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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.