Chapter 18: Flexible Machine Elements
Scientists study the world as it is,
engineers create the world that has
never been.
Theodore von Karman
Image: An assortment of chains and
belts and their associated sprockets
and pulleys. Courtesy of Sterling
Instrument Co.
©1998 McGraw-Hill
Hamrock, Jacobson and Schmid
Open Flat Belt
Figure 18.1 Dimensions, angles of contact, and center distance of open
flat belt.
©1998 McGraw-Hill
Text Reference: Figure 18.1, page 828
Hamrock, Jacobson and Schmid
Weighted Idler
Figure 18.2 Weighted idler used to maintain desired belt tension.
©1998 McGraw-Hill
Text Reference: Figure 18.2, page 832
Hamrock, Jacobson and Schmid
Timing Belt
Figure 18.3 Synchronous, or
timing, belt.
©1998 McGraw-Hill
Text Reference: Figure 18.3, page 832
Hamrock, Jacobson and Schmid
V-Belt in Sheave Groove
Figure 18.4 V-belt in sheave groove.
©1998 McGraw-Hill
Text Reference: Figure 18.4, page 834
Hamrock, Jacobson and Schmid
Driven unit
Agitato rs
Liquid
Semiliquid
Co mpressor
Centrifugal
Reciprocating
Co nveyo rs and elevators
Package, oven
Belt
Fans and blowers
Centrifugal, calculating
Exhausters
Fo od machiners
Slicers
Grinders and mixers
Generators
Farm lighting and exciters
Heating and ventilating
Fans and oil burners
Stokers
Laundry machinery
Dryers and ironers
Washers
Machine to ols
Home workshop and woodworking
Pumps
Centrifugal
Recprocating
©1998 McGraw-Hill
Overload
facto r
1.2
1.4
Overload Factors
1.2
1.4
1.2
1.4
1.2
1.4
1.2
1.4
1.2
Table 18.1 Overload service
factors (f1) for various types of
driven unit.
1.2
2.4
1.2
1.4
1.4
1.2
1.4
Text Reference: Table 18.1, page 835
Hamrock, Jacobson and Schmid
Minimum Pulley Pitch Diameter
Belt
type
2L
3L
4L
Size of belt, in.
1/4 x 1/8
1/4 x 7/32
1/2 x 5/16
Minimum pitch diameter, in.
Recommended
Absolute
1.0
1.0
1.5
1.5
2.5
1.8
Table 18.2 Recommended minimum pitch diameters of pulley for three
belt sizes.
©1998 McGraw-Hill
Text Reference: Table 18.2, page 836
Hamrock, Jacobson and Schmid
Recommended Pulley Diameter
Motor
horsepower, hp
0.50
0.75
1.00
575
2.50
3.00
3.00
Motor speed, rpm
695
870
1160
Recommended pulley diameter, in.
2.50
2.50
2.50
2.50
2.50
3.00
2.50
2.50
1750
2.25
Table 18.3 Recommended pulley diameters in inches for three electric
motor sizes.
©1998 McGraw-Hill
Text Reference: Table 18.3, page 836
Hamrock, Jacobson and Schmid
Arc Correction Factors
Loss in arc of
contact, deg
0
5
10
15
20
25
30
35
40
45
Correction
factor
1.00
0.99
0.98
0.96
0.95
0.93
0.92
0.89
0.89
0.87
Loss in arc of
contact, deg
50
55
60
65
70
75
80
86
90
Correction
factor
0.86
0.84
0.83
0.81
0.79
0.76
0.74
0.71
0.69
Table 18.4 Arc correction factors for various angles of loss in arc of contact.
©1998 McGraw-Hill
Text Reference: Table 18.4, page 837
Hamrock, Jacobson and Schmid
Power Ratings for Light Duty V-Belt
S peed of faster
shaft, rpm
1.00
1160
1750
3450
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
0.05
0.07
0.14
0.04
0.05
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
Pulley effective outside diameter, in.
2.00
3.00
4.00
5.00
Rated horsepower, hp
0.08
0.12
0.16
0.19
0.13
0.20
0.25
0.28
0.24
0.35
0.44
0.44
0.05
0.06
0.08
0.10
0.08
0.12
0.16
0.19
0.12
0.17
0.22
0.25
0.15
0.23
0.28
0.32
0.18
0.27
0.34
0.39
0.21
0.31
0.40
0.41
0.24
0.35
0.44
0.44
0.28
0.38
0.46
0.31
0.42
0.35
6.00
0.21
0.34
0.12
0.21
0.30
0.39
0.44
0.47
Table 18.5 Power ratings for light duty V-belt. (a) 2L section with wt=1/4 in.
and ht=1/8 in.
©1998 McGraw-Hill
Text Reference: Table 18.5, page 838
Hamrock, Jacobson and Schmid
Power Ratings for Light Duty V-Belt (cont.)
S peed of
faster shaft,
rpm
1160
1750
3450
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
1.50
0.07
0.09
0.11
0.04
0.07
0.09
0.10
0.11
0.11
0.11
0.11
0.10
0.09
Pul ley effective outside diameter, in.
1.75
2.00
2.25
2.50
2.75
Rated horsepower, hp
0.13
0.18
0.23
0.28
0.34
0.17
0.25
0.32
0.39
0.46
0.25
0.38
0.50
0.62
0.73
0.07
0.09
0.12
0.14
0.17
0.12
0.16
0.21
0.25
0.30
0.15
0.22
0.29
0.35
0.41
0.19
0.27
0.35
0.43
0.51
0.21
0.31
0.41
0.51
0.60
0.23
0.35
0.45
0.57
0.68
0.25
0.38
0.50
0.62
0.74
0.26
0.40
0.54
0.66
0.78
0.25
0.42
0.56
0.68
0.80
0.26
0.42
0.57
0.69
0.80
3.00
0.39
0.54
0.83
0.19
0.34
0.47
0.59
0.69
0.78
0.84
0.88
0.90
0.89
Table 18.5 Power ratings for light duty V-belt. (b) 3L section with wt=3/8 in.
and ht=1/4 in.
©1998 McGraw-Hill
Text Reference: Table 18.5, page 838
Hamrock, Jacobson and Schmid
Power Ratings for Light Duty V-Belt (cont.)
S peed of
faster shaft,
rpm
1160
1750
3450
500
1000
1500
2000
2500
3000
3500
4000
4500
5000
2.00
2.25
0.12
0.12
0.02
0.08
0.11
0.12
0.11
0.09
0.06
0.02
-
0.23
0.28
0.30
0.14
0.21
0.26
0.30
0.31
0.31
0.30
0.27
0.22
0.15
Pulley effective outside diameter, in.
2.50 2.75 3.00 3.25
3.50
Rated horsepower, hp.
0.34 0.45 0.56 0.67
0.77
0.44 0.60 0.75 0.90
1.05
0.57 0.83 1.07 1.30
1052
0.19 0.24 0.29 0.34
0.39
0.31 0.41 0.50 0.60
0.69
0.40 0.54 0.67 0.81
0.94
0.47 0.65 0.82 0.99
1.15
0.53 0.73 0.94 1.13
1.32
0.56 0.79 1.02 1.24
1.45
0.57 0.83 1.07 1.31
1.53
0.56 0.83 1.09 1.33
1.55
0.54 0.81 1.07 1.30
1.51
0.47 0.75 1.01 1.23
1.41
3.75
4.00
0.88
1.20
1.73
0.44
0.78
1.07
1.31
1.51
1.65
1.73
1.75
1.69
1.66
0.98
1.34
1.92
0.49
0.87
1.20
1.47
1.69
1.84
1.92
1.92
1.84
1.65
Table 18.5 Power ratings for light duty V-belt. (c) 4L section with wt=1/2 in.
and ht=9/32 in.
©1998 McGraw-Hill
Text Reference: Table 18.5, page 839
Hamrock, Jacobson and Schmid
Center Distances
Pulley combination
Driver pitch Driver pitch
Normal center distance
S hort center
Medium center
diameter, in.
diameter, in.
Belt
number
2.0
3.0
2.0
2.0
3.0
2.0
2.0
2.25
2.5
3.0
2.0
2.0
3.0
2.0
2.0
2.0.
1.5
2.0
3.0
2.5
3.0
4.5
3.5
4.0
4.5
5.0
6.0
5.0
6.0
9.0
7.0
9.0
10.0
9.0
3L200
3L250
3L210
3L220
3L290
3L240
3L250
3L270
3L290
3L330
3L250
3L310
3L410
3L340
3L390
3L420
3L390
Center
distance,
in.
6.4
7.4
6.6
6.7
8.2
7.3
7.2
7.7
8.1
8.9
8.0
8.6
10.3
9.2
9.9
10.4
10.1
Belt
number
3L250
3L310
3L270
3L280
3L350
3L300
3L310
3L330
3L350
3L390
3L340
3L370
3L470
3L400
3L450
3L480
3L450
Center
distance,
in.
9.4
10.4
9.6
9.7
11.2
10.3
10.3
10.7
11.1
11.9
11.0
11.6
13.4
12.2
13.0
13.6
13.3
Table 18.6 Center distances for various pitch diameters of driver and driven pulleys.
(a) 3L type of V-belt.
©1998 McGraw-Hill
Text Reference: Table 18.6, page 839
Hamrock, Jacobson and Schmid
Center Distances (cont.)
Driver
pitch
diameter,
in.
2.5
3.0
3.0
4.0
3.0
3.5
3.0
4.0
3.0
3.5
4.0
3.0
4.0
3.0
3.5
2.0
4.0
2.4
2.5
2.8
2.0
2.0
2.5
3.0
2.0
Driver
pitch
diameter,
in.
2. 5
3. 0
4. 5
6. 0
6. 0
7. 0
7. 5
10.0
9. 0
10.5
12.0
10.5
14.0
12.0
14.0
9. 0
18.0
12.0
18.0
14.0
11.0
12.0
15.0
13.0
14.0
Minimum center
Center
Belt
distance,
number
in.
4L170
4. 0
4L200
4. 8
4L240
5. 5
4L300
6. 5
4L280
6. 2
4L320
7. 0
4L320
6. 8
4L410
8. 5
4L360
7. 5
4L420
8. 8
4L470
9. 6
4L410
8. 6
4L530
10.5
4L450
9. 1
4L520
10.4
4L350
7. 5
4L650
12.8
4L440
8. 9
4L480
9. 3
4L510
10.3
4L400
8. 0
4L430
8. 5
4L530
10.3
4L630
12.2
4L490
9. 5
Short center
Center
Belt
distance,
number
in.
4L150
8.0
4L280
8.8
4L320
9.6
4L380
10. 6
4L360
10. 3
4L400
11. 1
4L400
11. 0
4L490
12. 5
4L440
11. 7
4L500
13. 0
4L550
13. 8
4L490
12. 9
4L610
15. 0
4L530
13. 4
4L600
14. 8
4L430
11. 8
4L730
17. 3
4L520
13. 3
4L560
14. 3
4L590
14. 7
4L480
12. 5
4L510
130
4L610
14. 9
4L710
16. 8
4L570
14. 1
Medium center
Center
Belt
distance,
number
in.
4L330
12.0
4L360
12.8
4L400
13.6
4L460
14.5
4L440
14.3
4L480
15.1
4L480
15.0
4L570
16.7
4L520
15.8
4L580
17.1
4L630
18.0
4L570
17.0
4L690
19.1
4L610
17.6
4L680
19.0
4L510
15.9
4L810
21.6
4L600
17.5
4L640
18.5
4L670
19.0
4L560
16.7
4L590
17.3
4L690
19.2
4L790
21.2
4L650
18.4
Table 18.6 Center distances for various pitch diameters of driver and driven pulleys.
(b) 4L type of V-belt.
©1998 McGraw-Hill
Text Reference: Table 18.6, page 840
Hamrock, Jacobson and Schmid
Wire Rope
Figure 18.5 Cross section of wire rope.
©1998 McGraw-Hill
Text Reference: Figure 18.5, page 841
Hamrock, Jacobson and Schmid
Rope Lay
Figure 18.6 Two lays of wire rope. (a) Lang; (b) regular.
©1998 McGraw-Hill
Text Reference: Figure 18.6, page 842
Hamrock, Jacobson and Schmid
Wire Rope Data
Rope
Wei g ht
per
height,
l b/f t
Mini mu
m s heave
di ameter,
in.
1 .50d 2
42 d
Rope
di a meter,
d, i n.
Materi al
Si ze of
outer
wi res
d/9
d/9
d/9
d/13-d/1 6
d/13-d/1 6
d/13-d/1 6
d/ 22
d/ 22
d/15-d/1 9
d/15-d/1 9
-
Modulus
of
a
elasticity
psi
Strength
ps i
b
Mo nit or s teel
14 x 10 6
10 0 x 103
6
P low st eel
14 x 10
8 8 x 10 3
6
M il d pl ow s teel
14 x 10
7 6 x 10 3
2
6
3
6 x 19
1 .60d
2 6d-34d
1/4 - 2 3/ 4
Mo nit or s teel
12 x 10
10 6 x 10
6
3
St and ard
P low st eel
12 x 10
9 3 x 10
6
3
hoi st ing
M il d pl ow s teel
12 x 10
8 0 x 10
2
6
1 .55d
18 d
1/4 - 3 1/ 2
Mo nit or s teel
11 x 10
10 0 x 103
6
6 x 37 Sp ecial
P low st eel
11 x 10
8 8 x 10 3
2
6
fl exibl e
1 .45d
2 1d-26d
1/4 - 1 1/ 2
Mo nit or s teel
10 x 10
9 2 x 10 3
6
8 x 1 9 Ext ra
P low st eel
10 x 10
8 0 x 10 3
2
fl exibl e
1 .70d
1/ 1 6 - 3/ 8
Corros io n12 4 x 103
7 x 7 Aircraft
res is tant s teel
3
Carbo n s teel
12 4 x 10
2
3
1 .75d
1/8 - 1 3/ 8
Corros io n13 5 x 10
7 x 9 Aircraft
res is tant s teel
Carbo n s teel
14 3 x 103
2
2 .15d
1/3 2 - 5 /16
Corros io n16 5 x 103
19 -Wi re
res is tant s teel
aircraft
Carbo n s teel
16 5 x 103
a
The modul us of el as ti city is o nl y app roximate; it is affected by the loads o n t he rope and, in gen eral , i n creas es
wi th t he l ife of th e ro pe.
b
The s tren gth i s bas ed o n t he n ominal area of t he rope. The figu res gi v en are o nly approxi mat e and are b as ed on 1 i n. rop e si zes and 1/ 4 in . ai rcraft cable s izes.
6 x 7 Haulag e
1/4 - 1 1/ 2
Table 18.7 Wire rope data [From Shigley and Mitchell (1983)]
©1998 McGraw-Hill
Text Reference: Table 18.7, page 843
Hamrock, Jacobson and Schmid
Application
Track cables
Guys
Mine shafts, ft
Up to 500
1000-2000
2000-3000
Over 3000
Hoisting
Haulage
Cranes and derricks
Electric hoists
Hand elevators
Private elevators
Hand dumbwaiters
Grain elevators
Passenger elevators, ft/min
50
300
800
1200
1500
Freight elevators, ft/min
50
300
800
1200
1500
©1998 McGraw-Hill
Safety factora, n s
3.2
3.5
8.0
7.0
6.0
5.0
5.0
6.0
6.0
7.0
5.0
7.5
4.5
7.5
7.60
9.20
11.25
11.80
11.90
Minimum Safety
Factors for Wire Rope
Table 18.8 Minimum safety factors
for variety of wire rope
applications. [from Shigley and
Mitchell (1983)]
6.65
8.20
10.00
10.50
10.55
Text Reference: Table 18.8, page 844
Hamrock, Jacobson and Schmid
Loss in Rope Strength vs. D/d Ratio
Figure 18.7 Percent strength loss in wire rope for different D/d ratios.
©1998 McGraw-Hill
Text Reference: Figure 18.7, page 846
Hamrock, Jacobson and Schmid
Service Life vs. D/d ratio
Figure 18.8 Service life for different D/d ratios.
©1998 McGraw-Hill
Text Reference: Figure 18.8, page 846
Hamrock, Jacobson and Schmid
Maximum Allowable Bending Pressures for
Wire Rope
a
Wood
Rope
Regular Lay
6 x7
6 x 19
6 x 37
8 x 19
150
250
300
350
Material
Cast Iron Cast stee lc Chilled cast
iron d
Allowable be aring pressure, pall, psi
b
300
480
585
680
550
900
1075
1260
650
1100
1325
1550
Lang Lay
6 x7
165
350
600
715
6 x 19
275
550
1000
1210
6 x 37
330
660
1180
1450
a
On end grain of beech, hickory or gum
b
For H B(min.)=125.
c
30-40 carbon; H B(min.)=160.
d
Use only with uniform surface hardness.
e
For high sp eeds with balanced sheaves having ground surfaces.
Manganese
stee le
1470
2400
3000
3500
1650
2750
3300
Table 18.9 Maximum allowable bending pressures for various sheave materials and
types of rope. [From Shigley and Mitchell (1983)]
©1998 McGraw-Hill
Text Reference: Table 18.9, page 847
Hamrock, Jacobson and Schmid
Rolling Chain
Figure 18.9 Various parts of a rolling chain.
©1998 McGraw-Hill
Text Reference: Figure 18.9, page 849
Hamrock, Jacobson and Schmid
Strengths of Rolling Chains
Chain
number
a
25
35a
b
41
40
50
60
80
100
120
140
160
180
200
240
a
b
Pitch
P t , in.
1/4
3/8
1/2
1/2
5/8
3/4
1
1 1/4
1 1/2
1 3/4
2
2 1/4
2 1/2
3
Roller
Diameter
Width,
in.
in.
0.130
0.200 a
0.306
5/16
2/5
15/32
5/8
3/4
7/8
1
1 1/8
1 13/32
1 9/16
1 7/8
1/8
3/16
1/4
5/16
3/8
1/2
5/8
3/4
1
1
1 1/4
1 13/32
1 1/2
1 7/8
Pin
diameter
, d, in.
0.0905
0. 141
0. 141
0. 156
0. 200
0. 234
0. 312
0. 375
0. 437
0. 500
0. 562
0. 687
0. 781
0. 937
Link
plate
thickness,
a
0.030
0.050
0.050
0.060
0.080
0.094
0.125
0.156
0.187
0.219
0.250
0.281
0.312
0.375
Average
ultimate
strength,
S u, lbf
875
2100
2000
3700
6100
8500
14500
24000
34000
46000
58000
76000
95000
130000
Weight
per foot,
lbf
0.084
0.21
0.28
0.41
0.68
1.00
1.69
2.49
3.67
4.93
6.43
8.70
10. 51
16. 90
Witho ut ro llers
Li ghtwei ght rollers
Table 18.10 Standard sizes and strengths of rolling chains.
©1998 McGraw-Hill
Text Reference: Table 18.10, page 850
Hamrock, Jacobson and Schmid
Chordal Rise
Figure 18.10 Chordal rise in rolling
chains.
©1998 McGraw-Hill
Text Reference: Figure 18.10, page 851
Hamrock, Jacobson and Schmid
Transmitted Power
Table 18.11 Transmitted power of single-strand, no. 25 rolling chain.
©1998 McGraw-Hill
Text Reference: Table 18.11, page 853
Hamrock, Jacobson and Schmid
Rolling Chain Service Factors
Type of driven
load
Smooth
M oderate shock
Heavy shock
Type of input power
Internal
Electric motor
combustion engine
or
with hydraulic
turbine
drive
1.0
1.2
1.4
1.0
1.3
1.5
Internal
combustion
engine with
mechanical
drive
1.2
1.4
1.7
Table 18.12 Service factors for rolling chains.
©1998 McGraw-Hill
Text Reference: Table 18.13, page 854
Hamrock, Jacobson and Schmid
Multiple-strand Factors
Number of strands
2
3
4
Multiple-strand factor, a2
1.7
2.5
3.3
Table 18.13 Multiple strand factors for rolling chains.
©1998 McGraw-Hill
Text Reference: Table 18.14, page 854
Hamrock, Jacobson and Schmid
Dragline
Figure 18.11 Typical dragline.
©1998 McGraw-Hill
Text Reference: Figure 18.11, page 856
Hamrock, Jacobson and Schmid