Design of Shaft
A shaft is a rotating member usually of
circular cross section(solid or hollow),
which is used to transmit power and
rotational motion.
Axles are non rotating member and
that’s the type we will analyze.
Shafts do not always rotate themselves,
as in the case of an axle – but axles
support rotating members.
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Elements such as gears, pulleys
(sheaves), flywheels, clutches ,and
sprockets are mounted on the shaft and
are used to transmit power from the driving
device(motor or engine) through a machine.
T h e r o t a t i o n a l f o r c e ( t o r q u e ) i s
transmitted to these elements on the shaft
by press fit, keys, dowel, pins and splines.
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The shaft rotates on rolling contact or bush
bearings.
Various types of retaining rings, thrust
bearings, grooves and steps in the shaft are
used to take up axial loads and locate the
rotating elements.
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Elements Attached to a
Shaft
Shoulders provide axial positioning location, &
allow for larger center shaft diameter – where
bending stress is highest.
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Three Common Shafts
Commercial
Stepped
crank
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Automobile manual transmission
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Worm gear box
Reduces speed, increases torque output.
Power = F.v (force x velocity)
For rotational power
Power P = Torque x angular velocity
P = T.w (w in rad/sec)
w = 2 p n/60 (n is rpm)
T= 63,025HP/n (in-lb)
T= 9,550,000kW/n (N
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Other shaft examples
Bevel gear box: changes Lawn mower drive:
rotational axis Belt pulley
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Shaft Loads
• Torsion due to transmitted torque
• Bending from transverse loads (gears, sprockets, pulleys/sheaves)
• A pulley and a sheave are essentially the same thing Steady or Fluctuating
•Steady transverse-bending load fully reversing bending stress (fatigue failure)
Attachments and Stress Concentrations
Steps and shoulders are used to locate attachment (gears, sheaves, sprockets)
Keys, snap rings, cross pins (shear pins), tapered pins
Use generous radii to reduce stress concentrations
Clamp collars
Split collar
Press fits and shrink fits
Bearings may be located by the use of snap rings, but only one bearing is fixed
Issues - axial location, disassembly, and element phasing (e.g., alignment of gear
teeth for timing)
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Loads on shaft:
Shaft loaded in only torsion: torsion may have a steady (Tav)
and a cyclic (Tr) component.
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τ r , J
Kt : fatigue stress concentration factor in torsion
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Shaft loaded in only bending: bending may have a
steady (Mav) and a cyclic (Mr) component.
σ c
Km : fatigue stress concentration factor in bending
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Shaft loaded by steady load , torsion and
bending
N=s.f
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Which called a static design
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Shaft loaded by steady twisting moment and
fluctuating bending moment
Se : endurance stress
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Common Shaft Materials
•Typically shafts are machined or cold-drawn from
plain hot-rolled carbon steel. Applications
requiring greater strength often specify alloy steels
(ST50).
•Some corrosion applications call for brass,
stainless, Ti, or others.
•Aluminum is not commonly used (low modulus,
low surface hardness).
From table ( )
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D : pitch diameter
Ф : pressure angle =20 : 25 (
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Loads on shaft due to gears
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•From power and rpm find the torque (T), which
gives rise to shear stress.
•From Torque (T) and diameter (d), find Ft = 2T/d.
From Ft and pressure angles of gears you can find Fr
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•Fr and Ft are orthogonal to each other and are
both transverse forces to the shaft axis, which will
give rise to normal bending stress in the shaft.
•When shaft rotates, bending stress changes
from tensile to compressive and then
compressive to tensile, ie, completely reversing
state of stress.
•Fa will give rise to normal axial stress in the
shaft
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Flat Belt Drive Example
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T : torque
HP: horse power
ω : Angular speed
n : rotational speed (r.p.m)
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Loads on shaft due to pulleys and fly-
wheels
Pulley torque (T) = Difference in belt
tensions in the tight (t1) and slack (t2)
sides of a pulley times the radius (r), ie
T = (t1-t2)xr
Left pulley torque
T1 = (7200-2700)x380=1,710,000 N-mm
Right pulley has exactly equal and
opposite torque:
T2 = (6750-2250)x380=1,710,000 N-mm
FV2
Bending forces:
Left pulley: FV1=900N; FH1=7200+2700 =
9900N
Right pulley: FV2=900+6750+2250=9900N;
FH2=0
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Bending moment and torque diagrams for the pulley flywheel system
From Horizontal forces (FH) and vertical forces (Fv),
Bending moments MH & MV are drawn seperately.
Then the resultant moments at various points on the
shaft can be found from
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Example 1
Find required dia. of the shaft shown in fig
below
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T = 1000 N.m =100 Kp.m
Material Table ( )
Sy = 32 Kp/mm2 Se = 25 Kp/mm2 Sut = 45
Kp/mm2
Safety factor N = 2.1
From Table ( )
Km = 2 Kt = 1.6
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From Table ( )
Take d = 70 mm
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• A key can be def in ed as a machine
element which is used to connect the
transmission shaft to rotating machine
elements like pulleys, gears, sprockets
or flywheels.
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KEY-JOINT
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Various types of keys for transmitting torque
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Various types of collar pins
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Splines in hubs and shafts allow axial motion
and transmits torque
All keys, pins and splines give rise to
stress
concentration in the hub and shaft
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D i s t r i b u t i o n o f f o r c e i s q u i t e
complicated. The common
assumption is that the torque T is
carried by a tangential force F acting
on radius r:
T = Fr
F r o m T = F r, b o t h s h e a r a n d
compressive bearing stresses may be
calculated from the width and length
of the key.
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The safety factor ranges from n = 2
(ordinary service) to n = 4.5 (shock).
The stress concentration factor in the
keyway ranges from 2 to 4.
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Example
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Design of key at point C
1-Select the type of key (Flat parallel side key)
2-From Table ( ) , and according to the shaft
diameter
d b(w) h t1 t2 L(range)
70 20 12 7.5 4.9 56:220
3-Select the material of key ( ST60)
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s.f = 2.9
4-Calculate the key length L
a-
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b-
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L = 178.57 mm
From a and b take L larger
From table ( )
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Bearing
Design the bearing at A
From Table ( ) at the shaft diameter d=70 mm
d D t L
70 80 0.5 160
Check according to:
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From table ( ) at V =ω*r
Safe
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Example (1)
A shaft supported at the ends in ball bearings
carries a straight tooth spur gear at its mid span
and is it to transmit 5.5 hp at 300 r.p.m. The pitch
circle diameter of the gear is 150 mm.The
distances between the centre line of bearings and
gear are 100 mm each.Determine the diameter of
the shaft . Show in a sketch how the gear will be
mounted on the shaft. Also indicated the ends
where the bearings will be mounted. The pressure
angle of the gear may be taken as 20°.
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Power=5.5 hp , N = 300 r.p.m , D = 150 mm
•The torque transmitted by the shaft:
•The tangential force on the gear:
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Material Table ( )
Sy = 32 Kp/mm2 Se = 25 Kp/mm2 Sut = 45
Kp/mm2
Safety factor N = 2.1
From Table ( )
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From table ( ),
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From table ( ),
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