Engine balance

If the weight— or the weight distribution— of moving parts is not uniform, their movement can cause out-of-balance forces, leading to vibration. For example, if the weights of pistons or connecting rods are different between cylinders, the reciprocating motion can cause vertical forces. Similarly, the rotation of a crankshaft with uneven web weights or a flywheel with an uneven weight distribution can cause a rotating unbalance.

Even with a perfectly balanced weight distribution of the static masses, some cylinder layouts cause imbalance due to the forces from each cylinder not cancelling each other out at all times. For example, an inline-four engine has a vertical vibration (at twice the engine speed). These imbalances are inherent in the design and unable to be avoided, therefore the resulting vibration needs to be managed using balance shafts or other NVH-reduction techniques to minimise the vibration that enters the cabin.

A reciprocating imbalance is caused when the linear motion of a component (such as a piston) is not cancelled out by another component moving with equal momentum moving in the opposite direction in the same plane.

Types of reciprocating phase imbalance are:

• Mismatch in counter-moving pistons, such as in a single-cylinder engine or an inline-three engine.
• Unevenly spaced firing order, such as in a V6 engine without offset crankpins

Types of reciprocating plane imbalance are:

• The offset distance between crankpins causing a rocking couple on the crankshaft from the equal and opposite combustion forces, such as in a boxer-twin engine, a 120° inline-three engine, 90° V4 engine, an inline-five engine, a 60° V6 engine and a crossplane 90° V8 engine.

In engines without overlapping power strokes (such as engines with four or fewer cylinders), the pulsations in power delivery vibrates the engine back and forth rotationally on X-axis, similar to a reciprocating imbalance.

A rotating imbalance is caused by uneven mass distributions on rotating assemblies

Types of rotating phase imbalance are:

• Unbalanced eccentric masses on a rotating component, such as an unbalanced flywheel

Types of rotating plane imbalance are:

• Unbalanced masses along the axis of rotation of a rotating assembly causing a rocking couple, such as if the crankshaft of a boxer-twin engine did not include counterweights, the mass of the crank throws located 180° apart would cause a couple along the axis of the crankshaft.[2]

• Lateral motion in counter-moving pairs of assemblies, such as a centre-of-mass height difference in a pair of piston/conrod assemblies. In this case, a rocking couple is caused by one conrod swinging left (during the top half of its crank rotation) while the other is swinging right (during the bottom half), resulting in a force to the left at the top of the engine and a force to the right at the bottom of the engine.

Harmonic damper for a 1937 Pontiac engine

Torsional vibration is caused when torque is applied at offset distances along a shaft.

This occurs along the axis of a crankshaft, since the conrods are usually located a different distances from the resistive torque (e.g. the clutch). This vibration is not transferred to outside of the engine, however fatigue from the vibration could cause crankshaft failure.

Radial engines do not experience torsional imbalance.

0: Engine block (black)
1: Piston (blue)
2: Conrod (green)
3: Crankshaft (blue)

A piston travels further during the top half of its motion than during the bottom half of its motion, which results in non-sinusoidal vibrations called secondary vibration.

The difference in distance travelled is due to the rotation of the connecting rod. At 90 degrees after top dead centre (TDC) the crankshaft end of the conrod is exactly at the halfway point of its stroke, however the angle of the conrod (ie the left-right movement, when looking down the crankshaft) means that the piston end of the conrod must be lower than the halfway point, in order for the conrod to maintain a fixed length. The same also applies at 270 degrees after TDC, therefore the piston end travels a greater distance from 270 degrees to 90 after TDC than it does in the 'bottom half' of the crankshaft rotation cycle (90 degrees to 270 degrees after TDC). In order to travel this greater distance in the same amount of time, the piston end of the connecting rod must experience higher rates of acceleration during the top half of its movement than in the bottom half.

This unequal acceleration results in higher inertia force created by the mass of a piston (in its acceleration and deceleration) during the top half of crankshaft rotation than during the bottom half. In the case of an inline-four engine (with a traditional 180-degree crankshaft), the upwards inertia of cylinders 1 and 4 is greater than the downwards inertia of cylinders 2 and 3. Therefore, despite an equal number of cylinders moving in opposite directions at any given time (creating perfect primary balance), the engine nonetheless has a non-sinusoidal imbalance. This is referred to as a secondary imbalance.

Mathematically, the non-sinusoidal motion of the crank-slider mechanism can be represented as a combination of two sinusoidal motions:

• a primary component with the frequency equal to the crank rotation (equivalent to the piston motion with infinitely long conrod)
• a secondary component which occurs at double the frequency[4] and is equivalent to the effect of conrod tilting angle that lowers the small-end position from when it is upright

The pistons do not move in exactly this fashion, it is still a useful representation for analyzing its motion. This analysis is also the origin of the terms primary balance and secondary balance, which are now also used outside of academia to describe engine characteristics.

Balance shaft system: 1922 design by Lanchester Motor Company

The vibration caused by this secondary imbalance is relatively small at lower engine speeds, but it is proportional to the square of the engine speed, potentially causing excessive vibration at high RPM. To reduce these vibrations, some engines use balance shafts. A balance shaft system most commonly consists of two shafts with an identical eccentric weight on each shaft. The shafts rotate at twice the engine speed and in opposite directions to each other, thus producing a vertical force which is designed to cancel out the force caused by the engine's secondary imbalance. The most common use of balance shafts is V6 engines and large displacement inline-four engines.

Straight-twin engine with different crankshaft angles

Straight-twin engines most commonly use the following configurations:

• 360° crankshaft- this configuration creates the highest levels of secondary imbalance,[5] however the primary plane imbalances are minimised and the even firing order provides smoother power delivery (albeit without overlapping power strokes of engines with more than four cylinders)
• 180° crankshaft- this configuration produces primary plane imbalances and an uneven firing order,[6] however the secondary imbalances are half as strong (and at twice the frequency) compared with a 360° straight-twin engine.
• 270° crankshaft- this configurations minimises secondary imbalances, however a primary rotating plane imbalance is present and the firing order is uneven. The exhaust note and power delivery resembles those of a 90° V-twin engine.

Straight-three engines most commonly use a 120° crankshaft and have the following characteristics:

• An evenly spaced firing interval (although the power strokes are not overlapping).
• Primary and secondary reciprocating plane balance is perfect.
• Primary and secondary rotating plane imbalances are present.

Straight-four engines (also called "inline-four engines") typically use an 'up-down-down-up' 180° crankshaft design and have the following characteristics:

• An evenly spaced firing interval (although the power strokes are not overlapping).
• Primary and secondary reciprocating plane imbalances are present.
• Secondary reciprocating forces are high, due to all four pistons being in phase at twice the rotating frequency.
• Counterweights have been used on passenger car engines since the mid-1930s,[7] either as full counterweight or semi-counterweight (also known as half-counterweight) designs.

Straight-five engines typically use a 72° crankshaft and have the following characteristics:

• An evenly spaced firing interval with overlapping power strokes, resulting in a smoother idle than engines with fewer cylinders.
• Primary and secondary reciprocating plane balance is perfect.
• Primary and secondary rotating plane imbalances are present.

Straight-six engines typically use a 120° crankshaft, a firing order of 1-5-3-6-2-4 cylinders and have the following characteristics:

• An evenly spaced firing interval with overlapping power strokes. Two simple three-into-one exhaust manifolds provides uniform scavenging, since the engine is effectively behaving like two separate straight-three engines in this regard.
• Primary and secondary reciprocating plane balance is perfect.
• Primary and secondary rotating plane balance is perfect.

Fork-and-blade connecting rods

V-twin engines have the following characteristics:

• With a V angle of 90 degrees and offset crank pins, a V-twin engine can have perfect primary balance.
• If a shared crank pin is used (such as in a Ducati V-twin engine), the 360° crankshaft results in an uneven firing interval. These engines also have primary reciprocating plane and rotating plane imbalances. Where the connecting rods are at different locations along the crankshaft (which is the case unless fork-and-blade connecting rods), this offset creates a rocking couple within the engine.

V4 engines come in many different configurations in terms of the 'V' angle and crankshaft configurations. Some examples are:

• The Lancia Fulvia V4 engines with narrow V angle have crank pin offset corresponding to the V angle, so the firing interval matches that of a straight-four engine.
• Some V4 engines have irregular firing spacing, and each design needs to be considered separately in terms of all the balancing items. The Honda RC36 engine has a 90 degree V angle and a 180° crankshaft with firing intervals of 180°-270°-180°-90°, which results in uneven firing intervals within 360 degrees and within 720 degrees of crankshaft rotation. On the other hand, the Honda VFR1200F engine has a 76 degree V angle and a 360° crankshaft with shared crank pins that have a 28° offset, resulting in 256°-104°-256°-104° firing interval. This engine also has an usual connecting rod orientation of front-rear-rear-front, with a much wider distance between cylinders ('bore spacing') on the front cylinder bank than on the rear, resulting in reduced rocking couples (at the expense of wider engine width).[8]

V6 engines are commonly produced in the following configurations:

• 60 degree V angle- this design results in a compact engine size, and the short crankshaft length reduces the torsional vibrations. Rotating plane imbalances. The staggering of the left and right cylinder banks (due to the thickness of the connecting rod and the crank web) makes the reciprocating plane imbalance more difficult to be reduced using crankshaft counterweights.
• 90 degree V angle- this design historically derives from chopping two cylinders off a 90 degree V8 engine, in order to reduce design and construction costs. An early example is the General Motors 90° V6 engine, which has an 18° offset crankshaft, resulting in an uneven firing interval. Newer examples, such as the Honda C engine, use 30° offset crank pins, resulting in an even firing interval. As per V6 engines with 60 degree V angles, these engines have primary reciprocating plane and rotating plane imbalances, staggered cylinder banks and smaller secondary imbalances.

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

[Precision: A 'flat' engine is not necessarily a 'boxer' engine. A 'flat' engine may either be a 180 degree vee engine or a 'boxer' engine. A 180 degree vee engine as used in the Ferrari 512BB has opposed cylinder pairs whose connecting rods use the same crank throw. Contrary to this, in a 'boxer' engine as applied in BMW motorcycles, each conrod has its own crank throw which is positioned 180 degrees to the crank throw of the opposed cylinder.]

Flat-twin engines typically use a 180° crankshaft, separate crank throws and have the following characteristics:

• Primary and secondary reciprocating plane balance is perfect.
• Primary and secondary rotating plane imbalance is present.

Flat-four engines typically use a left-right-right-left crankshaft configuration and have the following characteristics:

• Primary imbalances are caused by the rocking couples of the opposing pistons being staggered (offset front to back). The intensity of this rocking couple is less than a straight-four engine, since the pairs of connecting rods swinging up and down move at different centre of gravity heights.
• Secondary imbalances are minimal.

Flat six engines typically use a boxer configuration and have the following characteristics:

• An evenly spaced firing interval with overlapping power strokes. A simple three-into-one exhaust for each cylinder bank provides uniform scavenging, since the engine is effectively behaving like two separate straight-three engines in this regard.
• Primary reciprocating plane and rotating plane imbalances, due to the distance along the crankshaft between opposing cylinders. A flat-six engine would have perfect primary balance if fork-and-blade connecting rods were used.
• Secondary imbalances are minimal, because there are no pairs of cylinders moving in phase, and the imbalance is mostly cancelled out by the opposing cylinder.
• Torsional imbalances are lower than straight-six engines, due to the shorter length of a flat-six engine.

Builders photo of NZR K class (K 88) showing drivers (without tender).

All the driving wheels have an out-of-balance which is caused by their off-center crank pins and attached components. The main driving wheels have the greatest unbalance since they have the biggest crankpin as well as the revolving portion of the main rod. They also have the valve gear eccentric crank and the back end of the eccentric rod. In common with the linked driving wheels they also have their own portion of the side rod weight. The part of the main rod assigned a revolving motion was originally measured by weighing it supported at each end. A more accurate method became necessary which split the revolving and reciprocating parts based on the position of the center of percussion. This position was measured by swinging the rod as a pendulum.[11] The unbalance in the remaining driving wheels is caused by a crankpin and side rod weight. The side rod weights assigned to each crankpin are measured by suspending the rod on as many scales as there are crankpins or by calculation.

The reciprocating piston/crosshead/main rod/valve motion link is unbalanced and causes a fore-and-aft surging. Their 90 deg separation causes a swaying couple.[12]

The whole locomotive tends to move under the influence of unbalanced inertia forces. The horizontal motions for unbalanced locomotives were quantified by M. Le Chatelier in France, around 1850, by suspending them on ropes from the roof of a building. They were run up to equivalent road speeds of up to 40 mph and the horizontal motion was traced out by a pencil, mounted on the buffer beam. The trace was an elliptical shape formed by the combined action of the fore-and-aft and swaying motions. The shape could be enclosed in a 5/8" square for one of the unbalanced locomotives and was reduced to a point when weights were added to counter revolving and reciprocating masses.[13]

The effect of vertical out-of-balance, or varying wheel load on the rail, was quantified by Professor Robinson in the U.S. in 1895. He measured bridge deflections, or strains, and attributed a 28% increase over the static value to unbalanced drivers.[14]

The residual unbalance in locomotives was assessed in three ways on the Pennsylvania Railroad testing plant. In particular, 8 locomotives were tested at the Louisiana Purchase Exposition in 1904. The three measurements were:

1. the critical speed. This was defined as the speed at which the unbalanced reciprocating parts reversed the pull of the locomotive. At higher speeds this motion was damped by throttling oil flow in dashpots. The critical speed varied from 95 rpm for a Baldwin tandem compound to over 310 rpm for a Cole compound Atlantic.
2. the horizontal motion at the pilot. As an example, the Baldwin compound Atlantic moved about 0.80" at 65 mph compared with 0.10" for the Cole compound Atlantic.
3. a qualitative assessment of the load on the plant supporting wheels. A 0.060" diameter wire was run under the wheels. Measuring the deformed wire gave an indication of the vertical load on the wheel. For example, a Cole compound Atlantic showed little variation from a 0.020" thickness for all speeds up to 75 mph. In contrast, a Baldwin compound Atlantic at 75 mph showed no deformation, which indicated complete lifting of the wheel, for 30 degrees wheel rotation with a rapid return impact, over only 20 degrees rotation, to a no-hammer blow deformation of 0.020" .[15]

Qualitative assessments may be done on a road trip in terms of the riding qualities in the cab. They may not be a reliable indicator of a requirement for better balance as unrelated factors may cause rough riding, such as stuck wedges, fouled equalizers and slack between the engine and tender. Also the position of an out-of-balance axle relative to the locomotive center of gravity may determine the extent of motion at the cab. A. H. Fetters related that on a 4-8-2 the effects of 26,000 lb dynamic augment under the cg did not show up in the cab but the same augment in any other axle would have.[16]

Balance weights are installed opposite the parts causing the out-of-balance. The only available plane for these weights is in the wheel itself which results in an out-of-balance couple on the wheel/axle assembly. The wheel is statically balanced only.

A proportion of the reciprocating weight is balanced with the addition of an extra revolving weight in the wheel, i.e. still only balanced statically. The overbalance causes what is known as hammer blow or dynamic augment, both terms having the same definition as given in the following references. Hammer blow varies about the static mean, alternately adding to and subtracting from it with each wheel revolution.[17] In the United States it is known as dynamic augment, a vertical force caused by a designer's attempt to balance reciprocating parts by incorporating counterbalance in wheels.[18]

The term hammer blow does not describe what takes place very well since the force varies continuously and only in extreme cases when the wheel lifts from the rail for an instant is there a true blow when it comes back down.[19]

Up until about 1923 American locomotives were balanced for static conditions only with as much as 20,000 lb variation in main axle load above and below the mean per revolution from the unbalanced couple.[20] The rough riding and damage led to recommendations for dynamic balancing including defining the proportion of reciprocating weight to be balanced as a proportion of the total locomotive weight, or with Franklin buffer,[21] locomotive plus tender weight.

A different source of varying wheel/rail load, piston thrust, is sometimes incorrectly referred to as hammer blow or dynamic augment although it does not appear in the standard definitions of those terms. It also has a different form per wheel revolution as described later.

As an alternative to adding weights to driving wheels the tender could be attached using a tight coupling that would increase the effective mass and wheelbase of the locomotive. The Prussian State Railways built 2-cylinder engines with no reciprocating balance but with a rigid tender coupling.[22] The equivalent coupling for late American locomotives was the friction-damped radial buffer.[23][24]

The crankpin-and-rods weight on the wheels is in a plane outside the wheel plane location for the static balance weight. 2-plane, or dynamic, balancing is necessary if the out-of-balance couple at speed needs to be balanced. The second plane used is in the opposite wheel.

2-plane, or dynamic, balancing of a locomotive wheel set is known as cross-balancing.[12] Cross-balancing was not recommended by the American Railway Association until 1931. Up to that time only static balancing was done in America, although builders included cross-balancing for export locomotives when specified. Builders in Europe adopted cross-balancing after Le Chatelier published his theory in 1849.[25]

Maximum wheel and axle loads are specified for a particular bridge design so the required fatigue life of steel bridges may be achieved.[26] The axle load will not usually be the sum of the 2 wheel loads because the line of action of the cross balancing will be different in each wheel.[27] With the locomotive's static weight known the amount of overbalance which may be put into each wheel to partially balance the reciprocating parts is calculated.[28] Strains measured in a bridge under a passing locomotive also contain a component from piston thrust. This is neglected in the above calculations for allowable overbalance in each wheel. It may need to be taken into account.[29]

Since the rotating force alternately reduces the wheel load as well as augmenting it every revolution the sustainable tractive effort at the contact patch drops off once per wheel revolution and the wheels may slip.[30] Whether slipping occurs depends on how the hammer blow compares on all the coupled wheels at the same time.

Excessive hammer blow from high slipping speeds was a cause of kinked rails with new North American 4-6-4s and 4-8-4s that followed the 1934 A.A.R. recommendation to balance 40% of the reciprocating weight.[9]

Out-of-balance inertia forces in the wheel can cause different vertical oscillations depending on the track stiffness. Slipping tests done over greased sections of track showed, in one case, slight marking of the rail at a slipping speed of 165 mph but on softer track severe rail damage at 105 mph.[31]

The steam engine cross-head sliding surface provides the reaction to the connecting rod force on the crank-pin and varies between zero and a maximum twice during each revolution of the crankshaft.[32]

Unlike hammer blow, which alternately adds and subtracts for each revolution of the wheel, piston thrust only adds to the static mean or subtracts from it, twice per revolution, depending on the direction of motion and whether the locomotive is coasting, or drifting.

In a double-acting steam engine, as used in a railway locomotive, the direction of the vertical thrust on the slide bar is always upwards when running forward. It varies from nothing at the end of stroke to a maximum at half stroke when the angle between the con-rod and crank are greatest.[33] When the crank-pin drives the piston, as when coasting, the piston thrust is downwards. The position of maximum thrust is shown by the increased wear at the middle of the slide bars.[34]

The tendency of the variable force on the upper slide is to lift the machine off its lead springs at half-stroke and ease it down at the ends of stroke. This causes a pitching and, because the maximum up force is not simultaneous for the 2 cylinders it will also tend to roll on the springs.[33]

The dynamic balancing of locomotive wheels, using the wheels as the balancing planes for out-of-balance existing in other planes, is similar to the dynamic balancing of other rotors such as jet engine compressor/turbine assemblies. Residual out-of-balance in the assembled rotor is corrected by installing balance weights in 2 planes that are accessible with the engine installed in the aircraft. One plane is at the front of the fan and the other at the last turbine stage.[35]