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    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:

    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 it's 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.

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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.

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.

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.

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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 it's 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.

    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.

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    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).

"Harley-Davidson" name for reference purposes only. Not affiliated with Harley-Davidson Motor Co.

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