Copyright © 2011 KSAE 1229−9138/2011/058−01 International Journal of Automotive Technology, Vol 12, No 3, pp 315−320 (2011) DOI 10.1007/s12239−011−0037−5 EVALUATION OF IDLE STABILITY THROUGH IN-SITU TORQUE MEASUREMENT IN AUTOMATIC TRANSMISSION VEHICLES Y SHIM , S K KAUH and K.-P HA 1)* 1) 2) School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-744, Korea Power Train R&D Center, Hyundai Motor Company & Kia Motor Corporation, 772-1 Jangdeok-dong, Hwaseong-si, Gyeonggi 445-706, Korea 1) 2) (Received May 10 2010; Revised November 2010) ABSTRACT−Idle stability directly affects a vehicle’s NVH (Noise, Vibration and Harshness) and is closely related to driver satisfaction The present study proposes a method of measuring an engine’s idle roughness, which is useful in quantifying the idle stability Engine brake torque was measured directly using a torque sensor, which can be installed without modification of the engine’s mounting structure In addition, angular acceleration was measured at the same position as the torque measurement, to compare dynamic characteristics of the angular acceleration with the torque variation Both torque and angular acceleration oscillate between positive and negative values In this study, torque data were divided into several regions, and each region starts from the point where the torque data changes its sign from negative to positive The root mean square values of both torque and angular acceleration were calculated for each region This calculation showed a very good correlation between the torques and the angular accelerations The idle stability was evaluated with the standard deviation of the measured torque, and the cycle-to-cycle variation is a more dominant factor in the idle stability than is the cylinder-tocylinder variation Because it is easier to measure the angular acceleration than to measure the torque, the variations of angular accelerations are usually compared between engines However, the present study showed that the moment of inertia of an engine and the angular acceleration should be considered together when comparing the idle stability between engines KEY WORDS : Torque, Angular acceleration, Idle stability, Moment of inertia NOMEMCLATURE Generally, the idle stability can be improved by increasing engine speed Fuel economy, however, should also be strongly considered because the regulation of energy usage has been reinforced Therefore, it is important to achieve higher idle stability with minimum fuel usage Typically, IMEP’s for 300 cycles were calculated for every cylinder, and the SDIMEP was calculated as the indication of combustion stability at idle Recently, various ways to evaluate idle stability have been studied as an alternative to SDIMEP A cyclic averaging separation method was used to separate the torque into a periodic component and a random component The torque was calculated from the combustion pressure, which was measured at every cylinder It was verified that the idle combustion stability is directly related to the random torque component caused by cycle-to-cycle variation and that the random torque more directly quantifies the excitation experienced by the vehicle than does SDIMEP (Beikmann, 2001) It takes significant time and effort to set up experimental equipment for measuring the combustion pressure in cylinders Additionally, the evaluation of idle combustion stability through combustion pressure cannot reflect dynamic crank motion Teng presented an alternative way to evaluate combustion stability using flywheel angular : angular acceleration (rad/s ) : measured angular acceleration (rad/s ) : moment of inertia of overall powertrain system (kg·m ) SDT : standard deviation of torque (Nm) SDα : standard deviation of angular acceleration (rad/s ) Tα : mean torque (Nm) Tb : engine brake torque (Nm) Tb,c : calculated engine brake torque (Nm) Tb,d : torque difference between measured torque and calculated torque (Nm) Tb,m : measured engine brake torque (Nm) IMEP : indicated mean effective pressure RMS : root mean square SDIMEP:standard deviation of indicated mean effective pressure α αm Io 2 2 INTRODUCTION There has been a continuous effort to improve idle stability because it is closely related to the driver satisfaction *Corresponding author e-mail: mcjunkie75@gmail.com 315 316 Y SHIM, S K KAUH and K.-P HA acceleration It is based on the fact that the flywheel angular acceleration has a direct relationship with the engine torque The RMS values of the flywheel angular acceleration were calculated within a cylinder’s dominating period Next, the cylinder-to-cylinder variation and cycle-to-cycle variation were evaluated with the standard deviation of those RMS values (Teng, 2003) Zhen utilized the crank position sensor signals to calculate the crank angular acceleration, and they also evaluated the combustion quality using the RMS values of calculated angular acceleration An algorithm specially developed for identifying a missing tooth or teeth was used to convert the crank position sensor signal into crank angular acceleration The correlation between RMS values of angular acceleration and IMEP was presented (Zhen and An, 2009) In this study, the engine brake torque was measured directly with a torque sensor that replaces the driveplate that connects a crankshaft and a torque-converter of a transmission In addition, the angular acceleration was measured at the same position as the torque measurement, to compare the dynamic characteristics of the angular acceleration with the torque variation The moment of inertia of the overall powertrain system, including the engine and the transmission, and the mean torque were determined experimentally The idle stability was evaluated through the measured torque and angular acceleration, and the results were compared et al INSTRUMENTATION 2.1 Torque Measurement Figure shows the torque sensor installation position and experimental setup The torque sensor is located between an engine cylinder block and torque-converter, and the engine brake torque can be measured directly without modification of the engine’s mounting structure in a vehicle The output signal from strain gauges that are attached to the torque sensor is digitized by an analog to digital converter and a microprocessor The digitized signal is transmitted wirelessly through a Bluetooth module A telemetry system is essential because the torque sensor rotates at a very high speed The Bluetooth module that receives the transmitted data is fixed on the cylinder block, Figure Schematic diagram of in-situ torque and angular acceleration measurement Figure Block diagram of the process of torque and angular acceleration measurement and finally the data are transferred to a PC via a USB interface (Lee, 2007) 2.2 Angular Acceleration Measurement Designing the circumferential part of the torque sensor as ring gear shape, allowed the angular acceleration to be measured at the same position as the torque measurement The magnetic pickup is fixed adjacent to the torque sensor, as shown in Figure The output signal from the magnetic pickup is transferred to a PC after going through a timer and an analog to digital converter, as shown in Figure 2, and the angular acceleration was calculated In this study, the torque and the angular acceleration were measured for two different SI engines The torque sensor was made individually for each engine and was calibrated against a standard torquemeter Engine A is a 3.3 Table Specification of the engines Engine A Engine B Engine type V6 L6 Displacement volume (cc) 3342 2996 Bore (mm) 92 85 Stroke (mm) 83.8 88 Type Type Valvetrain type (direct acting) (end pivot) Variable valve timing Yes Yes (Intake) Variable valve lift (Intake) No Yes Variable valve timing Yes Yes (Exhaust) EVALUATION OF IDLE STABILITY THROUGH IN-SITU TORQUE MEASUREMENT 317 L, V6 type, and engine B is a 3.0 L, L6 type Table shows several major specifications of both engines EXPERIMENTAL RESULT 3.1 Torque and Angular Acceleration The torque of engine A in neutral idle is presented in Figure For consecutive cycles, the torque variation per each cycle is shown The cylinder-to-cylinder and cycle-tocycle torque variation can be seen easily, and the torque oscillates between positive and negative values The maximum value of each peak in the graph represents the maximum positive torque reached during the combustion stroke for each cylinder The positive torque means that the force created from combustion drives a crankshaft On the other hand, the negative torque means that the crankshaft is driven by the inertial force before the combustion stroke in the next cylinder The angular acceleration at the same point in time is presented in Figure It shows a similar trend to the torque graph, but the fluctuation of the angular acceleration is larger than the fluctuation of the torque on the whole The interaction of the torque from combustion in every Figure Torque of engine A in neutral idle during consecutive cycles Figure Correlation between RMS torque and RMS acceleration for engine A in neutral idle cylinder results in dynamic crankshaft motion Teng, however, considered that the region from a local minimum point to the next local minimum point is a cylinder’s dominating period The RMS values were calculated for each region (Teng, 2003) Physically speaking, it is reasonable to divide the regions with reference to the local minimum points, but it is difficult to make an exact division This is because the fluctuation of measured data is much larger near the local minimum points In this study, a cylinder’s dominating period is divided with reference to plus zero crossing points, at which the torque data changes from negative to positive Figure and Figure are the results of the plus zero crossing of torque The validity of plus zero crossing points as a reference will be discussed in detail later Dividing the regions with reference to the torque’s plus zero closing points, the RMS values of torque and angular acceleration were calculated for each region Figure shows the correlation between the RMS torque and the RMS acceleration for engine A in neutral idle There is a very good correlation between the two Most notably, the correlation between torque and angular acceleration is higher than that between IMEP and RMS acceleration (Teng, 2003; Zhen and An, 2009; Hartwig , 2005) This means that the torque reflects dynamic crankshaft motion better than IMEP It also suggests that the torque fluctuation can be understood relatively exactly through the measurement of angular acceleration et al Figure Angular acceleration of engine A in neutral idle during consecutive cycles 3.2 Moment of Inertia and Mean Torque The crankshaft motion is affected by the torque from such factors as combustion, inertia, and friction Supposing that the effect of inertia and friction is consistent at a given speed, the relationship between engine brake torque and crankshaft angular acceleration can be represented simply as follows (Heywood, 1998) Tb = I o α + Tα (1) 318 Y SHIM, S K KAUH and K.-P HA The torque created in the engine is generally reduced due to the engine friction or lost from driving the engine’s accessories, such as the valvetrain In this study, the engine brake torque, on which the energy loss is already reflected, was measured directly Therefore, there is no explicit friction term in equation (1) Supposing that both the moment of inertia and the mean torque are constant in equation (1), the torque can be calculated from equation (2) using the measured angular acceleration T b, c = Ioαm + Tα (2) The torque difference between measured torque and calculated torque is defined by equation (3) T b, d = Tb m – Tb c , , Figure Measured and calculated torque of engine A in drive idle The torque difference is also presented (3) The moment of inertia and the mean torque were evaluated by the least square method to minimize the square of the torque difference described in equation (3) Then the torque was calculated with those moments of inertia and the mean torque from equation (2) For the following cases in both engines, the moment of inertia and the mean torque are presented in Table For engine A, the moment of inertia in neutral idle is almost same as that in drive idle The mean torque in drive idle is aproximately 3.5 times higher than in neutral idle, which means that the engine was driven under higher load than in neutral idle The moment of inertia of engine B is smaller than that of engine A, so it can be expected that the angular acceleration variation due to the torque variation would be higher in engine B The mean torque of engine B in neutral idle is higher than that of engine A Though there is not much difference in engine speed at neutral idle, engine B was driven under approximately 1.7 times higher load For engine A in drive idle, Figure shows measured torque, calculated torque, and torque difference Generally, calculated torque is consistent with measured torque Meanwhile, the fluctuation of calculated torque is larger than the fluctuation of measured torque because the fluctuation of measured angular acceleration is larger The mean torque determined experimentally as described above is almost the same as the arithmetic average of measured torque This is because the engine brake torque Table Moment of inertia and mean torque Engine A Engine A Engine B Neutral idle Drive idle Neutral idle Moment of 0.110 0.112 0.079 inertia (kg·m2) Mean torque 5.86 20.35 10.12 (Nm) Figure Cylinder-to-cylinder and cycle-to-cycle variation of engine A in neutral The idle stability was evaluated with reference to local minimum, plus zero crossing, and mean torque crossing each was measured directly, and it means that equation (1) is valid 3.3 Evaluation of Idle Stability Idle stability was evaluated through the measured torque and angular acceleration Both cylinder-to-cylinder variation and cycle-to-cycle variation were quantified using the RMS values of torque and angular acceleration within a cylinder’s dominating period The cylinder-to-cylinder variation can be represented by the standard deviation of mean RMS values of all cylinders The average of the standard deviations of the RMS values of all the individual cylinders gives the cycle-to-cycle variation To calculate the RMS values of torque, a cylinder’s dominating period was divided by three different references, which are local minimum, plus zero crossing, and mean torque crossing The cylinder-to-cylinder variation and the cycle-to-cycle variation were calculated for each case Figure shows that the results are almost the same, even though the references are different from each EVALUATION OF IDLE STABILITY THROUGH IN-SITU TORQUE MEASUREMENT Figure Comparison of idle stability for each case The idle stability was evaluated with reference to the plus zero crossing of torque other Because the torque variation is large near local minimum points, it is difficult to divide the region exactly, but the plus zero crossing points can be determined more clearly Considering the efficiency of numerical manipulation, it is better to take the plus zero crossing points as reference Therefore, the idle stability was evaluated with reference to the plus zero crossing points The evaluation results of idle stability for both engines are presented in Figure For all cases, the cycle-to-cycle variation is larger than the cylinder-to-cylinder variation For engine A, the difference in cycle-to-cycle variation between neutral idle and drive idle is much bigger than that in cylinder-to-cylinder variation Comparing the idle stability at neutral idle between engine A and engine B, both cylinder-to-cylinder variation and cycle-to-cycle variation are much different It is highly possible that the difference in cylinder-to-cylinder variation is caused by the difference in engine specifications such as engine type and valve drive mode The valve timing control is working for both engines, and the difference in control parameters may result in the difference in cylinderto- cylinder variation (Kim and Choi, 2006) The difference in cycle-to-cycle variation can be considered through mean torque difference As mentioned above, the mean torque of engine B is higher than that of engine A This means that the engine B was driven under higher load, and it contributed to a reduction in the cycle-to-cycle variation The results described above show that the cycle-to-cycle variation is a more dominant factor in the idle stability than is the cylinder-to-cylinder variation, and the amount of the cycle-to-cycle variation is especially sensitive to the engine load The idle stability was also evaluated with the angular acceleration A cylinder’s dominating period to calculate the RMS values of angular acceleration was divided by the plus zero crossing points of angular acceleration The idle stability of the engine A in drive idle and engine B in 319 Figure Idle stability of engine A in drive idle and engine B in neutral idle, which are evaluated with angular acceleration The difference in moment of inertia between engines is not considered Figure 10 Idle stability of engine A in drive idle and engine B in neutral idle, which are evaluated with angular acceleration The difference in moment of inertia between engines is considered neutral idle is presented in Figure Contrary to the result in Figure 8, the variation of engine B in neutral idle is higher than that of engine A in drive idle There exists the difference in moment of inertia between engines To normalize engine B against engine A, SDα of engine B in Figure was multiplied by the moment of inertia of engine B in neutral idle, then divided by the moment of inertia of engine A in drive idle Figure 10 shows the comparison result to which the difference in moment of inertia is reflected A similar trend with torque is shown The difference in moment of inertia should be considered when comparing the idle stability between different engines using angular acceleration only CONCLUSION The engine brake torque and the angular acceleration were 320 Y SHIM, S K KAUH and K.-P HA measured for vehicles with automatic transmissions, and the idle stability was evaluated The main result can be summarized as follows: (1) The engine brake torque was measured directly with the torque sensor, and the sensor replaces the driveplate that connects a crankshaft and a torque-converter of a transmission To obtain the dynamic characteristics in accordance with the torque variation, the angular acceleration of the plate was measured (2) The torque data were divided into several regions, and each region is between the points where the torque data changes its sign from negative to positive It was verified that the angular acceleration has good correlation with the torque (3) The moment of inertia of the overall powertrain system, including the engine and the transmission, and the mean torque were determined experimentally using the measured torque and the angular acceleration (4) The cylinder-to-cylinder variation and the cycle-tocycle variation were calculated using the measured torque to evaluate the idle stability The cycle-to-cycle variation affects the idle stability more than does the cylinder-to-cylinder variation (5) Idle stability was also evaluated through the angular acceleration, and the result was compared with that using the torque The difference in moment of inertia should be considered when comparing the idle stability between different engines using angular acceleration only ACKNOWLEDGEMENT−The authors gratefully acknowledge the financial support by the second stage of the Brain Korea 21 Project in 2009 REFERENCES Beikmann, R S (2001) Roll-down considerations in idle quality SAE Paper No 2001-01-1501 Hartwig, M., Via, J and Govindswamy, K (2005) Evaluations of combustion parameters using engine speed fluctuation measurements SAE Paper No 2005-012533 Heywood, J B (1988) Internal Combustion Engine Fundamentals Int Edn McGraw-Hill Singapore Kim, D S and Cho, Y S (2006) Idle performance of an SI engine with variations in engine control parameters Int J Automotive Technology 7, 7, 763−768 Lee, J Y (2007) A Study on In-vehicle Torque Measurement of an Engine and Engine Accessories Using Bluetooth Ph D Dissertation School of Mechanical and Aerospace Engineering Seoul Nat’l University Seoul Korea Teng, C (2003) Evaluation of idle combustion stability using flywheel acceleration SAE Paper No 2003-011673 Zhen, L and An, Z (2009) A new method to convert crankshaft position sensor (CPS) signals into angular acceleration for engine combustion evaluation SAE Paper No 2009-01-2052 International Journal of Automotive Technology, Vol 12, No 3, pp 321−329 (2011) Copyright © 2011 KSAE 1229−9138/2011/058−02 DOI 10.1007/s12239−011−0038−4 SLIDING-MODE OBSERVER FOR UREA-SELECTIVE CATALYTIC REDUCTION (SCR) MID-CATALYST AMMONIA CONCENTRATION ESTIMATION M.-F HSIEH and J WANG * Department of Mechanical and Aerospace Engineering, The Ohio State University, Columbus, OH 43210, USA (Received 14 May 2010; Revised October 2010) ABSTRACT−This paper presents an observer design for SCR mid-catalyst ammonia concentration estimation using tailpipe NOx and ammonia sensors Urea-SCR has been popularly used by Diesel engine powered vehicles to reduce NOx emissions in recent years It utilizes ammonia, converted from urea injected at upstream of the catalyst, as the reductant to catalytically convert NOx emissions to nitrogen To simultaneously achieve high SCR NOx conversion efficiency and low tailpipe ammonia slip, it is desirable to control the ammonia storage distribution along the SCR catalyst Such a control method, however, requires a mid-catalyst ammonia sensor The observer developed in this paper can replace such a mid-catalyst ammonia sensor and be used for SCR catalyst ammonia distribution control as well as serves for fault diagnosis purpose of the mid-catalyst ammonia sensor The stability of the observer was shown based on the sliding mode approach and analyzed by simulations Experimental validation of the observer was also conducted based on a medium-duty Diesel engine two-catalyst SCR system setup with emission sensors KEY WORDS : SCR, Ammonia concentration estimation, Sliding mode observer, Diesel engine NOMENCLATURE Hsieh , 2009) Due to the stringent vehicle emission regulations worldwide, selective catalytic reduction (SCR) systems have been widely used by Diesel engine vehicles to reduce tailpipe NOx emissions to acceptable levels Among different SCR systems, urea-SCRs have been proved of being able to reduce more than 90% of engineout NOx emissions and have been favored by the automotive industry (Song and Zhu, 2002) Urea-SCR (simply denoted as SCR in the rest of the paper) utilizes ammonia as the reductant to reduce NOx emissions to nitrogen molecule and water by the catalytic reactions in the SCR catalyst Because ammonia is considered a hazardous material that cannot be directly carried in vehicles, 32.5% aqueous urea solution (AdBlue) has been specified as the standard precursor of ammonia for vehicle applications (Shimizu and Satsuma, 2007) However, improper urea injection control (overdose) can lead to tailpipe ammonia slip which is highly undesired On the other hand, less urea injection, even though tends to avoid tailpipe ammonia slip, can result in insufficient SCR reductant and thus induces the potential of higher tailpipe NOx emissions Such contradictions necessitate sophisticated urea injection control particularly during engine transient operations as have been proposed in recent years (Song , 2002; Shimizu , 2007; Hsieh , 2011a; Hsieh , 2009; Chi , 2005; Schar , 2006; Upadhyay , 2006; Herman , 2009; Wang , 2009) The study in (Willems , 2007) has pointed out that et al : temperature (K) : ideal gas constant (J/(K·mole)) : exhaust volume flow rate (m3/sec) : catalyst volume (m3) : mole concentration of species in the catalyst (mole/m3) : mole concentration of species at the inlet of the catalyst (mole/m3) MNH : catalyst ammonia coverage ratio -θNH ΘMNH : number of mole of ammonia adsorbed on the catalyst (mole) Θ : catalyst ammonia storage capacity (mole) : estimated state xˆ x˜ : estimation error of state xˆ Bet SCRs:between SCR catalysts (mid-catalyst) Bef SCRs:before SCR catalysts Aft SCRs:after SCR catalysts T R R V Cx x Cx,in x * 3 * x x: (x- ) INTRODUCTION Aftertreatment systems for Diesel engine emission reductions have been popularly studied in recent years (Jung , 2010; Lee , 2008; Hsieh , 2010; Wang, 2008; et et al * et al Corresponding author al et al al al e-mail: wang.1381@osu.edu et al et al et al et al et al et al et al 321 et et 322 M.-F HSIEH and J WANG feedback was necessary for SCR control to compensate system uncertainties during real-world driving as well as test cycles Recent control strategies utilize tailpipe emission sensors, i.e NO sensor and/or NH sensor, to provide feedback signals for controlling the urea dosing However, due to the nonlinearities and complexities of the SCR dynamics, state distributions in the catalyst are difficult to know from the tailpipe measurements, especially for large size SCR catalysts where the state variations are significant from upstream to downstream With inadequate understanding about the in-SCR state distributions, a high SCR efficiency, i.e low tailpipe NO and ammonia emissions and less urea injection, is difficult to be realized in vehicle applications (Willems , 2007) To achieve high SCR efficiency, the study of (Hsieh and Wang, 2011a) suggested that one of the approaches is to control the ammonia storage distribution in the axial direction of the catalyst To achieve this control objective, a backstepping based control algorithm has been designed in the authors’ work of (Hsieh , 2009) The control strategy and controller were experimentally validated in (Hsieh, 2010) For the ammonia storage distribution control strategy, by retaining ammonia storage at a high level at the upstream part of the SCR catalyst and by limiting the amount of ammonia storage at the downstream part, the SCR NO reduction efficiency can be kept high and the tailpipe ammonia emissions can be constrained to a low level Experimental analyses based on the US06 test cycle results in (Hsieh, 2010) also showed that, comparing to the case without considering the storage distribution along the axial direction of the catalyst, the cumulative tailpipe NO and ammonia emissions can be substantially reduced by taking the ammonia axial direction dynamics into considerations However, such control systems require tailpipe NO and ammonia sensors as well as another ammonia sensor at the middle of the SCR catalyst to estimate the ammonia storage at the upstream part of the SCR catalyst The ammonia sensor at the middle of the SCR catalyst is undesired from the production cost viewpoint To address this concern, an observer is proposed in this study to replace the physical sensor The observer utilizes the tailpipe NO and ammonia sensors to estimate the ammonia concentration at the middle of the SCR catalyst Stability of the observer was proved based on the sliding mode technique and analyzed by simulations An experiment was also conducted based on a two-catalyst SCR system setup with an ammonia sensor being placed between the two catalysts to provide the actual mid-catalyst ammonia concentration signal for validating the observer estimation The rest of the paper is organized as follow A brief introduction of basic SCR operational principles and the SCR control-oriented model are introduced at first Following that, the observer design is described with theoretical proof of the error convergence Then, simulation results and analyses are presented followed by an x x et al et al x x x x experimental validation Finally, conclusive remarks are summarized UREA-SCR SYSTEM OPERATING PRINCIPLES AND CONTROL-ORIENTED MODEL 2.1 SCR System Operating Principles The urea-SCR NO reduction process includes three main steps: AdBlue to ammonia conversion, ammonia adsorption/ desorption, and NO reduction The AdBlue to ammonia conversion generally consists of three reactions: AdBlue evaporation, urea decomposition, and isocyanic acid hydrolyzation (Piazzesi , 2006), as listed in Equation (1), Equation (2), and Equation (3), respectively AdBlue evaporation: x x et al NH – CO – NH (liquid) → NH – CO – NH + xH O (1) * 2 2 Urea decomposition: NH2 − − CO NH2 → + NH3 (2) HNCO Isocyanic acid (HNCO) hydrolyzation: → + H2O NHCO NH3 + (3) CO2 For evaporation and decomposition reactions, studies have pointed out that with sufficient exhaust-gas temperature (above 200 degree C), the reaction rates are very fast and the AdBlue can usually be completely converted to ammonia and isocyanic acid before entering the SCR catalyst (Kim , 2004; Way , 2009) Hydrolyzation, on the other hand, has limited reaction rate under 400 degree C However, in the presence of a SCR catalyst, this reaction becomes very fast, which can be two orders of magnitude faster than the SCR DeNO reactions as reported in (Yim , 2004) With proper catalyst geometry design, experimental studies have shown that this reaction can be completed at the very upstream part of a SCR catalyst (Hsieh, 2010) Thus, it is rational to assume 100% AdBlue to ammonia conversion before the SCR catalyst (Hsieh, 2010) The ammonia adsorption and desorption reactions in the SCR catalyst can be explained by the following equation et al et al x et al NH3 ↔ * NH3 (4) * represents the ammonia which has been where adsorbed on the SCR substrate For SCRs, most NO reductions are completed by the reactions with the adsorbed ammonia instead of the gaseous ammonia in exhaust gas, such that the ammonia adsorption and desorption reactions are very critical in the SCR dynamics The ammonia storage capacity can be seen as the summation of the amount of ammonia adsorbed by the NH3 x SLIDING-MODE OBSERVER FOR UREA-SELECTIVE CATALYTIC REDUCTION (SCR) catalyst 3* and the free catalyst substrate θ The main SCR NOx reduction process can be summarized by the following three reactions NH free *+4 + *+ + *+3 NH3 NO NH3 NO N2 NO2 +6 N2 , (5) H2O N2 → 3.5 NO2 NH3 → +6 → +3 O2 H2O , (6) (7) H2O The first reaction in Equation (5) is typically known as the “standard SCR” due to the fact that this reaction rate is fast and majority of the engine exhaust NOx is NO The second reaction in Equation (6) is called “fast SCR”, because the reaction rate can be one order of magnitude faster than the standard SCR reaction as studied in (Grossale , 2008) The third reaction of Equation (7) is commonly known as “slow SCR” because its reaction rate is generally slower From these chemical reactions, it can be understood that the adsorbed ammonia is utilized as the reductant for the selective catalytic reduction Moreover, it is important to note that reaction rates of these processes increase with increasing amount of adsorbed ammonia and the NOx concentrations (Upadhyay , 2006; Hsieh, 2010) In other words, if the available ammonia amount is fixed, to achieve better ammonia usage efficiency, i.e to reduce more NOx with the same amount of ammonia, ammonia should be distributed to the regions where the NOx concentrations are high (Song , 2002) Besides the aforementioned three main reaction processes, SCR catalysts can also perform as an oxidation catalysts for some specific gases The main oxidation reactions in the SCR catalyst used in this study are listed below (Hsieh, 2010) et al et al et al *+3 + NH3 NO O2 →2 N2 →2 +6 , (9) 2.2 SCR Control-oriented Model Based on the preceding reactions, by assuming the SCR catalyst to be a continuously stirred tank reactor (CSTR), a 0-D control-oriented SCR model was developed as below in the authors’ work (Hsieh and Wang, 2011b) - CNO in – r1CNOCO2θNH3Θ V – 1- r2CNOCNO2θNH3Θ V – r5CNOCO2V – F- CNO + F V V F F – - r2CNOCNO2θNH3Θ V + r5CNO CO2V – - CNO2 + - CNO2 V V Θr (1 – θ ) + F- + 1-r Θθ + F-C –C C· NO C· NO2 = C· NH3 catalyst temperature (K) The positive constants of the model (model parameters) were derived by minimizing the differences of the model outputs (NOx and ammonia concentrations between and after the SCR catalysts) and the sensor measurement based on several sets of experimental data Details of the parameter derivation and model validation can be found in the authors’ work (Hsieh and Wang, 2011b) 2.3 Two-cell SCR Model for SCR Control The CSTR model assumes all the states inside the catalyst are homogeneous This assumption is inappropriate when the catalyst volume is large In reality, SCR states, e.g NOx concentration, NH3 concentration, ammonia storage, and etc, can change from upstream to downstream, and the variations increase with enlarged catalyst volume A single CSTR model in Equation (10) is not capable of capturing the catalyst state changes along the axial direction To deal with this problem, a multi-cell model is necessary In this study, considering the system controllability and observability, a two-cell model is used The model equations and a schematic presentation are shown in Equation (13) and Figure 1, respectively As can be seen in Figure the SCR catalyst is modeled by two separated smaller CSTR models (two-cell), i.e upstream SCR model and downstream SCR model By modeling the two smaller volumes separately, the CSTR assumption can better represent the real plant and also the state differences at upstream and downstream parts of the catalyst can be pronounced (13) (8) H2O NO2 O2 323 The corresponding physical states of the subscript can be found in Figure The SCR model in Equation (13) has been validated with experimental data, and the results showed that the model can well capture the main SCR catalyst dynamics at various engine operating conditions Details of the SCR modeling work and experimental validation can be found in authors’ work (Hsieh and Wang, 2011b) i , , in (10) V V NH3 V NH3 – θNH3(r4FCNH3V + r3CO2V + r4R + r1CNOCO2V2 + r2CNOCNO2V2) + r4FCNH3V NH3 θ· NH3 4F NH3 , in Ej rj = Kje RT, j = 1, 2, …, 5, (11) Θ = S e S T, (12) – – where Kj , Ej , , S1 S2 are positive constants, and is the T Figure Schematic presentation of a two-cell SCR model 454 D PARK, J YOO, J PARK and S HONG Figure Problem caused by priority overlap In addition to the conditions given by Zuberi (2000), we derive two additional conditions for further stack sharing These four conditions are listed in Table The first three conditions group mutually exclusive tasks in a given application mode The last indicates that any two tasks in two different application modes are mutually exclusive by definition Condition C1 says that any two non-preemptive basic tasks are mutually exclusive because no other task can preempt a non-preemptive basic task, as a basic task always runs to completion Condition C2 holds true because accesses to an internal resource serialize the execution of accessing tasks Condition C3 holds true because a preemptive basic task can be preempted only by higher priority tasks While Zuberi (2000) used only conditions C1 and C3, our approach utilizes all four for extensive stack sharing We demonstrate the stack sharing mechanism using an example task set listed in Figure Using the conditions in Table 1, we derive two mutually exclusive task sets {T1, T2, T3} and {T4, T5}, each of which shares a single task stack Specifically, tasks T1, T2 and T3 are mutually exclusive because (1) C1 is true for T1 and T3, (2) C2 is true for T2 and T3 and (3) C3 is true for T1 and T2 Tasks et et al al T4 and T5 are mutually exclusive because C4 holds true for them We can allocate a shared stack to each task set A stack of 120 bytes is allocated for T1, T2 and T3, and a stack of 180 bytes is allocated for T4 and T5 As a result, the total stack size is reduced from 600 bytes to 300 bytes, as shown in Figure 3 LIGHT-WEIGHT READY QUEUE HANDLING A ready queue is a kernel data structure that holds a list of tasks that are ready to execute whenever the CPU is available to them OSEK OS mandates that the OSEK kernel should maintain ready tasks in priority order so that it can efficiently select a task for dispatching In many OSEK OS implementations, a ready queue is constructed with a simple array for efficiency Each element in the array corresponds to a priority level Because OSEK OS allows multiple tasks to have the same priority in some configurations, an element becomes another array This gives rise to a ready queue with a two-dimensional array In other OSEK configurations, all tasks are forced to have distinct priorities In this case, the two-dimensional array Figure Priority reassignment scheme to avoid priority overlap REDUCING THE MEMORY FOOTPRINT OF OSEK-BASED SYSTEMS 455 Figure Example application configuration in an OIL file design of a ready queue leads to memory wastage In this section, we present a light-weight ready queue design specialized for various OSEK kernel configurations In doing so, we take into consideration dynamic priority changes due to task synchronization 3.1 Examining Conformance Classes and Task Synchronization OSEK OS provides different OS profiles, called conformance classes (CC), to prevent excessive resource use by offering only minimally needed services for an application Specifically, it defines two types of conformance classes: CC1 and CC2 They differ in that CC2 allows for multiple tasks with the same priority and multiple activations for a basic task whereas CC1 does not Thus, for both basic and extended tasks, there are four class combinations: BCC1, BCC2, ECC1 and ECC2 OSEK OS uses the well-known Priority Ceiling Protocol (PCP) for task synchronization (Goodenough and Sha, 1988; Locke et al., 1988) This protocol deals with a race condition, in which multiple tasks try to use a shared resource simultaneously The PCP helps avoid unbounded priority inversions and deadlocks In the PCP, each shared resource is assigned its own priority and the OSEK OS specification provides the following rule for safe priority assignment: • The resource priority shall be set to at least the highest priority of all tasks that access a resource or any of the resources linked to this resource The resource priority shall be lower than the lowest priority of all tasks that not access the resource and that have priorities higher than the highest priority of all tasks that access the resource (OSEK Group, 2004) When a task initiates the use of a shared resource, it temporarily inherits the resource priority if its priority is lower than the resource’s Due to this dynamic priority inheritance of the PCP, any two distinct tasks may have the same priority even though the OSEK kernel is configured as CC1 This complicates the ready queue design for CC1 3.2 Ready Queue Specialization and Non-overlapping Priority Reassignment We propose a ready queue design specialized for conformance classes Conceptually, a prioritized ready queue must be implemented with a two-dimensional array to support tasks with the same priority as in CC2 Conversely, a ready queue for CC1 can be simplified into a one-dimensional array because task and resource priorities not overlap Figure Ready queue design for CC1 and CC2 depicts a general ready queue structure that works for CC2 and a light-weight ready queue structure for CC1 We can further shorten the one-dimensional array by removing priorities which are not used by any tasks or resources Figure Ready queue design for CC1 and CC2 also shows such an optimization for a case where tasks use only four distinct priorities Unfortunately, such a straightforward design of the CC1 ready queue can encounter a problem when the PCP is used for task synchronization Figure illustrates the case where there exists priority overlap between a task and a shared resource When task T1 acquires resource myRes at time t1, its priority is promoted to 30 At t2, task T3 is activated and preempts task T1 The scheduler stores T1 into the ready queue at priority 30 At t3, task T2 is activated and immediately enters the ready queue at priority 30 However, the scheduler cannot store T2 in the onedimensional array ready queue because that priority is already occupied To rectify this problem, we propose a priority reassignment scheme that avoids priority overlap between tasks and resources It attempts to reassign tasks and resources distinct priorities while maintaining their relative priority order Figure Priority reassignment scheme to avoid priority overlap illustrates, with the same task set as in Figure Problem caused by priority overlap., how task priorities are reassigned In this example, tasks T1, T2 and T3 are reassigned priorities 0, and 3, respectively 456 D PARK, J YOO, J PARK and S HONG Figure OSEK application development process with OIL Resource myRes is reassigned priority As a result, when T1 acquires myRes at t1, its priority becomes At t3, the scheduler can safely store T2 into the ready queue Clearly, such a priority reassignment is not always possible In that case, even a CC1 application must be configured to use the CC2 ready queue Fortunately, such applications are rare in practice EXTENDING OIL FOR THE PROPOSED MECHANISMS An OIL interpreter and code generator realize the stack sharing and light-weight ready queue handling mechanisms in an OSEK OS implementation after obtaining the kernel and application configuration information written in OIL It is thus necessary to extend the original OIL with the additional task attributes required for the proposed mechanisms In this section, we review the OIL and its accompanying tools; we then identify task attributes that must be included in the extended OIL and show a revised code generation process via a code example 4.1 Configuring Applications and Generating Code using OIL OSEK OS offers the OIL as a configuration language so developers can describe task attributes and declare kernel objects in their applications Because OSEK OS defines only a library kernel, an application code is statically linked with the kernel code and built into a single executable image Additionally, OSEK OS mandates that all kernel objects such as tasks, alarms, events and resources be created statically Such static linking and kernel object creation help avoid dynamic memory allocation, which increases the complexity of kernel design and decreases the Figure Task stack declarations for example tasks of Figure Figure 10 Context initialization code included in the schedule() API predictability of task execution Figure depicts a code fragment of an application configuration written in OIL Configurations for Task3, Resource1, Alarm1 and Event1 are described in the example From the descriptions, we know that Task3 is a non-preemptive basic task and its priority is 20 The task requires 100 bytes for its stack and is executed in application modes A and B, and it does not invoke the Schedule() API In the subsection that follows, we explain the code generation process for the extended OIL Figure 11 Specialized ready queue implementation for CC1 and CC2 REDUCING THE MEMORY FOOTPRINT OF OSEK-BASED SYSTEMS 457 Figure 12 Total stack size reductions for different numbers of non-preemptable basic tasks The OIL comes with two tools, an OIL interpreter and a C code generator Together, they parse an OIL file and generate C source code files as described in the OIL file Figure OSEK application development process with OIL demonstrates the OSEK application development process in our implementation The file “intvect.c” contains an interrupt vector table, and “tcb.h” and “tcb.c” together describe task attributes, alarms, events and resources These files are dependent on our mechanisms because they contain kernel data structures such as task control blocks They are also dependent on the underlying hardware architecture because they describe an interrupt vector table and interrupt priorities Thus, it was necessary to redesign the OIL interpreter and C code generator As shown in Figure 8, the generated files were compiled with the OSEK kernel code and application code Together, they become an executable image for the target hardware 4.2 Extending OIL for Augmented Task Attributes An OIL file describes the properties of tasks such as priority, preemptability, multiple activations, auto-start, resource usage, events and messages We identify all task properties required for the proposed mechanisms and introduce new properties to the OIL if they are not originally supported First, we identify extra information required for the stack sharing mechanism This information includes application mode, the existence of a call to Schedule() and task stack size We respectively denote them as the UsedMode, UsingSchedule and StackSize fields Note that a nonpreemptive task that shares an internal resource with others must not call Schedule() The UsingSchedule field is false if Schedule() is not called in the task The StackSize field explicitly describes the stack size of a task Second, we derive the additional information required for the light-weight ready queue design To select an appropriate ready queue design for use in a given application, developers must know the task types, their multiple activations and the number of tasks with the same priority They can obtain such information from an ordinary OIL file 4.3 Code Generation Using Extended OIL We demonstrate how the OIL interpreter and C code generator work with task descriptions in an extended OIL file In Figure Task stack declarations for example tasks of , we show a code fragment generated for the stack sharing tasks in the example of Recall that tasks T1, T2 and T3 can share a stack of 120 bytes and that tasks T4 and T5 can share a stack of 180 bytes The code fragment contains the stack declaration of the tasks saying that T1, T2 and T3 share stack0 and T4 and T5 share stack1 Figure 10 shows a code fragment initializing task context Conventional OSEK OS implementations build the context of a task onto the task stack during the boot-up process of the system Our OSEK OS implementation, however, cannot initialize the context of stack sharing tasks during the boot-up process because they use the same stack Instead, the context of such tasks is initialized during context switching time To so, the scheduler must know whether the context of a task to run next is already initialized The stackAlloc flag retains such information It is set to false when the task’s state is changed from suspended to ready and it becomes true after context initialization Figure 11 gives a code example of our light-weight ready queue design The ready queue for CC1 is a simple array of characters and that for CC2 is an array of structures As explained above, a ready queue holds as many elements as the sum of distinct task priorities and resources priorities In CC2, each element points to a circular queue that holds multiple tasks with the same 458 D PARK, J YOO, J PARK and S HONG Figure 13 Total stack size reductions for different numbers of tasks sharing an internal resource priority priorityQueue arrays in the example are used for this purpose EXPERIMENTAL EVALUATION We implemented the proposed mechanisms in an OSEKcompliant operating system that we developed for an evaluation board equipped with an MPC5554 processor We extended OIL as described in Section and augmented the OIL interpreter and C code generator For the experiments, we made OIL files that described synthetically produced task sets and generated the source code for the tasks using the OIL files Each task set consisted of 50 randomly generated tasks We then measured the total stack size demand of each task set by summing individual task stack sizes declared in the generated source code The proposed mechanisms achieved memory footprint reduction by extending OIL and modifying the C code generator, while the dynamic behavior of tasks remained unchanged Thus, there was no performance degradation associated with reducing the memory footprint To compare our approach with others, we measured three different total stack size demands as follows: • S1: Total stack size when stack sharing is not applied • S2: Total stack size when the two conditions proposed in Zuberi (2000) are applied S3: Total stack size when all the conditions proposed herein were applied et al • Task attributes such as task type, preemptability, resource usage, priority, stack size and application mode affect total stack sizes In our experiments, we used three of these attributes as test variables: (1) the number of basic tasks in a task set, here, either 20 or 40; (2) the number of non-preemptable tasks in a task set, ranging from to 50; and (3) the number of basic tasks sharing an internal resource, ranging from to 50 We did not choose the application mode as a test variable because it is straightforward to estimate the effect of condition C4 involving the application mode We used only one application mode in our experiments Other task attributes were randomly selected Each task’s priority was a uniformly distributed random value over the range [0, 63] Each task stack size was also a uniformly distributed random value in the range of 100-500 KB We performed two kinds of experiments First, we varied the number of non-preemptable tasks while the other two test variables were fixed Second, we varied the number of tasks that shared an internal resource while the other two test variables were fixed For each task set, we measured two total stack sizes, one with 20 basic tasks and the other with 40 basic tasks We performed 100 memory measurements and averaged the total stack sizes Figure 12 depicts the variation in total stack size as the number of non-preemptable tasks is varied We set the number of basic tasks that shared an internal resource at 10 The results show that S3 was only 40% of S1 on average S3 was smaller than or equal to S2 because the conditions in our mechanism subsume those proposed in Zuberi (2000) Figure 13 depicts the variation in the total stack size of task sets as the number of tasks sharing an internal resource is varied We set the number of non-preemptable tasks at 20 Because only condition C2 is related to internal resources, S2 was not affected in this case The results show that S3 was only 32% of S1 on average S3 was also smaller than or equal to S2, which is 59% of S1 et al RELATED WORK The run-time memory of an executing program can be subdivided into three disjoint segments: code, data and REDUCING THE MEMORY FOOTPRINT OF OSEK-BASED SYSTEMS stack segments In the prior literature, most attempts to reduce the run-time memory requirement of an OSEK OS implementation have focused on code and stack segments because there is little room for optimizing a data segment for a given microcontroller Zuberi et al (2000), Chen, et al (2005) and Chen et al (2005) addressed stack size reduction via sharing the same stack among multiple tasks These approaches differ in the task conditions for stack sharing In principle, any two disjoint tasks can occupy the same stack if they are never executed simultaneously In Chen et al (2005) and Chen et al (2005), only nonpreemptable basic tasks were allowed to share a stack In Zuberi et al (2000), basic tasks at the same priority level are additionally included for stack sharing, based on the fact that a basic task runs to completion and can be preempted only by higher priority tasks In our approach, we further include in stack sharing basic tasks accessing the same internal resource and tasks belonging to different application modes This effectively increases the number of stack sharing tasks To realize such extensive stack sharing, we added two extra fields in the OIL task descriptions, i.e., the application mode in which a task runs and a flag denoting whether a task invokes a schedule API call We also developed an OIL interpreter and C code generator that support the extended OIL In Zuberi et al (2000), Chen et al (2005), Chen et al (2005) and Barthelmann (2004), multiple stack emulation is proposed to reduce the per-task stack space It is quite often the case in automotive applications that an OSEK OS implementation is hosted on a low-end microcontroller that has only a single stack pointer register For the sake of simplicity and efficiency, legacy OSEK kernels support only per-task stacks and use them for interrupt handling and alarm handling as well as for task execution This leads to a per-task stack size increase because an extra space is reserved in each task stack for interrupt and alarm handling To avoid this problem, Zuberi et al (2000), Chen et al (2005) and Chen et al (2005) offered an additional interrupt stack separate from a task stack by emulating multiple stack pointers and stack switching ProOSEK, discussed in Barthelmann (2004) uses a separate kernel stack as well as an interrupt stack In Barthelmann (2004), intertask register allocation was adopted for ProOSEK in that a compiler allocates a separate register group to each task This helps reduce the stack size of a task because the number of registers that must be saved in a stack during context switching is decreased Additionally, it is important to precisely estimate the maximum stack size requirement of a task because such information is specified in an OIL file The C code generator uses this information later to statically allocate a task stack In Gu et al (2005) and in Barthelmann (2004), a compiler is used to calculate the tight stack size bound of a task, whereas other legacy OSEK kernels rely on manually calculated stack size information 459 There have several previous attempts to reduce the memory space used by kernel data structures such as a ready queue In Zuberi et al (2000), (Chen et al., 2005; Chen et al 2005), a one-dimensional array, rather than a two-dimensional array, is used as a ready queue for conformance classes BCC1 and ECC1 In this case, the length of the array is equal to the number of priorities supported by the kernel Our approach uses the same ready queue for BCC1 and ECC1 However, it differs from the prior schemes by Zuberi et al (2000), Chen et al (2005) and Chen et al (2005) in the sense that it further reduces the size of the ready queue by reassigning distinct priorities to resources and tasks to eliminate unused priorities and hence unused array elements CONCLUSIONS In this work, we proposed two kernel mechanisms for reducing the dynamic memory requirements of OSEKbased systems, namely, stack sharing among tasks and lightweight ready queue handling specialized for OSEK OS conformance classes Our stack sharing mechanism saves memory by exploiting the conditions derived from the runto-completion property of a basic task The light-weight ready queue works safely due to the priority reassignment scheme that avoids the priority overlap problem We also presented implementation methods for the proposed mechanisms by extending OIL and associated tools We performed extensive experiments to measure the degree of memory footprint reduction The results show that our approach reduced the memory requirement by 36% on average in comparison with conventional OSEK OS implementations This result was achieved without incurring run-time performance degradation We are currently working to extend the proposed mechanisms for application to OSEKTime, which is a kernel standard for a time-triggered real-time operating system (OSEK Group, 2001) Because OSEKtime has a different scheduling policy than OSEK OS, it may require additional stack sharing conditions ACKNOWLEDGEMENT−The work reported in this paper was supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MEST) (No 20100027809 and No 2010-0001201) REFERENCES Barthelmann, V (2004) Advanced Compiling Techniques to Reduce RAM Usage of Static Operating Systems Ph D Dissertation Friedrich-Alexander University of ErlangenNuremberg Erlangen Chen, T., Chen, W., Wang, X and Hu, W (2005) Implementing and evaluation of an OSEK/VDXcompliant configurable real-time Kernel IEEE Networking, Sensing and Control, 555−559 460 D PARK, J YOO, J PARK and S HONG Chen, W., Wu, Z and Wang, X (2005) Minimizing memory utilization of task sets in SmartOSEK, Advanced Information Networking and Applications, 2, 552−558 Goodenough, J B and Sha, L (1988) The priority ceiling protocol: A method for minimizing the blocking of high priority ADA tasks Proc 2nd Int Workshop on Realtime ADA Issues Gu, Y., Wu, Z and Yue, L (2005) AlphaOS, An automotive RTOS based on OSEK/VDX: Design and test IEEE Networking, Sensing and Control, 174−179 John, D (1998) OSEK/VDX history and structure IEE Seminar 523 OSEK/VDX Open Systems in 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2011 KSAE 1229−9138/2011/058−18 International Journal of Automotive Technology, Vol 12, No 3, pp 461−468 (2011) DOI 10.1007/s12239−011−0054−4 PERFORMANCE OPTIMIZATION OF CVT FOR TWO-WHEELED VEHICLES C H ZHENG , W S LIM and S W CHA 1) 2)* 3) School of Mechanical and Aerospace Engineering/SNU-IAMD, Seoul National University, Seoul 151-742, Korea Department of Automotive Engineering, Seoul National University of Science and Technology, Seoul 139-743, Korea School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-742, Korea 1) 2) 3) (Received 21 June 2010; Revised 16 November 2010) ABSTRACT−Continuously Variable Transmission (CVT) is one of the most promising automotive transmission technologies because of its continuously variable gear ratio and reduced shift shock CVT is different from Manual Transmission and Automatic Transmission, and it is possible to operate the power source in its high efficiency region with CVT in the drive train Several types of CVT exist that can be categorized based on the mechanism of power transmission, such as the belt pulley, traction drive, and hydrostatic types This paper investigates the belt pulley CVT, which consists of a thrust actuator, driver pulley, belt, driven pulley, and preload spring of the output shaft A complete CVT is constructed, and based on that a simulation program that analyzes the static performance of a CVT is implemented in Matlab/Simulink From these simulation results, methods for improving the efficiency of the CVT are discussed The coefficient of the torque capacity factor is proposed as affecting the matching between a power source and a CVT, and methods for improving the matching effect are also investigated KEY WORDS : CVT (Continuously Variable Transmission), Dynamic modeling, Static performance, Coefficient of torque capacity factor (CTCF) INTRODUCTION DYNAMIC MODELING OF A CVT Energy supply and pollution emissions have become major issues because of the prevalence of automotive transportation, leading to forecasts of oil shortages and price increases The use of Internal Combustion Engines (ICE) in transportation also increases pollution emissions, which must be prevented to sustain the quality and viability of life on Earth To achieve better fuel economy and lower emissions, a great deal of research had been conducted on improving the efficiency of the power train, developing other energy sources, and shifting from the concept of conventional power train vehicles to Electric Vehicles (EV), Hybrid Electric Vehicles (HEV), and Fuel Cell Electric Vehicles (FCEV) To improve the efficiency of the power train, manual or automatic multilevel transmissions and CVTs have been developed to satisfy vehicle performance requirements and to improve ICE efficiencies CVT is different from Manual Transmission (MT) and Automatic Transmission (AT) in that it offers a continuously variable gear ratio between desired limits without shift shock, allowing the power source to operate in its high efficiency region Previously, researchers have studied an integrated CVT system and the mechanism of driver and driven actuators (Kim and Lee, 1994; Yeo et al., 2004; Srivastava and Haque, 2008, 2009; Park et al., 2009), as well as the control strategies of CVT (Cho and Vaughan, 2006; Oh et al., 2005) A rubber belt pulley CVT system consists of a thrust actuator, driver pulley, belt, driven pulley, and a preload spring of an output shaft In this study, each part is dynamically modeled to evaluate and analyze the CVT performance Figures and illustrate the operation of a CVT and define its performance parameters The rotational speeds of the driver and driven pulleys are ω and ω , respectively, and the rotational speeds of the contact parts *Corresponding author e-mail: limws@snut.ac.kr Figure Schematic diagram of the belt and pulley 461 462 C H ZHENG, W S LIM and S W CHA Figure Schematic view of the CVT of the belts are θ· and θ· , respectively, for the driver and driven pulleys The contact angles of the driver and driven pulleys are β1 and β2, respectively One of the flanges on each pulley is movable and the belt undergoes both radial and tangential motion depending on the loading conditions and the axial forces applied to the pulley flanges Torque is transmitted from the driver pulley to the driven pulley, resulting in friction between the belt and pulleys 2.1 Tension of the Belt The differential equation for belt tension can be obtained by considering the belt segment as shown in Figures 3, 4, and The belt moves along both the radial and tangential directions; thus, the two different friction coefficients µ and µθ are considered as two directional coefficients The forces applied to the two sides of the belt segment from two flanges are expressed as dp and dp´, respectively, and the tensions applied to the two cross sections are expressed as T and T + dT, respectively Dynamic equations for the belt segment can be obtained in each direction based on Figures 3, 4, and 5, and can be expressed as follows r Figure Schematic diagram of the cross section Figure Schematic diagram for the dynamic equations (1) Figure Schematic view of the belt segment PERFORMANCE OPTIMIZATION OF CVT FOR TWO-WHEELED VEHICLES 463 Figure Illustrates the forces applied between the belt and pulley The mass and three-dimensional acceleration of the belt segment can be expressed as below, where ρ is the density of the rubber belt and Ab is the cross sectional area of the belt dm = ρAbRdθ ar = R·· – Rθ· aθ = Rθ·· + 2Rθ· (2) az = z··b (3) Figure Schematic diagram of forces applied between the belt and pulley For simplicity, we define the two parameters as follows 2- + µr cos α 2cs = sin α (4) 2- – µr sin α 2cc = cos α From equation (1), the differential equation of the belt tension can be finally derived taking definition (4) into account dT- + µ - T = ⎛a – µ -a ⎞ ρA R (5) dθ cs ⎝ cs r⎠ b We define θ = as the position where the belt and pulley begin to come into contact and θ = β as the position where they become separated Based on this, the belt tension is defined as follows T(θ = 0) = T (6) T(θ = β) = T Assuming that cs, µθ , µr, aθ , ar, R are all constants in the region of ≤ θ ≤ β, the solution of equation (5) can be obtained as follows θ θ θ Solution (8) expresses the belt tension when the belt is in contact with pulleys 2.2 Driver and Driven Pulleys This part derives the dynamic equations of the driver and driven pulleys From this diagram, the dynamic equations of the two pulleys in both the rotational and axial directions can be obtained as (9) and (10), where and represent the input and output shafts, respectively Ip ω· = Tq – µθ R (dP + dP′) 1 1 1∫ (9) R1 Ip2ω· = Tq2 – µθ2R2 ∫ (dP + dP′) R2 -1 – µr1 sin α -1⎞⎠ ∫ dP mp1z··p1 = Fn1 – ⎛⎝cos α 2 R1 mp z··p = –Fn + ⎛⎝cos – µr sin ⎠ ∫ dP′ 2 2 α -2 α -2⎞ (10) R2 Where Ip represents the inertia of the pulley, Tq represents the torque applied to the shaft, mp represents the mass of the movable flange, z··p represents the axial acceleration, and Fn represents the force applied to the shaft Now, consider the connection between the two pulleys as shown in Figure Assuming that the length of the belt is lb and the center distance between the two pulleys is ls, then the geometric relationships can be derived as follows β c-s a – a ⎞ ρA R (7) + ⎛⎝ -r⎠ b µ cT can be derived by taking definition (6) into consideration Finally, (7) can be expressed as follows T = cT e ( –µ θ ⁄ cs )θ T = T0 e θ ( –µ θ ⁄ cs )θ θ c-s a – a ⎞ (1 – e + ρAbR⎛⎝ -r⎠ µ θ θ (–µ θ ⁄ cs )θ ) (8) Figure Kinematic relationship between the belt and pulley 464 C H ZHENG, W S LIM and S W CHA lb = R1β1 + R2β2 + 2ls cos γ β1 = π – γ β2 = π + γ (11) – R1 sin γ = R -ls R and R can be expressed using parameters from relationship (11) 1-(lb – (2γ + π )ls sin γ – 2ls cos γ) R1 = 2π R = 2π-(lb – (2γ – π )ls sin γ – 2ls cos γ) (12) The relationships among the axial displacement of the belt zb, the pulley radius R, and the axial displacement of the pulley zp can be derived based on Figure and When the gear ratio is 1, we define the radius of both the driver and the driven pulleys as R When the sheave angle of the pulley α is constant, these relationships can be obtained as follows 2-⎞⎠ (R – R ) zb = tan ⎛⎝ α (13) 2-⎞⎠ (R – R ) zb = – tan ⎛⎝ α zp = zb , zp = zb 1 2 1 2 2.3 Axial Thrust Force of the Driver and Driven Pulleys This part derives the dynamic equations of the roller and the thrust forces of the driver and driven pulleys based on Figure µrp represents the friction coefficient between the roller and the fixed flange, and µmf represents the friction coefficient between the roller and the movable flange ξ and ξ represent the angles between the two flanges and the input shaft Relationship (14) can be derived from the moment equilibrium of the roller if we ignore the rotational inertia of the roller and define the friction force of the roller as Fcf in Figure The axial and radial dynamic equations of a roller are expressed as (15) in which mc represents the mass of one roller, and Rc and zc represent the distances shown in Figure µrpFrp = µmf Fmf = Fcf (14) mcz··c = Frp sin ξ1 – Fmf sin ξ2 – Fcf( cos ξ1 – cos ξ2), mcRc(ω )2 – mcR··c = Frp cos ξ1 + Fmf cos ξ2 + Fcf( sin ξ1 + sin ξ2) (15) The movement of the roller is restricted by the ramp plate and the movable flange, so (16) can be obtained based on the geometric relationship illustrated in Figure The ramp plate is fixed to the input shaft; thus, ξ is fixed, and ξ is variable -c = tan ξ zc = zc(Rc), dR dzc (16) zp = f(zc, Rc) = f( zc(Rc), Rc) = f(Rc) 1 The axial thrust force of the driver pulley can be expressed as (17) in which Zroller represents the number of rollers Fn = ZrollerFmf sin ξ (17) ξ = f( zc, Rc) = f( zc( Rc ), Rc) = f( Rc ) The axial thrust force of the driven pulley depends on the preload spring in the output shaft This force can be expressed according to the following equation in which k represents the spring constant, and c represents the damping coefficient 2 2 Fn2 = k2zp2 + c2z·p2 + Fn2 preload (18) , SIMULATION OF THE STATIC PERFORMANCE OF A CVT This part implements a simulation program in Matlab/ Simulink to test the static performance of a CVT The results of the simulation are also discussed 3.1 Construction of the Simulation Program To determine the static performance of a CVT, we reconsider the equations presented in the previous section at a constant speed The parameters ls, lb, R , R ,min, R max, R min, R max, α , α , k , Fn ,preload, mc, Zroller, ξ can be measured for a specific CVT to determine the coefficients of the dynamic equations presented in the previous section Given the load torque Tq that operates on the output shaft of the CVT, relationship (19) can be obtained from equations (1) and (9) at a constant speed 2, 2, 2 1, n2 -Tq2 = –Tq2 belt = –2µθ2R2 F cc (19) , Figure Schematic view of the thrust actuator of the driver pulley From (13), (18), and (19), relationship (20) can be obtained if we assume that is zero c in (18) PERFORMANCE OPTIMIZATION OF CVT FOR TWO-WHEELED VEHICLES 465 Figure 12 CTCF versus z p1 Figure Determination of R The radius of the driver pulley R can be obtained from Figure 10, and the axial displacement of the driver pulley z can be derived from relationship (13) and Figure After that, R and ξ can also be obtained from relationships (16) and (17) For a specific CVT, the relationships can be measured as illustrated in Figure 11 At a constant speed, the following relationship (21) can be derived from the dynamic equation (15) and relationship (17) T - 2R F - R- ⎛ ⎛α -⎞ – -µ = c = c ⎝– 2k tan ⎝ ⎠ (R – R ) + F q2 θ2 c2 n2 2 c2 2 (20) ⎞ ⎠ n2, preload From relationship (20), the radius of the driven pulley R can be determined given the load torque T and the friction coefficient of the driven pulley µθ Figure illustrates relationship (20) and shows that two solutions of R can be obtained Between them, R is the real solution based on the relationship between R and µθ , which is that µθ decreases as R increases From (12), R and R have one relationship for a specific CVT, as shown in Figure 10 q2 * (1 ) 2 2 2 p1 c F n-1 = Z mR (21) cot ξ + cot ξFrom (9) and (10), the relationship between F and T at constant speed can be obtained as shown in (22), and (21) and (22) yield the following relationship (23) ω 21 c roller c n1 q1 n1 -T q1 = µθ R F cc (22) R- -F - = R Z - mR T - = -c c cot ξ + cot ξ q1 µθ1ω 21 c1 n1 ω 21 roller c1 c (23) c T -In (23), ω , the Coefficient of Torque Capacity Factor (CTCF), is important for improving the overall vehicle efficiency as it affects the match between a power source and a CVT This determines the operating point of the power source A parameter that is proportional to the CTCF can be defined by transferring some constants from RR the right side of (23) to the left side, yielding -cos ξ + cos ξ- Figure 12 illustrates the relationship between this parameter q1 Figure 10 Relationship between R and R 1 Figure 11 R versus z and ξ versus z c p1 p1 Figure 13 Friction coefficients with slip speeds c 466 C H ZHENG, W S LIM and S W CHA and zp for a certain CVT The CTCF forms a series of parabolas on the power source’s speed-torque plane Thus, if µθ is given, the operating point of the power source can be identified by the CTCF and the speed-torque characteristics of the power source as illustrated in Figure 22 In (20) and (23), we assume that µθ and µθ have linear relationships with the slip speed ω –θ· and ω –θ· , respectively, as shown in Figure 13 Assuming relationship (24) and considering (8) at a constant speed, equation (25) can be derived 1 1 R θ· = R θ· T = Tβ , T 1 e (– 2 01 µ θ1 ⁄ cs 1)β1 –1 02 = Tβ (– (24) –1 e θ1 1 ⎧ T01 ⎫ –1 ⎫ 2⎧ e ⎨ ⎬ = ρAbR1θ· 1⎨ –µθ2 c β2 ⎬ ⎩e ⎩ T02 ⎭ –1 ⎭ (– µ θ ⁄ cs )β2 µ ⁄c ( ⁄ s s ) β ) Figure 15 Developed simulation program (25) Whether or not we consider the impact of the belt inertia, for T and T to exist in equation (25) it must have infinite solutions Thus, relationship (26) can be obtained from (25) Incorporating (26) into (23), the following relationship (27) can be derived 01 02 µ β µ β e –1 –1 - = e -= µ β µ β –1 e –1 e (– θ ⁄ cs 1) (– θ ⁄ cs2 ) (– θ ⁄ cs ) (– θ ⁄ cs ) µθ2β-2 = ⇒ µ = –⎛ β -2⎞ ⎛ c -s1⎞ µ µθ1β-1 + θ1 ⎝ β1⎠ ⎝ cs2⎠ θ2 cs1 cs2 T - = –⎛ -β-⎞ ⎛ c ⎞ ⎛ R Z -⎞ ⎛ -m R -⎞ -⎝β ⎠ ⎝c ⎠ ⎝ c ⎠ ⎝ cos ξ + cos ξ ⎠ q1 µθ2ω 21 s1 s2 roller c c1 c (26) Figure 16 Characteristics of the power source (27) rshift = ω ⁄ ω Assuming that the value µθ of is known, the operating point of the power source (ω , Tq ) can be found by considering (27) together with the speed-torque characteristics of the power source since β and β can be derived by relationship (11) This also requires knowledge of the speed-torque characteristics of the power source at different throttle positions After all the processes outlined above, µθ , θ· , ω can be derived by relationships (26), (24) and Figure 13, respectively, and then the gear ratio and efficiency of the CVT can be obtained using (28) and (29) 1 1 2 Figure 14 Block diagram of the modeling process (28) ηCVT = T q ω = -T -q Tq ω rshift Tq 2 1 (29) Figure 14 describes the overall process of modeling the CVT, including all the approaches carried out in this part of the study The arrows represent input signals, output signals, and the signals that the block needs Based on Figure 14, a simulation program was developed in Matlab/Simulink to analyze the static CVT performances Figure 15 presents the main interface of the simulation program The input parameters are Tq , µθ , and throttle position, and the output is CVT efficiency Figure 2 PERFORMANCE OPTIMIZATION OF CVT FOR TWO-WHEELED VEHICLES Figure 17 Relationship between T and R when µθ is constant q2 2 467 Figure 20 Relationship between m and CVT efficiency c 16 illustrates the characteristics of the power source used in this simulation 3.2 Simulation Results The simulation program developed in the previous part provides a range of results that can be used to validate the program The results are obtained when the CVT output torque T and the throttle position are fixed Figure 17 shows the relationship between the torque applied to the output shaft of the CVT T and the radius of the driven pulley R when the friction coefficient µθ is constant R increases as T increases under these conditions Figure 18 shows the relationship between the preload spring constant k and the CVT efficiency As k changes, q2 q2 2 Figure 21 Relationship between m and ω c q2 2 Figure 22 Influence of CTCF on the operating points Figure 18 Relationship between k and CVT efficiency some parameters, such as the pulley radii R and R , the input torque T , and the gear ratio r , also change Under these conditions, efficiency increases as k increases Figure 19 shows the relationship between the sheave angle of the driver pulley α and the CVT efficiency As α changes, some parameters also change, such as R , R , T , and r Under these conditions, efficiency decreases as α increases Figure 20 shows the relationship between the mass of one roller m and the CVT efficiency As m changes, some parameters, such as R , R , T , and r , also change This result is obtained under the condition where r is less than Figure 21 shows the relationship between the mass of one roller m and the speed of the driver pulley ω ω q1 shift 1 shift q1 c c q1 shift shift Figure 19 Relationship between α and CVT efficiency c 1 468 C H ZHENG, W S LIM and S W CHA decreases as m increases under these conditions, and this result can be explained by the CTCF, which is mentioned in (23) and Figure 12 above The CTCF is a very important parameter for matching a power source with a CVT Figure 22 illustrates the principles used to determine the operating point of the power source, which could be an engine or a motor The parabolas are from different CTCFs and are determined by different CVTs The points illustrated in Figure 22 are operating points of the power source, and the speed of the power source is greater for smaller CTCFs Relationship (23) shows that the CTCF is affected by several design parameters, such as the number of rollers Z and the mass of one roller m These two parameters are proportional to the CTCF when the other parameters are held constant Figure 21 can be interpreted in terms of the relationships mentioned here The CTCF increases as m increases, so the speed of the driver pulley decreases c roller c c ACKNOWLEDGEMENT−This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (No 2011-0001276) REFERENCES Cho, B and Vaughan, N D (2006) Dynamic simulation model of a hybrid powertrain and controller using cosimulation-part : Control strategy Int J Automotive Technology , , 785−793 Kim, H and Lee, J (1994) Analysis of belt behavior and slip characteristics for a metal V-belt CVT Mech Mach Theory , , 865−876 Oh, W H., Lee, J H., Kwon, H G and Yoon, H J (2005) Model-based development of automotive embedded systems: A case of continuously variable transmission (CVT) Proc RTCSA’05 Park, N G., Ryu, J H., Lee, H W., Jeon, Y H and Zhang, N (2009) Development of the inner spherical CVT for a motorcycle Int J Automotive Technology , , 341− 346 Srivastava, N and Haque, I (2008) Transient dynamics of metal V-belt CVT: Effects of band pack slip and friction characteristic Mech Mach Theory, , 459−479 Srivastava, N and Haque, I (2009) A review on belt and chain continuously variable transmission (CVT): dynamics and control Mech Mach Theory, , 19−41 Yeo, H., Song, C H., Kim, G S and Kim, H S (2004) Hardware in the loop simulation of hybrid vehicle for optimal engine operation by CVT ratio control Int J Automotive Technology , , 201−208 7 CONCLUSION The first objective of this study was to improve the efficiency of the CVT Dynamic modeling was carried out for each part of the CVT using all of the dynamic equations A simulation program was implemented in Matlab/Simulink to analyze the static CVT performance Based on the results of the simulation program, the radius of the driven pulley increases as the torque applied to the output shaft of the CVT increases when the friction coefficient between the belt and the driven pulley is constant The effects of the design parameters k2, α1, and m on the CVT efficiency were also derived, showing that CVT efficiency increases as k2 increases and decreases as α1 and m increase These results should be considered when designing a CVT to make an effective transmission The second objective of this study was to improve the total efficiency of two-wheeled vehicle systems equipped with a CVT The CTCF was defined and was important to improve the total efficiency of vehicles equipped with CVTs The CTCF value determines the operating points of the power source, with an ideal CTCF letting the power source operate within its effective region If the power c c source is an electric motor, then an ideal CTCF would be greater at the start of the motor operation than at other regions of motor operation so that the motor produces enough torque at the start The CTCF is affected by several CVT design parameters, and these parameters should be taken into account in the design of a CVT to make effective vehicle systems 29 10 43 44 3