Force polygon for link 2
JUVINALL: Machine Design Fig. 2-8 W-27
0 Fb (bone 0.5 in. compression force)
3 in.
Ft (tendon force)
10 lb 10 lb pinch
Ft = 60 lb
Fb = 55 lb Force polygon for finger
JUVINALL: Machine Design Fig. 2-9 W-28
V
+
V
Positive shear force M
+
M
Positive bending moment
w
F R1 Fb L
V
R1
R2 a
b L
Fa L
R2
wb 2 2L
a
b L
+wb2/2L
Fb + L
wb (a + b/2 ) L
b2 2L
V Fa – L
+
2 wb2 a+ b 2L 4L
Fab L
M
M (a)
(b)
Single concentrated load
Distributed load
JUVINALL: Machine Design Fig. 2-10 W-29
–
wb (a + b/2 ) L
Critical section
2667 lb
2864 lb 2667 lb
III
C
B 4444 lb 1087 lb 2864 lb
III
Loads IV
C
B
4444 lb 2 in.
IV
1087 lb 5 in.
2 in.
+ 1580 lb Shear
V – 1087 lb –2864 lb 2174 in..lb
Moment
M
–5728 in..lb 5000 lb.in.
Torque
T
JUVINALL: Machine Design Fig. 2-11 W-29A
2864 lb 4444 lb T = 5000 lb.in.
IV M = 5728 lb.in.* C V = 1580 lb
JUVINALL: Machine Design Fig. 2-12 W-30
* Actually slightly less, depending upon the width of gear C
b F
2b
d
d
F
b
F
m
a
JUVINALL: Machine Design Fig. 2-13 W-31
F
Fork
Pin
Blade 4'
5 2
6
F
F
4' 5
1
2
1
4' 2 2
2 3
3
4
F
4
F
4' 3
3
1
1 2
2
7
JUVINALL: Machine Design Fig. 2-15 W-33
w lb/ft
JUVINALL: Machine Design Fig. 2-16 W-34
Spring in tension k1 = 10 lb/in. 10␦ 100 lb 100 lb
40␦ Spring in compression k2 = 40 lb/in.
(a)
JUVINALL: Machine Design Fig. 2-17 W-35
(b)
JUVINALL: Machine Design Fig. 2-18 W-36
Outer row Middle row
1
pi tc h
Inner row
Bottom strap
Left plate
Top Right strap plate
Top strap
Bottom strap
(a)
Outer row
Inner row Outer row
Inner row
1
pi tc h
Area
(c) (b)
bp Plate
s Plate
Strap
Bearing with plate Shear
bs
Bearing with strap Strap
(d)
(e)
1 strap
2 straps
3 Straps
d le p
r pa
6 7
th
th
a th
r pa
4
In n e
M id
O u te
5
Bearing with straps 8 Shear 9 Bearing with plate
Plate 1
2 (f)
JUVINALL: Machine Design Fig. 2-19 W-37
Wall channel, C
g
2 in. r= 1.25 in. A Density =
r= 1.25 in. B Density =
JUVINALL: Machine Design Fig. P2.2 W-38
1500 N
1500 N B 45°
C
45° 1000 mm
A
45°
D
45°
JUVINALL: Machine Design Fig. P2.3 W-40
A
1000 N B
125 N
JUVINALL: Machine Design Fig. P2.4 W-39
10 in.
Direction of rotation Motor 1 hp 1800 rpm Gear box
JUVINALL: Machine Design Fig. P2.6 W-41
Blower 6000 rpm
50 mm 50 mm
A
B Forward air velocity Clockwise rotation
JUVINALL: Machine Design Fig. P2.7 W-42
4:1 ratio gear reducer
Motor 1.5 kW 1800 rpm
Direction of rotation Connecting tube C Pump 450 rpm C' A A'
B'
B
JUVINALL: Machine Design Fig. P2.8 W-43
These units are attached to a fixed support.
Engine
Engine is attached to aircraft structure here. Reduction gear, ratio = 1.5 Propeller
JUVINALL: Machine Design Fig. P2.9 W-44
Vertical drive shaft
Z Rotation X
Mounting flange Y Z
Foward direction of boat travel
500 mm
X
Mx
Propeller rotation
Mz
My
Y 2:1 ratio bevel gears are inside this housing
150 mm
JUVINALL: Machine Design Fig. P2.10 W-45
Suggested notation for moments applied to mounting flange
800 N 160 40 R
330 R
330 R 100 R
400
600
JUVINALL: Machine Design Fig. P2-11 W-46
100 mm D A
C
100 mm B
1800 rpm
Bevel gear reducer
600 rpm
Attaches to motor
Attaches to load
JUVINALL: Machine Design Fig. P2-12 W-47
4 in.
8 in.
Output shaft
Rear bearings
Front bearings
Mountings
6 in.
Housing and gear-shaft assembly details
100 lb.ft
Reducer assembly
Output
6 in. dia. gear
Motor input torque 100 lb.ft 2 in. dia. pinion Front bearings
JUVINALL: Machine Design Fig. P2-13 W-48
Right-front wheel axle shaft–400 rpm
Engine 2400 rpm 100 lb.ft torque
24 in.
Y
A X
D
Left-front wheel axle shaft–400 rpm
12 in. C
B
Transmission 2.0 ratio
Y Front drive shaft–1200 rpm Rear drive shaft–1200 rpm
Rear axle (not part of free body) JUVINALL: Machine Design Fig. P2-14 W-51
X
Motor g Mass of mixer system = 50 kg A
B
Direction of rotation
Radial flow Mixing paddle 200 mm
JUVINALL: Machine Design Fig. P2-15 W-49
Mounting width = 75 mm to 150 mm Radial air flow
g
Fan
B Direction of rotation A
Mass of blower system = 15 kg
Motor
JUVINALL: Machine Design Fig. P2.16 W-50
Y 45 mm
D
30 mm
20 mm
FC
20°
Z B
Gear 1 50-mm dia.
A Shaft
FA C 20°
X Gear 2 24-mm dia.
JUVINALL: Machine Design Fig. P2-17 W-52
100 N A
100 N B
200
300
A
B 200
JUVINALL: Machine Design Fig. P2-18 W-53
300
140
50 N
12 in.
48 in.
Cable 27 in. 100 lb
Cable
12-in. pulley radius 100 lb JUVINALL: Machine Design Fig. P2-19 W-54
Fr = 600 N
Ft = 2000 N Fa = 1000 N
50 A
B
40
Motor attaches to this end of shaft
60
JUVINALL: Machine Design Fig. P2-20 W-55
Fr = 200 N
Ft = 1000 N Fa = 100 N
100 A
B
50
Pump shaft is coupled to this end of shaft
150
JUVINALL: Machine Design Fig. P2-21 W-56
Fr = 400 N
Ft = 1000 N
200 N
Fa = 200 N 40
30
A
B
20
80
JUVINALL: Machine Design Fig. P2-22 W-57
20
Fr = 500 N Ft = 1500 N Fa = 150 N 150 A
B
200
300
120
140
100 N
250 N
JUVINALL: Machine Design Fig. P2.23 W-58
A L F
t/2
b
R
Key
t
r
Section on A-A A
JUVINALL: Machine Design Fig. P2.24 W-59
F
t
d D
JUVINALL: Machine Design Fig. P2-25 W-60
Total gas force = F
a
2a
a d
JUVINALL: Machine Design Fig. P2-26 W-61
f
t
t B
A
d D
R
L
P
L
L P
d D F
A
JUVINALL: Machine Design Fig. P2-27 W-62
A
B E
C
D
JUVINALL: Machine Design Fig. P2-28 W-63
k
k
a
a
k
k 100 N
JUVINALL: Machine Design Fig. P2-29 W-64
P
t' t
F t'
Rivet diameter = 10 mm
JUVINALL: Machine Design Fig. P2-31 W-65
F
C Su = 66
Stress (ksi)
60
A 40
B
F (Fracture) Sy = 39 Se = 36
20 Slope = modulus of elasticity, E
0
0.2% offset Strain ⑀ (arbitary nonlinear scale)
JUVINALL: Machine Design Fig. 3-1 W-66
Su = 66 ksi
Stress (ksi)
60
C
D
Sy = 39 ksi
40 B A
F
Se = 36 ksi Hot-rolled 1020 steel
20
0 0
0
G 10 20
H 30 40
50
60
70 80 90 100 110 120 130 140 150 160 Strain ⑀ (%)
1.1 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 Area ratio R
0.1
0.2
0.3
0.4 0.5 Area reduction Ar
JUVINALL: Machine Design Fig. 3-2 W-67
0.6
Transition region
Elastic region
Plastic strain-strengthening region
200
True stress T (ksi (log))
⑀Tf = 0.92 115
100 80 60 40 30 20 T
10 3
=
T E⑀
(E
=
30
×
) si 3 k 0 1
4 5 6 7 8 0.1
15 m ( 0 = 1
T = Sy = 39 ksi
2
3
ks
0.2 i, m =
F
2)
⑀T T = 0
4 5 6 7 8 1.0 2 3 4 5 6 7 8 10 True strain ⑀T (% (log))
JUVINALL: Machine Design Fig. 3-3 W-68
2
3
4 5 6 7 8 100
True stress T (log)
"Ideal" material Curve I ( T = Se ≈ Sy ) Se2 Se1 Se3
Plastic line ( T = 0⑀Tm ) Curve II
Elastic line ( T = E⑀T ) True strain ⑀T (log)
JUVINALL: Machine Design Fig. 3-4 W-69
Su
Stress
F Sy Se
0
Se E
⑀f Strain ⑀
JUVINALL: Machine Design Fig. 3-5 W-70
1000
900
KB, ratio Su /HB
800 d D
2 0. 3 0. 4 0. 5 0. 6 0.
700
600
500 d = indentation dia. D = ball dia. 400 Steel 300
0
0.1
0.2 0.3 0.4 0.5 m, strain hardening exponent
JUVINALL: Machine Design Fig. 3-6 W-71
0.6
0.7
200 250 300
Diamond pyramid hardness (Vickers)
350 400 450 500 550 600 650 700
680 750 700 720
800
740 850 760 900 950
72
(0)
80
(10)
20 30 40 Rockwell C hardness
90 100 Rockwell B hardness
(110)
JUVINALL: Machine Design Fig. 3-7 W-72
50
60
70
60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300
Ultimate tensile strength (ksi)
150
100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540 560 580 600 620 640 660
Brinell hardness
100
Shore hardness 30 40 50 60 70 80 90 22 24 26 28 32 34 38 42 46 55 65 75 85 95
Rockwell C hardness
Distance from quenched end (b)
(a)
JUVINALL: Machine Design Fig. 3-8 W-73
1000 Diamond WC
Cermets W
Engineering alloys
Beryllium
Mg0 Steels Ni alloys
Cast irons
100
Cu alloys
Min. energy storage per unit volume Yield before buckling
Al alloys Common Cement rocks Mg alloys +
Sn
Lead
Ash Oak Pine
10 Mel
II to grain Epoxies
CFRP uniply Ti alloys GFRP
Brick etc
CFRP Laminates GFRP
Concrete
Youngs Modulus, E (GPa)
Zn alloys
Si C
Boron
Mo alloys
Glasses
Si3N3 Al203
Zr 02 Silicon Ge
Be0
Engineering ceramics
Engineering composites
Porous ceramics PMMA
PS
S = 0.1 E
Balsa
S = 10–4 E
PVC Nylons Wood products Polyester PP Ash Oak
Woods
1.0
Pine ⊥ to grain
0.1
PTFE
Balsa
S = 10–3 E
S = 10–2 E
Design guide lines
HDPE
Engineering polymers
LDPE
S =C E S 3/2 =C E
Polymers foams Hard butyl
Pu
Silicone
1
Buckling before yield
Elastomers S2 =C E
Cork
0.01 0.1
Max energy storage per unit volume
Soft butyl 10
100 Strength S (MPa)
JUVINALL: Machine Design Fig. 3-11 W-74
1000
10,000
10,000 Engineering ceramics
Diamond Si3N4 Sialons Al203
Si C
Zr02
B Mg0
Glasses
CFRP GFRP Uniply KFRP CFRP Be
1000 Engineering composites
Si
Ge
Steels Pottery
Al alloys Mg alloys
Strength S (MPa)
Parallel to grain
PS
Balsa Ash Oak Pine Fir Perpendicular to grain LDPE
Woods 10
Mel PVC Epoxies Polyesters HDPE PTFE
Soft butyl
Ni alloys Cu alloys
Lead alloys
Cement concrete
Porous ceramics
PU
Engineering polymers
Silicone
Balsa
Cast irons
Engineering alloys
PP
Wood products
Mo alloys
Stone, Zn rock alloys
Nylons PMMA
Ash Oak Pine Fir
W alloys
Ti alloys
GFRP Laminates KFRP
100
Cermets
Guide lines for minimum weight design
Elastomers
Polymers foams 1
Engineering alloys
Cork
S =C S 1/2 =C
S 2/3 =C 0.1 0.1
0.3
3
1 Density (Mg/m3)
JUVINALL: Machine Design Fig. 3-12 W-74a
10
30
10,000 Engineering ceramics
Porous ceramics Engineering alloys Engineering composites
SiC
1000
CFRP Uniply KFRP
Zr02
Glasses
Strength at temperature S (T) (MPa)
Si3N4
Tialloys
Mg alloys
Nylons PC
Polymides
PMMA
PP PVC
Woods
Compression
Brick etc.
GFRP
⊥ to grain
Mullites Ni alloys
Steels
CFRP Laminates
Zn alloys
⊥ to grain
Al203
GFRP
Al alloys
100
Mg0
Epoxies
PF
HDPE Polyesters
II to grain
PTFE LDPE Engineering polymers
10
Butyls
Ice
Silicones
Elastomers 1 T-Independent Yield strength
Polymer foams
Upper limit on strength at temperature
Range typical of alloy series
0.1
0
100
200
300 400 Temperature T (C)
JUVINALL: Machine Design Fig. 3-13 W-74b
600
800
1000
1400
Hardness (Rockwell C)
70 60 50 40 30 20 10 0
10
20 30 40 Distance from quenched end (mm)
JUVINALL: Machine Design Fig. P3-14 W-75
50
P
E
P 2
E
P 2 (a) Isometric view of tensile link loaded through a pin at one end and a nut at the other.
P
+
E
(b)
(c)
Enlarged view of element E
Direct view of element E
=
D
A=
P A
(d) Equilibrium of left half showing uniform stress distribution at cutting plane
+
Nut (e) View showing "lines of force" through the link
JUVINALL: Machine Design Fig. 4-1 W-76
D2 4
P
3 3
1
4
5
1 2
5 6
(a)
P
JUVINALL: Machine Design Fig. 4-2 W-77
(b)
2 3
3
P P 1
JUVINALL: Machine Design Fig. 4-3 W-78
P
P
JUVINALL: Machine Design Fig. 4-4 W-79
T E E (b) Enlarged view of element
T (a)
Positive shear
Isometric view E
Negative shear
E
(c)
Positive shear (d)
Direct view of element E
Shear sign convention
JUVINALL: Machine Design Fig. 4-5 W-80
Negative shear
T Torque axis Line "A" 1
2 2
3
p To b
Sid
T a
Maximum shear stress exists along this line. (a) Zero shear stress exists along all edges.
JUVINALL: Machine Design Fig. 4-6 W-81
F ro
e
nt
(b) Enlarged view of element 2
Neutral (bending) surface M
M (a) Entire beam in equilibrium max c
y
Neutral surface
c M
Transverse cutting plane (b) Partial beam in equilibrium
Neutral bending axis and centroidal axis
JUVINALL: Machine Design Fig. 4-7 W-82
(c) Typical cross sections
Neutral (bending) surface M
M (a) Entire beam in equilibrium Neutral bending axis and centroidal axis
max c
CG
CG
CG
y
M (b)
Neutral surface
Partial beam in equilibrium
(c) Typical cross sections
JUVINALL: Machine Design Fig. 4-8 W-83
CG
Hyperbolic stress distribution with increased stress at inner surface
Centroidal surface
CG co
M Neutral surface
(a) Initially straight beam segment
e ci
M
(b) Typical cross section
Neutral surface displaced distance "e " toward inner surface
Center of initial curvature (c) Initially curved beam segment JUVINALL: Machine Design Fig. 4-9 W-84
d b
c
Centroidal surface c' Neutral surface CG
co
y
c
ci
ro
a
d'
c
d
M
e
y
e
ri
rn
r
r M
Center of initial curvature
JUVINALL: Machine Design Fig. 4-10 W-85
rn
Centroidal axis Neutral axis
b 8
r
b 4
c
3.5 A
U or T
B
b
A
B c 3.0 Round or elliptical Values of K in Eq. 4.11: = K
Mc I
B
A B
A c
2.5 b 2
Trapezoidal
2.0 I or hollow rectangular
b 3 B
b 6 B
1.5
B
A
b
c A b
A r
Values of Ki for inside fiber as at A
1.0
Values of Ko for outside fiber as at B
I or hollow rectangular
0.5
U or T Round, elliptical or trapezoidal 0 1
2
3
4
5
6 Ratio r / c
JUVINALL: Machine Design Fig. 4-11 W-86
7
8
9
10
b
M
M
Centroidal axis
b
dA = b d
h
h
M
JUVINALL: Machine Design Fig. 4-12 W-87
M
c=h 2
r=h CG
(a)
(b)
Unloaded "curved beam"
Loaded "curved beam"
JUVINALL: Machine Design Fig. 4-13 W-88
dA
dA
b y
c
y0
Neutral axis
x
dA (M + dM)y/I
My/I
dx
V V
y M M + dM N.A. M
Enlarged view of beam segment
JUVINALL: Machine Design Fig. 4-14 W-89
(a)
(b)
Marked and unloaded
Loaded as a beam
JUVINALL: Machine Design Fig. 4-15 W-90
av = V/A max =
av = V/A
4 V/A 3
N.A.
max = N.A.
JUVINALL: Machine Design Fig. 4-16 W-91
3 V/A 2
V
V
M
M
JUVINALL: Machine Design Fig. 4-17 W-92
80,000 N
80
60 X
X 40
40,000 N
60
100
40,000 N 100
+40,000 N V –40,000 N
M
JUVINALL: Machine Design Fig. 4-18 W-93
dx
dx
dx
dA = 60dy 10–
dA = 60dy
dA = 60dy
10+
40 b = 60
b = 20
dA = 20dy
b = 20 (a)
(b)
JUVINALL: Machine Design Fig. 4-19 W-94
(c)
= 32.61 MPa
0
= 22.83 MPa = 7.61 MPa
JUVINALL: Machine Design Fig. 4-20 W-95
+ max yx
S
(a)
0
Marked eraser
x
y
+
S' yx (d) Mohr's circle
(b) Loaded eraser
y y x
x
x
x
y Direct view
Oblique view
S
S' S S S'
S'
Direct view
Oblique view
(c)
(e)
Enlarged view of element
Element subjected to max
JUVINALL: Machine Design Fig. 4-21 W-96
+ y y x T
T
#2
+
0
#1 x
(a)
(c) Mohr's circle
Marked eraser (for twisting)
1
2 y x
#2 #1
x y (b)
(d)
Enlarged element
JUVINALL: Machine Design Fig. 4-22 W-97
2 in. 3 in. rad.
1 in.
2000 lb
JUVINALL: Machine Design Fig. 4-23 W-98
2 in. A Top of shaft B "B" is at bottom of shaft, opposite "A"
JUVINALL: Machine Design Fig. 4-24 W-99
V = 2000 lb
A B
2000 lb
M = 4000 in.lb
4000 in.lb
T = 6000 lb in. Load diag.
2000 lb
2000 lb
V
Shear diag. 2000 lb
M
Moment diag. 4000 lb
JUVINALL: Machine Design Fig. 4-25 W-100
xy
yx y 2 in. x x
(a) Isometric view
yx y
x A
A
x
y
xy
yx
x
A
x xy
A
xy x
x
y yx
y
x xy
yx
(b)
(c)
(d)
Enlarged isometric view
Direct view
Isometric view
Calculated values: = 40.8 ksi = 30.6 ksi
JUVINALL: Machine Design Fig. 4-26 W-102
+ y (0, +30.6)
max = 37 ksi 34° yx = 30.6 ksi xy
y 1 = 57 ksi 2 = –17 ksi
0
+
x xy
56°
A
x
y yx
x (40.8, –30.6)
Direct view of element A
JUVINALL: Machine Design Fig. 4-27 W-103
x = 40.8 ksi
28° 1 = 57 ksi y x
A
x
y 2 = –17 ksi
JUVINALL: Machine Design Fig. 4-28 W-104
= 20 ksi 17°
= +37 ksi y x
A
x
= –37 ksi
y
JUVINALL: Machine Design Fig. 4-29 W-105
= 20 ksi
+ x + y
x – y 2
2 (x, xy) 2 –
1
2
+
0
(1, 0)
(2, 0) (y, yx)
xy2 +
x – y
– JUVINALL: Machine Design Fig. 4-30 W-106
2
2
+ 1 + 2
1 – 2
2
2
cos 2
1 – 2
2
2
0
2 1
2 1
JUVINALL: Machine Design Fig. 4-31 W-107
sin 2 +
y
(3) (1)
(2)
(3)
(3)
x A
A
z
(1)
A
(1)
(2)
(2) (= z) (a) Original element
(b) Principal element
(c) 1-2 plane
JUVINALL: Machine Design Fig. 4-32 W-108
(d) 1-3 plane
(e) 2-3 plane
+ max = 37 Principal circle
3 (–17, 0)
2
1
(0, 0)
(57, 0)
JUVINALL: Machine Design Fig. 4-33 W-109
+
+
Correct value of max Erroneous value of max obtained if 3 is neglected
1 (tangential)
A
0 3 A 2 (axial)
3 = 0 (radial)
JUVINALL: Machine Design Fig. 4-34 W-110
2
1
+
3.0 r 2.8 M
M
d
D
2.6 nom = Mc = 32M I d 3
2.4 2.2 Kt
(a)
2.0 1.8 1.6 1.4 1.2 1.0
0
0.1
0.2
0.3
D/d = 6 3 1.5 1.1 1.03 1.01
r/d 2.6
r P
P d
D
2.4 2.2
nom = P = 4P A d 2
2.0 Kt
(b)
1.8 1.6
D/d = 2 1.5 1.2 1.05 1.01
1.4 1.2 1.0
0
0.1
0.2
0.3
r/d 2.6
r T
2.4 2.2
d
D
T
nom = Tc = 16T J d 3
2.0 Kt
(c)
1.8 1.6 1.4 D/d = 2 1.2 1.09
1.2 1.0
0
0.1
0.2 r/d
JUVINALL: Machine Design Fig. 4-35 W-111
0.3
3.0
r
2.8 M
M
d
D
2.6 nom = Mc = 32M I d 3
2.4 2.2
(a)
Kt 2.0 1.8 1.6 D/d ≥ 2 1.1 1.03 1.01
1.4 1.2 1.0
0
0.1
0.2
0.3
r/d 3.0
r
2.8
P
P d
D 2.6
nom = P = 4P A d 2
2.4 2.2
(b)
Kt 2.0 1.8 1.6 D/d ≥ 2 1.1 1.03 1.01
1.4 1.2 1.0
0
0.1
0.2
0.3
r/d r
2.6 T
2.4 2.2
d
D
T
nom = Tc = 16T J d 3
2.0 Kt
(c)
1.8 1.6 1.4 D/d ≥ 2 1.1 1.01
1.2 1.0
0
0.1
0.2 r/d
JUVINALL: Machine Design Fig. 4-36 W-112
0.3
3.0 T
M
M P
2.8
P
T
D
2.6
d Axial load:
2.4
P nom = P ≈ A (D2/4) – Dd
2.2 Kt 2.0
Bending (in this plane):
1.8
M nom = Mc ≈ I (D3/32) – (dD2/6)
1.6 Torsion: T nom = Tc ≈ J (D3/16) – (dD2/6)
1.4 1.2 1.0
0
0.1
0.2
0.3
d/D
JUVINALL: Machine Design Fig. 4-37 W-113
3.0 2.8 M
2.6
H
M
h
2.4
r
2.2
nom = Mc = 6M I bh2
Kt 2.0
b
1.8 1.6
H/h = 6 2 1.2 1.05 1.01
1.4 1.2 1.0
0
0.05
0.10
0.15 r/h (a)
0.20
0.25
H
h
0.30
3.0 2.8
P
2.6
P
r
2.4
nom
2.2
b = P = P A bh
Kt 2.0 1.8
H/h = 3 2 1.5
1.6
1.15 1.05
1.4 1.2 1.0
1.01 0
0.05
0.10
0.15 r/h (b)
0.20
JUVINALL: Machine Design Fig. 4-38 W-113A
0.25
0.30
3.0 2.8 M 2.6
M
H
h r
2.4
b nom = Mc = 6M A bh2
2.2 Kt 2.0 1.8
H/h = ∞ 1.5 1.15 1.05 1.01
1.6 1.4 1.2 1.0
0
0.05
0.10
0.15 r/h (a)
0.20
0.25
0.30
3.0 2.8
P
P H
h
2.6
b
2.4
r
2.2
nom = P = P A bh
Kt 2.0
H/h = ∞ 1.5 1.15
1.8 1.6
1.05
1.4
1.01
1.2 1.0
0
0.05
0.10
0.15 r/h (b)
0.20
JUVINALL: Machine Design Fig. 4-39 W-114
0.25
0.30
3.0 M
2.8
h
d
b
M
2.6 nom = Mc = 6M I (b-d)h2
d/h = 0
2.4 2.2
0.25 Kt 2.0
0.5
1.8
1.0
1.6
2.0
1.4 1.2 1.0
0
0.1
0.2
0.3 d/b (a)
0.4
0.5
0.6
7 Pin loaded hole
6
P
h
d
b
P
nom = P = P A (b-d)h
5 Kt 4 Unloaded hole 3
2
1 0
0.1
0.2
0.3 d/b (b)
0.4
JUVINALL: Machine Design Fig. 4-40 W-114A
0.5
0.6
18
P
17 16
t
w
nom = P = P A wt r/w = 0.050 r/w = 0.10 r/w = 0.20
h/w = 0.5
15 r 14
h W
13 12 0.5
11 10 Kt
0.75
9
0.5
8 0.75 1.0
7 6 5
0.75 1.0
4
1.0 3.0
3
3.0 3.0
2 1 1.5 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 3.0 W/w
JUVINALL: Machine Design Fig. 4-41 W-115
Same cross-section area = K
F
F
Stress con. factor = K = 2
F
F
(a) Unnotched
(b) Notched av = Sy /2 max = Sy
= Sy Stress F=
F = ASy
ASy
Stress
2
(d)
(c)
= Sy
Su Sy
Stress
b
F
d
⑀ (e)
(f )
JUVINALL: Machine Design Fig. 4-42 W-116
a c
0
+
–Sy
Sy
–
–0+
0
+
=
(a) Load causes no yielding 0
+
–
Sy
–0+
0
+
=
(b) Load causes partial yielding 0
+
–
Sy
–0+
0
+
=
(c) Load causes partial yielding 0
+
–2Sy
Sy
–
+
–Sy
0
–0+
=
(d) Load causes total yielding
Load stress
+
Load removal stress change
JUVINALL: Machine Design Fig. 4-43 W-117
=
Residual stress
2 Z = bh 6 (0.025)(0.050)2 Z= 6 Z = 1.042 × 10–5 m3
300 mPa 0 F1
10 mm
F2
50 mm F2 F1
10 mm M1
M1
–300 MPa
25 mm
(a) Given information (see text) 0
300 396
–
(b)
–
–396
+
+
Load stress
0
62
–238 –
62
Residual stress
+
–
+
=
0
–
Residual stress
+
+
–96 0
0
–
Residual stress
+
+
–
Total stress (straight beam) 0
=
=
Load stress 0
–122 –
–
396 238 –
–
–204 62
=
Load stress
62
(e)
Residual stress –200
–
–96 0
–
–
–62 –
–
–
=
–104 0
–
(d)
=
–
Load removal stress change
–96 0
(c)
–96 0
–
300
–
Total stress (ready to yield) –300
0 –60
–
Load stress
JUVINALL: Machine Design Fig. 4-44 W-118
=
=
–
–
Total stress (ready to yield)
P = 0 lb
10.000 in.
10.008 in.
T = 80°F
T = 480°F
P = 0 lb
P = 60,000 lb
JUVINALL: Machine Design Fig. 4-45 W-119
P = 60,000 lb
10 mm dia.
P
60 mm P = 400 kN
20 mm
JUVINALL: Machine Design Fig. 4-61 W-142
A
B
C D
E
JUVINALL: Machine Design Fig. P4-2 W-120
F
di = 20 mm
T max = 100 mm do = 24 mm
JUVINALL: Machine Design Fig. P4-10 W-121
T
T
T T
2r b
JUVINALL: Machine Design Fig. P4-11 W-122
b h
r
M
M
JUVINALL: Machine Design Fig. P4-18 W-123
200 lb 3 in. 1-in.-dia round rod
4 in. 200 lb
JUVINALL: Machine Design Fig. P4-19 W-124
A 40
80
A 60 P
Q
120
70,000 N
JUVINALL: Machine Design Fig. P4-21 W-125
b
h c X a
JUVINALL: Machine Design Fig. P4-23 W-126
3 in. 4
F 2 in.
3 in. 16
1 in.
JUVINALL: Machine Design Fig. P4-24 W-127
3 in. 16
13 in. 16
24 mm
A
5 mm 30 mm
8 mm 5 mm
30 mm
A
Section AA
12,000 N
JUVINALL: Machine Design Fig. P4-25 W-128
100
B Free end of shaft
T
20-mmdia. shaft
100
S
2000 N A
400 N
120-mm-dia. sheave
Connected to flexible coupling and clutch JUVINALL: Machine Design Fig. P4-27 W-131
1
3 2 in.
1 2 in.
8 in.
3 in. 8 1 2 in.
JUVINALL: Machine Design Fig. P4-29 W-129
12 kN Cement
5
L 2
5
50
5
5
40
JUVINALL: Machine Design Fig. P4-30 W-130
L 2
200 mm
25-mm-dia. round rod bent into crank 250 mm
100 mm 1000 N
JUVINALL: Machine Design Fig. P4-34 W-132
1-in. dia. shaft
3000-lb belt tension
Motor 6-in. dia. 1000-lb belt tension 1 in.
JUVINALL: Machine Design Fig. P4-36 W-133
F B
100-mm dia. 50-mm dia.
30-mm dia. A
50 mm 4000 lb 100 mm
50 mm
JUVINALL: Machine Design Fig. P4-40 W-134
B 1-in.-dia. shaft
2 in. A
1000 lb 3 in.
4 in. 500 lb 4 in.
3 in.
JUVINALL: Machine Design Fig. P4-38 W-134a
A
JUVINALL: Machine Design Fig. P4-41 W-135
30 y x 18
45
JUVINALL: Machine Design Fig. P4-46 W-136
20 ksi Free surface, 3 = 0 30 ksi
JUVINALL: Machine Design Fig. P4-49 W-139
75
350 100
JUVINALL: Machine Design Fig. P4-52 W-140
5000 N
200 mm
30 mm
15 mm 25 mm
JUVINALL: Machine Design Fig. P4-52 W-141
5000 N
1000 N r = 5 mm d = 40 mm
d = 40 mm
A
B D = 80 mm
500 mm
250 mm
RA
RB
JUVINALL: Machine Design Fig. P4-54 W-137
5000 N
50 mm
100 mm
5000 N
15 mm 25 mm JUVINALL: Machine Design Fig. P4-55 W-138
Calculated elastic stress (MPa)
400
200
0
–200
0
1
2
3
4
5
6 Time
7
8
JUVINALL: Machine Design Fig. P4-65 W-143
9
10
11
12
(a)
(b)
(c)
JUVINALL: Machine Design Fig. 5-1 W-144
(d)
(e)
Y
Unloaded element Element loaded in uniaxial tension in X direction (with deflections shown exaggerated)
z dy (neg.)
y dx
Z
x X dz (neg.)
dx ⑀x = lim x x→0
dy ⑀y = lim y y→0
dz ⑀z = lim z z→0
JUVINALL: Machine Design Fig. 5-2 W-145
Y
dx yx y xy Z
X
x
␥xy (shown counterclockwise, hence negative) ␥yx (shown clockwise, hence positive)
dx absolute value = lim = tan ≈ y y→0
JUVINALL: Machine Design Fig. 5-3 W-146
+␥/2
⑀y y ␥xy
⑀1
⑀2 ⑀x
+⑀ 0
x
JUVINALL: Machine Design Fig. 5-4 W-147
(a) Single-element gages oriented to sense horizontal strain
(b) Two-element rosettes oriented to measure horizontal and vertical strain
(d) Three-element rectangular rosettes
(c) Three-element equiangular rosettes
JUVINALL: Machine Design Fig. 5-5 W-148
⑀2
⑀120
⑀2
⑀120
⑀2
⑀240
120°
+␣ 240°
+␣ ⑀0
+␣
⑀1 +␣
⑀0
+␣ ⑀0
⑀1
⑀1
+␣
⑀240
⑀240 (a)
(b)
JUVINALL: Machine Design Fig. 5-6 W-149
⑀120 (c)
⑀1 = +0.0020 240° gage (⑀ = +0.00185)
17° 0° gage (⑀ = –0.00075) ⑀2 = –0.0010 120° gage (⑀ = +0.0004)
JUVINALL: Machine Design Fig. 5-7 W-150
+␥ /2 120°
⑀2 = – 0.001
–0.00075
+0.00185
⑀1 = +0.0020 +⑀
34° +0.0004 240° 0°
JUVINALL: Machine Design Fig. 5-8 W-151
⑀90
⑀0
⑀2 ⑀45
⑀45
⑀0
⑀2 +␣
90°
⑀2 +␣
+␣ 45°
+␣ ⑀90
⑀0
⑀90
+␣ ⑀1
⑀1
⑀1
+␣ ⑀45 (a)
(b)
JUVINALL: Machine Design Fig. 5-9 W-152
(c)
+2600 m/m
+450 m/m –200 m/m
⑀90 = +450 ⑀45 = –200
(a)
⑀0 = +2600 (b)
JUVINALL: Machine Design Fig. 5-10 W-153
⑀1 = +3560
⑀2 = –510
⑀90 = +450 ⑀45 = –200
29° 119° ⑀0 = +2600
JUVINALL: Machine Design Fig. 5-11 W-154
+␥ /2 0° 45°
58°
–510
3560
0 450 –200
+⑀ 2600
90°
JUVINALL: Machine Design Fig. 5-12 W-155
+␥ /2
+
⑀2 = –0.001
2 = –24
⑀3 = –0.0005
3 = 0 +
0
+⑀
0
⑀1 = 0.002
1 = 134
(a)
(b)
JUVINALL: Machine Design Fig. 5-13 W-156
2.5 kN
1.5 kN 200
100 50
10
10
50 d = 50
d = 60
d = 40
d = 30
200
d = 40 1.8 kN
V, shear force (kN)
2.2 kN 2.2
2 1
Area = 220 kN•mm
0.7 Area = 140 kN•mm
0
Area = 360 kN•mm
M, bending moment (kN•mm)
–1 –2
–1.8
400
255
220 200
Area = 58,000 kN•mm2
22
18
A = 11,000
4
A= 0.457 × 10–3 5.12
0.85 2.67
5.67
2.47 1.94 0.220 × 10–3
0.419 × 10–3
A = 0.565 × 10–3
Initially assumed location of zero slope
A = 13 × 10–6
1.2 0.8 0.4
A= 0.270 × 10–3 0.69 0.28
A = 3 × 10–6
0.838 0.835 0.270 A = 0.120 mm
0.8 0.4
A = 0.011 0
–0.8 –1.2
0.007 –0.4 –0.220
–0.677 –1.096 –1.109
Location of zero absolute slope
–0.4
0
0.022 A= 0.093 mm
–0.8
True line of zero deflection
0
+0.001
–0.04 –0.08 –0.12
0.093 0.115 0.126
0.119
Tangent point
JUVINALL: Machine Design Fig. 5-14 W-159
Parallel to true line of zero deflection
Absolute slope (mrad)
M , (10–6/mm) EI
9.80
8.46 8
0
Relative slope (milliradians)
A = 36,000
0
12
Deflection (mm)
360
325
Area = dU'
dQ
Area = U' Load
Area = dU
Q Area = U
0 Deflection
JUVINALL: Machine Design Fig. 5-15 W-160
∆
P x
dx h
P/2
L
L/2
JUVINALL: Machine Design Fig. 5-16 W-161
P/2
b
P = 5000 N
h = 50 mm 2500 N
L = 400 mm
200 mm
JUVINALL: Machine Design Fig. 5-17 W-162
2500 N
b = 25 mm
x
c
b L h y a
P
Q
JUVINALL: Machine Design Fig. 5-18 W-163
R
F
F
R
␦
P F
h
M
F
V 2R
b
(a)
(b)
JUVINALL: Machine Design Fig. 5-19 W-164
R – R cos
1.0 2 Avg value =
sin
0.5
∫
0
/2 0
sin d = 1;
∫
0
sin
d = 2;
∫
2 0
sin d = 0
2 can be determined) (From this, average value =
–0.5
–1.0 1.0 2 Avg value =
cos
0.5
∫
0
/2 0
cos d = 1;
∫
0
cos d = 0;
∫
2 0
cos d = 0
–0.5
–1.0 1.0
∫ ∫
sin2
Avg value = 0.5 0.5
0 1.0
∫ ∫
cos2
Avg value = 0.5 0.5
0
/2 0 2 0
/2
0
(0.5) = ; 2 4
∫
0
∫
0
sin2 d = (0.5) =
2
cos2 d = (0.5) =
2
sin2 d =
0 2
sin2 d =
cos2 d =
(0.5) = ; 2 4
cos2 d =
(0.707)(0.707) = 0.5 2 1 Avg value = 0.5 = = (Half of avg value shown in sin plot) sin cos
0.5
∫ ∫
0
–0.5
0
/2
3/2 (radians)
/2 0 2 0
sin cos d =
1 1 = ; 2 2
sin cos d = 0
2
JUVINALL: Machine Design Fig. 5-20 W-165
∫
0
sin cos d = 0
2 R=
.0
in.
E = 18 × 106 psi G = 7 × 106 psi F
F ␦ h = 0.3 in. b = 0.2 in. 2R = 4 in. (a)
JUVINALL: Machine Design Fig. 5-21a W-166
0.035 Copper Cast iron Steel
Deflection, ␦ (in.)
0.030 0.025 0.020 0.015 0.010 0.005 0.000 0.2
0.4
0.3 Width, h (in.) (b)
JUVINALL: Machine Design Fig. 5-21b W-167
0.5
0.035
Deflection, (in.)
0.030 0.025
Copper Cast iron Steel
0.020 0.015 0.010 0.005 0.000 1.0
1.5
2.0 Radius, R (in.)
JUVINALL: Machine Design Fig. 5-21c W-168
2.5
3.0
Deflection, ␦ (in.)
0.06 0.05 0.04 0.03 0.02 0.01 0.2
0. 1 0.3 Wid th
,h
(in.
0. 2
0.4
)
0. 3 0.5
JUVINALL: Machine Design Fig. 5-21d W-169
,b ess ckn Thi
) (in.
1.2 m
500 kg mass
10 m Point of zero deflection F
a y 3m
JUVINALL: Machine Design Fig. 5-22 W-170
3
Pa/2
a
M0 2
P/2
P 1
y b 2
M0
P/2
3' Pa/2 2' a
M0
b 2
P
M0
x P/2 M0
(a)
P/2 M0
P/2
JUVINALL: Machine Design Fig. 5-23 W-171
(b)
P/2
P P
y x
x y
Axis of least I and becomes neutral bending axis when buckling occurs. With column formulas, always use I and with respect to this axis.
L or Le e
(b) Column cross section
P P (a) Two views of column
JUVINALL: Machine Design Fig. 5-24 W-172
0.100
0.010
Scr E
0.001
0.0001
10
100
Slenderness ration Le /
JUVINALL: Machine Design Fig. 5-25 W-173
180
1200 1100
160
1000
800 700 600 500 400 300
Critical unit load Scr (ksi)
Critical unit load Scr (MPa)
140 900
120
Sy = 689 MPa A
Arbitrary values for illustration
C
100 Sy = 496 MPa 80
B
D
60 Euler, E = 203 GPa (steel)
40
200 20 100 0
Euler, E = 71 GPa (alum) 0
20
40
60 80 100 120 Slenderness ratio Le /
JUVINALL: Machine Design Fig. 5-26 W-174
140
E F 160
(Buckled shape shown dotted)
Le Le = L
L
Le
L
Le
L
Le 2
L
(a)
(b)
(c)
(d)
(e)
Theoretical
Le = L
Le = 0.707L
Le = 0.5L
Le = L
Le = 2L
Minimum AISC Recommend
Le = L
Le = 0.80L
Le = 0.65L
Le = 1.2L
Le = 2.1L
Source: From Manual of Steel Construction, 7th ed., American Institute of Steel Construction, Inc., New York, 1970, pp. 5–138.
JUVINALL: Machine Design Fig. 5-27 W-175
180
1200 1100
160
1000
800 700 600 500 400 300
Critical unit load Scr (ksi)
Critical unit load Scr (MPa)
140 900 120 100 80
0
Sy = 496 MPa B D
Sy = 689 MPa Johnson, E = 203 GPa, Sy = 689 MPa
60 40
200 100
C
A
Johnson, E = 71 GPa, Sy = 496 MPa
Tangent points
Euler, E = 203 GPa Euler, E = 71 GPa
20 E F 0
20
40
60 80 100 Slenderness ratio Le /
JUVINALL: Machine Design Fig. 5-28 W-176
120
140
160
D 80,000 N
80,000 N 1m SF = 2.5 Sy = 689 MPa E = 203 GPa (steel)
JUVINALL: Machine Design Fig. 5-29 W-177
D
80,000 N
80,000 N 200 m
SF = 2.5 Sy = 496 MPa E = 71 GPa (aluminum)
JUVINALL: Machine Design Fig. 5-30 W-178
600 550
80
500 70
Euler curve
400
60
ec/ 2 = 0
350
0.05
50
0.1 300 40 250
0.3
200
0.6
30
150
ec/ 2 = 1.0
20
100 10 50
0
20
40
0 60 80 100 120 140 160 180 200 Slenderness ratio Le /
JUVINALL: Machine Design Fig. 5-31 W-179
Critical unit load Scr (ksi)
Critical unit load Scr (MPa)
450
(a) Wrinkling, or "accordian buckling" of thin-wall tube
(b) Typical local buckling of an externally pressurized thin-wall tube
JUVINALL: Machine Design Fig. 5-32 W-180
(c) Wrinkling of thin, unsupported flanges of a channel section
Beam
Tetrahedron
Triangle
Pentahedron
Quadrilateral
Hexahedron
JUVINALL: Machine Design Fig. 5-33 W-180A
1
(2)
3
(5)
5
(7) (3)
(10)
7
(9) (11)
(6) 6
(1) (8) 4 (4) 2
JUVINALL: Machine Design Fig. 5-34 W-180B
W
␦3x 3' F (7) 3y
F (7) 3x
␦3x
3
L
F (7) 6y 6' F (7) 6x 6 ␦6x
JUVINALL: Machine Design Fig. 5-35 W-180C
␦6x
F3
F (7) 3x 3
F (7) 3y
␦3x
3'
␦
L A, E
6
JUVINALL: Machine Design Fig. 5-36 W-180D
3N 2N
2
␦2y
2'
(Constant A, E) 3.464 m
2m
␦2x (2)
1
4m
(3)
JUVINALL: Machine Design Fig. 5-37 W-180E
3
␦3x 3'
F (1) 2y
F (2) 2y F (1) 2x
2
F (2) 2x 2
(1)
3.464 m 2m
F (1) 1y
F (2) 3y
(2) F (1) 1x
F (2) 3x
1
3
(3) F 1y
F (3) 1x
F (3) 3y F (3) 3x
(3) 1
4m
JUVINALL: Machine Design Fig. 5-38 W-180F
3
1.
Tension or compression
␦=
␦
L
PL AE
k=
P AE = ␦ L
K=
T K'G = L
P Cross-section area = A
2.
Torsion
L T K' a = section property. For solid round section, K' = J = d 4/32.
3.
Bending (angular deflection)
TL K'G For solid round bar and deflection in degrees, 584TL ° = d 4G =
=
ML EI
K=
M EI = L
␦=
ML2 2EI
k=
M 2EI = ␦ L2
␦=
PL3 3EI
k=
P 3EI = ␦ L3
L M
I = moment of inertia about neutral bending axis
4.
Bending (linear deflection) ␦
L
M
I = moment of inertia about neutral bending axis
5.
Cantilever beam loaded at end L
P
␦
I = moment of inertia about neutral bending axis
JUVINALL: Machine Design Table 5-1 W-157
di
d
4 K' = J = d 32
do
K' = J = (d 4 – d 4i ) 32 o
t 4 K' = dt 32
d
2b
3 3 K' = a b 2 a + b2
2a
K' = 0.0216a4 a
K' = 2.69a4 a
b
3 4 K' = ab 16 – 3.36 b 1 – b 16 3 a 12a4
a a
K' = 0.1406a4
a
JUVINALL: Machine Design Table 5-2 W-158
⑀120 = +625
⑀0 = +950
⑀240 = +300
JUVINALL: Machine Design Fig. P5-4 W-181
⑀135 = –380 ⑀0 = –300
⑀90 = –300
⑀45 = –380 ⑀270 = –200 Gage readings
⑀0 = –200 Equivalent rosettes
JUVINALL: Machine Design Fig. P5-9 W-183
100 mm A F 100 mm
k = 5 N/mm B
F 100 mm C F
JUVINALL: Machine Design Fig. P5-14 W-182
200 mm
100 mm A
25 mm-dia. steel 1000 N
JUVINALL: Machine Design Fig. P5-15 W-184
4 kN d = 30
d = 50
d = 40
2 kN 100
200
JUVINALL: Machine Design Fig. P5-16 W-185
150
a Z Solid round rod of properties E, G, A, I, and J.
b X
Y T (used in Problem 5.18)
F (used in Problem 5.17)
JUVINALL: Machine Design Fig. P5-17 W-186
w = 200 lb/in. 0.75d
0.75d d
5 in.
15 in.
JUVINALL: Machine Design Fig. P5-19 W-186a
5 in.
a
F
a
F
b
JUVINALL: Machine Design Fig. P5-20 W-187
R
P
JUVINALL: Machine Design Fig. P5-21 W-188
b 2 b 2
L F
h
JUVINALL: Machine Design Fig. P5-22 W-189
500 mm
5 kN
S
300 mm
JUVINALL: Machine Design Fig. P05-23 W-190
2
1
1
2
JUVINALL: Machine Design Fig. P5-27 W-191
12 mm-dia. tie-rod
1m 0.7 m Boom
0.7 m 1m
JUVINALL: Machine Design Fig. P5-29 W-192
6 kN
P
P
t t 2c c 2w
w
P
P
(a) Center crack
(b) Edge crack
JUVINALL: Machine Design Fig. 6-2 W-194
P
7075–T651 Aluminum, Su = 78 ksi, Sy = 70 ksi, Kic = 60 ksi
2c
t = 0.06 in. =1
2w
i n.
=6
in.
P
JUVINALL: Machine Design Fig. 6-3 W-195
in.
P
a
2c 2w
P
JUVINALL: Machine Design Fig. 6-4 W-196
t
P Ti – 6Al – 4V (annealed) titanium plate
a
2c
2w = 6 g = 0.73 Sy
in. P
a/2c = 0.25
JUVINALL: Machine Design Fig. 6-5 W-197
t = 1 in.
+
+
(max = 60)
(max = 50)
2 = 40 ksi 1 = 80 ksi
2 = 3 = 0
3 = 0 +
(a) Proposed application involving 1 = 80, 2 = – 40, 3 = 0
1 = 100 ksi +
(a) Standard tensile test of proposed material. Tensile strength, S = 100 ksi
JUVINALL: Machine Design Fig. 6-6 W-198
Uniaxial compression
+2
Uniaxial tension
Sut
+
Sut
Suc 0
+
Suc
Sut 0
Principal Mohr circle must lie within these bounds to avoid failure Suc For biaxial stresses (i.e., 3 = 0), 1 and 2 must plot within this area to avoid failure (b) 1 – 2 plot
(a) Mohr circle plot
JUVINALL: Machine Design Fig. 6-7 W-199
+1
+2 Syt +
Uniaxial tension
Principal Mohr circle must lie within these bounds to avoid failure
Syt
Syt
+
0
For biaxial stresses (i.e., 3 = 0), 1 and 2 must plot within this area to avoid failure (b) 1 – 2 plot
(a) Mohr circle plot
JUVINALL: Machine Design Fig. 6-8 W-200
+1
Principal plane
Octahedral plane
Principal planes
JUVINALL: Machine Design Fig. 6-9 W-201
Shear diagonal (1 = –2) +2 (0, 100)
(100, 100)
(–100, 100) Shear stress theory
Distortion energy theory
(–58, 58)
(–100, 0)
(100, 0) 0
(50, –50)
+1
Normal stress theory (58, –58) Note: 3 = 0
(–100, –100)
(100, –100) (0, –100)
JUVINALL: Machine Design Fig. 6-10 W-202
+2 +Sut +
Suc
Sut 0
+
Suc
Sut 0
Principal Mohr circle must lie within these bounds to avoid failure For biaxial stresses (i.e., 3 = 0), 1 and 2 must plot within this area to avoid failure
Suc
(b) 1 – 2 plot
(a) Mohr circle plot
JUVINALL: Machine Design Fig. 6-11 W-203
+1
+2 Sut
Suc
Sut 0
+1 Shear diagonal
Suc
JUVINALL: Machine Design Fig. 6-12 W-204
2 = –25 ksi Note: 3 = 0
1 = 35 ksi
1 = 35 ksi
Steel, Sy = 100 ksi 2 = –25 ksi
JUVINALL: Machine Design Fig. 6-13 W-205
0
35
58
66
100
1 (ksi)
Normal load point –25 theory D.E. theory theory (58, –58)
Load line
–100
Shear diagonal
2 (ksi)
JUVINALL: Machine Design Fig. 6-14 W-206
Limiting points
Stress (% of ultimate strength)
100 Fracture
SF = 2 based on strength, Eq. 6.9
50 SF = 2 based on load, Eq. 6.10
0
50 100 Load (% of ultimate load)
JUVINALL: Machine Design Fig. 6-15 W-207
Frequency p(x) and p(y) 0
y (stress)
x (strength)
y
x
40 70 Strength (x), and stress (y) (MPa or ksi)
JUVINALL: Machine Design Fig. 6-16 W-208
Frequency p(z)
z (margin of safety) z 0
30 Margin of safety, z, where z = x – y
JUVINALL: Machine Design Fig. 6-17 W-209
1 Frequency p(x)
1 < 2 < 3
0
2 3
Quantity x
JUVINALL: Machine Design Fig. 6-18 W-210
x1 x2
Frequency p(x)
Inflection point
Inflection point
34.13%
34.13% of total area
2.14%
2.14%
0.13%
0.13% 13.60%
–3
–2
–1
13.60%
+1
Quantity x
JUVINALL: Machine Design Fig. 6-19 W-211
+2
+3
99.99
0.01
99.9 99.8
0.05 0.1 0.2
1
98
2
95
5
90
10
80
20
70
30
60
40
50
50
40
60
30
70
20
80
% of failures –k
10 5
95
% of survivors
2
98
1
99
Fatigue life, strength, etc.
0.5 0.2 0.1 0.05 0.01
Extreme values
–4
–3
99.8 99.9
k = –4, 99.99683% reliability k = –5, 99.9999713% reliability k = –6, 99.9999999013% reliability
–2
–1 0 +1 +2 Number of standard deviations, k
JUVINALL: Machine Design Fig. 6-20 W-212
+3
+4
99.99
% of failures or P, % cumulative probability of failure
% reliability (% of survivors or % cumulative probability of survival)
0.5 99
One bolt in 500 twists off
Frequency p(x) and p(y)
x = 1 N • m y = 1.5 N • m
0
y (wrench twist-off torque)
x (bolt twistoff strength)
y
x
(14.8)
20.0
Torque x and y (N • m) (a)
kz Frequency p(z)
One bolt in 500 twists off z=x–y
z 0
(5.22) Torque z (N • m) (b)
JUVINALL: Machine Design Fig. 6-21 W-213
2 = 100 MPa
1
a
2
2 = –100 MPa
1 = 200 MPa
1
b
2
JUVINALL: Machine Design Fig. P6-13 W-214
1 = 150 MPa
Sy = 500 MPa
xy = 100 MPa x
x = 50 MPa xy
JUVINALL: Machine Design Fig. P6-23 W-215
c
m
m
m
k
k
(a)
(b)
JUVINALL: Machine Design Fig. 7-1 W-216
k
(c)
100
100
80
80
70 60
60 50
50
Ultimate strength Su
40
Total elongation
30 20
40 30
Yield strength Sy
20
10
10
0 10–6 10–5 10– 4 10–3 10–2 10–1 1 Average strain rate (s–1)
JUVINALL: Machine Design Fig. 7-2 W-217
101
102
0 103
Elongation (%)
Su and Sy (ksi)
70
Ratio Sy /Su
Sy / Su (%)
90
90
W Guide rod h
Elastic-strain energy stored 1
in structure = 2 Fe ␦
Force Fe W
␦ k
Work of falling weight = W (h + ␦) k
W
O ␦st
h Deflection
␦ (a)
(c)
(b)
JUVINALL: Machine Design Fig. 7-3a-c W-218
2d
L/2
d2 Area = A = 4 L
L/2 d
d
(b)
(a)
JUVINALL: Machine Design Fig. 7-4 W-219
W
h
Bumper of cross section A; volume = AL L
JUVINALL: Machine Design Fig. 7-5 W-220
30 in. 100 lb
2 × 4 white pine E = 106 psi Mod. of rupture = 6 ksi
100 lb/in.
5
12 in.
5
1 8 in. × 3 8 in., I = bh3/12 = 6.46 in.4 Z = I/c = 3.56 in.3 60 in.
JUVINALL: Machine Design Fig. 7-6 W-221
100 lb/in.
250 mm 20-mm dia 120-mm dia
100-mm dia
20 mm
20 mm
JUVINALL: Machine Design Fig. 7-7 W-222
700 Aluminum Cast iron Steel
Shaft shear stress (MPa)
600 500 400 300 200 100 5.0
7.5
10.0 Shaft radius (mm)
12.5
15.0
Torsional deflection of shaft (deg)
40 35
Aluminum Cast iron Steel
30 25 20 15 10 5 0 5.0
7.5
10.0 Shaft radius (mm)
JUVINALL: Machine Design Fig. 7-7b W-223
12.5
15.0
K i = 1.5
d
K i = 1.5
JUVINALL: Machine Design Fig. 7-8 W-224
K i = 1.5
Ki = 3 d 2 d K i = 1.5
JUVINALL: Machine Design Fig. 7-9 W-225
Head Ki = 3.4 Ki = 3.4 A = 700 mm2
Ki =1.5 A = 300 mm2
"Very long" (>10d)
Shank d Ki = 1.5 Ki = 3.5 A = 600 mm2
Ki = 3.0 A = 600 mm2
"Negligible" (a) Original design
JUVINALL: Machine Design Fig. 7-10 W-226
(b) Modified design
K = 1.55 Drop weight K =4
24 mm dia.
30 mm dia.
K = 1.4
JUVINALL: Machine Design Fig. 7-10 W-229
Axial hole
(a)
(b)
JUVINALL: Machine Design Fig. 7-11 W-227
K =2
1-in dia. 0.1-in dia. hole
"Very long"
K =2
JUVINALL: Machine Design Fig. 7-13 W-232
Steel cable A = 2.5 in.2 E = 12 × 106
JUVINALL: Machine Design Fig. P7-2 W-228
v = 4 km/hr m = 1400 kg
K = 5000 N/mm L=5m Rope
JUVINALL: Machine Design Fig. P7-5 W-228
Thread: Area = A K = 2.6
Thread: Area = 600 mm2 K = 3.9
K = 1.3
Area = 800 mm2
Area = 800 mm2
"Very long"
K = 1.3
A = 600 mm2 K = 3.9
Area = A K = 2.6
Platform
Original design
New design
(a)
(b)
JUVINALL: Machine Design Fig. P7-11 W-230
Hole dia., d
K = 2.2
K = 1.5
250 mm
Assume that hole drilled to this depth, does not significantly change the K = 3.8 factor at the thread.
dia. = 36 mm (Fracture location) A = 800 mm2 K = 3.8
3 mm (negligible) Original design
Modified design
(a)
(b)
JUVINALL: Machine Design Fig. P7-12 W-231
Small region behaves plastically Main body behaves elastically
JUVINALL: Machine Design Fig. 8-2 W-234
Test specimen
Flexible coupling
9 8" R 7
Motor 0.300" Revolution counter C Weights 110-Volts AC
JUVINALL: Machine Design Fig. 8-3 W-235
Fatigue strength, or Peak alternating stress S (ksi)
50 + + + + + + 40 + + + + + + + 30 +
Not broken +++
20 Sn' (endurance limit) 10 0 0
10
20
30
40 50 60 70 80 Life N (cycles ⫻ 106)
90 100
(a) Linear coordinates (not used for obvious reasons)
Fatigue strength, or Peak alternating stress S (ksi)
50
+ +
40
+
+
++ + ++
30
Not broken + ++ + +
+ +
20 Sn' (endurance limit) 10 0 103
104
105
106 107 Life N (cycles (log))
108
Fatigue strength, or Peak alternating stress S (ksi (log))
(b) Semilog coordinates
100 80 70 60 50
8:7 ratio +
40 30 20
+ + "Knee" of curve Not broken + + + + + + + + + + 7:1 ratio Sn' (endurance limit)
10 103
104
105
106 Life N (cycles (log))
(c) Log-log coordinates
JUVINALL: Machine Design Fig. 8-4 W-236
107
108
S = 0.9Su (in ksi, S ⬇ 0.45
Bhn; in MPa, S ⬇ 3.10 Bhn)
1.0 0.9
S/Su (log)
0.8 0.7
Not broken
0.6 0.5 Sn' 0.4 103
2
4
6
104
2
4 6 105 2 Life N (cycles(log))
4
JUVINALL: Machine Design Fig. 8-5 W-237
6
106
2
4
6
107
Sn' = 0.5 Su (in ksi, Sn' ⬇ 0.25 Bhn; in MPa, Sn' ⬇ 1.73 Bhn)
140
187
229
Hardness (HB) 375 285
477
653
900 120
Endurance limit S 'n (ksi)
100
700 600
80
500 60 400 0.25 Bhn 300
40 SAE SAE SAE SAE
20
0 0
10
20
30 40 50 Hardness (Rockwell C)
JUVINALL: Machine Design Fig. 8-6 W-238
4063 5150 4052 4140
60
200 100
70
Endurance limit S 'n (MPa)
800
Actual maximum stress Calculated maximum stress (Mc /I )
M
M
JUVINALL: Machine Design Fig. 8-7 W-239
500
60
400
50 300
40 35
250
30
200
25
Wrought
20 18 16 14
Permanent mold cast
150
100
12 75
10 8 7 6 5 103
Sand cast 50
104
105
106 Life N (cycles (log))
107
JUVINALL: Machine Design Fig. 8-8 W-240
108
109
S (MPa (log))
Peak alternating bending stress S (ksi (log)
80 70
2014-0, T4, and T6 2024-T3, T36 and T4 6061-0, T4 and T6
6063-0, T42, T5, T6 7075-T6
30
150
20 S n' = 19 ksi
100
S n' = 0.4S u
10
50 0
0 0
0
10
50
20
100
150
30
200
40 50 Tensile strength Su (ksi) 250
300 Su (MPa)
350
JUVINALL: Machine Design Fig. 8-9 W-241
60
400
70
450
500
550
S n' (MPa)
Fatigue strength at 5 108 cycles S n' (ksi)
Alloys represented: 1100-0, H12, H14, H16, H18 3003-0, H12, H14, H16, H18 5052-0, H32, H34, H36, H38
40 35 200
25 Extruded and forged
20 18 16
150
100
14
Sand-cast
12 10 9 8
75
7
50
6 5 105
2
4
6 8 106
2 4 6 8 107 Life N (cycles (log))
JUVINALL: Machine Design Fig. 8-10 W-242
2
4
6 8 108
S (MPa (log))
Peak alternating stress S (ksi (log))
30
Sn = Sn' = 0.5Su 0.5 Bending Axial (no eccentricity)
0.3
Torsion
Sn = 0.9Sn' = 0.45Su Sn = 0.58Sn' = 0.29Su
Ratio,
peak alternating stress, S or Ss (log) Su
1.0
S103 = 0.9Su S103 = 0.75Su S103 = 0.9Sus (≈ 0.72Su)
0.1
103
104
105 Life, N (cycles (log))
JUVINALL: Machine Design Fig. 8-11 W-243
106
107
2 Sn 1.2 Note: Dotted portion is superfluous for completely 1.0 reversed stresses 0.8 0.6 0.4 Reversed bending
0.2 1 Sn
–1.2
–0.8
–0.4
0 – 0.2
0.4
0.8
1.2
1 Sn
DE theory
– 0.4
Reversed torsion
– 0.6 – 0.8 –1.0
Reversed bending –1.2
JUVINALL: Machine Design Fig. 8-12 W-245
Hardness (HB) 120 160 200 240 280 320 360 400 440 480 520 1.0 Mirror-polished 0.9 Fine-ground or commercially 0.8 polished
Mac hine d or
Surface factor Cs
0.7 0.6
cold -dra wn
0.5 Hot -rol led
0.4 0.3
As f orge d
0.2 0.1
Corroded in tap water Corroded in salt water
0 60
0.4
80
0.6
100 120 140 160 180 200 220 240 260 Tensile strength Su (ksi)
0.8
1.0
1.2
1.4
Su (GPa)
JUVINALL: Machine Design Fig. 8-13 W-246
1.6
1.8
Equal surface stresses
(a) d = (0.3" or 7.6 mm)
(b) d > (0.3" or 7.6 mm)
(c) d < (0.3" or 7.6 mm)
JUVINALL: Machine Design Fig. 8-14 W-247
a max
a Stress
max + 0 –
m m
a
min
min m = mean stress; a = alternating stress (or stress amplitude) max = maximum stress; min = minimum stress m = (max + min)/2 a = (max – min)/2
JUVINALL: Machine Design Fig. 8-15 W-248
103 ~
F
Values from S–N curve
Sy A" 104 ~ E D
105 ~
10 3
106 ~ H'
10 4
H
Sn
~
~
C 10 6
a
10 5
~
~ G
A' – Sy
A – m (compression)
0
JUVINALL: Machine Design Fig. 8-16 W-249
m (tension)
Sy
B Su
90 4
7
10
40
20
10
10
20
20 ) 30 f S u o
30
–40
–20
0
–1 0
–60
20 40 60 80 Minimum stress min (% of Su)
–2 0
–80
–3 0
0 –100
30 M ea 40 n st re 5 ss 0 m (% 60 of S
50
u)
70
10 3× 5 10 6 10
% 40 a( ss 50 stre g in 60 nat r te Al
60
10
80
4
70
70
10
80
3 le life 10 -cyc 3 0 3×1
80
Maximum stress max (% of Su)
90
90
10 0
Su
100
JUVINALL: Machine Design Fig. 8-17 W-250
100
80
80
60 50
si 40 ss
5
st
re
10
3 M 0 ea n
6
20
10 7 10 9 10 10
10
4×
10
–20 0
0
20 40 60 Minimum stress min (ksi)
–1
– 40
0
– 60
–2
0 – 80
m
(k
5
10
20
20
)
4
10
i) 30 (ks a
Maximum stress max (ksi)
4×
ss
30
4
10
40 stre g in at 50 ern t Al
40
60
50
life 3 cycle 10 -
70
60
70
Su 70
JUVINALL: Machine Design Fig. 8-18 W-251
80
70 60 4
5 (k 0 si ) 10
10
0
– 20 –1 0
– 40
20 40 60 Minimum stress min (ksi)
–2 0
– 60
–3 0
0 – 80
3 M 0 ea n st 40 re ss
5
10 7 4× 6 10 10 9 10
20
20
m
5
10
20
30
10
10
4×
i) 30 (ks a
Maximum stress max (ksi)
4
10
s 40 tres s g
40
fe le li
in 50 nat r te Al
50
3 - cyc 10
60
60
70
70
80
80
JUVINALL: Machine Design Fig. 8-19 W-252
80
Calculated fluctuating axial stress (ignoring yielding)
Su a
Sy Sn a
(e)
a m
(d)
0
(c) (b)
– Sn
(a)
JUVINALL: Machine Design Fig. 8-20 W-253
m
(f)
d < 2.0 in.
Commercially polished surface
P(t)
P(t)
P(t) 0 Sy = 120 ksi Su = 150 ksi
JUVINALL: Machine Design Fig. 8-21 W-254
t
Peak alternating stress, S (log)
Axial loading stresses in ksi
S = 0.75Su = 0.75(150) = 112 112
Sn = Sn' CLCGCS = (0.5 × 150)(1)(0.9)(0.9) = 61
92 75 61
103
104
105 Life N (cycles (log))
120
106
107
Sy
112 ksi Axial loading stresses in ksi
100
92 ksi
10 4
80
75 ksi
10 5
61 ksi
A
10 3
~
~
10 6
a
~
~
3
2
40 1 a m = 0.67 (used in Sample Problem 8.2)
20 Point O –120 Sy
–100
– 80 – 60 – 40 – m (compression)
– 20
0
20
JUVINALL: Machine Design Fig. 8-22 W-255
40
60 80 100 +m (tension)
120 Sy
150 Su
(a) Unnotched specimen ("u")
d
(b) Notched specimen ("n")
Calculated nominal stress S
d
U nn
103
104
o tc h
ed sp e c im ens Not che ds pec ime ns
105 Life N (cycles)
106
Sn(u) S (u) Kf = n Sn(n)
Sn(n)
107
(c) Illustration of fatigue stress concentration factor, Kf
JUVINALL: Machine Design Fig. 8-23 W-256
Use these values with bending and axial loads Use these values with torsion 1.0 0.9 0.8 0.7 0.6 q 0.5
Steel Su (ksi) and Bhn as marked
180 (360 Bhn) Bhn) (400 200 0 Bhn) 120 (24 Bhn) 0 8 2 0 Bhn) ( 80 (16 140 hn) n) B 0 20 Bh 60 (1 (20 ) 100 n h 0B ) (16 Bhn 80 (120 hn) B 60 (100 Aluminum alloy (based on 2024-T6 data) 50
0.4 0.3 0.2 0.1 0 0 0
0.02
0.04
0.06 0.08 0.10 Notch radius r (in.)
0.12
0.14
0.16
0.5
1.0
1.5 2.0 2.5 Notch radius r (mm)
3.0
3.5
4.0
JUVINALL: Machine Design Fig. 8-24 W-257
Calculated notch stress (P/A)Kf (MPa)
600
Calculated stresses
300
0
(a)
(b)
(c)
(d)
Actual notch stress (P/A)Kf + residual (MPa)
Sy 300
Actual stresses
0
– 300
300 280
(a)
(b')
(c')
(d')
d' d c'
a (MPa)
c 200
b' a
106 ~ Life 105 ~ Life 104
~ Life 103
100
0
100
Constantlife fatigue diagram
b
200 300 m, tension (MPa)
JUVINALL: Machine Design Fig. 8-25 W-258
~ Life
400
450 Su
r
d
D
T = 1000 ± 250 N • m
T = 1000 ± 250 N • m D/d = 1.2 r/d = 0.05 SF = 2.0
Commercial ground finish Heat-treated alloy steel, Su = 1.2 GPa, Sy = 1.0 GPa
JUVINALL: Machine Design Fig. 8-26 W-259
Alternating torsional stress a (MPa)
Assuming 10 mm < d < 50 mm
Sn = Sn' CLCGCS =
(0.58)(0.9)(0.87) = 272 MPa max = Ssy
300 10 6 ~
200
=∞
100
–100
life
B'
150 116 N'B
B A NA
0' – 200
1200 2
0
100
200
NB 300 400 500 600 Ssy ≈ 0.58(1000) = 580
Mean torsional stress m (MPa)
JUVINALL: Machine Design Fig. 8-27 W-260
700 800 900 Sus ≈ 0.8(1200) = 960
50 mm Ft
Fn r = 5 mm rad., machined surface
100 mm
D = 18 mm (bearing bore) d = 16 mm (shaft dia.)
Alternating bending stress ea (MPa)
f = 0.6 (between the object and the disk) T = 12 N • m (friction torque)
Sn = Sn' CLCGCS =
Sy = 750 MPa
900 2
(1)(0.9)(0.72) = 291 MPa
"Failure point"
300
10 6
200
100
0
Su = 900 MPa
~=∞
max = Sy life
Sy = 750 Su = 900
(15.7, 65.0) "Operating point" 0
100
200
300 400 500 600 700 Mean bending stress em (MPa)
JUVINALL: Machine Design Fig. 8-28 W-261
800
900
0 – 40 – 80 Representive 20-second test
80 60 50 40 103
(a) Stress-time plot
104
105
40
100
3.8 × 104
Stress (ksi)
80
120
1.6 × 104
Reversed stress S (ksi (log))
140
105 N (cycles (log)) (b) S-N curve
JUVINALL: Machine Design Fig. 8-29 W-262
106
107
Representative 6-sec test 500
0 –100 2~
– 200
3~
a
– 300
1~ d
2~ c
b
c'
300 250 200 150
100 103 104 d'' c''
1~ b
b'
105
106
N (cycles)
(a)
(c)
Stress-time plot
S-N plot
107 b''
d'
400 d
Bending stress at critical notch
c' 300
σa (MPa)
a'
3.5 × 106
100
d'
400
2 × 104
200
2.5 × 103
Reversed stress S (MPa)
Bending stress (MPa)
300
P(t) Part c
200
Aluminum alloy Sy = 410 MPa Su = 480 MPa
b' b a' 100
(d)
a
0
100
200 300 m (MPa)
400 Sy
500 Su
(b) m – a plot
JUVINALL: Machine Design Fig. 8-30 W-263
108
T Tensile stress and strength (ksi)
(d) Strength
(c) Total stress, (a) + (b) (a) Load stress Pmax
Compressive stress (ksi)
(b) Residual stress 0
Axis of specimen symmetry and axis of load
Pmax
JUVINALL: Machine Design Fig. 8-31 W-264
P r = 2.5 mm P 35 mm
30 mm 30 mm 30 mm 30 mm P
r = 2.5 mm
P (1)
(2)
JUVINALL: Machine Design Fig. P8-26 W-265
F lb 3 in.
3 in. 2 in. 2 in.
1 in.
1
1 in. dia.
1 16
F lb 2
R
1 4 in. dia.
1 in. dia.
1 8
R
JUVINALL: Machine Design Fig. P8-27 W-266
1 8
R F lb 2
2-mm rad. 24 mm
0.8-mm rad.
20 mm
JUVINALL: Machine Design Fig. P8-28 W-267
24 mm
r = 81 in. Kt = 1.7
4 in.
0.1094 in. F High-carbon steel, 490 Bhn, machined finish 3 4
JUVINALL: Machine Design Fig. P8-30 W-268
in.
0.050 in. 1 2
in. 0.191-in. rad.
0.125-in. dia.
JUVINALL: Machine Design Fig. P8-37 W-268a
60 mm
5-mm rad.
50 mm
5-mm rad.
60 mm
50 mm
+80
Nominal stress (MPa)
1.5 rad.
0 –16 Time
JUVINALL: Machine Design Fig. P8-38 W-268b
1.2-in. dia.
7000 lb • in.
1.0-in. dia. Torque
0.1-in. rad.
1 16
-in. dia. hole
3000 lb • in.
0.1-in. rad. Time
JUVINALL: Machine Design Fig. P8-39 W-268c
25-mm solid round shaft Fillet 2000 N
750 N
Bending Kf = 2.0 Torsional Kf = 1.5 Axial Kf = 1.8
500 N
Pump
Helical spur gear
50 25 0-m m
dia .
JUVINALL: Machine Design Fig. P8-44 W-268d
mm
y x
B
A
Forces act at 500-mm dia. C z
A
B 550 C
400
D
D 400
450
Fy = 1.37 kN Fz = 5.33 kN Fz = 0.3675Fy
Fx = 0.2625Fy
120 dia.
Fy
(1)
Fx = 1.37 kN Forces act at 375-mm dia.
E
Keyway
80 dia.
(Kf = 1.6 for bend and torsion; 1.0 for axial load. Use CS = 1 with these values.) (2)
JUVINALL: Machine Design Fig. P8-45 W-268e
Torsion stress (ksi)
30 20 10 0 –10 – 20 – 30 30 seconds
JUVINALL: Machine Design Fig. P8-46 W-268f
Iron electrode with surplus of electrons
~ +~ + ~ + ~ + + ~ ~ + + ~ ~ ~ +~ ~ + ~ + + ~ ~
Fe2+ ions in solution
Electrolyte
JUVINALL: Machine Design Fig. 9-1 W-269a
~ ~ ~~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~
Plating, as tin or zinc (cathode or anode) Exposed iron (anode or cathode)
Electrolyte
JUVINALL: Machine Design Fig. 9-2 W-269b
A B
~ ~ ~ ~ ~
~ ~ ~ ~
~ ~ ~
~
~
~
Electrolyte
JUVINALL: Machine Design Fig. 9-3 W-269d
Outlet
Inlet
Magnesium anode Insulated copper wire
Magnesium anode
(b) Underground pipe
(a) Water tank
Zinc anodes
Zinc strips between steel spring leaves (c) Leaf spring
JUVINALL: Machine Design Fig. 9-4 W-269e
(d) Ship
–
+
Insulated copper wire
Steel tank
JUVINALL: Machine Design Fig. 9-5 W-269f
Rust particles
Rust particles
Steel
Steel
Steel
(a)
(b)
Rust begins at center of drop
"Crevice corrosion"
JUVINALL: Machine Design Fig. 9-6 W-269g
Steel bolt and nut
Aluminum plates
Nonporous, pliable electrical insulator
JUVINALL: Machine Design Fig. 9-7 W-270
Salt water
All
Ceramics, Glasses
PTFE Epoxies LDPE/HDPE PP PS PVC Nylons
Lead alloys Nickel alloys S-steels Cu-alloys Ti-alloys
Polymers Polyesters Phenolics PMMA
Alloys
Composites GFRP CFRP PTFE, PP Epoxies, PS, PVC Nylons Polymers PMMA HDPE, LDPE, Polyesters Phenolics Lead alloys Alloys Steels CuAlTi-alloys alloys alloys Ni-alloys Cast irons
A
B
KFRP CFRP
Gold Lead Alloys Ti-alloys S-steels Ni-alloys
Al-alloys Cast irons
KFRP
Aerated water
All
GFRP
Composites Ceramics, Glasses
PTFE PVC
Al-alloys
HDPE LDPE, Epoxies Elastomers
Alloys Low alloy steels
C-steel Cast irons
Nylons Polyesters CFRP Phenolics CFRP PS PU Composites PMMA KFRP
Csteels
Mg 0 Zr02 Vitreous ceramics
C-steels
C
D
D
C
B
Al-alloys Many elastomers PTFE PVC PMMA
Ceramics, Glasses KFRP CFRP GFRP
U-V radiation
Glasses
Ceramics, Al203 Glasses Si C
All
Composites
Strong acids
Polymers
Alloys
Nylons
Polymers
PS PVC Most elastomers
LDPE Epoxies, HDPE polyesters, PP, phenolics, PS Filled polymers
Composites GFRP CFRP
All
Alloys All
A Ni-alloys Steels S-steels Cast irons Ti-alloys
PMMA Elastomers Phenomics Si02 Polymers Nylons GFRP Glasses Polyesters LDPE/HDPE Vitreous P.V.,PS,PP,PTFE KFRP ceramics Composites PVC,Epoxy
Polymers KFRP
Cu-alloys Zn-alloys
Si3N4 Si02
Phenomics Polyesters PU LDPE HDPE Epoxies Nylons PP
Ceramics Glasses
Ceramics, Glasses
Strong alkalis
CFRP
Si C, Si3N4 Al203 Zr02 Graphites All
Alloys PTFE
Organic solvents
JUVINALL: Machine Design Fig. 9-8a W-271a
A B C D
Excellent Good Poor Bad
JUVINALL: Machine Design Fig. 9-9 W-272
Mo Cr Co Ni Fe Nb Pt
Zr
Ti Cu Au Ag Al Zn Mg Cd Sn Pb In
In Pb Sn Cd Mg Zn Al Ag Au Cu Ti Zr Pt Nb Fe Ni Co Cr Mo
Two liquid phases One liquid phase, solid solubility below 0.1% Solid solubility between 1 and 0.1% Solid solubility above 1% Identical metals
W
JUVINALL: Machine Design Fig. 9-11 W-274
Increasing compatibility; hence, increasing wear rate
Identical metals Compatible metals Adhesive wear
Poor lube
Unlubed
Unlubed
Good lube Good lube
Poor lube
Unlubed
Incompatible metals
2-body
High abr. 3-body concentr.
10–2
Excellent lube
Poor lube
Good lube
Lubed
Low abr. concentr. Unlubed
Fretting
Good lube
Unlubed
Nonmetal on metal or nonmetal Abrasive wear
Excellent lube
Poor lube
Unlubed
Partly compatible
Excellent lube
10–3 10–4 10–5 Wear coefficient, K
JUVINALL: Machine Design Fig. 9-12 W-275
Lubed
10–6
Exc. lube
F = 20 N
Copper pin 80 Vickers
Pin
Pin
Steel disk 210 Brinell r = 16 mm
Pin volume lost = 2.7 mm3
Disk
Disk volume lost = 0.65 mm3
Disk t=0h
Initial profiles n = 80 rpm
JUVINALL: Machine Design Fig. 9-13 W-276
t=2h Final profiles
z z
Contact area Contact area
R2
p0 p R1 a
p
a y x
x
p0
y
L b y
(a)
(b)
Two spheres
Two parallel cylinders
JUVINALL: Machine Design Fig. 9-14 W-277
– p0 – 0.8p0 0
Stress – 0.4p0
0
0.4p0
0
x = y
Stress – 0.4p0
b
a
0
0.4p0
y x
2b
2a
max 3a p0 = max. contact pressure 4a (a) Two spheres (a is defined in Fig. 9.13a)
Distance below surface
Distance below surface
z
– p0 – 0.8p0
z
3b max 4b
5b
6b p0 = max. contact pressure 7b (b) Two parallel cylinders (b is defined in Fig. 9.13b)
JUVINALL: Machine Design Fig. 9-15 W-278
max ≈ 0.3p0
z ≈ – 0.7p0 0.3p0
y ≈ – 0.1p0
+
0.2p0 0.1p0 +
0 z ≈ – 0.7p0
y ≈ – 0.1p0
x ≈ – 0.25p0 x ≈ – 0.25p0 One plane of maximum shear stress
– 0.6p0
– 0.4p0
JUVINALL: Machine Design Fig. 9-16 W-279
– 0.2p0
0
0.2p0
F
b z
A
y z
B
yz
yz y
A
B
F
0.3p0 0.5b below surface 0.2p0
Stress yz
0.1p0 0 – 0.1p0 p0 = max contact pressure – 0.2p0 – 0.3p0 – 4b
– 3b
– 2b –b 0 b 2b Distance y from load plane
JUVINALL: Machine Design Fig. 9-17 W-280
3b
4b
y
z
Driving cylinder Direction of rotation
yzt = fp0
yt = – 2fp0
yt = 2fp0
y
y yt = 2fp0
yt = – 2fp0
yzt = fp0 b
b
Loaded cylinder (resists rotation to cause some sliding)
Direction of rotation
z
p0 = maximum contact pressure f = coefficient of friction
JUVINALL: Machine Design Fig. 9-18 W-281
2000 N 10.1 mm Hardenedsteel sphere
Hard-bronze bearing alloy spherical seat
JUVINALL: Machine Design Fig. 9-19 W-282
10 mm
Maximum contact stress p0 (MPA)
250 Cast iron Copper Steel
200
150
100
50 5.00
5.01
5.02 Sphere radius, R1 (mm)
JUVINALL: Machine Design Fig. 9-19b W-283
5.03
5.04
Computed maximum elastic contact stress p0 or z (ksi)
800 700 600
Pa ral Rad lel ial rol bal ler l s bea Ang ring ula r-co s nta ct b all Ro bea lle ring rb s ea rin gs
500 400 300
200 150
100 105
Spur gears–high-quality manufacture, case-hardened steel, 60 Rockwell C (630 Bhn) 106
107 108 Life N (cycles (log))
JUVINALL: Machine Design Fig. 9-21 W-285
109
1010
C Key:
+
10 C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
X
Protected ("noble", more cathodic)
11
1 2
13
3
14 C
4
15 Legend: X – Not compatible C – Compatible P – Compatible if not exposed within two miles of a body of salt water F – Compatible only when finished with at least one coat of primer *Applicable forms: 301, 302, 321, and 347 sheet and 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 least one coat of primer.
6 7
15 16 17 18 19 20
C
C
C
C
C
C
C
C
X
C
C
C
C
X
C
C
C
C
C
X
C
C
C
C
C
C
X
C
C
C
C
C
C
X
X
C
C
C
C
C
C
X
X
X
Silver, high-silver alloys
Titanium
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,
8 QQ-B-671, MIL-C 20159, silver solder per QQ-5-561 9 10 11
12 13
Rhodium, graphite, palladium
Nickel, manel, cobalt, high-nickel and high-cobalt alloys
5
14
Gold, platinum, gold-platinum alloys C
12
Commercial yellow brass and bronze; QQ-B-611 brass
Leaded brass, naval brass, leaded bronze C
C
C
C
C
C
C
X
X
X
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
C
X
P
C
X
X
X
C
C
C
C
C
X
P
X
P
C
X
X
X
C
C
C
C
C
X
X
X
X
X
C
X
X
X
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
C
C
X
C
P
X
X
X
P
X
P
C
X
X
X
C
F
F
C
P
X
P
X
X
X
X
P
X
X
C
X
X
X
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
F
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
F
Magnesium
Corroded ("active", more cathodic) –
JUVINALL: Machine Design Tab. 9-1 W-269c
Rivets Total exposed area = 100 cm2 Metal plates Total exposed area = 1 m2
JUVINALL: Machine Design Prob. 9-1 W-269
Chromium-plated steel cap screws Total exposed area = 110 cm2 301 Stainless steel plates Total exposed area = 1.5 m2
Electrolytic environment
JUVINALL: Machine Design Prob. 9-4 W-286
Drain plug (steel)
Insert rod (magnesium) Oil
Crankcase (steel)
JUVINALL: Machine Design Prob. 9-8d W-287
30 cycles/day, every day 100 N
100 N Steel, 100 Bhn Steel, 300 Bhn
30 mm Latch closed
Latch open
JUVINALL: Machine Design Prob. 9-12 W-287a
Locking plate Arm Geneva wheel
100-mm radius
JUVINALL: Machine Design Prob. 9-20 W-288
End of thread
L p
End of thread
L p
End of thread
(a) Single thread–right hand
(b) Double thread–left hand
JUVINALL: Machine Design Fig. 10-1 W-289
p p 8
Crest
60⬚ 30⬚
p 4
Root Root (or minor) dia. dr
Major dia. d Pitch dia. dp
Axis of thread
JUVINALL: Machine Design Fig. 10-2 W-290
Nut tolerance zone Basic profile (as shown in Fig. 10.2) Nut
Basic profile Screw
Screw tolerance zone
JUVINALL: Machine Design Fig. 10-3 W-291
p
p 2
p 2
2␣ = 29⬚
p 2␣ = 29⬚
p 2
0.3p
d
d dr
dm
dr
(a) Acme
dr
(c) Square
d
␣ = 5⬚
p
p
p 2 p 2
dm
(b) Acme stub
p
p 2
dm
0.163p ␣ = 7⬚
5⬚
dm
dr
p 2
d
(d) Modified square
JUVINALL: Machine Design Fig. 10-4 W-292
45⬚ 0.663p
dr
dm
(e) Buttress
d
Weight a dc
Force F
(a)
(b)
JUVINALL: Machine Design Fig. 10-5 W-293
(c)
w A ␣n
fn
dm q L q
n cos ␣n
dm fn
A Scale 4:1
JUVINALL: Machine Design Fig. 10-6 W-294
␣n
n
Section A A (normal to thread)
h ␣n
b tan ␣n = h
b
Screw axis
Section B-B (normal to thread) A h
B
␣ b/cos ␣ tan ␣ =
A
B
Section A-A (through screw axis)
JUVINALL: Machine Design Fig. 10-7 W-295
b h cos
100
f=
90
1 0.0 f=
80
2 0.0 f=
5 0.0 f=
70
0 0.1
Efficiency, e (%)
f= 60
5 0.1
f=
0 0.2
50
40
30 e= 20
cos ␣n – f tan , where cos ␣n + f cos 1
␣n = tan–1 (tan 14 2 ⬚ cos )
10 0 0⬚
10⬚
20⬚
30⬚
40⬚ 50⬚ Helix angle,
60⬚
JUVINALL: Machine Design Fig. 10-8 W-296
70⬚
80⬚
90⬚
Weight = 1000 lb a dc = 1.5 in.
fc = 0.09 Force F f = 0.12 1-in. double-thread Acme screw
JUVINALL: Machine Design Fig. 10-10 W-298
Total = P
Force flow lines
Clamped member
Total = P
Bolt 1 A - shear fracture line for nut thread stripping
2 t
B - shear fracture line for bolt thread stripping
3
A
B dr di dp d
JUVINALL: Machine Design Fig. 10 -11 W-299
Nut
Clamped member
Bolt
Nut
JUVINALL: Machine Design Fig. 10-12 W-300
Pilot surface of bolt
JUVINALL: Machine Design Fig. 10-13 W-301
Motor
Spur gears Motor
Ball thrust bearings
Material being compressed
Material being compressed
Thrust washers
Thrust washers Ball thrust bearings
(a) Screws in compression (poor)
(b) Screws in tension (good)
JUVINALL: Machine Design Fig. 10-14 W-302
Flat washer
(a) Screw
(b) Bolt and nut
(c) Stud and nut
JUVINALL: Machine Design Fig. 10-15 W-303
(d) Threaded rod and nuts
0.65d d 1.5d (b) Square head
(c) Round head
(e) Fillister head
(f ) Oval head
(a) Hexagon head
(d) Flat head
(g) Hexagon socket head
(h) Hex socket headless setscrew (i) Carriage bolt
(j) Round head with Phillips socket
JUVINALL: Machine Design Fig. 10-16 W-304
(Plug in socket) (a) Conventional screwdriver will tighten but not loosen the screw
(5-sided head)
("Spanner head")
(b) Special tool required to tighten or loosen screw
JUVINALL: Machine Design Fig. 10-17 W-305
(c) Break-away heads
T4 T3 Fi
Sy 2
per max theory
Stresses with torques applied Fi
Fi
T1
max =
+
y x
Fi T2
Fi
y
y
Stresses after torques are relieved
y'
x'
Fi
+
x (, –)
Mohr circles
JUVINALL: Machine Design Fig. 10-18 W-307
Direct tension, galvanized
Direct tension, black oxide
Bolt tension
Torqued tension, galvanized and lubricated
Torqued tension, galvanized (high friction)
Torqued tension, black oxide
Bolt elongation
JUVINALL: Machine Design Fig. 10-19 W-308
(a) Helical (split) type
(b) Twisted-tooth type (Teeth may be external, as in this illustration, or internal.)
JUVINALL: Machine Design Fig. 10-20 W-309
(a)
(b)
JUVINALL: Machine Design Fig. 10-21 W-310
(a) Insert nut (Nylon insert is compressed when nut seats to provide both locking and sealing.)
(b) Spring nut (Top of nut pinches bolt thread when nut is tightened.)
JUVINALL: Machine Design Fig. 10-22 W-311
(c) Single thread nut (Prongs pinch bolt thread when nut is tightened. This type of nut is quickly applied and used for light loads.)
Starting
Fully locked
Spring- top nut (Upper part of nut is tapered. Segments press against bolt threads.)
Nylon-insert nuts (Collar or plug of nylon exerts friction grip on bolt threads.)
Distorted nut (Portion of nut is distorted to provide friction grip on bolt threads.)
(a)
(b)
(c)
JUVINALL: Machine Design Fig. 10-23 W-312
Fe
Fb = Fi
Fc = Fi
Fe (a) Complete joint
Fb
Fe (b) Free body without external load
JUVINALL: Machine Design Fig. 10-24 W-313
(c) Free body with external load
Fc
g Fe
Fc
Fb (a)
(b)
Fi
Fc = Fi
Fb
Fc
Soft gasket
b =
Fb
F
Fc Fc
Fb and Fc
F
i a n
d
F
e
Fb
0
Fe (Separating force per bolt)
(c) (d)
JUVINALL: Machine Design Fig. 10-25 W-314
"Rubber" portion of bolt
Fb
Fi
Fc
g Fb
Fc
Fb and Fc
Fb
Fb = Fi
Fc = Fi – Fe
Fe Fc = 0
Fb
"O-ring" gasket
0 (a)
(b)
(c)
JUVINALL: Machine Design Fig. 10-26 W-315
Fe (Separating force per bolt) (d)
Force
Fb = Fi +
kb F kb + kc e
Fb = Fe
B
Fb
⌬ Fb
Fc
⌬ Fc
Fi
kc Fc = Fi – F kb + kc e
C
A
Fc = 0
0 External load Fe
JUVINALL: Machine Design Fig. 10-27 W-316
Fluctuations in Fb and Fc corresponding to fluctuations in Fe between 0 and C
Conical effective clamped volume
d g
30°
d1
d2 d3
JUVINALL: Machine Design Fig. 10-28 W-317
(Hexagonal bolt head and nut)
P
Connecting rod and cap a
a A
A P
(a) Bolt bending caused by nonparallelism of mating surfaces. (Bolt will bend when nut is tightened.)
(b) Bolt bending caused by deflection of loaded members. (Note tendency to pivot about A; hence, bending is reduced if dimension a is increased.)
JUVINALL: Machine Design Fig. 10-29 W-318
Rotating shaft
9 kN Pillow block Metric (ISO) screw
JUVINALL: Machine Design Fig. 10-30 W-319
F 2
F 2 F
F 2
F F 2
(a)
(b)
Normal load, carried by friction forces
Overload, causing shear failure
JUVINALL: Machine Design Fig. 10-31 W-320
150 24 kN
500
24 kN D
400
150
D
150 E
100 A
JUVINALL: Machine Design Fig. 10-32 W-321
144-kN applied overload F 150
F
144 kN 180
180 100
48 CG of bolt group cross section 144 kN (150 mm) = 21.6 kN m
200
F
200 180
48
JUVINALL: Machine Design Fig. 10-33 W-322
48
V
Case 2 – Fi = 38.3 kN (bolt tightened to full yield strength)
40
Bolt yields slightly, with no increase in load or stress during first application of Fe
38.3 Fb
Force (kN)
35.3
Fc
30 29.3
20
Case 1 – Fi = 10 kN 13 Fb
10
9
Fc Fe
4 0 Bolt tight, machine not yet turned on
Machine operating at normal load
Machine turned off
Time (a) Fluctuation in Fb and Fc caused by fluctuations in Fe 900 Su = 830 800 Sp = 660 700 Sp = 600
Stress, (MPa)
600 500
Fluctuation in thread root stress – Case 2, Fi = 35.3 kN 505
400
Fluctuation in thread root stress – Case 1, Fi = 10 kN
300 12% elongation @ Su specified for class 8.8 200 = 0.0032 @ Sy = 660 on idealized curve
100 0 0
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 Strain, (b) Idealized (not actual) stress–strain curve for class 8.8 bolt steel
JUVINALL: Machine Design Fig. 10-34ab W-323
Alternating stress, a (MPa)
400
300
Sn = Sn' CLCS CG = 830 (1)(1)(0.9) = 373 MPa 2 ⬁ Life
Operation at overload on verge of causing eventual fatigue failure 4
200 130 100 0 0
During normal operation
2
Sy = 660
77
200 400 Mean stress, m (MPa)
Su = 830
600
800 1 After initial 3 tightening After shut-down following normal operation
(c) Mean stress-alternating stress diagram for plotting thread root stresses
JUVINALL: Machine Design Fig. 10-34 W-324
Steel bolt, 1 '' – 13 UNC, 2
Fmax
0 to Fmax
External load Fe
grade 5 with cut threads 0 to Fmax, fluctuating external force
g = 2''
Fe
Steel member
Time (b) Fluctuating separating force versus time
(a) Simplified model of machine members bolted together
SSnn == SS'n' CLCG CS ==
a (ksi)
60
40
120 120 (1)(0.9)(1) (1)(0.9)(1) == 54 54 ksi ksi 22
Limiting point for case a Limiting point for case a
a = 37
Limiting point for case b Limiting point for case b
a = 23 20
a = 22.7 Suy = 120 Sy = 92
0 0
20
40
60 m (ksi)
80
(c) Fatigue diagram for thread root
JUVINALL: Machine Design Fig. 10-35a-c W-325, 326a
100
120
Aluminum cover plate, E = 70 GPa
Class 8.8 steel bolt g/2 g/2
Fe "O-ring" gasket
250 mm 350 mm
JUVINALL: Machine Design Fig. 10-36 W-327
Cast-iron cylinder, E = 100 GPa
Weight = 10,000 lb a dc = 2.0 in.
fc = 0.10 Force F f = 0.13 1-in. double-thread Acme screw
JUVINALL: Machine Design Fig. P10-1 W-328
1/2 in. Acme thread dc = 5/8 in.
5 in.
JUVINALL: Machine Design Fig. P10-09 W-330
Fe
Fe = 0 to 8,000 lb kc = 6kb
Fe
JUVINALL: Machine Design Fig. P10-17 W-329
A
Spring washer
A
1000 N 1000 N
1000 N
1000 N
Spring washer
(1)
(2)
JUVINALL: Machine Design Fig. P10.26 W-331
JUVINALL: Machine Design Fig. P10-28 W-332
230 mm
140 mm 280 mm
JUVINALL: Machine Design Fig. P10-39 W-333
80
Fb and Fc
Force (kN)
60
Heavy load 40 Light load
30 kN
Light load Fe
20
15 kN
15 kN
Initial tighten 0 Time
JUVINALL: Machine Design Fig. P10-41 W-334
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
22
JUVINALL: Machine Design Fig. P10-44 W-335
JUVINALL: Machine Design Table 10-4 W-306
Before setting After setting
JUVINALL: Machine Design Fig. 11-1 W-336
Full tubular
Bifurcated (split)
Metal-piercing (a) Semitubular
(b) Self-piercing
JUVINALL: Machine Design Fig. 11-2 W-337
(c) Compression
Back (blind) side not accessible
Back (blind) side not accessible
Acute corner "Built-up" lightweight structure
JUVINALL: Machine Design Fig. 11-3 W-338
Mandrel breaks after seating and rivet expansion Trim or grind mandrel
Pulling head Self-plugging blind rivet Blind side upset
Mandrel head collapses as rivet is expanded and pulled through rivet
Pull-through blind rivet Blind side upset
Closed-end break mandrel blind rivet Blind side upset
Open-end break mandrel blind rivet Blind side upset
Drive pin blind rivet
Blind side upset
JUVINALL: Machine Design Fig. 11-4 W-339
(a)
(b)
JUVINALL: Machine Design Fig. 11-5 W-340
(c)
60⬚
60⬚
(a)
(b)
(c)
JUVINALL: Machine Design Fig. 11-6 W-341
45⬚
(d)
t = 0.707
t
h
h
t
h
h
(a" ) Concave weld bead (poor practice)
(a' ) Convex weld bead (a)
(b)
F
F A
A D
B
D
B
C
C
50 mm
mm 50
F
F
(c) Parallel loading
(d) Transverse loading
JUVINALL: Machine Design Fig. 11-7 W-342
(e) Transverse loading
Y 300 100 B
X
A
X
–y G x– 150 20 kN
C Y
20
(a) 295.7 T (45) = t J
80
B
T G
A
B G
802 + 452 J
525.8 t
20 kN T
T (80) 525.8 = J t
80 t
5600 N m •
105 T
1052 + 202 J
T (105) 690.0 = t J
691.9 t
T (20) 131.4 = J t
690.0 t
80 t
131.4 t
(b)
(c)
Torsional stresses
Torsional plus direct shear stresses
JUVINALL: Machine Design Fig. 11-8 W-343
295.7 t
674.1 t
70
A X
A
B 60
B D
=
X 120
26.3 t
=
121.2 t
124 Resultant stress = t
C 160 10 kN
(a)
(b) Stresses on weld AB
JUVINALL: Machine Design Fig. 11-9 W-344
Y' Y
t
G (CG of total weld group) L /2
X
X
y
b
X'
X' G ' (CG of this weld segment) L /2
a Y'
Y
JUVINALL: Machine Design Fig. 11-10 W-345
a 30 m = 60 = 0.5
a (ksi)
13.6
0
19
50 m (ksi)
JUVINALL: Machine Design Fig. 11-11 W-346
62
Removing this material reduces stress concentration at bond edges
(a) Adhesive-bonded metal lap joint
(b) Brazed tubing fittings
JUVINALL: Machine Design Fig. 11-12 W-347
(c) Glued wood joint
F
F
15 mm
JUVINALL: Machine Design Fig. P11-4 W-348
Weld length = 90 mm Sy = 400 MPa SF = 3 E70 series weld
F
3.0 in.
E60 series welding rods Sy = 50 ksi (plates) h = 0.375 in. SF = 3 Note: There are two 3 in. welds.
F JUVINALL: Machine Design Fig. P11-07 W-349
60 kN 100 mm 75 mm 55 mm
Note: Each plate has two 75 mm welds and one 100 mm weld.
JUVINALL: Machine Design Fig. P11-11 W-350
4 in.
4000 lb
3 in.
Note: There are two 4 in. welds.
JUVINALL: Machine Design Fig. P11-12 W-351
Fixed end
Bearing Torsion bar portion
Spline Generous radius Bearing
d Spline
(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 Design Fig. 12-1 W-352
FF
F
F
F d T= D
FD 2
d
F
T= D
F
F
D F d End surface ground flat
(c) Tension spring
(a) Compression spring (ends squared and ground) JUVINALL: Machine Design Fig. 12-2 W-353
(d) Top portion of tension spring shown as a free body in equalibrium
FD 2
=
Tc J
T
0
(a) Straight torsion bar
c
a T
Plane m
n T
= Tc J
Plane
0
d
⬎
b
Tc ⬎ J
(b) Curved torsion bar
JUVINALL: Machine Design Fig. 12-3 W-354
Tc J
T
18
1.8
Ks = 1 + 1.7
0.5 (shear correction only, C use for static loading)
16
1.6
14
1.5
12
Kw and Ks
KwC KsC
1.4
10
8
1.3
Kw
1.2
Ks
1.1
6
Preferred range, ends ground
4
Preferred range, ends not ground 1.0 2
4
6 8 10 Spring index, C = D/d
JUVINALL: Machine Design Fig. 12-4 W-355
12
2 14
KwC and KsC
Kw = 4C – 1 + 0.615 (shear and curvature C 4C – 4 corrections, use for fatigue loading)
JUVINALL: Machine Design Fig. 12-5 W-356
JUVINALL: Machine Design Fig. 12-6 W-357
Wire diameter (in.) 0.004
0.008
0.020
0.040
0.080
0.200
0.400
0.800
450 3000
2500
350 ASTM A313 (302)
ASTM A228 music wire (cold-drawn steel) 300
2000
ASTM A401 (Cr-Si steel)
ASTM A229 ASTM A227
250
ASTM A230 (oil-tempered carbon steel)
1500
ASTM A232 (Cr-Va steel) 200
Inconel alloy X-750 (spring temper)
ASTM A229 (oil-tempered carbon steel) 150
1000
ASTM A227 (cold-drawn carbon steel)
ASTM B159 (phosphor bronze)
100
ASTM A313 (302 stainless steel) 500
50
0 1 0.10
2
3
4
5 6 7 8 91 1.0
2
3
4
5 6 7 8 91 10.0 Wire diameter (mm)
JUVINALL: Machine Design Fig. 12-7 W-358
2
3
4
0 5 6 7 891 100.0
Minimum ultimate tensile strength (ksi)
Minimum ultimate tensile strength (MPa)
400
(a) Ls = (Nt + 1)d
(b) Ls = N t d
(c) Ls = ( Nt + 1)d
JUVINALL: Machine Design Fig. 12-8 W-359
(d) Ls = N t d
(a) Contoured and plate
(b)
(c)
JUVINALL: Machine Design Fig. 12-9 W-360
(d)
0.75 0.7 0.65 Ratio, deflection–free length, ␦/L f
0.6 0.55
Unstable
0.5 0.45 0.4 0.35 A
0.3 B
0.25 0.2 Stable
0.15 0.1 0.05 2
3
4 5 6 7 8 9 10 Ratio, free length–mean diameter, L f /D
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 )
JUVINALL: Machine Design Fig. 12-10 W-361
11
60 lb
D+d ⬍ 1.5 in.
105 lb 1 in. 2
(Spring free)
Lf
(Spring with ⬍ 2.5 in. min. load)
(Spring with max. load)
JUVINALL: Machine Design Fig. 12-11 W-362
Cash allowance
Fs
(Spring solid)
Ls
80 70
0.9Sus ⬇ 0.72 Su
Stress S (% Su)(log)
60 0.54 Su 50 0.395 Su
40
Sn = Su CLCS CG 2 Su = (0.58)(1)(1) 2 = 0.29 Su
30
20 103
104
105 Life N (cycles (log))
JUVINALL: Machine Design Fig. 12-12 W-363
106
0.8
m = 0
0.72
0
a m = 1
0.7
a /Su
0.6
0.54
0.3 0.2
Region of interest
103⬃
0.5 0.4
0
a m ⬍ 1
104⬃
0.395
(0.38, 0.38) 0.29
105⬃
106 + ⬃
0
(0.325, 0.325)
P Static load
0.1
0
a m = 0
(0.265, 0.265) (0.215, 0.215) 0.1
0.2
0.3
0.4
0.5
0.6
0.7 m /Su
0.8
JUVINALL: Machine Design Fig. 12-13 W-364
0
0.80
0.76 0.65
103 ⬃ 104 ⬃
0.53
0.60
max /Su
0.43
0.40
105 ⬃ 106 + ⬃
P
0.20
0
0.20
0.40 min /Su
0.60
JUVINALL: Machine Design Fig. 12-14 W-365
0.80
Torsional stress Ss, max (% Su)
80
76
Calculated curve (from Fig. 12.14) 65
70
Note: For zero-to-max torsional stress fluctuation
60
53
50
43
Shot-peened wire 40 Design curves [1] Non-shot-peened wire 30 103
104
105 Life N, (cycles)
JUVINALL: Machine Design Fig. 12-15 W-366
106
107
1000
(965, 965)
800 800
Infinite life with shot peening (862, 862)
689
Infinite life without shot peening
max (MPa)
510 600
(Static load line) 400
(Load line, slope 600/300 for Sample Problem 12.2)
200
0
200
600 400 min (MPa)
800
JUVINALL: Machine Design Fig. 12-16 W-367
1000
Load stress Load stress plus residual stress +
Without presetting With presetting
0 –
resid from presetting
JUVINALL: Machine Design Fig. 12-17 W-368
600 N
300 N
Squared and ground ends, ASTM A232 spring wire
25 mm 600 N 300 N
Cam
n= 650 rpm
Shaft Key
+ 25
JUVINALL: Machine Design Fig. 12-18 W-369
1200
1000
max (MPa)
800
975
750
600 540 400 max 600 = min 300 200
0
200
400
600 min (MPa)
800
JUVINALL: Machine Design Fig. 12-19 W-369A
1000
1200
F
F
d
r1
d
A r3
r2 r4
B
D D Bending stress at Sec. A: 16FD r1 = r3 d3
Torsional stress at Sec. B: 8FD r4 = d3 r2
JUVINALL: Machine Design Fig. 12-20 W-370
F
JUVINALL: Machine Design Fig. 12-21 W-371
2F L
F
F
L
L
F
L
L
2F = =
6FL bh2 6FL3 Ebh3
(a) Quarter-elliptic (simple cantilever)
2F = =
6FL
=
bh2 6FL Ebh
3
3
(b) Semi-elliptic
JUVINALL: Machine Design Fig. 12-22 W-372
=
6FL bh2 12FL3 Ebh3
(c) Full-elliptic
=
Mc 6Fx = I wt 2
If and t are constant, then x /w must be constant.
L
If and w are constant, then x /t 2 must be constant.
L b
b
x b
F F w
h
F h
h L
t
(a)
(b) t is constant; w varies linearly with L
JUVINALL: Machine Design Fig. 12-23 W-373
(c) w is constant; t varies parabolically with L
F
L
F
L
h
h n leaves Half of nth leaf Half of 3rd leaf Half of 2nd leaf b
Main leaf Half of 2nd leaf Half of 3rd leaf
b n
Half of nth leaf
(a)
(b)
JUVINALL: Machine Design Fig. 12-24 W-374
Clips Fixed pivot
Shackle (permits small fluctuations in spring length)
Fixed pivot
JUVINALL: Machine Design Fig. 12-25 W-375
800 F = 1000 to 5000 N 2F Bolt, Kf = 1.3
Sn a (MPa)
F
a m = 0.67
life, bending
Design overload point
a = 525 400
h = 7 mm k = 30 N/mm
Sy 0
(a)
400
800 m (MPa) (b)
JUVINALL: Machine Design Fig. 12-26 W-376
1200
Su 1600
=
b = 416
6FL3 Ebh3
= 0.0144
FL3 Eh3
;
k=
F Eh3 = 69.33 L3
L = 682 (a) Triangular-plate solution to Sample Problem 12.4
L = 682
L = 682 L = 682 83
b = 416
Eh
3
L3
+
b = 333
1 =
k = k1 + k2 k = 76.30
=
6FL3 Ebh
3
= 0.0180
FL3 Eh
3
83
2 =
4FL3 Ebh
3
= 0.0482
3
k1 =
F Eh = 55.55 1 L3
(b) Trapezoidal plate solution to Sample Problem 12.5
JUVINALL: Machine Design Fig. 12-27 W-377
k2 = 20.75
Eh
3
L3
FL3 Eh3
F
F d
a D
JUVINALL: Machine Design Fig. 12-28 W-378
Thickness = h
F
a
JUVINALL: Machine Design Fig. 12-29 W-379
F
b
Factors for inner surface stress concentration Ki, round and Ki, rect
1.6
1.5
1.4
1.3
1.2
Ki, round Ki, rect
1.1
1.0 2
4
6
8
Spring index, C =
10 D D or d h
JUVINALL: Machine Design Fig. 12-30 W-380
12
Belleville
Wave
Slotted
Finger
JUVINALL: Machine Design Fig. 12-31 W-381
Curve
Internally slotted (as used in automotive clutches)
In series
In parallel
JUVINALL: Machine Design Fig. 12-32 W-382
In series-parallel
JUVINALL: Machine Design Fig. 12-33 W-383
(b) Electric motor brush spring (a) Constant-force extension springs
+
+
+
+
Storage drum
Output drum
Storage drum
Output drum
(c) Two forms of constant spring motors
JUVINALL: Machine Design Fig. 12-34 W-384
Door stop
Center of gravity of 60-lb door 24 in.
110⬚ Torsion bar
End attached to door Fixed end
JUVINALL: Machine Design Fig. P12-3 W-385
Force
Threaded bolt Nut B Support Force
C A
Spring Deflection Deflection Retainer
JUVINALL: Machine Design Fig. P12-11 W-386
F = 3.0 kN di do
Do = 45 mm do = 8 mm No = 5
Di Do
JUVINALL: Machine Design Fig. P12-15 W-387
Di = 25 mm di = 5 mm Ni = 10
F
F = 45 to 90 lb Deflection = 0.5 in. D = 2 in.
F
Squared and ground end
JUVINALL: Machine Design Fig. P12-28 W-388
Valve acceleration
3600 engine rpm 1800 camshaft rpm
+ 0
Cam angle
– "Reversal point" "Reversal point" Valve lift is 0.201 in.
Valve lift is 0.384 in. (maximum-on "nose" of cam)
JUVINALL: Machine Design Fig. P12-34 W-389
Adjusting nut Cap screw
Spring
Support
Roller follower
Stationary guide Oscillating assembly
Cam
Key
Shaft
JUVINALL: Machine Design Fig. P12-35 W-390
F e
JUVINALL: Machine Design Fig. P12-37 W-392
Stationary support
Handle
Tire 35 mm Pivot A
Brake shoe
Spring
Stationary support
Pin stops
JUVINALL: Machine Design Fig. P12-39 W-391
110 mm dia.
25 mm shaft Cable 110 mm dia.
Torsion springs
Cable
JUVINALL: Machine Design Fig. P12-46 W-393
Connecting rod Connecting rod bearing Thrust bearing (flanged portion of main bearing)
Main bearing
Main bearing Crankshaft
Main bearing cap Connecting rod bearing cap
JUVINALL: Machine Design Fig. 13-1 W-395
(a) Hydrodynamic (surface separated)
(b) Mixed film (intermittent local contact)
JUVINALL: Machine Design Fig. 13-2 W-396
(c) Boundary (continuous and extensive local contact)
Oil inlet
Bearing Journal Oil flow
W
W
W
e
W (a) At rest
Minimum film thickness, h0 W (b) Slow rotation (boundary lubrication)
JUVINALL: Machine Design Fig. 13-3 W-397
Resultant oil film force W
(c) Fast rotation (hydrodynamic lubrication)
Boundary lubrication
f Mixed-film lubrication Hydrodynamic lubrication
A n/P (viscosity × rps ÷ load per unit of projected bearing area)
JUVINALL: Machine Design Fig. 13-4 W-398
T
Rubber element Fluid element
Cross-sectional area, A
(a)
␦
Surface velocity, U
F
F h
h
Fh AG where G = shear modulus
Fh A where = absolute viscosity
(b)
(c)
At equilibrium, torque T produces elastic displacement, ␦, across a solid element
At equilibrium, torque T produces laminar flow velocity, U, across a fluid element
␦=
U=
JUVINALL: Machine Design Fig. 13-5 W-399
Temperature (°F) 80
100
120
140
160
180 200
220 240 260 280
104
103
5 3 2
3 2
103
102
5 5
3 2
3 2
102
5 4 3
5
40
4 3
20
2
2 10 1.0 0.9 5
0.7 0.6
4
0.5 3 0.4
2 10
0.3 20
30
40
50
60 70 80 Temperature (°C)
90
JUVINALL: Machine Design Fig. 13-6 W-400
100 110 120 130 140
Absolute viscosity (reyn)
Absolute viscosity (mPa • s)
10 SA E 60 70 50
Overflow rim
Level of liquid in bath Saybolt viscometer
Oil
Bath
Kinematic viscosity, 58 s at 100°C
Bottom of bath Orifice
JUVINALL: Machine Design Fig. 13-7 W-401
n
L
R
c
D
JUVINALL: Machine Design Fig. 13-8 W-402
5000 N Oil viscosity, 50 mPa • s D = 100 mm n = 600 rpm
R = 50 mm
c = 0.05 mm L = 80 mm
JUVINALL: Machine Design Fig. 13-9 W-403
Oil hole W
Partial bronze bearing
Oil level
Journal
JUVINALL: Machine Design Fig. 13-10 W-404
Fixed bearing
Lubricant Rotating journal
W
( + ∂ dy) dx dz ∂y
Lubricant flow
dx dy
Coordinates: x = tangential y = radial z = axial
p dy dz
JUVINALL: Machine Design Fig. 13-11 W-405
dy dx dx dz
(p +
dp dx) dy dz dx
Rotating journal
U
h
Lubricant flow
y
Stationary bearing
JUVINALL: Machine Design Fig. 13-12 W-406
0
1.0
0.1
0.9 L /D = ∞
0.2
1
0.7
1 2
Max.load
0.6
0.3 0.4
Min. friction
1 4
0.5
0.5
0.4
0.6
0.3
0.7
0.2
0.8
0.1
0
0.9
Optimum zone 0.01
0.02
0.04 0.06 0.08 0.1
0.2
0.4
Bearing characteristic number, S =
JUVINALL: Machine Design Fig. 13-13 W-407
0.6 0.8 1.0 R c
2
n P
2
4
6
1.0 8 10
Eccentricity ratio, e/c
Minimum film thickness variable,
h0 c
0.8
200
100
Coefficient of friction variable,
R f c
50 40 30 20 L /D =
1 4
10 1 2
5 4 3
1
2
∞
1
0
0.01
0.02
0.04
0.08 0.1
0.2
0.4
0.6 0.8 1.0
Bearing characteristic number, S =
JUVINALL: Machine Design Fig. 13-14 W-408
R c
2
n P
2
4
6
8 10
1.0
P pmax (gage)
0.8
Minimum film pressure ratio,
0.9
0.6
L /D = ∞
0.7
1
0.5 0.4
1 2
0.3
1 4
0.2 0.1 0
0.01
0.02
0.04 0.06
0.1
0.2
0.4 0.6 0.81.0
Bearing characteristic number, S =
JUVINALL: Machine Design Fig. 13-15 W-409
R c
2
n P
2
4
6
8 10
100
Position of minimum film thickness, (deg*)
90 80 L /D = ∞
70 60
1
50 40
1 2
30
1 4
20 10 0
0.01
0.02
0.04 0.06
0.1
0.2
0.4 0.6 0.8 1.0
Bearing characteristic number, S = * Defined in Figure 13.20
JUVINALL: Machine Design Fig. 13-16 W-410
R c
2
n P
2
4
6
8 10
100
25
L /D = ∞
1 2
1
20
max
70 60
1 4
15
50 1 2
40
10
30 1 5
20 p
0
10
p
∞
0.04 0.06 0.08 0.1
0.2
max
0
0.01
0.02
0.4
Bearing characteristic number, S = * Defined in Figure 13.20
JUVINALL: Machine Design Fig. 13-17 W-411
0.6 0.8 1.0 R c
2
n P
2
4
6
8
0
Position of maximum film pressure, p
Terminating position of film, p (deg*) 0
80
(deg*)
1 4
90
6
L /D =
1 4
L /D =
1 2
5 L /D = 1
Flow variable,
Q RcnL
4
L /D = ∞
3
2
1
0
0.01
0.02
0.04
0.1
0.2
0.4 0.6 0.81.0
Bearing characteristic number, S =
JUVINALL: Machine Design Fig. 13-18 W-412
R c
2
n P
2
4
6
8 10
1.0 L /D = 0.9
1 4
0.8 1 2
Flow ratio,
Qs Q
0.7 0.6 0.5 1
0.4 0.3 0.2
L /D = ∞
0.1 0
0.01
0.02
0.04
0.1
0.2
0.4 0.6
Bearing characteristic number, S =
JUVINALL: Machine Design Fig. 13-19 W-413
R c
1.0 2
n P
2
4
6
8 10
W
n
Oil of viscosity and flow rate Q
e
R = D/2 h0
p
0
p
max
pmax
Film pressure, p Average film pressure = P = W DL
JUVINALL: Machine Design Fig. 13-20 W-414
1000 lb SAE 20 Oil Tavg = 130°F D = 2.0 in. n = 3000 rpm
R = 1.0 in.
c = 0.0015 in. L = 1.0 in.
JUVINALL: Machine Design Fig. 13-21 W-415
Steel backing Bearing material Oil hole Axial groove
JUVINALL: Machine Design Fig. 13-23 W-417
Ungrooved bearing Oil film pressure
Grooved bearing
Oil inlet hole
L 2 Circumferential groove
L 2
D
JUVINALL: Machine Design Fig. 13-24 W-418
Piston Piston pin or wrist pin "Rifle drilled" passage in connecting rod* Oil in
Oil in
Circumferential groove in main bearing
Drilled passage in crankshaft Circumferential groove in rod bearing Circumferential groove in main bearing *If omitted, piston pin bearing is splash lubricated.
JUVINALL: Machine Design Fig. 13-25 W-419
W = 17 kN Force feed, SAE 10 oil Tavg = 82°C D = 150 mm n = 1800 rpm
R = 75 mm
c = ? mm L = ? mm f=?
Power loss = ?
Qs = ?
Oil temperature rise = ?
JUVINALL: Machine Design Fig. 13-26 W-420
0.006 0.005 0.004 0.003
Max. load
h0, minimum oil film thickness (mm)
f, coefficient of friction
0.007
0.015
0.010
200
Q 150
100
Qs f
0.005
50
0.002 0.001 0
Optimum band* 0 0
0.05 0.10 c, radial clearance (mm)
*As defined in Fig. 13.13
JUVINALL: Machine Design Fig. 13-27 W-421
0.15
Q and Qs, oil flow rate (cm3/s)
h0
0.009 0.008
Min. friction
0.020
0.010
Runner
Ro Ri
a>b a
b
Pads
JUVINALL: Machine Design Fig. 13-28 W-422
SAE 10 Oil Tavg = 150°F D = 4.0 in. n = 900 rpm
R = 2.0 in.
c = 0.002 in. L = 6.0 in.
JUVINALL: Machine Design Fig. P13-12 W-423
JUVINALL: Machine Design Fig. P13-27 W-424
4.5 kN SAE ? Oil Tavg = ?°C D = ? in. n = 660 rpm
R = ? in.
c = ? in. L=?
L=?
JUVINALL: Machine Design Fig. P13-29D W-425
1
2
3 (b) Steps in assembly
JUVINALL: Machine Design Fig. 14-1b W-426
4
Extraextralight series
Extralight series
Light series
Medium series
(LL00) (L00)
(200)
(300)
(a) Relative proportions of bearings with same bore dimension
Extraextralight series
Extralight series
Light series
Medium series
(LL00)
(L00)
(200)
(300)
(b) Relative proportions of bearings with same outside diameter
JUVINALL: Machine Design Fig. 14-2 W-427
Loading grooves
(a) Filling notch (loading groove) type
JUVINALL: Machine Design Fig. 14-3a W-428
(c) Double row
JUVINALL: Machine Design Fig. 14-3c W-428
(d) Internal self-aligning
JUVINALL: Machine Design Fig. 14-3d W-428
(e) External self-aligning
JUVINALL: Machine Design Fig. 14-3e W-428
One shield
Snap ring and one shield
Two shields
One seal
Snap ring and two shields
Two seals
Snap ring and one seal
JUVINALL: Machine Design Fig. 14-4 W-429
Shield and seal
Snap ring and two seals
Snap ring
Snap ring shield and seal
Added stabilizing ring (b) One-direction locating
(c) Two-direction locating
JUVINALL: Machine Design Fig. 14-5 W-430
Spherical roller head Crowned roller body
Ro ller axi s Bearing axis Common apex
JUVINALL: Machine Design Fig. 14-8 W-433
(d) Idler sheave (unground bearing)
(e) Rod end bearing
JUVINALL: Machine Design Fig. 14-10 W-436
(h) Integral spindle, shown with V-belt pulley
JUVINALL: Machine Design Fig. 14-10h W-437
+ r dS
+ r
JUVINALL: Machine Design Fig. 14-11 W-438
dH
24 22
Percentage of failures
20 18 16 14 12 10 8 6 Median
4 2 1
2
3
4
5
6 7 Life
8
9
JUVINALL: Machine Design Fig. 14-12 W-439
10 11 12
1.0
Life adjustment reliability factor Kr
0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
90
91
92
93 94 95 96 Reliability r (%)
97
JUVINALL: Machine Design Fig. 14-13 W-440
98
99 100
Radial bearing
1800 rpm
Angular bearing
1800 rpm
Ft = 1.5 kN, Fr = 1.2 kN Light-to-moderate impact Eight hours/day operation
JUVINALL: Machine Design Fig. 14-14 W-441
Case a: 90 percent reliability
Case b: 30,000-hour life No. 211 radial-contact bearing, C = 12.0 kN
1800 rpm
Fr = 1.2 kN Ft = 1.5 kN
100 mm 55 mm
Light-to-moderate impact, Ka = 1.5
21 mm
JUVINALL: Machine Design Fig. 14-15 W-442
Radial load (kN)
7 6 5 4 3 2 1 0
Fr 1000 rpm
1
50%
2
30% 100%
3
No. 207 radialcontact bearing Ka = 1.0 (uniform load)
1
20%
Time
JUVINALL: Machine Design Fig. 14-16 W-443
Note spacers
JUVINALL: Machine Design Fig. 14-17 W-444
JUVINALL: Machine Design Fig. 14-18 W-445
F1
F2
F2
L1
2L1
3L1
JUVINALL: Machine Design Prob. 14-6 W-446
3500 rpm
No. 204 radial ball bearing Fr = 1000 N, Ft = 250 N 90% reliability Light-moderate shock loading L = ? hr life
JUVINALL: Machine Design Prob. 14-10 W-447
Gear
Shaft
JUVINALL: Machine Design Prob. 14-19 W-449
Bearing
A 150-mm dia. 1.2 kN 20°
60 mm
B 300 mm 60 mm
100 mm
Gear 120-mm dia.
JUVINALL: Machine Design Prob. 14-20 W-448
Chain sprocket Clamping supports
2.25 ft
Rotating shaft
1.75 ft
Chain
0.75 ft
600 lb
JUVINALL: Machine Design Prob. 14-21d W-450
600 lb
Right-angle gearing
Parallel gearing
JUVINALL: Machine Design Fig. 15-1 W-451
JUVINALL: Machine Design Fig. 15-2 W-452
Driven gear
Line of centers
Point of contact Pitch point P
Driving gear
Common normal (to tooth surfaces at point of contact)
JUVINALL: Machine Design Fig. 15-3 W-453
Involute curves Base pitch, pb Base circle
JUVINALL: Machine Design Fig. 15-4 W-454
p
Pinion pitch circle
dp
c P (pitch point)
dp
JUVINALL: Machine Design Fig. 15-5 W-455
g
Gear pitch circle
p Pinion base circle
a
(pressure angle)
P b
Gear base circle
JUVINALL: Machine Design Fig. 15-6 W-456
g
Pinion
Base circle Pitch circle
rp a
d g c
P
Pitch circle
f b
Base circle
e
rg
Gear
JUVINALL: Machine Design Fig. 15-7 W-457
Pinion (driving)
Dedendum circle rp
Base circle Pitch circle 0p
Addendum circle Angle of approach
Angle of recess
Dedendum Addendum Position of teeth entering contact Addendum
Position of teeth leaving contact
n a p
c b
Angle of approach Dedendum
Angle of recess
n
Addendum circle Pitch circle Base circle Dedendum circle rg
Gear (driven)
0g
JUVINALL: Machine Design Fig. 15-8 W-458
To p
la nd
Fa ce
wi dt h
b
t0
Fa ce
Addendum ci rcle
Dedendum
Tooth thickness t
Width of space
Pitch
circle
la nd
Whole depth
Fl an k
Working depth
Circular pitch p
Bo tto m
Addendum
Clearance Fillet radius
Dedendum circle Clearance circle (mating teeth extend to this circle)
JUVINALL: Machine Design Fig. 15-9 W-459
6
7
18
20
28
5
80
24 10
26
12
11
JUVINALL: Machine Design Fig. 15-10 W-460
14
30
48
32
22
8
16
36
64
9
40
4
Rack
p Circular pitch
Pinion
JUVINALL: Machine Design Fig. 15-11 W-461
Pitch circle
Dedendum circle
Base circle Base circle
Pitch circle
JUVINALL: Machine Design Fig. 15-12 W-462
Addendum circle
Gear blank rotates in this direction
Rack cutter reciprocates in a direction perpendicular to this page
JUVINALL: Machine Design Fig. 15-14 W-464
01
1
Driven gear
Base circle (This portion of profile is not an involute)
Pitch point, P
b
Addendum circles
a
Interference is on flank of driver during approach Base circle (This portion of profile is not an involute)
Driving gear 2
02
JUVINALL: Machine Design Fig. 15-15 W-465
rp P = 6 teeth/in. = 20° p = –3.0 g
c = 4 in. rg
JUVINALL: Machine Design Fig. 15-16 W-466
(Driving pinion rotates clockwise) p Pitch circle (pinion)
dp
Ft
P Fr
F Fr
F
P
dg g
JUVINALL: Machine Design Fig. 15-17 W-467
Ft
Pitch circle (gear)
b N = 36 teeth (idler)
c N = 28 teeth (output gear) (a)
a N = 12 teeth (input pinion) P=3
600 rpm; 25 hp
Resultant force (applied by shaft to gear) = (1313 + 478)
2 = 2533 lb.
20°
Hcb = 478 lb
45°
(b) c
b
20° a
Hab = 1313 lb Vab = 478 lb
JUVINALL: Machine Design Fig. 15-18 W-468
Vcb = 1313 lb
F
Fr
Ft F h b rf a Constantstrengh parabola
x t
JUVINALL: Machine Design Fig. 15-20 W-470
0.60 0.55
=
Lewis form factor Y
0.50
0.45
25
°
th tee ub t s 0°, =2
=
20
°
0.40 0.35
=
14
1° 2
0.30 0.25 0.20 0.15 12
15
17
20 24 30 Number of teeth N
35 40 4550 60 80 125 275 ∞ (Rack)
JUVINALL: Machine Design Fig. 15-21 W-471
Load
1 revolution Fa = Fm = F 2
F
Time Driving and driven gears
Load
0
Fa = F Fm = 0
F
Driving gear
Idler gear
0 Time F
1 revolution Idler gear
Fat. strength for reversed loading (idler)
40% higher fat. strength for o-max loading (driver and driven) a a
m
Sn
a
0
m (b) Stress fluctuation
JUVINALL: Machine Design Fig. 15-22 W-472
Su
Driven gear
0.60 1000
0.55 r gea ting a in m th tee f o er mb Nu
0.50 Geometry factor J
85 50 35 25 17
0.45 0.40
Load applied at highest point of single-tooth contact (sharing)
0.35 Load applied at tip of tooth (no sharing)
0.30 0.25 0.20 0.15 12
35 15
17
20 24 30 Number of teeth N
45
60
40 50
125 275 ∞
80
(b) 20° full-depth teeth 1000
0.60 0.55
Geometry factor J
0.50 er mb Nu
0.45
ear gg atin m h in eet of t
Load applied at 85 highest point of 50 single-tooth 25 contact 17 (sharing)
Load applied at tip of tooth (no sharing)
0.40 0.35 0.30 0.25 0.20 0.15 12
35 15
17
20 24 30 Number of teeth N (b) 25° full-depth teeth
JUVINALL: Machine Design Fig. 15-23 W-473
45 40 50
60
125 80
275 ∞
Pitch line velocity V (m/s) 0
10
20
30
5 D
cu
tte
rs
*
4
or
m
3
,f
s,
Hob
C
nd and grou , shaved Precision d shaved and groun High precision,
2
1
pin sha
*
tters
g cu
bs Ho
Velocity factor Kv
E
B A
d Highest precision, shaved and groun
0
1000
2000
3000 4000 5000 Pitch line velocity V (ft/min)
* Limited to about 350 Bhn JUVINALL: Machine Design Fig. 15-24 W-474
6000
7000
Electric motor 1720 rpm
Conveyor drive (involves moderate shock torsional loading) 860 rpm
Pinion P = 10 Np = 18 (teeth) 20° full-depth teeth Steel, 330 Bhn
Gear Steel, 290 Bhn (manufacture of pinion and gear corresponds to curve D, Fig. 15.24)
JUVINALL: Machine Design Fig. 15-25 W-475
Gear (driver)
Common normal
Gear (driver)
Common tangent
Vpt Sliding velocity Vp
Vgt
Common normal
Vpt = Vgt Vp = Vg
Vg Vgn = Vpn
Vgn = Vpn
Common tangent Pinion (driven)
Pinion (driven)
(a) General contact position sliding velocity as shown
(b) Teeth in contact at pitch point no sliding
JUVINALL: Machine Design Fig. 15-26 W-476
2.0 1.8 1.6 1.4 1.2 CLi 1.0 0.8 0.6 104
105
106
107 108 Surface fatigue life (cycles)
JUVINALL: Machine Design Fig. 15-27 W-477
109
1010
1011
•
Win = 100 hp 3600 rpm
Negligible shock loading Life: 5 years, 2000 hours/year Full power: 10 percent of time Half power: 90 percent of time Failure in 5 years: 10 percent likely
900 rpm
JUVINALL: Machine Design Fig. 15-28 W-477A
p1 Motor (input)
g2
a
c
Driven machine (output)
b g1
p2
JUVINALL: Machine Design Fig. 15-29 W-478
Ring R
R Planet Arm Sun
P
A
P
P
A
S
S
P
(a) With three planets (typical)
(b) With one planet (for analysis only)
JUVINALL: Machine Design Fig. 15-30 W-479
2Ti /3R
Ti 2Ti
R
3R
4Ti /3R P
R/2 2Ti /3R
2Ti 3R
4Ti R + S 4 R S = Ti 1 + R
To =
4Ti /3R R+S 4
4Ti
A
2Ti 3R
4Ti 3R
3R To Ti
(R = input; A = output; S = fixed member)
JUVINALL: Machine Design Fig. 15-31 W-479A
=
i o
=1+ S R
i V
P R 2
V 2
R+S 4
0 A S
R
(R = input; A = output; S = fixed member)
JUVINALL: Machine Design Fig. 15-32 W-480
i 0 =
V R/2 V/2 (R + S)/4
i S 0 = 1 + R
1
90° = 17 2 teeth (ring)
R Planet will fit here P
S Planet will NOT fit here
Planet will NOT fit here
Planet will fit here P
JUVINALL: Machine Design Fig. 15-33 W-481
90° = 5 teeth (sun)
45 teeth c P = 5, = 25° 15 teeth
Driven machine coupled to this shaft
1 kW, 1200-rpm motor coupled to this shaft B a A b 25 mm
45 teeth
100 mm
25 mm
JUVINALL: Machine Design Prob. 15-21 W-482
To driven machine
36T B 24T, P = 6 64T 2'' A
2''
8''
18T, P = 9
Coupled to 20 lb.in. torque motor
JUVINALL: Machine Design Prob. P15-23 W-482A
Motor
Driven machine
a a
JUVINALL: Machine Design Prob. 15-26 W-483
1700-rpm motor 100-lb.in. torque
16T
32T 2.0''
1'' 90°
A B
JUVINALL: Machine Design Prob. 15-27 W-484
24T
To driven machine
4 5
1
9
3
2 8
Low (L)
7
Neutral (N) High (H)
6 7
4 Hub 4 can "overrun" in this direction
3 Member 2 pushes here to disengage pawl 3
(a)
(b)
JUVINALL: Machine Design Prob. 15-45 W-485
P2
P1 Arm
Output
S1 Input
S2 P2
P1
JUVINALL: Machine Design Prob. P15-47 W-485A
P1 (101 teeth) P2 (102 teeth) Arm S2 (99 teeth) Output
Input S1 (100 teeth)
P1
P2
JUVINALL: Machine Design Prob. P15-50 W-485B
P3 (33 teeth)
P1 (27 teeth) P2 (24 teeth)
S1 (27 teeth) S2 (30 teeth)
S3 (21 teeth) Input
Output
Reverse brake band holds S2 fixed
Low brake band holds S3 fixed
JUVINALL: Machine Design Prob. 15-51 W-486
(b) Rotated spur gear laminations approach a helical gear as laminations approach zero thickness.
JUVINALL: Machine Design Fig. 16-1 W-487
pn
b
d
Section NN (normal plane) b
N
p
R
R
n
a
pn
pa
e c
p N
JUVINALL: Machine Design Fig. 16-4 W-490
Section RR (in plane of rotation)
N
R
R
N
Re =
Section NN (normal plane)
d Section RR (plane of rotation)
JUVINALL: Machine Design Fig. 16-5 W-491
d 2 cos2
Spur gear (helical gear with = 0⬚)
Helical gear Ft
Pitch cylinder
Fr
Pitch cylinder Fa
Ft
Ft
F
Fr
Fr
Section RR (plane of rotation) N
Ft
Isometric view showing helical gear forces
Ft R Top of tooth
N
Fb
R Fa
Top of tooth
d Fr F n Fb
Section NN (normal plane)
JUVINALL: Machine Design Fig. 16-6 W-492
Fr Ft
Fa
Input shaft of driven machine 600 rpm
= 30⬚ (left hand)
Direction of rotation Np = 18 (teeth) Pn = 14 (normal n = 20⬚ plane)
Electric motor hp 1800 rpm
1 2
= 30⬚ (right hand) (a)
(b) Isometric view of motor shaft and pinion
JUVINALL: Machine Design Fig. 16-07 W-493
0.70
500 150 60 30 20 18 16 14 12
0.50
0.40
Number of teeth
Geometry factor J
0.60
0.30 0⬚
5⬚
10⬚
15⬚ 20⬚ Helix angle
25⬚
30⬚
35⬚
500 150 75 50
1.00
30 20
0.95
0.90 0⬚
5⬚
10⬚
15⬚ 20⬚ Helix angle
JUVINALL: Machine Design Fig. 16-8 W-494
25⬚
30⬚
35⬚
Teeth in mating gear
J-factor multiplier
1.05
Pitch cone angles
Pitch cone length, L ␥p b
Pinion back cone
Pinion pitch ␥p cone
r bp
dp
Dedendum
Gear pitch cone
Addendum
Dedendum
Gear pitch dia., dg Gear back cone
Developed back cone radius, r bg
JUVINALL: Machine Design Fig. 16-9 W-495
Circular pitch Face advance
Mean radius
JUVINALL: Machine Design Fig. 16-10 W-496
Spiral angle
Fn F b
Ft
b 2
Fr
Fr
Fn Fa
Ft d 2 dav 2
␥
JUVINALL: Machine Design Fig. 16-12 W-498
Note: Fn is normal to the pitch cone.
0.40 100
0.38 0.36 80
Geometry factor J
0.34 0.32
Teeth in mating gear
0.30
60
50
0.28
40
0.26
30
0.24
20
0.22 15
0.20 0.18 0.16 0
10 20 30 40 50 60 70 80 90 100 Number of teeth in gear for which geometry factor is desired
JUVINALL: Machine Design Fig. 16-13 W-499
65 mm 140 mm
Load D
B
Rotation
Motor
A
C
250 mm
140 mm
JUVINALL: Machine Design Fig. 16-13 W-517
0.36 100 Geometry factor J
0.32 80 60
0.28
50 0.24 40 0.20
30 Teeth in mating gear 12 15 60 80 20 40 Number of teeth in gear for which geometry factor is desired
25 20
0.16 0
JUVINALL: Machine Design Fig. 16-14 W-500
100
0.11
Ng = 100 90
0.10 80
Geometry factor I
0.09
Ng = 70 60
0.08
Ng = 50
0.07
40 20
0.06 15 0.05 0
10
25
30
Teeth in gear
20 30 Number of teeth in pinion NP
JUVINALL: Machine Design Fig. 16-15 W-502
40
50
0.18
0.16
Geometry factor I
Ng = 100 0.14
80
0.12
60
0.10
50 40 0.08 30 0.06 0
15 10
20
25
20 30 Number of teeth in pinion NP
JUVINALL: Machine Design Fig. 16-16 W-503
Teeth in gear 40
50
P
P (planet) R R (ring) S (sun)
S
R
S A
P Fixed arm, A P
JUVINALL: Machine Design Fig. 16-17 W-504
Arm (input member)
P S
R
Left axle
Right axle
P
JUVINALL: Machine Design Fig. 16-18 W-505
Lead, L Axial pitch, P Worm outside dia., dw, out
Worm lead angle, , and gear helix angle,
Pitch dia., dw
Center distance c Pitch dia., dg Keyway
Note: and are measured on pitch surfaces.
Face width, b
JUVINALL: Machine Design Fig. 16-19 W-506
Worm-driving torque
Fwt
Fwa Fwr Fgr
Fgt
Fga
JUVINALL: Machine Design Fig. 16-20 W-507
f Fn cos f Fn cos
Fn cos n sin Fn
f Fn sin
Direction of
Fn cos n cos
Fgt and Fwa
f Fn
f Fn sin
Fn cos n cos
Direction of Fgt and Fwa
Fn cos n sin
Direction of Fga and Fwt n
Fn
Fn sin n
Fn cos n
Direction of Fga and Fwt
Fn sin n
Direction of Fgr and Fwr
Fn cos n
Fn n Direction of Fgr and Fwr
(a) Worm driving (as in Fig. 16.20)
Fn cos n
(b) Gear driving (same direction of rotation)
JUVINALL: Machine Design Fig. 16-21 W-508
Vs
Vg
Gear rotation
Vw Worm Worm rotation Gear
JUVINALL: Machine Design Fig. 16-22 W-509
0.14
Coefficient of friction f
0.12
0.10
0.08
0.06
0.04
0.02
0 0 1
2
4 6
10
2
4 6 100 2 4 6 1000 Sliding velocity Vs (ft /min)
JUVINALL: Machine Design Fig. 16-23 W-510
2
4 6 10,000
Worm: Steel, hardened and ground Nw = 2, RH, p =
5 8
Motor 2 hp., 1200 rpm
1
in., n =14 2 ⬚
Worm Gear
60 rpm Gear: Bronze
JUVINALL: Machine Design Fig. 16-24 W-511
c = 5 in.
80
Coefficient C
ft lb
min ft2 F
70 With fan (as in Fig. 16.26)
60 50 40
Without fan 30 20 10 0 0
400
800 Worm rpm, nw
JUVINALL: Machine Design Fig. 16-25 W-512
1200
1600
Worm: hardened steel rpm =1200
Worm Gear
c ≈ 6 in. Gear: Chill-cast bronze
Speed ratio, 11:1
JUVINALL: Machine Design Fig. 16-27 W-514
JUVINALL: Machine Design Table 16-1 W-501
Pa b
p
JUVINALL: Machine Design Fig. P16-5 W-516
24 teeth
40 teeth
Output
20 teeth
JUVINALL: Machine Design Fig. P16-08 W-515
Input
60 teeth
100 50 teeth 200 125
25 teeth = 0.35 rad right hand
B Motor
A 20 teeth = 0.50 rad left hand 50 teeth Output
JUVINALL: Machine Design Fig. P16-14 W-518
Pinion
Gear 1000 rpm
400 rpm
JUVINALL: Machine Design Fig. P16-19 W-519
Bevel gears: 35 hp Np = 36 Ng = ? b = 2 in. = 20⬚ P=6
1500 rpm
Pinion A
B
Flexible coupling to machine
Gear 3 in.
3 in.
JUVINALL: Machine Design Fig. P16-23D W-520
Bevel gears: 50 hp Np = 30 Ng = 60 b = 3 in. = 20⬚ P=6
Worm Gear
c = 8 in.
Nw = 2 Ng = 55 P=?
JUVINALL: Machine Design Fig. P16-30 W-521
1200 rpm
Gear material: Chill-cast bronze Worm material: Hardened steel Nw = 3 p = 0.5 in. f = 0.029 Ng = 45 n = 20⬚
c = 4.5 in.
b= 1.0 in.
JUVINALL: Machine Design Fig. P16-34 W-522
w 2
h 2
w
h w
w
d
d
w ≈ d/4
w ≈ d/4;
(a) Square key
Key usually has drive fit; is often tapered
h ≈ 3w/4
(b) Flat key
(c) Round key
Keys are tapered and driven tightly; for heavy-duty service
Widely used in automotive and machine tool industries
(d) Kennedy keys
(e) Woodruff key
Usually tapered, giving tight fit when driven into place; gib head facilitates removal
Key is screwed to shaft; hub is free to slide axially – easier sliding is obtained with two keys spaced 180° apart
( f ) Gib-head key
(g) Feather key
JUVINALL: Machine Design Fig. 17-1 W-523
d
D (a) Straight round pin
(b) Tapered round pin (c) Split tubular spring pin
Grooves are produced by rolling, and provide spring action to retain pin (d) Grooved pin
JUVINALL: Machine Design Fig. 17-2 W-524
Basic
Inverted
Basic
Inverted
Internal rings (fit in housing) E-ring External rings (fit on shaft) (a) Conventional type, fitting in grooves
I
I
I
Section II
External ring (fit on shaft)
I
Section II
Internal ring (fit in housing)
(b) Push-on type – no grooves required Teeth deflect when installed to "bite in" and resist removal (less positive than conventional type)
JUVINALL: Machine Design Fig. 17-3 W-525
4-spline
6-spline
10-spline
16-spline
(a) Straight-sided
JUVINALL: Machine Design Fig. 17-4 W-526
(b) Involute
(a) Single mass Mass, m
␦st
Gravitational force, w
Shaft of spring rate k = w/␦st
JUVINALL: Machine Design Fig. 17-5a W-527
(b) Multiple masses ␦1
m1 w1 m1
w1
␦2
␦3
m2
m3
w3
w2 m2
m3
m4
w2
w3
w4
m5
JUVINALL: Machine Design Fig. 17-5b W-527
w5
(c) Shaft mass only
␦st
JUVINALL: Machine Design Fig. 17-5c W-527
Fc (= 2500 N) 30° 50
300
50
Chain
60
FT (= 1000 N) Chain sprocket 100 diameter
Track d T1 A
Track sprockets
T2 B
Track
C
Track sprocket 250 diameter (a) General arrangement
JUVINALL: Machine Design Fig. 17-6a W-528
A
B T2
T1
C
S
d
55
Small gap or spring washer
(b) Shaft layout
Vertical forces A
T1
2490
S
T2
C
T1
B 325
Horizontal forces
687.5
A 2165
50
55
245
50
S 500 (Ft /2)
T2
B C
500 (Ft /2) 937.5
60
VV
1250
VH
113,700 95,800
130,000 MH
MV 80,300 125,000 62,500 Torque (c) Loading diagrams
Sn = S'n CLCGCS = (0.5)(550)(1)(0.9)(0.78) = 186
ea (MPa)
200
"Design overload" point
165
100
ea em = 2.9
0
100
530 200
75,000 90,600
300 em (MPa)
400
(d) Fatigue diagram
JUVINALL: Machine Design Fig. 17-6b-d W-530
450 500
d/8 d/4 d
(a) Loosely fitted key
(b) Key tightly fitted at top and bottom
d/4
d
(c) Shear failure of a tightly fitted key
JUVINALL: Machine Design Fig. 17-7 W-531
Sled-runner keyway
Steel
Profiled keyway
Fatigue stress concentration factor, K f * Bending
Torsion
Bending
Torsion
Annealed (less than 200 Bhn)
1.3
1.3
1.6
1.3
Quenched and drawn (over 200 Bhn)
1.6
1.6
2.0
1.6
* Base nominal stress on total shaft section.
JUVINALL: Machine Design Fig. 17-8 W-532
JUVINALL: Machine Design Fig. 17-9 W-533
Bonded rubber element
(a) Basic shear-type coupling
(b) Constant-stress, constant strain shear coupling
(c) Tube form shear coupling
JUVINALL: Machine Design Fig. 17-10 W-534
(a) Basic Oldham type
(b) Modified type
JUVINALL: Machine Design Fig. 17-12 W-536
JUVINALL: Machine Design Fig. 17-13 W-537
Flexible coupling Motor
0.25-in.-dia. shaft
20 in.
JUVINALL: Machine Design Fig. P17-1 W-538
50 kg
25-mm dia.
600 mm
600 mm
JUVINALL: Machine Design Fig. P17-7 W-539
120 lb 80 lb 2-in.-dia. shaft
20 in.
40 in.
JUVINALL: Machine Design Fig. P17-11 W-540
30 in.
Driven machine Motor
Coupling (2) Shaft
Bearing (2)
(a) Connecting shaft
Electric generator rotor Driver 56 kw
Bearings Shaft Driven 28 kw Bearing (2)
Hydraulic turbine
Driven 28 kw
(c) Hydroelectric generator shaft
(b) Gear input shaft
Bearing (2) Driver
Shaft
Idler
Driven
(d) Idler gear shaft
Needle bearing (2) Shaft Driver
Driven
Shaft
Driver (e) Gear countershaft
Shaft
Driven ( f ) Stationary countershaft
JUVINALL: Machine Design Fig. P17-13a-f W-541,542,543
Fr = 450 lb Fa = 400 lb
3 in. rad Bearing A Ft = 800 lb
5 in. 2 in.
JUVINALL: Machine Design Fig. P17-14 W-544
Bearing B
Fr = 2.4 kN Ft = 4.0 kN A
B
Fa = 1.5 kN
Note: Gear forces act at a 75-mm radius from shaft axis.
125 mm
50 mm
JUVINALL: Machine Design Fig. P17-15 W-545
Chain sprocket
Chain sprocket Clamping supports
Clamping supports
Rotating shaft
Stationary shaft
(a)
(b)
JUVINALL: Machine Design Fig. P17-16 W-546
Friction lining material
Driving shaft
dr Ring element subjected to clamping pressure, p
Driven shaft
ri ro
Provision for axial movement
JUVINALL: Machine Design Fig. 18-1 W-547
r
Flywheel
Clutch plate (driven disk) Pressure plate
Friction planes
Spring Cover
Engine crankshaft
Release bearing
Housing
To transmission
To release Release lever
JUVINALL: Machine Design Fig. 18-2 W-548
Disks a – driving disks (4 disks, 6 friction surfaces) Disks b – driven disks (3 disks, 6 friction surfaces) Seals Oil chamber (pressurized to engage clutch) Piston
Bushing
Oil passage
Output
Key
ri ro Input
Key
Oil passage
JUVINALL: Machine Design Fig. 18-3 W-549
␣ Cone angle
Cone Key
dr sin ␣
Spline (sliding fit) dr
r
ro
ri
␣ F
Spring Cup
Shifting groove
Local pressure = p (b)
(a)
JUVINALL: Machine Design Fig. 18-5 W-551
c
Av
F
F
b
Lever
Ah a
Shoe (block)
A N
Direction of rotation r
A
fN
(b) Shoe and lever as a free body
O Drum
b (a) Brake assembly
a
N fN Inertial and/or load torque, T
Oh Ov
O
(d) Lever proportions for a self-locking brake
(c) Drum as a free body
JUVINALL: Machine Design Fig. 18-6 W-552
120 120
F
400
4 5 3
2
400
Shoe width, 80 mm f = 0.20 pmax = 0.40 N/mm2
300
250 rad.
6
45°
45°
(a) 90°
90° 1 300 F
H45 = 4F H25 = 4F
5
1 O25
80
V25 = F
80
(b)
All dimensions in millimeters
(c) H43 = 4F
H34 = 4F
H54 = 4F 4
H52 = 4F
3 V16 = 0.70F
V63 = 0.2H63 H63 = 10.53F
H36 = 10.53F
6 V36 = 2.11F
H26 = 7.07F O16 T = 880F
(rotation) H13 = 6.53F O13
2
V26 = 1.41F
H16 = 3.46F
(f)
V13 = 2.11F (d)
H62 = 7.07F
V62 = 0.2H62 V12 = 2.41F
H12 = 3.07F (e)
JUVINALL: Machine Design Fig. 18-7 W-553
V52 = F
O12
A'
A ␦n

␣ O3'
␣
O3
B
JUVINALL: Machine Design Fig. 18-8 W-554
O2
c F
0 (18 in d s sin =d
°–
)
dN A
fd
d
2
N
O2
1
r O3
180° – Drum rotation
B
Note: d = O2O3 b = width of shoe
d cos (180° – ) = – d cos
JUVINALL: Machine Design Fig. 18-9 W-555
F
Force to release brake 300 Spring compressed to force F 150 300 rpm
150
200
150
Cast-iron drum Molded composite shoe lining of width b = 50
All dimensions in millimeters
2
O3
C = 500
150
45°
45° 1
200
O2
d 150
(a) Complete brake (b) Drum and right shoe
JUVINALL: Machine Design Fig. 18-10 W-558
F
N Pivot P fN
2
rf 2
r
JUVINALL: Machine Design Fig. 18-10 W-556
O2
f dN2 + f dN2' P f dN1 f dN2' ⑀
⑀ f dN2
dN2
rf
dN1 dN2'
r
JUVINALL: Machine Design Fig. 18-12 W-557
Hydraulic wheel cylinder Drum
Return spring
Rotation r
O3
C 2
Adjusting cam d
1
Brake lining O2 Anchor pins
JUVINALL: Machine Design Fig. 18-13 W-559
Brake lining
Anchor pin Hydraulic wheel cylinder
Brake drum
Brake shoe Adjusting cam and guide Return spring
Forward rotation
Adjusting cam and guide Hydraulic wheel cylinder Anchor pin
JUVINALL: Machine Design Fig. 18-14 W-560
Band of width = b
Rotation
Cutting plane for free-body diagrams
r
F a
P1 P1
P2 P2 c
JUVINALL: Machine Design Fig. 18-15 W-561
d/2
d/2
P + dP
P d dN
Rotation
JUVINALL: Machine Design Fig. 18-16 W-562
Band of width = b Rotation
P2
F
s P1 a c
JUVINALL: Machine Design Fig. 18-17 W-563
Band width, b = 80 mm Rotation = 270°
Friction coefficient, f = 0.20 Maximum lining pressure, pmax = 0.5 MPa r = 250 mm P2
P1 s = 35 mm
a = 150 mm c = 700 mm
JUVINALL: Machine Design Fig. 18-18 W-564
F
Pads of diameter = 60 mm
125 mm
320 mm pmax = 500 kPa f = 0.30
JUVINALL: Machine Design Fig. P18-12 W-567
4m/s
1000 kg
JUVINALL: Machine Design Fig. P18-14 W-565
Friction clutch
Electric motor
Rotary inertial load, I = 0.7 N • m • s2
Gear reducer
T = 6 N • m, 600 rpm
JUVINALL: Machine Design Fig. P18-17 W-568
F = 1500 N 400 mm
500 mm
Rotation
200 mm 340 mm
JUVINALL: Machine Design Fig. P18-17 W-569
F 250 mm
320 mm
A
240 mm
Rotation 150 mm
400 mm
JUVINALL: Machine Design Fig. P18-22 W-570
500 mm Spring
400 mm 300 mm
350 mm
JUVINALL: Machine Design Fig. P18-23 W-571
Woven lining 23 in. 4 6 5 in.
5 in.
Cast- iron drum
3
30 in.
5 Rotation
5
25 in.
18 in.
150
18 in.
2
JUVINALL: Machine Design Fig. P18-24 W-572
1
Rotation
500 mm
F = 300 N
JUVINALL: Machine Design Fig. P18-31 W-573
75
258° 240
72 55
370
F
JUVINALL: Machine Design Prob. 18-33 W-574
270°
a s
Wt.
c
JUVINALL: Machine Design Prob. 18-34 W-575
Tight side Pivot
Motor rotation
Overhang (b) Pivoted, overhung motor
Adjustment Pivot
Idler
Weight Tight side (a) Manual adjustment (c) Weighted idler pulley
JUVINALL: Machine Design Fig. 19-1 W-576
A
0.88 in.
0.66 in.
0.50 in.
C
0.41 in.
0.31 in.
0.53 in.
B 1.50 in. 1.25 in. E
D
0.91 in.
0.75 in.
(a) Standard sizes A, B, C, D, and E
1.0 in. 0.62 in. 0.38 in.
8V 0.54 in.
3 V 0.32 in. 5V
(b) High-capacity sizes 3V, 5V, and 8V
JUVINALL: Machine Design Fig. 19-2 W-577
0.88 in.
dN/2 sin 
dN 2
dN
2 ≈ 36°
(a)
(b)
JUVINALL: Machine Design Fig. 19-4 W-579
Rubber Fabric cover Tensioncarrying cords
JUVINALL: Machine Design Fig. 19-5 W-581
p
p
r
Chordal rise, r – rc A
A
B
B Pitch circle
rc
(a)
rc
(b)
JUVINALL: Machine Design Fig. 19-7 W-583
r
Pitch p
(a)
JUVINALL: Machine Design Fig. 19-9 W-584A
A
Gasket Case
Core or inner shroud
i
Impeller Turbine
Oil particle
Fluid circulation
r
Input shaft
r2 r4 (D/2)
Oil seal
r3
Output shaft D
r1
To Ti i
o
Blades
A
Section AA
JUVINALL: Machine Design Fig. 19-10 W-584B
360
320 100 280 Percent slip 20 16 14 12
Percent rated torque
240
8
10
7
200
6
Electric motor torque curve
160
5 120
4
Maximum coupling torque
80
3 2
40
0
0
200
400
600
800 1,000 1,200 Input speed i (rpm)
JUVINALL: Machine Design Fig. 19-11 W-584C
1,400
1,600
1,800
Impeller Turbine
Fluid circulation
Input shaft
Output shaft Reactor
JUVINALL: Machine Design Fig. 19-12 W-585
Turbine
Impeller
Reactor
Input shaft
Output shaft
JUVINALL: Machine Design Fig. 19-13 W-586
One-way clutch
3.2
100
2.8 Converter efficiency
Torque ratio
Coupling efficiency 60
2.0
40
1.6 Converter torque ratio
20
1.2 Coupling torque ratio 0.8
0
0.2
0.4 0.6 Speed ratio
JUVINALL: Machine Design Fig. 19-14 W-587
0.8
0 1.0
Efficiency (%)
80
2.4
␣ ␣ 1
r2
r1
2
␣ ␣ c
JUVINALL: Machine Design Fig. P19-3 W-588
C
B A D
JUVINALL: Machine Design Fig. P19-4 W-589
V-belt  = 18° f = 0.20 n = 4000 rpm
r = 100 mm Pulley radius = 170°
Belt maximum tension = 1300 N Belt unit weight = 1.75 N/m
JUVINALL: Machine Design Fig. P19-8 W-590
Electric motor n = 1780 rpm 55% rated power
Driven machine
Fluid coupling — performance curves — Fig. 19.11
JUVINALL: Machine Design Fig. P19-15 W-591
3.7 in. dia. Multiple V-belt,  = 18°, size 5V Unit weight = 0.012 lb/in. Power input = 25 hp Pmax = P1 = 150 lb f = 0.20
Driving pulley n = 1750 rpm 165° angle of wrap
Driven pulley Number of belts = ?
JUVINALL: Machine Design Fig. U19-1 W-580
Fluid coupling
B1 C1
B2 C2
Gear interface
Gear
Torque ratio Tout /Tin
Neutral
–
1
3.66
B3
Neutral
Front planetary train
Fluid coupling
Rear planetary train
Bearing
S1, P1, R1
B1 C1
B2 C2
S2, P2, R2 S3, P3, R3
B1 C1
B2 C2
1.44
2.53
B1 engaged
B2 engaged
1.00
2.53
C1 engaged
B2 engaged
B3
1
S1, P1, R1
No clutches or brakes engaged
S2, P2, R2 S3, P3, R3
2
2.53
39% B3
3
2
1.44
1.44
1.00
61%
B1 engaged S1, P1, R1
39%
S2, P2, R2 S3, P3, R3 4 B1
C1
B2 C2
1.00
Reverse
B1
B2 C2
C2 engaged
1.44
–2.99
B1 engaged
B3 engaged
B3
(b) Power flow block diagram
Gear
Ratio
Neutral
–
1
3.66
2
2.53
3
1.44
4
1
Reverse
–4.31
C1
B1
4
S1, P1, R1
S2, P2, R2 S3, P3, R3
B1 C1
B2 C2
B3
Reverse
S1, P1, R1
1.00
61%
C1 engaged
–4.31
S2, P2, R2 S3, P3, R3
C1
1.00
B3
3
S1, P1, R1
C2 engaged
S2, P2, R2 S3, P3, R3
(a) Internal power flow diagram
(c) Gear shift pattern
JUVINALL: Machine Design Fig. 20-2 W-594
C2
B2
B3
54-tooth ring P Ti × 3 27 Input torque Ti
15-tooth planet Ti P 81
Ti P 40.5
7.5 P 27 P
R1
P1
12-tooth sun
Ti P 81 12 P
Ti P 81
S1
Ti P 81 Ti P 81
Torque from B1: T P 12 (3) TB1 = i 81 P
Ti P 81 Ti P 81
TB1 = 0.44Ti Arm
Ti P 40.5 Output torque: Ti P 19.5 To = (3) 40.5 P To = 1.44Ti
19.5 P To
Ti P 40.5
JUVINALL: Machine Design Fig. 20-3 W-595
A1
Ti P 40.5
Ti P 67.5
Ti P 67.5
12-tooth planet Ti P P2 33.75 Ti P
TB2 =
Ti P 34.5 (3) P 67.5
TB2 = 1.53 Ti
67.5 6 P
Ti
R2 S2
Ti P 67.5
22.5 P
45-tooth sun
Ti 3
•
P 22.5
Ti P 67.5
34.5 P Ti P 67.5 69-tooth ring
Output torque: Ti P 28.5 To = (3) P 33.75
Ti P 33.75
To = 2.53 Ti
28.5 P A2
Ti P 33.75
Ti P 33.75 Arm
JUVINALL: Machine Design Fig. 20-4 W-596
Ti P 67.5
12-tooth planet Ti P P2 33.75
Ti P 67.5
34.5Ti P
Ti
R2, S3
675 S2 Ti P
34.5 •
67.5 Ti P 67.5
10
10 P
22.5 P Ti P 67.5
Ti P 67.5
34.5Ti P 67.5
45-tooth sun
34.5 P
Ti P 67.5
P3 69Ti P
34.5Ti P
675
675
69-tooth ring and 20-tooth sun
16-tooth planet Ti P 33.75
69Ti P 675
28.5 P
18 P
Output torque: Ti P 69Ti P 18 28.5 To = – P P 33.75 675 To = –2.99Ti
A2, A3
Arms
JUVINALL: Machine Design Fig. 20-5 W-597
3
Torque from reverse lock, B3 34.5Ti P 26 TB3 = (3) P 675 TB3 = 3.99Ti
34.5Ti P 675 R3
26 P
34.5Ti P 675 34.5Ti P 675
52-tooth ring
JUVINALL: Machine Design Fig. 20-5 W-598
Torque from C1: T P 12 TC1 = i 3 81 P TC1 = 0.44Ti Ti P 40.5
24-tooth sun Ti P 81 12 P Ti P 81
Output torque: To = 1.00Ti
TC1
A1
TC1 To
19.5 P
S1 Ti P 81 Ti P 40.5
Arm
JUVINALL: Machine Design Fig. 20-6 W-599
Ti P 40.5
For equilibrium of P2: Tf P T P = C2 Tf = 0.39Ti 67.5 103.5 TC2 = 0.61Ti Tf + TC2 = Ti
TC2P 103.5 Tf P
P2
67.5
Clutch torque TC2
0.0117Ti P
28.5 (3) P
To = 1.00Ti R2
S2
22.5 P
Output torque: To = 0.117Ti P
12-tooth planet Tf
∴ Planet pin force = 0.0117Ti P
28.5 P A2
To 34.5 P
45-tooth sun
Arm 69-tooth ring
JUVINALL: Machine Design Fig. 20-7 W-600
h y b Rectangle
h y b Triangle
d
Circle
d
di
Hollow circle
JUVINALL: Machine Design Fig. B-1 W-601
y
d L
z
x Rod y t d
x
z Disk y
b
c
z
a Rectangular prism y
d z
L x Cylinder y
di do z
L x
Hollow cylinder
JUVINALL: Machine Design Fig. B-2 W-602
240 4130
220
Ultimate strength
200
Yield strength
1095
4130 180
160
1050
140
1095
ksi 1040 120
1030 1050
100
1040
80
1030
60
60
1030, 1040, 4130 Reduction of area
1050 1095
40
Elongation
% 20
1030, 1040 1095, 4130
0 400
1050 600
800 1000 Tempering temperature (°F)
JUVINALL: Machine Design Fig. C-5a W-603
1200
200
180
1095 Ultimate strength
160 Yield strength
1050 140 ksi 120
1095 1040 1050
100 1040 80
60
60
1040 Reduction of area
1050 40 1095
Elongation
% 20
1040 1095
0 400
1050 600
800 1000 Tempering temperature (°F)
JUVINALL: Machine Design Fig. C-5b W-604
1200
300
280 9255 Ultimate strength
260 9255
4140, 4340 Yield strength
240 4140 220
4340
ksi 200 180
160
140
120
100 60
Reduction of area 4140
40 4340
%
Elongation 9255 9255
20 4140 0 400
4340 600
800 1000 Tempering temperature (°F)
JUVINALL: Machine Design Fig. C-5c W-605
1200
Diameter of test specimen (mm) 0
200
400
600
800
1000
190
1300
Su Sy
180
1200 170
4340
160
1100 4340
150 1000 140 4140 900
130 3140
ksi
MPa
120 800 110 4140 700
100 3140 90
1040
600
80 500 70
60
50
1040
0
1
2 3 Diameter of test specimen (in.)
JUVINALL: Machine Design Fig. C-6 W-606
400
4
P
L x –PL
␦max P
V
+
V=P
␦
0 0
M –
M = –PL
JUVINALL: Machine Design Fig. D-1(1) W-607
P a
b
x –Pa
␦max
P
V M
+
␦ V=P
0 0 –
M = –Pa
JUVINALL: Machine Design Fig. D-1(2) W-607
L w
wL2 2 V
␦max
x wL +
V = wL
0 0 M –
M = –wL2/2
JUVINALL: Machine Design Fig. D-1(3) W-608
x
–Mb
␦max P
V M
L
␦
Mb
0 0 –
–Mb
JUVINALL: Machine Design Fig. D-1(4) W-608
P
␦ P 2 + V
P 2
L
0 – +
M
x P/2
L 2
–P/2 PL/4
0
JUVINALL: Machine Design Fig. D-2(1) W-609
a Pb L + V
x
P
␦
b
Pb/L
0 – +
M
Pa L
L
Pab/L
–Pa/L
0
JUVINALL: Machine Design Fig. D-2(2) W-609
w wL 2
x L
+ V
wL 2
wL /2
0 –
wL2 2
– wL 2
+ M
0
JUVINALL: Machine Design Fig. D-2(3) W-610
Pb a
L z x ␦ a
V
+ 0 –
M
0 –
P ␦max
PL a b
P
–Pb/a
–Pb
JUVINALL: Machine Design Fig. D-2(4) W-610
a
M0
x M0 L
b L M0 L
+ V
0 M0a L
+ M
M0 L
0 –
–
M0b L
JUVINALL: Machine Design Fig. D-2(5) W-611
M0 a
L x' x
␦ a
V
␦max M0
0 –
M
M0 a b M – a0
0 – M0
JUVINALL: Machine Design Fig. D-2(6) W-611
–
PL 8 P 2 V
P 2
+ 0 –
0 –
L 2
␦
PL 8
+ M
L P
x
–
PL 8
JUVINALL: Machine Design Fig. D-3(1) W-612
PL 8 P 2
–
P 2
–
PL 8
a P 2 – Pab L2
V
M
L b
x
Pa2b L2
2
Pb (3a + b) L3 Pb2 + (3a + b) L3 0 – 2Pa2b2 + L3 0 –
Pab2 – L2
Pb2 (a + 3b) L3 –
Pb2 (a + 3b) L3
–
Pa2b L2
JUVINALL: Machine Design Fig. D-3(2) W-612
L x –
wL2 12 wL 2 V
w
wL 2
+ 0 –
M
␦
wL2 24
+
wL2 12 wL 2
–
wL 2
–
wL2 12
0 – –
wL2 12
JUVINALL: Machine Design Fig. D-3(3) W-612
RB 82.63
85.00
101.6
95.00
RA
2582.21 N • m
122.17
144.81 ROOT 175.84 PITCH 206.88 O.D.
8.68 kN
2
1
3 107
4
5
6
7
10
8
152
9 276 400 530 646 680 716 1060 A shaft with integral worm, dimensions in millimeters.
JUVINALL: Machine Design Fig. D-4 W-613
Class of fit
1
2
3
4
5
6
7
s
h hole h Bar graph (basic hole system)
a
8
h s
h a
a
s
h
s
h
s h
h
s s
s shaft Heavy force and shrink fit
Loose fit
Free fit
Medium fit
Snug fit
Wringing fit
Tight fit
Medium force fit
Cb
.0216 (.0025)
.0112 (.0013)
.0069 (.0008)
.0052 (.0006)
.0052 (.0006)
.0052 (.0006)
.0052 (.0006)
.0052 (.0006)
Cs
.0216 (.0025)
.0112 (.0013)
.0069 (.0008)
.0035 (.0004)
.0035 (.0004)
.0052 (.0006)
.0052 (.0006)
.0052 (.0006)
Ca
.0073 (.0025)
.0041 (.0014)
.0026 (.0009)
.00025 (.00025) .0005 (.0005)
.0010 (.0010)
Ci
0
(0) 0
(0)
Note: Numbers in the table are for use with all dimensions in millimeters, except for those in parentheses, which are for use with inches.
JUVINALL: Machine Design Fig. E-1 W-614
JUVINALL: Machine Design p754 b1 W-???
JUVINALL: Machine Design p754b2 W-604