Machine Design Databook Episode 2 part 6 pptx

19-16 The total axial force on i number of clutch disk or plates FIGURE 19-16 A typical clutch operating lever.. 19-18 When the grooved rim clutch being engaged, the equa-tion of equilib

SELLERS’ CONE COUPLING (Fig 19-10)

The length of the box

The outside diameter of the conical sleeve

Outside diameter of the box

The length of the conical sleeve

HYDRAULIC COUPLINGS (Fig 19-11)

Torque transmitted

Percent slip between primary and secondary speeds

The mean radius of inner passage (Fig 19-11)

The mean radius of outer passage (Fig 19-11)

The number of times the fluid circulates through the

torus in one second is given by

D1¼ 1:875d to 2d þ 0:0125 SI ð19-63aÞwhere D, d in m

D1¼ 1:875d to 2d þ 0:5 USCS ð19-63bÞwhere D, d in in

mo
r2

Power transmitted by torque converter

19.2 CLUTCHES

POSITIVE CLUTCHES (Fig 19-12)

Jaw clutch coupling

The area in shear

The shear stress assuming that only one-half the total

number of jaws i is in actual contact

Mt
Kn2

where

K ¼ coefficient—varies with the design

n ¼ speed of driven shaft, rpm

D ¼ outside diameter of vanes, m (in)

FIGURE 19-12 Square-jaw clutch.

FRICTION CLUTCHES

Cone clutch (Fig 19-13)

The axial force in terms of the clutch dimensions

Axial force in terms of normal force (Fig 19-13)

The tangential force due to friction

Torque transmitted through friction

 ¼ one-half the cone angle, deg

¼ ranges from 158 to 258 for industrial clutchesfaced with wood

¼ 12.58 for clutches faced with asbestos or leather

The force necessary to engage the clutch when one

member is rotating

The ratio (Dm=b)

The value of Dmin commercial clutches

DISK CLUTCHES (Fig 19-14)

The axial force

The torque transmitted

FIGURE 19-14 Multidisk clutch.

The clutch capacity at speed n1

The speed factor

DIMENSIONS OF DISKS (Fig 19-15)

The maximum diameter of disk

The minimum diameter of disk

The thickness of disk

The number of friction surfaces

The number of driving disks

The number of driven disks

FIGURE 19-15 Dimensions of disks.

P ¼ design power at speed, n

ks¼ speed factor obtained from Eq (19-89)

DESIGN OF A TYPICAL CLUTCH

OPERATING LEVER (Fig 19-16)

The total axial force on i number of clutch disk or

plates

FIGURE 19-16 A typical clutch operating lever.

The force acting on disks of one operating lever of the

clutch (Fig 19-16)

The total force acting from the side of the bushing

(Fig 19-16)

The force acting from the side of the bushing on one

operating lever (Fig 19-16)

The thickness of the !ever very close to the pin (Fig

m

; MPa ðpsiÞMta¼ allowable torque, N m (lbf in)

0 ae3

bh



i0db

26

37

1=3

ð19-100Þ

wheredb¼ design bending stress for the material

of the levers, MPa (psi)Ratio of b=h ¼ 0:75 to 1

d ¼

ffiffiffiffiffiffiffi2Fr

d

s

ð19-101Þwhere

Fr¼ resultant force due to F1and P1cotð þ Þ onthe pin, kN (lbf )

d¼ design shear stress of the material of the pin,MPa (psi)

EXPANDING-RING CLUTCHES (Fig 19-17)

Torque transmitted [Fig 19-17(a)]

FIGURE 19-17 Expanding-ring clutch.

The moment of the normal force for each half of the

band [Fig 19-17(a)]

The force applied to the ends of the split ring to

expand the ring [Fig 19-17(a)]

If the ring is made in one piece (Fig 19-7(b)] an

addi-tional force required to expand the inner ring before

contact is made with inner surface of the shell

The total force required to expand the ring and to

produce the necessary pressure between the contact

surfaces

RIM CLUTCHES (Fig 19-18)

When the grooved rim clutch being engaged, the

equa-tion of equilibrium of forces along the vertical axis

After the block is pressed on firmly the equation of

equilibrium of forces along the vertical axis

Torque transmitted

where

¼ one half the total arc of contact, rad

w ¼ width of ring, m (in)

when
  rad

Fe¼Ewt36L

1d1
1d



ð19-105Þwhere

d1¼ original diameter of ring, m (in)

d ¼ inner diameter of drum, m (in)

w ¼ width of ring, m (in)

t ¼ thickness of ring, m (in)

F ¼ pwr þEwt

36L

1d1
1d

b ¼ inclined face, m (in)

2 ¼ angle of contact, rad

The width of the inclined face

Frictional force

Torque transmitted in case of a flat rim clutch when

i1¼ 1 and the number of sides b is only one-half

that of a grooved rim

CENTRIFUGAL CLUTCH (Fig 19-19)

Design of shoe

Centrifugal force for speed !1 (rad/s) at which

engagement between shoe and pulley commences

Centrifugal force for running speed!2(rad/s)

The outward radial force on inside rim of the pulley at

speed!2

The centrifugal force for!1¼ 0:75!2

D ¼ pitch diameter, m (in)2 ¼ V-groove angle, deg

FIGURE 19-18 Grooved rim clutch.

Torque required for the maximum power to be

transmitted

The equation to calculate the length of the shoe (Fig

19-19)

Spring

The central deflection of flat spring (Fig 19-19) which

is treated as a beam freely supported at the points

where it bears against the shoe and loaded centrally

by the adjusting screw

The maximum load exerted on the spring at speed!1

The cross section of spring can be calculated by the

l ¼Fc

bp¼ w

y ¼1Wl3

OVERRUNNING CLUTCHES

Roller clutch (Fig 19-20)

The condition for the operation of the clutch

The force crushing the roller

The torque transmitted

The allowable load on roller

The roller diameter

The number of roller

LOGARITHMIC SPIRAL ROLLER CLUTCH

(Fig 19-21)

The radius of curvature of the ramp at the point of

contact (Fig 19-21)

The radius vector of point C (Fig 19-21)

The radius of the contact surface on the driven

member in terms of the roller radius and functions

angles and  (Fig 19-21)

The tangential force

FIGURE 19-20 Roller clutch.

k0¼ coefficient of the flattening of the roller



ð19-129Þ

The normal force

The torque transmitted

The maximum compressive stress at the surface area

of contact between the roller and the cage made of

different materials

The maximum compressive stress at the surface

area of contact between the roller and the cage for

vc¼ vr¼ 0:3

The maximum compressive stress at the surface area

of contact between the roller and the cage made of

same material (Ec¼ Er¼ E) and vc¼ vr¼ 0:3

Rrþ 1Rc



1
v2 r

Er þ1
v2c

Ec



266

377

1=2ð19-131Þ

cðmaxÞ¼

0:35F

1

Rrþ 1Rc



l

1

Erþ 1

Ec



266

377

Rrþ 1

Rc

l

24

351=2

ð19-133aÞ

cðmaxÞ¼ 0:418

ffiffiffiffiffiffiffiFE

r

ð19-133cÞwhere

The design torque transmitted by the clutch

For further design data for clutches

19.3 BRAKES

ENERGY EQUATIONS

Case of a hoisting drum lowering a load:

The decrease of kinetic energy for a change of speed of

the live load from v1to v2

The change of potential energy absorbed by the brake

during the time t

The change of kinetic energy of all rotating parts such

as the hoist drum and various gears and sheaves

which must be absorbed by the brake

Mtd¼ildRdcðmaxÞtan

ko¼ radius of gyration of rotating parts, m (mm)

!1; !2¼ angular velocity of the rotating parts, rad/s

TABLE 19-5

Preferred dimensions and deviations for clutch facings (all dimensions in mm)

The work to be done by the tangential force F
at the

brake sheave surface in t seconds

The tangential force at the brake sheave surface

Torque transmitted when the blocks are pressed

against flat or conical surface

The operating force on block in radial direction (Fig

19-22)

Torque applied at the braking surface, when the

blocks are pressed radially against the outer or inner

surface of a cylindrical drum (Fig 19-22)

Driving machine

Gas engine, multiple cylinder 1.0

Hoists, elevators, cranes, shovels 2.0

Hammer mills, ball mills, crushers 2.0

TABLE 19-7Shear strength for clutch facings

Shear strength

A Solid woven or plied fabric with

or without metallic reinforcement

The tangential frictional force on the block (Fig 19-22)

Torque applied when
is less than 608

BRAKE FORMULAS

Block brake formulas

For block brake formulas

Band brake formulas

For band brake formulas

The magnitude of pressure between the band and the

TABLE 19-8

Formulas for block, simple, and differential band brakes

Suitable drum diameter according to Hagenbook

Suitable drum diameter in terms of frictional

horse-power

Mt69

1=3

< 10D <

Mt54

1=3

< D <

Mt4

1=3

USCS ð19-162Þwhere Mtin lbf and D in in

ð79:3PÞ1=3< 100D < ð105:8PÞ1=3 SI ð19-163aÞwhere P in kW and D in m

ð60PÞ1=3< D < ð80PÞ1=3 USCS ð19-163bÞwhere P in hp and D in in

P is taken as the maximum horsepower to be pated in any 15-min period

b 2 e
þ b 1

e

1

 (19-153)

Counterclockwise

F ¼F
a

b 1 e
þ b 2

e

1

 (19-154)

If b 2 ¼ b 1 F is the same for rotation in either direction

F ¼F
ba

CONE BRAKES (Fig 19-24)

The normal force

The radial force

The tangential force or braking force

The braking torque

CONSIDERING THE LEVER (Fig 19-24)

The axial force

The relation between the operating force F and the

DISK BRAKES

The torque transmitted for i pairs of friction surfaces

The axial force transmitted

For design values of brake facings

INTERNAL EXPANDING-RIM BRAKE

Forces on Shoe (Fig 19-25)

FOR CLOCKWISE ROTATION

The maximum pressure

The moment Mtof the frictional forces

The moment of the normal forces

ð
2

1

sin
ðr
a cos
Þ d
ð19-174aÞ

Mtn¼pabrasin
a

ð
2

1

TABLE 19-9

Design values for brake facings

Permissible unit pressure

coefficient of

Cast iron on cast iron

Leather on cast iron

Note: 1 kpsi¼ 6.894757 MPa or 1 MPa ¼ 145 psi.

The actuating force

The torque Mtapplied to the drum by the brake shoe

The hinge-pin horizontal reaction

The hinge-pin vertical reaction

FOR COUNTERCLOCKWISE ROTATION (Fig.

19-25)

EXTERNAL CONTRACTING-RIM BRAKE

Forces on shoe (Fig 19-26)

FOR CLOCKWISE ROTATION

The moment Mtof the friction forces Fig 19-26

The moment of the normal force

F ¼Mtnþ Mt

Rx¼ pabrsin
a

ð
2

1

sin
ðr
a cos
Þ d
ð19-183Þ

Mtn¼ pabrsin
a

The actuating force

The horizontal reaction at the hinge-pin

The vertical reaction at the hinge-pin

FOR COUNTERCLOCKWISE ROTATION

HEATING OF BRAKES

Heat generated from work of friction

Heat to be radiated for a brake lowering the load

The heat generated is also given by the equation

F ¼Mtnþ Mt

Rx¼ pabrsin
a

The rise in temperature in8C of the brake drum or

clutch plates

The rate of heat dissipation

The required area of radiating surface

Approximate time required for the brake to cool

Gagne’s formula for heat generated during a single

m ¼ mass of brake drum or clutch plates, kg

C ¼ specific heat capacity

¼ 500 J/kg 8C for cast iron or steel

¼ 0:13 Btu/lbm8F for cast iron

¼ 0:116 Btu/lbm8F for steel

where Hd in J

Hd¼ 0:25C2
TAr Metric ð19-195bÞwhere C2¼ radiating factor from Table 19-13



ð19-198ÞwhereðTav
TaÞ ¼ temperature differencebetween the brake surface and theatmosphere,8C

Refer to Table 19-15 for values of C

Refer to Tables 19-11 to 19-17

Comparison of hoist brakes

Axial brakes

or water steam or gas

Alternators and generators (excluding

welding generators), induced-draft fans,

printing machinery, rotary pumps,

compressors, and exhausters, conveyors

Woodworking machinery, machine tools

(cutting) excluding planing machines,

calenders, mixers, and elevators

Forced-draft fans, high-speed reciprocating

compressors, high speed crushers and

pulverizers, machine tools (forming)

Rotary screens, rod mills, tube, cable and

wire machinery, vacuum pumps

Low-speed reciprocating compressors,

haulage gears, metal planing machines,

brick and tile machinery, rubber

machinery, tube mills,

generators(welding)

TABLE 19-13

Radiating factors for brakes

Temperature Radiating factor, C 2 C 2
T

26.97 2.75

Continuous service with short rest periods and with poor radiation

13.73 1.40 Continuous operation with good

radiation as with an oil bath

40.70 4.15TABLE 19-15

Values of beat transfer coefficientC for rough block

surfaces

Heat-transfer coefficient, C Velocity, v,

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

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

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

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

Coefficient of friction and permissible variations on dimensions for automotive brakes lining

Tolerance on width Tolerance on thickness

coefficient Permissible

of friction, variation in 5 mm >5 mm 5 mm >5 mm

Type I—rigid molded sets or flexible molded

rolls or sets

Type II—rigid woven sets or flexible woven

rolls or sets

7 Vallance, A., and V L Doughtie, Design of Machine Members, McGraw-Hill Book Company, New York,1951.

8 Lingaiah, K., and B R Narayana Iyengar, Machine Design Data Handbook, Engineering College CooperativeSociety, Bangalore, India, 1962

9 Lingaiah, K., and B R Narayana Iyengar, Machine Design Data Handbook, Vol I (SI and Customary MetricUnits), Suma Publishers, Bangalore, India, 1986

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

11 Lingaiah, K., Machine Design Data Handbook, McGraw-Hill Publishing Company, New York, 1994

12 Bureau of Indian Standards, New Delhi, India

20

SPRINGS

SYMBOLS

A area of loading, m2(in2)

b width of rectangular spring, m (in)

width of laminated spring, m (in)

b0 width of each strip in a laminated spring, m (in)

c1, c2 constants taken from Table 20-1 and to be used in Eqs (20-1) to

(20-36)C1, C2 constants to be used in Eqs (20-20) and (20-21) and taken from

Fig 20-3

d diameter of spring wire, m (in)

diameter of torsion bar, m (in)

d1, d2 diameter of outer and inner wires of concentric spring, m (in)

D mean or pitch diameter of spring, m (mm) overall diameter of

the absorber, m (in)D1 mean or pitch diameter of outer concentric spring, m (in)

smallest mean diameter of conical spring, m (in)

D2 mean or pitch diameter of inner concentric spring, m (in)

largest mean diameter of conical spring, m (in)

e0sr surface influence coefficient

E modulus of elasticity, GPa (psi)

F frequency, cycles per minute, Hz

steady-state load [Eq (20-84)]

Fmax maximum force that can be imposed on the housing, kN (lbf )

ko force to compress the spring one meter (in)

N/m (lbf/in) [spring rate, N/m (lbf/in)]

Fcr critical load, kN (lbf )

g acceleration due to gravity, 9.8066 m/s2

9806.06 mm/s2(32.2 ft/s2; 386.4 in/s2)

G modulus of rigidity, GPa (psi)

h height (thickness) of laminated spring, m (in) axial height of a

rectangular spring wire, m (in)

i total number of strips or leaves in a leaf spring number of coils

in a helical spring

i0 total number of full-length blunt-ended leaves in a leaf spring

k4 correction factor

Kl factor depends on the ratio lo=D as shown in Fig 20-8

reduced stress correction factor or Wahl stress factor or fatigue

stress correction factor

kr shear stress correction factor

lf or lo free length of helical spring, m (in)

L i
D length of the coil part of torsion spring, m (in)

effective length of bushing, m (in)

overall length of the absorber (Fig 20-15), m (in)

M constant depends on do=dias indicated in Fig 20-3

Mt twisting moment, N m (lbf in)

na actual factor of safety or reliability factor

U resilience, N m (lbf in)

energy to be absorbed by a rubber spring, N m (lbf in)

V volume of spring, m3, mm3(in3)

 specific weight of the spring material, N/m3(lbf/in3)

W weight of spring, kN (lbf )

weight of effective number of coils i involved in the operation of

the spring [Eq (20-77)], kN (lbf )

ycr critical deflection, m (in)

Z section modulus, m3, cm3(in3)

Zo polar section modulus, m3, cm3(in3)

, 0 constant from Table 20-3

, 0 constants from Table 20-3

f endurance lirnit (also used for reversed cycle)

o endurance limit for repeated cycle

LEAF SPRINGS (Table 20-1)1;2;3

The general equation for the maximum stress in