I no longer subscribe to this list, but since I wrote this thing for
the jag-lovers list anyway, thought you guys might appreciate it. If
you wish to reply, remember you should address me directly.
For those who may be interested, I will endeavor to explain the
vibration analysis of various engine configurations. In layman's
terms, no less -- no calculus or the like.
For an example, I will explain the analysis of the four cylinder
inline engine.
Stationary parts of an engine, of course, do not contribute to
vibration. Since rotating parts can presumably be balanced statically
and dynamically, presumably they do not contribute to vibration
either. The analysis therefore considers only the reciprocating
masses: pistons, rings, pins, and the upper half of the connecting
rod. The valve train may also contribute, but it does not lend itself
to analysis, since a change in cam configuration would negate the
analysis. It is also generally a very small contribution, since the
parts move much more slowly than the pistons and are much smaller.
In the four cylinder motor, when the crankshaft is positioned at 0
degrees, pistons 1 and 4 are at TDC and pistons 2 and 3 are at BTD.
The center of mass of these four parts will therefore be between the
#2 and #3 cylinder, and vertically at the midway point of the stroke.
When the crankshaft is positioned at 180 degrees, pistons 1 and 4 are
at BDC and 2 and 3 are at TDC. The center of mass will therefore be
at exactly the same place.
When the crankshaft is at 90 degrees, all four pistons are at the
midway point of their stroke. But wait! It is NOT the midway point!
True, the crank throws are all either at 90 degrees or 270 degrees,
and the centerline of the crank journals is vertically halfway between
TDC and BDC. But the connecting rods are not vertical; rather, they
are at an angle out to the journals, which are not directly under the
piston but to one side or the other. The height of the pistons
vertically above the crank journal is slightly less than the length of
the connecting rod at this point; the actual distance is a simple
trigonometric function of the crank throw (1/2 the stroke) and the
connecting rod length.
The result is that all four pistons are actually slightly below the
midpoint of their stroke. Therefore, the center of mass of the four
parts is still between the #2 and #3 cylinders, but is slightly below
the midpoint of the stroke. The same condition occurs when the crank
is positioned at 270 degrees.
Now, this means that the center of mass is at the midpoint at 0
degrees, below the midpoint at 90 degrees, back at the midpoint at 180
degrees, below the midpoint once again at 270 degrees, and at the
midpoint again back at 0. The center of mass of these four parts is
moving up and down twice every time the engine turns around once.
The four cylinder inline engine has an inherent vibration, up and down
at twice the engine speed. This leads to the familiar four cylinder
"buzz", since four-bangers tend to rev pretty high to begin with and
the vibration is at twice the engine speed.
The four cylinder inline can be balanced, but it requires the
installation of a pair of counterrotating counterbalances, one on each
side of the engine, turning and twice the engine speed. There are
several engines available with this feature, and most people are
puzzled as to why a couple unbalanced shafts are in there that aren't
driving anything.
A similar analysis can be performed on any engine configuration. The
results for the most common engines are described as follows:
The six-cylinder inline engine is inherently balanced -- no
corrections necessary. This is a major reason this engine
configuration has been so popular for so long. The 60-degree V-12,
being effectively two 6-cylinder inlines, is also inherently balanced.
The eight-cylinder inline (with crank throws at 45 degree angles) is
inherently balanced, just as the six-cylinder is. They are no longer
popular because they are an ungainly arrangement.
The 90-degree V8, it must be noted, is NOT effectively two four
cylinder inlines. The crankshaft has throws 90 degrees apart rather
than at 180, with the result that a separate analysis is necessary.
The net motion of the masses within a V8 result in a circular
imbalance at each end of the engine. Basically, the front end of the
engine is trying to wallow around in a circle, and the back end is
doing the same thing only 180 degrees opposite. The engine is trying
to gyrate.
All of this is at the same speed as the crankshaft, so the imbalance
is incredibly simple to correct. All that is required is to provide
offset counterbalances at each end of the crankshaft, and the engine
is perfectly balanced. Sometimes these counterbalances are cast into
the flywheel and crank pulley, and other times they are cast into the
crankshaft itself.
It should be noted that the counterbalances are designed for a
particular mass of piston, rings, pin and connecting rod. If the
engine is rebuilt with parts that weigh more or less than the
originals, the counterbalances must be corrected accordingly, or
vibrations will result.
The three-cylinder inline has no net up-and-down vibration. It does,
however, have an up-and-down on one end along with a down-and-up on
the other end, resulting in a bucking bronco type of pitching motion.
Correction would require two pairs of counterrotating counterweights,
one at each end of the engine and turning the same speed as the
crankshaft.
An opposed six cylinder engine can be inherently balanced, but it
requires six separate crank throws; three throws with the opposing
pistons connecting to the same throw won't cut the mustard. Porsche
911s HAVE such a six-throw crank.
There are at least three distinct layouts of V6: the 60 degree V6, the
even-firing 90 degree V6, and the uneven-firing 90 degree V6. NONE of
these are balanced, all shake, no one seems to care anymore. This is
in large part to fantastic improvements in motor mounts and other
vibration-damping methods which allow an engine to shake without
transmitting a lot of discomfort to the passengers.
The new Dodge V-10 shakes, but not much, and it was designed for
pickup trucks and nobody cares.
As an interesting footnote, in THEORY it is possible to completely
balance any piston-and-cylinder arrangement (even a one-cylinder!) by
two steps: First, a counterweight should be hung off the bottom end of
the connecting rod such that the counterweight will balance the entire
weight of the piston, rings, pin and connecting rod around the
crankshaft journal. Second, the crankshaft must be fitted with
counterbalance weights large enough to counter the entire weight of
the piston, rings, pin, connecting rod and end cap counterweight. It
should be obvious that such an arrangement would be INCREDIBLY
massive, and in no way worthwhile.
--
--- Kirbert
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| Kirby Palm, P.E. |
| palmk@freenet.tlh.fl.us |
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|