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force

n

pulley

piessllres

and

coffesponding

high

surface riction

i,vhjch

equilibrates

the

torque

-

provided

dghterirg

is

sufficient.

Torque

may be

transferred

also

at

any point

along

a shaft

by

u

gear.,belt

:,?:iflil,

pulley,

or chain

sprocketor

example,

mounted

shait

+F

on

the

shaft as described

above,

These

common

.&. f ' .

g

elements

pply

orces

offset r-om

he

shaft

axis,

r=F' andtherefore sefui orqueT mustbe

accompanied

y a conesponding

adial

oad

with

consequential

ending

this

s

why

the

generalised

haftdesign

model

- ,ffi.incorporate

both

orque

and

bending

moment

oad

components.

A

spur

gearand

a belt pulley

are

sketched,

ach

ubjected

o loading

tangential

o

its

effectiae

r

pitch

cylinder

of diameter

D. The

oad

on

the

spur

geat arises rom

inter-tooth

contact

..

..ipursearptch

with ts matingger andcompriseswo

',,.i;i4l^ds"

components

theuseful

angential

omponent

ffilffi

F,

and

he

unwanted

ut unavoidable

adial

"\ry

cofnponent

{

(commonly

0.36F,

).

Gegr orms

other

han spur

-SVe

rise

also o

a load

component

parallel

to the

shaft

axis

-

but for

all

gears,

shifting

the

offset

forceasabove,

=F.D/2.

. - :

A

beIt,

being flexible,

cannot

withstand

compression

the puIley

is

thereforesubjected o two

sfand

tensions F",*

and

F"*

both

of which

must

exceed

zero.The

net

torque

T

=

(F-u*

F"""

)

D/2is

clockwise

here.

The

tension

ratio

F*",,1F,*

must iie

between

a lower

iimit

of unity

(corresponding

o no

torque

transfer)

and

an

upper

limit

dictated

by

incipient

belt

slip

around

the pulley.

(rhis

may

be demonstrated

by

equally

pulling

the

ends

of

a bit

of

rope vwapped

around

a posf

then

progressively

ncreasing

he puil

on

one

end.) A

chain

sprocket

s

similar

though

the

minimum

tension

rl:ray

top

to zero

due

to

the

positive drive not relying on friction.

The mounting

of

a

half-coupling

and

the like

on a shaft is, localIp

intrinsically indeterminate.

This is

exemplified

by the

pulley

boss

illustrated which

extends

rom

A

to C

along the

stepped

shaft. The

actual

distributions

of

bending

and

torque

n

the

shaft

4

q

are shown.

To the left of A and

to

the

right of C there

rt,*tff',

-\

are no immed,iate

ransverse oads,

so

the bending

^"T\4':-

to theshaft's tiffness ndalsodistributeshe pulley

load

graduaily

nto

the shaft,

o

hebending

moment

variation

s

non-linear. imilarly

he orque

s

some

constant alue

zero

ere)

n

the

shaft

o the eft

of A

T

.

,0.

a

F

Dl

Al

a

areno immed,iate

ransverseoads,

o

hebending

^"T\fi'l-

moment

s

linear.But

within

AC

the

boss

contributes

rtvvrc

i

r,,,,,t

and another

onstant

alue

T

to

the

right

of C

-

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l,.trpr1s

f.a

-If.