chapter 5 - shaft design

8/13/2019 Chapter 5 - Shaft Design

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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.

2Department of Material and Engineering Design,Faculty of Mechanical and Manufacturing Engineering,

Universi ty of Tun Hussein Onn Malaysia (UTHM) Johor.


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5.1 - Introduction

-.

5.3 - Shaft Layout

.

5.5 - Limits and Fits




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BDA 3083 Mechanical Engineering Design I

CHAPTER 5 Shaft Design

.

~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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.

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



- 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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.




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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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.




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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.



CHAPTER 5 Sh ft D i


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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.



CHAPTER 5 Sh ft D i


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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

=



BDA 3083 M h i l E i i D i I CHAPTER 5 Shaft Design


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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



BDA 3083 M h i l E i i D i I CHAPTER 5 Shaft Design


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.





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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



.



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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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g

.

-

Fatigue failure curve on the ASME Ellipt ic diagram

2222

3 3434

161

+

+

+

= mfsmfafsaf

S

TK

S

MK

S

TK

S

MK

dn


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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.

-

Fatigue failure curve on the Soderberg diagram

[ ] [ ]

+++= 2/1222/122

3 )(3)(4

1)(3)(4

1161mfsmf

yt

afsaf

e

TKMKS

TKMKSdn


[ ] [ ] 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



.



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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





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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





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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





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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





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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,



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



min F . . .

chapter 5 - shaft design

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