design of socket and spigot joint
TRANSCRIPT
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TITLE
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A cotter is a flat wedge shaped piece of rectangular cross-section and its
width is tapered (either on one side or both sides) from one end to another
for an easy adjustment.
The taper varies from 1 in 48 to 1 in 24 and it may be increased up to 1 in 8, if a
locking device is provided. The locking device may be a taper pin or a set screw
used on the lower end of the cotter.
The cotter is usually made of mild steel or wrought iron.
A cotter joint is a temporary fastening and is used to connect rigidly two co-axial
rods or bars which are subjected to axial tensile or compressive forces.
It is usually used in connecting a piston rod to the crosshead of a reciprocatingsteam engine, a piston rod and its extension as a tailor pump rod, strap end of
connecting rod etc.
INTOODUCTION
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Types of Cotter JointsFollowing are the three commonlyused cotter joints to connect tworods by a cotter:
1. Socket and spigot cotter joint,
2. Sleeve and cotter joint, and
3. Gib and cotter joint'
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Socket and spigot Cotter joint
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P = Load carried by the rods,
d = Diameter of the rods,
d 1 = Outside diameter of socket,
d2= Diameter of spigot or inside diameter of socket,
d3= Outside diameter of spigot collar,
t 1= Thickness of spigot collar,
d 4= Diameter of socket collar, c = Thickness of socket collar, b = Mean width of cotter,
t = Thickness of cotter,
I = Length of cotter,
a = Distance from the end of the slot to the end of rod, t= Permissible tensile stress for the rods material,
= Permissible shear stress for the cotter material, and
c= Permissible crushing stress for the cotter material.
NOTATION USED
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Design procedure
The dimensions for a socket andspigot cotter joint may beobtained by considering the
various modes of failure
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1) Failure of the rod in tension
The rod may fail in tension due to the tensileload P .
We know that
resisting tearing= (/4)*d2
Tearing strength of rods=(/4)*(d2)* (t)
From this equation, diameter of the rod (d) may be calculated
Equating this to load (P), we have
P=[ (/4)*(d2)2]*t
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2)Failure of spigot in tension across theweakest section (or slot )
Since the weakest section of the spigot is that section
which has a slot in it for the cotter , thereforeArea resisting tearing of the spigot across the slot
=[ (/4)*(d2)2- (d2)*t ]
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2)Failure of spigot in tension across theweakest section (or slot )
Since the weakest section of the spigot is that section which
has a slot in it for the cotter , thereforeArea resisting tearing of the spigot across the slot
=[ (/4)*(d2)2- (d2)*t ]
Tearing strength of the spigot across the slot
=[ (/4)*(d2)2- (d2)*t ]*(t)
Equating this to load (P), we have
P=[ (/4)*(d2)2- (d2)*t ]*(t)
From this equation, diameter of spigot or inside
diameter of socket (d2)may be determined.
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3)Failure of the rod or cotter in crushing
We know that the area that resist crushing ofthe cotter= (d2)*t
Tearing strength of rods= (d2)*t * (t)
Equating this to load (P), we have
P=[(d2)*t ]*t
From this equation, the induced crushing stress may be checked.
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4)Failure of socket in tension across the slot
We know that
Area resisting to the tearing of the socket across the slot
=(/4)*[(d1)2 - (d2)
2]-(d1-d2)*t
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4)Failure of socket in tension across the slot
We know that
Area resisting to the tearing of the socket across the slot
=(/4)*[(d1)2 - (d2)
2]-(d2-d1)*t
Tearing strength of the socket across the slot
= {(/4)*[(d1)2
- (d2)2
]-(d1-d2)*t}*(t)
Equating this to load (P), we have
P= {(/4)*[(d1)2 - (d2)2]-(d1-d2)*t}*(t)
From this equation, diameter of the rod (d1) may be calculated
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5)Failure of COTTER IN SHEAR
Considering the failure of cotter in shear as shown in figure.
Since the cotter is in double shear , therefore shearing area of thecotter=2*b*t
And shear strength of the cotter =2*b*t*
Equating this to load (P) we have
P=2*b*t*
. From this equation width of cotter
(b) is determined
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6.1)Failure of socket collar in crushing.
Considering the failure of socket collar in crushing as
shown in figure
We know that area that resists crushing of socket collar
=[(d4)- (d2) ]* t
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6.2)Failure of socket collar in crushing.
Crushing strength of socket collar
=[(d4)- (d2) ]* t*t
Equating this to load (P) we have
P=[(d4)
- (d2) ]* t*t
. From this equation the diameter of socket collar( d4) May be determined
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7) Failure of socket end in
Since the socket end is in the double shear.
Therefore area that resist s shearing of socket collar
=2*[(d4)- (d2) ]*c
And the shearing strength of socket collar=2*[(d4)
- (d2) ]*c*
Equating this to load (P) We get
P=2*[(d4)- (d2) ]*c*
From this above equation the the thickness of socket
collar ( c ) may be obtained.
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8) Failure of rod end in shear
Since the rod end is in the double shear.
Therefore area that resists shearing of rod end.
=2*a*(d2)
And the shearing strength of rod end=2*a*(d2)*
Equating this to load (P) We get
P=2*a*(d2)*
rom this above equation the the thickness of rod end ( c ) may be obtained
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9)Failure of spigot collar in crushingt
Considering the failure of the spigot collar in crushing as
shown in figure.We know that Area resisting to the crushing of the spigotcollar
=(/4)*[(d3)2 - (d2)
2
Crushing strength of the collar
=(/4)*[(d3)2
- (d2)2
*(c)
Equating this to load (P), we have
=(/4)*[(d3)2 - (d2)
2*(c)
From this equation, diameter of the rod (d3) may be calculated
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10)Failure of spigot collar in shearing
Considering the failure of the spigot collar in shearing as
shown in figure.We know that Area that resists shearing
of the collar=()*(d2)*(t1)
And the shearing strength of the collar
=()*(d2)*(t1) *
Equating this to load (P), we have=()*(d2)*(t1)*
From this equation, diameter of the rod (t1)may be calculated
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Failure of cotter in bendingIn all the above relation it is assumed thatload is uniformly distributed over the variouscross-section of the joint . But in actualpractice this does not happen and the cotteris subjected to bending . In order to find outthe bending stress induced ,it is assumedthat the load on the cotter in the rod end is
uniformly distributed while in the socket endit various from zero at the outer diameter d4and maximum at the inner diameter d2asshown in figure.
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Failure of cotter in bending
The maximum bending moment occurs at the centre
of the cotter and is given by
MMAX=P/2[1/3*(d4-d2)/2+d2/2]- P/2[d2/4
MMAX=P/2[(d4-d2)/6+d2/2-d2/4]
MMAX=P/2[(d4-d2)/6+d2/4]
We know that section modulus of the cotter ,
Z=t*b2/6
Bending stress induced in the cotter,
b= (MMAX/Z)
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Failure of cotter in bending
Bending stress induced in the cotter,
b= (MMAX/Z)
Bending stress induced in the cotter,
b
= P/2[(d4-d2)/6+d2/4]/( t*b2/6)
Bending stress induced in the cotter,
b= P[(d4)+0.5 *d2]/(2* t*b2)
This bending stress induced in the cotter
should be less than the allowable bending stress of the cotter.
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Other dimensions of the cotter joint
The length of the cotter(l) is taken asl=4d
The taper in cotter should not exceed 1
in 24. In case the greater taper isrequired then a locking device must beprovided.
The draw of the cotter is generallytaken as 2 to 3 mm
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When all the parts of the joint are made of steel,the following proportions in terms of the
diameter of the rod (d) are generally adopted
D1=1.75d
D2=1.21d
D3=1.5d
D4=2.4d
A=c=0.75d
B=1.3d
L=4d
T=0.31dT1=0.45d
E=1.2d
Taper of cotter=1 in 25 and draw of cotter= 2 to 3 mm.
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If the rod and cotter are made
of steel or wrought iron then=0.8t
And c= 2tMay be taken.
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FINISHING
DESIGNPROCEDURE OF
COTTER JOINT