# Engine balance

Engine balance refers to those factors in the design, production, tuning, maintenance and the operation of an engine that benefit from being balanced. Major considerations are:

• Longevity and performance
• Power and efficiency
• Performance and weight/size/cost
• Environmental cost and utility
• Noise/vibration and performance
• Structural and operational elements within an engine

## Items to be balanced

There are many factors that could throw an engine off balance, and there are many ways to categorize them. The following is an example of categorizing the items that need to be balanced for a smooth running piston engine. In the category descriptions, 'Phase' refers to the timing on the rotation of crankshaft, 'Plane' refers to the location on the crankshaft rotating axis, and 'CG' refers to the center of gravity.

• Mechanical
• Static Balance - Static balance refers to the balancing of weight and the location of CG on moving parts.
1. Reciprocating mass - e.g. Piston and conrod weight and CG uniformity.
2. Rotating mass - e.g. Crank web weight uniformity and flywheel concentricity
• Dynamic Balance - In order for a mass to start moving or change its course in the motion, it needs to be accelerated. In order for a mass to be accelerated, a force is required, and that force needs to be countered (supported) in the opposite direction. Dynamic balance refers to the balancing of these forces and friction.
All accelerations of a mass can be divided into two components opposing in the direction. For example, in order for a piston in a single cylinder engine to be accelerated upward, something must receive (support) the downward force, and it is usually the mass of the entire engine that moves downward a bit as there is no counter-moving piston. This means one cause of engine vibration usually appears in two opposing directions. Often the movement or deflection in one direction appears on a moving mass, and the other direction appears on the entire engine, but sometimes both sides appear on moving parts, e.g. a torsional vibration killing a crankshaft, or a push-pull resonance breaking a chain. In other cases, one side is a deflection on a static part, the energy in which is converted into heat and dissipated into the coolant.
• Reciprocating mass - Piston mass needs to be accelerated and decelerated, resisting a smooth rotation of a crankshaft. In addition to the up-down movement of a piston, a conrod bigend swings left and right on a typical single cylinder engine.
3. Phase balance - e.g. Pistons on 90 degree V6 without a offset crankshaft reciprocate with unevenly spaced phases in a crank rotation
4. Plane balance - e.g. Boxer Twin pistons travel on two different rotational planes on the crankshaft, which creates forces to rock the engine on Z-axis[1]
• Rotating mass
5. Phase balance - e.g. Imbalance in camshaft rotating mass could generate a vibration with the frequency equal to 2 crank rotations in a 4 cycle engine
6. Plane balance - e.g. Boxer Twin crankshaft without counter weights rocks the engine on Z-axis[2]
7. Torsional balance - e.g. If the rigidity of crank throws on an inline 4 cylinder engine is uniform, the crank throw farthest to clutch surface (#1 cylinder) normally shows the biggest torsional deflections. It is usually impossible to make these deflections uniform across multiple cylinders except on a radial engine. See Torsional vibration
• 8. Static mass - A single cylinder 10 HP engine weighing a ton is very smooth, because the forces that comprise its imbalance in the operation must move a large mass to create a vibration. As power to weight ratio is important in the design of an engine, the weight of a crankcase, cylinder block, cylinder head, etc. (i.e. static mass) are usually made as light as possible within the limitations of strength, cost and safety margin, and are often excluded in the consideration of engine balance.
However, most vibrations of an engine are small movements of the engine itself, and are thus determined by the engine weight, rigidity, location of CG, and how much its mass is concentrated around the CG. So these are crucial factors in engine dynamic balance, which is defined for the whole engine in reciprocal and rotational movements as well as in bending and twisting deflections on X, Y and Z axis, all of which are important factors in the design of engine mounts and rigidity of static parts.
It is important to recognize that some moving mass must be considered a part of static mass depending on the kind of dynamic balance consideration (e.g. camshaft weight in analyzing the Y-axis[3] rotational vibration of an engine).
• Friction
9. Slide resistance balance - e.g. A piston slides in a cylinder with friction. A ball in a ball bearing also slides as the diameter of inner and outer laces are different and the distance of circumference differs from the inside and out. When a ball bearing is used as the main bearing on a crankshaft, eccentricity of the laces normally create slide friction
10. Rolling resistance balance - e.g. A ball in a ball bearing generates friction in rolling on a lace
• Fluid - Pressure, Flow and Kinetic balance on gas, oil, water, mist, air, etc.
• Torque Balance - Torque here refers to the torque applied to crankshaft as a form of power generation, which usually is the result of gas expansion. In order for the torque to be generated, that force needs to be countered (supported) in the opposite direction, so engine mounts are essential in power generation, and their design is crucial for a smooth running engine.
11. Amount of torque - e.g. Normally, the amount of torque generated by each cylinder is supposed to be uniform within a multi-cylinder engine, but often are not
12. Direction of torque - e.g. The conrod of a late-igniting cylinder pushes the crankshaft most at a different angle when compared to an early-igniting cylinder
13. Phase balance - e.g. Firings on a single cylinder 4 cycle engine occur at every 720 degrees in crankshaft rotation
14. Plane balance - e.g. Torque is applied to the crankshaft on the crank rotational plane where the conrod is located, which are at different distances to power take off (e.g. clutch surface) plane on an inline multi-cylinder engine
• Drag - Negative torque that resists the turning of crankshaft
• Pressure balance - Not only the compression in a cylinder, but also any creation of positive (as in oil pressure) and negative (as in intake manifold) pressure are sources of resistance, which benefit from being uniform
15. Phase balance - e.g. Compression on a single cylinder 4 cycle engine occurs every 720 degrees in crank rotation phase
16. Plane balance - e.g. Compression on a boxer twin engine occurs at different planes on the crankshaft at different distances to clutch surface. A single plane (single row) radial engine does not have this plane inbalance except for a short mismatch between the power generating plane where the conrods are, and the power take off plane where the propeller is.
• Flow resistance
17. Phase balance - e.g. If only one cylinder of a multi-cylinder engine has a restrictive exhaust port, this condition results in increased resistance every 720 degrees on crank rotation on a 4 cycle engine
18. Plane balance - e.g. If only one cylinder of a multi-cylinder inline engine has a restrictive exhaust port, it results in increased resistance on the crank rotational plane where that cylinder/conrod is located.
• 19. Kinetic resistance - Oil, water, vapor, gas and air do have mass, that needs to be accelerated in order to be moved for the operation of an engine. Rolls Royce Merlin received rear-facing stub exhaust pipes in its development, resulting in a measurable increase in the maximum speed of Supermarine Spitfire and De Havilland Mosquito. This is a form of jet propulsion using kinetic energy in the exhaust, implying that the balancing of kinetic resistance arising from fluid components of an engine is not insignificant. Crank webs partially hitting the oil in oil pan (accelerating the oil mass rapidly) could be a big source of vibration.
• 20. Shearing resistance - Metallic parts in an engine are normally designed not to touch each other by being separated by a thin film of oil. But a cam sometimes touches the tappet, and metal bearing surface wears with insufficient oil or with too much / too little clearance. A film of liquid (especially oil) resists being sheared apart, and this resistance could be a source of vibration as often experienced on an over-heating engine that is nearing a seizure.
• 21. Thermal - Thermal balance is crucial for the durability of an engine, but also has a profound effect on many of the above balancing categories. For example, it is common for a longitudinally-mounted inline engines to have the front-most cylinder cooled more than the other cylinders, resulting in the temperature and torque generated on that cylinder less than on other phase and planes. Also, thermal inbalance creates variations in tolerance, creating varied sliding frictions.

## Inherent balance

When comparing piston engines with different configurations in the number of cylinders, the V angle, etc., the term "inherent balance" is used. This term often describes just two categories in the above list that are 'inherent' in the configuration, namely, 3. (Phase balance on reciprocating mass), and 13. (Phase balance on torque generation).

In rare cases when considering a boxer twin, the categories 4. (Plane balance on reciprocating mass), 6. (Plane balance on rotating mass) and sometimes 14. (Plane balance on torque generation) are included, however, statements like "A flat-8 boxer engine has a perfect inherent balance"[4] ignore these three categories as flat-8 boxer configuration has inherent imbalance in these categories by having the left and right banks staggered (not positioned symmetrically in plan view) in the same manner as in boxer twin.

"Inherent mechanical balance" further complicates the discussion in the use of the word 'mechanical' by implying to exclude balances on torque generation and compression for some people (as in the above categorization) while not excluding them for others (as they are the results of mechanical interaction among piston, conrod and crankshaft).

While many items on the above category list are not inherent to a configuration of a multi-cylinder engine, it is safe for a meaningful discussion of inherent balance on multi-cylinder engine configurations to include at least the balances on:

• Reciprocating mass (3.Phase and 4.Plane)
• Rotating mass (6.Plane)
• Torque generation (13.Phase and 14.Plane)

and preferably:

• Compression (15.Phase and 16.Plane)

### Two cylinder engines

There are three common configurations in two-cylinder engines: parallel-twin; V-twin; and boxer twin (a common form of flat engine).

Secondary imbalance is the strongest on a parallel twin with a 360 degree crankshaft[5] (that otherwise has the advantage of 13. an evenly spaced firing, and lack of 4. & 6. imbalances), which moves two pistons together. Parallel twin with a 180 degree crankshaft[6] (that has the disadvantage of 13. uneven firing spacing and strong 4., 6., 14. & 16. imbalance) produces the vibration a half as strong and twice as frequent. In a V-twin with a shared crank pin (e.g. Ducati 'L-twin'), the strong vibration of the 360°-crank parallel twin is divided into two different directions and phase separated by the same amount of degrees as in the V angle, with 13. unevenly spaced firing as well as the imbalances 4., 6., 14. and 16.

BMW R50/2 boxer-twin engine viewed from above, showing the left & right cylinders being offset

A boxer engine is a type of flat engine in which each of a pair of opposing cylinders is on separate crank throws, offset at 180° to its partner, with 13. an evenly spaced firing. If the pistons could lie on the same crank rotational plane, then the design is inherently balanced for the momentum of the pistons. But since they cannot, the design, despite having a perfect 3. phase balance largely cancelling the non-sinusoidal imbalance, inherently has 4. plane imbalance on reciprocating mass, 6. plane imbalance on rotating mass, 14. plane imbalance on torque generation, and 16. plane imbalance on compression (these four kinds of imbalance are also known as "rocking couple") due to the crank pin rotating planes being offset.[7]

Fork and Blade conrods. This is the type used on Allison V-1710, which was retrofitted to many racing Merlins post-war.

This offset, the length of which partly determines the strength of the rocking vibration, is the largest on the parallel twin with a 180° crankshaft, and does not exist on a V or a flat engine that has a shared crank pin with "fork and blade" conrods (e.g. Harley-Davidson V-twin engine. See illustration on right). Other configurations fall in between, depending on the bigend and crank web thickness (if it exists in between the throws), and the main bearing width (if it exists in between the throws).

### Three cylinder engines

Inline 3 with 120° crankshaft is the most common three cylinder engine. They have 13. evenly spaced firing and perfect 3. phase balance on reciprocating mass, with 4. plane imbalance on reciprocating mass, 6. plane imbalance on rotating mass, 14. plane imbalance on torque generation, and 16. plane imbalance on compression. Just like in a crossplane V8, these first order rocking couples can be countered with heavy counterweights, and the secondary balance is comparable to, or better than an ordinary inline 4 because there is no piston pairs that move together.

This secondary balance advantage is beneficial for making the engine compact, for there is not as much need for longer conrods, which is one of the reasons for the popularity of modern and smooth turbo-charged inline 3 cylinder engines on compact cars. However, the crankshaft with heavy counterweights tend to make it difficult for the engine to be sporty (i.e. quick revving up and down) because of the strong flywheel effect.

Unlike in a crossplane V8, the bank of three cylinders have evenly spaced exhaust pulse 240° (120° if two stroke) crank rotational angle apart, so a simple three-into-one exhaust manifold can be used for uniform scavenging of exhaust (needed for 11. and 12.), further contributing to the size advantage.

## Primary Balance

The terminology "Primary balance" is another source of confusion in the discussion of multi-cylinder piston engine configurations. Primary, "first order" or "first harmonic" balance are supposed to mean the balancing of items that could shake an engine once in every rotation of the crankshaft, i.e. having the frequency equal to one crank rotation. Secondary or "second order" balance should refer to those items with the frequency of twice in one crank rotation, so there could be tertiary (third order), quaternary (fourth order), quinary (fifth order), etc. balances as well.

A cylinder in 4 cycle engines fires once in two crank rotations, generating forces with the frequency of a half the crankshaft speed, so the concept of "half order" vibrations, is sometimes used when the discussion is on the balances on torque generation and compression.

However, it is simpler to focus on bigger sources of imbalance and ignore the rest, and it is somewhat customary to discuss only the "3. Phase balance on reciprocating mass" in the comparison of multi-cylinder engine configurations, in which 'Primary' is meant to be the sinusoidal component of piston and conrod motions, and 'Secondary' is meant to be the effects of non-sinusoidal component of the same in slider-crank mechanism as described below.

## Secondary (Non-sinusoidal) Balance

When a crank moves 90 degrees from the top dead center (TDC) in a single cylinder engine positioned upright, the bigend up-down position is exactly at the half-way point in the stroke, but the conrod is at the most tilted position at this time, and this tilt angle makes the small-end position to be lower than the half-way point in its stroke.

Because the small-end position is lower than the half-way point of the stroke at 90 degrees and at 270 degrees after TDC, the piston moves less distance when the crank rotates from 90 degrees to 270 degrees after TDC than during the crank rotation from 90 degrees before TDC to 90 degrees after TDC. In other words, a piston must travel a longer distance in its reciprocal movement on the top half of the crank rotation, than on the bottom half.

Assuming the crank rotational speed to be constant, this means the reciprocating movement of a piston is faster on the top half than on the bottom half of the crank rotation. Consequently, the inertia force created by the mass of a piston (in its acceleration and deceleration) is stronger in the top half of crank rotation than on the bottom half.

So, an ordinary inline 4 cylinder engine with 180 degrees up-down-down-up crank throws may look like cancelling the upward inertia created by the #1-#4 piston pair with the downward inertia of the #2-#3 pair and vice versa, but in fact the upward inertia is always stronger, and the vibration caused by this imbalance is traditionally called the Secondary Vibration.

When a conrod bigend rotates, its up-down movement (like it is seen from the side of an inline 4 cylinder engine) can be plotted on a graph (with the position on the stroke on Y-axis, rotational position of the crank in degrees on X-axis) with a clean Sine curve, and so this is called the sinusoidal movement. Its left-right changes in position is exactly the same, as it is equivalent to just changing the view point from the side to the top of the engine. However, the up-down position of a conrod small-end (and the piston) does not move in this fashion as described above, thus is considered not sinusoidal.

The inertia force created by this non-sinusoidal reciprocating motion is equivalent to the mass times the acceleration of change in the position, which is expressed as:

$\Delta x = l + r \cos \Delta \alpha \,$

where $\Delta x$ is the change in up-down location, $l$ is the center-to-center conrod length, $r$ is the radius of the crank (i.e. a half of stroke), $\Delta \alpha$ is the change in crank rotational angle from TDC.

This means the imbalance is proportional to the ratio of conrod length to stroke, i.e. the longer the conrod in relation to stroke, the less this imbalance becomes. Also, inertia force is created not by a steady speed, but by acceleration and deceleration of mass movement, so the strength is proportional to the square of crankshaft rotational speed, making the imbalance particularly speed sensitive.

This non-sinusoidal motion can mathematically be considered as a combination of two hypothetical sinusoidal motions, one with the frequency equal to the crank rotation (equivalent to the piston motion with infinitely long conrod) which is called the 'primary' component, another with double the frequency[8] (equivalent to the effect of conrod tilting angle that lowers the small-end position from when it is upright), which is the 'secondary' component. Although pistons do not move in the fashion defined by either of these two components, it is somewhat easier to understand the motion as a combination of the two, so the use of the terms primary and secondary became popular outside of mathematical analysis.

The vibration caused by this inertia force (or the difference of its strength between the top and bottom half of crank rotation) is small at lower engine speed, but it grows exponentially with the increase in crank rotational speed, making it a major problem in high-revving engines.[9] Inline 4 cylinder and 90 degree V8 engines with flat-plane crankshaft move two pistons always in synch, making the imbalance twice as large (and a half as frequent) as in other configurations that move all pistons in different, evenly spaced, reciprocal phases (e.g. Crossplane inline-four and crossplane V8).

Non-sinusoidal imbalance can almost never be completely cancelled (balanced) with a single-crankshaft multi-cylinder configuration without balancer shafts.[10] But boxer engines with many cylinders show the least effect by cancelling all but the (4.) plane imbalance in the cancelling forces.

In designing a balancer for this purpose, it is common to create a sinusoidal force mirroring the hypothetical secondary component with two counter-rotating eccentric weights that rotate at twice the crankshaft speed, as the use of a counter-moving slider-crank as the balancer is less efficient.

## Steam locomotives

Steam locomotives commonly have balancing weights on the driving wheels to control wheel hammer caused by the up and down motion of the coupling rods and, to some degree, the connecting rods.