Engine balance


Engine balance refers to how the forces are balanced within an internal combustion engine or steam engine. The most commonly used terms are primary balance and secondary balance. Unbalanced forces within the engine can lead to vibrations.

Causes of imbalance

Although some components within the engine have complex motions, all motions can be separated into reciprocating and rotating components, which assists in the analysis of imbalances.
Using the example of an inline engine, the main reciprocating motions are:
While the main rotating motions that may cause imbalance are:
The imbalances can be caused by either the static mass of individual components or the cylinder layout of the engine, as detailed in the following sections.

Static mass

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.

Cylinder layout

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. 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.

Types of imbalance

Reciprocating imbalance

A reciprocating imbalance is caused when the linear motion of a component 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:
Types of reciprocating plane imbalance are:
In engines without overlapping power strokes, the pulsations in power delivery vibrates the engine back and forth rotationally on X-axis, similar to a reciprocating imbalance.

Rotating imbalance

A rotating imbalance is caused by uneven mass distributions on rotating assemblies
Types of rotating phase imbalance are:
Types of rotating plane imbalance are:
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. 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.

Primary balance

The primary balance of an engine refers to vibrations which occur at the fundamental frequency of the engine speed. These vibration therefore occur at a frequency equal to the crankshaft speed. A primary vertical imbalance can be present in an engine with an odd number of cylinders, since the inertia of each piston moving upwards is not cancelled out by another piston moving downwards.
In a four-stroke engine, each cylinder has a power stroke once every two rotations of the crankshaft, which can cause vibrations at half of the crankshaft speed. These vibration are sometimes referred to as "half order" vibrations. Alternatively, sometimes all of the non-sinusoidal vibrations are referred to as secondary vibrations and all the remaining vibrations are referred to as primary vibrations.

Secondary balance

Cause of imbalance

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 the crankshaft end of the conrod is exactly at the halfway point of its stroke, however the angle of the conrod 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. 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 during the top half of crankshaft rotation than during the bottom half. In the case of an inline-four engine, 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, 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:
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.

Effects and reduction measures

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.
In an engine where pairs of pistons move in sync with each other, the secondary imbalance forces are twice as large and half as frequent than in engines where all pistons are out of phase with each other.

Effect of cylinder layout

For engines with more than one cylinder, factors such as the number of pistons in each bank, the V angle and the firing interval usually determine whether reciprocating phase imbalances or torsional imbalances are present.

Straight engines

s most commonly use the following configurations:
Straight-three engines most commonly use a 120° crankshaft and have the following characteristics:
Straight-four engines typically use an 'up-down-down-up' 180° crankshaft design and have the following characteristics:
Straight-five engines typically use a 72° crankshaft and have the following characteristics:
Straight-six engines typically use a 120° crankshaft, a firing order of 1-6-2-5-3-4 cylinders and have the following characteristics:
s have the following characteristics:
V4 engines come in many different configurations in terms of the 'V' angle and crankshaft configurations. Some examples are:
V6 engines are commonly produced in the following configurations:
s typically use a 360° crankshaft, separate crank throws and have the following characteristics:
Flat-four engines typically use a left-right-right-left crankshaft configuration and have the following characteristics:
Flat six engines typically use a boxer configuration and have the following characteristics:
This section is an introduction to the balancing of two steam engines connected by driving wheels and axles as assembled in a railway locomotive.
The effects of unbalanced inertias in a locomotive are briefly shown by describing measurements of locomotive motions as well as deflections in steel bridges. These measurements show the need for various balancing methods as well as other design features to reduce vibration amplitudes and damage to the locomotive itself as well as to the rails and bridges. The example locomotive is a simple, non-compound, type with 2 outside cylinders and valve gear, coupled driving wheels and a separate tender. Only basic balancing is covered with no mention of the effects of different cylinder arrangements, crank angles, etc. since balancing methods for 3 and 4 cylinder locomotives can be complicated and diverse. Mathematical treatments can be found in 'further reading'. For example, Dalby's "The Balancing of Engines" covers the treatment of unbalanced forces and couples using polygons. Johnson and Fry both use algebraic calculations.
At speed the locomotive will tend to surge fore-and-aft and nose, or sway, from side to side. It will also tend to pitch and rock. This article looks at these motions that originate from unbalanced inertia forces and couples in the 2 steam engines and their coupled wheels. The first two motions are caused by the reciprocating masses and the last two by the oblique action of the con-rods, or piston thrust, on the guide bars.
There are 3 degrees to which balancing may be pursued. The most basic is static balancing of the off-center features on a driving wheel, i.e. the crankpin and its attached parts. In addition, balancing a proportion of the reciprocating parts can be done with additional revolving weight. This weight is combined with that required for the off-center parts on the wheel and this extra weight causes the wheel to be overbalanced resulting in hammer blow. Lastly, because the above balance weights are in the plane of the wheel and not in the plane of the originating unbalance, the wheel/axle assembly is not dynamically balanced. Dynamic balancing on steam locomotives is known as cross-balancing and is 2-plane balancing with the second plane being in the opposite wheel.
A tendency to instability will vary with the design of a particular locomotive class. Relevant factors include its weight and length, the way it is supported on springs and equalizers and how the value of an unbalanced moving mass compares to the unsprung mass and total mass of the locomotive. The way the tender is attached to the locomotive can also modify its behaviour. The resilience of the track in terms of the weight of the rail as well as the stiffness of the roadbed can affect the vibration behaviour of the locomotive.
As well as giving poor human ride quality the rough riding incurs maintenance costs for wear and fractures in both locomotive and track components.

Measuring the effects of unbalance

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.
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.
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".
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.

Static balancing of wheels

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.

Static balancing of reciprocating weight

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.
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.
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.
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. 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, 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. The equivalent coupling for late American locomotives was the friction-damped radial buffer.

Dynamic balancing of wheel/axle assembly

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. 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.

Determination of acceptable hammer blow

Maximum wheel and axle loads are specified for a particular bridge design so the required fatigue life of steel bridges may be achieved. 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. 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. 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.

Response of wheel to hammer blow

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. 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.
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.

Piston thrust from connecting rod angularity

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.
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. 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.
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.

Similarities with balancing other machinery

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.