5_Threaded Fasteners.pdf

7/23/2019 5_Threaded Fasteners.pdf

1/41

Screw fasteners and non

permanent joints, Power

ScrewNut, Bolt, Stud, Screw

M. S. Dasgupta, BITS Pilani
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2/41

Threaded Fastners

Design of machine elements needs complex geometryand joints; single integral parts not possible

Parts are joined by fasteners and they are convenientlyclassified as permanent, semi-permanent and non-

permanent joints Permanent :Welded joints, adhesive bonding

Semi-permanent : Riveted joints

Non-permanent fasteners: Threaded / non threadedjoints

Non threaded joints- keys, pins, snap-fit etc.

Threaded joints- screws, bolts and nuts, studs etc.


3/41

Thread Standards and Definitions


4/41

Lead and multi-threaded screws

Lead is the distance moved by nut parallel to thescrew axis when the nut is given one turn.

l=p* multiplicity of threading

Single threaded, l=p

Double threaded, l=2p

Triple-threaded, l=3p


5/41

The Metric Thread

M121.75 mmNominal / major diameter of 12 mm

pitch of 1.75 mmmetric designation

d = major diameter

dr=minor diameter

= d - 1.226 869p

dp=pitch diameter= d - 0.649 519p

p = pitch

pH2

3

basic ISO 68 profile with 60symmetric threads


6/41

Square & Acme threads

Square thread Acme thread

Knuckle thread ?


7/41

Power screw or Screw jack mechanism

A device used in machinery to change angular motion intolinear motion, and, usually, to transmit power

Used in machines such as universal tensile testing

machines, lead screws of lathes and other machine tools,

automotive jacks, vises, linear actuators, adjustable floor

posts and micrometers etc


8/41

Bolts/Screw

The ideal bolt length is one in which only one or two

threads project from the nut after it is tightened

Locations of stress concentrationin a bolt

At the fillet

At the run-out

At the thread-root fillet in the plane of the nut

The washer face and washersare used to distribute theload under the bolt head and nut face. It also prevent

fatigue failure of bolt that may result when the burs on

the imperfectly drilled bolt holescut into the bolt head


9/41

Understanding Shear and Crushing failure in bolt


10/41

Understanding failure in plate (joint)


11/41

Nomenclature of bolt

or 0.4 mm

(See Table A-29; page-1053)

d, Nominal dia or

major dia

48

200

200125

125

252

122

62

,

d

L

L

L

d

d

d

LlengthThreaded T

45o


12/41

Table A-29; page-1053


13/41

CAP screws

Fillister

Flat Socket; may be hexagonal or square

See Table A-30, page-1054 for dimensions.


14/41

Machine screws

notice that there is no shank

driven all the way up to the head

into the part

sometimes having a hole for

screw head to seat in the part


15/41

Hexagonal nut

Jam nuts: they are thinner

(a) end view, general; (b) washer-faced regular nut; (c) regular nut chamfered on both

sides; (d) jam nut with washer face; (e) jam nut chamfered on both sides.

See Table A-31, page-1055 for dimensions.


16/41

Nut Varieties


17/41

Locking Mechanisms


18/41

Special purpose bolts & markings on bolt head

Bol ts with no markings are low strength


19/41

Note: the dimension H includesthe washer face thickness which is

normally 0.4 mm.

Table A31; Dimensions of Hexagonal Nuts

T i l i


20/41

-Roundup Table A-17

td lll ,lengthGrip

HlL Length,Fastener

Td LLl grip,inportionunthreadedofLength

dt lll grip,inportionthreadedofLength

2,

2min'length,Grip 2 d

thl

dhL 5.1Length,Fastener

Td LLl

portion,unthreadedusefulofLength

dt lll '

portion,threadedusefultheofLength48

200

200125

125

____

252

122

62

,

d

L

L

L

d

d

d

LlengthThreaded T

Terminologies


21/41

Bolt Stiffness

21

111

kkk

21

21

kk

kkk

t

tT

lEAk

d

ddl

EAk

td

tdb

kk

kkk

dttd

tdblAlA

EAAk

Scenario of

springs in

series

At

= Thread tensile stress area from Table 8-1

portiond)(unthreadeshanktheofarea;4

2dAd


22/41

Table 81 (p:412) Diameters and Areas of Metric Threads.

dr=minor diameter

= d - 1.226 869p

dp=pitch diameter

= d - 0.649 519p

The mean of drand dpwas

used to compute the

tensile-stress area.


23/41

Joints- Member Stiffness

im kkkkkk

1....

11111

4321

Scenario of

springs in

series

When one of the membersis a soft gasket, km is

simply the gasket stiffness.

If there is no gasket, the stiffness of the members is rather

difficult to obtain, except by experimentation, because thecompression spreads out between the bolt head and the nut

and hence the area is not uniform.

Itosultrasonic technique method shows that the pressure

stays high out to about 1.5 bolt radii and falls off farther

away from the bolt and suggested to use pressure cone

method for stiffness calculation.


24/41

Joints- Member Stiffness

Figure 815

Compression of a member with the equivalent elastic

properties represented by a frustum of a hollow cone.

Here, l represents the grip length.
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25/41

EA

dxPd

.

2tan

2tan

22tan)(

2222

dDx

dDx

dDxrrA io

dDdDtdDdDt

Ed

P

tan2

tan2

lntan.

dDdDt

dDdDt

EdPk

tan2

tan2ln

tan.

t

dDxdDx

dx

E

P

02tan2tan.

The Theory of the Frustum of a Hollow Cone


26/41

Resultant member stiffness:

dDdDt

dDdDt

dEk

iii

iii

ii

tan2

tan2ln

tan.

If for ithmember,

i=1, 2, n

nm kkkkkk

1....

11111

4321

When all members are made of same material then we will use only two

identical frusta arranged back to back, and hence

2

211111

21

kk

kkkkkk

m

m

dDdDt

dDdDtEd

km

tan2

tan2ln2

tan.


27/41

Resultant member stiffness

dDdDt

dDdDtEdkm

tan2

tan2ln2

tan.

Ito suggested an angle

= 45 to use, but Little reports that this overestimates theclamping stiffness. When loading is restricted to a washer-face annulus (hardened steel,

cast iron, or aluminum), the proper apex angle is smaller. Osgood reports a range of 25

33for most combinations.

If is 30o

dDdDt

dDdDt

Edkm

155.1

155.1ln

.5774.0


28/41


dl

dl

Edkm

5.25774.0

5.05774.05ln2

5774.0

If is 30o and D is taken as the waster face diameter dw.

The washer face diameter is roughly 1.5 the major diameter of the bolt.

ddddl

ddddlEdk

ww

wwm

tan

tanln2

tan.

If the members of the joint have the same Youngs modulusE withsymmetrical frusta back to back, then they act as two identical springs

in series (i.e. km= k/2). Using the grip as l = 2t and dwas the diameter

of the washer face, the spring rate of the members to be


29/41

Use table 8-7 to read A and B

or use graph.

Wileman et al. FEM results for the same situation: when all members weremade of same material and hence having same Youngsmodulus.

)/exp( lBdA

Ed

km A, Bare constants; l is the grip length;

dis the major diameter of bolt.



30/41

According to SAE or ASTM, the bolt strength is specifiedby its minimum tensile strength and its minimum proof

strength

Theproof load is the maximum load (force) that a bolt can

withstand without acquiring a permanent set (i.e. first

measurable deviation from elastic behavior, which is

approximately equal to 0.0001 in )

Theproof strength is the quotient of the proof load and thetensile-stress area

Use Table 811 (page:435) for proof strength of steel

For other materials, take Sp= 0.85 Sy

Bolt Strength


31/41

Estimation of Preload, Fi

For both static and fatigue loading

sconnectionpermanentF0.90

fastenersreuseds,connectionntnonpermaneforF0.75

p

p

forFi

whereFpis the proof load, obtained from the equation,

Fp= At Sp

HereAtis the tensile stress area obtained from Table 8-1

Spis the proof strength obtained from Table 811


32/41

Load Shared by Bolt and Member


33/41

Tension joints- The External load

where

is stiffness constant of the joint

ii

mb

bibb FCPF

kk

PkFPF

0m

F

ii

mb

mimm FPCFkk

PkFPF )1( 0

mF

mb

m

bmb

b

mbm

PPP

and

kkPPor

kkPP

m

m

b

b

kP

kP


34/41

Relating Bolt Torque to Bolt Tension

The torque required to produce a given preload

The dia of the washer face of a hexagonal nut is the same as the width acrossflats and equal to 1.5 times the nominal size. Therefore the mean collar dia is

2sectan

sectan

22sec

sec

2

ccimicci

m

mmi dfF

fl

fdFdfF

fld

fdldFT

dKFdFffl

f

d

dT

ddd

iicm

625.0sectan

sectan

2

25.12

)5.1(dc

Where K is called torque coefficient


35/41

The coefficient of friction depends upon the surface smoothness,accuracy, and degree of lubrication. On the average, bothf and fcare

about 0.15.

The interesting fact is thatK = 0.20 forf = fc= 0.15 no matter what

size bolts are employed and no matter whether the threads are coarseor fine.

Relating Bolt Torque to Bolt Tension

Table 815 :Torque Factors K

L d f f i ll l d d


36/41

Load factor for statically loaded

tension joint with preload

CP

F-ASfactorloadn

)/AF(CnPstrengthproofS

SstrengthprooftheisofvaluelimitingThe)/AF(CP/AFboltinstresstensile

FCPFP

loadboltresultantF

itp

tip

pb

titbb

iib

b


37/41

Fig illustrates the connection of a cylinder head to a pressure vesselusing 10 bolts and a confined gasket seal. The effective sealing

diameter is 150 mm. A=100, B=200, C=300, D=20, E=20 (all in

mm). The cylinder is used to store gas at a static pressure of 6

MPa. ISO class 8.8 bolts with a diameter of 12 mm have been

selected. Find load factor n?

Cylinder head is steel (E = 207 GPa )

Cylinder is grade 30 cast iron (E = 100 GPa)

Problem:


38/41

For a general case with constant preload and an externalload on per bolt is fluctuating between Pminto Pmax.

loading.fatigueforsolveto

equationsfailureellipticASMEandGerberGoodman,

instressesamplitudeandmidrangeabovetheSubstitute22

22

minmaxminmax

minmaxminmax

maxmax

minmin

t

i

t

m

t

bbm

t

a

t

bba

ib

ib

A

F

A

PPC

A

FF

A

PPC

A

FF

FCPF

FCPF

Fatigue Loading of Tension Joints


39/41

Fatigue Loading of Tension JointsThe statistics indicate that the bolts under dynamic loading failed 65% in the

thread at the nut face, 20% at the end of the thread (at the runout point) and 15%

under the head.

Table 817

Fully Corrected Endurance Strengths for Bolts and Screws with Rolled Thread

Table 817

Fatigue Stress- Concentration Factors Kf for Threaded Elements


40/41


tt

i

t

i

t

aA

CP

A

F

A

F

A

CP

22

1

2

1minmax

t

i

tt

i

t

i

t

mA

F

A

CP

A

F

A

F

A

CP

22

1

2

1minmax

In the common bolted joints of pressure cylinders, the

external load varies from a lower extreme of P=0 to the

upper extreme of P itself.

ima The equation of the load hence is,

In this case


41/41

1ut

m

e

a

S

S

S

SGoodman

1

2

ut

m

e

a

S

S

S

S

Gerber

1

22

p

m

e

a

S

S

S

S

ellipticASME


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