International journal of automotive technology, tập 11, số 6, 2010

Copyright © 2010 KSAE 1229−9138/2010/055−01 International Journal of Automotive Technology, Vol 11, No 6, pp 767−772 (2010) DOI 10.1007/s12239−010−0091−4 ACTIVE COOLANT CONTROL STRATEGIES IN AUTOMOTIVE ENGINES 1) 1) 1)* K B KIM , K W CHOI , K H LEE 2) and K S LEE Department of Mechanical Engineering, Hanyang University, Gyeonggi 426-791, Korea Department of Mechanical Engineering, Hanyang University, Seoul 133-070, Korea 1) 2) (Received 12 August 2009; Revised 24 May 2010) ABSTRACT−The coolant flow rate in conventional cooling systems in automotive engines is subject to the mechanical water pump speed, and high efficiency in terms of fuel economy and exhaust emission is not possible given this limitation A new technology must be developed for engine cooling systems The electronic water pump is used as a substitute for the mechanical water pump in new engine cooling systems The new cooling system provides more flexible control of the coolant flow rate and engine temperature, which previously relied strongly on engine driving conditions such as load and speed In this study, the feasibility of two new cooling strategies was investigated using a simulation model that was validated with temperatures measured in a diesel engine Results revealed that active coolant control using an electronic water pump and valves substantially contributed to a reduction of coolant warm-up time during cold engine starts Harmful emissions and fuel consumption are expected to decrease as a result of a reduction in warm-up time KEY WORDS : Flowmaster, Cooling, Warm-up, Emission emissions during cold starts A number of researchers have also proposed replacing the conventional water pump with an electrically-driven pump that can actively control the coolant flow rate based on the optimum driving temperature (Vegenas et al., 2004; Hnatczuk et al., 2000; Page et al., 2005; Cho et al., 2005; Cho et al., 2007; Chalgren., 2004; Chanfreau et al., 2003; Kim et al., 2009) In a typical automotive engine cooling system, the water pump coupled to the engine is driven by a crankshaft Thus, the pump speed and coolant flow rate are governed by the engine speed, which gives rise to unavoidable parasitic losses The mechanical cooling pump cannot supply sufficient flow for cabin heating at idle conditions because of its low efficiency A high rate of revolution of the crankshaft resulting from rapid acceleration is a direct cause of excessive engine cooling The pump must be independent of the engine for optimal operation so that both the amount of heat released by the engine to the coolant and the desired temperature of the engine can be controlled more precisely Application of this concept would reduce parasitic losses in engine power and downsize the engine cooling system In addition, active control of the coolant flow rate using an electronic water pump has several advantages such as high coolant temperature control and fast warm-up and post-cooling, and it is conducive to a reduction in fuel consumption and harmful emissions One concern with using an electrically-driven pump is the high voltage requirement, around 42 V, to drive the electric motor Fortunately, electronic pump and actuator technology has improved considerably, and research in this area is ongoing, so this difficulty is expected to be resolved in the near future (Chalgren, 2003) INTRODUCTION Research is being conducted with the goal of fulfilling stringent emission standards and improving the fuel economy of automotive engines Research trends are two-fold: an optimization of the combustion process and renovation of the cooling system The homogeneous charge compression ignition (HCCI) combustion technique has shown promising results in terms of near-zero NOx and PM emissions A particular variation of this technique, premixed charge compression ignition (PCCI) combustion, has recently drawn substantial attention (Noguchi et al., 1979; Onishi et al., 1979; Najt and Foster, 1983) Optimizing the geometry of the high thermal-efficiency direct injection (DI) diesel engine is also a strategy for better combustion performance and lower emissions Recent trends to increase the power output of an engine with a turbocharger or supercharger are increasing the demand on the capacity of engine cooling systems more than ever Several efforts have been made to handle the increased heat load on the system with innovative cooling strategies such as reverse cooling, split cooling, and nucleate boiling cooling (Ap et al., 2003, Ap and Tarquis, 2005; Kruger et al., 2008), while reducing the cooling system size and weight A heat accumulator can average out peak heat loads so that an unnecessarily large cooling inventory can be reduced in volume and weight (Vetrovec, 2008) This system is also advantageous for reducing engine warmup time, contributing to a significant decrease in harmful *Corresponding author e-mail: hylee@hanyang.ac.kr 767 768 K B KIM, K W CHOI, K H LEE and K S LEE Two strategies for more flexible control of the coolant temperature and flow rate using an electronic water pump and valves were investigated in this study Similar strategies have been studied to replace a wax-type thermostat with a valve to control the coolant flowing through radiator more efficiently However, there have been only rare efforts to prevent the coolant from flowing through an oil cooler and cabin heater during the warm-up period By reducing the warm-up time, the proposed strategies are expected to improve engine performance in terms of fuel savings and emissions penalties With these goals in mind, a simulation was carried out to explore how the innovated cooling system could contribute to shortening the warm-up period during a cold engine start MODELING AND VALIDATION To investigate the innovative cooling strategies, a diesel engine and its cooling circuit were modeled using onedimensional CFD code software (Flowmaster 2) The prototype used for modeling in this study was the 2.7L HSDI diesel engine test rig, as shown in Figure 1, which consists of a water cooler substituted for the radiator found in real vehicles, a water pump, a wax-type thermostat, an oil cooler, a heater core, and an emission sampling system (Horiba MEXA-7100DEGR) The specifications of the engine are also summarized in Figure Engine test rig used in the experiment Table Specifications of the engine employed in this study Cylinder array In line Swept volume 2696 cc Bore × Stroke 86.2 mm × 92.4 mm Number of valves 20 Compression ratio 18:1 Engine speeds 1600, 1800, 2000 rpm Engine torque 0, 3.1, 5.1 kgm Coolant temperature at engine 85~105°C Figure (a) Schematics of the engine test rig and (b) a simulation model corresponding to the engine test rig used in the experiment P, F, q, and ω in the model are control icons The spots shown in (a) are the locations where the thermocouples are installed Table 1, along with experimental conditions The coolant temperature at the engine can be higher than the typical boiling temperature of water at atmosphere because the pressure inside the coolant circuit is higher than ambient pressure All compartments in the test rig were designed with components provided by the software, and the required input data for each component were measured or provided by manufacturers A schematic of the engine test rig and a simulation model corresponding to the test rig are shown in Figure The simulation model was validated with the oil temperature and coolant temperatures measured using a thermocouple at four different positions in the cooling circuit Figure shows the thermocouple positions: at the engine, before and after the oil cooler, and after the cabin heater This validation study was performed for the two engine speeds of 2000 and 3000 rpm The temperatures measured at the four positions, and the oil temperature at these two speeds fell within 10% of the error ranges Figure shows temperature results obtained from the experiment and simulation at 3000 rpm for comparison of the two methods The simulation results were in excellent agreement with the experimental results measured at the four positions but did not agree with the oil temperature The overall deviations between the simulated and experi- ACTIVE COOLANT CONTROL STRATEGIES IN AUTOMOTIVE ENGINES 769 Table Simulation errors for 2000 and 3000 rpm RPM Oil Engine O/C in O/C out H/C out 2000 3.39 6.06 12.57 10.98 9.72 3000 18.42 7.99 4.78 2.39 2.7 mental results for the cases of 2000 and 3000 rpm were around and 4%, respectively, which provides confidence in the simulation model The simulation errors for 2000 and 3000 rpm are summarized in Table EXPERIMENTAL RESULTS FOR EMISSIONS AND BSFC A mechanically-driven water pump is coupled to the engine, which makes active control of the coolant flow rate impossible An unnecessarily high amount of coolant removes heat from the engine, deteriorating combustion efficiency Therefore, control of the coolant flow rate is crucial for Figure Comparison of oil and coolant temperatures obtained by experiment and simulation for a pump speed of 3000 rpm Figure Effect of coolant temperature on emission characteristics and BSFC 770 K B KIM, K W CHOI, K H LEE and K S LEE operation of the engine at the optimal temperature Figure shows the effects of various coolant temperatures on exhaust emissions and fuel consumption The data were obtained under steady state conditions while the coolant temperature was increased from 90 to 105oC A cooler was utilized to change and maintain the coolant temperature for the experiment The most significant fact is that the emissions of THC and CO were reduced when the coolant temperature was higher than 85oC Compared to the data at 85oC, THC and CO emissions at 105oC were reduced by 10% and 4%, respectively In addition, the BSFC was reduced by approximately 3% The higher coolant temperature increases the in-cylinder temperature, leading to more complete combustion of the fuel; thus, THC and CO emissions were shown to decrease while the BSFC improved to some degree However, NOx emissions were observed to increase because the higher coolant temperature contributed to an increase in the combustion temperature Another significant fact demonstrated in Figure is how much the emissions and fuel consumption could be improved using a coolant temperature control strategy Frequent changes in the coolant temperature resulting from passive control of the coolant flow rate are a direct cause of deterioration of the emission and fuel consumption characteristics of an engine Based on Figure 4, when the coolant temperature is maintained at 95oC, the engine performance in terms of emissions and BSFC is likely to be the optimum The test rig was used to show the effect of the coolant temperature on the emissions and fuel consumption and to validate the simulation model with temperature measurements However, it could not be used to show the reduction in the warm-up time due to two electrically-controlled valves because it is not equipped with the valves Building a test rig with the valves will be a future study, and the simulation was performed to investigate the effects of the aforementioned strategies on the reduction in the warm-up time SIMULATION RESULTS AND DISCUSSION Two engine cooling concepts with the goals of improving fuel consumption and emissions were investigated using the validated computational model of an engine cooling system As discussed above, the coolant temperature must increase as quickly as possible, especially during the cold start engine warm-up period A low coolant temperature is a direct cause of incomplete combustion, resulting in high exhaust emissions and high fuel consumption Approaches to decreasing the warm-up time begin with the idea of reducing the coolant flow rate or quantity during the warmup period A zero coolant flow rate can be achieved by pausing the operation of the water pump The mechanical water pump in a typical cooling system is coupled to the crank shaft by belts and therefore subject to the engine operating speed An electronic water pump is independent of engine Figure Effect of the zero flow strategy on coolant temperature Figure Schematics of coolant path control strategy operation, which makes it possible to more flexibly control the coolant flow rate When the rotation speed of the water pump was assigned to zero rpm in the simulation, the engine temperature increased quickly, as shown in Figure The warm-up time was reduced by approximately 25% using this strategy One problem with using the electrically-driven pump is its high voltage requirement, which is approximately 42 V, for driving the electric motor This voltage is achievable in hybrid or future electric cars but not in vehicles with a typical internal combustion engine From a system design and feasibility standpoint, preserving the passive cooling strategy may be more practical at this time As an alternative, a method to control the quantity of coolant by blocking the coolant flow pathway during the warm-up period was used This concept is illustrated in Figure This idea is similar to a thermostat in a conventional engine cooling system, but it is not identical The thermostat does not allow the coolant to flow through the radiator to avoid heat rejection; however, the coolant still passes through the oil cooler and heater core It slows down the engine warm-up Two electronic valves were placed in the coolant pathway, and temperature sensors measured the coolant temperature Based on the data from the sensors, the electronic control unit (ECU) determines the coolant path Initially Valve in Figure lets the coolant flow through the bypass until the engine temperature reaches a desirable level, normally 90oC Valve then blocks the coolant flow toward the bypass and sends it into the oil cooler Valve can block the coolant flow through the heater core, eventually reducing heat loss through the cabin heater during the summer when the heater core is unnecessary ACTIVE COOLANT CONTROL STRATEGIES IN AUTOMOTIVE ENGINES 771 ing strategy (2) Controlling the flow path also shortened the warm-up period A significant reduction of the warm-up period was achieved by closing the valve between the engine and the oil cooler (3) These two strategies show potential to reduce the overall harmful emissions and fuel consumption and are expected to satisfy the stringent emission regulations of the future ACKNOWLEDGEMENT−This work was done as a part of Figure Effect of coolant path control strategy on reduction of the coolant warm-up period In short, the two valves reduced the engine warm-up period and established a steady coolant temperature once the transient period was complete This approach was also examined using the simulation model, and the warm-up time of the system using the valve control strategy was shorter than that of conventional systems The simulation results are shown in Figure When the valve between the engine and the oil cooler (Valve 1) was closed, the warmup time was observed to decrease by approximately 25% As discussed before, a fast warm-up will contribute to a reduction in fuel consumption and harmful emissions based on the results shown in Figure A high engine temperature is beneficial for the chemical reaction of fuel in the combustion chamber, and it is accompanied by a decrease in CO and THC emissions An increase in NOx emissions is a concern based on the experimental results However, the amount of NOx produced during the start-up period might be small relative to the amount of NOx emitted during normal driving The active cooling strategies also have the advantage of a more prompt response to sudden changes in engine temperature resulting from acceleration or load change Frequently undergoing temperature changes leads to an increase in all harmful emissions Furthermore, the strategy of active coolant flow control using an electronic pump is expected to eliminate postcooling to prevent thermal soak, particularly in diesel engines, which is also conducive to reduced emissions CONCLUSIONS In this study, the feasibility of novel cooling strategies that use an electric water pump and electronic valves in the automotive cooling circuit was investigated During operation of an engine, the coolant quantity and flow rate were actively controlled at a more optimal temperature using electronic valves and an electric water pump, respectively The principle conclusions of this study can be summarized as follows: (1) The zero-flow warm-up strategy helped the engine temperature increase faster than the conventional cool- Industry sources development project The authors acknowledge the financial support for this research project provided by Korean Ministry of Knowledge Economy REFERENCES Ap, N., Guerrero, P., Jouanny, P., Potier, M., Genoist, J and Thuez, J L (2003) Ultimate Cooling New Cooling System Concept Using the Same Coolant to Cool All Vehicle Fluids IMechE 661−674 Ap, N and Tarquis, M (2005) Innovative engine cooling systems comparison SAE Paper No 2005-01-1378 Chanfreau, M., Gessier, B., Farkh, A and Geels, P Y (2003) The need for an electrical water valve in a thermal management intelligent system (THEMIS TM) SAE Paper No 2003-01-0274 Chalgren, R D (2003) Development and verification of a heavy duty 42/14V electric powertrain cooling system SAE Paper No 2003-01-3416 Chalgren, R D (2004) Thermal comfort and engine warmup optimization of a low-flow advanced thermal management system SAE Paper No 2004-01-0047 Cho, H., Jung, D and Assanis, D N (2005) Control strategy of electric coolant pump for fuel economy improvement Int J Automotive Technology , , 269−275 Cho, H., Jung, D., Filipi, Z S., Assanis, D N., Vanderslice, J and Bryzik, W (2007) Application of controllable electric coolant pump for fuel economy and cooling performance improvement J Engineering for Gas Turbines and Power, , 239−244 Hnatczuk, W., Michael, P., Bishop, L J and Goodell, J (2000) Parasitic loss reduction for 21st century trucks SAE Paper No 2000-01-3423 Kim, K., Hwang, K., Lee, K and Lee, K (2009) Investigation of coolant flow distribution and the effects of cavitation on water pump performance in an automotive cooling system Int J Energy Research, , 224−234 Kruger, U., Edwards, S., Pantow, E., Lutz, R., Dreisbach, R and Glensvig, M (2008) High performance cooling and EGR systems as a contribution to meeting future emission standards SAE Paper No 2008-01-1199 Najt, P M and Foster, D E (1983) Compression-ignited homogeneous charge combustion SAE Paper No 830264 Noguchi, M., Tanaka, Y., Tanaka, T and Takeuchi, Y (1979) A study on gasoline engine combustion by observation 129 33 772 K B KIM, K W CHOI, K H LEE and K S LEE of intermediate reactive products during combustion SAE Paper No 790840 Onishi, S., Jo, S H., Shoda, K., Jo, P D and Katao, S (1979) Active thermo-atmosphere combustion (ATAC) - A new combustion process for internal combustion engines SAE Paper No 790501 Page, R W., Hnatczuk, W and Kozierowski, J (2005) Thermal management for the 21st century-Improved thermal control & fuel economy in an army medium tactical vehicle SAE Paper No 2005-01-2068 Vegenas, A., Hawley, J G., Brace, C J and Ward, M C (2004) On-vehicle controllable cooling jets SAE Paper No 2004-01-0049 Vetrovec, J (2008) Engine cooling system with a heat load averaging capability SAE Paper No 2008-01-1168 International Journal of Automotive Technology, Vol 11, No 6, pp 773−781 (2010) DOI 10.1007/s12239−010−0092−3 Copyright © 2010 KSAE 1229−9138/2010/055−02 DEVELOPMENT OF AN ON-LINE MODEL TO PREDICT THE INCYLINDER RESIDUAL GAS FRACTION BY USING THE MEASURED INTAKE/EXHAUST AND CYLINDER PRESSURES * S CHOI, M KI and K MIN School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-742, Korea (Received September 2009; Revised 25 May 2010) ABSTRACT−The in-cylinder RGF (residual gas fraction) of internal combustion engines for new combustion concepts, such as CAI (controlled auto ignition) or HCCI (homogenous charged compression ignition), is a major parameter that affects the combustion characteristics Thus, measurement or prediction of the cycle-by-cycle RGF and investigation into the relation between the RGF and the combustion phenomena are critical issues However, on-line prediction of the cycle-by-cycle RGF during engine testing is not always practical due to the requirement of expensive, fast response exhaust-gas analyzers and/or theoretical models that are just too slow for application In this study, an on-line model that can predict the RGF of each engine cycle and cylinder during the experiment in the test cell has been developed This enhanced model can predict the in-cylinder charge conditions of each engine cycle during the test in three seconds by using the measured dynamic pressures of the intake, exhaust, and cylinder as the boundary conditions A Fortran77 code was generated to solve the 1-D MOC (method of characteristics) This code was linked to Labview DAQ as a form of DLL (dynamic link library) to obtain three boundary pressures for each cycle The model was verified at various speeds and valve timings under the CAI mode by comparing the results with those of the commercial code, GT-Power KEY WORDS : RGF (residual gas fraction), CAI (controlled auto ignition) combustion, Cyclic variation, MOC (method of characteristics) conditions with the control parameters, such as the speed and valve timing, and to study the relationship between the charge conditions and the combustion phenomena If the charge conditions, such as the RGF and the temperature, can be measured or predicted quickly during the engine test, it can be helpful for engineers to understand the phenomena at the developmental stage of new engines Several methods have been developed to measure and predict the in-cylinder RGF With regard to experimental measurement methods (F Galliot et al., 1990; Richard et al., 1999; F Schwarz et al., 2003), the in-cylinder RGF was obtained from an analysis of the CO2 or NO/HC concentrations during intake, exhaust, or in-cylinder gases These methods are real-time and accurate but require fast response analyzers and special, fast gas-sampling techniques, which are very expensive Gas exchange models (Heywood et al., 1993; Cho et al., 2001; Uwe et al., 2004; G Colin et al., 2007) and empirical models (Amer, 2006) predict the in-cylinder RGF by using simple gas exchange equations and empirical equations that require some engine parameters (e.g., the compression ratio, valve overlap, volumetric efficiency, A/F, speed, EGR, etc.) These models can quickly predict the in-cylinder RGF without expensive equipment and can be used to control the engine; however, the empirical coefficients have to be INTRODUCTION The residual gas fraction (RGF) level in a cylinder charge influences the combustion process of internal combustion (IC) engines In particular, in new combustion concepts (such as CAI, or controlled auto ignition) that auto-ignite fuels with high octane numbers, the RGF becomes more important because the combustion is controlled by the thermal energy of the high RGF up to 40% Though new combustion concepts have several advantages, e.g., low emission levels and high thermal efficiency (Koopmans et al., 2003; Zhao et al., 2001; Stanglmaier et al., 1999), combustion control is not easy because there is no direct method of controlling combustion, such as fuel injection timing and spark timing, which are used in diesel and SI engines, respectively (Kaneko et al., 2001) Compressed ignition (auto-ignition) is difficult because the ignition is completely governed by chemical kinetics and is therefore influenced by the fuel’s composition, the equivalence ratio, and the thermodynamic state of the mixture (Kelly-Zion, 2000) For these reasons, it is necessary to measure the charge conditions cycle-by-cycle to know the variation of these *Corresponding author e-mail: kdmin@snu.ac.kr 773 774 S CHOI, M KI and K MIN adjusted in accordance with the engine and the operational conditions Recently, an applied 1-D gas dynamics model was introduced (Liu , 2006) By using the measured dynamic pressures of the intake and exhaust ports as boundary conditions, this model shortened the length of the pipes in the computation range By solving 1-D gas dynamics (Liu , 1996) and cylinder energy equations, it was possible to predict the in-cylinder RGF much faster than conventional 1-D gas dynamics models An on-line tool was also developed with this model It predicts the in-cylinder RGF of a single cylinder engine within 20 seconds per engine cycle for 10 simulation cycles and within seconds for simulation cycles In this study, an on-line model was developed that can predict the RGF for each cycle and the cylinder during the engine experiment in the test cell The MOC (method of characteristics) was embedded in the Fortran code as the 1D gas dynamics solver Three measured dynamic pressures for the intake, exhaust, and in-cylinder gases were applied as the boundary conditions By utilizing this additional measurement of the dynamic pressure of the cylinder, this model no longer solves time-consuming cylinder energy equations and therefore substantially reduces the computational time This new model is verified by comparing its results with those from a commercial code (GT-Power) at various speeds and valve timings The model can be applied to both single cylinder and multi-cylinder engines for any valve timing and lift An on-line model was developed by inserting this model into a Labview DAQ system as a form of DLL (dynamic link library) On-line engine tests were performed for a single cylinder engine in the CAI mode During the test, the cyclic in-cylinder charge conditions were predicted by using the RGF model The investigation of the cyclic variation at a high load CAI operation through the on-line model is presented et al et al RGF PREDICTION MODEL 2.1 Major Features and Assumptions The RGF prediction model calculates the mass flow rate through the intake and exhaust pipes and predicts the incylinder charge conditions, such as the trapped mass, incylinder temperature, and RGF This model consists of two parts: a “pipe-flow solver” and a “cylinder-condition solver” The pipe-flow solver is a 1-D gas dynamics model that calculates the instantaneous mass flow rate through the intake and exhaust system This model uses three points at the ends of the intake and exhaust pipes as boundary conditions; the instantaneous pressures of the intake, exhaust, and cylinder are measured at these points Through this feature, the flow calculation commences from the positions of the intake and exhaust dynamic pressure transducers, as shown in Figure The calculation range and the solution time can be minimized The gas flow dynamics in the pipe are solved through the MOC (Benson, 1982) Figure Three locations for the boundary-pressure inputs and the calculation range of the gas-flow solver By simply solving the ideal-gas state equation, the cylinder-condition solver predicts the instantaneous in-cylinder charge conditions, such as the trapped mass, RGF, and temperature by the intake and exhaust mass flow rate (calculated with the pipe-flow solver), and measured cylinder pressure Consequently, with this simplified feature, the in-cylinder charge condition can be calculated much faster than through conventional 1-D gas dynamic models that solve computationally expensive conservative equations The code was generated by using Fortran 77 To simplify the model, several assumptions were made as follows • An ideal gas was assumed • The gas intake was assumed to be a homogeneous mixture • Perfectly burned products were assumed following combustion • Mixing at the valve ports through back flow was ignored Flow losses (through the change in area, friction, heat transfer, etc.) did not affect the mass-flow results for the single cylinder engine model due to the short length and simple geometry of the pipes in the calculation range For this reason, an isentropic MOC solver was used in the single cylinder engine model However, for a multi-cylinder engine model, flow losses are no longer negligible due to the complex geometries of the intake and exhaust in the MOC solver; the losses were considered through changes in the Riemann variables 2.2 Simulation Details 2.2.1 Gas dynamics simulation To calculate the pipe flow through the intake and exhaust system, a 1-D MOC is applied to the model The pipe flow can be assumed to be 1-D in the longitudinal direction Through this 1-D flow and the isentropic assumption, the continuity and momentum equations are solved through the MOC along the pipe length at every time step By using the ideal gas assumption, the flow condition can be characterized by the speed of sound (a) and the flow velocity (u); furthermore, the conservation equations are expressed in terms of the change in a and u along the pipe (x) and over DEVELOPMENT OF AN ON-LINE MODEL TO PREDICT THE IN-CYLINDER RESIDUAL GAS FRACTION Figure Diagram of the pipe meshing and the notation for the length/time grid time (t) The MOC solves the conservation equations by mapping a and u to non-dimensional physical variables, the so-called Riemann variables The Riemann variables, λ and β, are defined as in Equations (2) and (3) by using the nondimensional speed of sound (A), flow velocity (U), length (X), and time (Z) These variables are rendered dimensionless by using the reference speed of sound (aref) and the length (Lref), as shown in Equation (1) λ and β are the characteristics that represent the direction of the pressure wave; they respectively speak to the forward and backward directions κ is the specific heat ratio of gas A = -a , U = -u - , X = -x , Z = a ref -t Lref aref aref Lref dX dA κ – κ–1 = U + A , - = − , λ = A + U dZ dU 2 dX dA κ – κ–1 = U−A , - = + , β = A− U dZ dU 2 (1) (2) (3) The pipe is gridded along the length At each time step, new Riemann variables are calculated for all grids along the length by using the variables already determined in the preceding time step The details of the grid calculations are shown in Equation (4)~(5) and Figure In Equation (4)~(5), λI is the forward characteristic and λII is the backward characteristic Figure shows the mesh grid along the length and time step The symbol, m, refers to the length of the grid, whereas r indicates the time step grid The Riemann variables at each pipe end, (λ I)r+1,1 and (λ II)r+1,m+1, are obtained from the boundary conditions ( λI )r + m = ( λI ) r m + , ∆Z { b(λ ) −a( λ ) } {( λ ) − ( λ ) } I r m–1 II r m – I r m–1 I rm ∆X ( λII )r + m = ( λII )r m + ∆Z { b ( λ II ) r m +1 −a ( λ I ) r m +1 } { ( λ II ) r m +1 − ( λ II ) r m } ∆X , , , , where, a , , (4) , , κ , , (5) and b = κ + -) 2(κ – 1) 3– = –1 (κ the flow losses due to wall friction, wall heat transfer, and entropy change are considered by summing the variance in the Riemann variable that is caused by these losses A new Riemann variable, which is called the ‘path line characteristic (AA),’ is defined to represent the entropy-level change that is caused by the losses The total variance in the Riemann variable, λ (Equation 6), can be determined as the sum of the variance due to the entropy change (Equation 7), wall friction (Equation 8), and wall heat transfer (Equation 9) In the equations, the subscript P refers to the value of the previous mesh, whereas R refers to the value of the present mesh (6) dλ ( δλ )entropy ( δλ )friction ( δλ )heat + = When the MOC is applied for non-isentropic conditions, + ( δλ )entropy = ( λP + βP )( AAR′ – AAP)/AAP (7) xref ⎛ λP – βP-⎞ - -( δλ )friction = −( κ – 1) f∆X × D ∆X ⎝ κ – ⎠ β ⎛ β λ⎞ ∆Z β ⎝λ β ⎠ λ λ P– P P– P -P– P P+ P (8) ( δλ )heat = λ – β f∆X x κ P P - - ref - R⎛⎝ -2 ⎞⎠ ( Tw – Tg)∆Z λP – βP D ∆X aref (9) where, AA qx - -2 -fx ref λ R + β R ⎞ - -AAR′ = AAR + ( -κ – -) -R × ⎛⎝ -3-ref + ∆Z , D ( λR + βR ) aref κ–1 ⎠ f = τ -w -1 ρ u 2.2.2 Boundary conditions To determine the Riemann variables at each pipe boundary, different boundary conditions are applied Inflow boundary The inflow boundary condition is applied at the inlet of the intake system and the outlet of the exhaust system The measured intake and exhaust dynamic pressures are inserted into this boundary condition at each time step The equations that describe the inflow boundaries in accordance with the flow conditions and the input intake and exhaust dynamic pressures are presented as Equations (10)~(13) Inflow: λout aλin {bA20 ( a2)λin} = , 775 + – 1– a = -3 -– κ , b = 4⎛⎝ -κ – -⎞⎠ κ+1 Outflow: λout = κ+1 (11) A0 – λin Choke flow: λout κ +1 = 3– κ (10) (12) λin k – - ⎞ 2k -Pressure input: A0 = ⎛⎝ -p input Pref ⎠ (13) 776 S CHOI, M KI and K MIN Junction boundary The junction boundary condition is applied at the points where the pipes divide or converge Through the assumption of isentropic flow and equal pressure and density for adjacent pipe ends, the Riemann variable is determined by the following equations (Equations 14 and 15) in a multiple-branch pipe system Fn denotes the cross-sectional area of the nth pipe, and FT is the sum of the cross-sectional areas of the pipes at the junction (14) λout,n KK λin n , n = to m = KK = – ∑K λ , n= m n n=1 in,n , ∑ n= m 2F Kn = n , FT = Fn FT n=1 (15) Valve boundary The valve boundary condition is applied to the valve at the border of the intake and exhaust system that is connected to the cylinder From the pressure ratio between the cylinder and the pipe, the flow condition through the valve is determined When inflow occurs from the pipe to the cylinder, the valve is treated as a nozzle; therefore, the mass flow rate and the Riemann variable are determined by the nozzle boundary In the case of outflow from the cylinder to the pipe, the pressure drop, entropy change, and mass flow rate across the valve are calculated by using Equations (16)~(19) below As a boundary pressure, the measured cylinder dynamic pressure is input into the model, as shown in Equation (20) 1/2 ⎧ ⎫ ⎨ ⎛⎝ – 1⎞⎠ ⎬ f1 ( π ) = ψ π ⎩κ – π ⎭ ⎛ ⎞ B ⎜ κ–1 ⎟ −⎜ ⎟ =0 2 ⎜ – B ⎟ ⎝ κ–1 ⎠ (16) Pressure drop: sonic flow f2 ( π ) = π 2κ / κ – − ψ ( ) 2⎞ ⎛ B ( κ + ) / [2 ( κ – ) ] – ⎜ ⎟ κ –1 ⎛ ⎞ -⎜ -⎟ =0 ⎝ κ – 1⎠ ⎜ ⎟ B ⎝ κ–1 ⎠ Entropy change C aA2 2⎞ ⎛ – B ⎝ κ–1 ⎠ 1/2 = = - aA1 π -P Massflow rate m· = κ p ref F -U aref A2 Pressure input πα = p ⎞ λin/ ⎛⎝ input pref ⎠ κ -–1 2κ (17) (18) (19) (20) where, B C(π πα ) = – 2.2.3 Cylinder conditions and RGF tracking The cylinder conditions are determined by the ideal-gas state equation, without solving the energy equation At each time step, the trapped mass in the cylinder and the RGF are calculated from the instantaneous mass flow rate through the intake and exhaust valve Because the equivalence ratio of the intake gas is known and perfect combustion is Figure Trapped mass and RGF tracking (1500 rpm, IVO/ EVO = 418/140) assumed, the trapped mass can be calculated by simply adding the mass flows to the trapped mass from the preceding time step The RGF can also be determined from the initial trapped mass before the opening of the intake valve and the mass that is induced through the intake valve The results of the trapped mass and the RGF tracking are shown in Figure 3; the exhaust and intake mass flows are determined from the flow calculation The cylinder temperature can be determined at each time step by substituting the three known variables, i.e., the measured cylinder pressure, the calculated volume, and the gas composition as obtained from RGF, into the ideal-gas state equation 2.2.4 Calculation process The calculation commences from the IVC (intake valve closed) timing The first step is to input the required data and the initial conditions at the IVC The required data are as follows • Dynamic pressure at three points: intake, exhaust, and 902 T.-W KIM and H.-Y JEONG proposed; the lift forces for higher water depths were obtained first, and the lift force for a very shallow water depth was obtained by extrapolating the lift forces for higher water depths The full iteration method resulted in a converged solution of lift force as a function of speed, and the hydroplaning speed could be determined as the speed at which the lift force reached a critical load However, the full iteration method still requires a significant amount of computation time in a hydroplaning simulation for a patterned tire Thus, in this study, the full iteration method was modified such that no iteration or only one additional iteration was needed at each speed to reduce the computation time In the noiteration method, the deformed shape of a tire was obtained once in the whole simulation while only considering the vertical load However, in the one-iteration method it was obtained once at each speed while taking the vertical load and the pressure distribution obtained at the previous speed into account The hydroplaning speeds of a straight-grooved tire were determined for water depths of 5, 10, 15 and 20 mm by applying the full iteration method, no-iteration method and one-iteration method It was noted that the hydroplaning speed determined using the one-iteration method was almost the same as that determined using the full iteration method, but the speed was determined much more quickly Thus, the one-iteration method was applied to two patterned tires as well The hydroplaning speeds of the two patterned tires were determined and compared with the test data The comparison showed that the simulation results were in good agreement with the test results METHODOLOGY USING FDM, FEM AND ASYMPTOTIC METHODS 2.1 FDM The FDM code was developed based on the mathematical formulations of Browne (Browne, 1975; Browne and Whicker, 1983) Browne assumed the hydroplaning phenomenon to be two-dimensional because any variation through the thickness was negligible, and he used RANS (Reynolds Averaged Navier-Stokes) equations to consider the effect of turbulence In addition, he used an average of the longitudinal or lateral speed represented as a second-order polynomial function through thickness and defined a stream function that automatically satisfied the continuity equation The governing equations are given as follows µψy - +h∂ P =0 ∂ ψ y ∂ ψ xψ y - − - + 2 (1) ρh ∂y ρh G ρh ∂x µψ -− ∂ ψ µU-+h -∂ ψ ψ ∂P - − − (2) =0 ∂y ρh ∂x ρh G ρ h2 G h ∂ y where ψ is the stream function, and ψ and ψ are the ∂x x x x y x y y x y partial derivatives with respect to the longitudinal and lateral direction, respectively ρ, , µ and are the density, water depth, viscosity and pressure, respectively In addition, h P is the speed of the automobile, and and are parameters that account for the turbulence effect Moreover, he used the no-slip condition on the tire and road surface and prescribed zero pressure at the sides and the trailing edge; for the leading edge, the pressure was calculated from Bernoulli’s equation to consider the effect of a bow wave He also prescribed the stream function to be zero at the center line because there is no transverse flow in a symmetric tire Finally, he linearized the governing equations using the Newton-Raphson method, and solved the equations using the column-wise influence coefficient method The column-wise influence coefficient method was proven to be efficient in the analysis of gas bearing problems (Castelli and Pirvics, 1968) The FDM code was developed in the standard manner based on Equations (1) and (2) and the assumptions mentioned above Note that only a steady state solution can be obtained using the FDM code That is, the road surface must be smooth, and the tire pattern should be the same along the circumferential direction or the tire must lock up U Gx Gy 2.2 Full Iteration Method Although the deformation of a tire affects the hydroplaning speed, Browne did not consider it (Browne, 1975) However, in the iteration method that the authors proposed, an FEM simulation was incorporated with the FDM simulation to consider both the deformation of a tire and the pressure distribution due to water flow (Oh , 2008) First, an FEM simulation was conducted to obtain the deformed shape of a tire while only considering a vertical load Then, the FDM code was executed for the deformed shape of the tire for a low vehicle speed (10 km/h), and the pressure distribution of the water was obtained This pressure distribution was applied to the FE tire model as the traction boundary conditions along with the vertical load, and a new deformed shape of the tire was obtained The FDM code was executed again for the new deformed shape of the tire to obtain a new pressure distribution of water This iteration process was continued until a converged pressure distribution was obtained, and the lift force was calculated from the converged pressure distribution Once the lift force was obtained for the given speed, the procedure was repeated for other speeds (20 and 30 km/h, and so on) Then, the lift force could be shown as a function of speed This iteration method is shown schematically in Figure et al 2.3 Asymptotic Method The water depth, , is in the denominators in the governing equations, Equations (1) and (2) Consequently, the linearized matrix equations obtained from the governing equations become ill-conditioned around the contact zone because of very shallow water, and the pressure there hardly converges In other words, it is almost impossible to obtain a converged pressure distribution near the contact zone Thus, an asymptotic method was proposed The lift force (or the pressure distribution) was obtained by assuming that the h HYDROPLANING SIMULATIONS FOR TIRES USING FEM, FVM AND AN ASYMPTOTIC METHOD 903 (3) lift force h f H (4) f ch U where H is a fictitious additional water depth, and a, b and c are constants By using the least square method, a, b and c can be easily determined: 1.25, 2.0 and 0.000115 = + = Figure Schematic diagram of the iteration method for the hydroplaning simulation water depth is much greater than the actual depth; the lift force was obtained as the water depth decreased to a certain value that was still high enough to result in a converged solution The lift forces for several water depths and speeds (shown in Figure 2) indicate that it is possible to represent the lift force as a function of the actual water depth, the speed and the additional water depth, as in Equation (3) In addition, the numerator can be represented as an exponential function of the actual water depth and the speed, as in Equation (4) Figure Lift force for several water depths and speeds a b 2.4 No Iteration and One Iteration Methods The full iteration method results in a converged solution of pressure distribution, but it still requires a significant amount of computation time when simulating a patterned tire hydroplaning Thus, to reduce the computation time, two modified methods were proposed and evaluated First, the deformation of the tire due to only the vehicle load was obtained from the FEM simulation, and the lift force was calculated for every 10 km/h using only the FDM code for the deformed shape of the tire Thus, in the first modified method, the FEM simulation was conducted only once in the whole hydroplaning simulation, and no iteration between the FEM simulation and the FDM simulation was needed Second, the lift force was calculated for every 10 km/h by the FDM code for the deformed shape of the tire that was obtained from the FEM simulation considering the vehicle load and the pressure distribution obtained at the previous speed That is, when the FDM code was executed for a speed of 20 km/h, for example, the deformed tire shape was obtained from the FEM simulation considering the 904 T.-W KIM and H.-Y JEONG vertical load and the pressure distribution obtained for a speed of 10 km/h Thus, in the second modified method, the FEM simulation was conducted only once at each speed, and one iteration between the FEM simulation and the FDM simulation was needed at each speed SIMULATION RESULTS 3.1 Straight-Grooved Tire In this study, the hydroplaning phenomenon of a straightgrooved tire (P205/45R16) with four grooves with a width of 9.9 mm on a wet road covered with water 5, 10, 15 or 20 mm deep was simulated The FE tire model had about Figure FE model of a straight-grooved tire 35,000 nodes and 41,000 elements, and the FDM mesh had about 900 nodes The FEM simulation was executed using ABAQUS/Standard, and its model is shown in Figure First, the full iteration method was used, and the lift force was obtained for every 10 km/h The lift force is shown as a function of speed in Figure 4, where the symbols are the lift forces obtained from the simulation, and the lines are fitted curves Figure is the same as Figure in the authors’ previous paper because the full iteration method was used in the previous paper (Oh , 2008) The simulation result of the lift force seems to be qualitatively correct because it et al Figure Lift force obtained using the full iteration method Figure Lift forces obtained from three different iteration methods HYDROPLANING SIMULATIONS FOR TIRES USING FEM, FVM AND AN ASYMPTOTIC METHOD increases as the speed or the water depth increases There are several definitions of the hydroplaning speed, but in this study, it is defined to be the speed at which the net traction force becomes zero In an experiment, an automobile is accelerated over a layer of water, and the speed at which the longitudinal acceleration becomes zero is defined to be the hydroplaning speed Because the net traction force is the friction force subtracted by the air resistance, the rolling resistance and the water drag force, and the friction force is equal to the coefficient of friction times the contact force (which is equal to the lift force subtracted from the vertical load), the lift force at the hydroplaning speed can be expressed as Equation (5) The air drag coefficient, the rolling resistance coefficient and the coefficient of friction were assumed to be 0.3, 0.015 and 0.48, respectively (White, 1999; Gillespie, 1999) In addition, the drag force calculated from the simulation was about 350 N around a speed of 60 km/h Thus, the lift force at the hydroplaning speed became equal to about 1400 N from Equation (5), which was 37.2% of the vertical load Critical force = vertical load − (air resistance + rolling resistance + drag force)/coeff of friction ≅ 1400N (5) That is, the hydroplaning speed could be easily determined as the speed at which the lift force reached 1400 N, and the hydroplaning speed obtained by using the full iteration method is shown in Table Second, the no-iteration method and the one-iteration method were also applied to the straight-grooved tire Then, the lift forces for water depths of 5, 10, 15 and 20 mm obtained from all three different methods, i.e., the full iteration method, the no-iteration method and the one-iteration method, are shown as functions of speed in Figure The hydroplaning speed, total number of iterations (shown in the parenthesis) and error are also shown in Table 2, where the error is a relative error of the hydroplaning speed obtained from either the no-iteration method or the oneTable Hydroplaning speeds obtained using the full iteration method Water depth [mm] 10 15 20 Hydroplaning speed [km/h] 82.2 70.3 65.2 62.2 Table Hydroplaning speed (km/h), total number of iterations (in parenthesis) and error Water Full No One Error depth iteration iteration Error iteration [mm] method method [%] method [%] 82.2 (28) 87.3 (1) 6.2 81.4 (8) −0.97 10 70.3 (21) 76.8 (1) 9.2 72.5 (7) 3.1 15 65.2 (18) 69.6 (1) 6.7 67.4 (7) 3.4 20 62.2 (22) 66.0 (1) 6.1 63.9 (7) 2.7 905 iteration method with respect to that obtained from the full iteration method When the no iteration method was used, i.e., the deformed shape of the tire due to only the vehicle load was considered, the total number of iterations could be reduced significantly, but the hydroplaning speed was significantly higher than that obtained from the full iteration method However, when the one iteration method was used, i.e the deformed shape of the tire due to the vehicle load and the pressure obtained at the previous speed was used, the total number of iterations could be reduced significantly, and the hydroplaning speed was similar to that obtained from the full iteration method In order to compare the results obtained from the one iteration method with those from a full FE simulation using LS-DYNA, a tire and water film were also modeled using LS-DYNA The tire was modeled by FEM with Lagrangian elements, but the water film was modeled by FVM (Finite Volume Method) with Eulerian elements A coupling function was needed to transfer the forces between the two different kinds of elements On top of the Eulerian elements of the water film, another layer of Eulerian elements was also modeled as “void elements” through which water could splash The contact pressure distribution and displacement of the two FE tire models, i.e., an ABAQUS tire model used in the iteration method and an LS-DYNA tire model used in the full FE simulation, were compared to check whether the models deformed similarly after the inflation pressure and the vertical load were applied The contact pressures from the two models were similar, and the maximum pressures were 1.069×106 Pa and 1.096×106 Pa under a load of 3767 N In addition, the bead displaced 0.0336 m in the ABAQUS model, and it displaced 0.0338 m in the LS-DYNA model Thus, the two tire models are compatible and show similar structural characteristics In a full FE hydroplaning simulation using a commercial code such as LS-DYNA, two methods can be used: one is to model a rolling tire over a layer of still water, and the other is to model a rotating tire at a fixed location with water flowing into the tire (Oh , 2008) The lift forces for water depths of 5, 10, 15 and 20 mm obtained from the one-iteration method are shown in Figure along with the lift force for a water depth of 10 mm, which was obtained from the LS-DYNA simulation using the water flow model Figure looks almost the same as Figure in the authors’ previous paper because lift forces obtained from the oneiteration method in this study were almost the same as those obtained from the full iteration method, and the lift forces obtained from LS-DYNA simulation was exactly the same (Oh , 2008) Even though the one-iteration method resulted in a smoothly increasing lift force for higher speeds, LS-DYNA resulted in an oscillatory lift force like those from other simulations using DYTRAN or LS-DYNA (Nakajima , 2000; Okano and Koishi, 2001; Koishi , 2001) This oscillation stemmed not only from the explicit FE scheme LS-DYNA relies on but also from the rapid application of loading and speed condiet al et al et et al al 906 T.-W KIM and H.-Y JEONG Figure Lift forces obtained from the one iteration method and LS-DYNA tions The high lift force occurring around km/h and the negative lift force occurring between 20 and 50 km/h clearly resulted from the rapid application of the inflation pressure, vertical load and speed The negative lift force was also obtained from a hydroplaning simulation using DYTRAN (Okano and Koishi, 2001) This oscillation could have been reduced to some extent if the loading and the speed had been implemented for a longer period of time, but CPU time would have increased Thus, even though the structural characteristics of the FE model of LS-DYNA were similar to those of the FE model used in the oneiteration method, the full FE simulation using LS-DYNA or other commercial codes is not practical because the lift force is so oscillatory that the hydroplaning speed cannot be clearly defined and the computation time is quite long When a computer with 3-GHz CPU speed and 3-GB memory was used, the CPU time of a simulation using the full iteration method was about hours, but it was just over hour when using the one-iteration method The CPU time was about 24 hours when a rolling tire model was used in LS-DYNA, and it was about hours when a rotating tire model was used in LS-DYNA Therefore, it is noteworthy that the CPU time using the one-iteration method was a lot shorter than that using a full FE simulation with commercial code such as LS-DYNA 3.2 Patterned Tires Because the one-iteration method was proven to result in almost the same hydroplaning speed as the full iteration method, it was applied to two patterned tires, Tire A and Tire B (Figure 7), with a water depth of 10 mm Tires A and B have the same size (225/45R17), but they have different patterns For hydroplaning simulations, only the part of the tire that makes contact with water was meshed, and the FE model of Tire A had 56,347 nodes and 69,189 elements, and that of Tire B had 61,463 nodes and 72,397 Figure Two tires with different patterns elements Unlike a straight-grooved tire, a rotating patterned tire, even at a constant speed, is not in a quasi-static state due to an uneven configuration in the circumferential direction Figure Lift forces for tire A and B HYDROPLANING SIMULATIONS FOR TIRES USING FEM, FVM AND AN ASYMPTOTIC METHOD Figure Average lift force of tire A and B Table Hydroplaning speed (km/h) determined from test and simulation Tire A Tire B Improvement Test 81.6 86.8 6.3% Simulation 79.8 86.0 7.2% However, a locked-up tire skidding at a constant speed on water can be assumed to be in a steady state Thus, rotation of a patterned tire was assumed to be a combination of locked-up patterned tires rotated at different angles Thus, the hydroplaning simulation was conducted three times: the first simulation was for the tire without rotation, the second simulation was for the tire rotated by 5o, and the third simulation was for the tire rotated by −5o The lift forces obtained from the three simulations for Tire A and B are shown in Figure 8(a) and (b), respectively, and the average lift forces for both tires are shown in Figure Because the hydroplaning speed was determined to be a speed at which the lift force reached 1400 N, the hydroplaning speeds for Tires A and B were 79.8 and 86.0 km/h, respectively The hydroplaning speeds of the tires were also determined experimentally, and they are shown in Table along with the hydroplaning speeds determined from the simulations It is noteworthy that the hydroplaning speeds of Tires A and B determined from simulations were in good agreement with those determined from tests; Tire B had better hydroplaning performance by about 7.2% It is also noteworthy that the CPU time to determine the hydroplaning speed for each tire was only about hours CONCLUSIONS In the full iteration method, an FE tire model was incorporated with an FDM model in order to consider the deformation of a tire due to the vertical load and water pressure, and they were iteratively used until a converged water pressure distribution was obtained In addition, to obtain the water 907 pressure around the contact zone where the water was very shallow, an asymptotic method was proposed The full iteration method was modified to require no iteration or only one additional iteration at each speed, which significantly reduces the total number of iterations and the computation time The no-iteration method required just one FE simulation in the whole simulation for the deformed shape of a tire with consideration only a vertical load, but the one-iteration method required one FE simulation at each speed for the deformed shape of a tire considering the vertical load and the water pressure distribution obtained at the previous speed All three methods, i.e., the full iteration method, the noiteration method and the one-iteration method, were applied to a straight-grooved tire to determine the hydroplaning speed It was noted that although the CPU time was significantly reduced, unlike the no-iteration method, the oneiteration method resulted in almost the same hydroplaning speed as the full iteration method The simulation results obtained using both the full iteration method and the oneiteration method seemed to be reasonable in that the lift force monotonically increased as the speed or the water depth increased, and the hydroplaning speed monotonically decreased as the water depth increased Moreover, the one-iteration method was applied to two different patterned tires to determine the hydroplaning speed Strictly, the method should not be used for a non-steady state problem like a rotating patterned tire However, the tire was simulated three times, being rotated by −5o, 0o and 5o, and the lift forces and their average were obtained The average of the lift forces was compared with the critical load to determine the hydroplaning speed The hydroplaning speeds of the two patterned tires were compared with the test data, and it was proven that the hydroplaning speeds obtained from the simulation method proposed in this paper were in good agreement with the test data Therefore, it can be concluded that the one-iteration method proposed in this paper can be accurately and efficiently used for hydroplaning simulation, not only for straightgrooved tires but also for patterned tires, in significantly less CPU time ACKNOWLEDGEMENT−Advice and help of researchers at Hankook Tire R&D center are really appreciated REFERENCES Browne, A L (1975) Tire deformation during dynamic hydroplaning Tire Science and Technology TSTCA, 3, 16−28 Browne, A L and Whicker, D (1983) An interactive tirefluid model for dynamic hydroplaning ASTM, 130−150 Castelli, V and Pirvics, J (1968) Review of numerical methods in gas bearing film analysis Trans ASME, 777−792 Eshel, A (1967) A Study of Tires on a Wet Runway Ampex 908 T.-W KIM and H.-Y JEONG Corp RR 67−24 Gillespie, T D (1999) Fundamentals of Vehicle Dynamics SAE Grogger, H and Weiss, M (1996) Calculation of the threedimensional free surface flow around an automobile tire Tire Science and Technology TSTCA, , 39–49 Koishi, M., Okano, T., Olovsson, L., Saito, H and Makino, M (2001) Hydroplaning simulation using fluid-structure interaction in LS-DYNA 3rd European LS-DYNA Users Conf Martin, C S (1966) Hydrodynamics of Tire Hydroplaning Final Report, Project B-608 Georgia Institute of Technology Nakajima, Y., Seta, E., Kamegawa, T and Ogawa, H (2000) Hydroplaning analysis by FEM and FVM: Effect of tire rolling and tire pattern on hydroplaning Int J 24 Automotive Technology , , 26−34 Oh, C W., Kim, T W., Jeong, H Y., Park, K S and Kim, S N (2008) Hydroplaning simulation for a straightgrooved tire by using FDM, FEM and an asymptotic method J Mechanical Science and Technology, , 34− 40 Okano, T and Koishi, M (2001) A new computational procedure to predict transient hydroplaning performance of a tire Tire Science and Technology TSTCA, , 2−22 Saal, R N J (1936) Laboratory investigation into the slipperiness of roads Chemistry and Industry, , 3−7 Suzuki, T and Fujikawa, T (2001) Improvement of Hydroplaning Performance based on Water Flow around Tires Japan Automobile Research Institute White, F M (1999) Fluid Mechanics 4th Edn McGrawHill New York 1 22 29 55 Copyright © 2010 KSAE 1229−9138/2010/055−18 International Journal of Automotive Technology, Vol 11, No 6, pp 909−916 (2010) DOI 10.1007/s12239−010−0108−z DISCOMFORT OF VERTICAL WHOLE-BODY SHOCK-TYPE VIBRATION IN THE FREQUENCY RANGE OF 0.5 TO 16 HZ S J AHN * Vehicle Quality Engineering Department, Renault-Samsung Motor Company, Shinho-dong, Gangseo-gu, Busan 612-722, Korea (Received 16 February 2010; Revised 14 June 2010) ABSTRACT−Shock-type vibrations are frequently experienced in vehicles excited by impulsive input, such as bumps in the road, and cause discomfort Current national and international standard weightings were primarily developed for assessing exposure to sinusoidal or random vibrations and not impulsive excitations or shocks In this experimental study, various shock signals were systematically produced using the response of a one degree-of-freedom vibration model to hanning-windowed half-sine force input The fundamental frequency of the shock was varied from 0.5 to 16 Hz at a step of 1/3 of an octave The magnitude estimation method was used for fifteen subjects to compare the discomfort of shocks with various unweighted vibration dose values between 0.35 ms− and 2.89 ms− at each frequency The equivalent comfort magnitude of shock showed greater sensitivity at frequencies less than 0.63 Hz and at the resonance frequency of the human body between 5.0 Hz and 6.3 Hz The frequency weighting constructed by using both the equivalent comfort magnitude and the growth rate of discomfort obtained in this study was compared with the current standard weightings, W of BS 6841 and W of ISO 2631 The derived weightings for shock were applied to the acceleration of the shocks, and an enhanced correlation was proved between the magnitude estimations and the weighted physical magnitude of shock 1.75 1.75 b k KEY WORDS : Discomfort, Vehicle, Vibration, Shock, Impulsive force, Stevens’ power law, Frequency weighting function, Psychophysics, Nonparametric statistics, Magnitude estimation method INTRODUCTION The discomfort caused by whole-body vertical vibration depends on the frequency of vibration (Griffin, 1990; Ahn and Griffin, 2008; Ahn , 2007) The frequency dependence determined in laboratory studies has influenced the weightings in current standards, such as British Standard 6841 (1987) and International Standard 2631 (International Organization for Standardization, 1997), used to predict the discomfort and risks of injury caused by whole-body vibration in vehicles and other environments (Griffin, 1998) Although current standards specify methods for evaluating the severity of vibrations containing substantial peaks, there has been little systematic research of the way the fundamental frequency of a shock influences vibration discomfort In some laboratory studies, shock or transient vibration was artificially produced by using a half-sine or single or several cycles of a sine signal Some shocks observed were collected from field studies Some of these studies concluded that a more sophisticated procedure is necessary to properly evaluate shock or transient vibration Taped four-cycle sine bump motions equally spaced were filled with 8-Hz background motion at a level of 0.3 ms−2 r.m.s and a duration of 10 seconds (Griffin and Whitham, et al * Corresponding author 1980) While the total r.m.s value of the complex motions was the same, the number of bumps and the crest factor were varied from to 16 and from 8.15 to 2.12, respectively It was found that the motion of the highest crest factor caused greater discomfort The root-mean-quad value was suggested to evaluate the complex vibrations In another laboratory study, mechanical shocks of a single sine wave and a single half-sine wave in the middle of white noise were used to examine how their shape, frequency, and amplitude affect the discomfort response (Huston , 2000) The sine and half-sine shocks used were classified by crest factor (high: 8, low: 4) and frequency (2, 4, 5, 6, and Hz), but the shocks were artificially made to have similar power spectrum densities They found that the shock with a higher crest factor was more uncomfortable It was suggested that other factors besides frequency, such as waveform and crest factor, must be considered to evaluate the shocks In a field study, the Harbour and Forest Study (Wikstrom , 1991), fifteen experienced drivers who drove a terminal tractor and a large forwarder over three obstacles on a closed test track were employed to assess the discomfort, measure the vibration on the seat and analyze their correlation with different assessment methods: acceleration peak values, time-mean values, dose values, impulse values, acceleration response, and the displacement response method It was shown that a dose value based on an r.m.s et al et e-mail: sejin.ahn@renaultsamsungM.com 909 al 910 S J AHN or r.m.q calculation gave the best prediction of discomfort from the shocks produced by the obstacles Fifty shock stimuli were selected from a collection of vibrations measured in an operator’s seat in an off-road vehicle (Spang, 1997) It was concluded from the study that the maximum of the running r.m.s value showed the best correlation with human subjective response when applied to single event shocks Dupuis et al (1991) selected and tested vibration signals from a field experiment to prove that shock-type vibrations have strong effects on the discomfort of sitting persons It was concluded that several shock parameters, such as their form, frequency, and energy content, should be considered to improve the procedures for the assessment of transient whole-body vibration It is essential to define transient or shock vibrations as likely to happen in real situations to systematically study them and obtain useful findings In this study, the one degree-of-freedom vibration model and Hanning-windowed half-sine input force were used to produce various shock vibrations with different frequencies and magnitudes, which were defined as “shock-type vibrations” in the study It was hypothesized that the discomfort caused by shocks is logarithmically related to the shock magnitude according to Stevens’ power law and dependent on the fundamental frequency of the shock Figure Waveforms of shock-type vibrations with unit unweighted VDV METHOD 2.1 Shock Stimuli Shock-type vibrations were produced from the response of a one degree-of-freedom model to Hanning-windowed halfsine input forces, which is a simple simulation of the response of a vehicle excited by an impulsive input The half-sine signal is ideally used as the impulsive input in model simulation However, the start and end of the halfsine are not mathematically differentiable, and the shocktype response of the model is also not differentiable and not natural Hence, the half-sine input was windowed by the Hanning function, which has a smooth start and stop The Hanning-windowed half-sine is mathematically expressed as ⎧ ⎪ H(t)=⎨ ⎪ ⎩ Asin⎛⎝π t ⎞⎠ × 1-t 0 ⎛ ⎝ – cos t t π ⎞⎠ 0≤ t≤t 0 (1) otherwise Here, A and t mean the amplitude and duration of the half-sine input, respectively The mass and stiffness of the single degree-of-freedom model, as well as the duration and amplitude of the halfsine input force, were varied to produce various waveforms of shock-type vibrations with different fundamental frequencies and magnitudes Shocks with sixteen fundamental frequencies, at the preferred one-third octave frequencies from 0.5 Hz to 16.0 Hz, were produced At each frequency, the shocks were regene0 Figure Peak-to-peak value and “dose” values given by the exponent of (e.g., ( ∫ a (t) dt) ) for shocks of the same magnitude of unity unweighted vibration dose values ½ rated to have five different magnitudes of unweighted vibration dose values from 0.35 ms− to 2.89 ms− : 1.7− (lowest), 1.7− (low), 1.0 (middle), 1.7 (high), and 1.7 (highest) ms− A damping ratio of 0.1 at every frequency was objectively chosen to consider shock-type vibration with not only periodical but also transient characteristics Examples of waveforms of the shock-type vibrations are shown in Figure In this paper, both peak-to-peak and unweighted vibration dose values, VDV, are used to express the magnitudes of shocks to assist comparison with other reports For shocks with an unweighted VDV of 1.0 ms− , the peak-to-peak values and dose values given by an exponent of (e.g., ( ∫ a (t) dt) ) are shown in Figure Using the relationship in this figure, the physical magnitudes of the shocks can be converted between alternative measures for comparison with the previous studies 1.75 1.75 2 1.75 1.75 ½ 2.2 Apparatus and Subjects The shocks were generated on a one-meter stroke vertical hydraulic vibrator located in the ISVR (Institute of Sound and Vibration Research) at Southampton University Subjects sat on a rigid wooden seat (with no backrest) secured DISCOMFORT OF VERTICAL WHOLE-BODY SHOCK-TYPE VIBRATION IN THE FREQUENCY RANGE 911 Figure Photographic representation of apparatus and subject Figure Reference signal followed by a test signal of the vibration stimulus on the platform to the vibrator platform, as shown in Figure An accelerometer (Setra System, 141A type) on the seat measured vertical acceleration The motions were generated and monitored using an HVLab system (version 3.61) at 400 samples per second The acceleration was passed through a low-pass filter with a cut-off frequency of 40 Hz The peak-to-peak values (the difference between the maximum positive peak value and maximum negative peak value) and the unweighted vibration dose values (VDVs) of the shocks on the seat were calculated after the low-pass filter The b weighted VDV was also calculated from the acceleration after passing through the b weighting digital filter in HVLab to investigate the effect of the weighting on the estimation of discomfort Fifteen male subjects aged 22 to 39 years (average: 30.2, standard deviation: 5.2), weighing 54 to 105 kg (average: 75, standard deviation: 12.5) with a stature of 168 to 186 cm (average: 175.8, standard deviation: 5.3) participated in the study The subjects were asked to sit in a comfortable upright posture, with their thighs horizontal and lower legs vertical The height of the footrest was adjusted according to the stature of subjects to maintain the posture described The subjects wore a loose lap belt for safety, headphones to mask the ambient noise, and an eye mask to prevent them from seeing motion The experiment was approved by the Human Experimentation Safety and Ethics Committee of the Institute of Sound and Vibration Research where d ( ) is the desired acceleration and m( ) is the measured acceleration The average percentage acceleration distortion was 2.1% (standard deviation: 1.1%, with a range from 0.5% to 7.2%) The distortion was greater at the highest and the lowest magnitudes at each frequency, and there was the greatest distortion at the highest frequency of 16 Hz due to an overshoot of the first peak The method of magnitude estimation was used to compare the discomfort produced by the test stimuli with the discomfort produced by a reference stimulus The reference was a 2.5-Hz shock with an unweighted vibration dose value of 1.0 ms− (3.1 ms− peak-to-peak) Figure shows a combination of the reference and test stimuli as an example The reference stimulus was delivered within a foursecond period, followed by a two-second pause without motion, followed by the test stimulus The duration of the test stimuli depended on their frequency Each subject provided magnitude estimations for each of the five magnitudes at each of the 16 frequencies, which took around one hour, including a ten-minute intermediate rest The test stimuli were presented in independent random orders for each subject Prior to being exposed to shocks on the vibrator, subjects were familiarized with the magnitude estimation method by assigning numbers to the diameters of circles drawn on paper The paper practice was followed by real practice on the vibrator with six shocks made by two magnitues (lowest and highest) varing with three frequencies (0.5, 2.5 and 16.0 Hz) After experiencing each pair of reference and test stimuli, subjects were required to assign a number corresponding to the degree of discomfort caused by the test motion assuming that the reference motion was 100 They were also asked to indicate the location on the body where the test stimulus produced the greatest discomfort The locations were classified as follows: feet, legs, buttocks, abdomen, chest, back, shoulders, head, whole body, or nowhere Subjects were instructed as follows: W W 2.3 Procedure The distortions of the acceleration waveforms were examined by fitting all measured waveforms generated by the vibrator to the desired waveforms The difference between the measured and delivered acceleration was calculated using Distortion= ∫ ( ad( t ) – am ( t ) ) dt × 100 ( % ) ad( t ) dt ∫ (2) a t a 1.75 t 912 S J AHN “Your task is to assign a number that seems to correspond to the discomfort of the test motion, relative to the reference motion, which is set as 100, as well as saying the location of the body where the greatest discomfort is experienced during the test motion (e.g., whole body, feet, legs, buttocks, abdomen, chest, back, shoulders, head, nowhere, and so on).” To assist the application of the results, the normalized physical magnitude was employed Normalized physical magnitude= φ φ (3) test ref where ϕ is the peak-to-peak value, the unweighted or Wb weighted VDV of the test motion and ϕ is the peak-topeak, unweighted or Wb weighted VDV of the reference motion The magnitude of the reference motion was nominally 3.1 ms− peak-to-peak, 1.0 ms− unweighted VDV and 0.5 ms− Wb weighted VDV Table Most uncomfortable part of the body during shocktype vibration by using the sign test; U: upper body ( p < 0.01), u: upper body ( p