Machine Design – I

Code: ME- 216

Credit Hours: 2

Lecture
Design of Keys and Couplings

Dr. Muhammad Imran

Mechanical Engineering Department
University of Engineering & Technology
Taxila
 Topics
Types of keys.
Material.
Stresses on key and key Failures.
Key design.
Keyways.
 Keys

Key is a type of fastener inserted between

the shaft and the hub or boss of the pulley
to connect these together in order to
prevent relative motion between them.

✓ It is always inserted parallel

to the axis of the shaft.
✓ Keys are used as temporary
fastenings and are subjected
to considerable crushing
and shearing stresses.
 TYPE OF KEYS
The keys are standardized as to size and shape in several styles.
Following are the most important type of keys.
 (a) Sunk Keys
The sunk keys are provided half in the keyway
of the shaft and half in the keyway of the hub.
These are the types of the sunk keys.

1. Parallel key

2. Tapered key

3. Gib head key

4. Feather key

5. Woodruff Key
Rectangular sunk key
w = d / 4 ; and thickness of key, t = 2w / 3
=d/6
Square sunk key
w=t=d/4
Gib-head key
w=d/4;
t = 2w / 3 = d / 6
1. It accommodates itself to any taper in the hub or boss of the mating piece.
2. It is useful on tapering shaft ends. Its extra depth in the shaft *prevents any
tendency to turn

1. The depth of the keyway weakens the shaft.

2. It can not be used as a feather.
(b)
A flat saddle key is a taper key which fits in a keyway in the
hub and is flat on the shaft as shown in Fig.

It is likely to slip round the shaft under load. Therefore it is used for
comparatively light loads.
 3. Tangent keys
(c)

• The tangent keys are fitted in pair at right angles as shown in

Fig.
• Each key is to withstand torsion in one direction only.
• These are used in large heavy duty shafts

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 (d)
4. Round Keys
• Round keys are circular in section and fit into holes drilled partly
in the shaft and partly in the hub.
• Round keys are usually considered to be most appropriate for
low power drives.

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 5. Splines
(e)
• keys are made integral with the shaft which fits in the keyways
broached in the hub.
• shafts usually have four, six, ten or sixteen splines
• The splined shafts are used when the force to be transmitted is
large in proportion to the size of the shaft.

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 Backlash

When the torque changes sign in a parallel

key i.e. any clearance between the key and
the keyway will suddenly be taken up with
resulting impact and high stresses.
 MATERIAL
• It is important that the key does not
damage the objects it is fastening so it is
made up of a material that is weaker than
the material of the object they are
holding.
• This strategy causes the immediate
damage being done to the key instead of
the keyseat.
• The key acts like a shear pin in an
outboard motor to protect the more
expensive parts from damage. A key is an
inexpensive and is relatively easy to
replace if the keyseat is undamaged.
 MATERIAL
• Because keys are loaded in shear, ductile materials are
used. Soft, low-carbon steel is most common choice
unless a corrosive environment requires a brass or
stainless steel key.
• Square or rectangular keys are often made from cold
rolled bar stock and merely cut length. The special
keystock is used when a closer fit is required between
key and keyway. Tapered and woodruff keys are also
usually made from soft cold rolled steel.
FORCES ACTING ON SUNK KEYS
When a key transmits torque from a shaft to a rotor or a hub,
the following two types of forces act on the key:
1. Forces due to fit of the key in its keyway, as in a tight
fitting straight key or in a tapered key driven in place.
These forces produce compressive stresses in the key
which are difficult to determine in magnitude.
2. Forces due to the torque transmitted by the shaft. These
forces produce shearing and compressive (or crushing)
stresses in the key.
FORCES ACTING ON SUNK KEYS

✓ The distribution of the forces along the length of the

key is not uniform because the forces are concentrated
near the torque-input end. The non-uniformity of
distribution is caused by the twisting of the shaft within
the hub
✓ In designing a shaft the forces due to the fit of the key
are neglected and it is assumed that the distribution of
forces along the length of the key is uniform.
 Strength of a Sunk key
• T = Torque transmitted by the shaft,
• F = Tangential force acting at the circumference of the shaft,
• d = Diameter of shaft,
• l = Length of key,
• w = Width of key.
• t = Thickness of key, and
• τ and σc = Shear and crushing stresses for the material of key.
• Considering shearing of the key
F = Area resisting shearing × Shear stress = l × w × τ
• Torque transmitted

• Considering crushing of the key, the tangential crushing

force acting at the circumference of the shaft,

• F = Area resisting crushing × Crushing stress =

• Torque transmitted by the shaft,

The key is equally strong in shearing and crushing, if
 w/t = σc/2τ
Where,
w= width of the key,
t= thickness of key,
σc= crushing stresses for material of key,
τ= shear stresses for material of key.
 Length of a key

• In order to find the length of the key to transmit full power

of the shaft, the shearing strength of the key is equal to the
torsional shear strength of the shaft.

• We know that the shearing strength of key,

…………(i)

• and torsional shear strength of the shaft,

…………(ii)
• From equations (i) and (ii), we have

• When the key material is same as that of the shaft , then τ =τ1
 Designing a Key
A key is sized by using only a few variables.

a) KEY WIDTH: It is determined by the shaft

diameter at the keyseat, D/4
b) KEY HEIGHT: Key height is also the
penetration into the hub. It is also determined by
the key width,2W/3 or D/6
c) LENGTH OF THE KEY, L=1.751D
d) NUMBER OF KEYS USED PER HUB.
Example 1. Design the rectangular key for a shaft of 50 mm diameter.
The shearing and crushing stresses for the key material are 42 MPa
and 70 MPa.
 Keyway
A shallow longitudinal slot cut in a shaft or a hub for
receiving a key.
➢ Keyway seating machine is a machine tool for milling
keyways in shafts etc., using an end mill with the work
supported on a table at right angles to the tool axis.
➢ Keyway tool (keyway cutter) is a sloting machine tool used
for the vertical cutting of keyways, the tool being equal to
the width of the keyway.
Stress Concentrations in Keyways
• As the keys have sharp corners so the
keyways also have sharp corners this
causes significant stress concentrations.
End Milled Keyway- Single and Double
Edged
• This keyway is milled by an end-mill.
• It will have sharp corners at one or both ends.
Effect of Keyways
Example. A 15 kW, 960 r.p.m. motor has a mild steel shaft of 40 mm
diameter and the extension being 75 mm. The permissible shear and
crushing stresses for the mild steel key are 56 MPa and 112 MPa.
Design the keyway in the motor shaft extension. Check the shear
strength of the key against the normal strength of the shaft.
 Shaft coupling
• Shafts are usually available up to 7 meters length due to
inconvenience in transport.
• In order to have a greater length, it becomes necessary to join
two or more pieces of the shaft by means of a coupling.

➢ Shaft couplings are used in machinery for:

1. Connection of shafts of such as a motor and generator and
for disconnection for repairs or alternations.
2. For misalignment of the shafts or mechanical flexibility.
3. To reduce the transmission of shock loads
4. To introduce protection against overloads.
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 Requirements of a Good Shaft Coupling

1. It should be easy to connect or disconnect.

2. It should transmit the full power from one shaft to the
other shaft without losses.
3. It should hold the shafts in perfect alignment.
4. It should reduce the transmission of shock loads from one
shaft to another shaft.
5. It should have no projecting parts.

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 Types of Shafts Couplings
• Shaft couplings are divided into two main groups as follows:

1. Rigid coupling: It is used to connect two shafts which are

perfectly aligned.
(a) Sleeve or muff coupling
(b) Clamp or split-muff or compression coupling
(c) Flange coupling.

2. Flexible coupling: It is used to connect two shafts having both

lateral and angular misalignment.
(a) Bushed pin type coupling
(b) Universal coupling
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(c) Oldham coupling
 Sleeve or Muff-coupling
• It is the simplest type of rigid coupling, made of cast iron.
• It consists of a hollow cylinder whose inner diameter is the
same as that of the shaft.
• It is fitted over the ends of the two shafts by means of a gib head
key, as shown in Fig.

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• Outer diameter of the sleeve, D = 2d + 13 mm
• length of the sleeve, L = 3.5 d ,
where d = diameter of the shaft.

• T = Torque to be transmitted by the coupling,

• τc = Permissible shear stress for the material of the sleeve
which is cast iron.

➢ Design for key:

• The length of key is at least equal to the length of the sleeve
• The coupling key is usually made into two parts so that the
length of the key in each shaft
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• After fixing the length of key in each shaft, the induced shearing
and crushing stresses may be checked.

• We know that torque transmitted,

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Example 13.4. Design and make a neat dimensioned sketch of a muff coupling which
is used to connect two steel shafts transmitting 40 kW at 350 r.p.m. The material for
the shafts and key is plain carbon steel for which allowable shear and crushing
stresses may be taken as 40 MPa and 80 MPa respectively. The material for the muff
is cast iron for which the allowable shear stress may be assumed as 15 MPa.
 Design of split muff coupling

• The usual proportions of the muff for the clamp or compression

coupling are :
• Diameter of the muff or sleeve, D = 2d + 13 mm
• Length of the muff or sleeve, L = 3.5 d
• where d = Diameter of the shaft.
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 Clamp or Compression Coupling
• It is also known as split muff coupling.
• In this case, the muff or sleeve is made into two halves and are
bolted together.
• Number of bolts may be two, four or six.
• Used for heavy duty and moderate speeds.
• Advantage of this coupling is that the position of the shafts need
not be changed for assembling or disassembling of the coupling.

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➢ Design of muff and key: • L = Length of muff.
• The muff and key are designed • We know that the force
in the similar way as discussed exerted by each bolt
in muff coupling
➢ Design of clamping bolts:
• Let T = Torque transmitted • Force exerted by the bolts on
by the shaft, each side of the shaft
• d = Diameter of shaft,
• db = Root or effective diameter
of bolt, • Let p be the pressure on the
• n = Number of bolts, shaft and the muff surface
• σt = Permissible tensile stress due to the force
for bolt material,
• μ = Coefficient of friction
between the muff and shaft,
• Frictional force between each shaft and muff,
• F = μ × pressure × area =

• Torque that can be transmitted by the coupling,

• From this equation (root diameter of bolt) db cab be evaluated.

Example. Design a clamp coupling to transmit 30 kW at 100 r.p.m. The allowable
shear stress for the shaft and key is 40 MPa and the number of bolts connecting the
two halves are six. The permissible tensile stress for the bolts is 70 MPa. The
coefficient of friction between the muff and the shaft surface may be taken as 0.3.
 Flange coupling
• A flange coupling usually applies to a coupling having two
separate cast iron flanges.
• Each flange is mounted on the shaft end and keyed to it.

• This helps to bring the shafts into

line and to maintain alignment. The
two flanges are coupled together by
means of bolts and nuts. The flange
coupling is adopted to heavy loads
and hence it is used on large
shafting.

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 Types of Flange Coupling
1. Unprotected type flange coupling.
Each shaft is keyed to the boss of a flange with a counter sunk key and the flanges are
coupled together by means of bolts. Generally, three, four or six bolts are used. The
keys are staggered at right angle along the circumference of the shafts in order to
divide the weakening effect caused by keyways.

If d is the diameter of the shaft

or inner diameter of the hub,
then Outside diameter of hub,
D =2 d
2. Protected type flange coupling. In a protected type flange coupling,
as shown in Fig., the protruding bolts and nuts are protected by flanges
on the two halves of the coupling, in order to avoid danger to the
workman.

• The thickness of the protective

circumferential flange (tp) is
taken as 0.25 d. The other
proportions of the coupling are
same as for unprotected type
flange coupling.
3. Marine type flange coupling. In a marine type flange coupling, the
flanges are forged integral with the shafts as shown in Fig. The flanges
are held together by means of tapered headless bolts, numbering from
four to twelve depending upon the diameter of shaft. The number of
bolts may be chosen from the following table.

The other proportions for the marine

type flange coupling are taken as
follows :
 Design of flange coupling

• d = Diameter of shaft or inner diameter of hub,

• D = Outer diameter of hub,
• d1 = Nominal or outside diameter of bolt,
• D1 = Diameter of bolt circle,
• n = Number of bolts,
• tf = Thickness of flange,
• τs, τb and τk = Allowable shear stress for shaft, bolt and key
material respectively
• τc = Allowable shear stress for the flange material i.e. cast iron,
• σcb, and σck = Allowable crushing stress for bolt and key
material respectively.
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1. Design for hub:
• The hub is designed by considering it as a hollow shaft

• The outer diameter of hub is usually taken as twice the diameter

of shaft.
• Therefore from the above relation, the induced shearing stress in
the hub may be checked.
• The length of hub (L) is taken as 1.5 d

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2. Design for key:

• The key is designed with usual proportions and then checked for
shearing and crushing stresses.

• Length and width of key are related with the diameter of shaft.

• From above equation shear stress and crushing stress of key can be
evaluated.

• The material of key is usually the same as that of shaft. The length of
key is taken equal to the length of hub. 60
3. Design for flange:
• The flange at the junction of the hub is under shear while
transmitting the torque.
• T = Circumference of hub × Thickness of flange × Shear stress
of flange × Radius of hub

• The thickness of flange is usually taken as half the diameter of

shaft.
• Therefore from the above relation, the induced shearing stress in
the flange may be checked.

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4. Design for bolts:
• The bolts are subjected to shear stress due to the torque
transmitted. The number of bolts (n)
• Depends upon the diameter of shaft and the pitch circle diameter
of bolts (D1) is taken as 3d
• Load on each bolt

∴ Total load on all the bolts

• Torque transmitted,

• From this equation, the diameter of bolt (d1) may be

obtained
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• Now the diameter of bolt may be checked in crushing.
• We know that area resisting crushing of all the bolts

• Crushing strength of all the bolts

∴ Torque,

• From this equation, the induced crushing stress in the bolts may
be checked

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 Flexible Coupling
A flexible coupling is used to join the abutting ends of shafts when they are not
in exact alignment. In the case of a direct coupled drive from a prime mover to
an electric generator, we should have four bearings at a comparatively close
distance. In such a case and in many others, as in a direct electric drive from an
electric motor to a machine tool, a flexible coupling is used so as to permit an
axial misalignment of the shaft without undue absorption of the power which
the shaft are transmitting. Following are the different types of flexible
couplings :
1. Bushed pin flexible coupling
2. 2. Oldham's coupling
3. 3. Universal coupling

(a) Bellows coupling

(b) Elastomeric coupling
(c) Flanged coupling
(d) Flexible coupling
 Bushed-pin Flexible Coupling
A bushed-pin flexible
coupling, as shown in Fig., is a
modification of the rigid type
of flange coupling. The
coupling bolts are known as
pins. The rubber or leather
bushes are used over the pins.
The two halves of the coupling
are dissimilar in construction.
A clearance of 5 mm is left
between the face of the two
halves of the coupling. There
is no rigid connection
between them and the drive
takes place through the
medium of the compressible
rubber or leather bushes.
In designing the bushed-pin flexible coupling, the proportions of the rigid type
flange coupling are modified. The main modification is to reduce the bearing
pressure on the rubber or leather bushes and it should not exceed 0.5
N/mm2. In order to keep the low bearing pressure, the pitch circle diameter
and the pin size is increased.
 Since the pin and the rubber or leather bush
is not rigidly held in the left hand flange,
therefore the tangential load (W) at the
enlarged portion will exert a bending action
on the pin as shown in Fig. The bush portion
of the pin acts as a cantilever beam of
length l. Assuming a uniform distribution of
the load W along the bush, the maximum
bending moment on the pin,
Since the pin is subjected to bending
and shear stresses, therefore the
design must be checked either for
the maximum principal stress or
maximum shear stress by the
following relations :

Note: After designing the pins

and rubber bush, the hub, key
and flange may be designed
in the similar way as
discussed for flange coupling.
Since the induced shear and crushing stress in the key are less than the permissible
stresses of 40 MPa and 80 MPa respectively, therefore the design for key is safe.
Oldham Coupling
Universal (or Hooke’s) Coupling
Maximum Speed

Minimum Speed