Shafts and Axels

Shaft is a rotating member and it provides axis of rotation for gears,

pulley, flywheels, cranks, sprockets.

Axels are non rotating member, carries no torque and it is used to support

rotating wheels.

Design should consider the following

• Deflection,Bending deflection, Torsional deflection. Slope at the bearings and shaft support elements, shear deflection due to transverse loading

• Stress and Strength Static and FatigueStatic StrengthFatigue StrengthReliability

Example of shafts

Connections to the shaft

For Large Torque

Method of connections, cont.

Geometric Constrains• Deflections and slope

)263()([6

1

)263(6

)(6

2222

222222

llaaMlbbFEIl

llaaxEIl

xMlbx

EIl

bFy

iiiiiiA

iii

iii

AB

Use Method of superposition for complicated loadings

Torsional displacement ii

iii JG

lT

Strength Constraints

• Static Failure either based on Maximum shear theory or DET(Mises) Theory

• MSS

])(1[

16

])(1[

4

])(1[

32

16

432

43

2243

3

23

D

dD

TD

dD

P

D

dD

MD

T

D

P

D

M

x

x

MSS, cont.

2

122

3

3

23

2

122

3

2

122

3

])8()8[(4

16

432

]48)8[(4

])8()8[(4

TKPDKMKDn

SD

TK

D

PK

D

MK

TPDMDn

S

TPDMDn

S

tstatby

ts

tatbx

y

y

DET theory , Static

2

122

3])(48)8[(

4KtsTPDMK

Dn

Stb

y

Fatigue design of shafts

5.023

23

5.022_

5.023

23

5.022_

minmax

minmax

minmax

minmax

])16(3)

32[()3(

])16(3)

32[()3(

2

2

2

2

D

Tk

D

Mk

D

Tk

D

Mk

TTT

TTT

MMM

MMM

mfsmfmmm

afsafaaa

a

m

a

m

Fatigue, cont.

5.0225.0223

__

])(3)(41

])(3)(4[1161

1

mfsmfut

afsafe

ut

m

e

a

TkMkS

TkMkSDn

nSS

Natural frequency of the shaft

2ii

ii

W

Wg

W individual attachment weigh

deflection of the shaft at the attachment i