Flywheel Balance Factors
“Flywheel balancing” is the term
commonly used to describe making changes in the weight of certain areas
of the flywheels (crank-shaft) to compensate for the weight of the other
components. It is necessary for any motor’s flywheels to be “in balance”
to operate without damage. All flywheels are balanced at the factory, but
not to the same degree of precision as would be required for racing, or even by a careful
owner. The Harley-Davidson factory balance is only production-line quality,
and can be improved upon by diligent effort. In a V-twin this is especially
important, as these motors are inherently out of balance due to the irregular
nature of the firing impulses, and movement of the components.
The purpose of this Paper is not to discuss how
motors are balanced, but to explore what factors affect the degree of
compensation (the “balance factor” ) to be used to achieve “correct” balance. |
Component Definitions: |
The entire flywheel assembly must balanced
(with the exception of certain rotating components marked * in the list
below). The calculation requires dividing the components into 2 separate
categories: |
Rotating weight, which
is always in (generally) circular motion, and varies speed with engine
RPM. Included are: |
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left & right flywheel halves |
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crank-pin, key, roller bearings, cages, nuts & locks |
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lower half of both connecting rods, including the rod races |
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sprocket & pinion shafts, key(s), roller bearings, cages, nuts
& locks* (although theoretically part of the flywheel assembly, these
components have almost literally no effect on balance due
to their low weight, radially-symmetrical cross-section and very small radius of rotation). |
Reciprocating weight, which
is always in (generally) bi-directional linear motion: accelerating from
fully stopped @ TDC, traveling down, slowing & stopping @ BDC, then
reversing and accelerating in the other direction, slowing & stopping,
etc. The components (again, generally) come to a complete halt twice
in every revolution of the motor. These components vary speed with engine
RPM, but vary direction based on flywheel positon. Included are: |
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both pistons |
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piston pins, rings & locks |
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upper half of both connecting rods, including the piston pin bushings. |
All methods involve separating the rod
weight into reciprocating vs. rotating weight by suspension
of the rod(s) by one end and weighing the other, carefully keeping the
beam axis exactly horizontal. The process is then reversed, giving the
weight of the opposite end. The total (of course) equals the exact weight
of the rod. However... this makes the separation of reciprocating vs. rotating
weights dependent on the center of gravity, which is NOT a relevant
factor for balancing purposes. The exact center of the big end (the main
race insert, for example) is pure rotating weight (no rectilinear
motion), whereas the pin eye & bushing is pure reciprocating weight
(no rotational motion). If you stretched a rod by 1” in the exact balance
center (without adding any weight), the suspension-derived weight &
proportions would not change, but clearly the effect of the new rod on
balance would change, because the point of distinction between the reciprocating
and rotating ends is at the geometric center, not the center of
gravity. Since the big end is always much heavier than the small end, the
center of gravity will only begin to locate at the geometric center (50%
of the center to center distance) in a rod of infinite length; shorter
rods will tend to have more bias between the C-of-G and geometric center.
Therefore, the absolute length of the rod (as well as the rod ratio) has
an effect on balance.
This (partially) explains why some factors work
better on some motors. Motors with higher “n” values (long rod, short stroke,
rod-to-stroke ratio in the 1.75 - 2.1-1 range) have lower out-of-balance
forces: the mostly linear upper end of the beam walks back and forth through
a smaller range, and its maximum angle from vertical is smaller. Lower
“n” value motors' (short rod, long stroke, rod-to-stroke ratio in the 1.45
- 1.75-1 range) rod beams swing through a greater arc as the maximum deflection
from vertical is greater - more of the force is vectored at the cylinder
wall (rather than at the crank-pin). This affects selection of balance
factor. In my opinion, the separation (and assignment of weight fractions
to rotating vs. reciprocating) MUST include some compensation for the length
of the rod (as well as the rod to stroke ratio). An interesting experiment
would be to see where the mathematical center is (50% of center-to-center
distance; 3.71875” from either end of a 45, Sportster & 1973-* big
twin rod) vis-a-vis the balance point derived by the C-of-G (suspended)
method. |
Factors Affecting Balance: |
There have been many formulae published
to calculate the exact amount of adjustment to make to the flywheels to
compensate for these factors. The adjustment is usually made by removing
metal from the rim directly opposite the center of an imbalance caused
by excess weight. Of course, it’s also possible to add weight, but this
is more complex and not generally the first choice. If a known and trusted
“balance factor” (math formula or selection of components) is used, the
level of reliability and rider comfort in improved. However, even excellent
application of the wrong factor may cause very unsatisfactory results -
don’t be creative! Actually, no formula is “correct”, some just
come closer than others, by the “empirical” method - they've been tried
& adjusted by experiment. All formulae are compromises based
on motor details, but also including such dimensional & physical factors
as: |
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Rod to stroke length ratio: small ratios (long stroke, short rod) have
higher out-of-balance forces. |
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Angle between the cylinders: Harley-Davidson twin-cylinder motors (except the 1920
Sport, and VR) all have their cylinders placed 45° apart, but this
is certainly not the only practical method. For example: most Indian twins
are 42°, various
Japanese twins are between 60 & 70°, Ducati, Moto Guzzi &
Indian 841 military twins are 90°, and BMW, Marusho, Honda Gold
Wing, Ural, Douglas, Harley-Davidson Sport & XA are 180°. The
“V” angle is frequently a whole fraction
of a circle: 45° is 1/8, 60° is 1/6, etc. (Indian being the oldest exception). Large aircraft radial engines
were designed with 27 cylinders: 9 banks of 3 in-line cylinders each, 40°
apart. |
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RPM range normally used: a wide range must be more forgiving of “bad
spots”. The calculation must be made for the entire range, not just the
power curve (except for racing). |
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Amount of power developed: if necessary, the durability of the motor
is given preference to the rider’s comfort. |
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Rider tolerance of vibration: how long will the machine be ridden?
By whom? |
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Type of engine mount: solid? Rubber? Unit construction? How many points
of attachment? |
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Type of chassis: rubber mount? Belt drive? Isolated handlebars &
footpegs? |
Mathematical-based formulae using only
conventional factors will never predict accurately how well a given
motor will run, even at a given RPM, because the dynamic forces aren’t
limited to reciprocating vs. rotating weight. The forces acting on the
rod & crank-pin (mass inertia) are not only the reciprocating weight
(as listed above), but also the forces present in the cylinder and combustion
chamber above the piston. In this Paper, the author wishes to bring to the reader’s attention how complex the subject is, and cautions them to research the subject very
carefully before balancing their motor. |
Dynamic Factors; Pressure Acting
as Weight: |
The behavior of the gas in the combustion
chamber alters the effective (apparent) weight of the piston. The gas experiences
changes in density, volume, temperature & pressure continuously during
the motor’s operation due to various factors. The following text briefly
discusses some of these factors, and the changes they cause in apparent
piston weight.
If the motor were cycled without vacuum, compression
or combustion present (the piston acting only as a weight), the piston’s
inertia would resist movement at all times (Newton’s laws of motion), whether
the rod be going up or down. This would have the effect of reducing
the apparent weight on the 2 down-strokes (intake and power) and increasing
it on the 2 up-strokes (compression & exhaust).
However, when we add the dynamic effects of vacuum,
compression and combustion pressure, the effects are radically altered,
and they change not only as the details of the motor’s construction change,
but also as the flywheels rotate, and the demand (throttle opening &
vacuum) and RPM level of the motor changes.
As these factors come into play, the piston’s apparent
weight (and its effect on the flywheel) may increase dramatically, completely
vanish, or become a negative weight. |
Let’s call the effect on the piston’s
apparent weight caused by the cylinder’s internal pressure fluctuations
“pull”. Pull can be positive (simulating adding physical weight
to the reciprocating components) or negative (subtracting weight),
and can act in either direction (up or down). Pull acts on the rod
and flywheel assembly in the same way as the actual weight of the reciprocating
components themselves, but not at the same time, not continuously, and
varying in degree based on the construction and size of the motor and its
operating conditions. Even at the same speed, the degree of successful
compensation for out-of-balance forces will vary dramatically with throttle
opening. The motor will strangely vibrate as the throttle is opened, causing
the rider to fear broken mounts, loose chain, etc., but the vibration “goes
away” as the throttle is closed again. Compare these effects throughout
the engine’s 4 cycles of rotation: |
Example 1
A motor with 12-1 compression ratio cruising with partially open
throttle at 4000 RPM |
| Stroke |
Piston |
Effect |
Comment |
Intake |
Down |
Drag |
The piston’s “pull” (resistance to movement, as it affects the rod)
is high, as the cylinder is only partially full (low VE, or volumetric
efficiency, expressed in % of full displacement), and is still under partial
vacuum (15 psi) due to the small throttle opening. This means that the
rod “sees” a heavier piston than the actual component, but only
during this cycle and conditions. |
Compression |
Up |
Load |
Pull is low, as the low VE means only a small volume of mixture
is present to be compressed. However, cylinder pressure is still higher
than would be the case in a motor with lower CR. The rod “sees” a slightly
heavier
piston than the actual weight. |
Power |
Down |
Load |
Pull is low due to only a small volume of mixture being ignited,
but at a high ratio due to static CR. The pressure of the expanding gas
makes the piston’s weight go down past 0 and into positive force on the
rod, even with this low power level. The rod “sees” a lighter piston
than the actual weight. |
Exhaust |
Up |
Load |
Pull is probably very
low, due to the low volume of gas to expel.
The rod “sees” a slightly heavier piston than the actual weight. |
|
Example 2
The same motor, same speed, but with wide-open throttle |
| Stroke |
Piston |
Effect |
Comment |
Intake |
Down |
Drag |
Pull is less than with partially-closed throttle (above, #1)
because the higher VE means lower vacuum (as low as 0 psi under ideal conditions
at the torque peak) resisting the piston’s downward motion. Piston weight
will be neutral (pull = 0, reciprocating weight will be the only force)
if the vacuum is 0 psi, but pull will occur and rise with the vacuum if
VE is not 100%. The rod “sees” a slightly heavier piston than the
actual weight. |
Compression |
Up |
Load |
Pull is highest here, as the cylinder is nearly full, but resistance
on the compression stroke is very high. If the piston diameter is 3-7/16”,
the piston’s area is 9.28 Sq. In., so the 200 psi present during compression
will exert a force of 1850 lbs. on the piston! Nearly 100 VE (open throttle,
demand almost completely satisfied) means that cylinder pressure will be
much higher than in Example 1 (above). The piston “weighs” much more on
the compression stroke during full throttle than cruising. The rod “sees”
a much heavier piston than the actual weight. |
Power |
Down |
Load |
Pull is much less (high negative number). The 700 peak psi present
in the cylinder as the mixture burns subtracts 6500 lbs. from the reciprocating
weight, leaving a huge negative number, and the flywheels are momentarily
but very badly out of balance. The rod “sees” a much heavier piston
than the actual weight. |
Exhaust |
Up |
Load |
Negative pull is higher here than in the other Exhaust examples, as
the high VE means the cylinder is nearly full of gas. The resistance offered
by the gas increases the piston’s apparent inertia. The rod “sees” a heavier
piston than the actual weight. |
|
Example 3
The same motor, same speed, but with the throttle snapped shut |
| Stroke |
Piston |
Effect |
Comment |
Intake |
Down |
Drag |
Pull instantly jumps, as the cylinder is now almost completely empty
(VE approaching 0). Vacuum (which may reach 25+ psi) acting on the piston’s
area will exert a drag on the rod of 232 lbs. This is why race motors break
as they cross the finish line (it’s called “bringing the motor down against
compression”) - the inertia of the piston weight alone would be safe, but
the inertia + vacuum is enough to either pull the dome off the piston,
or pull the rod in half. The rod “sees” a much heavier piston than
the actual weight. |
Compression |
Up |
Load |
Pull is a small negative number, less than Example 1
as the VE is lower. The rod “sees” a slightly heavier piston than
the actual weight. |
Power |
Down |
Drag |
Pull is a smaller negative number than Example 1, same reason:
lower VE. Combustion pressure may be less than the frictional drag of the
piston, so the rod “sees” a slightly heavier piston than the actual
weight. |
Exhaust |
Up |
Load |
Pull is lowest here, even smaller than Example 1 - even less gas to
expel. The rod “sees” a slightly heavier piston than the actual
weight. |
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Dynamic Factors; Motion vs. Direction: |
The reciprocating components of a V
configuration behave quite differently from those of an single-cylinder,
in-line or opposed (180°) motor. Using the Harley-Davidson 45°
twin for example, let’s begin in mid-stroke (90° BTDC) with the
pistons rising towards TDC. Both pistons (and the other reciprocating components,
as listed previously) are moving in the same direction (even though not
in the same positions or at the same speeds). However, as the front piston reaches 45° BTDC
the rear piston has stopped at TDC. As the front piston rises to 44° BTDC, the rear piston is at 1° ATDC (the 45° separation angle is still present), and has
begun to move
down. The pistons will continue to move in opposite
directions for 45° of flywheel rotation, until the front piston reaches TDC (rear piston is at 45° ATDC), after which
both will be moving down.
A similar effect occurs approaching & passing
BDC. The relative directions of the pistons are the same, but the exact
positions are different due to the difference in piston speed at the bottom
of the stroke (the TDC motion vs. BDC motion speed differential and exact
piston position are functions of the rod-to-stroke ratio). Only at 22½°
from TDC and BDC are the 2 pistons in the same absolute position. |
| From front piston position 45° BTDC to
TDC and 45° BBDC to BDC, the front and rear pistons are moving
in opposite directions. |
The selection of the “V” angle itself
adds another complex factor to motor design. The narrow V angles (42°,
45°, etc.) have a relatively short period in which the reciprocating
weights of the two cylinders are moving in different directions - the same
as the V angle (45° is only 12.5% of the full 360° rotation
of the flywheel). However, the out of balance forces are relatively high,
and balancing is generally successful only over a narrow range of engine
speed. As the V angle widens (60°, etc.) the periods in which the
reciprocating weights are moving in different directions increases (60°
is 16.67% of the full 360° rotation of the flywheel), which appears
to make the problem worse, but the wider V angle motors appear more tolerant
of wider and higher RPM ranges, and the net effect is an improvement. However,
these motors generally require a longer and lower engine bay for clearance,
which frequently changes the entire frame design, including the
wheelbase, center of gravity, swing-arm length, gas tank position, etc. |
The bottom line is that the physics
and mathematics involved in how the motor operates are far too complex
to make a formula-based balance factor any more than a reasonable compromise.
These are only the factors that I've personally detected; there
are certainly more (of greater or lesser effect) than I am not capable of adequately describing, such as the elasticity of components, harmonic resonance, gyroscopic forces, precession, etc.
Once the factor has been selected, the remaining tasks are accurately to record the component
weights, and precisely adjust the flywheels to compensate. Your motor will
last longer and be more pleasant to ride afterwards.
My opinion: don’t try to be an innovator in
selecting a balance factor; use one that has stood the test of time &
experience, and has been successful in a motor very similar to yours (especially
with regard to stroke & rod length, piston gram weight, operating RPM
range, and compression ratio). |
