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De artment of Material and En ineerin Desi n,
Faculty of Mechanical and Manufacturing Engineering,University of Tun Hussein Onn Malaysia (UTHM) Johor.
BDA 3083 Notes Mechanical Engineering Design I
Week 6
Chapter 5
a es gn
Prepared by: Mohd Azwir Bin Azlan
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BDA 3083 Mechanical Engineering Design I CHAPTER 5 Shaft Design
,
appreciate the knowledge to:
select suitable material for shaft design
perform load, stress, and power calculations analytically as applied to.
design a shaft with some consideration on static and fatigue failure.
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BDA 3083 Mechanical Engineering Design I CHAPTER 5 Shaft Design
5.1 - Introduction
-.
5.3 - Shaft Layout
.
5.5 - Limits and Fits
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~a rotating member,
usually of circular crosssec on
What it is used for?!
~to transmit poweror
motion
~
rotation, or oscillation, of
elements such as gears,
, ,
and the like, and controls
the geometry of their
motion.
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BDA 3083 Mechanical Engineering Design I
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What is axle?!
An axle is a nonrotating member
that carries no torque and
What it is used for?!
is used to support rotating
wheels, pulleys and etc.
Train wheels are affixed to a straight
axle, such that both wheels rotate in
unison.
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What is spindle?!
A spindle is a short shaft. Terms
such as lineshaft, headshaft,
stub shaft, transmission shaft,
countershaft, and flexible shaftare names associated with
special usage.
Ta ered roller bearin s used in a
mowing-machine spindle. This design
represents good practice for situations
where one or more torque-transfer
elements must be mounted outboard.
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Many shafts are made from low carbon, cold-drawn or hot-rolled steel, such as ANSI
1020-1050 steels.
A good practice is to start with an inexpensive, low or medium carbon steel for the first.
If strength considerations turn out to dominate over deflection, then a higher strength
material should be tried, allowing the shaft sizes to be reduced until excess deflection
ecomes an ssue.
Shafts usually dont need to be surface hardened unless they serve as the actual journal
of a bearing surface. Typical material choices for surface hardening include carburizing
grades of ANSI 1020, 4320, 4820, and 8620.
Cold drawn steel is usually used for diameters under about 3 inches. The nominal
diameter of the bar can be left unmachined in areas that do not re uire fittin of
components.
Hot rolled steel should be machined all over.
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For large shafts requiring much material removal, the residual stresses may tend to
cause warping (bend out of shape - distortion and twisting).
If concentricity is important, it may be necessary to rough machine, then heat treat to,
dimensions.
In approaching material selection, the amount to be produced is a salient factor.
For low production - turning is the suitable process.
For High production - conservative shaping method (hot or cold forming, casting), and
.
the production quantity is high, and the gears are to be integrally cast with the shaft.
Stainless steel may be appropriate for some environments e.g. Involved in foodprocess ng.
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clamp
collar
snap ring
key
hubhub
stepshaft
bearing bearing
step stepstep
axialclearance
pressfi t
pressfi t
gearsprocket
frame framesheave
ssem y sassem y progress ve y sma er ameter towar t e en s
Axial clearance to allow machinery vibration
Keys/pins/rings to secure rotating elements ( gear, pulley, etc)
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Significant detail is required
to completely specify the
fabricate a shaft.
The geometry of a shaft is
generally that of a steppedcylinder.
The use of shaft shoulders is
an excellent means of axially
locating the shaft elementsan o carry any rus
loads.
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Common shaft
oa ng mec an sm:
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Splines
Setscrews
Press or shrink fits Tapered fits
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Round pins Taper pins Split tubular
spr ng p ns
- Pins are used for axial positioning and for the transfer of torque or thrust or both.- Some pins should not be used to transmit very much torque
- Weakness will generate stress concentration to the shaft
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.
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- Used when large amounts of torque are to be transferred
15Department of Material and Engineering Design,Faculty of Mechanical and Manufacturing Engineering,
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- tress concentrat on s genera y qu te mo erate
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Sleeve
Ring and groove
Split hub or tapered two-pieces hub
Collar and screw Pins
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BDA 3083 Mechanical Engineering Design I
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is a tube or enclosure used to couple two mechanical components together, oro re a n wo componen s oge er; s perm s wo equa y-s ze appen ages
to be connected together via insertion and fixing within the construction.
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means of axially locating the shaft
elements and to carry any thrust loads.
Example:
(a) Choose a shaft configuration to support and locate the two gears and two bearings.
b Solution uses an inte ral inion three shaft shoulders ke and ke wa and sleeve.
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Most o ular used because ive an economical
solution to some problem.
Bowed retaining rings provide restoring forces to
the com onents bein held.
Flat retaining rings allow small amounts of axialmotion of the held component.
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is a type of screw generally used
to secure an object within anotherobject. The set screw passes
through a threaded hole in the
outer object and is tightened
aga ns e nner o ec o preven
it from moving relative to the outerobject.
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is a simple, short ring fastened over a rod or shaft
found in many power transmission applications -
most notably motors and gearboxes.
used as mechanical stops, locating components,
and bearing faces. The simple design lends itself to
eas installation - no shaft dama e.
Since the screws compress the collar, a uniform
distribution of force is imposed on the shaft, leadingto a holding power that is nearly twice that of set
screw collars.
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It is not necessary to evaluate the stresses in a shaft at every point; a few.
Critical locations will usually be on the outer surface, at axial locations where the
bending moment is large, where the torque is present, and where stress
concentrations exist.
Most shafts will transmit torque through a portion of the shaft. Typically the torque
comes into the shaft at one ear and leaves the shaft at another ear. The tor ue
is often relatively constant at steady state operation.
The bending moments on a shaft can be determined by shear and bending
.
introduce forces in two planes, the shear and bending moment diagrams will
generally be needed in two planes.
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Resultant moments are obtained by summing moments as vectors at points of.
shaft, stresses near the bearing are often not critical since the bending moment is
small.
Axial stresses on shafts due to the axial components transmitted through helical
gears or tapered roller bearings will almost always be negligibly small compared
to the bending moment stress. They are often also constant, so they contribute
e o a gue.
Consequently, it is usually acceptable to neglect the axial stresses induced by the
ears and bearin s when bendin is resent in a shaft. If an axial load is a liedto the shaft in some other way, it is not safe to assume it is negligible without
checking magnitudes.
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The fluctuating stresses due to bending and torsion are given by: -
;;cM
K afa = cM
K mfm = cT
K afsa = cT
K mfsm =
Under many condi tions, the axial components F is either zero or so small that it can be neglected.
ssum ng a so s a w roun cross sec on, appropr a e geome ry erms
can be introduced for c, I, and J resulting in
;3
32
dK afa
=
3
32
dK mfm
= ;3
16
d
TK afsa
=
3
16
d
TK mfsm
=
26Department of Material and Engineering Design,Faculty of Mechanical and Manufacturing Engineering,
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Combining bending and shear stresses accordance to the von Misses stress
2/122
-
33
2122
3)3(' +
=+=
dd
asa
aaa
2/122
2/122 1632'
TKMKmfsmf
33
ddmmm
27Department of Material and Engineering Design,Faculty of Mechanical and Manufacturing Engineering,
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-
Fatigue failure curve on the modified Goodman diagram
[ ] [ ]
+++= 2/1222/122
3 )(3)(4
1)(3)(4
1161mfsmf
ut
afsaf
e
TKMKS
TKMKSdn
Equation for the minimum diameter
[ ] [ ]3/1
2/1222/122 )(3)(41
)(3)(4116
+++= mfsmfut
afsaf
e
TKMK
S
TKMK
S
nd
This criteria does not guard against yielding, so required separate check for possibility of static
29Department of Material and Engineering Design,Faculty of Mechanical and Manufacturing Engineering,
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.
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-
Fatigue failure curve on the Gerber diagram where
++=
2/12
3
211
81 e
AS
BS
Sd
A
n
22 )(3)(4 afsaf TKMKA +=
22 )(3)(4 mfsmf TKMKB +=
3/12/1
2
28
BSnA
This criteria does not guard against
++=ute ASS
,
possibility of static failure (yield occur)
in the first load cycle.
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BDA 3083 Mechanical Engineering Design I
g
.
-
Fatigue failure curve on the ASME Ellipt ic diagram
2222
3 3434
161
+
+
+
= mfsmfafsaf
S
TK
S
MK
S
TK
S
MK
dn
Equation for the minimum diameter
2/12222
343416
+
+
+
= mfsmfafsaf
S
TK
S
MK
S
TK
S
MKnd
This criteria takes yielding into account, but is not entirely conservative, so also required
yyee
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.
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-
Fatigue failure curve on the Soderberg diagram
[ ] [ ]
+++= 2/1222/122
3 )(3)(4
1)(3)(4
1161mfsmf
yt
afsaf
e
TKMKS
TKMKSdn
Equation for the minimum diameter
[ ] [ ] 2/1222/122 )(3)(41)(3)(4116
+++= mfsmfyt
afsaf
e
TKMK
S
TKMK
S
nd
This criteria inherently guards against yielding, so it is not required to check for possibility of
32Department of Material and Engineering Design,Faculty of Mechanical and Manufacturing Engineering,
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.
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g g g
.
max'
y
yn =Factor of safety
2/122 '''
where
max ma=
2/122
)(16)(32
+
+
TTKMMK mafsmaf33
dd
33Department of Material and Engineering Design,Faculty of Mechanical and Manufacturing Engineering,
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g g g
.
For a rotating shaft with constant bending and torsion, the bending stress is
completely reversed and the torsion is steady. Therefore
0=m 0=a
These will simply drops out some of previously terms.
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.
-
,
D is 42 mm, and the fillet radius is 2.8 mm. The bending moment is 142.4 Nm
and the steady torsion moment is 124.3 Nm. The heat-treated steel shaft has an
= = .
reliability goal is 0.99.
a Determine the fati ue factor of safet of the desi n usin each of the
fatigue failure criteria described in this section.
(b) Determine the yielding factor of safety.
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.
-
4.142=aM 0=mMNm Nm
0=aT 3.124=mT NmNm
a) Determine the fatigue factor of safety of the design:
8.2r
50.128
==d Kt = 1.68 (figure A-15-9)
Kts = 1.42 (figure A-15-8)
r = 2.8 . -
Sut = 0.735 GPaqs = 0.92 (figure 4-2)
.28
==d 58.1)168.1(85.01 =+=fK
39.1)142.1(92.01 =+=fsK
36Department of Material and Engineering Design,Faculty of Mechanical and Manufacturing Engineering,
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.
5.367)735(5.0' ==eS
2055.367814.087.0787.0 ==S
MPa 787.0)735(51.4 . == a
87.028
107.0
==
bkMPae
Applying Eq. DE-Goodman criteria gives
.
0.1=== fdc kkk
[ ] [ ] += 2/122/12
3 )(3
1
)(4
1161mfs
ut
af
eTKSMKSdn 814.0
=ek
[ ] [ ]
+= 6
2
6
2
3 10735
))3.124(39.1(3
10205
))4.142(58.1(4
)028.0(
16
xx
604.0)10407.010195.2(232004 66 =+= xx
65.1=n
37Department of Material and Engineering Design,Faculty of Mechanical and Manufacturing Engineering,
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.
Similarly, apply same technique for other failure criteria,
87.1=n DE-Gerber
. -
56.1=n DE-Soderberg
22
b) Determine the Yield factor of safety :
4.125)028.0(
..
)028.0(
..'
33max =
+
=
58.44.125
574
'max===
y
y
Sn
38Department of Material and Engineering Design,Faculty of Mechanical and Manufacturing Engineering,
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.
Interference Fits.
An interference fit is the condition that exist when,earance s.
No interference occur.
dimensions, mating parts
must be pressed together.
Transition Fits.
The fit can have either
clearance or interference.
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.
Definitions applied to a cylindrical fit.Capital letters always refer to the hole;
lowercase letters are used for the shaft.
D = basic size of hole
d = basic size of shaft
u = upper deviation
l = lower deviation
= fundamental deviation
D = tolerance grade for hole
d = tolerance grade for shaft
.
Thus, for the hole,
Dmax = D + D Dmin = D
, , , , ,
dmax = d + F dmin = d + F d
For shafts with interference fits k, n, p, s, and u,
40Department of Material and Engineering Design,Faculty of Mechanical and Manufacturing Engineering,
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min F max F
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.
Table 51
Descriptions of Preferred
Fits Using the Basic
Hole System
and Fits, ANSI B4.2-1978.
See also BS 4500.
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.
Table A11
A Selection of International Tolerance GradesMetric Series
(Size Ranges Are forOver the Lower Limit and Including the
Upper Limit.All Values Are in Millimeters)
, . - . .
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.
Table A12
Fundamental
Deviations for
ShaftsMetric Series
(Size Ranges Are forOver the Lower Limit
and Including the
Upper Limit.
All Values Are in
Millimeters)
Source: Preferred Metric Limits
and Fits ,ANSI B4.2-1978. See
also BSI 4500.
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.
Example 5-2 :
Find the shaft and hole dimensions for a loose running fit with a 34-mm basic size.
-
From Table 51, the ISO symbol is 34H11/c11. From Table A11, we find that tolerance
. . . .
Using Eq. (Dmax = D + D) for the hole, we get
max = . = . mm min = = . mm
The shaft is designated as a 34c11 shaft. From Table A12, the fundamental deviation is F= . mm. s ng q. or s a w c earance s , we ge e s a mens ons
dmax = d + F = 34 + (0.120) = 33.880 mm
44Department of Material and Engineering Design,Faculty of Mechanical and Manufacturing Engineering,
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min F . . .