design of keys,cooters and knuckle joint()

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Key fasteners

are used to prevent the rotation of wheels, gears etc. on
their shafts.

Types of Keys

The keys can be classified as per the shape and purpose for which they are
used. Following are the types of keys.

(a)


Sunk keys


(b)


Saddle keys

(c)


Tangent keys








(d)


Serrated shaft and Splines

(e)


Round keys or Taper

pins

Classification of Keys

Keys are classified into three types as follows:

(a)


Taper keys


(b)


Parallel or

Feather keys

(c)


Special keys

Taper Keys.



A
taper Key

is of rectangular cross section having
uniform width and tapering thickness. The taper keys are used to transmit
only the turning moment between the shaft and the hub without any rel
ative
rotational and axial motion between them. The examples of tapered keys are

(a)


Taper sunk key


(b)


Saddle key

(c)


Flat key





(d)


Gib head key

Parallel or Feather Keys.



A
parallel key

or
feather key

is also of
rectangular cross section of uniform width and thickness throughout. Parallel
keys are used to transmit the turning moment between the shaft and the
hub along with the provision to allow a small sliding axial mo
tion between
them wherever required. The examples of the parallel keys are:

(a)


Parallel sunk key


(b)


Peg key

(c)


Single head key


(d)


Double head key

(e)


Spline shaft.

Special Keys.


The
woodruff key
,
cone k
ey

and
pin key

are the special
purpose keys used for specific applications.

Sunk Keys













A key that engages a slot formed in both pulley and
shaft is known as
sunk keys
. The sunk keys are of following types:

(a)


Rectangular key



(b)


Square key

(c)


Gib head key
























(d)


Woodruff key

(e)


Feather key

Rectangular Key.


This type of key is rectangular in cross section and is
very commonly used. The dimensions of this type of key ar
e as follows:



Width of the key
W


=
D

/ 4

Thickness of the key
T
=
D

/

6



Where
D

is the diameter of the shaft.

A taper of 1 in 100 on the thickness and parallel in width is given to the key.
The taper is given on
the upper surface of the key, i.e. the hub side. The
recess in the hub is also given the same taper. The thickness of the key is
measured at the large end (Refer Fig 3).



The cross section


of the key is square and the dimension is:






Side of the key =
D / 4

A taper of 1 in 100 on the thickness and parallel in width is given to the key.
The taper is given on the upper surface of the key, i.e. the hub side. The
recess in the hub is also given the same taper (Refer Fig 4).
This type of key
is used for mounting pulleys or gears on shafts. Square keys are used for
shafts upto
17mm

in diameter.


Gib Head Key.



This key can be rectangular or square in cross section having a head at the
large end. The head makes it easier to re
move the key from the hub and
shaft. The slot for gib head key must have an open end to permit assembly.
For this reason it is placed at the end of a shaft. The dimensions of a gib
head key are given in Fig 5.

Dia of the Shaft = D





Width of Key ‘W’ = D/4



Thickness of the key ‘T’ =D/6




Taper on thickness = 1
in 100



h = 1.75 T, b = 1.5 T



Woodruff Key.



A woodruff key shown in Fig 6 is segmental in shape and is an easily
adjustable sunk key.

The key fits into a semicircular key way cut into the
shaft. The top of the key fits into a plain rectangular keyway in the hub. This
key has the advantage of aligning itself with the taper of the hub and will not
easily turn over, because of its extra de
pth in the shaft. Woodruff key largely
used in automobile work and machine tools. The dimensions of the woodruff
key are standardized. The dimensions of a woodruff key for
ød

and
ø22

shaft
are shown in Fig 7. A woodruff key is designated as :






Woodruff key 5 X 9 IS
:

2294

Where 5mm is the width and 9mm is the height of the key. IS: 2294 is BIS
code for woodruff key.




Feather Key.

The feather key is attached to the shaft or the hub and permits relative axial
movement. Fig 8 shows a feather key with a double gib head. Fig 9 shows a
feather key secured to the shaft with the help of two set screws. Fig 10
shows a feather key attached to the hub with the help of one set screw. Fig
11 shows a peg feather key. The p
eg of the key fits into the slot provided in
the hub.


Saddle Keys.



They are tapered keys and are of two types :

(a)


Flat saddle key

(b)


Hollow saddle key

Flat Saddle Key.




It is a tapered key which fits in the key way of the
hub and the flat surface on the shaft. It has got the tendency to slip round
the shaft, that is why, it is suitable for light duty. The Fig 12 shows the
proportions of a flat saddle key.

d = Dia
of the Shaft,


T = d/12,


W = d/4



Hollow Saddle Key

This

is also a tapered key fitting into the key way of the hub and the bottom
of the key is curved so as to fit the curved surface of the shaft. It is suitable
for light duty work. Fig 13 shows the
proportions of a hollow saddle key.

d = Dia of the Shaft,


T = d/12,


W = d/4



A key is a component inserted between the shaft and the hub of a
pulley, wheel, etc., to prevent relative rotation but allow sliding
movement along the shaft, if required.

The recess machined in a shaft or hub to accommodate the key is
called a keyway. Keyways can be milled horizontally or vertically,
as shown in the figure below. Keys are made of steel, in order to
withstand the considerable shear and compressive stresses
c
aused by the torque transmit.



There are two basic types of key:

(a)


Saddle keys
, which are sunk into the hub only. These keys
are suitable only for light duty, since they rely on a friction
drive alone.

(b)

Sunk keys
, which are sunk into the shaft an
d into the hub
for half their thickness in each. These keys are suitable for
heavy duty, since they rely on positive drive.

Hollow saddle keys
are used for very light duty, fig.(a)
below.

Flat saddle keys
are used for light duty, fig. (b) below.

Round keys

are used for medium duty, fig. (c) below.


Feather key
is used when the hub is required to slide along
the shaft. It is lightly fitted or secured by means of screws in
the shaft keyway, and is made to slide in the hub keyway,
fig. (a) below.

Rectangular
and square keys
can be parallel or tapered with

a basic taper of 1 in 100 to prevent sliding. These keys are
used for heavy
-
duty applications. It is advised to use square
keys for assembly
-
drawing solutions.
Gib heads

are
sometimes provided on taper keys t
o facilitate their
withdrawal, fig. (b) and fig. (c) below


Woodruff key

is an almost semi
-
circular disc which fits into a
circular keyway in the shaft. The top art of the key stands
proud of the shaft and fits into the keyway in the parallel or
tapered h
ub. As the key can rotate in the keyway, it can fit
any tapered hole in the hub, fig. (a) below.

A splined shaft
is used when the hub is required to slide
along the shaft. These shafts are used mostly for sliding
-
gear applications. The splines are usually
milled and the
splined holes broached, fig (b) below.

Square
-
head set screws
and
grub screws
are also used for
low
-
torque applications, fig. (c) below.

If the torque to be transmitted is too great for one
grubscrew or key, two may used set at 90
o

to 120
o

around
the shaft, but never at 180
o
.



DESIGN OF SQUARE AND FLAT KEYS

may be based on the
shear

and
compressive

stresses induced in
the key as a result of the torque being transmitted. The forces
acting on the key are shown in the figure. The forces
F


act as a
resisting couple to prevent the key from tending to roll in the
fitted keyway. The exact location of the force
F

is not known and
it is convenient to assume that it acts tangent to the surface of
the shaft. This force produces both shear and comp
ression
stresses in the key.



Resistance to the shaft torque
T

may then be approximated by
T = Fr
, where r is the radius of the shaft. The shearing stress
t

in
the key is





Key is placed so that part of it lies in a groove cut on the shaft, called
"
key seat
",
and part of it fits into a groove cut in a hub, called "
key way
". Therefore, after the
assembly locked together by the key, the shaft and hub will rotate together.

KEY TYPES

The simplest key is the
square key
, placed half in the shaft (H/2) and half in the
hub (H/2). A
flat key

is rectangular in cross section, used similarly as square key.


The
gib
-
head key

is tapered on its upper surface and is driven in to form a very
secure fastening. The head shape provid
es removal.


The most common key is the
Woodruff key
. This key is flat segmental disk with a
flat (A) or round (B) bottom. Key numbers are assigned to specify these keys


For very heavy duty, when keys are not sufficiently strong,
splined shafts and
hubs

are used, arranged so that they fit one within other.



DIMENSIONING OF KEYS

For unit production nominal dimensions may be given (Fig. 45 p. 528)

For quantity production, the limits of width (and depth if necessary)















DESIGN OF COTTERS

COTTER JOINT


A cotter joint is used to connect rigidly two co
-
axial rods or bars which are
subjected to axial tensile or compressive forces . It is a temporary fastening

A cotter is a flat wedge shaped piece of rectangular cross section and its width is
t
apered (either on one side or on both sides) from one end to another for an easy
adjustment.

Cotter joints are used to connect together two rods rigidly to transmit power in the
length
-
wise direction. Sometimes when it is required to increase the length of

the
rod or to connect a rod directly to the machine to transmit power through the rod
as in the case of a connecting rod end of a steam engine, a joint is used. Cotter
joints can be used for round or square rods. Some of the joints are described
below.

A
cotter is a flat, wedge shaped piece of steel, used to connect rigidly, two
parts which are subjected to axial forces only. The cotters have a uniform
thickness throughout the length and taper on one or both side (Fig 18). The
taper varies from 1 in 8 to 1

in 48. The cotters having large tapers need a
locking device.

Length of the cotter
L




=
3.5d

to
4d

Breadth of the cotter
B


=
d

to
1.32d

Thickness of the cotter
T

=
0.15d

to
0.25d

The cotter joints are subjected to axial forces such as
tensile or compressive
forces. The joints differ from key joints which are used to join shafts
subjected to torsional stresses only.


Comparison between Keys and Cotters

The main difference between keys and cotters are as follows:

(a)


Keys are drive
n parallel to the axis whereas cotters are driven
perpendicular to the axis.

(b)


Keys are used in parts subjected to torque whereas cotters are used
in parts subjected to tensile or compressive force.

(c)


Keys resist shear over a longitudinal
section whereas cotters resist
shear over two transverse sections.

Sleeve and Cotter Joint.

This type of joint is used for light transmission of axial loads from one rod to
another rod. The ends of the two rods are forced into a sleeve (Refer Fig
19). Two
slots are provided in the sleeve, and one slot each is provided in
the rods to take one cotter each.



Spigot and Socket Cotter Joint

This type of joint is used for round rods. The end of one rod is forged in the
shape of a socket and the other in the shape of a spigot (Refer Fig 21). Slots
are provided in the spigot and socket ends to accommodate the cotter. The
diameter of the spigot e
nd is increased to overcome the loss of strength due
to the slot. To make the joint rigid and perfectly tight, the slots are made
slightly out of alignment, so that when the cotters is driven in, it will tend to
force the spigot and socket ends towards eac
h other.


Gib and Cotter Joint for Square Rods.

This type of joint is used for joining two square rods. One end of the rod is
forged in the shape of a fork (Refer Fig 22). The other rod is pushed into the
fork. Slots are provided in the fork and the rod t
o accommodate the
gib

and
cotter

while assembling the parts. The gib is inserted first so that the
straight surface touches the slot of the fork and then cotter is hammered
into the rest of the slot. Care should be taken that the tapered side of the
gib an
d cotter should be face to face with each other.




A machine runs by the power supplied to it by a prime mover such as,
motor, engine, etc. The power is transmitted from the prime mover to the
machine through a coupler which couples the shafts of the pri
me mover and
the machine. The most commonly employed method to connect a shaft and
a part is to drive a small piece of metal, known as
key

between the shaft
and the hole made in the part mounted over it. The key will be driven such
that it sits partly into

the shaft and partly into the part mounted on it. To
introduce the key, axial grooves, called
key ways

are cut both in the shaft
and the part mounted on it. The key is fitted between the shaft and the part
mounted over it. While transmitting the power, th
e key will be subjected to
shear and crushing forces. Keys are extensively used to hold pulleys, gears,
couplings, clutches, sprockets, etc., and the shafts rigidly so that they rotate
together. They are also used to mount the milling cutters, grinding whe
els,
etc., on their spindles.

Rods of circular and square or rectangular cross sections subjected to axial
tensile or compressive forces, are connected together by a
cotter joint
. It is
a temporary method of fastening of the two rods which will have to be
frequently assembled and disassembled. Its chief advantages are that the
joint can be quickly assembled and disassembled and the rods occupy
exactly the same relative positions after assembly. The cotter joints are used
to connect the piston rod to the cro
ss head of the steam engine, pump or
compressor. Long tie bars in steel structures are sometimes built up of
round bar, of short lengths and joined together by cotter joints.


APPLICATIONS OF COTTER


1. Connection of the piston rod with the cross heads

2.
Joining of tail rod with piston rod of a wet air pump

3. Foundation bolt

4. Connecting two halves of fly wheel (cotter and dowel arrangement)


COMPARISON BETWEEN KEY AND COTTER


1. Key is usually driven parallel to the axis of the shaft which is subjected
to
torsional or twisting stress. Whereas cotter is normally driven at right angles to the
axis of the connected part which is subjected to tensile or compressive stress along
its axis.


2. A key resists shear over a longitudinal section whereas a cotter re
sist shear over
two transverse section.

DIFFERENT TYPES OF COTTER JOINTS


1. Socket and spigot cotter joint

2. Sleeve and cotter joint

3. Gib and cotter joint


A sleeve and cotter joint is used to connect two round bars transmitting axial force
in translat
ory motion. A sleeve or muff is used to slide over two rods, and two
cotters are inserted (one on each rod and sleeve) through rectangular holes
provided in the sleeve and rod ends, as shown in the The tapered sides of two
cotters face each other



The c
learance on the sleeve and rods (between the rectangular holes and the
cotters) is so adjusted that when the cotters are driven inside the holes, the two
edges come closer to each other, making the joint tight. Taper in cotter provided is
1: 24. The variou
s proportions of the joint as per empirical relations are:

13
-
4 GIB AND COTTER JOINT

In an ordinary cotter joint, there is a taper only on the cotter and the cotter
is inserted into the rectangular slots of socket and spigot ends of the rods.
Friction at
the edges between the socket holes and the cotter, and between
the spigot holes and the cotter, provide the necessary joining force. Bearing
surfaces are less and there is a tendency of the cotter to spring up and
making the joint loose.

A gib with negativ
e matching taper is inserted along with the cotter, thus
providing the joint a larger bearing area and a greater holding force between
the cotter and the rods to be connected through the cotter, as shown in
thereby considerably reducing the tendency of th
e cotter to slacken. Two
gibs can be used on two sides of a cotter. In this case, the cotter will have a
taper on both the sides. Sometimes to prevent loosening of cotter, a small
set screw is used through the rod which will jam the cotter

13
-
5 COTTER IN F
OUNDATION BOLT

Foundation bolts are used to connect base of machines to the foundation.
The head of the bolt is grouted in the foundation with the help of concrete.
The bolt is passed through a hole. Often, when it is inconvenient to use an
ordinary bolt,
then a cotter is used in conjunction with a foundation bolt to
hold down the bolts, in order to fasten heavy machines to the foundation. In
this case, a bolt with a rectangular slot at one end is dropped down from
above, through a hole at the base of the m
achine and the concrete
foundation, and then a cotter is inserted into the rectangular slot in the bolt
from one side. The diameter of the end of the bolt in which the cotter is
inserted is enlarged The assembly is tightened by screwing the nut on to
the
bolt, while the machine base and concrete slab provide more bearing
area in order to take up the tightening load on bolt, and the tightening force
is uniformly distributed over the large surface area.



DESIGN PROCEDURE FOR THE SPIGOT AND COTTER JOINT


To
understand the design steps let take a question and solve it step by step.


Q. Design a cotter joint subjected to a tensile load of 35 kN and a compressive load
of 40 KN . The allowable stresses are

tensile stress qt = 70N/mm2

compressive stress qc = 110 N
/mm2

shear stres t = 50 N/mm2



SOLUTION


STEP 1


Failure of rod in tension or compression


tensile stress = tensile load / area


qt=(Pt*40/(3.14*d*d)


where d is the diameter of the rod


from above equation we will find out the value of d and round it off

to the higher
integer. Now we apply the Standard shaft rule..i.e the diameter of the rod should
be of the given range


diameter increment in steps


1
-
10mm 1mm

10
-
24mm 2mm

24
-
45 mm 3mm

45
-
100 mm 5mm

above 100mm 10mm


we will make the value of the d such th
at it will satisfy the above table.


compressive stress = compressive load /area


qc=(4*Pc)/(3.14*d*d)


again find the value of d ,round it off ,make according to the above table and now
compare the two values of d .Take the value which is greater .



STEP

2


Failure of spigot in tension across slot


Pt=qt*[3.14/4*d1*d1
-
d1*t]


where t =d1/4

find the value of d1 and then t




Emperically d1=1.2*d


again find the value of d1 and choose which one is larger ..


STEP 3


Failure of rod or cotter in crushing


che
ck for the condition


Pt<= d1*t*qc


if the above condition meet then the value of d1 and t is correct else increase the
value of d1 and t to satisfy the condition .Because if the above condition is not
satisfied then cotter will be get crushed due to load
.



STEP IV


Tensile failure of socket across slot


Pt=qt[3.14/4(d3*d3
-
d1*d1)2
-
(d3
-
d1)t]


find the value of d3 from above equation


Emperically , d3=1.75d


choose the greater one.




STEP V


Crushing of cotter against collar of socket



Pt=qc(d4
-
d1)t


find

the value of d4


Emperically , d4=2.4d


choose the greater one .



STEP VI


Crushing of collar of spigot to socket



Pc=(qc*3.14*(d2*d2
-
d1*d1))/4


find the value of d2


Emperically , d2 =1.5d


choose the greater one.


STEP IX


Shear failure of spigot end
against cotter


Pt=2*T*d1*a


where T=shear stress


find the value of a


Emperically a=0.75d


choose the greater value of a



STEP X


Shear failure of spigot collar


Pt=3.14*d*h*T


find the value of h from the above equation


Emperically ,h=0.75d


Choose th
e greater value of h



Step XI


Double shear failure of collar of socket by cotter


Pt=2*T*(d4
-
d1)*e



find the value of e from the above equation


Emperically e=0.75d


Choose the greater value of e.


KNUCKLE

JOINT







Knuckle joints may be cast or fabricated or forged.


In the knuckle joint illustrated,
the rods are integral with the eye and fork (forged construction). However, the
knuckle joint is often separate to the rods, and the rods need to be welded or
screwed in
to the eye and fork.


In the knuckle joint illustrated, there is no separate
bearing and rotational or motion occurs between the pin and eye or pin and fork or
both. If there is considerable movement, it may be necessary to use bearings to
minimise frictio
n and wear. If this is the case, the pin is usually a tight fit in the eye
or held to the eye with a grub screw and bearings are provided in the fork. The
bearings may be plain bearings or rolling element bearings.

Good proportions

For steel knuckle joints

without bearings, good proportions are as follows:

Pin :



diameter d = rod diameter

Fork:



diameter D = 2d width a = O.75d

Eye:



diameter D = 2d width b = 1 .2d


Stress analysis

Complete stress analysis of a knuckle joint now follows.

Notes:



Some of the stresses are non
-
critical if the knuckle joint is of good
proportions.



Special formulas quoted below should be derived from first principles
so there is a clear understanding of how they were obtained.


Rod




Both ends are normally pinned so

there are no bending or shear loads
so the rod need be designed for tensile stress only. However, if there is a
compression load as well as a tension load, the rod should be checked for
buckling. That is ensure that Fcr> F where:


Notes:



These formulas a
re standard column formulas.



For a round rod, the radius of gyration k = d/4



Since force F is the critical buckling force, a safety factor should be
applied.