chapter 19

Hamrock Fundamentals of Machine Elements

Chapter 19: Flexible Machine Elements

Scientists study the world as it is; engineers create the world that

has never been.

Theodore von Karmen


Figure 19.1 Dimensions, angles of contact, and center distance of open flat belt.

Flat Belt

D1

D2

01 02

12

A

B

D

cd


Pivot

Idler

Weight

Tightside

Figure 19.2 Weighted idler used to maintain desired belt tension.

Weighted Idler


Circularpitch

Tooth includedangle Backing

Facing

Pulley face radius

Pulley pitch radius

Neoprene-encasedtension member

Neoprenetooth cord

A

A

Section AA

Figure 19.3 Synchronous, or timing, belt.

Synchronous Belt


ht

wt

dN/2sin

dN

2

236

V-Belt in Groove

Figure 19.4 V-belt in sheave groove.


Driven unit Overload factorAgitatorsLiquid 1.2Semisolid 1.4CompressorCentrifugal 1.2Reciprocating 1.4Conveyors and elevatorsPackage and oven 1.2Belt 1.4Fans and blowersCentrifugal, calculating 1.2Exhausters 1.4Food machinerySlicers 1.2Grinders and mixers 1.4GeneratorsFarm lighting and exciters 1.2Heating and VentilatingFans and oil burners 1.2Stokers 1.4Laundry machineryDryers and ironers 1.2Washers 1.4Machine toolsHome workshop and woodworking 1.4PumpsCentrifugal 1.2Reciprocating 1.4RefrigerationCentrifugal 1.2Reciprocating 1.4Worm gear speed reducers, input side 1.0

Table 19.1 Overload service factors f1 for various types of driven unit.

Overload Service Factors


Belt Size of Minimum pitch diameter, in.type belt, in. Recommended Absolute2L 14 18 1.0 1.03L 38 732 1.5 1.54L 12 516 2.5 1.8

Motor speed, rpmMotor 575 695 870 1160 1750

horsepower, hp Recommended pulley diameter, in.0.50 2.50 2.50 2.50 0.75 3.00 2.50 2.50 2.50 1.00 3.00 3.00 2.50 2.50 2.25

Table 19.2 Recommended minimum pitch diameters of pulley for three belt sizes.

Table 19.3 Recommended pulley dimensions in inches for three electric motor sizes.

Pulley Design Considerations


Loss in arc of Correctioncontact, deg. factor

0 1.005 0.9910 0.9815 0.9620 0.9525 0.9330 0.9235 0.8940 0.8945 0.8750 0.8655 0.8460 0.8365 0.8170 0.7975 0.7680 0.7485 0.7190 0.69

Table 19.4 Arc correction factor for various angle of loss in arc of contact.

Arc Correction Factor


Speed of Pulley effective outside diameter, in.faster shaft 1.00 2.00 3.00 4.00 5.00 6.00

rpm Rated horsepower, hp500 0.04 0.05 0.06 0.08 0.10 0.121000 0.05 0.08 0.12 0.16 0.19 0.211500 0.06 0.12 0.17 0.22 0.25 0.302000 0.08 0.15 0.23 0.28 0.32 0.392500 0.10 0.18 0.27 0.34 0.39 0.44

3000 0.12 0.21 0.31 0.40 0.31 0.473500 0.14 0.24 0.35 0.44 0.444000 0.16 0.28 0.38 0.464500 0.18 0.31 0.425000 0.20 0.35

(a)

Table 19.5 Power ratings for light-duty V-belts. (a) 2L section with wt = 1/4 in and ht=1/8 in.

Power Ratings for V-Belts


Speed of Pulley effective outside diameter, in.faster shaft 1.50 1.75 2.00 2.25 2.50 2.7 3.00

rpm Rated horsepower, hp500 0.04 0.07 0.09 0.12 0.14 0.17 0.191000 0.07 0.12 0.16 0.21 0.25 0.30 0.341500 0.09 0.15 0.22 0.29 0.35 0.41 0.472000 0.10 0.19 0.27 0.35 0.43 0.51 0.592500 0.11 0.21 0.31 0.41 0.51 0.60 0.69

3000 0.11 0.23 0.35 0.45 0.57 0.68 0.783500 0.11 0.25 0.38 0.50 0.62 0.74 0.844000 0.11 0.26 0.40 0.54 0.66 0.78 0.884500 0.10 0.25 0.42 0.56 0.68 0.80 0.905000 0.09 0.26 0.42 0.57 0.69 0.80 0.89

(b)

Table 19.5 Power ratings for light-duty V-belts. (b) 3L section with wt = 3/8 in and ht=1/4 in.

Power Ratings for V-Belts (cont.)


Speed of Pulley effective outside diameter, in.faster shaft 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00

rpm Rated horsepower, hp500 0.08 0.14 0.19 0.24 0.29 0.34 0.39 0.44 0.491000 0.11 0.21 0.31 0.41 0.50 0.60 0.69 0.78 0.871500 0.12 0.26 0.40 0.54 0.67 0.81 0.94 1.07 1.202000 0.11 0.30 0.47 0.65 0.82 0.99 1.15 1.31 1.472500 0.09 0.31 0.53 0.73 0.94 1.13 1.32 1.51 1.69

3000 0.06 0.31 0.56 0.79 1.02 1.24 1.45 1.65 1.843500 0.02 0.30 0.57 0.83 1.07 1.31 1.53 1.73 1.924000 0.27 0.56 0.83 1.09 1.33 1.55 1.75 1.924500 0.22 0.54 0.81 1.07 1.30 1.51 1.69 1.845000 0.15 0.47 0.75 1.01 1.23 1.41 1.66 1.65

(c)

Table 19.5 Power ratings for light-duty V-belts. (c) 4L section with wt = 1/2 in and ht=9/32 in.

Power Ratings for V-Belts (cont.)


Pulley combination Nominal center distanceDriver Driven Short center Medium centerpitch pitch Center Center

diameter, diameter, Belt distance, Belt distance,in. in. number in. number in.2.0 2.0 3L200 6.4 3L250 9.43.0 3.0 3L250 7.4 3L310 10.42.0 2.5 3L210 6.6 3L270 9.62.0 3.0 3L220 6.7 3L280 9.73.0 4.5 3L290 8.2 3L350 11.2

2.0 3.5 3L240 7.3 3L300 10.32.0 4.0 3L250 7.2 3L310 10.32.25 4.5 3L270 7.7 3L330 10.72.5 5.0 3L290 8.1 3L350 11.13.0 6.0 3L330 8.9 3L390 11.9

2.0 5.0 3L250 8.0 3L340 11.02.0 6.0 3L310 8.6 3L370 11.63.0 9.0 3L410 10.3 3L470 13.42.0 7.0 3L340 9.2 3L400 12.22.0 9.0 3L390 9.9 3L450 13.0

2.0 10.0 3L420 10.4 3L480 13.61.5 9.0 3L390 10.1 3L450 13.3

(a)

Center Distance for V-Belts

Table 19.6 Center distances for various pitch diameters of driver and driven pulleys. (a) 3L type of V-Belt.


Pulley combination Nominal center distanceDriver Driven Minimum center Short center Medium centerpitch pitch Center Center Center

diameter, diameter, Belt distance, Belt distance, Belt distance,in. in. number in. number in. number in.2.5 2.5 4L170 4.0 4L150 8.0 4L330 12.03.0 3.0 4L200 4.8 4L280 8.8 4L360 12.83.0 4.5 4L240 5.5 4L320 9.6 4L400 13.64.0 6.0 4L300 6.5 4L380 10.6 4L460 14.53.0 6.0 4L280 6.2 4L360 10.3 4L440 14.33.5 7.0 4L320 7.0 4L400 11.1 4L480 15.13.0 7.5 4L320 6.8 4L400 11.0 4L480 15.04.0 10.0 4L410 8.5 4L490 12.5 4L570 16.73.0 9.0 4L360 7.5 4L440 11.7 4L520 15.83.5 10.5 4L420 8.8 4L500 13.0 4L580 17.14.0 12.0 4L470 9.6 4L550 13.8 4L630 18.03.0 10.5 4L410 8.6 4L490 12.9 4L570 17.04.0 14.0 4L530 10.5 4L610 15.0 4L690 19.13.0 12.0 4L450 9.1 4L530 13.4 4L610 17.63.5 14.0 4L520 10.4 4L600 14.8 4L680 19.02.0 9.0 4L350 7.5 4L430 11.8 4L510 15.94.0 18.0 4L650 12.8 4L730 17.3 4L810 21.62.4 12.0 4L440 8.9 4L520 13.3 4L600 17.52.5 18.0 4L480 9.3 4L560 14.3 4L640 18.52.8 14.0 4L510 10.3 4L590 14.7 4L670 19.02.0 11.0 4L400 8.0 4L480 12.5 4L560 16.72.0 12.0 4L430 8.5 4L510 13.0 4L590 17.32.5 15.0 4L530 10.3 4L610 14.9 4L690 19.23.0 13.0 4L630 12.2 4L710 16.8 4L790 21.22.0 14.0 4L490 9.5 4L570 14.1 4L650 18.4

(b)

Center Distance for V-Belts (cont.)

Table 19.6 Center distances for various pitch diameters of driver and driven pulleys. (b) 4L type of V-Belt.


(b)(a)

Figure 19.6 Two lays of wire rope. (a) Lang; (b) regular.

Figure 19.5 Cross-section of wire rope.

Wire Rope


Minimum ModulusWeight sheave Rope Size of of

per height, diameter diameter, outer elasticity,a Strength,b

Rope lb/ft in. d, in. Material wires psi psi6 7 Haulage 1.50d2 42d 14 1 12 Monior steel d/9 14 106 100 103

Plow steel d/9 14 106 88 103Mild plow steel d/9 14 106 76 103

6 19 Standard 1.60d2 26d 34d 14 2 34 Monior steel d/13 d/16 12 106 106 103hoisting Plow steel d/13 d/16 12 106 93 103

Mild plow steel d/13 d/16 12 106 80 1036 37 Special 1.55d2 18d 14 3 12 Monior steel d/22 11 106 100 103

flexible Plow steel d/22 11 106 88 1038 19 Extra 1.45d2 21d 26d 14 1 12 Monior steel d/15 d/19 10 106 92 103

flexible Plow steel d/15 d/19 10 106 80 1037 7 Aircraft 1.70d2 116 38 Corrosion-resistant 124 103

steelCarbon steel 124 103

7 9 Aircraft 1.75d2 18 1 38 Corrosion-resistant 135 103steel

Carbon steel 143 10319-Wire aircraft 2.15d2 132 516 Corrosion-resistant 165 103

steelCarbon steel 165 103

a The modulus of elasticity is only approximate; it is affected by the loads on the rope and, in general, increases with the lifeof the rope.b The strength is based on the nominal area of the rope. The figures given are only approximate and are based on 1-in. ropesizes and 1/4-in. aircraft cable sizes.

Table 19.7 Wire rope data.

Wire Rope Data


Application Safety factor,a nsTrack cables 3.2Guys 3.5Mine shafts, ft

Up tp 500 8.01000-2000 7.02000-3000 6.0Over 3000 5.0

Hoisting 5.0Haulage 6.0Cranes and derricks 6.0Electric hoists 7.0Hand elevators 5.0Private elevators 7.5Hand dumbwaiters 4.5Grain elevators 7.5Passenger elevators, ft/min

50 7.60300 9.20800 11.251200 11.801500 11.90

Freight elevators, ft/min50 6.65300 8.20800 10.001200 10.501500 10.55

Powered dumbwaiters, ft/min50 4.8300 6.6800 8.0

a Use of these factors does not preclude a fatigue failure

Table 19.8 Minimum safety factors for a variety of wire rope applications.

Minimum Safety Factors


50

40

30

20

10

0 10 20 30 40

D/d ratio

Str

eng

th l

oss

, p

erce

nt

100

80

60

40

20

0 10 20 30 40 50 60

D/d ratio

Rel

ativ

e se

rvic

e li

fe, per

cent

Figure 19.7 Percent strength loss in wire rope for different D/d ratios.

Figure 19.8 Service life for different D/d ratios.

Effect of D/d Ratio


MaterialCast Cast Chilled Manganese

Wooda iron b steelc cast irond steele

Rope Allowable bearing pressure, pall, psiRegular lay6 7 150 300 550 650 14706 19 250 480 900 1100 24006 37 300 585 1075 1325 30008 19 350 680 1260 1550 3500Lang lay6 7 165 350 600 715 16506 19 275 550 1000 1210 27506 37 330 660 1180 1450 3300

Table 19.9 Maximum allowable bearing pressures for various sleeve materials and types of rope.

Allowable Bearing Pressures


Roller link

Pitch Pitch

Linkplate

Pinlink

RollerPin

Bushing

pt

rc

r

pt/2

A

Pitch

circle

B C

0

Figure 19.9 Various parts of rolling chain.

Figure 19.10 Chordal rise in rolling chains.

Rolling Chains


Link AverageRoller Pin plate ultimate Weight

Chain Pitch, Diameter, Width, diameter, thickness, strength, per foot,number pt, in. in. in. d, in. a, in. Su, lb lb

a25 1/4 0.130 1/8 0.0905 0.030 875 0.084a35 3/8 0.200 3/16 0.141 0.050 2100 0.21a41 1/2 0.306 1/4 0.141 0.050 2000 0.2840 1/2 5/16 5/16 0.156 0.060 3700 0.4150 5/8 2/5 3/8 0.200 0.080 6100 0.6860 3/4 15/32 1/2 0.234 0.094 8500 1.0080 1 5/8 5/8 0.312 0.125 14,500 1.69100 1 14 3/4 3/4 0.375 0.156 24,000 2.49120 1 12 7/8 1 0.437 0.187 34,000 3.67140 1 34 1 1 0.500 0.219 46,000 4.93160 2 1 18 1

14 0.562 0.250 58,000 6.43

180 2 14 11332 1

1332 0.687 0.281 76,000 8.70

200 2 12 1916 1

12 0.781 0.312 95,000 10.51

240 3 1 78 178 0.937 0.375 130,000 16.90

Table 19.10 Standard sizes and strengths of rolling chains.

Strength of Rolling Chains


Table 19.11: Transmitted power of single-strand, No. 25 rolling chain.

Number of Small sprocket speed, rpmteeth in 100 500 900 1200 1800 2500 3000 3500 4000 4500 5000 5500 6000 6500 7000 7500 8000 8500 9000 10000

small sprocket Type I Type II lubrication11 0.054 0.23 0.39 0.50 0.73 0.98 1.15 1.32 1.42 1.19 1.01 0.88 0.77 0.68 0.61 0.55 0.50 0.46 0.42 0.3612 0.059 0.25 0.43 0.55 0.80 1.07 1.26 1.45 1.62 1.36 1.16 1.00 0.88 0.78 0.70 0.63 0.57 0.52 0.48 0.4113 0.064 0.27 0.47 0.60 0.87 1.17 1.38 1.58 1.78 1.53 1.30 1.13 0.99 0.88 0.79 0.71 0.64 0.59 1.54 0.4614 0.070 0.30 0.50 0.65 0.94 1.27 1.49 1.71 1.93 1.71 1.46 1.26 1.11 0.94 0.88 0.79 0.72 0.66 0.60 0.5115 0.075 0.32 0.54 0.70 1.01 1.36 1.61 1.85 2.06 1.89 1.62 1.40 1.23 1.09 0.96 0.88 0.80 0.73 0.67 0.5716 0.081 0.34 0.58 0.75 1.09 1.46 1.72 1.98 2.23 2.08 1.78 1.54 1.35 1.20 1.07 0.97 0.88 0.80 0.74 0.6317 0.086 0.37 0.62 0.81 1.16 1.56 1.84 2.11 2.38 2.28 1.95 1.69 1.48 1.31 1.18 1.06 0.96 0.88 0.81 0.6918 0.097 0.39 0.66 0.86 1.23 1.66 1.95 2.25 2.53 2.49 2.12 1.84 1.52 1.43 1.28 1.16 1.05 0.96 0.88 0.7519 0.097 0.41 0.70 0.91 1.31 1.76 2.07 2.38 2.69 2.70 2.30 2.00 1.75 1.55 1.39 1.25 1.14 1.04 0.96 0.8120 0.103 0.44 0.74 0.96 1.38 1.86 2.19 2.52 2.84 2.91 2.49 2.16 1.89 1.68 1.50 1.35 1.23 1.12 1.03 0.8821 0.108 0.46 0.78 1.01 1.46 1.96 2.31 2.65 2.99 3.13 2.68 2.32 2.04 1.80 1.61 1.46 1.32 1.21 1.11 0.9522 0.114 0.48 0.82 1.06 1.53 2.06 2.43 2.79 3.15 3.36 2.87 2.49 2.18 1.93 1.73 1.56 1.42 1.29 1.19 1.0123 0.119 0.51 0.86 1.12 1.61 2.16 2.55 2.93 3.30 3.59 3.07 2.66 2.33 2.07 1.85 1.67 1.51 1.38 1.27 1.0624 0.125 0.53 0.90 1.17 1.69 2.26 2.67 3.07 3.46 3.83 3.27 2.83 2.48 2.20 1.97 1.78 1.61 1.47 1.35 1.1625 0.131 0.56 0.94 1.22 1.76 2.37 2.79 3.20 3.61 4.07 3.48 3.01 2.64 2.34 2.10 1.89 1.72 1.52 1.44 1.2328 0.148 0.63 1.07 1.38 1.99 2.67 3.15 3.62 4.28 4.54 4.12 3.57 3.13 2.78 2.49 2.24 2.04 1.86 1.71 1.4630 0.159 0.68 1.15 1.49 2.14 2.88 3.39 3.90 4.40 4.89 4.57 3.96 3.47 3.08 2.76 2.49 2.26 2.06 1.89 1.6232 0.170 0.73 1.23 1.60 2.30 3.09 3.64 4.18 4.71 5.24 5.03 4.36 3.83 3.39 3.04 2.74 2.49 2.27 2.06 1.7835 0.188 0.80 1.36 2.76 2.53 3.40 4.31 4.62 5.19 5.78 5.76 4.99 4.38 3.88 3.48 3.13 2.85 2.60 2.38 2.0440 0.217 0.92 1.57 2.03 2.93 3.93 4.63 5.32 6.00 6.67 7.04 6.10 5.35 4.75 4.25 3.83 3.48 3.17 2.91 2.4945 0.246 1.05 1.78 2.31 3.32 4.46 5.26 6.04 6.81 7.58 8.33 7.28 6.39 5.66 5.07 4.57 4.15 3.79 3.48 2.9750 0.276 1.18 1.99 2.58 3.72 5.00 5.89 6.77 7.64 8.49 9.33 8.52 7.48 6.63 5.93 5.35 4.96 4.44 4.07 3.4855 0.306 1.30 2.21 2.96 4.12 5.54 6.53 7.51 8.46 9.41 10.3 9.83 8.63 7.65 6.85 6.17 5.60 5.12 4.76 4.0160 0.336 1.43 2.43 3.15 4.53 6.09 7.18 8.25 9.30 10.3 11.3 11.2 9.83 8.72 7.80 7.03 6.38 5.83 5.35 4.57

Type II III Type IV lubrication

Chain Power Ratings


Type of input powerInternal combustion Electric motor Internal combustion

engine with or engine withType of driven load hydraulic drive turbine mechanical driveSmooth 1.0 1.0 1.2Moderate shock 1.2 1.3 1.4Heavy shock 1.4 1.5 1.7

Table 19.13: Multiple-strand factors for rolling chains.

Number of strands Multiple-strand factor, a22 1.73 2.54 3.3

Rolling Chain Data

Table 19.12 Service factors for rolling chains.


Drag rope

Gantry line system

15 ft

5 ft

Mast (20 ft)

Multi-part line

Hoist rope

Dragline

Figure 19.11 Typical dragline.

MARCOSTypewritten Text.

chapter 19

Documents

belt sizes

pulley diameter

machine toolshome workshop

type belt

recommended pulley dimensions

desired belt tension

arc of contact

arc of correctioncontact