Chapter 2

Power Generation Characteristics of Internal Combustion Engines

2.1 Introduction

The engine plays a dominant role in overall vehicle performance and it is essential to learn about its behaviour prior to performing vehicle studies. The internal combustion engine is a complicated system and its thorough analysis requires a multi-disciplinary knowledge of physics, chemistry, thermodynamics, fluid dynamics, mechanics, electrics, electronics and control. Electronics and control are becoming crucial parts of all modern engines and engine control units (ECUs) manage the engine operating parameters to try to achieve a good compromise between drivability, fuel consumption and emissions control.

Traditionally, in the literature on internal combustion engine design, the material discussed included: working fluids, thermodynamics, gas dynamics, combustion processes and chamber design, heat transfer, engine efficiency, friction, emissions and pollution. Also, the dynamics of engine moving parts and loads acting on the engine bearings and components are traditionally discussed in books on mechanism design or the dynamics of machinery. On the other hand, in areas related to the vehicle powertrain designs, the engine properties are needed as inputs to the system. Such vital information suitable for powertrain analysis cannot be found in the aforementioned books. Students have always seemed to have difficulties relating the engine design materials to powertrain design requirements. Moreover, it has been found that the engine performance characteristics described by full throttle engine maps usually given in the engine design books are misleading and confuse students, due to the fact that they try to explain the vehicle motion without sufficient information.

In this chapter, a review of internal combustion engine behaviour over a full range of operations is provided. This includes torque generation principles and characteristics as well as engine modelling for both petrol and diesel engines. This chapter is not intended to explain those materials generally covered by books written on the topics of internal combustion engines; instead, the torque generation principles of engines that are required in powertrain analysis will be the focus of this chapter.

2.2 Engine Power Generation Principles

In vehicle powertrain studies, the power generation properties of engines are of vital importance as the torque produced by the engine drives the vehicle in different and diverse driving situations. Internal combustion engines convert chemical energy contained in the fuel into mechanical power that is usually made available at a rotating output shaft. The fuel includes chemical energy that is converted to thermal energy by means of combustion or oxidation with air inside the engine. The pressure of the gases within the engine builds up because of the combustion process that is generating heat. The high pressure gas then expands and pushes the surfaces inside the engine. This expansion force moves the mechanical linkages of the engine and eventually rotates a crankshaft. The output shaft of an internal combustion engine is usually coupled to a gear box, as in the case of transport vehicles.

Most internal combustion engines are of the reciprocating type, having pistons that move back and forth inside cylinders fixed to the engine blocks. Reciprocating engines range from single cylinder engines up to several cylinders arranged in many different geometric configurations. Internal combustion engines can be classified in different ways but the classifying method according to ignition type is most common. Two major ignition types are spark-ignition (SI) and compression-ignition (CI) types. Details of the combustion processes in SI and CI engines depend entirely on the characteristics of the fuel used in each type. Since the combustion process is quite different between SI and CI engines, the types and quantities of the various exhaust emission materials that are formed vary as a result.

2.2.1 Engine Operating Modes

The slider-crank mechanism is a basic linkage to convert the reciprocating motion of the piston into the rotating motion of a crankshaft in reciprocating engines. The piston acts as the slider and moves inside the cylinder and with the provision of the valves and manifolds, an engine with the ability to compress and expand gases results. Figure 2.1 shows the schematic of a typical slider-crank mechanism used in a single cylinder engine. At zero crank angle θ, the piston is at the position known as top dead centre (TDC), because the piston speed reaches zero at this point. Rotation of the crank arm through 180° displaces the piston from TDC to the other bottom extreme, again with zero piston speed, called bottom dead centre (BDC). The total distance that the piston travels during this 180° rotation of the crank is called one stroke that is twice the radius of the crank. Returning from BDC to TDC will take another 180° rotation of the crank and the piston behaviour is reverse of that between zero and 180°.

Reciprocating engines, both spark ignition and compression ignition, need four basic phases, namely intake (or induction), compression, combustion (or power) and exhaust to complete a combustion cycle.

2.2.1.1 Four-Stroke Engines

Some engines are designed to have four distinctive strokes for the piston in a complete working cycle and are called four stroke engines. In a four-stroke engine, the piston has to go through four strokes in order to complete the cyclic thermodynamic processes. The crankshaft must perform two full turns in order that the piston completes four strokes. Figure 2.2 illustrates the basic parts of a four-stroke engine including the cylinder, the piston, the cylinder head, ports and valves.

Starting from TDC at the beginning of intake stroke, the inlet valve opens and the outlet valve closes. With the piston motion towards the BDC, fresh air (or mixture) flows into the cylinder. At BDC, the first stroke is complete and the inlet valve closes and the piston moves towards the TDC, compressing the gases inside the cylinder. At the TDC, the compression stroke ends and while both valves are closed, the power stroke starts with combustion and the resulting gases expand, pushing the piston down to the BDC at which the fourth and last stroke starts by opening the outlet valve to let the pressurized combustion products leave the cylinder. The motion of the piston to TDC helps the exhaust process by pushing the gases out. Table 2.1 summarizes these four strokes.

Table 2.1 The four strokes of a reciprocating engine.

Note that the valve opening/closing crank angles given in Table 2.1 are only theoretical values and will be different in practice. For example, when the next intake process starts, it is better to leave the outlet valve open for a while in order that the burned gases leaving the combustion chamber continue their flow due to their momentum (also the fresh air can push them out). This will provide more room for fresh air and increase the combustion efficiency. Similarly when the piston is starting to move towards the TDC at the beginning of compression stroke, it is better to leave the inlet valve open for a while, so that the incoming air continues to flow into the cylinder due to its momentum.

2.2.1.2 Two-Stroke Engines

A two-stroke engine performs the four basic phases of a combustion cycle only in two piston strokes. In the two-stroke engine, the inlet and exhaust valves are eliminated and the ports for the entrance and exit of the gases are built on the cylinder walls and crankcase instead. The piston covers and uncovers the ports when it moves back and forth inside the cylinder (see Figure 2.3).

Let us start the cycle with the combustion stroke. The mixture in the combustion chamber is ignited in the same way as in the four-stroke engine at the top of the stroke. The piston moves downwards and uncovers the outlet port, allowing the pressurized burned gases to flow out of the cylinder. The downward movement of the piston at the same time compresses the gases in the crankcase. Further down, the piston uncovers the transfer port and the compressed gases in the crankcase flow through the channel into the combustion chamber and push the combustion products out through the outlet port. So, in a single stroke of the piston both combustion and exhaust cycles are accomplished. The upward movement of the piston compresses the gases in the combustion chamber and simultaneously depressurizes the crankcase to allow the pressure of the atmosphere to fill the crankcase with fresh air. Further up, the compression stroke will end and a new cycle will start by the combustion process. Again in a single upward piston stroke, both induction and compression cycles are accomplished.

It appears that two-stroke engines are more advantageous since they perform the power cycle faster than four-stroke engines and do not need the valves and valve trains either. But, in practice, two-stroke engines are not as efficient as four-stroke cycle engines, especially at high speeds. Two-stroke engines are generally used in small SI engines for motorcycles and in large CI engines for locomotives and marine applications that work in lower speeds. At large CI engine sizes, the two-stroke cycle is competitive with the four-stroke cycle, because in the CI cycle, only air is lost in the cylinder (see Section 2.2.2).

In the rest of this chapter it will be assumed that the engine works only on the four-stroke basis.

2.2.2 Engine Combustion Review

It is common to refer to engines as either petrol (gasoline in the USA) or diesel, according to the nature of the ignition and combustion, however, the terms ‘spark ignition’ (SI) and ‘compression ignition’ (CI) are also used. In SI engines the air and fuel are usually premixed before the initiation of combustion by sparking. In CI engines the fuel burns as it is injected into hot compressed air and produces a combustible mixture.

In order to have ideal combustion, the amount of fuel must be related exactly to the amount of intake air. In fact, according to the burning chemistry, for a specific amount of air molecules, there must be specific number of fuel molecules for perfect burning of the fuel. This fuel/air ratio is called the stoichiometric ratio and the objective in engine combustion is to produce fuel/air ratios as close to the stoichiometric as possible. More details will be discussed in the following sections.

2.2.2.1 SI Engine Combustion

In SI engines, the fuel is mixed with the air in the intake system prior to entry to the cylinder. In the past, carburettors were used for the homogenized mixing of the air and fuel. The basis of a carburettor operation was a pressure drop when air passed through a venturi and an appropriate amount of fuel (at higher pressure) surged into the air flow at the venturi throat from the float chamber. The throttle opening controlled the air flow inside the venturi and as a result the amount of fuel entering the engine was adjusted accordingly. This type of fuel metering was very sensitive to atmospheric changes and could not maintain accurate fuel to air ratios and resulted in poor engine performance and high levels of pollution.

In newer generations of engines, fuel injection systems that replace the carburettors inject the fuel in more accurate amounts. Injection systems are electronically controlled systems – the air flow rate must be measured and the desired amount of fuel per cylinder that is required for a proper combustion must be calculated and injected accordingly.

Currently there are two different fuel injection systems, namely, throttle body injection (TBI) and multi-port injection (MPI). TBI systems are something like a carburettor which contains one or more injectors. When fuel is injected, it will be mixed with the air and the mixture will move in the inlet manifold exactly like in the case of carburettor. In MPI systems, instead of having a throttle body for all cylinders, air is moved directly to the inlet port of each cylinder without mixing. The fuel is injected just at the entrance to each cylinder and is mixed with the air. In MPI systems, therefore, the number of injectors is equal to the number of cylinders. MPI systems are more efficient than TBI systems; first, because the fuel is more precisely metered for each cylinder in MPI systems and, second, the fuel is completely moved into the cylinder, whereas in TBI some part of the fuel in contact with the surface of intake manifold will stick and remain.

The newer generation of injection systems for SI engines includes the gasoline direct injection (GDI) systems that use the injection concept in CI engines (see Section 2.2.2.2) in which the fuel is injected into the combustion chamber inside the cylinder. These systems allow the achievement of both the fuel efficiency of a diesel engine and the high output of a conventional petrol engine.

Regardless of the injection type, the SI engine cycle can be described as follows. During the intake process the inlet valve is open and the air and fuel mixture is inducted in the cylinder. After the inlet valve closes, the cylinder contents are compressed by the piston movement upwards. Before the piston gets to the TDC, a high voltage electric discharge across the spark plug starts the combustion process. Burning the fuel during the combustion process increases the temperature in the cylinder to a very high peak value. This, in turn, raises the pressure in the cylinder to a very high peak value. This pressure forces the piston down and a torque about the crank axis is developed. The expansion stroke causes the pressure and the temperature to drop in the cylinder. For a given mass of fuel and air inside the cylinder, an optimum spark timing produces the maximum torque.

Before the end of the expansion stroke, the exhaust valve starts to open and the burned gases find a way through the valve into the exhaust port and into the manifold. Pressure in the cylinder is still high relative to the exhaust manifold and this pressure differential causes much of the hot products to be blown out of the cylinder before the piston starts its upward motion. The piston motion during the exhaust stroke transfers the remaining combustion products into the exhaust manifold. The timing for the exhaust valve opening is important since an early opening will reduce the work on the piston (less output torque) and a late opening will need external work delivered to the piston during the exhaust phase (see Section 2.2.3.1).

The intake valve opens before TDC and the exhaust valve closes some time after in order to help the combustion products trapped in the clearance volume when the piston reaches TDC to leave and to replace them with a fresh mixture. This period when both the inlet and exhaust valves are open is called valve overlap. The combustion process of SI engines is divided into four phases, namely ignition, flame development, flame propagation and flame termination [1]. Flame development is sometimes taken as part of the first phase and a total of three phases is considered [2]. The flame development interval is between the spark discharge and the time when a fraction of the fuel-air mixture has burned. This fraction is defined differently such as 1, 5 or 10%. During this period, although ignition occurs and the combustion process starts, very little pressure rise and useful work is achieved.

In the interval between the end of the flame development stage and the end of the flame propagation process, usually the bulk of the fuel and air mass is burned and an energy release of about 90% is achieved. During this period, the pressure in the cylinder is greatly increased and thus the useful work of an engine cycle is the result of the flame propagation period. The remaining 5–10% of the fuel-air mass burning takes place in the flame termination phase. During this time, the pressure quickly decreases and combustion stops. The combined duration of the flame development and propagation phases is typically between 30° and 90° of the crank angle.

2.2.2.2 CI Engine Combustion

The operation of a typical four-stroke CI engine during the intake stroke is the same as for the intake stroke in an SI engine in terms of valve openings. The only difference is that air alone is inducted into the cylinder in this stroke. The compression ratio is higher for CI engines and during the compression stroke, air is compressed to higher pressures and temperatures than SI engines. The fuel is injected directly into the cylinder in the combustion stroke where it mixes with the very hot air, causing the fuel to evaporate and self-ignite and combustion to start. The power stroke continues as combustion ends and the piston travels towards BDC. The exhaust stroke is also the same as for SI engines.

In a CI engine at a given engine speed, the air flow is unchanged and the output power is controlled by only adjusting the amount of fuel injected. The nature of the fuel-air mixture in compression ignition engines is essentially different from SI engines. In SI engines, a homogeneous mixture is available and during the combustion process a flame moves through the mixture. In CI engines, however, the liquid fuel that is injected at high velocities through small nozzles in the injector tip, atomizes into small drops and penetrates into the hot compressed air inside combustion chamber. As a result, the nature of combustion is an unsteady process occurring simultaneously at many spots in a very non-homogeneous fuel-air mixture.

The process involved in the combustion of fuel after injection can be divided in four phases. The first phase is ‘atomization’ in which the fuel drops break into very small droplets. In the second phase called ‘vaporization’, due to the hot air temperatures resulting from the high compression, the droplets of fuel evaporate very quickly. After vaporization, because of the high fuel injection velocity and the swirl and turbulence of the air, in the ‘fuel-air mixing phase’ the fuel vapour will mix with the air to form a combustible mixture. Since the air temperature and air pressure are above the fuel's ignition point, spontaneous ignition of portions of the already-mixed fuel and air occurs in the ‘combustion phase’. The cylinder pressure increases as combustion of the fuel-air mixture occurs. It also reduces the evaporation time of the remaining liquid fuel. The injection of liquid fuel into the cylinder will continue after the first fuel injected is already burning. After the start of combustion when all the fuel-air mixture that is in a combustible state is quickly consumed, the rest of the combustion process is controlled by the rate at which the fuel can be injected. Since only air is compressed in the cylinder during the compression stroke, much higher compression ratios are used in CI engines compared to those of SI engines. Compression ratios of modern CI engines range from a minimum of 14 up to 24.

Engine types include naturally aspirated engines where atmospheric air is inducted directly, turbocharged engines where the inlet air is compressed by an exhaust-driven turbine-compressor combination, and supercharged engines where the air is compressed by a mechanically driven pump or blower. Both charging systems enhance engine output power by increasing the air mass flow per unit displaced volume, thereby allowing more fuel combustion energy.

2.2.3 Engine Thermodynamics Review

During real engine cycles (intake, compression, combustion and exhaust), the composition of the substances inside the process is changing. The variable state of gases makes the analysis difficult and to make the analysis manageable, real cycles are approximated with ideal air-standard cycles. This involves the following assumptions:

• The gas mixture in the cylinder is treated as an ideal gas with constant specific heats for the entire cycle.
• The real open cycle, in which the fresh air enters and combustion products leave it, is changed into a closed cycle by assuming that the exhaust gases are fed back into the intake system.
• Since air alone as the ideal gas cannot combust, the combustion process is replaced with a heat addition phase of equal energy value.
• The exhaust process is replaced with a closed system heat rejection process of equal energy value.

The processes are also idealized as reversible with the following properties:

• The intake and exhaust strokes are both assumed to be at constant pressure.
• Compression and expansion strokes are approximated by isentropic processes, and in spite of having small friction work and heat transfer within a cycle, these strokes are assumed to be reversible and adiabatic.
• The combustion process is idealized by a constant-volume process for SI engine and a constant-pressure process for CI engine.
• Exhaust blow-down is approximated by a constant-volume process.

Air standard cycles are the basis of determining the engine thermal efficiency and performance. These cycles are plotted in the pressure-displacement plane as the processes involved contain constant pressure, constant volume or isentropic processes, as explained above. On the other hand, the work carried out by pressure forces acting on the piston can be evaluated by integral. Therefore, the work done during a single engine cycle is the area enclosed by the cycle process curves on the pressure-volume diagram. Plots of pressure versus volume for reciprocating engines are called indicator diagrams since they are the basis for the estimation of the engine performance.

2.2.3.1 Spark Ignition Engines

The Otto cycle shown in Figure 2.4 is the theoretical cycle commonly used to represent the processes of the spark ignition engines. As described earlier, a fixed mass of air as working fluid is assumed to be used in the cycle and the piston moves from BDC to TDC and back again. The intake stroke of the Otto cycle starts with the piston at TDC (point 0) in a constant inlet pressure. The intake process of a real throttled engine will differ due to pressure losses in the air flow, therefore, Figure 2.4 represents an open throttle condition only. The compression stroke is an isentropic process from BDC to TDC (from point 1 to point 2). In a real engine, the intake valve is not fully closed at the beginning of the stroke and the spark plug is activated before TDC and thus the cycle is affected by these events. The heat input process from point 2 to point 3 represents the combustion process which in real engines occurs at close to constant-volume conditions. During this process an amount of energy is added to the air that raises the temperature to the peak cycle temperature at point 3. This increase of temperature during a constant-volume process also results in a large pressure at point 3. The expansion stroke (from point 3 to point 4) that follows combustion is approximated by an isentropic process in the Otto cycle. This is an acceptable approximation, as long as the stroke is frictionless and adiabatic.

The Otto cycle represents the exhaust blow-down process with a constant-volume pressure reduction process from point 4 back to point 1. The exhaust stroke occurs as the piston travels from BDC to TDC. The process from point 1 to point 0 is the exhaust stroke that occurs at a constant pressure of one atmosphere. At this point after two crank revolutions, the piston is at TDC and a new cycle begins.

Note that the processes from point 0 to point 1 and from point 1 to point 0 in the Otto cycle are thermodynamically opposite and cancel each other out during one complete cycle. Thus in cycle analysis the bottom line will no longer be needed.

A summary of the thermodynamic analysis will be presented for the cycle by considering the property of each stroke. Useful relationships for ideal gas are given in Table 2.2.

Table 2.2 Ideal gas formulae.

1	Basic relationship
2	In terms of specific volume
3	In terms of specific mass
4	Isentropic (adiabatic-reversible) process
5	Isentropic process
6	Constant volume process
7	Constant pressure process

The thermal efficiency η_T of the Otto cycle is defined by the ratio of net specific output work w_net (work per unit mass) to the net input specific energy q_in (energy per unit mass):

(2.1)

The specific output work is obtained by subtracting the outgoing energy q_out in the exhaust stroke (4–1) from the input energy during the combustion stroke (2–3):

(2.2)

in which from basic equations at constant volume (Table 2.2):

(2.3)

(2.4)

where c_v is the specific heat at constant volume and T is temperature. Substituting in Equation (2.1) gives:

(2.5)

The thermal efficiency can be simplified in the following simple form by using existing relations between the temperatures in isentropic compression and expansion strokes:

(2.6)

For an isentropic compression cycle (1–2), one can write:

(2.7)

in which v is specific volume and is the ratio of specific heats at constant pressure and constant volume. Defining the compression ratio r_C as the ratio of maximum to minimum absolute air volumes:

(2.8)

and combining Equations (2.6)–(2.8) will result in:

(2.9)

Equation (2.9) is very useful since if one knows only the compression ratio, the thermal efficiency can be determined. It also shows that the compression ratio is a fundamental parameter of the engines and that increasing compression ratio increases the cycle thermal efficiency. Figure 2.5 illustrates this relation graphically.

In practice, the compression ratio of SI engines is limited by the condition that the fuel-air mixture should not spontaneously start burning due to the high temperature reached after the compression phase. This will in turn depend on the fuel octane number. Higher octane numbers allow higher compression ratios. Due to this limitation, commercial SI engines are normally designed with compression ratios less than 10.

Additional equations for the Otto cycle can be obtained as follows.

The total combustion energy (heat) in one cycle is:

(2.10)

where m_m and m_f are the mixture and fuel masses, and η_c and Q_HV are the combustion efficiency and fuel heating value respectively. From Equation (2.10) the net temperature increase can be found:

(2.11)

in which AF is the air to fuel mass ratio and m_r is the exhaust residual mass of a cycle. By using Equations 2.1, 2.3 and 2.9, the net specific work is found:

(2.12)

The net work of the cycle is then:

(2.13)

Indicated mean effective pressure is defined as:

(2.14)

Indicated power P_i at a specific revolution speed n (rpm) is (in a four-stroke engine):

(2.15)

If mechanical efficiency η_m is known, the brake power (that is output mechanical power) and brake mean effective pressure are obtained as:

(2.16)

(2.17)

Engine output (brake) torque is:

(2.18)

The brake specific fuel consumption (BSFC) is defined as the ratio of fuel mass rate to the brake power:

(2.19)

The engine volumetric efficiency is defined as the ratio of air mass inducted into the cylinder m_a to the total air mass displaced by the piston (at the ambient air conditions):

(2.20)

in which is the density of ambient air and is the swept volume by the piston.

2.2.3.2 Compression Ignition Engines

In an ideal air standard diesel cycle shown in Figure 2.6, combustion takes place at a constant pressure rather than at the constant volume of the Otto cycle. The justification is that by controlling the fuel injection rate and thus the rate of chemical energy release during the expansion of the combustion gases, a constant pressure process could be achieved.

The thermodynamic analysis of the CI cycle is similar to that of the Otto cycle. However, in addition to the volumes V₁ and V₂ of the Otto cycle, in this case, a third volume V₃ also plays a role. Therefore, a ‘cut-off ratio’ is defined to relate this value to V₂ as:

(2.21)

The right-hand side equality holds owing to the constant pressure process. Starting with Equation (2.1) for the thermal efficiency of the cycle, the net specific output work is similar to Equation (2.2) but differs in that the input energy is given at a constant pressure rather than at a constant volume. Thus:

(2.22)

Substituting Equations (2.22) and (2.2) into Equation (2.1) results:

(2.23)

This equation cannot be simplified as in the case of SI engine. The simplest form of the equation reads:

(2.24)

that is, a function of both the compression and cut-off ratios. Other useful relations for the diesel cycle are obtained below.

The total combustion energy (input heat) in one cycle is (constant pressure process):

(2.25)

Equation (2.11) of the Otto cycle will have a minor change (c_p replaces c_v):

(2.26)

The rest of the relations are similar for the diesel cycle and those obtained for SI engines (Equations (2.12)–(2.20)) can be used also in this case.

2.2.3.3 Comparison of Standard SI and CI Cycles

The standard cycles for SI and CI engines may be compared for an equal displacement, as Figure 2.8 shows. For this case, the input condition is also similar and the difference in process 1–2 is due to the different compression ratios. It is clear that the SI cycle has a larger peak pressure and the surface under the closed cycle 1–2–3–4–1 of the SI engine is greater than that of 1–2_D–3_D–4–1 of the CI engine. Thus, the indicated specific work of the SI cycle is greater than the work of the CI engine with a similar displacement.

It is also clear from Figure 2.8 that the maximum pressure of the SI cycle is considerably higher than that of the CI engine. However, CI engines with higher compression ratios can have pressures as high as those of SI engines since in the engine design this would be the mechanical limitation. A different comparison, therefore, can be made by having both engines with equal high pressures as depicted in Figure 2.9. In this case, the area enclosed by the cycle 1–2_D–3–4–1 of the CI cycle is apparently greater than that of SI cycle 1–2–3–4–1 and thus the indicated specific work of the CI cycle would be greater than the work of the SI cycle when the maximum pressures are identical.

2.2.3.4 Real Engine Cycles

Typical real indicator cycles of SI and CI engines are given in Figures 2.10 and 2.11. In the SI case, the cycle differs in the constant volume exhaust blow-down process with the ideal Otto cycle. A greater difference can be seen in CI cycle. In addition to the same phenomenon of exhaust blow-down, a constant volume segment exists in the real cycle that is absent in the ideal cycle. This segment is due to an early fuel injection (before TDC) in real engines which builds up the pressure in the cylinder when the piston is close to TDC (constant volume). A dual cycle approximation (Figure 2.11b) is sometimes used to model the cycle more accurately.

2.2.3.5 Part Throttle SI Engine Cycle

So far it has been assumed that the intake air was unthrottled (wide open throttle, WOT) and that the inlet air in the intake manifold was at atmospheric pressure. At part throttle, the valve is partially open and restricts the flow, resulting in a lower than atmospheric inlet pressure. This will in turn cause a lower air mass to fill the cylinder and the required amount of fuel will also be lower, resulting in less thermal energy from combustion and less resulting work.

The typical air cycle for the part throttle engine is shown in Figure 2.12. According to Figure 2.12, the net work is less than that of the standard Otto cycle, since the upper loop of the cycle represents positive work output (power cycle), while the lower loop is negative work absorbed by the engine (pumping cycle).

2.2.3.6 Effect of a Turbocharger

Turbochargers or superchargers use the exhaust pressure or a mechanical power respectively to drive a compressor to pump the inlet air and increase the intake pressure to higher than atmospheric values. This increases the inlet air in the combustion chamber during the cycle and, clearly, the more mixture mass there is in the cycle, the more chemical energy is released and the resulting net indicated work is therefore increased. The effect of turbocharging or supercharging on the air standard cycles would be to increase the intake pressure at point 1 to higher values. For example, in the Otto cycle, the result would be similar to that shown in Figure 2.13. Again, the increase in the positive areas under the cycle loops is an indication of the increased net indicated work of the cycle.

2.2.4 Engine Output Characteristics

In the foregoing discussion it was observed that the standard cycles were able to generate the engine indicated outputs at WOT and desired working speeds (see Examples 2.2.1 and 2.2.3). Nevertheless, the net indicated work of the cycle was found to be independent of speed (Equation (2.13)). In practice, however, an engine works at diverse conditions of output speeds and powers. An important question is how the engine performance is related to the speed. The variation of engine output power and torque versus speed can be obtained from Equations (2.16) and (2.18) respectively. These equations can be rearranged in the following forms:

(2.27)

(2.28)

So according to the air standard cycles, the WOT engine output torque and power in the entire range of operation will be similar to that shown in Figure 2.14. This is true for both SI and CI engines and only the constant values T* and k_P will be different.

The characteristics of real engines are in general similar to the characteristics of ideal cycles but differ at low and high speeds. The reason is that the overall engine efficiency is not constant and varies with the engine speed. To see this, let us combine Equations 2.13, 2.14 and 2.17 (assume no residual mass in the cycle) to obtain:

(2.29)

Recalling and substituting in Equation (2.20) gives:

(2.30)

which eventually leads to the following equations for p_bme, torque and power (four-stroke engines):

(2.31)

(2.32)

(2.33)

As mentioned earlier, the overall efficiency of engine is not a constant and is dependent on several factors, including engine load and speed. The relation of to engine working parameters is very complex and is not well documented in the literature. For real engines, even the factors and are not constant and change with changing atmospheric conditions and engine speed.

Among the different factors influencing the overall engine efficiency, the one with substantial importance is the volumetric efficiency, since it governs how much air gets into the cylinder during each cycle. More inlet air means more fuel can be burned and more energy can be converted to output power. However, because of the limited cycle time available, the pressure losses across the air cleaner, the intake manifold, the intake valve(s), the reduction of mixture density due to hot cylinder walls and the gas inertia effects, less than the ideal amount of air enters the cylinder and reduces the volumetric efficiency. The variation of volumetric efficiency with engine speed is shown in Figure 2.15 for a typical spark ignition engine.

Torque and power characteristics of a real engine, therefore, will be affected especially at low and high engine speeds. The result will be a lowering of engine torque at low and high speeds. The maximum engine power will not occur at its maximum speed but at a lower speed. Typical WOT engine performance curves for an SI engine are shown in Figure 2.16.

2.2.5 Cylinder Pressure Variations

The piston is controlled by the cylinder pressure and its motion to produce the engine speed and output torque. The instantaneous pressure variation, therefore, controls the output characteristics of the engine. A suitable variable against which to express the engine pressure variations is the crank angle. As a result, the plot of pressure versus crank angle is commonly used. These curves, in addition, provide further understanding of the effect of engine torque variation with a spark or injection timing.

The values for the pressure of the cylinder were determined for air standard SI and CI cycles in Section 2.2.3, for the end points of each stroke. In order to plot the pressure variation, the pressures in the mid-region are also necessary. For this reason the cylinder volume must be related to the crank angle θ. It can be written as:

(2.34)

in which A_P is the piston area and (see Section 2.3.1):

(2.35)

(2.36)

Note that at θ = 0 the piston is at TDC and at θ = 180 degree it is at BDC. Also is the stroke. The cylinder pressure variations will be examined in Example.2.2.4.

The cylinder pressure can also be obtained from laboratory tests. A pressure sensor can detect the variation in cylinder pressure and produce an electric (or digital) signal proportional to it. With simultaneous recording of the crank rotation angles, test results for the pressure variation versus crank angle can be obtained. Tests are usually performed at specific constant engine speed. At different engine speeds, the pressure curve will be different and as a result the engine performance will also be different. A typical cylinder pressure versus crank angle variation of a real SI engine is given in Figure 2.19. The overall trend is seen to be quite similar to that of Figure 2.18 for the ideal engine.

2.3 Engine Modelling

In the preceding section, the principles of engine power generation based on the combustion of fuel inside the engine and the related energy release were discussed. The output power and torque obtained from such an analysis, however, are average and indicative. In order to find instantaneous outputs of an engine, two different approaches, illustrated in Figure 2.20, are available. Process modelling is a more elaborate method of what was discussed in Section 2.2, in which the details of fluid flow to the engine, valve timing, combustion process, thermodynamics, heat transfer and fluid flow out of the engine are all modelled. The accuracy of such modelling depends on how correct its subsystems are. This approach uses sophisticated software with a large number of inputs. The second approach is a mechanical analysis method which is rather simple and accurate, provided that accurate combustion pressure data are available.

In this section, we will use the second approach to develop relations for the engine's instantaneous torque by analyzing the engine kinematics and force balance. We will start with single cylinder engines and the outputs of multi-cylinder engines will be discussed later. The justification is that a single cylinder internal combustion engine is a building block for the multi-cylinder engines. Since all cylinders are similar in an engine, once a model is built for a single cylinder, it can easily be extended to the other cylinders.

2.3.1 Engine Kinematics

The kinematics of a single cylinder engine is that of a slider-crank mechanism. Figure 2.21 illustrates the terminology of the parts of a single cylinder engine and a simplified slider-crank mechanism. The piston travels up to the top dead centre (TDC) while the crank rotates. The displacement of the piston relative to the TDC is denoted by variable x. Revolution of the crank is considered positive clockwise and denoted by angle θ (crank angle). The crank radius is R and the length of the connecting rod between points A (wrist pin or gudgeon pin) and B (connecting rod journal bearing) is l.

The total distance travelled between TDC and bottom dead centre (BDC) is denoted by L and can be written as:

(2.37)

According to Figure 2.21, the displacement x can be expressed as:

(2.38)

The piston speed and acceleration are the first and second time derivatives of the displacement x:

(2.39)

(2.40)

Differentiation of Equation (2.38) with respect to time will lead to equations for the speed and acceleration of piston in following forms:

(2.41)

(2.42)

in which and are angular speed and acceleration of the engine respectively, defined as:

(2.43)

(2.44)

k_v and k_a can be obtained from the equations below:

(2.45)

(2.46)

In deriving Equations (2.45) and (2.46), the trigonometric relation between the two angles θ and β is used:

(2.47)

Also, to determine cosβ term in the above equations, β can be obtained from Equation (2.47):

(2.48)

Equations (2.45) and (2.46) can be simplified to approximate equations with good accuracy. The results are of the following forms [3]:

(2.49)

(2.50)

In Equation (2.42), the engine acceleration term also exists (first term) but vanishes for constant engine speeds. Nonetheless, this term is usually very small and negligible compared to the term resulting from the engine speed squared, especially at top speeds. In order to obtain an impression of the relative magnitudes of the piston acceleration terms related to tangential acceleration and centripetal acceleration , consider an extreme case in which an engine is accelerating from 1000 rpm to 6000 rpm in just 1 second. During this phase rotational acceleration is constant and equal to 523.6 rad/s² and rotational speed is increasing. At very low engine speeds the ratio of over is one order of magnitude, around 2000 rpm it becomes 2 orders of magnitude and at around 6000 rpm it gets close to three orders of magnitude. This will be further examined in the next example. It is, therefore, reasonable to always use only the second term in Equation (2.42) for the piston acceleration even when the engine is accelerating. Hence:

(2.51)

Once the piston kinematics are known, equations for the connecting rod kinematics including its rotational speeds and acceleration, and the speed and acceleration of its centre of gravity can be developed. Starting with velocity and acceleration vectors of point B, one can write according to classical dynamics:

(2.52)

(2.53)

In which radius vector is shown in Figure 2.26 and:

(2.54)

(2.55)

, and are a set of mutually perpendicular unit vectors fixed to the cylinder block. and as shown in Figure 2.26 are in horizontal and vertical directions and makes the third direction. The solutions of Equations (2.52) and (2.53) are:

(2.56)

(2.57)

Angular velocity and acceleration of the connecting rod can be obtained by relating the velocity and acceleration of the two ends of the connecting rod:

(2.58)

(2.59)

In which:

(2.60)

(2.61)

and vector is shown in Figure 2.26. Substituting for and in Equations (2.58) and (2.59) and making use of Equations (2.56) and (2.57), and are found after some manipulations to be:

(2.62)

(2.63)

In the derivation of Equation (2.63), a third term is also found but it is negligible. Moreover, the first term of Equation (2.63) is very small compared to the second term and can be ignored. It means that the connecting rod rotational acceleration mainly results from engine speed squared and not from engine acceleration.

With reference to Figure 2.27, the velocity and acceleration of connecting rod centre of mass G are:

(2.64)

(2.65)

The right-hand sides of both Equations (2.64) and (2.65) are all known quantities and after some operations the solutions are of the final forms:

(2.66)

(2.67)

With:

(2.68)

(2.69)

(2.70)

(2.71)

In Equation (2.67), a negligible term has been excluded. and in Equations (2.68)–(2.71) as illustrated in Figure 2.27 are the distances from the CG of the connecting rod to points A and B respectively.

2.3.2 Engine Torque

The pressure developed in the combustion chamber of an engine (Section 2.2.5) exerts a force on the piston top surface which pushes it down and in turn the connecting rod forces the crank to produce the engine torque T_e. Although this phenomenon looks simple, nonetheless the engine torque has no simple relation with the piston force as the line of action of this force, according to Figure 2.31, actually passes through point O, the axis of rotation of crankshaft. The complexity arises, on one hand, from the trigonometric relations and, on the other, from the inertia forces and torques acting on the connecting rod. These will be explained in this section.

In the following analyses, D'Alembert's principle will be applied in order to deal with a static problem instead of a dynamic one. To this end it suffices to include inertia forces and moments on the free-body diagrams of members under the study. The inertia force and the inertia torque acting on a body B are defined as:

(2.72a)

(2.72b)

in which m_B is the mass of body, I_B is the mass moment of inertia of the body around its centre of mass, is the centre of mass acceleration vector and is the angular acceleration vector of the body in planar motion. In spatial motions, the inertia torque has a more complex form [4].

The piston force F_P is generated due to the pressure build-up in the combustion chamber. Denoting this pressure by p and the piston area by A_P, the piston force simply is:

(2.73)

with units of Pascal and square metre for pressure and area, the piston force is in Newtons. If pressure is expressed in MPa (mega Pascal), obviously the force could still be in Newtons, provided the area is expressed in square millimetres.

Forces acting on the piston, illustrated in Figure 2.32a, include four components apart from the pressure force F_P. Forces A_x and A_y are horizontal and vertical components of the internal bearing force acting from connecting rod side on the piston. F_W is the normal contact force exerted by the cylinder wall to the piston. In practice, the contact force also has a component along the direction of motion resulting from friction. This component has been ignored by assuming frictionless motion between the piston and cylinder. The last force acting on the piston is the inertia force F_IP with magnitude:

(2.74)

where m_P is the mass of piston and all attached elements (pin and keys), and a_P is the piston acceleration (Equation (2.42)). Note that the direction of piston acceleration was considered to be positive downwards, thus the positive inertia force is shown upwards. Note also that the gravitational force has been disregarded due to its very small magnitude relative to the large forces involved. In addition, it has been assumed that the piston has only reciprocating motion with no rotation. In reality, however, the piston also rotates due to the backlash. This rotation, apart from producing an inertia torque, causes the contact forces to be present at both sides of the piston simultaneously. Moreover, it has been assumed that the line of action of the wall force passes directly through point A, in order to constrain the rotational balance of the piston.

The free body diagram (FBD) of the connecting rod is shown in Figure 2.32b. Two of the forces acting on the connecting rod are the reaction forces A_x and A_y (obviously in opposite directions to the piston forces). Similar bearing forces acting at point B are B_x and B_y respectively. The two other remaining forces are components of inertia force acting at the centre of gravity of the connecting rod G. The two components have the following magnitudes:

(2.75)

(2.76)

in which m_C is the mass of connecting rod, and a_Gx and a_Gy are the horizontal and vertical components of in Equation (2.67). It should be noted that the both acceleration components are negative (ignoring angular acceleration components) so that the directions of the inertia forces have been taken as positive in Figure 2.32b. T_IG is the inertia torque acting on the connecting rod resulting from its rotational acceleration. The magnitude of this torque is:

(2.77)

where I_G is the mass moment of inertia of connecting rod around its principal axis passing through its centre of gravity and is the angular acceleration of connecting rod (Equation (2.63)). Note that the acceleration of the connecting rod was taken to be positive clockwise, thus the direction of inertia torque is shown as counter-clockwise.

Figure 2.32c shows the free body diagram of the crankshaft. Apart from the reaction bearing forces B_x and B_y, the components of the main bearing force F_B (i.e. F_Bx and F_By) act at point O. Due to the crankshaft rotational acceleration, an inertia torque T_IC is present around O with magnitude:

(2.78)

in which I_C is the crankshaft mass moment of inertia around its rotation axis and is the engine angular acceleration. It should be noted that the centre of mass of the crankshaft and its counter-weight combined is assumed to be at point O. This is achieved by choosing an appropriate counter-weight. It is also assumed that the axis of rotation of the crankshaft is its principal inertia axis. It is worth mentioning that all bearings have been considered frictionless, otherwise the discussion would become more complicated.

The engine torque according to Figure 2.32c can be obtained by taking a moment sum around O:

(2.79)

B_x and B_y have to be obtained from the free body diagram of Figure 2.32b by writing equilibrium equations consisting of two force equations and one moment equation shown below:

(2.80)

(2.81)

(2.82)

There are four unknowns in the three equations above, thus we will need to write one equilibrium equation for Figure 2.32a as well. For the vertical direction we have:

(2.83)

From Equations (2.81)–(2.83), the two required unknowns B_x and B_y are found as:

(2.84)

(2.85)

The engine torque (Equation (2.79)) can be evaluated by making use of Equations (2.84) and (2.85). In this process, the other equations for the piston force and all inertia forces and torques will also be required. It is clear now that in calculating the engine torque from the piston force F_P, several other unknowns are necessary and the resulting equation for the engine torque is highly non-linear. Recalling that the pressure in combustion chamber is itself a function of several engine working parameters adds to the complexity of engine torque determination. Additional information regarding the external loads can also be determined from the foregoing analysis. The wall force F_W can be obtained by making use of Equation (2.80) together with an additional horizontal equation for Figure 2.32b. The result is:

(2.86)

The main bearing forces are determined from the force equilibrium of Figure 2.32a as:

(2.87)

(2.88)

in which F_ICW is the inertia force resulting from centripetal acceleration of the counter-weight with mass m_CW at a radius R_CW from the crank axis:

(2.89)

An alternative way to determine the engine torque is to consider the whole engine assembly under the action of external forces and moments shown in Figure 2.33. The main advantage of this approach is that the internal forces will not be present. Note that the inertia forces and torques are taken into account. Taking moments around the crankshaft axis of rotation results in the following relation for the engine torque:

(2.90)

in which:

(2.91)

2.3.3 A Simplified Model

The concept of excluding the internal forces from the analysis was used in Figure 2.33 and to derive Equation (2.90). Nonetheless, the evaluation of Equation (2.90) is still dependent on the availability of components that were obtained from the full separation method presented earlier. As a result the concept is not really useful unless all components can be obtained within the method itself.

Consider Figure 2.33 once again to analyse the problem for a stand-alone determination of all unknown loads in the engine assembly. This system involves four unknowns F_Bx, F_By, F_W and T_e, and is statically indeterminate. One additional equation, therefore, is necessary in order that the four unknowns can be determined. An approximate solution can be found by replacing the connecting rod with a two-force member. As such, in addition to providing an additional relation between the unknown external forces, the connecting rod inertia forces and moment will be removed from the model. To see how the additional relationship is formed, consider the engine model with a two-force connecting rod member shown in Figure 2.40. The connecting rod element will carry the force F along its direction. Resolving the forces along the direction γ perpendicular to the direction of F, will lead to the equilibrium of upper part:

(2.92)

This will serve as the additional equation.

However, the question remains of what justification can one use to replace the actual connecting rod with a two-force, mass-less member? Obviously by doing so, the dynamic properties of the system will change unless the replacement member keeps the dynamic properties of the original connecting rod.

The original connecting rod shown in Figure 2.41a has mass m, length l, moment of inertia I_C and its CG is located a distance l_A from point A (wrist pin) and a distance l_B to point B (crank pin). Let us examine the possibility of replacing this connecting rod with a mass-less link L of Figure 2.41b with two point masses m_A and m_B attached to it at endpoints A and B respectively. In order that the dynamical properties for the proposed system remain identical to the original connecting rod, the following conditions must be satisfied:

(2.93)

(2.94)

(2.95)

Equations (2.93)–(2.95) stand for the equality of mass, CG location and moment of inertia of the two systems. Since the locations of two point masses are chosen to coincide with points A and B, only two equations out of three are adequate to determine the two masses m_A and m_B. However, as long as the third equation is not satisfied, there is no guarantee that the two systems are dynamically equivalent. For instance, from Equation (2.93) and 2.94, the two masses are obtained as:

(2.96)

(2.97)

Substituting into Equation (2.95) results:

(2.98)

In practice for a real connecting rod, usually , which means if the two masses are fixed at A and B, the resulting moment of inertia from Equation (2.98) would be greater than the actual value. In other words, if an exact dynamic equivalence is to be used, then only one of the masses, say, m_B, can be fixed and the location of the other one together with the values of the two masses should be obtained from Equations (2.93)–(2.95). Calling the first mass in this case m_D and the other m_E, equations to calculate the unknowns l_E, m_D and m_E are:

(2.99)

(2.100)

(2.101)

Since , l_E is less than l_A and the mass m_E will be positioned below point A as indicated in Figure 2.41c.

The foregoing discussion indicated that in order to substitute a dynamically equivalent mass system for the connecting rod, one of the end masses will be located out of the rotation points A or B. This system, therefore, is not kinematically compatible with the engine motions and hence despite its accuracy it is not workable. On the other hand, placing the two masses over the required joints A and B, makes the mass system kinematically compatible, but dynamically different with the original system to some degree, mainly due to the change in the moment of inertia of the connecting rod. The resulting error for the increase of the connecting rod inertia may vary for different engines but is limited to around 30%. This difference will not make major deviations to the system outputs and hence this simplified mass system is generally used for the engine torque generation analysis.

With this substitution the simplified engine model will look like that of Figure 2.42 in which two point masses m_A and m_B are placed at wrist-pin and crank-pin points and the connecting rod is replaced by a rigid link L. According to the preceding discussions, the crank angular acceleration is not influential in the inertia force and torques of the components, therefore, inertia forces for the masses rotating with crank angular acceleration are considered only in radial directions. These include the inertia forces, F_IB belonging to mass m_B and F_ICW belonging to mass m_CW. The mass of the counter-weight can be selected properly to balance the inertia force F_IB and thus free the main bearing from the related loads. On the other side, m_A will move with piston and can be regarded as part of the piston mass. Therefore, the inertia force F_IP has the magnitude:

(2.102)

Now according to this simplified engine model all external forces will pass through point O, except F_W, the force acting on the cylinder wall. Therefore, the engine torque simply is:

(2.103)

in which h and F_W are obtained from Equations (2.91) and (2.92) respectively. Finding the main bearing forces for the simplified model is then straightforward and the results are:

(2.104)

(2.105)

2.3.4 The Flywheel

Since the pressure variation in the combustion chamber is speed dependent, each engine torque diagram is obtained for a specific engine speed. The variation of engine torque with the crank angle was studied in the previous section and typical diagrams were presented. On the other hand when the engine torque varies, it will also cause the engine speed also to vary. This is contradictory to the first assumption that the torque variation belongs to a specific (constant) engine speed. In this section, the objective is to clarify how a flywheel can resolve this conflict.

Consider an engine output shaft that is attached to a flywheel with inertia I_e (including inertia of crankshaft and other related masses) and drives a load L (Figure 2.48). According to Newton's Second Law of Motion in rotation, the net torque on the rotating mass with speed ω_e causes it to accelerate with acceleration α_e:

(2.106)

Assuming a constant load torque T_L, then in order to obtain a constant engine rotational speed, the instantaneous engine torque T_e(t) must be equal to the load torque. This means that the engine must produce a net torque that is not time-variant, contrary to what we found earlier that the engine torque was varying with the crank angle. Therefore, according to Equation (2.106), the speed fluctuations will be inevitable and the best one could do is to require an average engine speed with small fluctuations. The first step is to put the average engine torque T_av equal to the load torque:

(2.107)

By using the chain rule in differentiation, Equation (2.106) can be written in terms of the crank angle variations:

(2.108)

and can be integrated between two arbitrary points 1 and 2:

(2.109)

The right-hand side is the net kinetic energy of rotating inertia when its speed changes from ω₁ to ω₂. The left-hand side of the equation is the work done by the net external torque on the rotating mass from angle θ₁ to angle θ₂. The speeds ω₁ and ω₂ correspond to the crank angles θ₁ and θ₂. In other words the speed ω_i occurs when the crank angle is θ_i.

From Equation (2.109), it is clear that when the net work from point 1 to point 2 is positive, the speed ω₂ will be larger than speed ω₁ and vice versa. Of course it makes sense that the kinetic energy will increase when the work done by the external torques is positive. This work according to Equation (2.109) is the area under the T(θ) curve relative to T_av. Graphically in the torque diagram of Figure 2.49, the shaded areas above and below the average torque illustrate the positive and negative areas. On the left side of the positive shaded area, the crank angle and speed are θ₀ and ω₀ and at the right side θ₁ and ω₁ respectively. Thus ω₁ >ω₀ since from θ₀ to θ₁ the area under the torque-angle diagram is positive. A similar explanation results in ω₂ < ω₁, ω₃ > ω₂, etc.

Among all individual speeds ω_i, one will be the largest ω_Max and one the smallest ω_min. It is desirable to keep these two extreme speeds of the engine as close to each other as possible in order that the speed fluctuations remain small. The ideal situation is to have ω_Max equal to ω_min and both equal to the average engine speed ω_av. A fluctuation index i_F can be defined to quantify the speed fluctuations of an engine:

(2.110)

in which:

(2.111)

A desirable design goal is to have small values for the dimensionless factor i_F in order to ensure small speed fluctuations relative to the average engine speed. If ω₁ and ω₂ in Equation (2.109) are replaced by ω_min and ω_Max respectively, the right-hand side of equation will convert to:

(2.112)

The left-hand side of Equation (2.109) by this substitution is the net area under the engine torque curve between crank angles θ_min and θ_Max corresponding to speeds ω_min and ω_Max. Designating this net area by A* and using Equation (2.112), one simply finds:

(2.113)

which is an equation to estimate the flywheel inertia, provided that the area A* and the fluctuation index i_F are available. The latter should be chosen by experience and the former can be evaluated from the engine torque diagram.

Suppose there are k individual areas under the engine torque-θ curve. In order to determine the net area A*, first the crank angles θ_min and θ_Max should be found. Let us construct a table like Table 2.7 in which the individual areas are recorded in the second row. In the third row cumulative sum of areas up to that point is recorded. Since some of the areas are positive and some negative, one of the cells in ΣA row will have the minimum value and one the maximum value.

Table 2.7 Areas under the engine torque curve.

The cells with the minimum and maximum cumulative areas A_min and A_Max have θ_min and θ_Max points respectively. The net area under the curve between the minimum and maximum speed points simply is:

(2.114)

It is important to note that when the engine is connected to the vehicle driveline, the inertia resulting from the rotating masses and vehicle mass itself (see Section 3.9) is greater than that needed to keep the engine speed regular. In fact, the flywheel is a device that consumes energy to accelerate together with the engine and this energy is wasted in many circumstances, especially when the vehicle stops. Therefore, the best solution is to keep the flywheel as small as possible.

2.4 Multi-cylinder Engines

In practice, almost all automotive applications use multi-cylinder engines; single cylinder engines are extremely rare but may still be found in low duty earthmoving vehicles. A multi-cylinder engine is a combination of several single cylinder engines that share a single crankshaft. Different crank arrangements and firing orders are possible for multi-cylinder engines and these have important effects on the overall smoothness of power delivery.

2.4.1 Firing Order

In a multi-cylinder engine there must be a sequence in which the power stroke of each cylinder takes place, one after another. The power stroke always follows the compression stroke and thus the layout of crankshaft plays an important role in designating the power or firing order in an engine. Firing order also depends on the number of cylinders and by increasing this number, the choices for the firing order also increase.

In order to determine the firing order in an engine, it is necessary to first specify the crank layout and define the state of each cylinder relative to the state of cylinder 1. It is convenient to assume the first cylinder is in the combustion stroke and from the relative crank angles of the multiple cylinders, the state of each cylinder can be specified. When the cylinder 1 advances to the next stroke (exhaust), one of the cylinders that was in its compression stroke previously must fire at this stage. This sequence will continue until the first cylinder's turn starts over again.

This process can be illustrated graphically by specifying the foregoing information for a four-cylinder, four-stroke in-line engine in a chart format as shown in Figure 2.51. First the crankshaft layout is drawn vertically on the left side with the number of cylinders shown next to each crank. In front of each crank, four boxes are drawn on the right side indicating the successive strokes of each cylinder. For instance, cylinder 1 starts with power stroke and follows by exhaust, intake and compression strokes. Moving to cylinder 2, one must decide whether it is in exhaust or in compression stroke, since both cylinders 2 and 3 are in the same state and thus either can be in exhaust or compression. Selecting the exhaust for cylinder 2 will stipulate the states of the other cylinders as indicated in Figure 2.51. In fact, inside each row the stroke order for each cylinder is specified and in each column the relative state of all cylinders is denoted. Once the first left column is specified, the contents of each row are known by the permutation of strokes in each cylinder. On construction of the chart, the firing order can then be specified by taking the number of cylinders in each column that are in power stroke (from left to right). For instance, the engine of Figure 2.51 has a firing order of 1–3–4–2.

It was possible to select the compression stroke for the 2nd cylinder after cylinder 1. In that case the second and third rows would be swapped over and the firing order would become 1–2–4–3. The choice between these two options must be made according to other criteria since, as far as the engine operation is concerned, both choices are acceptable.

Other factors in choosing the firing orders are torsional loads on the crankshaft and uniform charge and discharge of intake and exhaust gases insides manifolds. For a four-cylinder inline engine, these factors are similar for both choices of firing order. Figure 2.52 illustrates how the two cases have symmetrical circulation of power strokes among the cylinders.

In the previous examples, the crank angles were all multiples of 180 degrees, however, in several types of engines the crank angles are different. For example, a six-cylinder inline engine has crank angles for different cylinders as multiples of 120 degrees. In such a case, the procedure for developing the firing order is similar to that explained earlier; nevertheless care must be taken in the construction of the crank layout and stroke shifts. Crank angles can be specified in the chart for each individual cylinder. We did this previously by writing the crank angle below each crank. The stroke shifts were all 180 degrees for flat crankshafts; for other types such as inline six-cylinder crankshaft the stroke shifts are multiples of 120 degrees. Let us construct the firing order chart for this six-cylinder engine. The crank layout is 0-240-120-120-240-0 and in order to make the layout clearer in the chart, a side view of crankshaft will be useful. Figure 2.55 shows this type of presentation. Starting from cylinder 1 as usual, the top row can easily be constructed. For cylinder 2, we note that according to the crank layout it has a 120 degree lag relative to cylinder 1, so the stroke order for this cylinder must be shifted accordingly. The stroke order can begin either from intake or from combustion, thus leaving two possibilities for the firing order (in Figure 2.55, the intake stroke is chosen). Cylinder 3 has a 240 degree lag relative to cylinder 1 and to construct the stroke order for this case, the excess over 180 degree (i.e. 60 degrees) is taken for the starting stroke. The stroke order can begin either from combustion or exhaust; here the former is considered. The processes for remaining cylinders are similar to those explained for cylinders 2 and 3.

As Figure 2.55 illustrates, the firing order for this engine is 1–5–3–6–2–4. However, if other choices for the stroke orders of cylinders 2 and 3 were considered, alternative firing orders could also be achieved. Other possibilities are: 1–6–5–4–3–2, 1–2–3–4–5–6, 1–4–2–5–3–6 and 1–4–5–2–3–6.

2.4.2 Engine Torque

Successive firings cause a continuous torque delivery to the crankshaft output. Since the torque generated by every individual cylinder is dependent on the crank angle, the resultant engine torque is a combination of all individual torques from all cylinders. In order to evaluate the net engine torque, information on the firing order must be available.

Let us assume all cylinders have identical pressure-crank angle profiles, otherwise the engine torque for each cylinder would be different. The torque variation of a single cylinder was obtained for its own crank angle variations. In order to add up the torques of all cylinders, they must be represented relative to a single reference. It is common to take the crank angle of the first cylinder as a reference for all cylinders. Therefore, the crank angle of each cylinder can be written in terms of the crank angle of first cylinder θ₁:

(2.115)

where is the crank angle of ith cylinder relative to the crank of cylinder 1. In order to write the torque of each individual cylinder in a form that can be added to the other torques, it is also necessary to express the cylinder pressure according to the correct state of that cylinder. If the pressure of cylinder 1 is denoted by then pressure for other cylinders can be written in the form:

(2.116)

in which the state angle is the angle of rotation of the crankshaft for the current state of the ith cylinder. Or simply for the states of combustion, exhaust, intake or compression, will be 0°, 180°, 360° and 540° respectively.

Once the correction angles and for all cylinders are obtained, the engine torque can be determined simply by adding up all individual torques of n cylinders in the following form:

(2.117)

In an alternative approach, ‘shift-sum’ processes can be used to add up the torques of individual cylinders to obtain the overall torque variation of a multi-cylinder engine. A torque diagram for a single cylinder engine can be divided into four sections according to the engine strokes (see Figure 2.56). The torque variation for cylinder 1 of a multi-cylinder engine is taken as the basis for all engine cylinders. Thus the permutation of torque segments for this cylinder according to Figure 2.56 simply is . The torque variation of other cylinders can be obtained according to their state angle. In order to construct the torque variation of another cylinder with state angle of , the base torque diagram should be shifted backwards by the amount of . Whatever falls off on the left end moves to the right end of the resulting diagram. For instance, if cylinder i has , the torque permutation for this cylinder will be . Once the torque variation of each cylinder is obtained, the summation of all torques will result in the total engine torque.

2.4.3 Quasi-Steady Engine Torque

The average engine torque is the mean value of the torque fluctuations during one complete engine cycle that can be considered at any arbitrary steady engine speed. It was, however, seen that the engine speed also had an unsteady nature and fluctuated around an average value. In practice, the average speed of the engine is treated as its steady speed. Strictly speaking, however, it can be considered as a quasi-steady speed. Hence, the average engine torque associated with its quasi-steady speed will be its quasi-steady torque.

The mean value of the engine torque at a specified speed was evaluated in the foregoing examples simply by averaging the values of torque at different crank angles. That process required the availability of the pressure variations of the cylinder(s) with the crank angle at the specified speed, as well as the dynamic properties of the engine elements. If only the quasi-steady engine torque is required, instead of using the pressure distribution at a specified speed, an alternative way is to work with the brake mean effective pressure p_bme (or bemp) which is similar to the indicative mean effective pressure p_ime defined in Section 2.2.3. In fact p_bme is related to the real (measured) engine output work whereas p_ime is related to the indicated work calculated from the standard engine cycles.

The work done by the pressure force in the ith cylinder of an engine during one revolution of the crankshaft is:

(2.118)

in which A_P and L are the piston area and stroke length respectively, and s is the number of strokes in the full cycle of engine operation (for a two-stroke engine, s is 2 and for a four-stroke engine, it is 4). At the engine speed of n (rpm), the engine power (work per second) for the ith cylinder is:

(2.119)

For an N cylinder engine, the engine power simply is:

(2.120)

Engine displacement V_e is defined as the total volume swept by all pistons:

(2.121)

The engine power, therefore, can be written as:

(2.122)

The engine power at the same time can be expressed in terms of the average engine torque T_av:

(2.123)

Combining Equations (2.122) and (2.123) leads to:

(2.124)

This equation indicates a direct relationship between the engine average torque and mean effective pressure at a given engine speed.

2.5 Engine Torque Maps

The foregoing discussions in Sections 2.3 and 2.4 were all focused on determination of the engine torque at certain speeds for single cylinder and multi-cylinder engines. In practice, engines work at an infinite number of different conditions depending on the input and output parameters. Each working condition of an engine corresponds to a torque and a speed (and hence power).

In the vehicle powertrain analysis process, the engine characteristics contain critical input information and hence inaccurate information for engine performance will result in unrealistic vehicle behaviour outputs. Hence, for a complete vehicle performance analysis, a full range of engine working conditions is necessary. Such information must be collected either from analytical engine models that solve the mathematical equations related to the engine fluid flow, combustion and dynamics, or from experiments. Due to the complexity of the full engine operation modelling, and the lack of fully developed technical software, the main trend so far has been to conduct experimental data collection for the engine performance using dynamometers.

2.5.1 Engine Dynamometers

A dynamometer, in general, is a device for measuring the power of a rotating source by simultaneously measuring its output torque and rotational speed. Dynamometers are of two general types, namely absorption (or passive) and driving (or active) dynamometers. The first category of dynamometers is used as loading devices for power generating machines such as engines. The second types of dynamometers are used to rotate machines such as pumps. A dynamometer can be designed to either drive a machine or to absorb power from a machine and is called a universal dynamometer.

A dynamometer applies variable braking loads on the engine and measures its ability to change or hold the speed accordingly. The main role of a dynamometer is to collect speed and torque measurements, but they can also be used in engine development activities such as combustion behaviour analysis, engine calibrations and simulated road loadings. Apart from engine dynamometers that are used for testing the engine and its components, the full vehicle powertrain can also be tested by using a chassis dynamometer that applies road loads to the driving wheels.

An engine dynamometer acts as a variable load that must be driven by the engine and it must be able to operate at any speed and any level of torque that engine can produce. The main task of a dynamometer is to absorb the power developed by the engine in the form of heat and dissipate it to the atmosphere or possibly convert the power to electrical energy. An engine dynamometer set-up is schematically shown in Figure 2.62.

A laboratory dynamometer requires measuring devices for the operating torque and speed. Dynamometers also need control systems in order to maintain a steady operating condition suitable for measurements. They can be controlled based on load speed or load torque. Dynamometers having torque regulators operate at a set torque and the engine operates at the full range of speeds it can attain while developing that specified torque. Conversely dynamometers with speed regulators develop a full range of load torques and force the engine to operate at the regulated speed. In addition, engine tests require standard or regulated atmospheric conditions. For this purpose dynamometers are equipped with peripheral air quality control systems.

Load torques can be produced by different means of energy absorption systems and this concept is the basis for the development of different types of dynamometers. Some dynamometers have absorber/driver units that can produce both load and driving torques. Figure 2.63 lists several types of dynamometers.

Eddy current (EC) dynamometers are currently the most popular type used in modern dynamometers. The EC absorbers provide quick load change rates for rapid load settling. Eddy current dynamometers use vehicle brake type cast-iron discs and use variable electromagnets to change the strength of the magnetic field to control the amount of braking torque. EC systems also allow controlled acceleration rates in addition to steady state conditions.

The power calculation from a dynamometer must be carried out indirectly from torque and angular velocity measurements. Measurement of the load torque can be achieved in several mechanical or electrical ways. In a purely mechanical way, the dynamometer housing is restrained by a torque arm that prevents it from rotating. The internal reaction torque exerted on the housing is borne by the torque arm and this torque can be determined by measuring the force exerted by the housing on the arm and multiplying it by the arm length from the centreline of the dynamometer. A load cell transducer can provide an electrical signal scaled in such a way that it is directly proportional to the load torque. Alternatively a torque-sensing coupling or torque transducer producing an electrical signal proportional to the load torque can be used.

Speed measurement is a simpler task and a wide selection of tachometer equipment with an electrical signal output proportional to speed is available for this purpose. Once the load torque and rotational speed signals have been obtained and transmitted to the data acquisition system of the dynamometer, the engine output power can simply be determined by multiplying the two quantities (in proper units).

In steady state tests, the engine is held at a specified rotational speed (within an allowed tolerance) by the application of variable brake loading and the necessary applied torque is measured. The engine is generally tested from idle to its maximum achievable speed and the output is the engine torque-speed graph. If the rated power of engine is required, then correction factors also have to be calculated and multiplied by the measured power (see Section 2.5.3). Sweep tests are performed by the application of a certain load torque while the engine is allowed to speed up continuously. The rate of engine acceleration is an indication of the engine power output during the test under the applied load and attached inertia. A modern engine dynamometer facility is shown in Figure 2.64 and a typical engine test report looks like that shown in Table 2.9.

Table 2.9 Typical engine dynamometer test report.

2.5.2 Chassis Dynamometers

An engine dynamometer measures speed and torque directly from the engine's crankshaft or flywheel on a test bed. The power losses in the drivetrain from the gearbox to the wheels are not accounted for in such tests. A chassis dynamometer is a device that measures power delivered to the driving wheels through the vehicle driveline and thus the effective vehicle power is measured. The vehicle is positioned on the dynamometer and the driving wheels are positioned on the surface of drive roller(s) which apply resistive loads on the vehicle driving tyres. In order to eliminate the potential wheel slippage on the drive rollers, some types of chassis dynamometers are attached directly to the wheel hub and apply the load torque directly.

Owing to frictional and mechanical losses of the drivetrain components, the measured wheel brake horsepower in general is considerably lower than the brake horsepower measured at the crankshaft or flywheel on an engine dynamometer. Typical figures for the overall driveline efficiency – including gearbox, differential gears and driveline friction losses – may be around 87–91% for manual transmissions and as low as 80% for automatic transmissions. However, these figures must be treated only as guidelines, since the actual efficiencies in practice depend on the driving cycle. For example, the losses in the torque converter of an automatic transmission are rather high for stop-start driving, but they reduce dramatically when the torque converter is locked for highway cruising.

However, the test conditions are very important and environmental changes can also have a great influence on the results. In addition to the driveline losses, other resistive loads such as rolling resistance, aerodynamic and slope (see Chapter 3) are also present during the vehicle motion on the road. One of the important uses of the chassis dynamometers in addition to measuring speed, torque and vehicle's effective power, is to determine vehicle fuel consumption (see Chapter 5) and emissions. To this end, dynamometers have to simulate and apply the associated road loads to the driving wheels. Dynamometers are also used to measure and compare the power flow at different points on a vehicle driveline. This is used is for the development and modification of the vehicle driveline components, usually at vehicle research centres.

2.5.3 Engine Torque-Speed Characteristics

From the point of view of overall powertrain analysis, the actions and interactions inside the engine are not essential. The important issue is how the engine produces shaft output power to be used for vehicle motion. Engine torque-speed characteristics demonstrate the output performance suitable for powertrain analysis use. Full throttle engine torque-speed maps provide some useful information regarding engine performance, but the part-throttle maps are necessary for the full performance analysis of vehicle motion.

2.5.3.1 Full Throttle Maps

Full throttle or full load or wide-open-throttle (WOT) maps are indications of the engine's peak power performance. Maximum engine torque and power can be obtained in this type of maps. A typical full throttle map for a spark ignition engine was already shown in Figure 2.15. A similar map for a compression ignition engine can be seen in Figure 2.65.

Important points on the typical full load engine performance map are specified in Figure 2.66. These are defined as:

Pm	Maximum engine power.
PT	Power at point of engine maximum torque.
Tm	Maximum engine torque.
TP	Torque at point of engine maximum power.
nP	Engine speed at engine maximum power.
nT	Engine speed at engine maximum torque.

Engine torque flexibility F_T and speed flexibility F_n are defined by:

(2.125)

(2.126)

The engine flexibility F_e is defined as the product of the two terms above:

(2.127)

Good flexibility means that maximum torque occurs at lower speeds. In general, diesel engines work at lower speeds compared to petrol engines at similar powers. It means that they produce higher torques at lower speeds. The naturally aspired diesel engines have the characteristics that can be interpreted as high engine flexibility. It is argued that higher engine flexibility will result in less frequent shifting [5].

The following example is designed in such a way that a better understanding is obtained regarding engine flexibility.

In this example, only the issue of engine flexibility is studied. Later, the effect of gear ratios on the overall vehicle working condition will be included in other chapters.

2.5.3.2 Part Throttle Maps

Full throttle operation is only a small part of the engine operation during normal vehicle motions. In other words, the full throttle maps are only the upper boundary of the engine performance area. Therefore, the full throttle information has only limited value in powertrain analysis. Throttling has different meanings in spark ignition and compression ignition engines. In SI engines there is a butterfly valve-type restriction in the air inlet of the engine (see Figure 2.68) that controls the amount of air input into the manifold. Diesel engines do not have such restrictions and the throttling effect is done by controlling the injection of fuel according to the demands of the driver when the accelerator pedal is depressed.

The definition of throttle opening is not clear and is sometimes misleading. The reason is explained by differentiating between the accelerator pedal displacement, the throttle butterfly valve rotation and the ratio of opening area to full area of the inlet pipe. When the accelerator pedal is depressed, usually a cable (wire) is pulled and the throttle valve is turned (Figure 2.69). When the pedal is released, the spring force returns the throttle to the closed position.

According to the schematic illustration of Figure 2.69, the quantities ‘pedal rotation angle’ θ_P, ‘throttle valve rotation angle’ θ, and ‘throttle opening ratio’ r_A (the ratio of opening area to the full bore cross-sectional area) are related as follows:

(2.128)

(2.129)

where k_T is a constant and θ₀ is the initial value of the throttle angle at closed position. The approximation sign of Equation (2.129) is for the effect on the throttle shaft diameter at large throttle angles. Equation (2.128) indicates that the throttle angle is proportional to the accelerator pedal angle (unless the mechanism used was non-linear). Therefore the driver's feeling of depressing the pedal is effectively transferred to the engine throttle. The throttle opening of Equation (2.129), however, shows a non-linear relation with the throttle angle (or pedal angle). As seen in Figure 2.70 for a 5-degree θ₀, the variation of throttle opening is highly non-linear at low pedal inputs. In order to have a similar definition for SI and CI engines when discussing part throttle curves, it is better to use the accelerator pedal displacement (or rotation) since no throttle valve is available for CI engines (the throttle is always fully open).

In SI engines the variation of engine torque with speed at different throttles is different due to different mass flow rates into the engine. In CI engines the mass of fuel injected is proportional to the pedal input which varies with the resulting engine torque. The part load performances of engines are measured on engine dynamometers during special procedures. The result is sometimes illustrated by a three-dimensional map with axes being engine torque, speed and throttle respectively. A typical map of this type is shown in Figure 2.71 based on engine dynamometer test results.

A more useful representation of the part throttle engine map, however, is in two dimensions. If a left view of the 3D picture is taken, in the torque-rpm plane a series of curves for different throttle values will be present. Such a plot is depicted in Figure 2.72 for the same engine.

At idle speed (0% throttle) only one operating point will exist on the map. With increasing throttle, the operating points will increase across the speed and torque axes. Part throttle maps are shown at specific throttle values. For working points in between, interpolation of two adjacent points can be used. For interpolation purposes it is often easier to use look-up tables instead of maps.

2.6 Magic Torque (MT) Formula for Engine Torque

As discussed earlier, the torque-speed characteristics of an engine over the full range of operation are usually expressed with part throttle look-up tables or maps and are used in powertrain analysis work to obtain the full range of engine operation outputs. The midpoints between available data in look-up tables are obtained by linear interpolations.

The availability of a universal formula for engine torque-speed-throttle dependency could provide several benefits for researchers by simplifying the processes as well as providing a mathematical relationship that can be utilized in many ways in the analyses. Research work was carried out at the Department of Automotive Engineering, IUST in Tehran, in order to discover the part throttle behaviour of SI engines. Three engines were fully tested on engine dynamometers and part throttle data were recorded. The data were then analyzed in order to determine whether a similar torque-speed property could be obtained for the tested engines. This work led to a universal mathematical relationship for the torque-speed characteristics of SI engines which was verified by the available test results.

2.6.1 Converting Part Throttle Curves

As may be seen from Figures 2.71 and 2.72, the part throttle curves do not follow a single rule. Part throttle plots of other engines also showed a similar trend. In order to explore the inherent characteristics of the torque-speed data, different representations were examined. The plot of a two-dimensional part throttle look-up table can be prepared in three different ways: (1) the torque-speed variations at different throttles, which is a popular form frequently used; (2) torque-throttle variation at different speeds; and (3) throttle-speed variations at different torques. When the latter plots were generated for all engines, although a better correlation was observed among the curves, it was not possible to identify a uniform trend. The variation of torque-throttle at different speeds, however, showed a good uniform trend for all engines. The result for one of the engines is given in Figure 2.73.

This result of course is explicable in that the torque increases with increasing the throttle at a specified speed, because increasing the throttle opening will increase the fuel-air mixture input rate and in turn the resulting torque. The consistent behaviour of the engines in the torque-throttle map allows the examination of different functions for the description of this relationship. Regression methods were applied to the problem and a universal equation for the SI engines named the MT (Magic Torque) formula was developed. (It also stands for Mashadi-Tajalli because of their contribution.)

2.6.2 The MT Formula

The MT formula has the following basic form:

(2.130)

in which is the full load or wide-open-throttle (WOT) engine torque-speed curve and coefficients A, B, C and D are four constants for a specific engine and can be determined from part load tests. Coefficients can be obtained in such a way that the torque, speed and throttle are in Nm, rpm and % respectively.

2.6.3 Interpretation

Each of the coefficients A, B, C and D in the MT formula has an influence on the output torque variation of the formula. In this section a brief explanation will be presented for the role of the coefficients. The first point to note is that the MT formula can be written as:

(2.131)

in which is a correction factor that is always smaller than unity and is the WOT curve of the engine. In other words, the part throttle values in an engine are shaped from its full throttle curve. Approaching full throttle curve at large throttle inputs can be examined in Equation (2.130) by observing:

(2.132)

Therefore all of the coefficients are influential only at part throttle, and at full throttle the MT formula will generate the WOT curve. The influence of each factor in the MT formula is explained below:

• Factor A: Coefficient A is called the magnitude factor since it controls the value of torque at a specified point. Reducing the magnitude of A decreases the torque magnitudes of a part throttle curve. The changes in magnitudes are different at different throttles and speeds.
• Factor B: This coefficient is called the throttle interval factor since it controls the interval between every two part throttle curves. In fact, reducing coefficient B displaces the part throttle curves further from one another and distributes the part throttle curves more evenly.
• Factor C: Coefficient C is called the low speed magnitude factor since it controls the torque values especially at low speed points. Reducing the magnitude of C increases the torque magnitudes of a part throttle curve especially in the low speed regions.
• Factor D: Coefficient D is called the high speed magnitude factor since it controls the torque values especially at high speed points. Increasing the magnitude of C decreases the torque magnitudes of a part throttle curve especially in the high speed regions.

2.7 Engine Management System

In the past, the engine functions such as fuel-air mixture and ignition control were achieved by mechanical devices like carburettors and advancing mechanisms (e.g. centrifugal advance units). An engine control unit, or ECU for short, is an electronic control system for engines that is responsible for monitoring and managing the engine functions that once were performed mechanically. Over the past three decades, the control of a few parameters for engine ignition has developed into the management of several variables that govern the performance of an engine. For this reason, the term ‘Engine Management System’ (EMS) is becoming increasingly popular. EMS is responsible for monitoring and controlling additional parameters such as exhaust-gas recirculation (EGR) and fuel evaporative emissions to ensure better fuel economy, much lower pollution, more power, easier cold start, smoother idling, and consistently good performance under all circumstances. Electronic engine management has also made possible sophisticated engine monitoring functions and provides diagnostics and warning information.

Modern engine management systems incorporate information from other vehicle systems by receiving inputs from other sources to control the engine performance. Examples are control of variable valve timing systems, communication with transmission control units and traction control systems. For engine maintenance and repair purposes, the ECU stores diagnostic codes based on sensor information. In conditions where the engine faces a problem, the ECU displays warning lights for the attention of the driver.

2.7.1 Construction

The engine management system in general includes an ECU that receives information from several sensors to control the ignition process of the engine. A fuel delivery system is responsible for working with the ECU and supplying sufficient fuel to the engine. The ignition system receives commands from the ECU for accurate control of the combustion. The sensors provide feedback to the ECU to indicate the way engine is running so that the ECU can make the necessary adjustments to the operation of the fuel delivery and/or ignition system for emission control, fuel economy and good driveability. Figure 2.75 illustrates the main components of an EMS (see also [6, 7]).

The ECU uses a microprocessor which can process the inputs from the engine sensors in real time and compute the necessary instructions. The hardware consists of electronic components based on a microcontroller chip (CPU). Memory is also needed in order to store the reference information and ECU software. The input information from sensors is conditioned to remove noise and digitizing (if necessary). The low energy command signals of ECU must be amplified by the output drivers before they are used to drive the actuators. Figure 2.76 schematically illustrates the basic parts of an engine electronic control unit.

2.7.2 Sensors

A sensor is a device that measures a physical quantity and outputs an electronic signal in proportion to the measured quantity. Engine sensors are responsible for measuring and reporting several important quantities to the ECU. These sensors include throttle position sensor, mass airflow sensor, temperature sensor, manifold pressure sensor, crank angle sensor, oxygen sensor and knock sensor. A brief explanation follows for each of these sensors (see also [8, 9]).

• Throttle position sensor (TPS): As the name implies, a throttle position sensor provides the ECU with information on the throttle rotation. This information produces the angle of throttle rotation as well as the driver's intention to accelerate the vehicle from the rate of changing the angle. The ECU will use this information to control the fuel delivery and ignition timing. Three examples are idle, heavy throttle input and braking. In idle conditions, the throttle is closed for a time period, so that the ECU will notice it is idle. In a sudden acceleration the accelerator pedal will be depressed rapidly. The ECU receives two signals: throttle angle and rate of change of throttle angle. Therefore, it determines the situation is acceleration and the combustion timing will usually be advanced more than under a light throttle input. In braking circumstances, the accelerator pedal is released suddenly and the signal will be to close the throttle and thus, the ECU will issue an injection cut-off command.
• Mass air flow sensor: The amount of fuel needed for a perfect combustion is proportional to the amount of air entering the engine. The measurement of the mass flow rate of air into the engine, therefore, is necessary to try and optimize the operation of an engine. There are different ways of measuring the amount of air entering the intake manifold. Hot wire sensors use electric current variations to keep the temperature of wire constant. Other methods include the vane system and the heated film method.
• Temperature sensors: The optimum spark advance depends on intake manifold temperature. The air temperature sensor measures the temperature of the air and the ECU modifies the fuel flow to suit the ambient air temperature. In some engines, the air temperature information is combined with information from the pressure sensor to calculate the intake air mass flow rate. The coolant temperature sensor is used to report to the ECU the operating temperature of the engine, allowing it to modify the fuel flow as the engine temperature changes, and to assist with warm-up and for maximum fuel economy at normal engine operating temperatures.
• Manifold pressure sensor: The pressure drop in intake manifold is an indication of air flow rate. The pressure drop is higher at lower throttle openings. This information is useful for the ECU to tailor fuel delivery and combustion timing for different operating conditions. The manifold absolute pressure (MAP) sensor (also called a vacuum sensor) measures the degree of vacuum in the engine's intake manifold. This type of sensor is used with some types of fuel injection systems.
• Angle/speed sensors: These sensors provide information to the ECU regarding the crankshaft turning position and speed respectively. The camshaft rotation may also be measured to obtain ignition timing. This information is used by the ECU to control fuel flow and ignition.
• Oxygen sensor: An oxygen sensor (also called a Lambda sensor) is placed in the exhaust system to measure the amount of oxygen leaving the engine together with combustion products. This quantity is used in a feedback loop to allow the ECU to control the fuel delivery system to provide a proper fuel-air ratio. With this information the ECU will continually correct itself in small time steps.
• Knock sensor: The knock sensor detects knocking and sends a signal to ECU to gradually retard ignition timing or to enrich the air-fuel mixture.

2.7.3 Maps and Look-up Tables

When controlling slow systems with few influencing parameters, the microprocessor can be provided with a mathematical control function to evaluate the best conditions for each set of input data and to generate an appropriate actuator drive signal. For complex, high-speed systems like engines, however, this method does not work since the control of an engine requires the high speed evaluation of several complicated non-linear equations, each with a large number of variables.

The solution to this problem is to use engine maps that are sets of pre-calculated results that cover all of the engine's possible operating conditions. During the engine operation the ECU receives sensor signals, calculates the preferred output values and passes them to the output driver circuits. Two basic examples are engine ignition and injection maps with typical shapes illustrated in Figures 2.77 and 2.78. The map of Figure 2.77 relates the ignition timing to engine speed and load and it is controlled by selecting the advance value determined from the data stored in the memory. The map of Figure 2.78 also relates the injection timing to the same two parameters.

The process of obtaining engine map data is called mapping and involves operating a fully instrumented test engine on a dynamometer throughout its entire speed and load range. While quantities such as the fuel-air ratio and the spark control are varied in a systematic manner, the fuelling and timing for maximum power and lowest emissions are obtained. Once the preliminary map data have been obtained, the engine is run in a test vehicle to calibrate the map for higher efficiency and performance in various working conditions.

The maps are then programmed into memories that are installed in production ECUs. In order to make very fast calculations possible, mapping results are stored in the form of look-up tables. The ECU microprocessor executes simple instructions in order to evaluate the output commands. Modern ECUs are able to hold numerous detailed maps relating each output variable to several input variables (sensor outputs).

2.7.4 Calibration

During the engine development phase, ECU maps are obtained by using engine dynamometers in laboratory conditions. At this stage the overall relations between the inputs and outputs are determined in the forms of typical functions. When an engine is fitted on a vehicle, the working conditions will be different from those tested during the dynamometer tests. By changing the working conditions such as different climatic conditions and altitudes, the data stored in the ECU memory must be adjusted.

With tougher legislations on emissions and rising customer expectations for increasing fuel economy, the ECU algorithms are growing in complexity, and the volume of software and data is increasing rapidly. This is why the EMS has progressed from a simple fuel metering device to a multi-functional control system with diagnosis and fault management capabilities. The calibration parameters on ECUs have also increased with increasing software complexity.

The calibration of an ECU involves multi-disciplinary knowledge of electrical, electronics, computer and mechanical engineering along with control and combustion theory.

2.8 Net Output Power

An engine is a device that converts chemical energy to mechanical energy. Inevitably, in this process a large portion of the energy is wasted and only a small part of it reaches the output shaft. The chemical (fuel) energy is not fully released during the combustion and some unburned fuel leaves the system together with the combustion products that also take out some energy with them. The released energy from the burned fuel turns into heat and fluid energy which then partly turns into mechanical energy. Engine internal components such as the oil pump and the camshaft consume power from the available shaft power. Friction between the contacting surfaces generates resistive forces against the engine rotation. In addition, in order to suck the air into the engine and pump the burned gases out, energy is needed. The vehicle accessories such as the air conditioning compressor and a power steering pump also use power from the shaft at the engine front end. The remaining power at the engine flywheel is left to provide tractive forces for vehicle motion. Figure 2.79 illustrates the energy flow inside the engine. Typical values for the energy balances are available in [10].

The input energy to an engine varies by the amount of fuel-air mixture in the engine combustion chamber. This is controlled either by throttling in SI engines or by fuel injection control in CI engines. The atmospheric conditions, too, have important effects on changing the amount of engine air input and resulting fuel energy release.

It is common to work with only three descriptions of power, namely indicated power P_i, brake power P_b and friction power P_F. The indicated power is the total mechanical power produced by engine and can be estimated from Equation (2.133) (see Section 2.2.4):

(2.133)

The total indicated power is divided into two parts; the useful mechanical power at the output shaft (brake power) and the friction power (lost power):

(2.134)

With this definition the friction power also includes all negative power such as pumping power as well as power used for internal uses.

2.8.1 Engine Mechanical Efficiency

Mechanical losses in an engine are described by the friction power of the engine and have several sources including:

• pumping losses that are due to the energy required to pump the air into the cylinders and also to pump the combustion products out of cylinders;
• frictional losses are due to friction of piston skirt and rings, bearing frictions and valve frictions;
• power losses of oil pump for engine lubrication;
• valve train power losses.

The ratio of the brake or useful mechanical power to the total indicated power is called the mechanical efficiency η_m:

(2.135)

The friction power can be divided into three main parts: frictional power by friction forces between moving surfaces (cylinder-piston, bearings, valves), power for internal uses (oil pump, camshaft, etc.); and the power required to pump air into the engine and burned gases out of the engine. The first two are dependent on the engine speed and the third is throttle dependent. Indicated power also is dependent on both throttle (volumetric efficiency) and speed (Equation (2.133)). Therefore, the mechanical efficiency depends on the throttle position as well as engine speed.

2.8.2 Accessory Drives

Engine mechanical power to accelerate the vehicle must be delivered to the crankshaft end or to the flywheel. The net engine output power is not fully available at the output shaft since there are different accessories that are receiving power from the crankshaft. Major accessories are the alternator, air conditioning compressor and power steering pump that are usually driven by belt drives. The water pump is also usually driven by an accessory drive belt. In automobiles these belt drives are typically placed in front of engine and for this reason they are called Front Engine Accessory Drive or FEAD in short. A typical single belt FEAD system is shown in Figure 2.80.

Each accessory consumes power from the engine and the net power available to be used for vehicle motion, therefore, is reduced. Figure 2.81 shows typical torque and power demands of different accessories.

2.8.3 Environmental Effects

The engine performance is highly dependent on the ambient air conditions, especially air pressure and temperature. These atmospheric effects can be viewed from two different perspectives. In the first point of view, the main concern is the differences between the performances of different engines in similar working conditions. In other words, different engine designs are being compared with each other in terms of overall performance when they work in similar conditions. The second point of view compares the performances of one particular engine when it works at different climatic conditions. Examples are the performance variations of a specific vehicle during different seasons and in different geographical areas. In order to provide a more accurate basis for comparisons between performances of different engines, it is necessary to carry out tests under equal standard conditions. Engine tests performed in such standard ambient conditions are comparable, otherwise obviously an engine performs differently in different atmospheric conditions.

For both perspectives the idea of introducing correction factors has proved useful. In the first approach, correction factors can make the comparisons more reliable. Correction factors for the second approach can indicate how differently an engine is expected to perform in atmospheric conditions other than the ideal standard condition.

2.8.3.1 Atmospheric Properties

Air properties in the atmosphere depend on the ambient temperature, pressure and humidity. Atmospheric air properties change not only by seasons, but also by altitude. Basic relations for estimating air properties can be developed by using ideal gas formulas. Typical equations are [11]:

(2.136)

(2.137)

(2.138)

In the above equations, T is air temperature (Kelvin), p is air pressure (kPa), ρ is air density (kg/m³) and H is altitude (m). Subscript ₀ indicates the values at sea level (H = 0). Standard or reference values for the three parameters are defined differently. One reference point is given as and . The variations of the three parameters with altitude up to 3000 metres are shown in Figure 2.82.

2.8.3.2 Engine Test Standards

Engine manufacturers perform standard tests on their products to measure the performances of engines for type approval (TA) tests or conformity of production (COP) tests. Type approval is the confirmation that production samples of a design will meet specified performance standards. Conformity of Production (COP) is a means of evidencing the ability to produce a series of products that exactly match the specification, performance and marking requirements outlined in the type approval documentation. Standard conditions are defined by standardization organizations such as the ISO, SAE, JIS, DIN and others. Typical standard atmospheric conditions for engine tests are given in Table 2.15. The exact provision of standard conditions for an engine test is a difficult and costly task. The level of control may include only input air temperature or at the same time humidity and pressure. In case of any deviations from the standard atmospheric conditions, within a limited range allowed by the standard, corrections are needed to adjust the measured engine power values. Application of such correction factors to the measured powers on engine dynamometers will establish a reference engine power comparable with other standard values.

Table 2.15 Standard or reference atmospheric conditions for engine tests.

Test procedures for obtaining and correcting engine powers are defined in detail by different standard organizations and tests must be carried out in accordance with the guidelines set out in each standard. Test procedures define which auxiliary equipment must be fitted and which must be removed from the engine. They also define setting conditions for the engine and tests, fuel specifications, cooling of engine and tolerances, and reference atmospheric conditions. According to different standards, the correction formula for the engine power is of the basic form:

(2.139)

In the above equation, P_S is the corrected engine power for the standard atmospheric conditions and P_m is the laboratory test result before correction. C_F is the power correction factor and for SI engines, it can be written in the following general form:

(2.140)

in which T_m (Kelvin) and p_m (kPa) are the standard air temperature and dry air pressure observed in actual test conditions. The values 99 and 298 are the standard values for the pressure and temperature and could differ according to different standards (see Table 2.15). The powers α and β are two constants defined by the standardization bodies (see Table 2.16 for different values according to different standards).

Table 2.16 Coefficients for correction factors.

The power definitions used in the correction equations are different for different standards, some use brake powers and some indicated powers. Theoretically speaking, the general form of the correction factor C_F (Equation (2.139)) is based on the one-dimensional steady compressible air flow through a restriction. For this reason it should be applied to the indicated power of an engine. However, the values of α and β may be used to adjust the formula differently.

The total brake power P_b of engine is the subtraction of friction power P_F from the ‘indicated power’ P_i (Equation (2.135)):

(2.141)

Assuming Equation (2.139) is written for indicated powers and substituting from Equation (2.141), it will give:

(2.142)

in which subscripts Sb and mb denote standard corrected and measured brake powers respectively. It is assumed that the friction power of engine is independent of small climatic differences (that are present during the test with respect to the reference values) and is taken to be identical for the test and standard conditions. Defining k_p as the ratio of friction power to the brake power:

(2.143a)

Then Equation (2.142) can be written in the following form:

(2.143b)

which is an alternative form for correcting the measured power. This time by calculating and applying the correction factor C_Fb, the brake power will be corrected directly. In this form of the correction, it is assumed that the friction power will also be measured during the engine test. If the engine friction power is not measured, with an assumption of 85% mechanical efficiency for the engine [12], the correcting formula reads:

(2.144)

The dry air pressure p_m used in the calculations is the total barometric pressure p_b minus the water vapour pressure p_v:

(2.145)

in which Φ and p_vs are the humidity and saturation vapour pressure respectively. Φ is used in percentage and p_vs can be calculated from the following approximate equation (in mbar):

(2.146)

in which for T in Kelvin:

(2.147)

and for T in °C:

(2.148)

Different standards propose different correction formulas for diesel engines. The EEC formula for the naturally aspirated diesel engines is similar to Equation (2.140) for SI engines but with β = 0.7. The SAE also introduces an engine factor which makes the correction formula different and more complicated. It should be noted that the correction formulas can only be used when the correction factor resulting from this procedure remains very close to unity by a margin specified by the standard (typically around ±5%). In other words, if the correction factor calculated for an engine test remains outside the allowed bounds, the test is not valid and must be repeated.

2.8.3.3 Engine Power under Normal Conditions

Usually, the rated powers of engines are provided by the manufacturers defined as the standard corrected brake power of engine obtained according to standard dynamometer tests. The actual engine power will differ from the rated power since the intake air density is a function of atmospheric temperature and pressure and hence in warm or cold weather, and at low or high altitudes the air density will differ and will affect the engine performance. Thus, if the engine test results for the standard condition were available, corrections must be applied when using the engine information for vehicle performance analyses under normal conditions. These corrections are not identical to those explained earlier for engine test correction factors since those factors were designed for small deviations in standard test conditions. For normal driving conditions, however, the climatic conditions may differ enormously from those of the standard test conditions.

Owing to the analytical complexity of engine power dependency on the environmental conditions, an accurate model has not yet been developed for this purpose. From simplified models for the one-dimensional steady compressible air flow through a restriction, however, equations for the air mass flow rate have been derived. Such equations are also based on the assumption that air is an ideal gas with constant properties. Application of this technique for engine air mass flow at full throttle, assuming that the mass flow rate of air entering the engine is almost proportional to its indicated power, provides a correction factor for the engine indicated power P_i in the following form [2]:

(2.149)

in which P_S is the standard brake power, P_F is the friction power (assumed independent of environmental changes) and the correction factor C_F is given below:

(2.150)

where s and m stand for the ‘standard’ and ‘measured’ values. It should be noted that pressure terms in the above equation must be for the dry air (absolute barometric pressure p_b minus the water vapour pressure p_v) and temperatures are in degrees Kelvin.

Equation (2.149) can be written in a more useful form of:

(2.151)

in which P_b and P_Sb are the actual and standard brake powers of the engine and k_p is the ratio of friction power to the brake power. The term is usually very small compared to unity and may be ignored. The simplified form of Equation (2.151), therefore, is:

(2.152)

Note that the temperature values must be used in Kelvin and pressure terms are the dry air pressures (though the water vapour pressure is usually very small). Equation (2.152) simply indicates that pressure drop reduces the engine power and overheated air entering the cylinders has the same effect on engine power as a drop in atmospheric pressure. At a certain altitude the daily and seasonal temperature variations change the engine power. At a certain temperature, an increase in altitude will reduce the air pressure and consequently reduce the engine power.

2.9 Conclusion

The power generation process in an internal combustion engine involves the flow of working fluids in and out of the engine, together with combustion and thermodynamics processes. Understanding engine behaviour in various working conditions, therefore, needs a thorough knowledge of several areas such as fuel and reaction chemistry, physics, thermodynamics, fluid dynamics and machine dynamics. Modern engines are controlled by electronic management systems that are very influential on the overall behaviour of the engine and make the understanding even more complex.

The objective in this chapter was to familiarize the students with the power generation principles of the internal combustion engines. Therefore, the intention was to simplify the working principles of an engine and explain them in manageable sections. The subjects covered in this chapter should be treated in context. For example, Section 2.2 and especially subsections 2.2.2 and 2.2.3 only review the basic rules of engine theory and must not, therefore, be considered as design methods since the results differ from those of real engines. The method of torque estimation presented in Sections 2.3 and 2.4 are accurate as long as the input information, especially the pressure distribution versus crank angle, is accurate.

The new engine MT formula presented in Section 2.6 is very helpful for powertrain analyses since it estimates a continuous output for all working conditions. Hence, it is a useful mathematical representation of an engine map that is valuable for whole vehicle performance calculations. Section 2.8 is very important in that it emphasizes the engine dynamometer test results must be corrected for accessory drive power consumption and weather conditions before using them in vehicle powertrain analyses.

2.10 Review Questions

2.11 Problems

Problem 2.1

Use the MATLAB program of Example 2.3.3 to study the effects of changing engine parameters on its torque generation performance:

Problem 2.2

Use the data of Problem 2.1 to study the effects of changing the engine parameters on the engine bearing loads.

Problem 2.3

Derive expressions for the gudgeon-pin and crank-pin bearing forces A and B of the simplified model according to the directions of Figure 2.32.

Results:

Problem 2.4

For the engine of Example 2.3.3 compare the gudgeon-pin and crank-pin resultant forces of the exact and simplified engine models at 3000 rpm.

Hint: To find the gudgeon-pin forces of the exact model, use Equations 2.80, 2.81, 2.84 and 2.85.

Problem 2.5

Show that for the exact engine model the average of term T_e-F_Wh during one complete cycle vanishes.

Problem 2.6

Construct the firing map for a three-cylinder in-line engine with cranks at 0-120-240 degrees.

Problem 2.7

Construct the firing map for a four-cylinder 60° V engine with cranks at 0-0-60-60 degrees.

Problem 2.8

Construct the firing map for a six-cylinder in-line engine with cranks at 0-240-120-0-240-120 degrees.

Problem 2.9

For an in-line, four-cylinder engine the firing order is 1-4-3-2:

Problem 2.10

Compare the torque outputs of an in-line four-cylinder, four-stroke engine at two firing orders of 1-3-4-2 and 1-2-4-3- using the information in Example 2.4.3.

Problem 2.11

Use the information in Example 2.4.3 to plot the variation of the torque of the three-cylinder engine of Problem 2.6 and calculate the flywheel inertia.

Problem 2.12

Compare the variation of the torque of the four-cylinder V engine of Problem 2.7 with an in-line layout. Use the information in Example 2.3.3.

Problem 2.13

Plot the variations of engine power losses with altitude and temperature changes for Example 2.8.2 in SI units.

Problem 2.14

The variation of gas pressure of a single cylinder four-stroke engine during two complete revolutions at a speed of 2000 rpm is simplified to the form shown in Figure P2.14. Other engine parameters are given in Table P2.14.

Table P2.14 Engine parameters.

Parameter	Value
Cylinder diameter	10 cm
Crank radius	10 cm
Connecting rod cent-cent	25 cm
Con rod CG to crank axis	7 cm
Con rod mass	1.0 kg
Piston mass	1.0 kg

Use the simplified engine model:

Problem 2.15

The torque-angle relation for a four cylinder engine at an idle speed of 1000 rpm is of the form:

Results:

(a) T_a,

(c) 0.0046.

Further Reading

Of all the topics in automotive engineering, engines have dominated when it comes to textbooks. Because of its role as the fundamental power source, the internal combustion engine (ICE) has been seen as the heart of the vehicle. But although its importance is undisputed, it nevertheless seems to have attracted more than its fair share of textbooks. Only a small selection of these is referenced here, but these will provide the interested reader with plenty of excellent background material on engine design.

The classic book on the fundamentals of thermodynamics of engine is by Heywood [2] and this has been used throughout the world as a university teaching text. It starts with the fundamentals of thermochemistry and then uses this to analyze the combustion processes of both spark ignition (SI) and compression ignition (CI) engines. All aspects of the thermodynamic design are covered – including engine cycle analysis, gas flows and heat transfer. Stone's book [13] has also been extensively used as a teaching reference text. As well as covering the thermodynamics aspects of the combustion processes within engines, the book also contains some introductory material on the modelling, mechanical design and experimental testing of engines. This material is brought together in the final chapter which looks at three practical case studies of different engine designs.

For more detailed information on the mechanical design of engines, the definitive reference is by Hoag [14]. He concentrates on the design of all the engine components – block, cylinder head, pistons, bearings, camshafts, etc. – and discusses how they are all brought together in an integrated engine design. He also discusses operational issues such as balancing, durability and the overall development process.

Of particular interest to powertrain system design is the question of how to represent the behaviour of an ICE – in other words, how to characterize its properties without necessarily representing all the details of the thermodynamic processes. For example, the simplest method is to use empirical data – measured on a dynamometer – to obtain an engine map. This is often referred to as an empirical model and can then simply be used as a look-up table to obtain the engine performance properties under different operating conditions. Although modelling of engines has received a huge amount of attention, much of the information only exists in journal and conference papers. However, a recent book by Guzzella and Onder [15] has brought together some of the available information in a useful textbook. In particular, the authors explain in some detail, two types of engine models – the Mean Value and Discrete Event approaches. The book then goes on to explain how engine control systems operate and provide an excellent overview of engine management systems.

References

[1] Pulkrabek, W.W. (2004) Engineering Fundamentals of the Internal Combustion Engine. Prentice Hall, ISBN 0131405705.

[2] Heywood, J.B. (1989) Internal Combustion Engine Fundamentals. McGraw-Hill Higher Education, ISBN 978-0070286375.

[3] Mabie, H.H. and Ocvirk, F.W. (1978) Mechanisms and Dynamics of Machinery, 3rd edn. John Wiley & Sons, Inc., ISBN 0-471-02380-9.

[4] Kane, T.R. and Levinson, D.A. (1985) Dynamics: Theory and Applications. McGraw-Hill, ISBN 0-07-037846-0.

[5] Lechner, G. and Naunheimer, H. (1999) Automotive Transmissions: Fundamentals, Selection, Design and Application. Springer, ISBN 3-540-65903-X.

[6] Chowanietz, E. (1995) Automobile Electronics. SAE, ISBN 1-56091-739-3.

[7] Ribbens, W.B. (2003) Understanding Automotive Electronics, 6th edn. Elsevier Science, ISBN 0-7506-7599-3.

[8] Denton, T. (2004) Automobile Electrical and Electronic Systems, 3rd edn. Butterworth-Heinemann, ISBN 0-7506-62190.

[9] Bonnick, A.W.M. (2001) Automotive Computer Controlled Systems: Diagnostic Tools and Techniques. Butterworth-Heinemann, ISBN 0-7506-5089-3.

[10] Martyr, A.J. and Plint, M.A. (2007) Engine Testing: Theory and Practice, 3rd edn. Butterworth-Heinemann, ISBN-13: 978-0-7506-8439-2.

[11] Rakosh Das Begamudre (2000) Energy Conversion Systems, in New Age International, section 5.2, ISBN 81-224-1266-1.

[12] SAE J1349, Engine Power Test Code, REV.AUG. 2004.

[13] Stone, R. (1999) Introduction to Internal Combustion Engines, 3rd edn. SAE International, ISBN 978-0-7680-0495-3.

[14] Hoag, K.L. (2005) Vehicular Engine Design. SAE International, ISBN 978-0-7680-1661-1.

[15] Guzzella, L. and Onder, C. (2009) Introduction to Modelling and Control of Internal Combustion Engine Systems, 2nd edn. Springer, ISBN-13: 978-3642107740.