Machine Design Databook 2010 Part 10 potx

Conditions for self-locking of differentialchain block The condition for self-locking For self-locking differential chain block The initial value of the ratio r R Power chains Roller chain

TABLE 21-37

Round strand galvanized steel wire ropes for shipping purposes

Tensile strength of wire, 1373–1569 MPa (140–160 kgf/mm 2 )

Approx.

Breaking strength Approx.

Breaking strength Approx.

Breaking strength Approx.

Breaking strength weight of rope, min weight of rope, min weight of rope, min weight of rope, min Diameter N/m kgf/m kN kgf N/m kgf/m kN kgf N/m kgf/m kN kgf N/m kgf/m kN kgf

TABLE 21-38

Dimensions and breaking strength of flat balancing wire ropes

b  s, a

Diameter section of Double-stitched Single-stitched of rope Double- Single- of the the strand,

TABLE 21-39

Dimensions and breaking strength of flat hoisting wire ropes

Minimum breaking Cross section Weight strength of ropeaNominal size, Nominal wire of strand,

TABLE 21-40

Tensile grade

Tensile strength range

Values ofC for wire ropes

Approximate wire rope and sheave data

SI units: d ¼ diameter of rope, m.

US Customary units: d ¼ diameter of rope, in.

Minimum Modulus of Weight per sheave Standard Size of outer elasticity,a Strength,b

Steel-mill ladles

Cranes

High speed elevators

Safety factor

100 or other figure laid down by the statutory authority

From Indian Standards

Ropes which are straight between terminal fittings

Hoisting, luffing and reeved bridle systems of inherently flexible crances

(e.g., mobile crawler tower, guy derrick, stiffleg derrick) where jibs are

supported by ropes or where equivalent shock absorbing devices are

incorporated in jib supports

From Other Sources Mine Shafts

hoisting equipment 8  19 filler wire

The working load for the ordinary steel BB crane

chain

The sheave diameter

Round steel short link and round steel link chain

LENGTH AND WIDTH (Figs 21-17 and 21-18):

The outside dimensions of the links shall fall between

the following limits:

Outside link length limits (Fig 21-17)

Maximum outside link width (Fig 21-18)

Minimum inside link width

Pitch (i.e., inside length)

Dimensions and lifting capacities and properties of

noncalibrated and calibrated chains

where d in m and Pwin kN

Pw¼ 13;600d2

USCS ð21-79bÞwhere d in in and Pwin lbf

Pw¼ 9:56d2

Customary Metric ð21-79cÞwhere d in mm and Pwin kgf

l j> 5dn for uncalibrated chain ð21-81aÞ

l j< 6dn for calibrated chain ð21-81bÞWmaxj> 3:5dn away from weld ð21-82aÞWmaxj> 1:05 (adjacent width) at weld

for noncalibrated chains ð21-82bÞWmax¼ 3:25dn for calibrated chain ð21-83Þ

Wt j< 1:25dn except at the weld for

Minimum energy Minimum breaking load absorption factor for 1-m Maximum safe working Proof load based on based on a stress of gauge length based on an load for nominal working Size a stress of 294.2 MPa energy absorption of 58.8 condition based on a stress (nominal 98.1 MPa (10 kgf/mm2) (30 kgf/mm2) MN-m/m2(6 kgf-m/mm2) of 49 MPa (5 kgf/mm2) diameter),

Chain passing over a sheave (Fig 21-19)

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

(Fig 21-19)

The efficiency of the chain sheave

FIGURE 21-18 Pitch length and width of link.

FIGURE 21-19 Chain passing over sheave.

Differential chain block (Fig 21-20)

RAISING THE LOADQ

The effort required for raising the load without

friction

The relation between the tension in the running-off

and running-on chains

The tension in the running-off chains

The tension in the running-on chain

where C ¼ 1:04 for lubricated chains

C ¼ 1:10 for chains running dry

 ¼ 1

where ¼ 0:96 for lubricated chains

 ¼ 0:91 for chain running dry

FIGURE 21-20 Differential chain block.

Po¼Q

where n ¼d

D¼ rR

The relation between effort (P), load (Q), T1and T2

The effort required for raising the load with friction

The efficiency for the differential chain hoist

Lowering the load

The equations for the tension in the running-on

running-off and pull (P0) required on the chain so as

to prevent running down of the load

The pull required on the chain so as to prevent

running down of the load

The efficiency for the reversed motion

For mechanical properties of the coil link chain and

the strength of hoisting chains in terms of bar from

which they are made

1
nC2ð1
nÞð1 þ CÞ

Conditions for self-locking of differential

chain block

The condition for self-locking

For self-locking differential chain block

The initial value of the ratio r

R

Power chains

Roller chains

The transmission ratio

The average speed of chain

P0¼QC

v ¼pz1n1

60 m=s or v ¼pz1n1

12 ft=min ð21-105Þwhere z1¼ number of teeth on the small sprocketand p in m (in)

TABLE 21-52

Mechanical properties of the coil link chain

Requirement

Mean stress at guaranteed minimum breaking load, F w min, h bar 30 40

Guaranteed minimum energy absorption factor, F w  A 0.054 kJ m
1mm
2 0.054 kJ m
1mm
2

The empirical formula for pitch

Bartlett formula relating speed (n1) and pitch ( p)

based on allowable amount of impact between a

roller and a sprocket

Maximum allowable chain velocity based on Eq

(21-107)

p  0:25

900n1

2=3

SI ð21-106aÞwhere p in m

p 

900n1

2=3

USCS ð21-106bÞwhere p in in

p  250

900n1

2=3

Customary Metric ð21-106cÞ

where p in mm,n1¼ speed of the small sprocket, rpm

n1¼1170p

ffiffiffiffiffiffiffiffiffiA

ffiffiffiffiffiffiffiffiffiA

ffiffiffiffiffiffiffiffiffiA

wfp

s

USCS ð21-107cÞ

wheren1in rpm, p in in, wf in lbf/ft, and A in in2

A ¼ ldr¼ projected area of the roller

dr¼ diameter of rollers

l ¼ width of chain or length of roller

vmax 19:48z1

ffiffiffiffiffiffiffiffiffiA

wf p

s

USCS ð21-108bÞ

Maximum speed based on the energy of impact per

tooth per minute

Maximum chain velocity based on Eq (21-109), m/s

Maximum sprocket speed based on the effect of

centrifugal force

where vmaxin ft/min, A in in2, p in in, and wfin lbf/ft

vmax 0:196z1

ffiffiA

wfp

sCustomary Metric ð21-108cÞ

where vmaxin m/s, A in mm2, p in mm, and wf inkgf/m

n 1437p3

ffiffiffiffiffiffiAwf

s

SI ð21-109aÞwhere A in m2, p in m, and wf in N/m

n 2000p3

ffiffiffiffiffiffiA

wf

s

USCS ð21-109bÞwhere A in in2, p in in, and wf in lbf/ft

n 6712p3

ffiffiffiffiffiffiAwf

s

Customary Metric ð21-109cÞwhere A in mm2, p in mm, and wf in kgf/m

vmax 24z13

ffiffiffiffiffiffiAwf

s

SI ð21-110aÞwhere vmaxin m/s, A in m2, and wf in N/m

vmax 166z13

ffiffiffiffiffiffiA

wf

s

USCS ð21-110bÞwhere vmaxin ft/min, A in in2, and wf in lbf/ft

vmax 0:11z13

ffiffiffiffiffiffiA

wf

s

Customary Metric ð21-110cÞwhere vmaxin m/s, A in mm2, and wf in kgf/m

n 36350p

ffiffiffiffiffiffiffiffiffiffiAz1wf

s

SI ð21-111aÞwhere p in m, A in m2, and wf in N/m

n 9516p

ffiffiffiffiffiffiffiffiffiffiAz1wf

s

USCS ð21-111bÞwhere p in in, A in in2, and wf in lbf/ft

Maximum velocity based on Eq (21-111)

Chain pull

For preliminary computation, the allowable pull

AGMA formula for allowable pull based on

velocity factor Cv¼ 3=ð3 þ vÞ and bearing pressure

of 29.4 MPa (4333 psi) for the pin

For dimensions of American Standard Roller

Chains—single-strand

vmax 600

ffiffiffiffiffiffiffiffiAz1wf

s

SI ð21-112aÞwhere vmaxin m/s, A in m2, and wf in N/m

vmax 793

ffiffiffiffiffiffiffiffiAz1

wf

s

USCS ð21-112bÞwhere vmaxin ft/min, A in in2, and wf in lbf/ft

vmax 0:2

ffiffiffiffiffiffiffiffiAz1

wf

s

Customary Metric ð21-112cÞwhere vmaxin m/s, A in mm2, and wf in kgf/m

l ¼ length of roller pins, m (in)

TABLE 21-54A

Dimensions of American Standard roller chains—single-strand

ANSI chain Minimum tensile Average weight, Roller diameter, Multiple-strand number Pitch, in (mm) Width, in (mm) strength, lb (N) lb/ft (N/m) in (mm) spacing, in (mm)

TABLE 21-54B

Rated horsepower capacity of single-strand single-pitch roller chain for a 17-tooth sprocket

ANSI chain number Sprocket speed,

Estimated from ANSI tables by linear interpolation.

Note: Type A—manual or drip lubrication, type B—bath or disk lubrication; type C—oil-stream lubrication.

Source: Compiled from ANSI B29.1-1975 information only section, and from B29.9-1958.

TABLE 21-54C

Rated horsepower capacity of single-strand single-pitch roller chain for a 17-tooth sprocket

ANSI chain number Sprocket

region; submit design to manufacturer for evaluation.

Source: Compiled from ANSI B29.1-1975 information only section, and from B29.9-1958.

TABLE 21-54D

Tooth correction factors,K1

For the rated horsepower capacity of

single-strand-single-pitch roller chains for 17-tooth sprocket and

P ¼ Fv102klks Customary Metric ð21-115cÞwhere

F¼ required chain pull in kgf and P in kW

kl¼ load factor from 1.1 to 1.5 and also obtainedfrom Chap 14

ks¼ service factor

¼ 1 for 10 h service per day

¼ 1.2 for 24 h operation and also obtained fromTable 21-54F

Service factor for roller chains,ks

Intermittent few hours per Normal 8 to 10 hours per Continuous Operating characteristics day, few hours per year day 300 days per year 24 hours per day

The rated horsepower of roller chain per strand

The corrected horsepower (Pc)

CHECK FOR ACTUAL SAFETY FACTOR

The actual safety factor checked by the formula

The number of strand in a chain, if F> Fa

Center distance of chain length

The proper center distance between sprockets in

w ¼ weight per meter of chain, N (lbf )

v ¼ velocity of chain, m/s (ft/min)

C ¼ center distance, m (in)ksz¼ coefficient for sag from Table 21-55

i ¼F

Cp¼ 20p to 30p or Cp¼ 40  10 pitches ð21-119Þwhere pCp¼ C

Coefficient forsag, ksg

Position of chain drive

k sg Horizontal <408 >408 Vertical

The maximum center distance

The chain length in pitches

The chain length, m or in

tan

180z

z1¼ number of teeth on a small sprocketz2¼ number of teeth on a large sprocket

 ¼ angle between tangent to the sprocket pitchcircle and the center line

 ¼ sin
1

d2
d12C



k ¼ a variable which depends onz1
z2

Cpand obtained from Table 21-56

Minimum center distance constant,Kmin

Transmission ratio, i Minimum center distance constant, K min

The chain length

The pitch diameter of a sprocket

Roller chain sprocket

Minimum number of teeth

Silent chain sprocket

Minimum number of teeth

The root diameter of sprocket

The width of sprocket tooth (Fig 21-22)

Maximum hub diameter

Power per cm of width in hp

The relationship between depth of sag, and tension

due to weight of chain in the catenary (approx.)

sin

180z



ð21-133bÞwhere

h ¼ depth of sag, m (in)

L ¼ distance between points of support, m (in)

S ¼ catenary length of chain, m (in)

F ¼ tension or chain pull, kN (lbf )

w ¼ weight of chain, kN/m (lbf/in)

Tension chain linkages

FIGURE 21-21 Notation for wheel rim of chain.

Wheel tooth gap form

The minimum value of roller seating radius, mm

sin180z

FIGURE 21-23 Notation for tooth gap form of roller

Tooth heights and top diameters (Fig 21-23)

The maximum limit of the tooth height above the

pitch polygon

The minimum limit of the tooth height above the

pitch polygon

The maximum limit of the tooth top diameter, mm

The minimum limit of the tooth top diameter, mm

FIGURE 21-24 Notation for minimum tooth gap form of roller chain.



0:5Dr ð21-144Þ

TDmax¼ PCD þ 0:625p
Dr ð21-145ÞTDmin¼ PCD þ p

0:5
0:4z



Dr ð21-146Þ

Wheel rim profile (Fig 21-22)

Tooth width

The minimum tooth side radius

The tooth side relief

Absolute maximum shroud diameter

For leaf chain dimension, breaking load, anchor

clevises and chain sheaves

The maximum limit of the tooth top diameter

The minimum limit of the tooth top diameter

The maximum limit of the tooth height above the

sin180z

1
1:6z

Cranked link dimensions

Width over bearing pins

Source: IS 3563, 1966.

TABLE 21-66

Recommended design data for silent chains

No of teeth Chain pitch, mm Speed of small sprocket Driver Driven Min center distance, mm

Maximum velocity for various types of chains, rpm

Number of sprocket teeth Bush roller chain

FIGURE 21-27 Notation for tooth gap form of bush chain.

FIGURE 21-28 Notation for minimum tooth gap form for bush chain.

FIGURE 21-29 Notation for maximum tooth gap form for bush chain.

The minimum limit of the tooth height above the

pitch polygon

WHEEL RIM PROFILE (Fig 21-26) The value of

tooth width for simple chain wheels (Fig 21-26)

The value of tooth width for duplex and triplex chain

wheels

The value of tooth width for quadruplex chain wheels

and above

The value of width over tooth

The minimum tooth side radius

The tooth side relief

Absolute maximum shroud diameter

For bush chains dimensions, breaking load, pitch

circle diameters, etc

REFERENCES

1 Maleev, V L., and J B Hartman, Machine Design, International Textbook Company, Scranton,Pennsylvania, 1954

2 Black, P H., and O E Adams, Jr., Machine Design, McGraw-Hill Book Company, New York, 1968

3 Norman, C A., E S Ault, and I F Zarobsky, Fundamentals of Machine Design, The Macmillan Company,New York, 1951

4 Shigley, J E., Machine Design, McGraw-Hill Book Company, New York, 1962

5 Shigley, J E., and C R Mischke, Mechanical Engineering Design, McGraw-Hill Book Company, New York,1989

6 Shigley, J E., and C R Mischke, Standard Handbook of Machine Design, McGraw-Hill Book Company, NewYork, 1986

7 Baumeister, T., ed., Marks’ Standard Handbook for Mechanical Engineers, McGraw-Hill Book Company,New York, 1978

8 Niemann, G., Maschinenelemente, Springer-Verlag, Berlin; Zweiter Band, Munich, 1965

9 Niemann, G., Machine Elements—Design and Calculations in Mechanical Engineering, Vol II, AlliedPublishers Private Ltd., New Delhi, 1978

10 Decker, K H., Maschinenelemente, Gestaltung and Berechnung, Carl Hanser Verlag, Munich, 1971

The value of tolerance shall be h=4

C2ðor C3Þ ¼ number of strands
1Tpþ C1

ð21-166Þwith a tolerance value of h=4

where Tp¼ transmission pitch of strands

11 Lingaiah, K and B R Narayana Iyengar, Machine Design Data Handbook, Engineering College operative Society, Bangalore, India, 1962.

Co-12 Lingaiah, K and B R Narayana Iyengar, Machine Design Data Handbook, Vol I (SI and Customary MetricUnits), Suma Publishers, Bangalore, India, 1973

13 Lingaiah, K., Machine Design Data Handbook, Vol II (SI and Customary Metric Units), Suma Publishers,Bangalore, India, 1986

14 Bureau of Indian Standards

15 Albert, C D., Machine Design Drawing Room Problems, John Wiley and Sons, New York, 1949

16 V-Belts and Pulleys, SAE J 636C, SAE Handbook, Part I, Society of Automotive Engineers, Inc., 1997

17 SI Synchronous Belts and Pulleys, SAE J 1278 Oct.80, SAE Handbook, Part I, Society of AutomotiveEngineers, Inc., 1997

18 Synchronous Belts and Pulleys, SAE J 1313 Oct.80, SAE Handbook, Part I, Society of Automotive Engineers,Inc., 1997

19 Wolfram Funk, ‘Belt Drives,’ J E Shigley and C R Mischke, Standard Handbook of Machine Design, 2ndedition, McGraw-Hill Publishing Company, New York, 1996

Cc critical viscous damping, N s/m (lbf s/in)

Ct coefficient of torsional viscous damping, N m s/rad

G modulus of rigidity, GPa (Mpsi)

h thickness of plate, m (in)

i integer (¼ 0, 1, 2, 3, )

I mass moment of inertia of rotating disk or rotor, N s2m

(lbf s2in)

J polar second moment of inertia, m4or cm4(in4)

k spring stiffness or constant, kN/m (lbf/in)

ke equivalent spring constant, kN/m (lbf/in)

kt torsional or spring stiffness of shaft, J/rad or N m/rad (lbf in/rad)

K kinetic energy, J (lbf/in)

l length of shaft, m (in)

me equivalent mass, kg (lb)

Mt torque, N m (lbf ft)

p circular frequency, rad/s

q damped circular frequencyð¼pffiffiffiffiffiffiffiffiffiffiffiffiffi1
2

Þ

R¼ 1
TR percent reduction in transmissibility

R2¼ D2=2 radius of the coil, m (in)

T temperature, K or8C (8F)

TR transmissibility

U vibrational energy, J or N m (lbf in)

potential energy, J (lbf in)

x1, x2 successive amplitudes, m (in)

xo maximum displacement, m (in)

_xx linear velocity, m/s (ft/min)

€xx linear acceleration, m/s2(ft/s2)

Xst static deflection of the system, m (in)

y deflection of the disk center from its rotational axis, m or mm (in)

 weight density, kN/m3(lbf/in3)

 ¼ C

Cc damping factor

deflection, m (in)

st static deflection, m (in)

 mass density, kg/m3(lb/in3)

 normal stress, MPa (psi)

shear stress, MPa (psi)

period, s

angular deflections, rad (deg)

angular velocity, rad/s

€ angular acceleration, rad/s2

! forced circular frequency, rad/s

SIMPLE HARMONIC MOTION (Fig 22-1)

The displacement of point P on diameter RS (Fig 22-1)

The wavelength