design of socket and spigot joint

8/11/2019 Design of Socket and Spigot Joint

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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)


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)


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)


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)


=(/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


b= (MMAX/Z)


b

= P/2[(d4-d2)/6+d2/4]/( t*b2/6)


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

design of socket and spigot joint

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