1

Shaft Design

Section VI

2

Shaft? Shaft Design ASME Shaft Equations Design of Shaft for Torsional

Rigidity Standard Sizes of Shafts Bending and Torsional Moments

Talking Points

3

Rotating machine element that transmits power.

Shaft?

Shafts are usually circular in cross-section, and may be either hollow or solid.

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Shaft Design Consists of the determination of

the correct shaft diameter to ensure satisfactory strength and rigidity when the shaft is transmitting power under various operating and loading conditions.

Design of shafts for ductile materials, based on strength, is controlled by the maximum-shear stress theory; while shafts of brittle materials would be designed on the basis of the maximum-normal stress theory. Shafts are usually

subjected to torsion, bending, and axial loads.

1) For axial loads: The tensile or compressive stress is:

shafts hollowFor 4

shafts solidFor 4

22

2

io

aa

aa

dd

Fd

F

a

shafts hollowFor 32

shafts solidFor 32

44

3

io

obb

bbb

dd

dMd

M

I

rM

2) For bending loads: The bending

stress (tension or compression)

is:

b3) For torsional loads: The torsional stress

is:

shafts hollowFor 16

shafts solidFor 16

44

3

io

oxy

xy

dd

Tdd

T

J

Tr

xy

5

Shaft Design – Cont.

6

Shaft Design – Cont.

7

ASME Shaft Equations The ASME code equation for hollow shaft combines torsion, bending,

and axial loads by applying the maximum-shear equation modified by introducing shock, fatigue, and column factor as follows:

2

22

4

3

8

1

1

16tt

oabb

so Mk

KdFMk

Kd

For solid shaft having little or no axial loading, the equation is:

223 16ttbb

so MkMkd

Where:

moment torsional toappliedfactor fatigue andshock combined

moment bending toappliedfactor fatigue andshock combined

diameter, insideshaft

diameter, outsideshaft

t

b

i

o

oi

k

k

md

md

ddK

keyway shaft withfor MPa) (40 psi 6000

keywayout shaft withfor MPa) (55 psi 8000 allowable

:shafting steel commercialFor

s

115for

115for 0044.0.1

1

:by computed bemay load, ecompressiv aFor

load. tensileafor unity

:)(factor action -Column

2

kLkLnE

kLkL

y

Where:

2mN n,compressioin stress yield

gyration, of radius

bearings. as ,restrainedpartly ends

for 1.6 and ends fixedfor 2.25or ends hingedfor 1

y

AImk

n

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ASME Shaft Equations – Cont.

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Design of Shaft for Torsional Rigidity

It is based on the permissible angle of twist. The amount of twist permissible depends on the particular application, and varies about 0.3 degree/m for machine tool shafts to about 3.0 degree/m for line shafting.

shaft hollowFor 584

shaft solidFor 584

44

4

io

t

t

ddG

LMGd

LM

Where:

2N ,elasticity of modulus Torsional

shaft, theoflength

deg twist,of angle

mG

mL

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Standard Sizes of Shafts

These sizes vary according to material specifications and supplier. Typical sizes for solid shafts are:

Up to 25 mm in 0.5 mm increments 25 to 50 mm in 1.0 mm increments 50 to 100 mm in 2.0 mm

increments 100 to 200 mm in 5 mm

increments

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Bending and Torsional Moment

These are the main factors influencing shaft design. One of the first steps in shaft design is to draw the bending moment diagram for the loaded shaft or the combined bending moment diagram if the loads acting on the shaft are in more than one axial plane. From the bending moment diagram, the points of critical bending stress can be determined. The torsional moment acting on the shaft can be determined from:

N.m min

9550

min2

601000

601000

2

1000 rev

kW

rev

kWM

NMMPower t

tt

2) For gear drive: The torque is found by:

N.m 21 pt RTTM

1) For belt drive: The torque is found by:

Where:

m pulley, of radius

N pulley,on belt of side lose

N pulley,on belt of sidetight

2

1

pR

T

T

tan

N.m

tr

gtt

FF

RFM

Where:

degrees angle,pitch gear

m gear, of radiuspitch

N force, radial

N radius,pitch at the force tangential

g

r

t

R

F

F