Machine Design Databook 2010 Part 6 pot

SOLID SHAFTS 1 Stationary shafts with static loads The diameter of shaft subjected to simple torsion The diameter of shaft subjected to simple bending The diameter of shaft subjected to

Trang 1

TABLE 12-15

Stress concentration factor,K

Stress concentration factor, K

Weld metal

Base metal

Stiﬀening ribs and partitions welded with end ﬁllet welds having

Butt and T-welded corner plates, but with smooth transitions in the 1.5 1.9

shape of the plates and with machined welds

TABLE 12-16

Allowable stresses for welds under static loads

Allowable stresses Tension, Compression, Shear,

Automatic and hand welding with shielded arc and butt welding t a t 0.65 t

Trang 2

13

RIVETED JOINTS

A area of cross-section, m2(in2)

the cross-sectional area of rivet shank, m2(in2)

b breadth of cover plates (also with suﬃxes), m (in)

c distance from the centroid of the rivet group to the critical rivet,

m (in)

d diameter of rivet, m (in)

Di internal diameter of pressure vessel, m (mm)

eor l eccentricity of loading, m (in)

F force on plate or rivets (also with suﬃxes), kN (lbf)

h thickness of plate or shell, m (in)

hc, h1, h2 thickness of cover plate (butt strap), m (in)

i number of rivets in a pitch ﬁne (also with suﬃxes 1 and 2,

respectively, for single shear and double shear rivets)

I moment of inertia, area, m4, cm4(in4)

J moment of inertia, polar, m4, cm4(in4)

K ¼ F

F0 coeﬃcient (Table 13-11)

Mb bending moment, N m (lbf in)

p pitch on the gauge line or longitudinal pitch, m (in)

pc pitch along the caulking edge, m (in)

pd diagonal pitch, m (in)

pt transverse pitch, m (in)

Pf intensity of ﬂuid pressure, MPa (psi)

Z section modulus of the angle section, m3, cm3(in3)

hoop stress in pressure vessel or normal stress in plate, MPa

(psi)

a allowable normal stress, MPa (psi)

c crushing stress in rivets, MPa (psi)

shear stress in rivet, MPa (psi)

a allowable shear stress, MPa (psi)

eﬃciency of the riveted joint

angle between a line drawn from the centroid of the rivet group

to the critical rivet and the horizontal (Fig 13-5)

Source: MACHINE DESIGN DATABOOK

Trang 3

PRESSURE VESSELS

Thickness of main plates

The thickness of plate of the pressure vessel with

The rivet diameter

FIGURE 13-1 Pitch relation

2

p2

2s

d ¼ 6 ffiffiffih

p

to 6:3pffiffiffih

CM ð13-5cÞwhere h and d on mm

TABLE 13-1

Suggested types of joint

Diameter of shell, mm (in) Thickness of shell, mm (in) Type of joint

Trang 4

TABLE 13-2

Minimum thickness of boiler plates

Diameter of shell, Minimum thickness after ﬂanging, Diameter of tube sheet, Minimum thickness,

Allowable stresses in structural riveting (b)

Rivets acting in single shear Rivets acting in double shear Rivet-driving

Trang 5

TABLE 13-5

Allowable stress for aluminum rivets,a

Allowable stressa, a

Values of working stressaat elevated temperatures

Minimum of the speciﬁed range of tensile strength of the material, MPa (kpsi) Maximum

Pitch of butt joints

Type of joint Diameter of rivets, d, mm Pitch, p

use for h 12:5 mm (0.5 in)

Trang 6

Butt joint

The transverse pitch

For rivets, rivet holes, and strap thick

pt ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi0:5pd þ 0:25d2

q

ð13-6bÞRefer to Tables 13-9, 13-10, and Fig 13-2

Rivet hole diameters

Diameter of rivet, mm Rivet hole diameters, mm (min)

Trang 7

Minimum transverse pitch as per ASME Boiler Code

For transverse pitches

Haven and Swett formula for permissible pitches

along the caulking edge of the outside cover plate

Diagonal pitch, pd, is calculated from the relation

MARGIN

Margin for longitudinal seams of all pressure vessels

and girth seams of power boiler having unsupported

heads

Margin for girth seams of power boilers having

supported heads and all unﬁred pressure vessels

pt¼ 1:75d þ 0:1ð p dÞ if p

d> 4 USCS ð13-8bÞwhere pt, d, and p in in

Refer to Table 13-8

pc d ¼ 14

ffiffiffiffiffiffi

h3 c

Pf

4

s

CM ð13-9aÞwhere pc, d, hcin cm, and Pf in kgf/cm2

pc d ¼ 21:38

ffiffiffiffiffiffi

h3 c

Pf 4

s

USCS ð13-9bÞwhere pc, d, hcin in, and Pf in psi

pc d ¼ 77:8

ffiffiffiffiffiffi

h3 c

Pf

4

s

SI ð13-9cÞwhere pc, d, hcin m, and Pf in N/m2

hc¼ 0:6h þ 0:0025 if h 0:038 m SI ð13-12aÞwhere hcand h in m

hc¼ 0:6h þ 0:1 if h 1:5 in USCS ð13-12bÞwhere hcand h in in

hc¼ 0:67h if h > 0:038 m SI ð13-12cÞwhere hcand h in m

hc¼ 0:67h if h > 1:5 in USCS ð13-12dÞwhere hcand h in in

13.6 CHAPTER THIRTEEN

RIVETED JOINTS

Trang 8

Alcn 2I þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

Alcn 2I

2

þ 1 s

lp

p 2 þ 1 ðn 2 1Þp 2

2 s

lp

p 2 þ 1 ðn 2 1Þp 2

2 s

Key:

n ¼ total number of rivets in a column

F ¼ permissible load, acting with lever arm, l, kN (lbf)

Source: K Lingaiah and B R Narayana Iyengar, Machine Design Data Handbook ( fps Units), Engineering College Cooperative Society, Bangalore, India, 1962; K Lingaiah and B R Narayana Iyengar, Machine Design Data Handbook, Vol I (SI and Customary Metric Units), Suma Publishers, Bangalore, India, 1983; and K Lingaiah, Machine Design Data Handbook, Vol II (SI and Customary Metric Units), Suma Publishers, Bangalore, India, 1986.

RIVETED JOINTS 13.7

RIVETED JOINTS

Trang 9

Thickness of the cover plate according to

Indian Boiler Code

Thickness of single-butt cover plate

Thickness of single-butt cover plate omitting alternate

rivet in the over rows

Thickness of double-butt cover plates of equal width

omitting alternate rivet in the outer rows

Thickness of the double-butt cover plates of unequal

width

For thickness of cover plates

The width of upper cover plate (narrow strap)

The width of lower cover plate (wide strap)

STRENGTH ANALYSIS OF TYPICAL

RIVETED JOINT (Fig 13-2)

The tensile strength of the solid plate

The tensile strength of the perforated strip along the

outer gauge line

The general expression for the resistance to shear of

all the rivets in one pitch length

The general expression for the resistance to crushing

of the rivets

The resistance against failure of the plate through the

second row and simultaneous shearing of the rivets in

the ﬁrst row

The resistance against failure of the plate through the

second row and simultaneous crushing of the rivets in

the ﬁrst row

The resistance against shearing of the rivets in the

outer row and simultaneous crushing of the rivets in

the two inner rows

h1¼ 0:625h for narrow strap ð13-17aÞ

h2¼ 0:750h for wide strap ð13-17bÞRefer to Table 13-10

Trang 10

EFFICIENCY OF THE RIVETED JOINT

The eﬃciency of plate

The eﬃciency of rivet in general case

For eﬃciency of joints

The diameter of the rivet in general case

The pitch in general case

For pitch of joint

THE LENGTH OF THE SHANK OF RIVET

c

i2þ i1h2h

Trang 11

FIGURE 13-4 Riveting of an angle to a gusset plate.

RIVETED BRACKET (Fig 13-5)

The resultant load on the farthest rivet whose distance

is c from the center of gravity of a group of rivets

MbcP

x2þPy2

2

þ 2

F

nn0

MbcP

x2þPy2

cos

#1=2ð13-33Þ

FIGURE 13-5 Riveted bracket (Bureau of Indian Standards.)

RIVETED JOINTS

Trang 12

For rivet groups under eccentric loading value of

coeﬃcient K

For preferred length and diameter of rivets

For collected formulas of riveted joints

5 Bureau of Indian Standards

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

BIBLIOGRAPHY

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

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

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

where

n ¼ number of rivets in one column

n0¼ number of rivets in one row

x, y have the meaning as shown in Fig 13-5Refer to Table 13-11

Refer to Figs 13-6 to 13-8 and Tables 13-12 to 13-13.Refer to Table 13-14

RIVETED JOINTS 13.11

RIVETED JOINTS

Trang 13

FIGURE 13-6 Rivets for general purposes (less than 12 mm diameter) For preferred length and diameter combination, refer to Table 13-12.

FIGURE 13-7 Rivets for general purposes (12 to 48 mm diameter) For preferred length and diameter combination, refer to Table 13-13.

RIVETED JOINTS

Trang 14

FIGURE 13-8 Boiler rivets (12 to 48 mm diameter) For preferred length and diameter combination, refer to Table 13-13.

RIVETED JOINTS 13.13

RIVETED JOINTS

Trang 25

14

DESIGN OF SHAFTS

b width of keyway, m (in)

c machine cost, $/m ($/in) (US dollars)

D diameter of shaft (also with subscripts), m (in)

Di inside diameter of hollow shaft, m (in)

Do outside diameter of hollow shaft, m (in)

E modulus of elasticity, GPa (Mpsi)

F axial load (tensile or compressive), kN (lbf)

Fm0 the static equivalent of cyclic load, (¼ Fm Fa), kN (lbf)

G modulus of rigidity, GPa (Mpsi)

h depth of keyway, m (in)

k radius of gyration, m (in)

material cost (also with subscripts), $/kg

K ¼Di

Do

ratio of inner to outer diameter of hollow shaft

Kb numerical combined shock and fatigue factor to be applied to

computed bending moment

Kt numerical combined shock and fatigue factor to be applied to

computed twisting moment

Mb bending moment, N m (lbf in)

Mt twisting moment, N m (lbf in)

Mbm0 static equivalent of cyclic bending moment Mbm Mba,

speciﬁc weight of material, kN/m3(lbf/in)

stress (tensile or compressive) also with subscripts, MPa (psi)

shear stress (also with subscripts), MPa (psi)

ratio of maximum intensity of stress to the average value from

compressive stress only

angular deﬂection, deg

Source: MACHINE DESIGN DATABOOK

Trang 26

Other factors in performance or in special aspect are included from time to time

in this chapter and, being applicable in their immediate context, are not given at

this stage

Note: and with the initial subscript s designates strength properties of

material used in the design which will be used and observed throughout this

handbook In some books on machine design and in this Machine Design

Data Handbook the ratios of design stresses sd=fd andsd=fd; and design

stresses yd,yd0,fd, andfd have been used instead ofsy=sf,sy=sf; and

yield strengths sy,sy and fatigue strengths,sf,sf in the design equations

for shafts [Eqs (14-1) to (14-65)] This has to be taken into consideration in

the design of shafts while using Eqs (14-1) to (14-65)

SOLID SHAFTS

(1) Stationary shafts with static loads

The diameter of shaft subjected to simple torsion

The diameter of shaft subjected to simple bending

The diameter of shaft subjected to combined

tor-sion and bending:

(a) According to maximum normal stress theory

(b) According to maximum shear stress theory

(c) According to maximum shear energy theory

D ¼

16Mt

Trang 27

The diameter of shaft subjected to axial load,

bending, and torsion:13

(a) According to maximum normal theory

(2) Rotating shafts with dynamic loads, taking

dynamic eﬀect indirectly into consideration13

For empirical shafting formulas

The diameter of shaft subjected to simple torsion

The diameter of shaft subjected to simple bending

bending and torsion

The diameter of shaft subjected to axial load,

bending, and torsion

þ

(

MbþFD8

2

þ M2 t

2

þ M2 t

24

35

1=3ð14-7Þ

D ¼ 16yd

MbþFD8

35

1=3ð14-8Þ

Refer to Table 14-1

D ¼

16

ydfðKbMbÞ2þ ðKtMtÞ2g1=21=3

ð14-12Þ

D ¼

16

DESIGN OF SHAFTS 14.3

DESIGN OF SHAFTS

Trang 28

The diameter of shaft based on torsional rigidity

(3) Rotating shafts and ﬂuctuating loads, taking

fatigue eﬀect directly into consideration13

The diameter of shaft subjected to ﬂuctuating

torsion

The diameter of shaft subjected to ﬂuctuating

bending

ﬂuc-tuating torsion and bending:

ydfM0bmþ ðM02

bmþ M02

tmÞ1=2g

1=3ð14-20Þ

D ¼

16

Trang 29

ﬂuctuating axial load, bending, and torsion

HOLLOW SHAFTS

(1) Stationary shafts with static loads

The outside diameter of shaft subjected to simple

torsion

bending

tor-sion and bending

D ¼

(16

and Fm0 ¼ Fmþsd

Do¼

16Mt

Trang 30

The outside diameter of shaft subjected to axial

load, bending, and torsion

(2) Rotating shafts with dynamic loads, taking

dynamic eﬀect indirectly into consideration13

torsion

bending

The outside diameter of shaft subjected to

com-bined bending and torsion

Do¼

(16

1=2!)1=3

ð14-31Þ

Do¼

(16

#1=2)1=3

ð14-32Þ

Do¼

(16

Trang 31

The outside diameter of shaft subjected to axial

load, bending and torsion

The outside diameter of shaft based on torsional

rigidity

(3) Rotating shaft with ﬂuctuating loads, taking

fatigue eﬀect directly into consideration

Please note: If the axial load does not produce column

action, the constant need not be used to multiply the

term [FDo (1 þ K 2 )/8] throughout this chapter.

DESIGN OF SHAFTS

Trang 32

com-bined ﬂuctuating torsion and bending

com-bined ﬂuctuating axial load, bending, and torsion

Do¼

16

1=2)#1=3

ð14-48Þ

Do¼

(16

#1=2!)1=3

ð14-49Þ

Do¼

(16

where Mbm0 , M0tm, and Fm0 have the same meaning as

in Eqs (14-22a), (14-22b), and (14-25a)

14.8 CHAPTER FOURTEEN

DESIGN OF SHAFTS

Trang 33

COMPARISON BETWEEN DIAMETERS OF

SOLID AND HOLLOW SHAFTS OF SAME

LENGTH

For equal strength in bending, torsion, and/or

com-bined bending and torsion, the diameter

(a) When materials of both shafts are same

(b) When materials of shafts are diﬀerent

For torsional rigidity

(a) When torsional rigidities are equal

(b) When torsional rigidities are diﬀerent

For equal weight

(a) When material of both shafts is same

(b) When materials of both shafts are diﬀerent

For equal cost

(a) For same material and machining cost for both

shafts

(b) For no machining cost for both shafts but with

diﬀerent material cost

(c) When machining costs are diﬀerent and material

Note: If the axial load does not produce column action, the

constant need not be used to multiply the term

[FDo (1 þ K 2 )/8] throughout this chapter

DESIGN OF SHAFTS

Trang 34

Instead of computing the transverse deﬂection, the

maximum distance between the bearings (in meters)

may be computed by the empirical formula to limit

the transverse deﬂection to 0.8 mm/m of length

RIGIDITY

Moor’s formula for the increase of the angle of twist

due to the keyway and applies only to the keyseated

length of shaft

EFFECT OF KEYWAYS

The lowering of the strength of shaft by keyways may

be taken into account by introducing a factor similar

to a stress-concentration factor (or Moor’s formula

for lowering the strength of shaft)

THE BUCKLING FACTOR

For short columns or when l=k 115

For long columns or when l=k 115 (Euler’s formula)

SHAFTS SUBJECTED TO VARIOUS

STRESSES

(1) Shaft subjected to steady torque and reversed

bending moment taking into consideration stress

ð14-65Þwhere

n ¼ 1 for hinged ends

¼ 2:25 for fixed ends

¼ 1:6 for both ends pinned or guided and partlyrestrained

( ¼ 1 for tensile load)

DESIGN OF SHAFTS

Trang 35

Diameter of solid shaft:

(a) According to maximum shear stress failure

theory using Soderberg [4] criterion for

(b) According to maximum shear stress theory of

failure using modiﬁed Goodman criterion for

Diameter of hollow shaft:

(c) According to distortion-energy theory of

failure using modiﬁed Goodman criterion

for fatigue strength

(d) According to distortion-energy theory of

failure combined with Gerber parabolic

(e) According to distortion-energy theory of

failure using ASME elliptic locus for fatigue

and yielding criterion (Langer) equation

com-bined with any theories of failure can be used to

predict the fatigue strength of shaft

Kf ¼ fatigue stress-concentration factor due tobending, tension, or compression

Kfr¼ fatigue stress-concentration factor due totorsion

Kf ¼ Kf ¼ 1 for ductile material under steadystate of stress

DESIGN OF SHAFTS

Trang 36

(2) Shaft subjected to ﬂuctuating loads, i.e., reversed

bending and reversed torque, taking into

consid-eration stress concentration

(a) The diameter of solid shaft according to

max-imum shear stress theory of failure using

Soderberg criterion for fatigue strength

(b) The diameter of hollow shaft according to

distortion-energy theory of failure combined

with Soderberg criterion for fatigue strength

(3) Shaft subjected to constant bending and torsional

moments and reversed torsional and bending

moments at the same frequency taking into

con-sideration stress concentration

max-imum distortion energy theory of failure using

modiﬁed Goodman criterion for fatigue

strength

(b) The diameter of solid shaft according to

max-imum shear stress theory of failure combined

with modiﬁed Goodman criterion for fatigue

strength

(c) The diameter of hollow shaft according to

maximum shear stress theory of failure using

Soderberg criterion for fatigue strength

D ¼

32n

Mbe¼ static equivalent of cyclic bending moment

syð1 K4Þð4Mbe2 þ 3M2

teÞ1=21=3

ð14-72Þwhere Mbeand Mtehave the same meaning as givenunder Eq (14-71)

D ¼

16n

D ¼

32n

DESIGN OF SHAFTS

Trang 37

(4) Cyclic axial load combined with reversed bending

and torsional moments taking into consideration

stress concentration as per ASME Code for

Design of Transmission Shafting

maximum shear stress theory of failure and

Soderberg relation for fatigue strength

(b) The diameter of hollow shaft according to

distortion-energy theory of failure combined

with modiﬁed Goodman relation for fatigue

strength

(5) The diameter of solid shaft subjected to axial,

bending, and torsional alternating loads

accord-ing to distortion-energy theory of failure

com-bined with Soderberg relation for fatigue as per

ASME Code for Design of Transmission Shafting5

D ¼ 32nsy

MbeþFaeD8

2

þ M2 te

1=2

ð14-76Þwhere Mbeand Mtehave the same meaning as givenunder Eq (14-71)

Fae¼ static equivalent axial load

a solid shaftThe value of is given by Eq (14-65)

D ¼ 32nsf

MbaþFaD2

2

þ3Mta24

1=2

þ

(32n

1=2)!1=3

ð14-78ÞNot explicit in D, use iterative methods to solve

Although ASME has withdrawn the ASME Code for Design

of Transmission Shafting, some of the ASME equations given

here have historic interest and hence are retained in this

book.

DESIGN OF SHAFTS

Trang 38

(6) The diameter of shaft made of brittle material,

which is subjected to reversed bending and

tor-sional moments taking into consideration stress

concentration as per maximum normal stress

theory of failure combined with modiﬁed

Good-man relation for fatigue strength

(7) Shaft subjected to combined axial, bending, and

torsional reversed loads taking into consideration

stress concentration and shock

(a) The diameter of hollow shaft according to

distortion-energy theory of failure using

Soderberg relation

The symbols used in Eqs (14-80) to (14-85) and Figs

14-1 and 14-2 are diﬀerent than that of the ANSI/

ASME standard B106 IM-1985 in order to remain

consistent with the symbols used in this Handbook

New ASME Code for design of transmission

shafting:

The diameter of shaft subjected to fully reversed

bending i.e., zero mean bending component and

torsional ﬂuctuating loads, i.e alternating loads

taking into consideration stress concentration

according to distortion energy theory of failure

combined with modiﬁed Goodman relation for

fati-gue as per new ANSI/ASME code for transmission

shafting

The factor of safety, n

D ¼

16n

Do¼

16n

sutð1 K4Þ½Mbe0 þ ðMbe02þ M02teÞ1=2

1=3

ð14-80Þfor hollow shaft, where Mbe0 and Mte0 have the samemeaning as given under Eq (14-77)

DESIGN OF SHAFTS

Trang 39

The diameter of shaft made of brittle material

sub-jected to reversed bending and torsional moments

taking into consideration stress concentration as per

maximum normal stress theory of failure combined

with modiﬁed Goodman relation for fatigue strength

For combined fatigue test data for reversed bending

combined torsion and combined with reversed torsion

on steel specimens

D ¼

16n

FIGURE 14-1 Results of fatigue Tests of steel specimens subjected to Reversed Bending and Torsion.

Source: Design of Transmission Shafting, American Society for Mechanical Engineers, New York, ANSI/ASME standard

Trang 40

See Tables 14-1 to 14-6 and Fig 14-2 for further

details on shafting design;3 refer to Table 14-4 for

shock load factors Ksband Kst

For further design details on shafting Refer to Tables 14-5 to 14-7

25 (0•416) 20 (0•333) 16 (0•266) 12•5(0•208) 6•3 5

10 (0•166)

FIGURE 14-2 Nomogram for determining diameter (d), speed (n), force (F), torque (Mt ), and power (P) in Customary Metric units and System International units (K Lingaiah, Machine Design Data Handbook, Vol II, Suma Publishers, Bangalore, India, 1986.)

This PDF has been modified using a demo version of ARTS PDF software This PDF has been modified using a demo version of ARTS PDF softw PDF

F softw

This PDF has been modified using a demo version of ARTS PDF s

This PDF has been modified

TSDESIGN OF SHAFTS

Định dạng
Số trang	80
Dung lượng	2,27 MB