Engine balance
Engine balance refers to how the forces (resulting from combustion or rotating/reciprocating components) are balanced within an internal combustion engine or steam engine. The most commonly used terms are "primary balance" and "secondary balance". "First-order balance" and "second-order balance" are also used. Unbalanced forces within the engine can lead to vibrations. Causes of imbalance. Although some components within the engine (such as the connecting rods) 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 (where the pistons  are vertical), 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 (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. Types of imbalance . Reciprocating imbalance. 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, but opposite in direction on the same plane. Types of "reciprocating phase imbalance" are: Types of "reciprocating plane imbalance" are: In engines without overlapping power strokes (such as engines with four or fewer cylinders), the pulsations in power delivery vibrate the engine rotationally on the "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: Torsional vibration. Torsional vibration develops when torque impulses are applied to a shaft at a frequency that matches its resonant frequency and the applied torque and the resistive torque act at different points along the shaft. The shaft must be designed such that its resonant frequency is outside the projected operating speed range, or if this is not possible, e.g. for reasons of weight or cost, it must be fitted with a damper. Vibration occurs around the axis of a crankshaft, since the connecting rods are usually located at 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. Primary imbalance. "Primary imbalance" produces vibration at the frequency of crankshaft rotation, i.e. the fundamental frequency (first harmonic) of an engine. Secondary imbalance. "Secondary imbalance" produces vibration at twice the frequency of crankshaft rotation. Cause. Because of the finite length of the connecting rod, piston motion is asymmetrical: A piston travels further during the top half of the crankshaft's rotation than during the bottom half - in the same  time. Thus the acceleration through TDC is considerably greater than that through BDC and the inertial forces of two pistons (and part of the connecting rods) moving with a phase difference of 180° will not completely cancel out, leaving a net upward force twice per crank revolution. This particularly affects 2 and 4 cylinder inline engines, and above a capacity of about 2.5 litres, they require balance shafts. The difference in distance travelled is due to the movement of the connecting rod. At 90 degrees after top dead centre (TDC) the crankshaft end of the connecting rod is exactly  at the halfway point of its stroke; however, the angle of the connecting rod (i.e. the left–right movement, when looking down the crankshaft) means that the piston end of the connecting rod must be lower than the halfway point, in order for the connecting rod 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 conventional 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: Though the pistons do not move in exactly this fashion, it is still a useful representation for analyzing their 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 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 engine speeds. 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 in V6 engines and large displacement inline-four engines. 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. Straight-twin engines most commonly use the following configurations: Straight-three engines most commonly use a 120° crankshaft design and have the following characteristics: Straight-four engines (also called "inline-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 design and have the following characteristics: Straight-six engines typically use a 120° crankshaft design, a firing order of 1–5–3–6–2–4 cylinders and have the following characteristics: V engines. V-twin engines 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: Flat engines. [Precision: A 'flat' engine is not necessarily a 'boxer' engine. A 'flat' engine may either be a 180-degree V engine or  a 'boxer' engine. A 180-degree V 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 connecting rod has its own crank throw which is positioned 180 degrees from the crank throw of the opposed cylinder.] Flat-twin engines typically use 180° crankshafts and 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: Steam locomotives. 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 two  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 three- and four-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 two steam engines and their coupled wheels (some similar motions may be caused by irregularities in the track running surface and stiffness). 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 three degrees to which balancing may be pursued. The most basic is static balancing of the off-centre 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-centre 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 two-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. Sources of unbalance. All the driving wheels have an out-of-balance which is caused by their off-centre 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 centre of percussion. This position was measured by swinging the rod as a pendulum. 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-degree separation causes a swaying couple. 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 -inch 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, eight locomotives were tested at the Louisiana Purchase Exposition in 1904. The three measurements were: 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 centre 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 two-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. Two-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. Two-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 two 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 is 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 two 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 two 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. References. Citations Sources