RogerBywater wrote:
The primary inertia force is positive at TDC and negative at
TDC so the positive secondary peaks increase the positive
acceleration at TDC and reduce the negative acceleration at
BDC. Hence there is more inertia force generated by a piston
passing TDC than at BDC so a counterweight attached to the
crank that is correct for one cannot be so for the other.
The negative secondary peaks create forces acting downward
at 90 and 270 degrees but at that point the counterweight
would be producing a horizontal force so cannot provide any
compensation.
No, but a weight off the end of the end cap of the con rod can.
It will surely now be obvious that counter-weighting on the
crankshaft cannot be effective at balancing out secondary
inertia forces.
Unless the conrod/piston assembly is balanced around the crank pin.
With regard to the hypothesis about adding mass to the
connecting rod to compensate primary and secondary forces
Which is what we’re discussing. Are you somehow considering all of
the above as some other discussion?
there seem to be two flaws to consider:-
- A connecting rod is subject to different actions at its
two ends. The big-end, as we call it, undergoes rotary
motion following the crankpin around which it is attached.
The little-end undergoes reciprocatory motion in unison with
the piston to which it is attached via the gudgeon pin.
Whilst it is possible to arrange the mass of the connecting
rod so that more of it can be considered to be one or the
other it is quite impossible to arrange for all of it to
conform to the action of one end alone.
Uhhh, no, it’s not. It is most certainly impractical, though, which
I said at the outset.
In other words,
however much mass is shifted or added to the big end it can
never prevent the small end from continuing to undergo
reciprocatory motion.
It doesn’t try to. Rather, it balances that reciprocatory motion
with its own motion. If you think about the motion such a weighted
conrod cap would make, it’ll make a sort of oval in which the
vertical axis is equal to the stroke but the horizontal axis is
GREATER than the stroke. The net motion of all this mass – a piston
reciprocating vertically, an end cap weight moving in a horizontal
oval, and a conrod that moves in a combo of these motions varying
continuously from one end to the other – adds up to the equivalent
of one mass moving in circles with the crank pin. Which is easily
counterbalanced with weights on the opposite side of the crank.
It is therefore impossible for the
entire connecting rod to be balanced as if it were
rotational mass.
No, it’s not. Not just conrod, either, but conrod, piston, pin, and
rings. We’re talking about a seriously massive conrod cap.
- Even if it were possible to regard the entire connecting
rod as rotational mass the geometry of the mechanism,
because of its attachment to the reciprocating piston
assembly, will inevitably generate secondary out-of-balance
forces at twice the frequency of the primaries, which cannot
be countered in the manner suggested.
Gee, it almost sounds as though you’re close to getting it! The
primary and secondary forces generated by the weight hanging off the
end of the end cap will exactly counter those generated by the
conrod/piston assembly.
I would have thought it is fairly obvious that because the
little end is restrained to linear motion, adding a mass of
sufficient size to the big end cap, in an attempt to
counterbalance the entire rod and piston, would act as a
pendulum sweeping through a path composed of two half
ellipses below the crankpin. This would surely generate a
substantial horizontal shake with an additional secondary
component, quite apart from any practical considerations.
Keep thinking, you’ll get there! You’ve got the vertical shake of
the piston, the horizontal shake of the end cap mass, both of which
add up to a rotational imbalance – which can be perfectly balanced
by counterweights on the crank. The same is true of the secondary
imbalances, except both of those are vertical.
The small mass close to the cap which prompted the original
question is hardly significant in this respect.
Agreed. Which is why I wondered why it was there at all, and whether
or not it could be safely sliced off by those interested in a bit
less reciprocating mass.
I do not know of any evidence to support the suggestion that
a single cylinder can be fully counterbalanced for either
primary or secondary forces by adding counterweights to the
crankshaft or connecting rod.
Just because it’s impractical doesn’t mean it’s impossible. And just
because it’s not covered in one of your books doesn’t mean it isn’t a
fact.
– Kirbert
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