Machine Design Databook Episode 2 part 8 doc

21-4b d ¼ pitch diameter of small sheave, in FLEXIBLE MACHINE ELEMENTS 21.23 Downloaded from Digital Engineering Library @ McGraw-Hill www.digitalengineeringlibrary.com... TABLE 21-26Cor

Mild Steel Pulley

Minimum length of boss (Fig 21-3)

FIGURE 21-3 Mild steel pulley

The crown height

Arms for mild steel pulleys

200 þ 0:24 in for double belt USCS ð21-29dÞ

Refer to Tables 21-16, 21-17A, and 21-17B.

FLEXIBLE MACHINE ELEMENTS 21.21

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The formula to obtain the maximum power in

kilo-watt which the V-belts of sections A, B, C, D, and E

can transmit (Table 21-22 and 21-23)

The equivalent pitch diameter

The formulas to obtain the maximum horsepower of

V-belts of A, B, C, D, and E sections

Refer to Eqs (21-35a) to (21-35e).

Belt Horsepower rating per strandsection (equations in USCS)

D P ¼ V
13:6

V0:09
93:9

kd
0:0848V2

(21-35d)

where

V ¼ belt speed, thousands of ft/min

k ¼ small-diameter factor for speed ratio of drive from Fig 21-4b

d ¼ pitch diameter of small sheave, in

FLEXIBLE MACHINE ELEMENTS 21.23

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FIGURE 21-4(a) Factors for power rating of V-belt for use with Eqs (21-30) to (21-35).

FLEXIBLE MACHINE ELEMENTS 21.25

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TABLE 21-25

Correction factors for arc of contact, Fd

Arc of contact (proportion of 1808 rating) Arc of contact (proportion of 1808 rating)

FIGURE 21-4(b) Factors for horsepower ratings of V-belts

for use with Eqs (21-35a) to (21-35e)

FIGURE 21-4(c) Correction factor K1 for angle ofcontact

TABLE 21-26

Correction factors for belt length, Fc

FLEXIBLE MACHINE ELEMENTS 21.27

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TABLE 21-27

Correction factors for industrial service, Fa

Type of driving unit

AC motors; normal torque, squirrelcage, synchronous and split phase

DC motors; shunt-wound, multiplecylinder internal combustion engines

>600 rpm

AC motors; high torque, high sliprepulsion induction, single phase,series-wound and slip-ring

DC motors; series-wound andcompound wound; single-cylinderinternal-combustion engines;multicylinder internal-combustionengines<600 rpm, line shafts, clutches,brakes, direct on-line starting

Light-duty Agitators for liquids,

blowers, and exhausters,

centrifugal pumps and

Belt conveyors for sand,

grain, etc; dough mixers; fans

over 7.5 kW (10 hp);

generators; line shafts;

laundry machinery; machine

tools; punches, presses and

shears; printing machinery;

positive-displacement rotary

pumps; revolving and

vibrating screens

Heavy-duty Brick machinery, bucket

elevators, exciters, piston

compressors, conveyors

(drag-pan-screw), hammer

mills, paper mill beaters,

piston pumps, positive

mills (ball-rod-tube), hoists,

and rubber

TABLE 21-28

Nominal inside length, nominal pitch lengths and permissible length variations for V-belts

Nominal pitch length, mm

FLEXIBLE MACHINE ELEMENTS 21.29

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TABLE 21-28

Nominal inside length, nominal pitch lengths and permissible length variations for V-belts (Cont.)

Nominal pitch length, mm, Cross section Pitch length variationNominal inside

Dimensions for standard V-grooved pulleys

Pitch Minimum height of Minimum depth of Center to center Edge of pulleyGroove width,lp, groove above pitch line, groove below pitch line, distance of grooves,e, to first groove

TABLE 21-30B

Standard V-belt sections

Minimum sheave hp range, one

TABLE 21-30E

Horsepower rating of standard V-belts

Belt speed, ft/min

FLEXIBLE MACHINE ELEMENTS 21.33

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Number of belts

The diameter of larger pulley

Nominal pitch length of belt

For nominal inside length, nominal pitch lengths

and permissible length variations for standard sizes

of V-belts

Dimensions for standard V-grooved pulley

For small-diameter factor, for speed ratio and length

of belt factor

Recommend standard pitch diameters of pulleys

For further data for design of V-belts in US

Customary system units for use with Eqs (21-35a) to

(21-35e)

Center distance for a given belt length and diameters

of pulleys

Maximum center distance

Minimum center distance

i ¼ PFa

PFcFd

ð21-36Þ where P ¼ drive power in kW

Obtain Fd, Fc, and Fafrom Tables 21-25, 21-26, and 21-27, respectively.

Refer to Figs 21-4a and 21-4b.

Refer to Table 21-30A.

Refer to Tables 21-30B and 21-30F, and Figs 21-4b and 21-4c.

C ¼ L

4

ðD þ dÞ 8 þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

L

4

ðD þ dÞ 8

2

ðD
dÞ28

Belt-length correction factor, K2

Nominal belt length, in

MINIMUM ALLOWANCES FOR

ADJUSTMENT OF CENTERS FOR TWO

TRANSMISSION PULLEYS

Lower limiting value

Higher limiting value

INITIAL TENSION

In order to give the initial tension, the belts may be

stretched to

Arc of contact angle

For V-belt and pulley dimensions as per SAE J 636C

standard

SYNCHRONOUS BELT DRIVE ANALYSIS

The transmission ratio of synchronous belt drive

Datum length of synchronous belt

The minimum number of meshing teeth

z1þ z2þ 

90 8 ðz2
z1Þ

 ð21-46bÞ

l  2C p

2 ðz1þ z2Þ þ

p 2

2

ðz2
z1Þ2

l approximate ð21-46cÞ

FLEXIBLE MACHINE ELEMENTS 21.35

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For S1 synchronous belts and pulley dimensions and

Standard pitch value

Standard belt center distance tolerances

Source: V-belts and Pulleys, SAE J 636 C Reprinted with permission

from SAE Handbook, Part I, 1977, Society of Automotive Engineers,

Inc

For determining the center distance of synchronous

belt pulleys.a

The distance from belt pitch line to the pulley—tip

circle radius (Fig 21-5C)

The permissible initial tensioning force range FA

The belt side-force ratio

Fu¼ the transmissible peripheral force, kN (lbf )

Fw¼ the effective shaft tensioning force, kN (lbf )

FIGURE 21-5C Pulley dimensions

TABLE 21.31D (b)

Pulley tolerance (mm)

Pitch to pitch tolerance

For each additional 25 mm or portion thereof þ0.025 to 0.00 mm

Outside diameter runout

Up to 75 mm, incl outside diameter 0.08 mm (max)

For each additional 25 mm or portion thereof 0.01 mm (max)

Axial runouta(side wobble)

Up to 250 mm, incl outside diameter 0.02 mm per 25 mm of diameter

For each additional 25 mm outside diameter add 0.01 mm

over 220 mm ad 0.01 mm

Diametrical taper

0.01 mm per 10 mm of face width

Groove helix

0.01 mm per 10 mm of face width

aFull indicator movement

The pitch line is situated outside thepulley-tip-circle radius at a distanceequaling that of the neutral axis

r0¼ d0

2¼ pulley pitch radius

do¼ pulley outside diameter

a ¼ distance between the pitch line ofbelt and the pulley tip circle radius

Belt length rangeBelt width 840, incl >840 to 1680, incl

Outside runout (side wobble)

Minimum recommended pulley diameters and flange dimensions (mm)

FIGURE 21-5D Belt section

TABLE 21.31D (h) Belt length tolerances (mm)

Tolerance on beltBelt length range pitch length

Pulley groove tolerances (mm) (Fig 21-5D)

Pulley Top curvature Max top radius Flank band Bottom curvature Depth band Upper

FIGURE 21-5E Pulley groove profile

Source: Synchronous Belts and Pulleys, SAE J 1313 Oct 80 Reprinted with permission from SAE Handbook, Part I, Society ofAutomotive Engineers, Inc., 1997

FLEXIBLE MACHINE ELEMENTS 21.41

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FIGURE 21-5F Determination of center distance of synchronous belts.

Source: J E Shigley and C R Mischke, Standard Handbook of Machine Design, 2nd edition, McGraw-Hill Book Company,New York, 1996

The power transmitted by synchronous belt

CONVEYOR (Tables 21-12, 21-14, 21-20, and

when a1in in when a1in mm For belts on three-

to five-step idlers when a1in m

when a1in in when a1in mm

P ¼ Ps

Cs

ð21-46hÞ where

Ps¼ standard capacity of the selected belt, kW (hp)

Cs¼ service correction factor

C ¼ 132a2to 154a2 SI ð21-49aÞ

C ¼ 5158a2to 6063a2 USCS ð21-49bÞ

FLEXIBLE MACHINE ELEMENTS 21.43

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The power required by a horizontal belt conveyor

FIGURE 21-5 Rockwood pivoted motor base

SHORT CENTER DRIVE

Rockwood drive (Fig 21-5)

1000 þ PT

SI ð21-50aÞ where W in N/m, v in m/s, L in m, and P in kW

102 þ PTMetric ð21-50bÞ where W in kgf/m, v in m/s, L in m, and P in kW

33 ;000 þ PT

USCS ð21-50cÞ where W in lbf/in, v in ft/min, L in in, and P in hp where

 ¼ coefficient of friction of idler bearing

¼ 0:15 for roller bearings

¼ 0:35 for grease lubricated idlers

Fn¼ required net pull, kN (lbf )

W ¼ weight of the motor, kN (lbf )

Manila rope (Tables 21-32 and 21-34)

The ultimate load

The maximum tension on the tight side

Pu¼ 7000d2

USCS ð21-54bÞ where d is diameter of rope in in and Puin lbf

F1¼ 137:5  104

d2¼ F þ F

2 þ Fc SI ð21-55aÞ where d in m and F1in N

F1¼ 200d2¼ F þ F

2 þ Fc USCS ð21-55bÞ where d in in and F1in lbf

F1¼ 0:14d2 Customary Metric ð21-55cÞ where d in mm and F1in kgf

P ¼ vð0:6
6:7  10
4FcÞ SI ð21-56aÞ where Fcin N, P in kW, and v in m/s

P ¼ 2v

105ð200
FcÞ USCS ð21-56bÞ where Fcin lbf and P in hp

Refer to Table 21-32 for Fc¼ values of coefficients for manila rope

F ¼
d2

where

br¼ breaking stress, MPa (psi)

¼ 9:81 MPa (1.42 kpsi) for white rope

¼ 8:82 MPa (1.28 kpsi) for tarred rope

TABLE 21-32

Value of coefficient Fcfor manila rope

Velocity, mps 7.50 10.00 12.50 15.00 17.50 20.00 22.50 25.00 27.50 30.00 32.50 35.00Coefficient, Fc 2.96 5.40 8.44 12.60 16.10 21.00 26.55 32.89 39.69 41.17 55.34 64.40

FLEXIBLE MACHINE ELEMENTS 21.45

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The load on the hemp rope in terms of nominal

diameter of rope

HOISTING TACKLE

The effort on the rope in case of single-sheave pulley

(Fig 21-6)

FIGURE 21-6 Rope passing over sheave

The effort on the rope in a hoist for raising the load

Refer to Table 21-33 for C.

FIGURE 21-7 Load on a hoist

Efficiency of hoist

Continuous system Fig (21-8)

FIGURE 21-8 Continuous system

The relation between ultimate load, bending and

service load in wire rope

The bending load

Another formula connecting ultimate strength of

rope, tensile load on rope (P), dimensions of the

rope, wire, and sheave diameter

Area of useful cross-section of the rope

The approximate ultimate strength of plow-steel



dwd



dwd

Pu¼ 76d2

USCS ð21-64bÞ where Puin lbf and d in in

Pu¼ 517;800d2for 6  37 ropes SI ð21-64cÞ where Puin kN and d in m

FLEXIBLE MACHINE ELEMENTS 21.47

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Breaking loadPitch

designation yards per density 2.6Ca

Duty factor and life of mechanism of electric wire rope hoists

The nominal bearing pressure

DRUMS

Wire rope drum

The number of turn on the drum for one rope member

(Fig, 21-9)

The length of the drum

FIGURE 21-9 Wire rope drum

The minimum diameter of groove of sheaves and

drums (d)

The thickness of wall of drum made of cast iron

The outside diameter of the drum (Fig 21-9)

The depth of groove in drum or sheave

The outside diameter of sheave (dos)

Stresses developed in drum

The maximum bending stress

The maximum torque on the drum

l ¼

2iS



ð21-72Þ where d ¼ diameter of rope

FLEXIBLE MACHINE ELEMENTS 21.49

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The maximum shear stress

The crushing stress

The combined stress according to normal stress

theory

HOLDING CAPACITY OF WIRE ROPE

REELS

The rope capacity (L) in meters in any size length may

be calculated by the formula

WIRE ROPE CONSTRUCTION

For wire rope strand construction, diameter, weight,

breaking load for different purposes

For wire rope data, factor of safety, values of C, and

Pw¼ 8:65d2

Customary Metric ð21-77cÞ where d in mm and Puin kgf

Pw¼ 60;310d2

SI ð21-78aÞ where d in m and Puin kN

where d in in and Puin lbf

Pw¼ 6:15d2

Customary Metric ð21-79Þ where d in mm and Puin kgf

TABLE 21-36

Steel wire ropes (from Indian standards)

Nominal breaking strength of ropeTensile strength of wire1568–1716 MPa 1716–1863 MPaDiameter Approx weight (160–175 kgf/mm2) (175–190 kgf/mm2)

TABLE 21-36

Steel wire ropes (from Indian standards) (Cont.)

Nominal breaking strength of ropeTensile strength of wire1568–1716 MPa 1716–1863 MPaDiameter Approx weight (160–175 kgf/mm2) (175–190 kgf/mm2)

TABLE 21-36

Steel wire ropes (from Indian standards) (Cont.)

Nominal breaking strength of ropeTensile strength of wire1568–1716 MPa 1716–1863 MPaDiameter Approx weight (160–175 kgf/mm2) (175–190 kgf/mm2)

FIGURE 21-13 Multistrand nonrotating ropes 34 7

FIGURE 21-15 Multistrand nonrotating ropes 17 7 and

18 7

FIGURE 21-16(a) Metal core

FIGURE 21-16(b) Metal core

FLEXIBLE MACHINE ELEMENTS 21.53

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TABLE 21-36

Steel wire ropes (from Indian standards) (Cont.)

Nominal breaking strength of ropeTensile strength of wire

TABLE 21-36

Steel wire ropes (from Indian Standard) (Cont.)

Nominal breaking strength of ropeTensile strength of wire1225.8–1373.0 MPa 1373.0–1520.0 MPa 1520.0–1667.0 MPa 1667.0–1814.2 MPa

TABLE 21-36

Steel wire ropes (from Indian Standard) (Cont.)

Nominal breaking strength of ropeTensile strength of wire1226–1373 MPa 1373–1520 MPa 1520–1667 MPa 1667–1814 MPa

TABLE 21-36

Steel wire ropes (from Indian Standard) (Cont.)

Nominal breaking strength of ropeTensile strength of wire1226–1373 MPa 1373–1520 MPa 1520–1667 MPa 1667–1814 MPa

Strand construction rope, mm N/100 m kgf/100 m 1569.3 MPa 160 kgk/mm2 1765.2 MPa 180 kgf/mm2

Haulage purposes in mines

FLEXIBLE MACHINE ELEMENTS 21.57

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TABLE 21-36

Steel wire ropes (from Indian Standard) (Cont.)

Minimum breaking load of ropeFor tensile designation

Approx weight (160 kgf/mm2) (180 kgf/mm2)Diameter of rope,

TABLE 21-36

Steel wire ropes (from Indian Standard) (Cont.)

Minimum breaking load of ropeFor tensile designation

Approx weight (160 kgf/mm2) (180 kgf/mm2)Diameter of rope,

FLEXIBLE MACHINE ELEMENTS 21.59

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Preferred Galvanized Steel Wire Ropes for Aircraft Controls