Unit 2 Design Of Shafts Keys and Couplings

Unit 2
Design of Shafts, Keys & Couplings
Prepared By
Prof. M.C. Shinde [9970160753]
Mech. Engg. Dept., JSCOE, Hadapsar

Unit 2
Design of Shafts ,Keys & Couplings
Session 2.1 Introduction to Transmission Shaft
Prepared By
Prof. M.C. Shinde

SPPU Syllabus Content
• Shaft design on the basis of strength, torsional rigidity and lateral rigidity,
A.S.M.E. code for shaft design. Transmission shaft:- Theoretical treatment
only. Design of keys and splines. Design of Flange Coupling and Flexible
Bushed Pin Coupling.

Transmission Shafts
• Rotating member, usually of circular cross section used to
transmit power or motion.
• supports transmission elements like gears, pulleys and sprockets.
• A transmission shaft supporting a gear in a speed reducer is
shown in Fig.
• The shaft is always stepped with maximum diameter in the
middle.
• portion and minimum diameter at the two ends, where bearings
are mounted.

• transmission shafts are made of medium carbon steels with a carbon content
from 0.15 to 0.40 per cent such as 30C8 or 40C8.
• Commercial shafts are made of low carbon steels.
• produced by hot-rolling and finished to size either by cold-drawing or by
turning and grinding.
• Steel bars up to 200 mm in diameter are commercially available.

Specific Categories Of Transmission Shafts
• Axle-supports rotating elements like wheels, hoisting drums. Used in
rear axle of a railway wagon, automobile rear axle.

• Spindle- A spindle is a short rotating shaft , used in all machine tools
such as the small drive shaft of a lathe or the spindle of a drilling
machine.

• Countershaft It is a secondary shaft, driven by the main shaft and
from which the power is supplied to a machine component. rotates
‘counter’ to the direction of the main shaft. used in multi-stage
gearboxes.

Stresses induced in the shaft
• Transmission shafts are subjected to axial tensile force, bending moment or
torsional moment or their combinations.
• tensile stress
• bending stresses
• torsional shear stress
When the shaft is subjected to combination of loads, the principal stress and
principal shear stress are obtained by constructing Mohr’s circle

Shaft Design On Strength Basis
1. Design of shaft by theories of failures
2. Design of shaft by A.S.M.E. Code

1.Shaft Design by theories of failures
i] Maximum Shear Stress Theory:- the shaft is subjected to bending and
torsional moments
These equations are used to determine shaft diameter on the basis of
maximum shear stress theory.
The maximum shear stress theory is applicable to ductile materials. Since the
shafts are made of ductile materials, it is more logical to apply this theory to
shaft design.

ii] Maximum Principal Stress Theory:- the shaft is subjected to bending and
torsional moments
These equations are used to determine shaft diameter on the basis of principal
stress theory
maximum principal stress theory gives good predictions for brittle materials.
Shafts are made of ductile material like steel and therefore, this theory is not
applicable to shaft design.

iii] Distortion Energy Theory:- the shaft is subjected to bending and torsional
moments
These equations are used to determine shaft diameter on the basis of
distortion energy theory.
The maximum shear stress theory is applicable to ductile materials. The design
of shaft by distortion energy theory is very accurate. Hence distortion energy
theory is most widely theory used for shaft design.

2. Shaft Design by A.S.M.E. CODE
A.S.M.E. code used for design of shaft is based on maximum shear stress
theory.
According to A.S.M.E. code the values of allowable shear stress are as follows;
[without keyway] take minimum of two values
According to A.S.M.E. code the values of allowable shear stress are as follows;
[with keyway] take minimum of two values
Note :- the keyway on the shaft reduces the strength of the shaft. This is due
to stress concentration near corners of keyway.

Shaft Design On Rigidity Basis
1. Design of shaft based on Torsional Rigidity
2. Design of shaft based on Lateral Rigidity

1. Design of shaft based on Torsional Rigidity
Torsional rigidity is defined as “ torque required to produce a torsional
deflection or an angle of twist of one radian in the shaft.”
This equation is used to design the shaft on the basis of torsional rigidity.
The permissible angle of twist for machine tool applications is 0.25° per metre
length. For line shafts, 3° per metre length is the limiting value. Modulus of
rigidity for steel is 79 300 N/mm2

2. Design of shaft based on Lateral Rigidity
Lateral rigidity of the shaft at given location is “the lateral force required to
produce a lateral deflection of one unit”.
This equation is used to design the shaft on the basis of lateral rigidity.
e.g. for cantilever beam maximum
deflection is given by,

Q.1 What are different materials used for manufacturing of shafts.
Q.2 What are stresses induced in the transmission shafts.
Q.3 Write down formula to design shaft using ASME Code.
Assignment 2.1

Unit 2
Session 2.2 Numerical on Design of Shafts
Prepared By
Prof. M.C. Shinde

Ex.1 A mild steel shaft transmits 20kW power at 200 r.p.m. If the
allowable shear stress for shaft material in 42 Mpa , determine the
diameter of shaft.

Ex. 2. A mild steel shaft transmits 20kW power at 200 r.p.m.it carries a central
load of 1000 N and is simply supported between bearings 2.5m apart. The
allowable shear stress for shaft material in 42 Mpa. If the shock & fatigue factors
for bending and torsion are 1.5 and 1.0, determine the diameter of shaft by
maximum shear stress theory.

A mild steel shaft transmits 40kW power at 400 r.p.m.it carries a
central load of 2000 N and is simply supported between bearings 5m
apart. The allowable shear stress for shaft material in 84 Mpa. If the
shock & fatigue factors for bending and torsion are 1.5 and 1.0,
determine the diameter of shaft by maximum shear stress theory
Assignment 2.2

Unit 2
Session 2.3 Numerical on Design of Shafts based on
Maximum Shear Stress Theory
Prepared By
Prof. M.C. Shinde

Ex. 3. A counter shaft with the bearings 800 mm apart receives 20kW power at 500 rpm
through a pulley 300mm in diameter and mounted at an overhung of 200 mm. A 360 mm
diameter pulley mounted midway between the bearings transmits torque to a shaft located
below it. Both the pulleys have vertical belt tensions and the coefficient of friction between the
bell and pulley is 0.3. if the required safety margin is 3. design the shaft using maximum shear
stress theory Use the following properties for shaft material.
1. Ultimate tensile strength=700 N/mm2,
2. Yield strength in tension=460 N/mm2
Important : Keep
Calculator with you
for solve problem]

Step I Permissible shear stress

Step III Bending Moment
Note:- Bending Moment at A & D is zero

Step III Bending Moment
Maximum Bending Moment is at C =

Step IV Maximum Shear Stress Theory
Note:- Assume Kb = Kt = 1

A counter shaft with the bearings 1000 mm apart receives 220kW
power at 1000 rpm through a pulley 600mm in diameter and
mounted at an overhung of 400 mm. A 720 mm diameter pulley
mounted midway between the bearings transmits torque to a shaft
located below it. Both the pulleys have vertical belt tensions and the
coefficient of friction between the bell and pulley is 0.6. if the required
safety margin is 6. design the shaft using maximum shear stress
theory .
Use the following properties for shaft material.
Ultimate tensile strength=800 N/mm2,
Yield strength in tension=360 N/mm2
Assignment 2.3

Unit 2
Session 2.4 Numerical on Design of Shafts based on
ASME Code
Prepared By
Prof. M.C. Shinde

Ex. 5. A transmission shaft is supporting a spur gear B and pulley D, as shown in fig. The shaft is
mounted on two bearings A & C. the diameter of pulley and gear are 500 mm and 350 mm
respect. A 20kW power is transmitted at 500 r.p.m. from the pulley D to the gear B. F1 & F2 are
the belt tensions in the tight and slack sides, while Ft & Fr are tangential and radial components
of the gear tooth forces. Assume F1=3F2 and Fr=Ft tan 20. the gear and pulley are keyed to the
shaft. If the material for the shaft is 50C4(Sut=700 N/mm2 and Syt= 460 N/mm2), determine
the shaft diameter using ASME code, if Kb=Kt=1.5

Given
To find the shaft diameter using ASME code

Step I Permissible shear stress [ASME]
Note:- Given Shaft with keyway effect

Vertical Support Reactions at A

Horizontal Support Reactions at A & C

Step III Vertical Bending Moment

Step III Horizontal Bending Moment
Note:- Bending Moment at A ,C & D is zero

Step III Resultant Bending Moment

Step IV A.S.M.E. Code
Note:- Kb =1.5, Kt = 1.5

Assignment 2.4
A transmission shaft is supporting a spur gear B and pulley D, as shown in fig. The shaft is
mounted on two bearings A & C. the diameter of pulley and gear are 700 mm and 350 mm
respect. A 40kW power is transmitted at 1000 r.p.m. from the pulley D to the gear B. F1 & F2
are the belt tensions in the tight and slack sides, while Ft & Fr are tangential and radial
components of the gear tooth forces. Assume F1=3F2 and Fr=Ft tan 20. the gear and pulley
are keyed to the shaft. If the material for the shaft is 50C4(Sut=500 N/mm2 and Syt= 260
N/mm2), determine the shaft diameter using ASME code, if Kb=Kt=1.0

Unit 2
Prepared By
Prof. M.C. Shinde

Ex. 6. The layout of an intermediate shaft of a gear box, supporting two spur
gears B & C ,is shown in fig. the shaft is mounted on two bearings A & D. the pitch
circle diameter of gears B & C are 900mm & 600mm respect. The material of the
shaft is steel FeE 580(Sut=770N/mm2 & Syt=580N/mm2). The factors Kb & Kt are
1.5 & 2.0 respectively . Determine the shaft diameter using the ASME code.
Assume that the gears are connected to the shaft by means of keys.

Vertical Support Reactions at A & D

Horizontal Support Reactions at A & D

Note:- Kb =1.5, Kt = 2.0

Assignment 2.5
The layout of an intermediate shaft of a gear box, supporting two spur gears B
& C ,is shown in fig. the shaft is mounted on two bearings A & D. the pitch circle
diameter of gears B & C are 900mm & 600mm respect. The material of the shaft
is steel FeE 580(Sut=770N/mm2 & Syt=580N/mm2). The factors Kb & Kt are 1.5
& 2.0 respectively . Determine the shaft diameter using the ASME code. Assume
that the gears are connected to the shaft by means of keys.

Unit 2
Prepared By
Prof. M.C. Shinde

Ex. 4. The shaft shown in fig. is driven by pulley D from an electric motor, while another belt
drive from pulley C is running a compressor. The belt tensions for pulley C are 1500 N & 600 N,
while the ratio of belt tensions for pulley D is 3.5. find the shaft diameter by A.S.M.E. code. Yield
strength and ultimate tensile strength for shaft material are 380 N/mm2 and 720 N/mm2
respectively. Take Kb=1.75 and Kt=1.25.

Step I Permissible shear stress [ASME]
Note:- Assume Shaft with keyway effect

Vertical Support Reactions at A & B

Horizontal Support Reactions at A & B

Step III Vertical Bending Moment
Note:- Bending Moment at A & B is zero

Note:- Kb =1.75, Kt = 1.25

Assignment 2.6
The shaft shown in fig. is driven by pulley D from an electric motor, while another belt drive
from pulley C is running a compressor. The belt tensions for pulley C are 3000 N & 1200 N,
while the ratio of belt tensions for pulley D is 2.5. find the shaft diameter by A.S.M.E. code.
Yield strength and ultimate tensile strength for shaft material are 420 N/mm2 and 720
N/mm2 respectively. Take Kb=1. 5 and Kt=1.05.

Unit 2
Session 2.7 Design of Splined Shafts & Design of Keys
Prepared By
Prof. M.C. Shinde

Splines
• Multiple keys which are made integral with the shaft.
• Prevent the relative rotary motion ,but permit the relative axial motion
between the shaft and hub.
• Splines transmit much higher torque than the single key between the shaft
and hub.
• Used in automobile gear boxes and machine tool gear boxes.
• Splines are designated as N*d*D;
N- no. Of splines
D- Major diameter of splined shaft(mm)
d- minor diameter of splined shaft(mm)

Design of Splines
• As there exists a relative axial motion between the splined shaft and the hub, the
bearing pressure between the external splines on shaft and the internal splines
on hub must be considered.

Bearing Pressure between Splines(Pb)

Direct Shear Stress in Splines

Ex. 9. A standard splined connection 8*52*60mm is used for the gear and shaft
assembly of gear box. A 20kW power at 300 r.p.m. is transmitted by the splines. If
the normal pressure on the splines is limited to 6.5 N/mm2 and the coefficient of
friction is 0.06. calculate:
i) The length of hub of the gear
ii) The force required to shift the gear
Given

Torque to be transmitted to splined shaft

Tangential force to shift the gear

Frictional force to shift the gear

Keys
• A machine element which is used to connect
the transmission shaft to rotating machine
elements like pulleys, gears, sprockets or
flywheels.
• A keyed joint consisting of shaft, hub and key
• The primary function of the key is to transmit
the torque from the shaft to the hub of the
mating element and vice versa
• The second function of the key is to prevent
relative rotational motion between the shaft
and the joined machine element like gear or
pulley.
• A recess or slot machined either on the shaft
or in the hub to accommodate the key is
called keyway

Sunk keys:-
• A sunk key is a key in which half the thickness of the key fits into the keyway on the
shaft and the remaining half in the keyway on the hub.
• keyways are required both on the shaft as well as the hub of the mating element.
• In sunk key, power is transmitted due to shear resistance of the key.
• sunk key is suitable for heavy duty application, since there is no possibility of the key
to slip around the shaft.
• A sunk key with rectangular cross-section is
called a flat key.
a) Rectangular key
b) Square key
c) Parallel key
d) Gib headed key
e) Feather key
f) Woodruff key

Stresses induced in the Sunk Keys

Crushing or compressive stress in key
Note:- compressive stress induced in a square key due to torque transmitted is
twice the shear stress.

Ex. 7. A square key is to be used to fix a gear to a 35 mm diameter shaft. The hub
length of the gear is 60mm. Both the shaft and key are to be made of the same
material, having an allowable shear stress of 55 N/mm2. if the torque to be
transmitted is 395 N-m. determine the minimum dimensions of key cross section.
Given
To find dimensions of key cross section.

Direct shear stress in the key

Ex. 8. A 16*10 mm2 cross section parallel key is to be used to transmit 60kW
power at 1440 rpm from a shaft of 45mm diameter. The key is made of plain
carbon steel with yield strength of 300 N/mm2. if the required safety margin is 3,
determine the key length.
Given
To find length of key cross section.

Torque to be transmitted to the key

Crushing stress in the key
Ans:. Select larger value of l=35.36

Assignment 2.7
1. Explain Splined shaft with neat sketch
2. What is key? Explain different types of keys
3. Write stresses induced in the keys with equations.
4. A standard splined connection 4*26*30mm is used for the gear and shaft
assembly of gear box. A 50kW power at 800 r.p.m. is transmitted by the
splines. If the normal pressure on the splines is limited to 8.5 N/mm2 and the
coefficient of friction is 0.06. calculate: a) The length of hub of the gear b)
The force required to shift the gear

Unit 2
Session 2.8 Introduction ,Classification of Couplings &
Design of muff coupling
Prepared By
Prof. M.C. Shinde

Couplings
• It is the mechanical element used to connect two shafts of a transmission system.
• The couplings are located as near as possible to bearing so as to minimize
deflection.
• mechanical device that permanently joins two rotating shafts to each other.

Purposes of Couplings
• It provides for the connection of shafts of two different units such as an electric
motor and machine.
• It makes the provision for disconnection of two units for repairs or alternations.
• It introduces mechanical flexibility between two connected units.
• It reduces the transmission of vibrations and shocks between two connected
units.

Rigid Couplings Flexible Couplings
Used to connect two shafts which are
perfectly aligned
Used to connect two shafts which are
having small misalignment.
Cannot tolerate any misalignment
between two shafts
Can tolerate small amount of lateral
or and angular misalignment
between two shafts
Cannot absorb shock & vibrations Can absorb shock & Vibrations
Less expensive More expensive
e.g. muff coupling, split muff, rigid
flange
e.g. bushed pin type, oldham
coupling and universal coupling

Couplings
Rigid Couplings
Muff/Sleeve
Coupling
Used for Line
Shaft
Split
Muff/Clamp
Coupling
Used for Line
Shaft
Rigid Flange
Coupling
Used for
connecting
electric motor
to pump
Flexible
Couplings
Bushed Pin
Type
Used for
connecting
diesel engine
to generator
Oldham
Coupling
Used for
connecting two
eccentric
shafts
Universal
Coupling
Used between
gear box and
differential of
automobile

Design of Muff (Sleeve) Couplings
• It is the simplest type of rigid coupling used to connect two shafts rigidly.
• Design of Muff coupling involve following steps
1. Design of Shaft
2. Dimensions of sleeve as standard proportions
3. Design of sleeve
4. Design of key

Step 1: Design of Shaft
• Same as discussed in earlier session 2.1 & 2.2

Step 2: Dimensions of sleeve as standard proportions
• Outside diameter of sleeve D=2d
• Length of Sleeve L=3.5d
Where , d=diameter of shaft, mm

Step 3: Design of Sleeve
• Torsional Shear Stress induced in Sleeve is given by
Where ,k=d/D
For the safety of sleeve against shear failure ,the torsional shear stress induced in a
sleeve must be less than allowable shear stress for sleeve i.e.

Step 4: Design of Key
• The key dimensions are calculated as discussed in design of key session
• For design purpose length of key is taken as l=L/2

Assignment 2.8
1. Give Classification of Couplings
2. Explain steps for design of muff couplings.
3. Differentiate between Rigid and Flexible Couplings

Unit 2
Session 2.9 Design of Rigid Flange Coupling &
Numericals
Prepared By
Prof. M.C. Shinde

Design of Rigid Flange Couplings
A rigid flange coupling consist of two flanges one keyed to the driver shaft and
other to driven shaft.
Types of Rigid Flange Coupling
1.Unprotected type rigid flange coupling
2. Protected type rigid flange coupling
3. Marine type rigid flange coupling

Ex. A protected type rigid flange coupling is used to transmit 25kW power at 500
rpm from an engine to a machine. Design a coupling for an overload capacity of
25% .Assume following permissible stresses for components of coupling. Assume
number of bolts as 6.

d-diameter of shaft, mm
D-Outer diameter of hub ,mm
D1- diameter of bolt circle ,mm
D2- outer diameter of flange, mm
D3- diameter of flange recess, mm
l-length of hub, mm
tf- thickness of flange, mm
tp- thickness of protective flange, mm
db- nominal diameter of bolt, mm
N- no. of bolts

Step 3. Design of key
Let us select square key.

Considering crushing of key.

Considering shearing of key.

Selecting largest of three values of length(l)

Step 4. Design of hub
Length of hub , l=79 mm
Outer diameter of hub, D=2d= 2*45=90 mm
Shear stress induced in hub given by
Hence, hub is safe against shear failure

Step 5. Design of flange
Thickness of flange,
Thickness of protective flange,
Diameter of bolt circle,
Outer diameter of flange,
Diameter of flange recess,

Step 5. Design of flange
Direct shear stress induced in a flange at junction with hub is
Hence flange is safe against shear failure

Step 6. Design of bolts
a. Considering Shearing of bolt

Step 6. Design of bolts
b. Considering Crushing of bolt

Assignment 2.9
1. Design a flange coupling for steel shaft transmitting 20kW power at 250
r.p.m. the maximum torque is 30% greater than full load torque. The
material properties are as follow:
• Allowable shear stress for shaft and key =40MPa
• Allowable shear stress for bolts =30MPa
• Allowable crushing stress for shaft & key =80MPa
• Allowable shear stress for flange =14MPa
• Allowable compressive stress for bolts =60MPa
• Number of bolts =4

Ex.1 A transmission shaft supporting a helical gear B and an overhung bevel gear D is shown in Fig. The shaft is
mounted on two bearings, A and C. The pitch circle diameter of the helical gear is 450 mm and the diameter of the
bevel gear at the forces is 450 mm. Power is transmitted from the helical gear to the bevel gear. The gears are
keyed to the shaft. The material of the shaft is steel 45C8 (Sut = 600 and Syt = 380 N/ mm2). The factors kb and kt
of ASME code are 2.0 and 1.5 respectively. Determine the shaft diameter using the ASME code.

Ex.2. The armature shaft of a 40 kW, 720 rpm electric motor, mounted on two bearings A and B, is shown in Fig.
The total magnetic pull on the armature is 7 kN and it can be assumed to be uniformly distributed over a length of
700 mm midway between the bearings. The shaft is made of steel with an ultimate tensile strength of 770 N/mm2
and yield strength of 580 N/mm2. Determine the shaft diameter using the ASME code if, kb = 1.5 and kt = 1.0
Assume that the pulley is keyed to the shaft.

Ex.3. It is required to design a square key for fixing a gear on a shaft of 25 mm diameter. The
shaft is transmitting 15 kW power at 720 rpm to the gear. The key is made of steel 50C4 (Syt =
460 N/mm2) and the factor of safety is 3. For key material, the yield strength in compression
can be assumed to be equal to the yield strength in tension. Determine the dimensions of the
key.
Ex.4. The standard cross-section for a flat key, which is fitted on a 50 mm diameter shaft, is 16 *
10 mm. The key is transmitting 475 N-m torque from the shaft to the hub. The key is made of
commercial steel (Syt = Syc = 230 N/mm2).Determine the length of the key, if the factor of
safety is 3.

Unit 2 Design Of Shafts Keys and Couplings

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