Reciprocating engine dynamic properties
1. Combustion engines main principles and definitions
2. Reciprocating combustion engines architecture
3. Reciprocating engines dynamic properties
4. Engine components and systems
5. The engine management system for gasoline and Diesel engines
6. The emission Requirements & Technology
7. Engine vehicle integration
7.1 Engine layout and mounting
7.2 Engine-vehicle cooling system
7.3 Intake system
7.4 Exhaust system
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Reciprocating engine dynamic properties
Reciprocating engines dynamic properties
1. Engine operation forces
2. Engine Excitation Mechanisms (Single Cylinder Engine)
3. Key issue on masses balancing
 In line 4 cylinder engine balance
 Flat 4 cylinder engine balance
 In line 5 cylinder engine balance
 In line 6 cylinder engine balance
 V60° 6 cylinder engine balance
 V90°- 30°crank offset 6 cylinder engine balance
 V90° 8 cylinder engine balance
 V90° - flat crankshaft 8 cylinder engine balance
 John Heywood, Internal Combustion Engine Fundamentals / McGraw-Hill
 Charles F. Taylor, The internal Combustion Engine in Theory and Practice /The M.I.T. Press
 Automotive Handbook – R. Bosch/SAE
 Advanced engine technology (Heinz Heisler) – Butterworth/Heinemann
 Light and Heavy Vehicle Technology (M.J. Nunney) - CGIA, MSAE, MIMI
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Reciprocating engine dynamic properties
Engine operation forces
 The purpose of the piston-connecting rod-crankshaft assembly in the reciprocating piston-engines
is to transform the gas forces generated during combustion within the working cylinder into a piston
stroke, which the crankshafts converts into useful torque available at the flywheel. The cyclic
operation leads to unequal gas forces, and the acceleration and deceleration of the reciprocating
power-transfer components generate inertia forces.
 The mass inertia properties of the piston-connecting rod-crankshaft assembly are a composite of
the rotating mass of the crankshaft about their axis and the reciprocating masses in the cylinder
direction.
 The inertial properties of a single cylinder engine are determined by the piston mass,
exclusively oscillating mass, the crankshaft mass, exclusively rotating mass, and the
corresponding connecting-rod mass components, usually assumed to amount to 1/3 for rotating
and to 2/3 for oscillating mass.
 The inertia force components are identified as inertial forces of the 1st, 2nd, 4th order,
depending upon their rotational frequencies, relative to engine speed: in general only the 1st and 2ndorder components are significant.
 In the case of multi-cylinder engines, free moments of inertia are present when all the complete
crankshaft assembly’s inertial forces combine to generate a force couple at the crankshaft.
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Reciprocating engine dynamic properties
Inertia or mass forces
Eccitanti alterne di inerzia in un motore alternativo monocilindro
Eccitanti alterne di inerzia in un motore alternativo monocilindro
Massa
alterna ma
acc = r * w * [cos q + l cos( 2q)]
2
w = dq / dt
Force = m a * acc = FI + FII
Il Motore comeof
sorgente
vibrazioni
e rumore
The alternate motion
thedi con
rod
- crank system
Fig. 1.1
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Reciprocating engine dynamic properties
Considerations on gas forces
 The gas forces are generated by the fuel combustion acting on the piston to be
transferred to the crankshaft by connecting- rod through the expansion stroke:
therefore during the complete cycle they depend on the crankshaft position.
 When multiplied by the crank radius, the gas forces produce a periodically
variable torque value.
 The diagram shows the curve of the engine
torque as a function of crankshaft position: this
is one of the most important characteristics in
assessing the dynamic engine behavior.
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Reciprocating engine dynamic properties
Considerations on gas forces
 In multiple cylinder engines, the torque curve of the individual cylinders are
superimposed with a phase shift dependent on the numbers of cylinders,
their configuration, crankshaft design and firing sequence. The resulting
composite curve is characteristics of the engine design and covers a full working
cycle.
 Harmonic analysis can lead to a “torsional harmonics” by a series of sinusoidal
oscillations featuring whole-number multiples of the basic frequencies.
 The cyclic torque fluctuation leads to a variations of the
crankshaft’s rotation speed, called cyclic variation and
defined as:
 =
w
max
w
w
E ffe tto d e l fra zio n a m e n to s u ll’irre g o larità di c o p pia
E ffe tto d e l fra zio n a m e n to s u ll’irre g o larità di c o p pia
An
An
min
min
 Energy storage devices, as the flywheel and the clutch
spring, must be design to adequately compensate for the
variations of rotation speed in normal applications.
F ig. 1.4a
Il M o to re co m e so rgen te d i v ib ra
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Concetti generali
Engine order meaning
Engine Orders
Engine orders are simply the amplitudes of the frequency components which are the multiples
of the rotating frequency. Engine orders, which are determined by an order analysis are
extensively used in the vibration and noise work to identify the source of excitation (order) and,
hence, its frequency of an engine induced problem. For example, a four cylinder in-line engine
will always has its second order component as the dominant excitation.
2E
In four-cylinder four-stroke engines this notation is often used to denote an engine order
where the frequency is two times the engine rotational speed.
3E
Basic firing frequency of a six-cylinder four-stroke engine.
4E
Two times engine firing frequency of a four-cylinder four-stroke engine. It is the basic firing
frequency of an eight-cylinder four-stroke engine.
7
Progettazione meccanica motori – Alessandro Piccone 2004/2005
Reciprocating engine dynamic properties
Engine Excitation Mechanisms (Single Cylinder Engine) 1/5
Inertia Force - The displacement of the piston with respect to crank angle can be derived from simple
trigonometry. This can then be differentiated to yield velocity and acceleration of the piston. The expressions
obtained tend to be very complicated and can be simplified into the expression containing only first order
(once per revolution), second order (twice per revolution), and a negligible fourth order.
where
Fi = Inertia force [N]
MREC = Reciprocating mass (piston mass plus approximately 2/3 conrod mass)
θ = Crank angle (zero at top dead centre)
R = Crankshaft radius [m]
L = Conrod length [m]
N = Rotational speed [rpm]
Note: if R/L<0.3 it is accurate enough to use just the
first two terms.
Inertia force is obtained by multiplying the piston acceleration by the reciprocating mass and acts only in
the line of the cylinders.
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Reciprocating engine dynamic properties
Engine Excitation Mechanisms (Single Cylinder Engine) 2/5
Gas Forcing
The rate of rise and peak cylinder pressure of the diesel (13MPa at approximately 20° after TDC) are
approximately twice that of the gasoline with the angle the peak occurs at typically 5° earlier.
Diesel and gasoline combustion is random even at full load, worse at part load and particularly poor at
idle. Therefore, it is normal to talk about the average peak cylinder pressure (Pmax mean) and standard
deviation of Pmax. This variability both cycle to cycle and cylinder to cylinder is one source of half order
excitation.
Equilibrium of Forces
The gas force that acts on the piston also acts on
the cylinder head. The force on the piston splits into
two components, one acting down the rod and one
acting sideways on the cylinder wall. The forces are
reacted at the main bearing but a couple exists
between the horizontal reaction at the bearing and
the piston side force. This couple is equal to the
crankshaft output torque, so the crankshaft torque
is reacted by forces on the engine structure.
The gas force components of the vertical force at the
bearing is equal and opposite to the force acting on
the cylinder head, but of course the inertia component
is unbalanced.
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Reciprocating engine dynamic properties
Engine Excitation Mechanisms (Single Cylinder Engine) 3/5
Torsional Excitation of Crankshaft and Engine Structure - The total torque acting on the crankshaft of
the single cylinder engine results from the effect of the gas and inertia forces on the crank slider
mechanism.The torque resulting from piston motion is often called the INERTIA torque and is
represented by the equation:
where
ti = Inertia torque [Nm]
Torque resulting from piston motion alone for a single cylinder engine.
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Reciprocating engine dynamic properties
Engine Excitation Mechanisms (Single Cylinder Engine) 4/5
The torque resulting from gas pressure alone is represented by the equation:
where
tg = Gas torque [Nm]
Pg = Gas pressure [Nm-2]
A = Area of top of piston [m-2]
Torque resulting from gas pressure alone for a single cylinder engine.
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Reciprocating engine dynamic properties
Engine Excitation Mechanisms (Single Cylinder Engine) 5/5
The total torque is found by summing these two components.
Note that the torque from gas pressure dominates (for the engine firing case).
Total torque for a single cylinder engine
The sum of the inertia and the gas torques is present at the flywheel and
has to be reacted by the engine structure
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Reciprocating engine dynamic properties
Simplified understanding of Primary and Secondary inertia forces
Primary inertia forces. These arise from the force that must be applied to accelerate the piston over the
first half of its stroke, and similarly from the force developed by the piston as it decelerates over the second
half of its stroke. When the piston is around the mid-stroke position it is then moving at the same speed as
the crankpin and no inertia force is being generated. For an engine to be acceptable in practice, the
arrangement and number of its cylinders must be so contrived that the primary inertia forces generated in
any particular cylinder are directly opposed by those of another cylinder. Where the primary inertia forces
cancel one another out in this manner, as for example in an in-line or a horizontally opposed four-cylinder
engine with the outer and inner pair of pistons moving in opposite directions, the engine is said to be in
primary balance.
Secondary inertia forces. These are due to the angular variations that occur between the connecting rod
and the cylinder axis as the piston performs each stroke. As a consequence of this departure from straightline motion of the connecting rod, the piston is caused to move more rapidly over the outer half of its stroke
than it does over the inner half. That is, the piston travel at the two ends of the stroke differs for the
same angular movements of the crankshaft. The resulting inequality of piston accelerations and
decelerations produces corresponding differences in the inertia forces generated. Where these differing
inertia forces can be both matched and opposed in direction between one cylinder and another, as for
example in a horizontally opposed four-cylinder engine with corresponding pistons in each bank moving over
identical parts of their stroke the engine is said to be in secondary balance. It is not always practicable for
the cylinders to be arranged so that secondary balance can be obtained, but fortunately the vibration effects
resulting from this type of imbalance are much less severe than those associated with primary imbalance
and can usually be minimized by the flexible mounting system of the engine. This is confirmed by the longestablished and popular in-line four-cylinder engine, which possesses primary balance but lacks secondary
balance. However, the continuing search for greater refinement of running with this type of engine led, in the
mid 1970s, to a revival of interest in the use of twin counterbalancing shafts for cancelling out these
secondary inertia forces. (http://www.epi-eng.com/piston_engine_technology/piston_motion_basics.htm)
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Reciprocating engine dynamic properties
Key issue on masses balancing
 Some measures are employed to get partial or complete compensation of the forces
and moments of inertia generated from the crankshaft assembly.
 All masses are externally balanced when no free inertial forces or moments are
transmitted to the outside through the cylinder block. However, the remaining internal
forces and moments apply various loads and deformative-vibratory stresses to the engine
mounts and block.
 The simplest way to balance rotating mass is to use counterweights to generate an
equal force to oppose the centrifugal one.
 The 1-st order inertial forces are propagated at crankshaft speed, while the periodicity
of the 2nd-order forces is twice the crankshaft's rotational rate. These forces are
compensated by a counterweight balance system designed for opposed rotation at
a rate equal to or twice that of the crankshaft. The balance forces’ magnitudes must
equal those of the rotating inertial force vectors acting in the opposite direction.
 In multiple cylinder engine, the mutual counteractions of the various components in the
crankshaft assembly are one of the key factor determining the crankshaft configuration
and consequently the engine design. The inertial forces are balanced if the common
center of gravity for all moving components lies at the crankshaft midpoints: i.e. if
the crankshaft is symmetrical.
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Reciprocating engine dynamic properties
Firing sequence
 The firing sequence is the sequence in which combustion is initiated in the
cylinders.
 The arrangement of the crankthrows is determined by the requirements for
even firing intervals of the cylinders and for spacing the successive power
impulses as far apart as possible along the crankshaft, so as to reduce torsional
deflections or twisting effects. For any four-stroke engine the firing intervals
must, if they are to be even, be equal to 720° divided by the number of
cylinders.
 The firing sequences determines the position of the crankthrows
defined considering:
and is
 engine design configuration
 uniformity of ignition intervals
 ease of crankshaft manufacture
 minimization of crankcase load patterns
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Reciprocating engine dynamic properties
1-st and 2-nd order free forces and
moments for the most common
engine configurations
F r = m r  r w 2
F = m a  r  w 2  cos q
1
F = m a  r  w 2  l  cos 2q
2
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Reciprocating engine dynamic properties
1-st and 2-nd order free forces and
moments for the most common
engine configurations
F r = m r  r w 2
F = m a  r  w 2  cos q
1
F = m a  r  w 2  l  cos 2q
2
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Reciprocating engine dynamic properties
Optimum cylinder number vs engine displacement
500
1000
1500
2000
2500
3000
3500
4000
2Cil
3Cil
4Cil
5Cil
6Cil
8Cil
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Reciprocating engine dynamic properties
In line 4 cylinder engine
The Inline-four engine or Straight-four engine is an internal combustion engine with all four cylinders
mounted in a straight line, or plane along the crankcase.
For in-line four-cylinder engines the first and fourth crankthrows are therefore indexed on one side of the
crankshaft and the second and third throws on the other side. The firing order of these engines, numbering
from the front, may then be either 1-3-4-2 or 1-2-4-3 at 180° intervals.
The inline-four is not a fully balanced configuration. An even-firing inline-four engine is in primary balance
because the pistons are moving in pairs, and one pair of pistons is always moving up at the same time as the
other pair is moving down. However, piston acceleration and deceleration are greater in the top half of the
crankshaft rotation than in the bottom half, because the connecting rods are not infinitely long, resulting in a
non sinusoidal motion. As a result, two pistons are always accelerating faster in one direction, while the other
two are accelerating more slowly in the other direction, which leads to a secondary dynamic imbalance that
causes an up-and-down vibration at twice crankshaft speed. This imbalance is tolerable in a small, lowdisplacement, low-power configuration, where alternate weight and stroke are moderate, but the vibrations
get worse with increasing size and power. Above 2.0 L, most modern inline-four engines now use balance
shafts to eliminate the second-order harmonic vibrations. In a system invented by Dr. Frederick W.
Lanchester in 1911, and popularized by Mitsubishi Motors in the 1970s, an inline-four engine uses two
balance shafts, rotating in opposite directions at twice the crankshaft's speed, to offset the differences in
piston speed.
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Reciprocating engine dynamic properties
Flat 4 cylinder engine (boxer)
A flat-4 or horizontally-opposed-4 is a flat engine with four cylinders arranged horizontally in
two banks of two cylinders on each side of a central crankcase. The pistons are usually
mounted on the crankshaft such that opposing pistons move back and forth in opposite
directions at the same time, somewhat like a boxing competitor punching their gloves together
before a fight, which has led to it being referred to as a boxer engine.
However, the flat-4 does have a less serious secondary imbalance that causes it to rotate
back and forth around a vertical axis twice per crankshaft revolution (2nd order free moment).
This is because the cylinders cannot be directly opposed, but must be offset somewhat so the
piston connecting rods can be on separate crank pins, which results in the forces being
slightly off-centre. The vibration is usually not serious enough to require balance shafts.
The configuration is characterized by a low centre of gravity, and a very short engine length,
however the two overheads imply a higher production cost and a higher complexity of the
intake and exhaust system layout; generally the ground clearance of the bottom side can be
a problem.
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Reciprocating engine dynamic properties
SUBARU
New Diesel boxer engine
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Reciprocating engine dynamic properties
Inline 5-cylinder engine
The straight-five engine or inline-five engine is an internal combustion engine with five
cylinders aligned in one row or plane, sharing a single engine block and crankcase.
A five-cylinder engine gets a power stroke every 144 degrees (720° ÷ 5 = 144°). Since
each power stroke lasts 180 degrees, this means that a power stroke is always in effect.
Because of uneven levels of torque during the expansion strokes divided among the five
cylinders, there is increased secondary-order vibrations. At higher engine speeds, there is
an uneven third-order vibration from the crankshaft which occurs every 144 degrees.
Because the power strokes have some overlap, a five-cylinder engine may run more
smoothly than a non-overlapping four-cylinder engine, but only at limited mid-range speeds
where second and third-order vibrations are lower.
In conclusion the main disadvantage is that a straight-five design has free moments
(vibrations) of the first and second order on the cylinder plane: the first one may be
balanced by a balance shaft, rotating in opposite directions at the crankshaft's speed, and
by proper weight (rotational component) on the crankshaft itself.
Firing order can be 1-2-4-5-3 or 1-5-4-3-2: with the last one the 2° order free moment is
lower while higher the first one.
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Reciprocating engine dynamic properties
Inline 6 cylinder engine
The straight-six engine or inline-six engine is a six cylinder internal combustion engine with all six
cylinders mounted in a straight line along the crankcase. The single bank of cylinders may be oriented
in either a vertical or an inclined plane with all the pistons driving a common crankshaft.
The crankthrows are spaced in pairs with an angle of 120° between them: hence, the first and sixth
crankthrows are paired, as are the second and fifth, and likewise the third and fourth. The firing order
may then be such that no two adjacent cylinders fire in succession; that is, either 1-5-3-6-2-4 or 1-4-26-3-5 at, of course, 120° intervals.
An inline six engine is in perfect primary and secondary mechanical balance. The engine is in
primary balance because the front and rear trio of cylinders are mirror images, and the pistons move in
pairs; that is, piston #1 balances #6, #2 balances #5, and #3 balances #4, largely eliminating the polar
rocking motion that would otherwise result. Secondary imbalance is avoided because an inline six
cylinder crankshaft has six crank throws arranged in three planes offset at 120°. The result is that
differences in piston speed at any given point in rotation are effectively canceled.
Crankshafts on six cylinder engines generally have either four or seven main bearings: larger
engines and diesels tend to use the latter because of high loadings and to avoid crankshaft flex.
Many of the more sporty high-performance engines use the four bearing design because of better
torsional stiffness (e.g., BMW small straight 6's, Ford's Zephyr 6). The accumulated length of main
bearing journals gives a relatively torsionally flexible crankshaft. The four main bearing design has only
six crank throws and four main journals, so is much stiffer in the torsional domain. At high engine
speeds, the lack of torsional stiffness can make the seven main bearing design susceptible to torsional
flex and potential breakage.
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Reciprocating engine dynamic properties
V60° - 6 cylinder engine
A V6 engine is a V engine with six cylinders mounted on the crankcase in two banks of three cylinders,
usually set at either a right angle or an acute angle to each other, with all six pistons driving a common
crankshaft.
Due to the odd number of cylinders in each bank, V6 designs are inherently unbalanced, regardless of
their V-angle. All straight engines with an odd number of cylinders suffer from primary dynamic
imbalance, which causes an end-to-end rocking motion. Each cylinder bank in a V6 has an odd number
of pistons, so the V6 also suffers from the same problem unless steps are taken to mitigate it. In the
horizontally-opposed flat-6 layout, the rocking motions of the two straight cylinder banks offset each
other, while in the inline-6 layout, the two ends of engine are mirror images of each other and
compensate every rocking motion. Concentrating on the first order rocking motion, the V6 can be
assumed to consist of two separate straight-3 where counterweights on the crankshaft and a counter
rotating balancer shaft compensate the first order rocking motion. At mating, the angle between the
banks and the angle between the crankshafts can be varied so that the balancer shafts cancel each
other 90° V6 (larger counter weights) and the even firing 60° V6 with 60° flying arms (smaller
counter weights). The second order rocking motion can be balanced by a single co-rotating balancer
shaft.
The most efficient cylinder bank angle for a V6 is 60 degrees, minimizing size and vibration. While
60° V6 engines are not as well balanced as inline-6 and flat-6 engines, modern techniques for
designing and mounting engines have largely disguised their vibrations. Unlike most other angles, 60
degree V6 engines can be made acceptably smooth without the need for balance shafts. When Lancia
pioneered the 60° V6 in 1950, a 6-throw crankshaft was used to give equal firing intervals of 120°.
However, more modern designs often use a 3-throw crankshaft with what are termed flying arms
between the crankpins, which not only give the required 120° separation but also can be used for
balancing purposes. Combined with a pair of heavy counterweights on the crankshaft ends, these can
eliminate all but a modest secondary imbalance which can easily be damped out by the engine mounts.
Two firing order are possible: 1-5-3-6-2-4 or 1-2-4-6-5-3.
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Reciprocating engine dynamic properties
V90° /30° offset - 6 cylinder
engine
The Buick V6 was notable because it introduced the concept of uneven firing, as a result of using the
90° V8 cylinder angle without adjusting the crankshaft design for the V6 configuration. Rather than
firing every 120° of crankshaft rotation, the cylinders would fire alternately at 90° and 150°, resulting
in strong harmonic vibrations at certain engine speeds. These engines were often referred to by
mechanics as "shakers", due to the tendency of the engine to bounce around at idle speed. To
overcome the problem of uneven firing intervals with a 90° V6 engine, Buick in America retained threethrow crankshaft but ingeniously replaced the common, double-length, crankpins by adjacent single
crankpins that were staggered by 30° in opposite directions to produce a so-called ‘split-pin’
crankshaft.
More modern 90° V6 engine designs avoid these vibration problems by using
crankshafts with offset split crankpins and often by adding balancing shafts to
balance the 1st order free moment. Examples include the later versions of the Buick V6,
and earlier versions of the Mercedes-Benz V6 and AUDI V6. The Mercedes V6, although
designed to be built on the same assembly lines as the V8, used split crankpins, a counterrotating balancing shaft, and careful acoustic design to make it almost as smooth as the
inline-6 it replaced. However, in later versions Mercedes changed to a 60° angle, making
the engine more compact and allowing elimination of the balancing shaft. Despite the
difference in V angles, the Mercedes 60° V6s were built on the same assembly lines as
90° V8s.
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Reciprocating engine dynamic properties
V90° /30° offset - 6 cylinder
engine
Balancing shaft to balance
the 1st order free moment
30°Split crank
pin
AUDI – V6/90° Gas
engine
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Reciprocating engine dynamic properties
V90° - 8 cylinder engine
Share the same crank pin
There are two classic types of V8s which differ by crankshaft:
 The cross-plane or two-plane crankshaft (crank pins at a 90° angle) is the configuration used in most V8 road cars. The
first and last of the four crank pins are at 180° with respect to each other as are the second and third, with each pair at 90°
to the other, so that viewed from the end the crankshaft forms a cross. The last cylinder is not in the same position as the first,
so there is end-to-end vibration again, which can be solved by adding counterweights to the crankshaft which balance the
forced created by the pistons This makes the cross-plane V8 a slow-revving engine that cannot speed up or slow down
very quickly compared to other designs, because of the greater rotating mass. While the firing of the cross-plane V8 is
regular overall, the firing of each bank is LRLLRLRR. In stock cars with dual exhausts, this results in the typical V8 burble
sound that many people have come to associate with American V8s, In all-out racing cars it leads to the need to connect
exhaust pipes between the two banks to design an optimal exhaust system, resulting in an exhaust system that resembles a
bundle of snakes as in the Ford GT40. This complex and encumbering exhaust system has been a major problem for singleseater racing car designers, so they tend to use flat-plane crankshafts instead.
 The flat-plane or single-plane crankshaft (crank pins at 180°) - In its simplest form, it is basically two straight-4 engines
sharing a common crankshaft. When the engine runs, the pistons shoot up and down, the first and last pistons of the bank
occupying matching positions on either end of the array, so that the force on both ends is equal and the system is balanced.
However, this simple configuration, with a single-plane crankshaft, has the same secondary dynamic imbalance problems
as two straight-4s, resulting in vibrations in large engine displacements. The induced vibrations can be eliminated by the use
of balance shafts, with a counter rotating pair flanking the crankshaft to counter second order vibration transverse to the
crankshaft centerline. As it does not require counterweights for the primary balance, the crankshaft has less mass and
thus inertia, allowing higher rpm and quicker acceleration. The design was popularized in modern racing with the
Coventry Climax 1.5 L (~92 cu in) V8 that evolved from a cross-plane to a flat-plane configuration. Flat-plane V8s on road cars
come from Ferrari, (every V8 model they ever made, from the 1973 308 GT4, to today's F430 and California), Lotus (the Esprit
V8 ), and TVR (the Speed Eight). This design is popular in racing engines, the most famous example being the Cosworth DFV.
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Reciprocating engine dynamic properties
V90° - 8 cylinder engine
BMW– V8/90°
Motorsport
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Reciprocating engine dynamic properties
V90° - 8 cylinder engine
20
8 cil V90°- Cross-plane crankshaft
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