Machine Design Databook 2010 Part 7 pdf

effective length of knuckle pin, m indedendum for a flat root involute spline profile, m in dc core diameter of threaded portion of the taper rod, m in dmor dpm mean diameter of taper pin,

FIGURE 16-18 Power absorption and starting torque for

balanced and unbalanced seals (M J Neale, Tribology Handbook,

Butterworths, London, 1973.)

PACKINGS AND SEALS 16.33

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5 Whalen, J J., ‘‘How to Select the Right Gasket Material,’’ Product Engineering, Oct 1860.

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

7 Neale, M J., Tribology Handbook, Butterworths, London, 1975.

8 Ratelle, W J., ‘‘Seal Selection, Beyond Standard Practice,’’ Machine Design, Jan 20, 1977.

9 ‘‘Packings and Seals’’ Issue, Machine Design, Jan 1977.

10 Faires, V M., Design of Machine Elements, Macmillan Book Company, 1955.

11 Bureau of Indian Standards.

12 Rothbart, H A., Mechanical Design and Systems Handbook, McGraw-Hill Book Company, New York, 1985.

13 Lingaiah, K., Machine Design Data Handbook, McGraw-Hill Book Company, New York, 1994.

16.34 CHAPTER SIXTEEN

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effective length of knuckle pin, m (in)

dedendum for a flat root involute spline profile, m (in)

dc core diameter of threaded portion of the taper rod, m (in)

dm(or dpm) mean diameter of taper pin, m (in)

pitch diameter, m (in)

force on the cotter joint, kN (lbf)

pressure between hub and key, kN (lbf)

F0, F00 force applied in the center of plane of a feather keyed shaft

which do not change the existing equilibrium but give a couple, kN (lbf)

F20, F200 two opposite forces applied on the center plane of a double

feather keyed shaft which give two couples, but tending to rotate the hub clockwise, kN (lbf)

minimum height of contact in one tooth, m (in)

length of couple (also with suffixes), m (in)

length of sleeve, m (in)

lo, so space width and tooth thickness of spline, m (in)

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p pressure, MPa (psi)

tangential pressure per unit length, MPa (psi)

hub is shifted lengthwise, kN (lbf)

number of splines

ROUND OR PIN KEYS

The large diameter of the pin key

STRENGTH OF KEYS

Rectangular fitted key (Fig 17-1, Table 17-1)

Pressure between key and keyseat

17.2 CHAPTER SEVENTEEN

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Crushing strength

The tangential pressure per unit length of the key

at any intermediate distance L from the hub edge

(Fig 17-1, Table 17-2)

The torque transmitted by the key (Fig 17-1)

The general expression for torque transmitted

accord-ing to practical experience

For dimensions of tangential keys given here.

Shearing strength

The torque transmitted by the key (Fig 17-1)

The shear stress at the dangerous point (Fig 17-1)

TAPER KEY (Fig 17-2, Table 17-3)

The relation between the circumferential force Ftand

the pressure F between the shaft and the hub

The pressure or compressive stress between the shaft

and the hub

where
1¼ coefficient of friction between the shaft

and the hub

TABLE 17-2

Dimensions (in mm) of tangential keys and keyways

diameter,D Height,h Width, b Radius,r chamfer, a diameter, D Height,h Width, b Radius,r chamfer, a

Notes: (1) The dimensions of the keys are based on the formula: width 0.3 shaft diameter, and thickness¼ 0.1 shaft diameter; (2) if it is not possible

to fix the keys at 1208, they may be fixed at 1808; (3) it is recommended that for an intermediate diameter of shaft, the key section shall be the same

as that for the next larger size of the shaft in this table

Source: IS 2291, 1963

KEYS, PINS, COTTERS, AND JOINTS 17.5

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Dimensions (in mm) of taper keys and keyways

The necessary length of the key

The axial force necessary to drive the key home

(Fig 17-2)

The axial force is also given by the equation

FRICTION OF FEATHER KEYS (Fig 17-3)

The circumferential force (Fig 17-3)

The resistance to be overcome when a hub connected

to a shaft by a feather, Fig 17-3a and subjected to

torque Mt, is moved along the shaft

The equation for resistance R, if
and
2are equal

The equation for torque if two feather keys are used,

Fig 17-3b

The force F2applied at key when two feather keys are

used, Fig 17-3b

The resistance to be overcome when the hub

con-nected to the shaft by two feather keys Fig 17-3b

and subjected to torque Mtis moved along the shaft

For Gib-headed and Woodruff keys and keyways

FIGURE 17-3 Feather key

KEYS, PINS, COTTERS, AND JOINTS 17.7

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Parallel-sided or straight-sided spline

The torque which an integral multispline shaft can

Source: Courtesy H L Horton, ed., Machinery’s Handbook, 15th ed., The Industrial Press, New York, 1957.

KEYS, PINS, COTTERS, AND JOINTS 17.11

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Straight sided splines (all dimensions in mm)

Minor MajorNominal size No of diameter, diameter, Width, d1,a e,a

Involute-sided spline

AMERICAN STANDARD (Table 17-7) The

adden-dum a and dedenadden-dum b for a flat root, Table 17-7

The area resisting shear, Table 17-7

The minimum height of contact on one tooth

The corresponding area of contact of all z teeth

The torque capacity of teeth in shear

The torque capacity of the spline in bearing with

 D

Splined hub For centering on inner

diameter or flanks

For centering on inner

diameter

KEYS, PINS, COTTERS, AND JOINTS 17.13

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TABLE 17-10

Straight-sided splines for machine tools (all dimensions in mm)

4 SplinesNominal size, Minor Major

TABLE 17-11

Undercuts, chamfers, and radii for straight-sided splinesa(all dimensions in mm)

External splines

i  d  D B d1, min g, max f , min h r1, max m n r2 k, max r3, max of hub

i  d  D B d1, min g, max f , min h r1, max m n r2 k, max r3, max of hub

The theoretical torque capacity of straight-sided

spline with sliding according to SAE

Equating the strength of the spline teeth in shear to

the shear strength of shaft, the length of spline for a

hollow shaft

The length of spline for a solid shaft

The effective length of spline for a hollow shaft used in

practice according to the SAE

For diametrical pitches used in involute splines (SAE



where

i ¼ number of splines D; d ¼ diameter as shown in Table 17-7, m

d ¼ inside diameter of spline, m

D ¼ pitch diameter of spline, m

L ¼ length of spline contact, m

h ¼ minimum height of contact in one tooth of spline, m

Mtin N m

Mt¼ 1000i



D þ d 4

Di¼ internal diameter of a hollow shaft, m (in)

Dme ¼ minor diameter (external), m (in)

3 me

612

816

1020

1224

1632

2040

2448

3264

4080

4896

The number of teeth

The minor diameter of the internal spline (Fig 17-4a)

The major diameter of the external spline (Fig 17-4a)

The minor diameter of the external spline (Fig 17-4a)

FIGURE 17-4(a) Reference profile of an involute-sided spline (Source: IS 3665, 1966.)

FIGURE 17-4(b) Nomenclature of the involute spline profile

FIGURE 17-5 Measurement between pins and measurement over pins of an involute-sided spline (Source: IS 3665, 1966.)

KEYS, PINS, COTTERS, AND JOINTS 17.17

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The value of tooth thickness and space width of spline

PINS

Taper pins

The diameter at small end (Figs 17-6 and 17-7, Tables

17-16 and 17-17)

The mean diameter of pin

FIGURE 17-6 Tapered pin

Sleeve and taper pin joint (Fig 17-7)

AXIAL LOAD

The axial stress induced in the hollow shaft (Fig 17-7)

due to tensile force F

The bearing stress in the pin due to bearing against

the shaft an account of force F

The bearing stress in the pin due to bearing against

the sleeve

The shear stress in pin

The shearing stress due to double shear at the end of

The axial stress in the sleeve

TORQUE

The shear due to twisting moment applied

For the design of hollow shaft subjected to torsion

Taper joint and nut

The tensile stress in the threaded portion of the rod

(Fig 17-8) without taking into consideration stress

concentration

FIGURE 17-8 Tapered joint and nut

The bearing resistance offered by the collar

The diameter of the taper d2

Provide a taper of 1 in 50 for the length (l
l1Þ

Knuckle joint

The tensile stress in the rod (Fig 17-9)

The tensile stress in the net area of the eye

Stress in the eye due to tear of

Tensile stress in the net area of the fork ends

Stress in the fork ends due to tear of

Compressive stress in the eye due to bearing pressure

of the pin

Compressive stress in the fork due to the bearing

pressure of the pin

Shear stress in the knuckle pin

The maximum bending moment, Fig 17-9 (panel b)

The maximum bending stress in the pin, based on the

assumption that the pin is supported and loaded as

shown in Fig 17-9b and that the maximum bending

moment Mboccurs at the center of the pin

The maximum bending moment on the pin based on

the assumption that the pin supported and loaded

as shown in Fig 17-10b, which occurs at the center

of the pin

The maximum bending stress in the pin based on the

assumption that the pin is supported and loaded

 b

4 þ a 3

FIGURE 17-9 Knuckle joint for round rods

KEYS, PINS, COTTERS, AND JOINTS 17.23

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The initial force set up by the wedge action

The force at the point of contact between cotter and

the member perpendicular to the force F

The thickness of cotter

The width of the cotter

Cotter joint

The axial stress in the rods (Fig 17-10)

Axial stress across the slot of the rod

Tensile stress across the slot of the socket

The strength of the cotter in shear

Shear stress, due to the double shear, at the rod end

Shear stress induced at the socket end

The bearing stress in collar

Crushing strength of the cotter or rod

Crushing stress induced in the socket or cotter

The equation for the crushing resistance of the collar

Shear stress induced in the collar

Shear stress induced in the socket

The maximum bending stress induced in the cotter

assuming that the bearing load on the collar in the

rod end is uniformly distributed while the socket

end is uniformly varying over the length as shown in

Fig 17-10b

Gib and cotter joint (Fig 17-11)

Threaded joint

COUPLER OR TURN BUCKLE

Strength of the rods based on core diameter dc, (Fig.

17-12)

The resistance of screwed portion of the coupler at

each end against shearing

From practical considerations the length a is given by

The strength of the outside diameter of the coupler at

the nut portion

F ¼ 

F ¼ 

FIGURE 17-11 Gib and cotter joint for round rods FIGURE 17-12 Coupler or turn buckle

KEYS, PINS, COTTERS, AND JOINTS 17.25

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The outside diameter of the turn buckle or coupler at

the middle is given by the equation

The total length of the coupler

3 Faires, V M., Design of Machine Elements, The Macmillan Company, New York, 1965.

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

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

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

7 Juvinall, R C., Fundamentals of Machine Component Design, John Wiley and Sons, New York, 1983.

8 Deutschman, A D., W J Michels, and C E Wilson, Machine Design—Theory and Practice, Macmillan Publishing Company, New York, 1975.

9 Bureau of Indian Standards.

18

THREADED FASTENERS AND

SCREWS FOR POWER

TRANSMISSION

Ab area of cross section of bolt, m2(in2)

Abr area of base of preloaded bracket, m2(in2)

major diameter of external thread (bolt), m (in)

dm¼ d2 mean diameter of square threaded power screw, m (in)

major diameter of internal thread (nut), m (in)

Di inside diameter of a pressure vessel or cylinder, m (in)

mean diameter of inside screw of differential or compound screw, m (in)

screw, m (in)

Eb, Eg moduli of elasticity of bolt and gasket, respectively, GPa (Mpsi)

tightening load on the nut, kN (lbf )

preload in each bolt, kN (lbf )

thickness of a cylinder, m (in)

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h2 thickness of the flange of the cylindrical pressure vessel, m (in)

FIGURE 18-1 Flanged bolted joint

number of bolts

I moment of inertia of bracket base, area (Fig 18-6), m4or cm4

(in4)

distance from the inside edge of the cylinder to the center line of

bolt, m (in) lead, m (in)

suffixes), m (in)

pc circular pitch of bolts or studs on the bolt circle of a cylinder

cover, m (in)

o, i respective helix angles of outside and inside screws of

differential or compound screws, deg

i, o respective coefficient of friction in case of differential or

compound screw

0

allowable bearing pressure between threads of nut and screw,

MPa (psi)

18.2 CHAPTER EIGHTEEN

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c compressive stress, MPa (psi)

Gasket joint (Fig 18-2)

Final load on the bolt

3 7

Refer also to Table 18-1 for values of K

FIGURE 18-2 Gasket joint

THREADED FASTENERS AND SCREWS FOR POWER TRANSMISSION 18.3

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According to Bart, the tightening load for a screw of a

steamtight, metal-to-metal joint

Tightening load for screw of a gasket joint

Cordullo’s equation for the tightening load on the

nuts

Bolted joints (Fig 18-2)

The flange thickness of the cylinder or pressure vessel

The bolt diameter

Circular pitch of the bolts or studs on the cylinder

cover to ensure water and steamtight joint

pc¼3:5d for pressure from 1.2 MPa

TABLE 18-1

Values of K for use in Eq (18-4)

Soft, elastic gasket with studs 1.00

Soft gasket with through bolts 0.90

Soft copper corrugated gasket 0.40

18.4 CHAPTER EIGHTEEN

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The average stress for screw for sizes from 12.5 to

75 mm

Unwin’s formula for allowable stresses in bolts of

ordinary steel to make a fluidtight joint

TENSION BOLTED JOINT UNDER

EXTERNAL LOAD

Spring constant of clamped materials and

bolt (Fig 18-3A)

The spring constant or stiffness of the threaded and

unthreaded portion of a bolt is equivalent to the

stiffness of two springs in series.

The basic equations for deflection (), and spring

constant (k) of a tension bar/bolt subject to tension

load.

The effective spring constant/total spring rate in case

of long bolt consisting of the threaded and

unthreaded portion having different area of

cross-sections, the clamped two or more materials of two

or more different elasticities which act as spring with

different stiffness sections in series.

Spring constant of the clamped material

Spring constant of the threaded fastener

where avin psi and d in in

d¼ 17;537:4d2þ 11 for rough joint SI ð18-14aÞ where din MPa and d in m

where din psi and d in in

s¼ 33;828:9d2þ 17:3 for faced joint SI ð18-14cÞ where din MPa and d in m

THREADED FASTENERS AND SCREWS FOR POWER TRANSMISSION 18.5

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Approximate effective area of clamped material

PRELOADED BOLT (Fig 18-3B)

The external load

The bolted joint in Fig 18-3A subjected to external

load Fais such that the common deflection is given by

The load shared by bolt

The resultant/total bolt load

The resultant load on the clamped material

Am¼

4 ðD2 eff
d2Þ where

Deff ¼ effective diameter, m

d ¼ round bolt of diameter equal to shank, m

lt¼ threaded length of bolt, m

lunt¼ unthreaded portion of bolt length, m

Fm¼ portion of load Fataken by member/material, kN

Ft¼ preload, kN

acting on the joint

18.6 CHAPTER EIGHTEEN

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The joint constant or stiffness parameter

The preload to prevent joint separation occurs when

Fm¼ 0

The external load required to separate joint

The tensile stress in the bolt

Preload under static and fatigue loading as per the

recommendation of R, B and W,aand Bowman

The proof stress load that has to be used in Eq (18-15p)

The load factor

The load factor guarding against joint separation

GASKET JOINTS

For design of gasket bolted joint

PRELOADED BOLTS UNDER DYNAMIC

LOADING

The mean forces felt by the bolt

The alternating forces felt by the bolt

Ft¼

0:75F

p for reused bolt connections

0 :90Fp for permanent bolt connections

ð18-15pÞ where Fpis proof load, N

aRussel, Bardsall and Ward Corp., Helpful Hints for Fastener Design and Application, Mentor, Ohio 1976, p 42

THREADED FASTENERS AND SCREWS FOR POWER TRANSMISSION 18.7

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The stress due to the preload Fi

The fatigue safety factor by using modified Goodman

criterion

The alternating component of bolt stress

The mean stress

The factor of safety according to the Goodman

criterion

Solving of Eqs (18-16c) and (18-16d) simultaneously

The factor of safety on the basis of yield strength

For specification of SAE, ASTM and ISO standard

steel bolts

The depth of tapped hole (Fig 18-2)

The distance l from the inside edge of the cylinder to

the center line of bolts (Fig 18-2)

The diameter of bolt circle

The safe load on each bolt

The number of bolts

Another expression for the number of bolts

m¼ aþ Fi

At¼ CP 2Atþ Fi

Stress in tensile bolt

Seaton and Routhwaite formula for working stress

for bolt made of steel containing 0.08 to 0.25%

carbon and with diameter of 20 mm and over

Applied load

Rotsher’s pressure-cone method for stiffness

The elongation of frustum of a cone (Fig 18-3C)

The spring stiffness of the frustum

¼ 23:3  108(15,000) for alloy–steel bolts

¼ 0:33  108(1000) for bronze bolts The values of C inside parentheses are for US Cus- tomary System units, and values without parentheses are for SI units.

Ed tan  ln

ð2t tan  þ D
dÞðD þ dÞ ð2t tan  þ D þ dÞðD
dÞ ð19-25aÞ

k ¼ F a¼

Ed tan 

ln ð2t tan  þ D
dÞðD þ dÞ ð2t tan  þ D þ dÞðD
dÞ

ð18-25bÞ

TABLE 18-2

Approximate bolt tension and torque values

Minimum bolt tension Equivalent torque

Major Stress Design stress,w Permissible load

THREADED FASTENERS AND SCREWS FOR POWER TRANSMISSION 18.9

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FIGURE 18-3C Compression of a member assumed to be

confined to the frustum of a hollow cone

FIGURE 18-3D Forms of threads for power screw

18.10 CHAPTER EIGHTEEN

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The spring stiffness of the frustum when cone angle of

frustum  ¼ 308

For the members of the joint having same modulus of

elasticity E with symmetrical frusta back to back which

constitute as two springs in series and using the grip as

l ¼ 2t and dw as the diameter of the washer face, the

effective spring constant for the system.

The effective spring constant for the case of back to

back cone frusta with a washer face dw¼ 1:5d and

 ¼ 308 from Eq (18-25d).

Power screw

The helix angle of a V-thread (Fig 18-3E)

The tangential force for a square thread at mean

radius of screw

Torque required to raise the load by a power screw

The tangential force for V-thread or angular thread at

mean radius (Fig 18-4)

The total frictional torque including collar friction

torque for square thread

ln ð1:15t þ D
dÞðD þ dÞ ð1:15t þ D þ dÞD
dÞ

ð18-28aÞ

Mt¼ W d2

2

 tan  þ 

FIGURE 18-3E Helix angle of a single-start thread

TABLE 18-4 Coefficient of friction for power screws

Lubricant Coefficient of friction,Machine oil and graphite 0.07

THREADED FASTENERS AND SCREWS FOR POWER TRANSMISSION 18.11

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FIGURE 18-3F Power screw FIGURE 18-3G Differential screw.

FIGURE 18-4 Forces acting on a triangular thread

TABLE 18-5a

Coefficient of friction on thrust collar, c

Coefficient Coefficient

of running of starting

Soft steel on cast iron 0.121 0.170

Hardened steel on cast iron 0.092 0.147

Soft steel on bronze 0.084 0.101

Hardened steel on bronze 0.063 0.081

TABLE 18-5b Torque factor Kfor use in Eq (18-30c)

18.12 CHAPTER EIGHTEEN

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