5_threaded fasteners.pdf
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Screw fasteners and non
permanent joints, Power
ScrewNut, Bolt, Stud, Screw
M. S. Dasgupta, BITS Pilani
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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.
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Thread Standards and Definitions
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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
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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
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Square & Acme threads
Square thread Acme thread
Knuckle thread ?
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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
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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
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Understanding Shear and Crushing failure in bolt
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Understanding failure in plate (joint)
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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
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Table A-29; page-1053
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CAP screws
Fillister
Flat Socket; may be hexagonal or square
See Table A-30, page-1054 for dimensions.
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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
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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.
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Nut Varieties
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Locking Mechanisms
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Special purpose bolts & markings on bolt head
Bol ts with no markings are low strength
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Note: the dimension H includesthe washer face thickness which is
normally 0.4 mm.
Table A31; Dimensions of Hexagonal Nuts
T i l i
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-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
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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
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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.
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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.
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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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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
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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.
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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
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Resultant member stiffness
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
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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.
Resultant member stiffness
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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
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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
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Load Shared by Bolt and Member
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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
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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
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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
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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
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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:
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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
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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
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Fatigue Loading of Tension Joints
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
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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
Fatigue Loading of Tension Joints
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