| From Graham Patterson of
Upper Orara in NSW comes this months winning question, straight
off the Internet. Over now to our patient.
Q. An article on the Internet was extolling the virtues of
fitting an unbalanced propeller with the heavy blade opposite the
piston at TDC to help balance the engine. My interest is in vintage
team race engines with iron pistons: my question is whether a weighted
hub or blade on the propeller would have any benefit or am I having
myself on?
A. My diagnosis is idiopathic delusions arising from too
much rotation at F2C speeds. In short, I don't know the answer to
your question. The system you are describing is complex, involving
a reciprocating piston, an oscillating conrod and rotating counterweights
and propeller: all of these have some degree of elasticity, and
I aint Euler or Newton. There is a theory that may help us to some
degree, so lets consider.. With Mp the mass of the piston, r the
crank length, w the angular velocity and that the momentary angle
between the crank and line of motion of the piston, the primary
disturbing force Frecip caused by motion of piston alone is given
by:
Frecip = Mp * r * w * w * COS(t)
This primary unbalance could be cancelled by a second piston moving
the opposite way, as in a horizontally opposed twin. However all
we have is a rotating counterweight, so lets look at that. With
Mb the mass of the counterweight, rb the length of the crank supporting
Mb, then the centripetal force Fb due to this rotating mass is given
by:
Fb = Mb * rb * w * w
This force has 2 components, one parallel to the line of stroke
and
one across the line of stroke. These are in turn:
Fparallel = Fb * COS(t)
Facross = Fb * SIN(t)
To cancel out Frecip we want to use the countervailing force Fparallel,
as these are oppositely directed. Thus we have full primary balance
when:
Frecip = Fparallel
Substituting the above equations yields:
Mb * rb = Mp * r
This is fine, but we still have F across acting without any countervailing
force. Things keep on shaking just the same, but in a different
direction! The introduction of the rotating balance mass merely
served to change the direction of the disturbing force from parallel
to the line stroke to across the line of stroke!
It is preferable then to only partially balance the primary force.
Thus we set:
Mb * rb = c * Mp * r with c < 1
The number c is chosen arbitrarily, but the unbalanced force on
the
engine mount is least when c = .5. Note that we have not considered
the
unbalance due to the weight of the conrod. It turns out that a counterbalance
for the rod must spin at twice the engine RPM, something of a nuisance,
I think you will agree !
Now reconsider that unbalanced prop set opposite top dead centre.
If we like , this can be considered an additional weight added to
the counterbalance. It will therefore have the same characteristics,
altering the primary partial balance. If the engine manufacturer
has carefully set c = .5, then c will no longer have this value
and force at the engine mount will be greater. According then to
this theory, perhaps using unbalanced props may not be so smart:
unless, of course, the manufacturer screwed up anyway.
This may well be the case. Graham points out that Metkemeyer and
Flores of FMV T/R fame had to go to great lengths with tungsten
counterweights to achieve c = .5 However, there is more to this
story. At least the counterweight is almost in line with the reciprocating
mass of the piston, and is thus slightly dynamically unbalanced
on the shaft axis. But the propeller unbalance weight is well forward
of the piston, by the length of the shaft, so there is a couple
formed between the piston and the prop unbalance.
This couple introduces a rocking mode of vibration, and I think
we
don't really want to add new modes of unbalanced vibrations ! Indeed,
if we want to improve the piston/counterweight dynamic balance,
the heavy prop tip should be on the same side as TDC !Perhaps one
could conclude, for prop imbalance opposite TDC, that primary balance
may be improved for engines with c somewhat less than .5, but possibly
at some small expense of dynamic balance , which loads the front
and rear bearings. It may well be worth a try !
To finish off,I will dwell briefly on the 3 modes a propeller must
be balanced. Firstly, if you set your prop horizontally on the balancer
and file the tips to get balance, you have achieved radial static
balance. My feeling is that this is the most important balance mode,
despite the Internet ravings. Secondly, you may set the prop vertically
on the balancer and remove material from the sides of the hub, so
that the prop stays vertical. This achieves lateral static balance.
Thirdly, you may spin the prop and check the tracking of the tips.
By removing facing material from the hub, you can get the tips to
track true. You have then (hopefully !) achieved dynamic balance.
I know Merv Bell, with his superb propellers, took great pains with
this tracking.
Well I hope you are feeling better now Graham, those Internet viruses
can be hard to shake off! Let me know what you would like as a prize
to the value of $30 of Supercool props or my book Propeller Dynamics.
So readers do send in your questions, give the Prop Doctor a call,
maybe you could win !
Reference: Machine Design 2, Volume 2, P. Weir, 1983.
|
