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Advances in Mechanical Engineering
Volume 2012 (2012), Article ID 937917, 9 pages
Power Balancing of Inline Multicylinder Diesel Engine
1Department of Mechanical Engineering, M. E. Society's College of Engineering, Pune 411001, India
2Department of Mechanical Engineering, Government College of Engineering, Pune 411005, India
Received 26 July 2012; Accepted 3 October 2012
Academic Editor: Mehdi Ahmadian
Copyright © 2012 S. H. Gawande et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In this work, a simplified methodology is presented for power balancing by reducing the amplitude of engine speed variation, which result in excessive torsional vibrations of the crankshaft of inline six-cylinder diesel engine. In modern fuel injection systems for reciprocating engines, nonuniform cylinder-wise torque contribution is a common problem due to nonuniform fuel supply due to a defect in fuel injection system, causing increased torsional vibration levels of the crankshaft and stress of mechanical parts. In this paper, a mathematical model for the required fuel adjustment by using amplitude of engine speed variation applied on the flywheel based on engine dynamics is suggested. From the found empirical relations and FFT analysis, the amplitude of engine speed variation (i.e., torsional vibration levels) of the crankshaft of inline six-cylinder diesel engine genset can be reduced up to 55%. This proposed methodology is simulated by developing MATALB code for uniform and nonuniform working of direct injection diesel engine of SL90 type manufactured by Kirloskar Oil Engine Ltd., Pune, India.
The internal combustion engine plays an important role in our society as means for transforming liquid and gaseous fuels to other more useful energy forms. Internal combustion engines are used in applications ranging from automotive to power generation. One of the drawbacks with combustion of fossil fuels is the emissions of carbon oxides (), nitrogen oxides (), and sulphur oxides (). The emissions of these chemical compounds from mainly power generation industry and automotive vehicles have been in focus during the last 40 years and have been one of the main drivers of the development of internal combustion engines. With the advances in electronics and digital technologies in the 1970s, it became feasible to electronically control the fuel injections to increase the fuel combustion efficiency and at the same time reduce emissions. The problem with cost efficient electronic fuel-injection systems is the need of periodic calibration of the cylinder-wise fuel injections. Without calibration, the amounts of fuel injected into the cylinders deviate significantly. In diesel engines, fuel can be delivered in several distinct injection pulses. The injection timing and quantity of each injection is important to provide better control of the combustion process. Depending on the operating conditions, different injection strategies are used; therefore, the ability to distinguish between fueling imbalances is important. The three most prominent approaches to estimate cylinder imbalance are based on three different feedback measurement variables: exhaust oxygen concentration, in-cylinder pressure, and crankshaft speed. The exhaust oxygen concentration-based approaches focus on estimation of air-fuel ratio imbalances, whereas in-cylinder pressure and the crankshaft speed-based approaches focus on estimated torque (fuel) imbalances. Due to these reasons in modern fuel injection systems for reciprocating engines, nonuniform cylinder-wise torque contribution is a common problem, causing increased torsional vibration levels of the crankshaft and stress of mechanical components. Engine balancing is the process of tuning an engine so that all of its cylinders produce the same amount of power for a given load. Therefore in this work the focus is on correcting power imbalance due to misfuel/misfire in medium-speed power plant engine.
The control objective of automotive cylinder-balancing methods is usually to equalize the cylinder-wise torque contributions [1–3]. Given a rigid crankshaft, this control objective is equal to minimizing the torsional vibrations of the crankshaft. In practice, the crankshaft can only be assumed rigid for lower vibratory frequencies, which consequently limits the types of engines that can be balanced. In addition, considering pump and valve torques, and misalignments and unbalances in the rotating system, it follows that a minimization of torsional vibration level implies more uniform cylinder torque contributions .
Compared to automotive applications, there is a set of specific problems which needs to be addressed for medium-speed engines. First of all, to reconstruct the superposed oscillating gas torque from angular speed measurements of medium-speed engines, the dynamic influence of the flexible coupling and load needs to be considered . Secondly, the dynamics of flexible couplings include uncertainties, which for some coupling types may significantly deteriorate the accuracy of the reconstructed gas torque. To ensure the performance, these uncertainties should be taken into account. Thirdly, for engines with many cylinders, frequencies need to be analyzed for which the crankshaft can no longer be assumed rigid. In order to accurately balance the engine, means for considering the dynamics of the crankshaft have therefore to be developed. Given that the engine is decoupled from the load for the set of torque frequencies generated by the fuel combustions, the superposed oscillating gas torque can be calculated from measurements of the angular speed of the flywheel, that is, it can be assumed that the load torque affecting the engine is more or less constant. Due to the lower rotational speed of medium-speed engines, the lower torque-order excitations from the fuel combustions are usually in the vicinity of the lowest resonant frequencies of the crankshaft system. As a consequence, the dynamic influence of the flexible coupling and load on the engine needs to be considered  in order to reconstruct the superposed oscillating gas torque correctly. The dynamics of flexible couplings include uncertainties which for some coupling types need to be considered . In addition, the dynamics also depend on many different factors such as age, temperature, and vibratory frequencies. These uncertainties may induce significant errors in the estimated oscillating gas torque which affects the overall performance of the cylinder balancing. The problem of relating the calculated superposed oscillating torque to the consecutive cylinder firings is simplified if the crankshaft can be assumed rigid for the considered set of frequencies. For medium-speed engines, this assumption is generally valid only for lower vibratory orders. As a consequence, cylinder balancing using the assumption of an inflexible crankshaft can only be used for engines with few cylinders. Some methods have been suggested which take into account the dynamics of the crankshaft [7–9]. The usual approach is to increase the order of the lumped mass-spring model in order to capture the fundamental dynamics of the crankshaft. For engines where not all parameters are sufficiently known, off-line parameter identification methods have been proposed . For manufacturers with a large engine portfolio and many various types of installations, the parameter management becomes a problem, making the study of methods for online parameter estimation well motivated.
According to Kiencke and Nielsen , the demanded and the actual amounts of fuel injected in the cylinders differ up to 25%, due to different characteristics of the fuel injectors , varying pressure differences between the rail and the cylinders, clogging of injector nozzles, , and so forth. This deteriorates the control of fuel injections and results in variations from average torque contributions of the various cylinders. The varying torque applied on the crankshaft causes increased torsional vibrations, imposing increased stresses and inevitable wear of mechanical components. The problem is therefore to adjust the cylinder-wise fuel injections so that the torque contributions can be balanced.
Balancing the cylinder-wise torque contributions of automotive and other high-speed engines was addressed by reconstructing the cylinder-wise net indicated torques [14–16] by direct use of the angular acceleration [17, 18] or by reconstructing only the relative torque contributions of the cylinders . Taraza et al.  suggested a method where the measured angular speed was directly related to the nonuniform torque contribution. Hence, in order to determine the cylinder-wise net indicated torque, the oscillating torque applied on the flywheel is reconstructed from measurements of the angular speeds of the crankshaft. Hence it is required to assume that the crankshaft is rigid and that the engine is sufficiently decoupled from the transmission and load and it is observed that the oscillating torque can be reconstructed by using a single mass engine model and one angular speed measurement, [11, 14, 19, 20]. To obtain an estimate of the prevailing load torque, the authors of  use the fact that the instantaneous torque from the engine is zero at top-dead center (TDC) and bottom-dead-center (BDC), whereas Rizzoni  use a linear relationship between the root mean-square (RMS) value of the oscillating torque amplitude and net indicated torque applied on the flywheel. Instead of estimating the engine load, the authors of  proposed an observer-based method, which uses the measured engine load torque directly to reconstruct the cylinder-wise net indicated torques of a 6-cylinder engine. Kim et al.  used an engine model for a genset, in which the load was modeled with an additional mass. However, the dynamic link between the generator and grid was not included, although it has a significant impact on the dynamics. Moreover, engine models which include flexible couplings generally assume that the stiffness and damping are constant [7, 11]. However, as the stiffness and damping of flexible couplings used in these kinds of generator sets depend significantly on the vibration frequency, the nonlinearities of the couplings should be taken into account to accurately reconstruct the oscillating torque.
During this work, it is seen that when applying any cylinder fault/misfire/imbalance detection method on medium speed diesel engine, it is required to focus on three aspects: (a) the modeling of the engine, (b) the modeling of the flexible coupling, and (c) the modeling of the load. As medium-speed engines have a nominal speed which is normally below 1500 rpm, the excitation orders of the cylinder-wise torque contributions are very close to the first natural frequency of the rotating system. This makes it necessary to include the dynamics of the load in the engine model. Therefore in order to overcome the above stated deficiencies and to suggest alternative solution to the existing problems in current fuel injection system of diesel engine, the problem of cylinder balancing of medium-speed internal combustion engines is investigated in this research with the objective of minimizing torsional vibrations due to engine speed variation by harmonic analysis. By analyzing the gas torque of cylinder and angular speed of the crankshaft, fuel-injection adjustments are determined to minimize the variation in engine speed which results in reduction of torsional vibrations of the engine crankshaft.
2. Problem Formulation and Objective
As per the past literature and industrial survey carried in engine manufacturing industry located in MIDC, Pune, namely, Greaves Cotton Ltd., and Kirloskar Oil Engine Ltd., in an internal combustion reciprocating diesel engine, the quantity of fuel actually injected into each cylinder and at each injection may be different from the nominal fuel quantity requested by the electronic control unit (ECU) which is used to determine the energizing time of the injector [3, 11, 12]. The energizing time of the injector depends on the dispersion and the time-drift variations of the injector’s characteristics, due to the production process spread and aging of the injection system. In fact, the current injector production processes are not accurate  enough to produce injectors with tight tolerances; moreover, these tolerances become worse with aging during the injector life-time. As a result, for a given energization time and a given rail pressure, the quantity of fuel actually injected may be different from one injector to another. This difference in fuel injected quantity results in a cylinder-by-cylinder torque imbalance, causing some problems such as differences in pressure peak, differences in heat release, and dynamic effects on a crankshaft which ultimately results in excessive torsional vibrations.
Hence in order to overcome the above stated disadvantages in current fuel injection system of diesel engine, following objectives were set to satisfy the purpose of engine power balancing:(i)tune the engine to some nominal state specified by the vendor for performance and fuel consumption,(ii)balance the average power within each cylinder so as to minimize the engine vibration and stresses on the engine components.
3. Experimental Setup and Measurements
In order to study the effect of detection of imbalance and balancing, the required experimental setup was developed as shown in Figure 1.
Figure 1 shows schematic layout of test setup developed for the measurement of engine speed to analyze and measure the variations in time and engine speed. Figure 1 shows position of a six-cylinder engine, flywheel with alternator, gear wheel, sensor, and FFT spectrum analyzer. Crankshaft angular speed of internal combustion engines is usually measured by means of a gear or measurement disk and a speed-pickup. As the gear wheel rotates the tooth on gear or mark passes the sensor, a step formed voltage is generated, called pulse train, which is used for calculating the angular speed. The power balancing method proposed in this work uses the determination of the angular velocity at every edge of the gear wheel signal as it rotates. The crankshaft angle was measured at every ten degrees, that is, when a new edge on the gear is sensed by sensor as shown in Figure 2. The measured speed responses in time domain as shown in Figure 4 and Figure 5 for uniform and non-uniform engine operation are obtained to calculate angular velocity to decide the position of the crank shaft. The angular velocity is calculated, when a positive edge appears, using the differential Equation (1) as follows: where is the known sector angle described by the set of pulses for which the engine speed is measured and is the measured time, and is the number of teeth on gear. The time is measured by a digital timer set in FFT spectrum analyzer which is controlled by the zero crossings of pulse signal. Figure 2 shows the gear wheel mounted on crankshaft next to flywheel with position of hall effect sensor when engine is in rotating position with speed of 1500 rpm. Here speed was measured by digital display mounted on engine housing as well as digital tachometer. Figure 3 shows the measurement of engine speed in terms of the speed step response in time domain. Here FFT spectrum analyzer is used to plot the harmonic spectrum of speed step response corresponding to engine harmonic order.
Figures 7 and 8 show the comparison of the speed signal for the normal operation and non-uniform operation when cylinder 5 is cut off, in Cartesian and polar coordinates, respectively. This shows that average engine speed is 1501.359 rpm for normal working and 1503.437 rpm for misfuel in cylinder no. 5.
Figure 6 shows measured time for six-cylinder diesel engine for normal working and misfuel in cylinder no. 5.
Figure 7 illustrates a graph of engine speed (in rpm) versus crankshaft position (in degrees) for a considered six-cylinder engine over one complete engine cycle. It is seen that the actual instantaneous speed of the engine varies significantly from its average speed (1500 rpm) as each of the engine cylinders fires in turn (the peaks in the figure represent successive firings of the engine cylinders). It is also seen that the peaks do not all lie at the same value, indicating different power contributions from each cylinder as it fires. A cylinder having a greater power contribution will increase the engine speed to a higher level than the firing of cylinders having a lower power contribution. This work comprehends the use of fast Fourier transform (FFT), in order to relate the data to engine order, using the engine crank angle as the independent variable. It is theoretically possible to calculate the cylinder power contribution of a six-cylinder engine from the first three engine orders. When all FFT components are zero, the power contribution of the engine cylinders is equally balanced. Once the FFT calculation has been completed, then the focus is to calculate the fuel adjustments to be applied to the fuel injection system for each cylinder in order to drive the FFT components to zero.
4. Development of Algorithm for Cylinder Power Balancing
In this section an algorithm for engine cylinder power balancing is explained which comprise the following steps:(1)measurement of instantaneous speed of the engine crankshaft during a working cycle by speed pick up,(2)perform a fast Fourier transform (FFT) upon the sensed engine speed, thereby producing at least one Fourier transform component corresponding to the harmonic orders 0.5, 1, and 1.5 of the engine,(3)determine a cylinder power imbalance condition from a phase of the Fourier transform component,(4)balancing is carried by using predetermined adjustment selected based on the observations in step (3). Figure 9 illustrates the relationship between each of the first three engine harmonic orders and common cylinder imbalance conditions which increase the magnitude of these orders in the FFT results. As shown in Figure 9(b), contribution to power imbalance at the 0.5 order is primarily due to one cylinder imbalance (cylinder 1). This indicates that the relative fueling is different for cylinders, causing the under or over fueled cylinder to produce substantially different power. Figure 9(c) illustrates cylinder bank-to-cylinder bank symmetric imbalances which contribute primarily to the 1.0 order. Finally, Figure 9(d) illustrates cylinder bank-to-cylinder bank offsets, in which one bank of cylinders has substantially different fueling from the other cylinder bank, which contributes primarily to the magnitude of the 1.5 order.
Figures 9(b), 9(c), and 9(d) illustrate the general shape of the FFT data for each of the first three engine orders. As seen in Figure 9(b), the 0.5 engine order results in a cosine wave having a period of 720° crank degrees. The 1.0 engine order illustrated in Figure 9(c) is also a cosine wave, having a period of 360° degrees. Finally, the 1.5 engine order illustrated in Figure 9(d) is a cosine wave having a period of 240° crank degrees.
For the Kirloskar six-cylinder engine, the cylinder firing order is 1-5-3-6-2-4. The cylinders firing instantaneous positions are shown in Figures 9(b), 9(c), and 9(d) to indicate which cylinder is firing at the time the data was produced.
Figure 9(b) illustrates the 0.5 order component of the FFT when cylinder 1 is high (higher than average output power developed by the cylinders) or when cylinder 6 is low (lower than average output power developed by the cylinders). The phase of the waveform in Figure 9(b) would be translated to the left or to the right if another engine cylinder was high or low. For example, the peak in the waveform of Figure 9(b) would occur at 240° of crank angle if cylinder 4 was high or cylinder 3 was low. A substantially flat waveform for the 0.5 order component of the FFT indicates that no substantial single cylinder imbalances are occurring within the engine. Hence in the present work, an attempt is made to apply the fuelling correction to the engine in order to iteratively drive the 0.5 order component of the FFT to zero to achieve a balanced condition.
Similarly, the presence of a 1.0 order component in the FFT, as illustrated in Figure 9(c), indicates that pair of cylinders on opposite banks of the engine is either high or low. For example, the waveform of Figure 9(c) indicates that cylinder 1 and cylinder 6 of the engine are both high with respect to the average power developed by the cylinders. Similar to 0.5 order waveform, the phase of the 1.0 order waveform shown in Figure 9(c) will be translated to the left or to the right when other pairs of cylinders are either high or low. The present work is therefore operative to make changes in the fueling correction to the engine in order to iteratively drive the waveform of Figure 9(c) to zero which results in balanced state of the engine.
Figure 9(d) illustrates the 1.5 order FFT component, indicating bank-to-bank offsets in the engine. The waveform illustrated in Figure 9(d) indicates that cylinders 1, 2, and 3 are high, while cylinders 4, 5, and 6 are low. The opposite condition in the engine (cylinders 1, 2, and 3 low and cylinders 4, 5, and 6 high) will produce a 120° phase shift in the waveform of Figure 9(d). The presence of a 1.5 order component in the FFT data needs to adjust the fueling correction to the engine to iteratively drive the 1.5 order component of the FFT to zero to achieve a balanced condition.
5. Determination of Fueling Corrections
Once the first three engine order components of the FFT are determined, the present work then utilizes this information in order to determine the fueling corrections to be applied to the fuel system for each engine cylinder. Therefore a matrix is defined for the fueling corrections for a 6-cylinder engine as follows: where is fueling correction for cylinder 1, is fueling correction for cylinder 2, is fueling correction for cylinder 3, is fueling correction for cylinder 4, is fueling correction for cylinder 5, and is fueling correction for cylinder 6.
From Figure 9(b), it is seen that in order to correct the 0.5 order component when cylinder 1 is high, it will be necessary to reduce the fueling to cylinder 1 by a relatively great amount, increase the fueling for cylinder 6 by relatively great amount, reduce the fueling to cylinders 4 and 5 by a relatively smaller amount, and increase the fueling to cylinders 2 and 3 by a relatively smaller amount. These changes to the fueling of the cylinders will have a tendency to flatten out the waveform of Figure 9(b). Likewise, Figure 9(b) indicates that the fueling to cylinders 1 and 6 should be reduced by a relatively greater amount, while the fueling to cylinders 2, 3, 4, and 5 should be increased by a relatively smaller amount. Again, this will have the tendency to flatten out the waveform of Figure 9(c). Finally, Figure 9(d) indicates that the fueling to cylinders 1, 2, and 3 should be reduced by the same amount that the fueling to cylinders 4, 5, and 6 are increased by the same amount. These changes to the fueling for the situations indicated in Figures 9(b), 9(c), and 9(d) may be expressed in matrix form as shown in equation (3) as follows: where “” is an iteratively determined constant based on trial error method. Value of “” is iteratively determined for the engine and fuel system. Using the FFT waveform magnitude of fueling correction is determined. The magnitude of fueling corrections for each of the cylinder is represented as shown in equation (3) by the factors 1 and 2 corresponding to minimum and maximum values, respectively.
For 6-cylinder medium speed engine the value of “” is selected and used for determinations of fueling correction as per equation (4) as follows: Further, by taking the summation of equation (3), changes to the fueling may be expressed in matrix form as follows: As per the above discussion, it is seen that the following matrices are used to correct any combination of engine cylinder power imbalance in a 6-cylinder engine.
Adjustments for 0.5 order components are as follows: Cyl.1 high or cyl.6 low:.
Similarly; cyl.2 high or cyl.5 low: , cyl.3 high or cyl.4 low: , cyl.4 high or cyl.3 low: , cyl.5 high or cyl.2 low: , cyl.6 high or cyl.1 low: .Adjustments for 1.0 Order Components: cyl.1, 6 high:
Similarly; cyl.2, 5 high: , cyl.3, 4 high: , cyl.3, 4 low: , cyl.2, 5 low: , cyl.1, 6 low: ,Adjustments for 1.5 Order Components: Cyl.1, 2, 3, high: Similarly; Cyl.4, 5, 6, high: Based on these investigations the following condition is proposed.
Condition 1. For a well power-balanced six-cylinder 4-strokes (4-S) reciprocating diesel engine, the resultant of magnitude of the amplitudes of first three harmonic orders (0.5, 1, and 1.5) is always zero.
Proof. A matrix is defined for the experimentally measured fueling corrections for a 6-cylinder engine (as per Figure 9) as follows: From the above investigation, it is seen that of sum of the corrections of the FFT components of 0.5, 1.0, and 1.5 engine orders is found to be zero, zero, and zero which implies that for well power balanced engine the sum of magnitude of the amplitudes of first three harmonic orders (0.5, 1, and 1.5) of four stroke reciprocating diesel engine is always zero.
6. Simulation Code for Uniform and Nonuniform Engine Operation
In order to validate and execute the calculated and simulated fuel adjustments in an operating six-cylinder diesel engine of SL90 type, MATLAB code was developed for uniform and nonuniform engine operation. Here the focus is to observe the dynamic behavior of engine by simulating different parameters such as piston velocity, gas torque, mass torque, mass gravity torque due to piston weight and reciprocating parts, total torque, and engine speed. The combined effect of gas torque, mass torque, and mass gravity torque on engine speed for uniform and non-uniform engine operation is investigated and effect on lower engine order is noted and explained in details.
6.1. Comparison of FFT Waveform of Simulated Engine Speed for Six-Cylinder Engine Order
In this subsection, the comparison of FFT waveform of lower engine harmonic order (0.5, 1, 1.5) for uniform and nonuniform engine operation with experimental and simulated results is explained. A closed match between experimental and simulated fueling correction is observed. From simulated results with engine nonuniform operation as shown in Figures 10, 11, and 12, it is observed that after applying fueling correction, the level of torsional vibration reduces from 0.8 (1/s) to 0.5 (1/s) for 0.5 engine order, from 0.42 5(1/s) to 0.32 (1/s) for 1 engine order, and from 0.4 (1/s) to 0.18 (1/s) for 1.5 engine order.
The primary objective of this work was to get insight into how torsional vibrations due to engine speed variations play an important role in basic design calculations, performance diagnosis of reciprocating internal combustion engine by detecting and correcting power imbalance in operating six-cylinder diesel engines. The objective was achieved with the help of extensive analytical work, computer aided simulation tools, commercially available softwares, and experimental investigations. The new approach presented for power balancing to reduce the torsional vibrations due speed variation can be effectively used for considered six-cylinder diesel engine. The use of Fourier transform of engine speed signal for one complete cycle (0–720°) can be effectively used to detect power imbalance and balancing, as an imbalanced engine results in nonzero magnitudes and balanced engine results in zero (0) magnitudes of the FFT components that correspond to the 0.5, 1.0, and 1.5 engine orders. The compensation scheme suggested in this work uses the iteration to reduce the magnitudes of these components to zero (0) if the engine is detected to be imbalanced. From further investigation, it is found that when all FFT components (of 0.5, 1.0, and 1.5 engine orders) are flatten nearer to zero (0), and the power contribution of the engine cylinders is said to be equally balanced. To execute and validate the findings, simulation code is developed in MATLAB. From experimental work and simulated results, it is seen that the proposed fueling corrections for power balancing are in good agreement. From simulated results with engine nonuniform operation, it is observed that after applying fueling corrections, the level of torsional vibration reduces from 0.8 (1/s) to 0.5 (1/s) for 0.5 engine order, from 0.425 (1/s) to 0.32 (1/s) for 1 engine order, and from 0.4 (1/s) to 0.18 (1/s) for 1.5 engine order.
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