International Journal of Automotive Technology, Vol 12, No 6, pp 787−794 (2011) DOI 10.1007/s12239−011−0091−z Copyright © 2011 KSAE 1229−9138/2011/061−01 COMBUSTION INSTABILITIES AND NANOPARTICLES EMISSION FLUCTUATIONS IN GDI SPARK IGNITION ENGINE A E HASSANEEN1)*, S SAMUEL2) and I WHELAN2) 1) Department of Automotive Technology, Helwan University, Cairo, Egypt 2) School of Technology, Oxford Brookes University, OX33 1HX, UK (Received 26 October 2010; Revised 16 May 2011) ABSTRACT−The main challenge facing the concept of gasoline direct injection is the unfavourable physical conditions at which the premixed charge is prepared and burned These conditions include the short time available for gasoline to be sprayed, evaporated, and homogeneously mixed with air These conditions most probably affect the combustion process and the cycle-by-cycle variation and may be reflected in overall engine operation The aim of this research is to analyze the combustion characteristics and cycle-by-cycle variation including engine-out nanoparticulates of a turbocharged, gasoline direct injected spark ignition (DISI) engine at a wide range of operating conditions Gasoline DISI, turbo-intercooled, 1.6L, cylinder engine has been used in the study In-cylinder pressure has been measured using spark plug mounted piezoelectric transducer along with a PC based data acquisition A single zone heat release model has been used to analyze the in-cylinder pressure data The analysis of the combustion characteristics includes the flame development (0-10% burned mass fraction) and rapid burn (10-90% burned mass fraction) durations at different engine conditions The cycle-by-cycle variations have been characterized by the coefficient of variations (COV) in the peak cylinder pressure, the indicated mean effective pressure (IMEP), burn durations, and particle number density The combustion characteristics and cyclic variability of the DISI engine are compared with data from throttle body injected (TBI) engine and conclusions are developed KEY WORDS : DISI engine, Cyclic variability, Combustion characteristics, Nanoparticulates INTRODUCTION has been proved to be a good potential for automobile engines The advantages of DISI engines reflect in their higher thermal efficiency due to the higher volumetric efficiency of the unthrottled charge, better potential for reducing the specific fuel consumption, and better control of injection quantity and timing (Gao et al., 2005) Significant advancements have been made in recent years in the development of combustion systems for DISI engines which have resulted in larger fuel economy benefits, better exhaust emissions, and significant power advantages compared to throttle-body (TB) and port fuel (PF) injected engines (Kume et al., 1996; Ando; 1996, Jackson et al., 1996; Itoh et al., 1998; Geiger et al., 1999) DISI engines, however, have their drawbacks due to the time limitations and gasoline direct injection characteristics which may affect the fuel evaporation, charge homogeneity, and the stability of the entire combustion process which lead to an intense cyclic variability Moreover, it is difficult to know exactly what type of flame is propagating for any particular ignition event in a DISI engine due to the direct fuel injection and the highly turbulent motion inside the combustion chamber The cyclic variability in gasoline engine which were investigated by many researchers affects the engine fuel economy and it may decrease the mean effective pressure by as much as 20% (Litak et al., 2009) Brown et al (1996), concluded on their work that the The instabilities in the combustion processes were observed from the very beginning of spark ignition engine development (Clerk, 1886) These instabilities were identified as a fundamental combustion problem and it may cause fluctuations in the flame propagation pattern, the burned fuel mass, the indicated mean effective pressure, and consequently the power output in SI engines (Patterson, 1966) The main factors of combustion instabilities as classified by Heywood (1988) are aerodynamics in the cylinder during combustion, amounts of fuel, air, and recycled exhaust gases supplied to the combustion chamber, and composition of local mixture near the spark plug These factors will affect the combustion characteristics and lead to a significant cycle-by-cycle variation in the combustion process Furthermore, a disturbing feature of these combustion instabilities is the unpredictable character of their occurrence (Sawamoto et al., 1987; Wagner et al., 1993; Eriksson et al., 1997; Muller et al., 2001; Matsumoto et al., 2007) Direct injection spark ignition engine (DISI) technology *Corresponding author e-mail: geushey@hotmail.com 787 788 A E HASSANEEN, S SAMUEL and I WHELAN cycle-by-cycle variation in combustion should be characterized by the coefficient of variation (COV) of the indicated mean effective pressure (IMEP) in preference to the COV of the in-cylinder peak pressure They also added that cycle-by-cycle variations are lower when the early combustion is more rapid They also found that the COV of IMEP is a minimum in the region of MBT ignition timing Hinze and Cheng (1998) concluded that the variations in flow field and the inhomogeneous charge in SI engines contribute to almost 50% of the cycle-by-cycle variations of IMEP This paper presents a study of the combustion characteristics and cycle-by-cycle variations of a turbointercooled gasoline direct injection (DISI) engine at different engine speeds and loads These characteristics include the in-cylinder peak pressure, the indicated mean effective pressure (IMEP), burn durations, and the coefficient of variation of these parameters and the nanoparticulates emission from cycle-to-cycle These characteristics will be compared to those of an older throttle body injected (TBI) engine EXPERIMENTAL APPARATUS 2.1 Engine The DISI engine used for this research was a 1.6L, four cylinders, direct-injection, four-stroke, water cooled, turbocharged and intercooled engine The TBI engine was a 1.4L, four cylinders, naturally aspirated, four-stroke, and water cooled engine A list of the complete engine specifications for the DISI and TBI engines are provided in Table and Table respectively A schematic diagram of the test rig is shown in Figure Both engines were designed to run at stoichiometric air-to-fuel ratio for the sake of efficient performance of the catalytic converter Table DISI test engine specifications Bore (mm) 77.0 Stroke (mm) 85.8 Displacement (cc) 1598 Compression ratio 10.5:1 Rated power 125 kW @ 6000 RPM Rated torque 220 Nm @ 4000 RPM Table TBI test engine specifications Bore (mm) 75 Stroke (mm) 79 Displacement (cc) 1398 Compression ratio 9.5:1 Rated power 69 kW @ 6250 RPM Rated torque 122 Nm @ 4500 RPM Figure Schematic of test rig The DISI engine utilises wall guided direct-injection (WGDI) at a pressure of 120bar WGDI engines introduce the fuel into the combustion chamber via a side mounted swirl injector The mixture is then guided toward the spark plug by the reverse tumble turbulent motion and the bowl shaped pocket in the piston crown At this fuel injection pressure, the spray velocities are on average an order of magnitude faster than piston velocities and spray penetration distances are of the same order as the stroke Therefore, it is inevitable that the fuel spray will impact upon the piston crown and cylinder walls Any form of fuel impingement on the walls of the combustion chamber can cause lubricating oil to mix with the bulk gas This can result in increased PM and HC emissions Most wall wetting occurs when the fuel injection is advanced, i.e when the piston is near top dead centre on the intake stroke The degree of fuel evaporation from these surfaces decreases with injection retard With the optimised flow motion in the combustion chamber of modern DISI engines, the amount of wall wetting may be reduced in relation to the first generation DISI engines 2.2 Particulates Measurements A Differential Mobility Spectrometer, DMS-500, was used to analyse the exhaust gas sample The DMS-500 provides a number and size spectrum for particles between 5-1000 nm Particles above 1000 nm are removed by a cyclone separator upstream to reduce the need for cleaning The DMS-500 consists of a classifier column (consisting of 22 grounded electrometer rings), a high voltage electrode, space charge guide and a conductive tube The classifier column operates at sub-atmospheric pressure, obtained using a scroll vacuum pump Within the conductive tube, the particles become ionised, i.e charged The particles are therefore classified according to their charge to drag ratio 2.3 Test Method All the tests have been carried out at steady-state conditions at fully warmed-up temperatures (coolant temperature is 83oC, oil temperature is 89oC) Due to the dynamometer loading limitations, the engine operating COMBUSTION INSTABILITIES AND NANOPARTICLES EMISSION FLUCTUATIONS points used for the statistical analysis were 1600, 2400 and 3200 RPM and a load range of 20-120 Nm (1.57 – 9.42 bar BMEP) in increments of 20 Nm For the in-cylinder pressure analysis a single zone heat release model based on the first law of thermodynamics without heat transfer was employed in the present work Average cycle obtained over 100 engine cycles were used for the heat release analysis DISI and GDI refer to the same gasoline direct injected engine elsewhere in the paper HEAT RELEASE MODEL The heat release analysis is based on a single-zone model in which the burned and unburned zones in the combustion chamber are treated as a single zone The model is based on the first law of thermodynamics applied to the in-cylinder control volume as follow (Heywood, 1988): dQhr − dQhl = dU + dW 789 The motivations behind the use of direct injection of gasoline in spark ignition engines are mainly its better fuel economy as it appears in Figure where brake specific fuel consumption and thermal efficiency almost approach those values of the conventional Diesel engines especially at part loads (Heywood, 1988; Roy, 2011) It is shown from the figures that fuel consumption dropped from 450 (g/kW.hr) at low loads to around 230 (g/ kW.hr) at high loads It seems from the figures that a finer control of ignition timing is needed to eliminate the differences between the fuel consumption values at different speeds especially at the middle load range 4.2 Combustion Characteristics The combustion characteristics include the analysis of incylinder peak pressure, indicated mean effective pressure, and burn durations The in-cylinder peak pressure, its location and rate of rise at different engine loads and Where dQhr represents the fuel chemical energy released, dQhl represents the heat loss to the cylinder walls, dU and dW represent the change in the sensible internal energy and the work done on the piston respectively Using the thermodynamic relationships and neglecting the heat losses term, the above equation of the first law is simplified to the following form: n dQhr = VdP + PdV n–1 n–1 Where V and P is the instantaneous in-cylinder volume and pressure respectively, n is the polytropic exponent RESULTS AND DISCUSSION 4.1 Fuel Economy and Thermal Efficiency Figure Fuel economy and brake thermal efficiency (GDI engine) Figure peak cylinder pressure, its location, and rate of pressure rise 790 A E HASSANEEN, S SAMUEL and I WHELAN Figure Early combustion durations as a function of BMEP speeds are shown in Figures 3, 4, and It can be seen from the figures that minimal variation in the peak pressure and its rate of rise is maintained at most of the engine speeds except at very high loads This minimal variation may be attributed to the better control of the air-to-fuel ratio in the case of GDI engines At high loads, this better control of air-to-fuel ratio is challenged by the time limitation for the huge amount of fuel to be vaporised and well mixed with air The location of peak pressure is also maintained at the relatively high engine speed while at low speed it is retarded as shown in the figure The rate of pressure rise of the GDI engine was found to be much higher than the rate of pressure rise of the TBI engine This difference in the Figure Rapid burn duration as a function of BMEP rate of pressure rise may be due to the fact that the mode of combustion in GDI engines most likely a mix of stratified, homogeneous, and heterogeneous regimes In order to achieve a stable operation for a gasoline direct injection engine, a precise control of ignition timing is crucial This is evident from the ignition timing chart shown in Figure where a wide range of ignition timing is adopted for better performance Combustion durations including flame development duration (Spark-10% bmf) and rapid burn duration (1090% bmf) are shown in Figures and The flame development duration (Spark-10%bmf) vary from 35 degree crank angle (oCA) at low loads to 13 (oCA) at high loads These durations are corresponding to ms at 1600 rpm at low load and 1.5 ms at high loads The rapid burn COMBUSTION INSTABILITIES AND NANOPARTICLES EMISSION FLUCTUATIONS 791 duration vary from 60 (oCA) at low loads to 20 (oCA) at high loads In terms of milliseconds, the duration drops from ms at 1600 rpm and low loads to less than ms at high loads It can be concluded that increasing the load on the engine decrease the burn time to 33% from its value at low loads regardless of engine speed as shown in Figure Comparison between the flame development and rapid burn duration for the DISI and TBI engines are shown in Figures and respectively It is shown that the flame development duration for the DISI engine is longer than that for the TBI engine at middle to high loads In the very low and very high range, however, the duration for the DISI engine is slightly shorter These last findings may be attributed to the longer time needed for the directly injected fuel in DISI engine to evaporate and mix with air to form a homogenous charge Due to the high throttling and the challenges to control the A/F ratio at the very low loads in TBI engine, the flame development duration tends to be larger than DISI engine The same trend continues to show up at vary high loads most probably because of the better chance to achieve rich A/F ratios in DISI engine 4.3 Cyclic Variations in Combustion Parameters 100 engine cycles were acquired and an average cycle was used for the statistical analysis The coefficient of variation (COV) in the combustion parameters is shown in Figure and It can be seen in the figure that the COV in peak pressure is maximum at medium loads at all engine speeds At very low load, however, COV show some improvement which may be attributed to the good control of air-to-fuel ratio (A/ F) at low loads in the gasoline direct injected unthrottled engines The comparison between DISI and TBI engines show that COV in peak pressure and IMEP for TBI engine are generally lower than those of DISI engines as shown in Figure COV in peak pressure and IMEP of TBI engine at very low load is higher than DISI engine due to the fact that A/F ratio in TBI engine is less controlled at low loads because of the throttle itself and the possible misdistribution of the charge over the individual cylinder As the load goes up, the fresh charge is better distributed over the individual cylinders in TBI engines and throttle effect becomes smaller which is reflected in an improved COV In DISI engine, however, as the load goes up, the amount of fuel injected becomes larger and more time for its evaporation is needed thus suggesting a pourer mixing process and most probably inhomogeneous charge is formed These all may lead to a higher COV in peak pressure and IMEP for DISI engines at high loads as shown in Figure and The comparison between the two engines in terms of the COV in the location where 90% of the mass is burned show a big difference to the favour of the TBI engine It reaches a value of 45% for DISI engine and drop to 15% for TBI engine as can be seen in Figure This Figure COV of combustion parameters as a function of BMEP difference may be attributed to the inhomogeneous mixture locally formed in the DISI engine combustion chamber 4.4 Cyclic Variations in Particulates Comparisons of the total particle number between the TBI and GDI engines are shown in Figure The total particle number density in GDI engine is almost two orders of 792 A E HASSANEEN, S SAMUEL and I WHELAN Figure Comparisons of COV in combustion parameters of the two engines magnitude higher than TBI engine The total particle number density of GDI engine is very close to the particle number density of diesel engine The cycle-by-cycle variation in the main combustion parameters seems to have a considerable effect on the fluctuations of the nano-scale particulates as can be seen in Figures and The variations in the particle number Figure PM and its COV as a function of MEP density for different diameter particles decreases with an increase in engine load as can be seen in Figure The variation in the 10 nm particles was higher than that in the 56 and 100 nm diameter particles at the same loading conditions Although the COV values of the 10 nm particles were higher than those for the 56 and 100 nm particles, its correlation coefficient with the engine brake mean effective pressure (BMEP) was far less than the correlations of the other two diameter particles (R2=0.14, COMBUSTION INSTABILITIES AND NANOPARTICLES EMISSION FLUCTUATIONS 793 ranges That is why COV of the particle number density is less correlated to engine speed than to engine load It is shown that the COV in the particle numbers increases with an increase in the COV of the combustion parameters with relatively stronger correlation coefficients with the COV in the combustion durations of the 10-90% burned mass fraction This is again could be attributed to the competition between the nucleation and oxidation processes which are affected by the fluctuations in the air-to-fuel ratio and incylinder temperatures at these different conditions CONCLUSIONS Two DISI and TBI engines were instrumented and tested for the combustion characteristics and cycle-by-cycle variations and conclusions were developed DISI engine achieved the brake thermal efficiency of Diesel engine (36%) The rate of Pressure rise of DISI engine (1.3 – 3.4 bar/oCA) is almost double that of TBI engine (1.5 – 2.5 bar/ o CA) The flame development duration (Spark-10% bmf) is longer for DISI engine than TBI engine The rapid burn duration (10-90% bmf) is shorter for DISI engine than TBI engine COV in peak pressure and IMEP for DISI engine are higher than those values for TBI engine at moderate and high loads At low loads, however, COV in both parameters for DISI engine are lower than the TBI engine The COV in the particle numbers increases with an increase in the COV of all these combustion parameters with relatively stronger correlation coefficients with the COV in the combustion durations of the 10-90% burned mass fraction REFERENCES Figure PM and its COV as a function of COV in combustion parameters 0.49, and 0.51 respectively) The same trends were observed at the various engine speeds as shown in the figure with less significant correlation coefficients for all particles The variations (COV) in the particle number density with the variation (COV) in the combustion parameters are presented in Figure The COV of the 10 nm particles seems to be less correlated to the load condition than the other two diameter ranges This may be due to the fact that the higher in-cylinder temperatures at higher loads act as oxidation factor that compete with the nucleation process thus producing more stable variation of the 10 nm particles range This proposed explanation of the COV in the 10 nm particles seems to be still valid at different engine speed and constant load condition which means more stable nucleation and oxidation process for the whole diameter Ando, H (1996) Combustion control technologies for gasoline engines Lean Burn Combustion Engine IMechE Seminar, Paper S433/001/96, 1996-1920 Brown, A G., Stone, C R and Beckwith, P (1996) Cycleby-cycle variations in spark ignition engine combustion – Part l: Flame speed and combustion measurements and a simplified turbulent combustion model SAE Paper No 960612 Clerk, D (1886) The Gas Engine Longmans Green London Eriksson, L., Nilsen, L and Glavenius, M (1997) Development of control algorithm stabilizing torque for optimal position of pressure peak SAE Trans J Engines, 106, 1216−1223 Gao, J., Jiang, D., Huang, Z and Wang, X (2005) Experimental and numerical study of high-pressureswirl injector sprays in a direct injection gasoline engine Proc IMechE, 219 Part A: J Power and Energy Geiger, J., Grigo, M., Lang, O., Wolters, P and Hupperich, P (1999) Direct injection gasoline engines – Combustion design SAE Paper No 1999-01-0170 Hinze, P C and Cheng, W K (1998) Effects of charge 794 A E HASSANEEN, S SAMUEL and I WHELAN composition on SI engine cyclic variations at idle 4th Int Symp COMODIA 98 Itoh, T., Liama, A., Muranaka, S and Tagaki, Y (1998) Combustion characteristics of a direct-injection stratified charge S.I engine JSAE Review, 19, 217−222 J B Heywood (1988) Internal Combustion Engine Fundamentals McGraw-Hill Int Series, Automotive Technology Series Boston Jackson, N S., Stokes, J., Whitaker, P A and Lake, T H (1996) A direct injection stratified charge gasoline combustion system for future european passenger cars Lean Burn Combustion Engine IMechE Seminar 1996− 1920 Kume, T., Iwamoto, Y., Lida, K., Murakami, M., Akishino, K and Ando, H (1996) Combustion control technologies for direct injection SI engines SAE Paper No 960600 Litak, G., Kaminski, T., Czarnigowski, J., Sen, A K and Wendeker, M (2009) Combustion process in a spark ignition engine: Analysis of cyclic peak pressure and peak pressure angle oscillations Meccanica, 44, 1−11 Matsumoto, K., Tsuda, I and Hosoi, Y (2007) Controlling engine system: A low-dimensional dynamics in a spark ignition engine of a motorcycle Z Naturforsch, 62a, 587−595 Muller, R., Hemberger, H and Baier, K H (2001) Engine control using neural networks; A new method in engine management systems Meccanica, 32, 423−430 Patterson, D J (1966) Cylinder pressure variations, a fundamental combustion problem SAE Paper No 660129 Roy, M R (2011) Performance and emissions of a diesel engine fueled by diesel-biodiesel blends with special attention to exhaust odor Canadian J Mechanical Sciences and Engineering 2, 1, 1−10 Sawamoto, K., Kwamura, Y., Kita, T and Matsushita, K (1987) Individual cylinder knock control by detecting cylinder pressure SAE Paper No 871911 Wagner, R M., Daw, C S and Thomas, J F (1993) Controlling chaos in spark-ignition engines Proc Central and Eastern States Joint Technical Meeting of the Combustion Institute, 15−17, New Orleans International Journal of Automotive Technology, Vol 12, No 6, pp 795−812 (2011) DOI 10.1007/s12239−011−0092−y Copyright © 2011 KSAE 1229−9138/2011/061−02 LARGE-EDDY SIMULATION OF AIR ENTRAINMENT DURING DIESEL SPRAY COMBUSTION WITH MULTI-DIMENSIONAL CFD U B AZIMOV and K S KIM* Department of Mechanical Design Engineering, Chonnam National University, Chonnam 550-749, Korea (Received 24 September 2009; Revised 26 June 2011) ABSTRACT−Large-Eddy Simulation (LES) was used to perform computations of air entrainment and mixing during diesel spray combustion The results of this simulation were compared with those of Reynolds Averaged Navier Stokes (RANS) simulations and an experiment The effect of LES on non-vaporizing and vaporizing sprays was evaluated The validity of the grid size used for the LES analysis was confirmed by determining the subgrid-scale (SGS) filter threshold on the turbulent energy spectrum plot, which separates a resolved range from a modeled one The results showed that more air was entrained into the jet with decreasing ambient gas temperatures The mass of the evaporated fuel increased with increasing ambient gas temperatures, as did the mixture fraction variance, showing a greater spread in the profile at an ambient gas temperature of 920 K than at 820 K Flame lift-off length sensitivity was analyzed based on the location of the flame temperature iso-line The results showed that for the flame temperature iso-line of 2000oC, the computed lift-off length values in RANS matched the experimental values well, whereas in LES, the computed lift-off length was slightly underpredicted The apparent heat release rate (AHRR) computed by the LES approach showed good agreement with the experiment, and it provided an accurate prediction of the ignition delay; however, the ignition delay computed by the RANS was underpredicted Finally, the relationships between the entrained air quantity and mixture fraction distribution as well as soot formation in the jet were observed As more air was entrained into the jet, the amount of air-fuel premixing that occurred prior to the initial combustion zone increased, upstream of the lift-off length, and therefore, the soot formation downstream of the flame decreased KEY WORDS : Large eddy simulation (LES), Diesel spray, Air entrainment, Diesel combustion, Lift-off length INTRODUCTION which occur at energy-negligible scales of the turbulent flow Thus, the LES approach has the advantages of both the Direct Numerical Simulation (DNS), with respect to universality and accuracy to a physical experiment, and the RANS, with respect to modeling efficiency and handling of high Reynolds numbers compared with DNS For use in the near future, LES may be considered the most promising approach to provide an accuracy level unattainable by RANS modeling The LES of chemically reacting turbulent flow has become a topic of much interest in recent years The LES of turbulent combustion has already been applied to a variety of combustion problems, including predictions of pollutants and engine combustion However, much of the necessary theory for combustion LES has yet to be developed, and the full predictive potential of combustion LES has not yet been reached In turbulent combustion at high Reynolds and Damkohler numbers, the essential rate-controlling processes of molecular mixing and chemical reactions occur at the smallest scales In non-premixed diffusion combustion regimes, for example, these coupled processes occur in the reactive-diffusion layers, which are much thinner than the resolved scales Hence, the rate-controlling processes not occur in the resolved, large scales and have to be modeled However, a Large-Eddy Simulation (LES) is a relatively new research field Much research has been carried out over the past years, but to realize the full predictive potential of LES, many fundamental questions still have to be addressed In LES, the major part of the turbulent kinetic energy is resolved directly, whereas the effects of remaining scales smaller than the computational grid size are accounted for in a subgrid-scale (SGS) model (Lesieur and Metais, 1996; Lesieur, 2005) To compute fluctuating quantities (temperature, velocity and pressure), the technique consists of calculating instant fields in a transient calculation, which solves the Navier-Stokes equations However, flow, being generally turbulent, cannot be solved explicitly at all scales Resolving the Kolmogorov scale (size of the smaller eddies) in three-dimensional calculations is out of the reach of present computers and will remain so for a long time The large eddy simulation technique can solve large eddies explicitly and model smaller eddies Compared to the wellknown Reynolds-Averaged Navier-Stokes (RANS) approach, the universality of LES is higher because LES model assumptions are made only about the subgrids, *Corresponding author e-mail: sngkim@chonnam.ac.kr 795 944 R DOSTHOSSEINI, A Z KOUZANI and F SHEIKHOLESLAM is optimal theory, calculus of variations, and Pontryagin’s maximum principle Casas (1997) used Pontryagin’s maximum principle and introduced a penalty problem by using Ekeland's principle to solve an optimal control problem with state constraints that were verified by semi linear parabolic equations To use this method, a two boundary value problem needs to be solved However, solving this would be very difficult through an analytic approach Numerical methods can provide the mean to solve the two boundary value problem, but some numerical methods produce suboptimal results (Perez et al., 2006) Wu et al (2008) used a comprehensive methodology based on particle swarm optimization (PSO) to achieve the powertrain and the control strategy parameter optimization for reducing fuel consumption, exhaust emissions, and manufacturing costs of HEVs For simplicity, they transferred the original problem into two single objective problems using a goal attainment method A control strategy called “Supervisory Control” for HEVs power management was introduced in ref (Perez et al., 2006; Perez et al., 2009; Perez et al., 2006) The authors had to solve an optimal control problem with a cost function subject to a state equation, and its initial values, and inequality constraints In ref (Perez et al., 2006; Perez and Pilotta, 2006; Brahma et al., 2000), the power management problem was solved by the dynamic programming in an inventory control which required high computational costs The dynamic programming can act as a benchmark to evaluate the performance of other control methods on this problem (Sciaretta et al., 2004) Perez and Pilotta, (2009) used the direct transcription and nonlinear programming (Betts, 1999, 2001) for optimal control problem in order to discretize the problem in time, and solve it Orthogonal functions have received considerable attention in dealing with various problems related to dynamic systems The main benefit of using orthogonal functions in optimal control is that the differential equations are reduced to a set of algebraic equations, and thus there is no need to solve two boundary value problems Therefore, the optimal solution is directly extracted by solving algebraic equations These approximation algorithms are known as direct methods (Yan et al., 2001) Depending upon the structure of the orthogonal functions, they are classified into three groups: a Piecewise constant orthogonal functions such as Haar wavelets and block-pulse functions b Orthogonal polynomials such as Legendre, Chebyshev, and Jacobi polynomials c Sine-Cosine functions such as the Fourier transform In this paper, the direct method is used to solve the optimal power management for electric hybrid vehicles with inequality constraints This method consists of reducing the optimal control problem with a two-boundaryvalue differential equation to a set of algebraic equations by approximating the state variable which is the energy of electric storage, and the control variable which is the power of fuel consumption This approximation uses orthogonal functions with unknown coefficients The operational matrix of product and the operational matrix of integration are used to evaluate the unknown coefficients Also, the inequality constraints are transferred into algebraic equalities (Marzban Razzaghi, 2003) Therefore, the necessary conditions for optimal power management are derived as algebraic equations in the unknown coefficients of the state and control variables and Lagrange multipliers These coefficients are determined in such a way that the necessary conditions for extremization are imposed The paper is organised as follows Section presents the basic formulation of the optimal energy management for HEVs Section describes approximation of the optimal control problem with isoperimetric and inequality constraints for HEVs through the direct method Section explains how a typical example is solved for demonstrating the accuracy of the presented numerical approach The results of Haar wavelets, Chebyshev and Legendre polynomials are presented and discussed Finally, conclusions are given in Section PROBLEM STATEMENT Although HEVs come in several types including series, parallel, or a combination of both series and parallel, they usually use two energy sources to move These sources include an internal combustion engine and an electric motor The internal combustion engine uses the fuel stored in a tank to function, however, the electric motor uses the energy stored in an electric storage device to operate In addition, a regenerative braking is employed to recharge the electric storage device, e.g batteries The vehicle’s kinetic energy, which is usually wasted as heat, is converted to electric energy and stored in the electric storage device For example, a parallel HEV is shown in Figure As can be seen from the figure, both the engine and the electric motor can deliver power to the wheels in parallel Also, the batteries can be charged by the engine or the regenerative braking In order to maximize the fuel and emissions efficiencies offered by HEVs, an optimal control strategy can be employed to minimize the energy used by vehicle This Figure Block diagram description of a parallel hybrid electric vehicle DIRECT METHOD FOR OPTIMAL POWER MANAGEMENT IN HYBRID ELECTRIC VEHICLES 945 where ECS0 is the initial energy in the combustion system Similarly, the energy consumed by the electric system at time t can be calculated as follows: t EES( t ) = EES0 + ∫ f( EES ( τ ) )dτ (3) where EES0 is the initial energy in the electric system In this equation, f represents the sign and the efficiency of the net electric power as follows: ⎧ ηES ( PES ( t ) )PES( t ) if PES ( t ) < f( EES ( t ) ) = ⎨ PES ( t ) if PES( t ) ≥ ⎩ ηES ( PES ( t ) ) Figure Power flow diagram of a HEV paper presents an optimal method of power management for the HEVs to reduce their fuel consumption and emissions Usually, an optimal problem includes a cost function, state equations, initial states, and some equality or inequality constraints These parameters can be linear or nonlinear, and also discrete or continuous Although most optimal problems have state equations, there exist problems that not have state equations The optimal problem tackled in this work does not have a state equation Figure shows a power flow diagram for a HEV (Perez et al., 2006; Perez and Pilotta, 2009; Rizzoni et al., 1999) As can be seen from the figure, the combustion system only delivers power However, the electric system both delivers and receives power Pcs(t) is defined as a continuous function representing the power delivered by the combustion system and the regenerative braking PES(t) is defined as a continuous function indicating the power delivered by the electric system Since part of Pcs(t) and Pcs(t) is wasted as heat, etc., we define efficiency coefficients to take into account the energy wastages ηCS(t) and ηES(t) are introduced as the efficiency coefficients that can vary within the interval [0,1] PCS(t) is considered as a positive function because the combustion system only delivers power On the other hand, PES(t) is considered as either a positive function when the electric system delivers power to the wheels, or a negative function when the electric power is stored in the storage device PD(t) is defined as the desired power that the vehicle needs to move According to Figure 2, we have: PCS( t ) + PES ( t ) = PD ( t ) (1) The energy consumed by the combustion system at time t can be calculated as follows (Perez et al., 2006; Perez and Pilotta, 2009; Rizzoni et al., 1999): t PCS ( τ ) ECS( t ) = ECS0 + ∫ -dτ ηCS( PCS( τ ) ) (2) (4) Equation (2) and Equation (3) are known as isoperimetric constraints that should be satisfied in power management (Kirk, 1970) To have an optimal solution for the power management in HEVs, it is necessary to introduce a cost function This cost function should be minimized to achieve an optimal solution There are some known cost functions such as minimum time, minimum control effort, tracking, or a combination of these (Kirk, 1970) In order to have a good power management in HEVs, it is required to select a modified cost function which consists of both control variable and state variable (Kirk, 1970) Therefore, the cost function to be used can be formulated as: tf PCS ( t ) -⎞ J( ECS ( t ), PCS ( t ) ) = ∫ ⎛⎝ dt ηCS ( PCS ( t ) )⎠ (5) or tf PD( t ) – PES( t ) -⎞ dt J( ECS ( t ), PES ( t ) ) = ∫ ⎛⎝ -ηCS ( PD ( t ) – PES ( t ) )⎠ (6) To use the first cost function, PCS(t) is assumed as control variable subject to its constraints (Equation (2)) To use the second cost function, on the other hand, PES(t) is assumed as control variable subject to its constraints (Equation (3)) Therefore, the problem is to find an admissible control variable PCS(t) or PES(t) subject to their constraints that minimize the cost function In this work, we optimize only first cost function (Equation (5)) The optimization of the second cost function can be carried out in the same manner Both combustion and electric powers should vary in their allowed boundary limitations as follows: ≤ PCS ( t ) ≤ PCSmax, t ∈ [ 0, tf ] (7) and PESmin ≤ PES( t ) ≤ PESmax ≡ PESmin ≤ PD ( t ) – PCS( t ) ≤ PESmax, t ∈ [ 0, tf ] (8) 946 R DOSTHOSSEINI, A Z KOUZANI and F SHEIKHOLESLAM To prevent depletion and overcharge of batteries, another inequality constraint is included: ηCS( PCS( t ) ) ≅ BT ηˆ CS EESmin ≤ EES( t ) ≤ EESmax, t ∈ [ 0, tf ] where ηˆ CS is a unknown vector related to PCS coefficients Therefore, (9) Therefore, the problem becomes how to find PCS(t) that minimizes the cost function of Equation (5) subject to isoperimetric constraint of Equation (2) and inequality constrains of Equation (7)~(9) for t ∈ [ 0, tf ] , where PD(t), ηCS(t) and f(t) are known functions (Perez and Pilotta, 2006; Perez et al., 2009; Rizzoni et al., 1999) (15) tf tf ∫ B dtP T CS T B PCSint P CS -=B -J = ∫ -dt = -tf Tˆ B ηCS BTintηˆ CS T ∫ B dtηˆ CS T (16) APPROXIMATION OF THE SYSTEMS USING ORTHOGONAL FUNCTIONS In order to find PCS(t) that minimizes the cost function of Equation (5), the system parameters are approximated as follows Let ⎧· T ⎪ EES ( t ) = B EdES ⎪ PCS ( t ) = BTPCS ⎨ ⎪ P D ( t ) = BT P D ⎪ T ⎩ ECS ( t ) = B ECS where Bint is the integration of B between to tf In most optimization problems, isoperimetric constraints like Equation (2) come in the form of total available fuel or energy for a required task (Kirk, 1970) In this work, the isoperimetric constraint can be devised as a differential equation constraint by differentiating it with respect to time as follows: EES( t ) = f( PES ( t ) ) = f( PD ( t ) – PCS ( t ) ) (17) Using the approximation method, this constraint is converted to where BT = [ B0( t ), B1( t), …, Bn – 1( t) ] is the base vector of order n, PCS(t), ECS(t) and EdES are unknown vectors, and is a known vector Also with the same rule EES( ) = BT E0 (11) where E0 is a known vector of order n By integrating · EES( t ) from to tf, EES(t) is obtained by ˆ BT EdES = BTF (18) ˆ where F is an unknown vector related to PD and PCS coefficients, and B can be omitted from the both sides The inequality constraints can be handled by introducing auxiliary function (Yen and Nagurka, 1991) These constraints are first replaced by the equality constraints as follows tf EES( t ) – EES( ) = ∫ BT EdESdt ≅ BT PTEdES (12) (19) where P is operational matrix of integration introduced by orthogonal polynomials P can be obtained from an approximation of the bases integration of order (n+1) to order n Then EES = BT( PT EdES + E0ES ) and (13) (20) By substituting approximated vectors in cost function, Equation (5) is converted to tf BT PCS dt J = ∫ ηCS ( BTPCS ) and (14) (21) To solve the problem using the direct method, the integration cost function should be transferred into an algebraic equation and time should be extracted from cost function Suppose ηCS(PCS(t)) can be approximated with orthogonal function as follows Where zi(t),i = 1,…,6 are auxiliary functions By expanding each zi(t) in terms of orthogonal functions, it is DIRECT METHOD FOR OPTIMAL POWER MANAGEMENT IN HYBRID ELECTRIC VEHICLES tf given as zi( t ) = B Zi, T 947 = 1, …, 6, (22) then ˜ z2i ( t) = ZTi BBTZi = ZTi Zi B, = 1, …, (23) ˜ where Zi is calculated from product operational matrix Also PCSmax , PESmin , PESmax , EESmin , and EESmax approximated by the following orthogonal functions (24) where PCSmax , PESmin , PESmax , EESmin , and EESmax are known vectors So Equations (17-19) are converted to L = ∫ BBT dt (28) The minimization problem is replaced by the following parameter optimization problem Find the coefficients of λ, Zi, PCS, and EES which minimize the cost function ˆ Jtot = J + Jc + λT ( EdES – F ) (29) where λ is an unknown Lagrange multiplier vector The determining equations for these vectors are ∂J tot = 0, i = 0, …, ∂Zi (30) ∂Jtot -=0 ∂PCS (31) ∂Jtot =0 ∂PES (32) ∂J tot =0 ∂λ (33) Note that Equations (30-33) are nonlinear and can be solved by nonlinear methods such as Newton’s iterative (25) EXAMPLE To add these constraints to the basic minimization problem, they are converted to another minimization problem in which PCS(t) and EES(t) should be find to minimize (26) where wi > 0, i = 1, …, are weight functions that can be scalar or matrix Here, for simplicity they are assumed as scalar constants Since Ci > 0, i = 1, …, are not related to time and wi > 0, i = 1, …, are constants, JC is transformed to (27) Consider an optimal problem for power management of a HEV during 40 seconds with the cost function of Equation (5), inequality constraints of Equations (7)~(9), and an isoperimetric constraint of Equation (3) Suppose PCS max = 40 kW, PES = -30 kW, PESmax = 30 kW, EES = kWh, EES max = kWh, f(PES) = 0.8 PES, η(PCS) = 0.005PCS + 0.2, EES(0) = 0.3 kWh, PD = 3.2t − 0.22t2 + 0.0035t3 + 0.7 This example is solved by the direct method as well as Chebyshev and Legendre polynomials and Haar wavelets These orthogonal functions solve the problem in the same manner but using different bases, operational matrix, and the product matrix Here, the results of each base are presented, and then compared against each other at the end 4.1 Solving the Problem using Legendre Polynomials Legendre polynomials, which are orthogonal on the interval [-1, 1], belong to the continuous group of orthogonal functions that satisfy the following recursive formula for the order n (Razzaghi et al., 2000): B0(t) = 1, B1(t) = where 948 R DOSTHOSSEINI, A Z KOUZANI and F SHEIKHOLESLAM Figure Results for, compared with the desired power using Legendre polynomials 2n – n–1 Bn ( t ) = - tBn – ( t ) – Bn – 2( t ) n n To use this base within [0, 40], a transferred form of Legendre polynomials should be used Thus t B0 ( t ) = 1, B1( t ) = – 20 2n – t n–1 Bn ( t ) = - ⋅ ⋅ Bn – 1( t) – Bn – ( t ) n 20 n The results for the first eight transferred bases are shown in Figure with the cost value J = 13800.07932 4.2 Solving the Problem using Haar Wavelets Haar wavelets are known as a piecewise orthogonal base in the form of square waves with magnitude of ±1 within [0, 1] A recursive formula for Haar wavelets within [0, 1] is (Hsiao, 2004) Figure Results for PCS(t), PES(t) compared with the desired power PD(t) using Haar wavelets Where δij is a known constant A recursive formula for the transferred Chebyshev polynomials in [0, 40] is t B0 ( t ) = 1, B1( t ) = – 20 t Bn ( t ) = ⎛⎝ – 1⎞⎠ Bn – 1( t ) – Bn – ( t ) 20 where they are orthogonal on [0, 40] with respect to the weight function w(t) The results for the first eight transferred bases are shown in Figure with the cost value J = 48375.8661 Also, Figure shows the three PCS(t) functions which are extracted from these orthogonal functions Considering the application of the direct method using ⎧ 1, ≤ t < 0.5 B0 ( t ) = 1, ≤ t < 1, B1 ( t ) = ⎨ ⎩ –1, 0.5 ≤ t < Bn(t) = Bn-1(2jt − k), n = 2jt + k, j ≥ 0, ≤ k < 2j t in which t is replaced by in order to convert [0, 1] to [0, 40 40] The results for using the first eight transferred bases are shown in Figure with the cost value J = 18420.56626 Figure Results for PCS(t) and PES(t) compared with the desired power PD(t) using Chebyshev polynomials 4.3 Solving the Problem using Chebyshev Polynomials The first kind of Chebyshev polynomials of degree n are orthogonal in [-1, 1] with respect to weight function w(t) = (1−t2)-0.5 as follows Bn(t) = cos(cos-1t), and ∫ B (t)B (t)(1 – t ) –0.5 i –1 j n≥0 i=j=0 ⎧ π, dt = ⎨ π ⎩ 2- δij, i, j > Figure PCS(t) results for each case DIRECT METHOD FOR OPTIMAL POWER MANAGEMENT IN HYBRID ELECTRIC VEHICLES Chebyshev and Legendre polynomials and Haar wavelets on the examined power management optimization example, based on the calculated cost values, it is evident that the best polynomial to solve this problem is the Legendre polynomials The advantage of the proposed method is that its computational complexity is less than that of the dynamic and non-linear programming approaches More importantly, to use the dynamic or non-linear programming, the problem should be discretized This results in the loss of optimization accuracy The proposed method, on the other hand, does not require the discretization of the problem This produces more accurate results CONCLUSION The paper employed the direct method using Legendre and Chebyshev polynomials and Haar wavelets to determine the optimal solution for power management in HEVs The method was applied to an off-line problem where all the necessary functions and constraints were known Since the developed method is not computationally expensive, it can be also employed for on-line problems in HEVs For simplicity, a simple example using eight bases was solved to show the efficiency of the approach For more complex cases, the evaluation time can be divided into smaller time segments within which the optimal solution for both combustion and electric systems are calculated The results will improve when the driving schedule doesn’t changed dramatically, and information from the future is provided by a predictor of the driving cycle In addition, the results show that the optimal solution using the direct method with Legendre polynomials are better than both Chebyshev polynomials and Haar wavelets REFERENCES Arce, A., Del Real, A J and Bordons, C (2009) MPC for battery/fuel cell hybrid vehicles including fuel cell dynamics and battery performance improvement J Process Control, 19, 1289–1304 Baumann, B M., Washington, G., Glenn, B C and Rizzoni, G (2000) Mechatronic design and control of hybrid electric vehicles IEEE/ASME Trans Mechatronic 5, 1, 58–72 Betts, J T (1999) A direct approach to solve optimal control problems Comput Sci Eng., 1, 73–75 Betts, J T (2001) Practical methods for optimal control using nonlinear programming Society for Industrial and Applied Mathematics Brahma, A., Guezennec, Y and Rizzoni, G (2000) Dynamic optimization of mechanical/electric power flow in parallel hybrid electric vehicles Proc AVEC 2000, 5th Int Symp Advanced Vehicle Control, Ann Arbor, Michigan, USA Casas, E (1997) Pontryagin’s principle for state 949 constrained boundary control problems of semilinear parabolic equations SIAM J Control Optim., 35, 1297– 1327 Hsiao, C H (2004) Haar wavelet direct method for solving variational problems Mathematics and Computers in Simulation, 64, 569–585 Huang, Y J., Yin, C L and Zhang, J W (2009) Design of an energy management strategy for parallel hybrid electric vehicles using a logic threshold and instantaneous optimization method Int J Automotive Technology 10, 4, 513−521 Kheir, N A., Salman, M A and Schouten, N J (2004) Emissions and fuel economy trade-off for hybrid vehicles using fuzzy logic Mathematics and Computers in Simulation, 66, 155–172 Kirk, D E (1970) Optimal Control Theory an Introduction Dover Publications, Inc New York Lin, C C., Kang, J M., Grizzle, J W and Peng, H (2001) Energy management strategy for a parallel hybrid electric truck Proc American Control Conf IEEE Arlington, VA, USA, 2878–2883 Lin, C C., Peng, H and Grizzle, J W (2003) Power management strategy for a parallel hybrid electric truck IEEE Trans Control Systems Technology 11, 6, 839– 849 Marzban, H R and Razzaghi, M (2003) Hybrid functions approach for linearly constrained quadratic optimal control problems Applied Mathematical Modeling, 27, 471–485 Montazeri, M., Poursamad, A and Ghalichi, B (2006) Application of genetic algorithm for optimization of control strategy in parallel hybrid electric vehicles J Franklin Institute, 343, 420–435 Perez, L V., Bossio, G R., Moitre, D and Garcia, G O (2006) Optimization of power management in an hybrid electric vehicle using dynamic programming Mathematics and Computers in Simulation, 73, 244–254 Perez, L.V., Bossio, G R., Moitre, D and Garcia, G O (2006) Supervisory control of an HEV using an inventory control approach Latin Am Appl Res., 36, 93–100 Perez, L V and Pilotta, E A (2009) Optimal power split in a hybrid electric vehicle using direct transcription of an optimal control problem Mathematics and Computers in Simulation, 79, 1959–1970 Razzaghi, M and Yousefi, S (2000) Legendre wavelets direct method for variational problems Mathematics and Computers in Simulation, 53, 185–192 Rimaux, S., Delhom, M and Combes, E (1999) Hybrid vehicle powertrain: Modelling and control Proc 16th Int Electric Vehicle Symp EVAAP, Beijing Rizzoni, G., Guzzella, L and Baumann, B (1999) Unified modelling of hybrid electric vehicles IEEE/ASME Trans Mechatronics, 4, 246–257 Sciaretta, A., Back, M and Guzzella, L (2004) Optimal control of parallel hybrid electric vehicles IEEE Trans 950 R DOSTHOSSEINI, A Z KOUZANI and F SHEIKHOLESLAM Control Syst Technol., 12, 352–363 Sun, H., Jiang, J H and Wang, X (2007) Optimal torque management strategy for a parallel hydraulic hybrid vehicle Int J Automotive Technology 8, 6, 791−798 Wu, J., Zhang, C H and Cui, N X (2008) PSO algorithmbased parameter optimization for HEV powertrain and its control strategy Int J Automotive Technology 9, 1, 53− 69 Yan, H., Fahroo, F and Roos, I M (2001) Optimal feedback control law by Legendre Pseudo spectral approximation Proc American Control Conf., Arlington, 2388−2393 Yen, V and Nagurka, M (1991) Linear quadratic optimal control via Fourier-based state parameterization ASME J Dynamic Systems, Measurement and Control 113, 2, 206–215 International Journal of Automotive Technology, Vol 12, No 6, pp 951−958 (2011) DOI 10.1007/s12239−011−0108−7 Copyright © 2011 KSAE 1229−9138/2011/061−18 RELATIONSHIP BETWEEN OCCUPANT INJURY AND THE PERTURBATION MARK ON THE VELOCITY INDICATOR ON A CLUSTER PANEL S.-J KIM1)*, W.-J JEON1), J.-J PARK1), B.-S MOON1), Y.-J CHO1), Y.-I SEO1), N.-K PARK2) and K SON3) 1) Science and Engineering Division, Southern District Office, National Forensic Service, Yangsan-si, Gyeongnam 626-810, Korea 2) Southern District Office, National Forensic Service, Yangsan-si, Gyeongnam 626-810, Korea 3) School of Mechanical Engineering, Pusan National University, Busan 609-735, Korea (Received 22 November 2010; Revised 27 April 2011) ABSTRACT−A perturbation mark is occasionally produced on the velocity indicator of the cluster panel of a vehicle during a vehicle collision This mark can be used to estimate the velocity of the vehicle at the moment of the vehicle’s impact In this study, the effect of the impact velocity and the deceleration of the vehicle on the perturbation mark were investigated, and an analysis of the driver's injury was also conducted through a numerical pulse representation and computer simulations Sled and pendulum tests were used to replicate the conditions that produce a perturbation mark on the velocity indicator of a cluster panel It was verified that a higher peak acceleration is more likely than the impact velocity to cause a perturbation mark According to the computer simulation results, a driver's injury could be more severe at higher peak accelerations with a constant impact velocity If a perturbation mark, which can be used to estimate the impact velocity, is found while investigating a vehicle accident, this mark reveals that the acceleration was higher than that listed in the related crash report Therefore, the injuries of the occupants could be more serious than those expected at the reported impact velocity KEY WORDS : Perturbation mark, Vehicle accident, Cluster panel, Velocity indicator, Frontal impact, Occupant injury INTRODUCTION This study investigates how the deceleration of a vehicle with a high stiffness affects the occurrence of a perturbation mark on the cluster panel The effect of the high peak deceleration at a constant impact velocity is also discussed with respect to the occupant injuries In a vehicle accident investigation, investigators aim to gather all possible evidence at the accident site Using the collected information, various analyses are conducted to determine the critical causes by reconstructing the accident The vehicle impact velocity is an important component necessary for reconstructing a vehicle accident in vehicleto-vehicle and vehicle-to-pedestrian collisions The impact velocity can be estimated from the skid marks on the road, the deformed regions and condition of the vehicle, film from closed-circuit television, and so forth Occasionally, a perturbation mark is produced on the velocity indicator of the cluster panel of a vehicle, and it can be used to predict the velocity of the vehicle at the moment of impact (Baker and Fricke, 1986) A perturbation mark is assumed to occur at a high impact velocity, which causes a higher oscillation amplitude on the velocity indicator Moreover, the stiffness of the vehicle also seems to affect the mark because the mark is often found in truck type vehicles, which not have a large crumble zone like the passenger type PERTURBATION MARK There are several types of accidents: car-to-car collisions, car-to-pedestrian collisions, car-barrier collisions, and so forth With car-to-car and car-to-barrier collisions, the vehicle deformation, before-and-after vehicle conditions, and skid and gouge marks can provide valuable evidence for the car accident investigation A perturbation mark occasionally is produced on the velocity indicator of the cluster panel of a vehicle during a vehicle collision (Figure 1) 2.1 Impact Velocity Estimation Perturbation marks usually appear on the cluster panel It is assumed that the velocity indicator, which may be scratched on the cluster panel, and the paint substance on the rear side of velocity indicator are simultaneously smeared Thus, a perturbation mark can be used to estimate *Corresponding author e-mail: sjkim43@koera.kr 951 952 S.-J KIM et al Figure Vehicle accident left a perturbation mark on the velocity indicator on the cluster panel Figure Structure of a cross-coil type indicator and a sample of an indicator a car’s velocity at the moment of impact Traffic accident data indicate that perturbation marks tend to occur more frequently with truck type vehicles than in passenger type ones panel also cause an oscillation from the disturbance The gaps and masses of the components and the flexibility affect the occurrence of perturbation marks under high acceleration conditions 2.2 Structure of the Velocity Indicator Instrument panels provide drivers with the status of the vehicle driving systems Instrument panels may be of two types: digital and analogue Analogue panels may contain three types of instruments: bimetal, cross-coil and step motor Cross-coil instruments are widely used for vehicle velocity indicators An example of a velocity indicator is illustrated in Figure (Kim et al., 2007) An electric current flows through the cross coil so that the magnetic field may be created around the low-housing The indicator is located on the axis of a permanent magnet and is rotated by the magnetic field Gaps exist among the low-housing, the spindle axis, the rear cover, and so forth The gaps and masses of these components cause an oscillation from the external disturbance The flexibility of the velocity indicator and the HAVERSINE PULSE MODEL There are four well-recognized shapes of a vehicle crash pulse: Haversine (sin2), sine, square wave, and symmetric triangular In this study, the haversine pulse model was selected to represent the vehicle frontal barrier impact pulse (Varat and Husher, 2003) Figure is a graphical representation of the vehicle acceleration, which can be written as follows: π⋅t a = Psin2⎛⎝ -⎞⎠ T (1) The computer simulation and sled test often require the generation of suitable acceleration-time histories with a proper set of shape, amplitude and duration characteristics Previous research have demonstrated the usefulness of analytical techniques such as the haversine representation for RELATIONSHIP BETWEEN OCCUPANT INJURY AND THE PERTURBATION MARK 953 Figure Graphical representation of the haversine function studying the severity of collisions (Varat and Husher, 2000) SLED TEST 4.1 Sled Test Pulse Generation To reproduce a perturbation mark, sled tests were performed at the first stage of this study From the vehicle frontal barrier impact test reports of NHTSA (National Highway Traffic Safety Administration), in accordance with FMVSS208 and NCAP protocols, the peak vehicle accelerations were found to be around 30–60 G at the impact velocity of 56 km/h For the sled test, the highest peak accelerations pulses within sled equipment capacity were chosen A perturbation mark was assumed to occur in a more severe impact condition than those of the regulations and NCAP tests At first, the haversine pulses were generated for four peak accelerations of 50, 60, 70 and 80 G as shown in Figure The time duration for each pulse was adjusted according to the limit velocity of the equipment The haversine pulses were used as the reference input pulses for the sled tests The applied sled test pulses are illustrated in Figure During the pulse generation on the sled test equipment, the haversine pulse of 80 G peak acceleration was excluded because of the limit of the equipment capacity 4.2 Motion of Velocity Indicator Two instrument panels were selected for the sled tests and were reworked to mount them on the test jig, as shown in Figure Color paint was pasted on the rear sides of the indicators to aid the determination of whether the velocity indicators contact the cluster panels From the sled tests with three different peak accelerations, no contact marks were checked out identically on the cluster panels The oscillating indicator motions at the 70 G peak acceleration pulse are illustrated in Figure While examining the high speed camera film, it was observed that the velocity indicators were oscillating without contacting the cluster panels The indicator center also oscillated Figure Haversine acceleration pulses and their integrated velocities significantly along the low-housing axis PENDULUM TEST 5.1 Truck Barrier Test Review From traffic accident investigations, it is recognized that the perturbation marks appear at a relatively high impact velocity in truck type vehicle accidents The data in Figure 8, which are from a truck manufacturer and not open to the public in detail, show an example of an A-pillar pulse from the frontal rigid barrier test of a truck type vehicle at the 48 km/h impact velocity The peak acceleration from the Apillar was higher than 120 G, and the time duration was about 40 msec The axis scales were removed because of a confidential issue Contrary to the structure of passenger cars, the front structures of truck type vehicles not have a large enough crumble zone to absorb the impact energy 5.2 Pendulum Impact Test After reviewing the truck vehicle impact test, supplemental pendulum impact tests were performed in addition to the previous sled tests The pendulum test equipment was modified from the calibration test equipment for the thorax and the pelvis of the ATD (Anthropometric Test Device) The pendulum impact test configuration is illustrated in 954 S.-J KIM et al Figure Oscillating indicator motions at the 70 G peak acceleration pulse Figure Sled acceleration pulses and their integrated velocities Figure A rubber pad was attached on the contact face of the pendulum to prevent the acceleration sensor from receiving extremely high noise signals One of the test results is shown in Figure 10 The peak accelerations from the repeated tests with three different cluster panel samples exceeded 200 G Perturbation marks occurred on the velocity indicators with all three samples One of the test results is shown in the Figure 10 Therefore, it can be assumed that a higher peak acceleration produces a more noticeable perturbation mark If a perturbation mark Figure Sled test setup to reproduce the perturbation mark on velocity indicator RELATIONSHIP BETWEEN OCCUPANT INJURY AND THE PERTURBATION MARK 955 Figure 10 Pendulum impact test results Figure Pulse from the truck frontal barrier test (48 km/h) 6.1 Simulation Model In this study, the effect of a high peak acceleration on driver injuries was reviewed with a constant impact velocity Figure 11 shows a frontal driver simulation model, which was constructed from the application database in MADYMO V.7.1 and was selected as the base model (TASS, 2009) The occupant restraint systems that was considered to consist of a single-stage airbag, retractor and buckle pretensioners; a single-stage seatbelt load limiter; and a non-collapsible steering column The base model was customized on NCAP (Dec 2004), and the 5-star rating score is summarized in Figure 12 6.2 Simulation Pulses The impact velocity was fixed at 56 km/h, which is at the same level as the regulations and the NCAP test The acceleration pulses were generated using the haversine representation as defined in Eq (1) Figure 13 shows the haversine pulses of 30, 50, 80, 100, 120 and 140 G together with the base pulse and the integrated velocities of those pulses The acceleration pulses were applied for the frontal occupant simulation input Figure Pendulum impact test configuration 6.3 Driver Kinematics and Injuries The driver kinematics for the 30 and the 140 G models at 40 msec are illustrated in Figure 14 The driver position in the 140 G model moved forward earlier than that in the 30 G model Thus, the driver position did not align with the is found on the cluster panel in a vehicle accident investigation, a relatively high acceleration and a high impact velocity should be considered to reconstruct the conditions of the accident OCCUPANT INJURIES If a perturbation mark occurs on the velocity indicator, a considerable peak acceleration was likely applied on both the vehicle structures and the occupants The peak level of that acceleration could be higher than those from the regulations and the NCAP tests Figure 11 Frontal driver simulation model 956 S.-J KIM et al Figure 12 NCAP 5-star rating score for the frontal driver simulation model deployed airbag Because the airbag firing times and the seatbelt were set to satisfy the regulations and NCAP protocols, such a close occupant position to the airbag might cause severe injuries to the head, neck and thorax The peak vehicle accelerations on the NCAP frontal impact are expected to be approximately 30–50 G The injury index results presented in Table and Figure 15 show that most injury index values increased as the peak acceleration was increased at a constant impact velocity Gradual increases are observed in Figure 15(a), (b), (d) and (e) Meanwhile, rapid increases are observed in Figures 15(c) and (f) at the peak acceleration of 50 G This results indicate that a higher peak acceleration should be avoided to reduce the level of occupant injuries CONCLUSIONS The conditions to reproduce a perturbation mark on the velocity indicator on the cluster panel of a vehicle were studied through sled and pendulum tests An analysis of the driver’s injury was also conducted through a numerical pulse representation and computer simulations The relationship between the perturbation mark and the occupant injury can be summarized as follows: (1) The data, which are from a truck manufacturer and not open to the public in detail, demonstrated that a Figure 14 Driver kinematics of the 30 G and the 140 G models Figure 13 Sled acceleration pulses and integrated velocities perturbation mark occurred at 48 km/h with an acceleration value higher than 120 G To repeat the accident situation, a pendulum test was performed, and a perturbation mark was observed at an acceleration value exceeding 200 G (2) A high peak acceleration can cause more severe occupation injury than an impact velocity of 56 km/h, which is the frontal impact condition of the regulation and the NCAP test (3) When a perturbation mark is found during a vehicle RELATIONSHIP BETWEEN OCCUPANT INJURY AND THE PERTURBATION MARK accident investigation, it can be used to estimate the impact velocity, and it reveals that the acceleration was higher than that listed in the related crash report 957 Therefore, the occupants’ injuries could be more serious than those expected at that impact velocity Figure 15 Simulation results of the injury index according to the acceleration peaks Table Summary of injury indices for the frontal collision simulations Injury index Base Haversine pulse B30 HS30 HS50 HS80 HS100 HS120 HS140 HIC15 835 996 1424 1746 2049 2068 2201 HIC36 953 1109 1662 2008 2078 2094 2244 Chest G's 57.00 59.00 95.00 95.00 92.00 89.00 90.00 Chest deflection (mm) 52.70 53.34 64.43 71.72 74.80 76.04 77.03 Left femur load (kN) 4.12 4.40 9.00 15.23 17.65 17.57 18.35 Right femur load (kN) 3.33 3.74 8.54 8.93 8.76 8.69 8.80 Neck Nij 0.339 0.362 0.466 0.657 1.063 1.076 1.022 Neck-tension (kN) 1.533 1.513 2.574 3.176 4.467 4.476 5.397 Neck-compression (kN) 0.003 0.019 0.003 0.034 0.004 0.004 0.004 958 S.-J KIM et al REFERENCES Baker, J S and Fricke, L B (1986) The Traffic-Accident Investigation Manual 9th Edn Northwestern University Traffic Institute Illinois Kim, M B., Jang, H S., Lee, J I and Jang, Y H (2007) Vehicle Electricity 1st Edn Golden Bell Seoul Korea TASS (2009) MADYMO Manual Release 7.1 TASS Netherlands Varat, M S and Husher, S E (2000) Vehicle impact response analysis through the use of accelerometer data SAE Paper No 2000-01-0850 Varat, M S and Husher, S E (2003) Crash pulse modeling for vehicle safety research 18th ESV, Paper No 501