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A study on high-accuracy test method for fuel consumption of heavy-duty diesel vehicles considering the transient characteristics of engines.

INTRODUCTION

Japan introduced a fuel consumption standard for heavy-duty diesel vehicles ahead of the world in 2006. At the same time, Japan commenced conducting a fuel consumption test [1]. Figure 1 shows the outline of this test method [2], which is based on an ancient method [3], [4], [5], that is, the fuel efficiency during driving in a test cycle is calculated according to the simulated fuel consumption. In this case, the map of fuel consumption (hereinafter referred to as the fuel consumption map) corresponding to the engine speed and torque as measured using an engine test cell under steady-state conditions is referred according to the engine speed and torque conditions (hereinafter referred to as the simulation method). In particular, as shown in Figure 2, the test cycle simulating urban driving and interurban driving is converted into the engine test cycle (every second); thereafter, the instantaneous fuel consumption during operation in the obtained test cycle is read from the fuel consumption map. By integrating the instantaneous fuel consumption, the fuel consumption of the test cycle as a whole and the fuel efficiency [km/L] are calculated. However, this test method does not take into account the transient characteristics of the engine. That is, the test method is based on the assumption that the fuel efficiency calculated by the simulation method (hereinafter referred to as the calculated fuel efficiency) is equivalent to the fuel efficiency measured during transient operation in the same test cycle.

Similar test methods of fuel consumption for heavy-duty diesel vehicles will be applied in the United States and Europe [6], [7], [8], [9]. In these test methods, fuel consumption and greenhouse gas emission are also calculated based on the fuel consumption map measured under steady-state condition using engine test cell.

Against the background of increasingly stringent emission regulations worldwide, the demand for improving fuel efficiency is growing. In this context, it is essential to install a turbocharger in the diesel engines of heavy-duty vehicles for achieving high boost and high exhaust gas recirculation (EGR) with reduced displacement. Under the transient operating condition of the engine when the accelerator is depressed, the delays in the response of boost and transient control of the EGR ratio cause the state to be different from the operation state at the same engine speed and torque under the steady-state condition. In other words, in the case of the recent high-boost engines, the calculated fuel efficiency easily deviates from the measured one.

A Method to correct the deviation between the measurement and calculated fuel consumption had been developed in studies [8] [9]. In these report, however, correction factor taking account of transient characteristics of an engine is calculated only as a total cycle value by measuring and calculating fuel consumption in the World-wide Harmonized Transient Cycle (WHTC). This method, therefore, cannot correct calculated fuel consumption accurately when the engine test cycle is changed from WHTC.

In this study, a diesel engine that is used in heavy-duty vehicles and complies with the post new long-term emission regulation (Japanese 2009 regulation) was used to evaluate the calculated fuel consumption by the conventional method shown in Figure 1 and the measured fuel consumption using engine test cell and determine the deviation between the two. Thereafter, methods of calculating the fuel consumption with higher accuracy by including correction for the fuel consumption based on the transient characteristics of individual engines were considered in order to propose an alternative to conventional method in each area.

EQUIPMENT AND METHOD OF EXPERIMENT AND ANALYSIS

Engine Test Cell

Table 1 lists the specifications of the studied test engine. This engine is a production type in-line four cylinder turbo diesel engine with a total engine displacement of 2999 [cm.sup.3]. It is commonly used in heavy-duty vehicles complying with the post new long-term emission regulation. The aftertreatment system includes only the diesel oxidation catalyst (DOC) and the diesel particulate filter (DPF); the combined use of two-stage turbo charger system and EGR system is introduced to reduce NOx.

Figure 3 shows a schematic of the engine test cell. A positive-displacement flow meter (FP-2140H made by Ono Sokki Co., Ltd.) was used as the fuel flow meter. On the basis of fuel temperature detected with the temperature sensor installed close to the exit of the fuel flow meter, the measured fuel flow was converted into volume units at a fuel temperature of 288 K (15[degrees]C) by referring to Table 2B of Attached Table II, JIS K2249-1987, "Table of Conversion Factor of Fuel Oil Temperature to Volume." In addition, the fuel flow was also evaluated in terms of mass by multiplying it with density at the same temperature. The indicated value of fuel injection quantity from the engine control unit (ECU) could also be recorded by controller area network (CAN).

Simulation Code for Fuel Consumption

The simulation code for fuel consumption was chosen from among those provided in the webpage of MLIT [101; the chosen code could be used for vehicles with manual transmission or automated manual transmission (FORTRAN version). This is an analytical model that predicts engine speed and torque for the lookup of fuel consumption from steady-state map. Note, however, that this code had been developed for the certification test, and hence, the test cycle and vehicle data cannot be provided freely. In this study, the source code was modified to allow calculation by taking into account the arbitrary test cycle data, vehicle data, and measurements of the engine's moment of inertia.

Experiment and Analysis Method

In order to compare the calculated fuel efficiency with the fuel efficiency measured under various transient conditions (differences in the engine speed change and torque change) of the engine, fuel efficiency was calculated and measured using data of several virtual vehicles differing in dimensions, weight, transmission gear ratio, tire size, etc. Table 2 lists the specifications of the virtual vehicles. All of the data listed were used in the fuel consumption or emission gas certification test for this test engine. Additionally, 15 types of data were set in total for different payloads classified as empty, half, and full load.

As mentioned above, for the simulation, the fuel consumption map must be determined in advance. In order to eliminate the effect of interpolation accuracy on the map, a large number of measurement points were considered (203 points, including idling). The fuel consumption map was established from both types of data: measurement values from the fuel flow meter and indicated values of fuel injection quantity obtained from the ECU via CAN. Figure 4 shows the measurement points for the fuel consumption map and the measured results of the fuel consumption map with the fuel flow meter that was used as a reference for the simulation.

SIMULATION METHOD CONSIDERING ENGINE TRANSIENT CHARACTERISTICS

Transient Correction Method in Simulation

In the case of the currently used engines, the operation states under steady-state and transient conditions tend to vary because of response delay or transient control of the engine intake and exhaust system and the EGR system. In particular, this phenomenon is conspicuous in engines with the high-boost and high EGR system.

Accordingly, a method of calculating the fuel efficiency with high accuracy was considered; in this method, fuel consumption was corrected (hereinafter referred to as the transient correction) on the basis of the transient characteristics of individual engines. Figure 5 shows a flowchart of this method. This method may be divided into three parts: Process (i), i.e., the experiment to acquire the measured data that are to be used to derive the Transient Correction Factor (TCF) calculation formula (TCF formula); Process (ii), i.e., the simulation to acquire the calculation data for deriving the TCF formula; Process (iii), i.e., the actual derivation of the TCF formula; Process (iv), i.e., the simulation method that comprises the conventional simulation method described in Figure 1 plus correction by multiplying the instantaneous fuel consumption by TCF.

In Process (i), the engine was operated over an arbitrary transient test cycle covering the wide operating range of the engine using engine test cell. Thus, the data on the instantaneous fuel consumption [FC.sub.exp](CAN), as calculated from the indicated value of fuel injection quantity obtained from the ECU via CAN, were obtained along with the engine speed [N.sub.e] and torque [T.sub.e] at the instantaneous moment (the sampling cycle 0.1 s). "(CAN)" means on the basis of CAN. Note that this method is based on a consideration that the indicated fuel injection quantity controlled by the ECU of this test engine under transient condition is defined by the arithmetic algorithm different from that under steady-state condition in order to obtain target torque.

In Process (ii), [N.sub.e] and [T.sub.e] obtained in Process (i) were set as the test cycle for the modified simulation code for fuel consumption. At the same time, the instantaneous fuel consumption [FC.sub.cal](CAN) was calculated by entering the fuel consumption map (CAN) derived from the fuel injection quantity obtained from the ECU via CAN and implementing the simulation code.

In Process (iii), the moving average of the measured data in 1 s was taken for [N.sub.e], [T.sub.e], [FC.sub.exp] (CAN), and FC .(CAN). Thereafter, for all instantaneous data, excluding those for idling and negative torque, multiple regression analysis was performed regarding [FC.sub.exp](CAN)/[FC.sub.cal](CAN) (= TCF), using [N.sub.e], [dN.sub.e]/dt, [T.sub.e] and [dT.sub.e]/dt as explanatory variables. Four conditions, as shown in Figure 6, were considered: a) [dN.sub.e]/dt > 0 and [dT.sub.e]/dt > 0, b) [dN.sub.e]/dt > 0 and [dT.sub.e]/dt [less than or equal to] 0, c) [dN.sub.e]/dt [less than or equal to] 0 and [dT.sub.e]/dt > 0 and d) [dN.sub.e]/dt < 0 and [dT.sub.e]/dt [less than or equal to] 0. Thus, the

TCF formula (1) was derived.

TCF = [AN.sub.e] + B [dN.sub.e]/dt + [CT.sub.e] + D [dT.sub.e]/dt + E (1)

In Process (iv), the instantaneous fuel consumption [FC.sub.cal_w/oTC](FFM) was calculated on the basis of the fuel consumption map obtained from the fuel flow meter (FFM). "(FFM)" means on the basis of FFM. Then, [FC.sub.cal_w/oTC](FFM) under each of the four abovementioned conditions, excluding the cases of idling and negative torque, was multiplied by the TCF determined using formula (1); thus, the instantaneous fuel consumption considering transient characteristics [FC.sub.cal_w/TC](FFM) and the fuel efficiency after the test cycle were calculated.

In Processes (i)-(iii), a highly-responsive instantaneous fuel consumption was demanded. Accordingly, the instantaneous fuel consumption calculated from the indicated value of fuel injection quantity obtained from the ECU via CAN was used.

Validation of Transient Correction

In this study, the WHTC shown in Figure 7 was applied for the arbitrary transient test cycle in Process (i) and Process (ii) because the WHTC covers a wide operation range of the engine. When the TCF formula was derived from the multiple regression analysis in Process (iii), the following methods were applied and compared:

Method 1. Derivation of the TCF formula through multiple regression analysis using [N.sub.e], [dN.sub.e]/dt, [T.sub.e], and [dT.sub.e]/dt as explanatory variables for each of the four conditions, as shown in Figure 6, followed by transient correction

Method 2. Derivation of the TCF formula through multiple regression analysis using only [dT.sub.e]/dt as the explanatory variable for each of the four conditions, as shown in Figure 6, followed by transient correction

Method 3. Derivation of the TCF formula through multiple regression analysis using [N.sub.e], [dN.sub.e]/dt, [T.sub.e], and [dT.sub.e]/dt as explanatory variables without separating the four conditions, as shown in Figure 6, followed by transient correction

Further details of the methods and their results will be given in the next section. To summarize, [dT.sub.e]/dt is the most critical factor for describing the engine operating state. [N.sub.e], [dN.sub.e]/dt, and [T.sub.e] are also representative and important factors. Hence, Method 1 is considered to provide the transient correction with higher accuracy than possible by Method 2 under various operating conditions. Transient correction is more effective when the TCF formula is established for each of the four conditions (Method 1) than when the formula is established without separating the conditions (Method 3). In this study, the explanatory variables necessary for the TCF formula were examined, and the transient correction methods were reviewed with a view of finding the more rational method.

RESULTS AND DISCUSSION

Comparisons between Calculated and Measured Fuel Consumption

By assuming the vehicle data listed in Table 2 for the test engine, the calculated specific fuel consumption (calculated SFC) [g/kWh] and fuel efficiency (calculated FE) [km/L] determined in the conventional simulation method shown in Figure 1 were compared with the measured SFC [g/kWh] and measured FE [km/L], respectively, obtained with the engine test cell during transient operation under empty, half-load, and full-load conditions. Note that, in this simulation method, urban and the inter-urban driving cycles as stipulated in the conventional simulation were replaced by the engine speed and torque measured during operation with the test cycle with the engine test cell. This was done to eliminate the effects of deviation of the measured engine speed and torque from the indicated values on the differences between the calculated and measured SFC and between the calculated and measured FE.

Figure 8 shows the summary of the comparison results of the calculated and measured SFC and the calculated and measured FE and their ratios relative to the weight to power ratio (WPR) [kg/kW]. In this figure, calculated values were obtained from the conventional simulation method shown in Figure 1 and measured values were obtained from the transient test using engine test cell. For each vehicle dataset, three plots indicating the empty, half-load, and full-load states are provided.

The urban driving cycle shows that for each vehicle dataset as the WPR increased, the measured SFC was greater than the calculated value, but the measured FE was smaller than the calculated value.

The ratio of the measured to calculated SFC and that of the measured to calculated FE diverged from 1.0 the most under the full-load condition for vehicle No. 5 for which the WPR was the largest.

The inter-urban driving cycle shows that the difference between the calculated and measured SFC and between the measured and calculated FE was 1% or less on average; the divergences seen in the urban driving cycle were not observed in the case of inter-urban driving. This is because of the cycle in which the vehicle speed was constant at 80 km/h; owing to the constant speed, the engine speed was constant at a relatively high value and only the torque fluctuated. In consequence, there was less effect of the transient on the whole cycle.

As observed above, a comparison of the measured and calculated values of SFC and FE showed that the simulation method for this test engine tended to underestimate SFC and overestimate FE with increasing WPR in the urban driving cycle.

Discussion of Engine Transient Characteristics

The previous section clarified that depending on the conditions, the calculated SFC and FE deviated considerably from their corresponding measured values. Figure 9 explains the phenomena in more detail; it shows part of the plots of the engine speed [N.sub.e] torque [T.sub.e], instantaneous fuel consumption FC(CAN) and the torque change ratio [dT.sub.e]/dt during operation of WHTC with the engine test cell in Process (i), [FC.sub.cal](CAN) obtained from the simulation in Process (ii) and [FC.sub.exp](CAN)/[FC.sub.cal](CAN). The instantaneous fuel consumption varied between the calculated value and the measured value at the instant when the torque varied greatly. In particular, [FC.sub.exp](CAN)/[FC.sub.cal](CAN) was higher than 1.0 when [dT.sub.e]/dt became positive and was less than 1.0 when [dT.sub.e]/dt became negative, indicating that [FC.sub.exp](CAN)/[FC.sub.cal](CAN) was correlated to [dT.sub.e]/dt.

Figure 10 shows the result of correlation between [dT.sub.e]/dt and [FC.sub.exp](CAN)/[FC.sub.cal](CAN) under conditions excluding idling and negative torque. The determination coefficient [R.sup.2] was 0.70, indicating their mutual correlation. Under the transient conditions of the test engine, the response delay of fresh air and EGR introduction relative to the changes in the torque or the transient control caused the in-cylinder combustion state to differ from the steady state. This phenomenon is attributed to the substantial dependency on the rate of change of torque. In order to enable high-accuracy transient correction while reflecting such engine transient characteristics in the simulation method, the method described in the previous section was applied.

Derivation of TCF Formula

It was confirmed that [FC.sub.exp](CAN)/[FC.sub.cal](CAN) is closely correlated with [dT.sub.e]/dt. Thus, the instantaneous fuel consumption obtained from the simulation method can be corrected depending on the transient characteristics of the engine according to its operating state. Accordingly, as described in the previous section, the TCF formula was derived to enable transient correction with increased accuracy. For this purpose, Methods 1, 2, and 3 were applied. Tables 3 to 5 list the coefficients A-D and the intercept E in the TCF formula, as calculated by the three methods. The results show that [dT.sub.e]/dt is a critical factor for representing the transient characteristics when it is considered that the coefficient D is larger than the coefficients of the other terms. On the other hand, other explanatory variables are also considered indispensable for transient correction with high accuracy under various operating conditions. The engine transient characteristics are represented more precisely by deducting the TCF formula for each of the four conditions (a) to (d) because coefficients A-D and intercept E in Methods 1 and 2 vary among the four conditions.

Accuracy Evaluation of Transient Correction

Now the instantaneous fuel consumption calculated in the simulation method was subject to transient correction by the TCF calculation formula established, and then SFC and FE were calculated. Figure 11 shows the summary of the ratios of the calculated SFC and FE values before and after transient correction relative to WPR. The figure also shows the ratios of calculated and measured SFC and calculated and measured FE, which were shown above in Figure 8 to check whether the effects of actual transient characteristics of the engine test cell can be represented similarly in the calculated SFC and FE after transient correction.

In the case of the urban driving cycle, it may be concluded that Methods 1 and 2 reproduced the tendency of SFC and FE after transient correction to deviate from the values before transient correction as WPR increased. In the case of Method 1, particularly, the ratios of the calculated SFC and FE values before and after transient correction tended to be closer to the ratio of the measured to calculated SFC and that of the measured to calculated FE, with the difference between both approximation curves being around 1% at most. When Method 3 was applied, however, the ratio of the calculated SFC before and after transient correction did not show any simple increasing trend as WPR increased; this is different from the behavior of the ratio of measured to calculated SFC.

In the case of the inter-urban driving cycle, the ratio of the measured to calculated SFC showed a slight increase and that of the measured to calculated FE showed a slight decrease as WPR increased. Methods 2 and 3 tend to yield excessive transient correction; Method 2 in particular showed substantial deviation from the measured to calculated SFC ratio and the measured to calculated FE ratio. However, Method 1 achieved approximately accurate transient correction, with the difference between the approximation curves of the measured to calculated SFC ratio and the measured to calculated FE ratio being around 1% at most.

In order to confirm the correction effect of instantaneous fuel consumption under transient conditions, Figure 12 shows [N.sub.e], [T.sub.e], instantaneous fuel consumption before transient correction [FC.sub.cal_w/o, TC](FFM), instantaneous fuel consumption after transient correction [FC.sub.cal_w/TC](FFM) and their ratio ([FC.sub.calw/TC](FFM) /[FC.sub.cal_w/o TC](FFM)), and [dT.sub.e]/dt in parts of urban and inter-urban driving cycles for the half-load condition for vehicle No. 5. For the urban driving cycle, no substantial difference could be confirmed between [FC.sub.cal_w/TC](FFM) with Method 1 and that with Method 2 or 3. However, at time points 171 s and 185-186 s where condition c) [dN.sub.e]/dt [less than or equal to] 0 and [dT.sub.e]/dt > 0 was satisfied, the [dT.sub.e]/dt and [FC.sub.cal_w/TC](FFM) IFCcal_w/o TC(FFM) obtained by Methods 2 and 3 had trends different from those obtained by Method 1. This suggests that Method 1 allowed making adequate transient correction according to the minute differences in operating conditions because the TCF formula applied was obtained using the explanatory variables [N.sub.e], [dN.sub.e]/dt, and [T.sub.e] in addition to [dT.sub.e]/dt for each of the conditions a) to d) of Figure 6. Such fine differences may have caused the differences as shown in Figure11.

On the other hand, in the inter-urban driving cycle, the vehicle speed remained constant, and hence, [N.sub.e] was almost constant. [T.sub.e] changed only at instants when the road gradient changed, as shown in Figure 2. Accordingly, transient correction was applicable only at such instants; the correction was applied to a greater extent in the case of Method 2 than in the case of Method 1. The correction in the case of Method 3 was slightly greater than that in the case of Method 1. Method 1 applied not only [dT.sub.e]/dt, but also [N.sub.e] and [T.sub.e] as explanatory variables, and multiple regression analysis was carried out for each of the four conditions; therefore, it is expected that the correction factor was calculated accurately and that the transient correction was performed with high accuracy.

As is evident from the values of coefficient D, the degree of effect of [dT.sub.e]/dt as an explanatory variable is considered to be substantial. However, transient correction with Method 2 using only [dT.sub.e]/dt as an explanatory variable was found to be inadequate under certain conditions. Even when other explanatory variables such as [N.sub.e], [dN.sub.e]/dt, and [T.sub.e] are used in addition to [dT.sub.e]/dt, Method 3 was found to be inadequate for representing the improvement effects expected from the inclusion of multiple explanatory variables sufficiently. On the other hand, transient correction with Method 1 proved to be adequate according to the minute differences in the operating conditions. It was confirmed that the overall SFC and FE were corrected quite accurately.

SUMMARY

Using a diesel engine for heavy-duty vehicles that also complied with the post new long-term emission regulation, the calculated and measured values of SFC and FE were evaluated and compared. The methods of calculating SFC and FE by correcting the instantaneous fuel consumption were reviewed on the basis of the transient characteristics of the engine. The findings of the study are summarized as follows:

1. For this test engine, the simulation method tends to underestimate the specific fuel consumption [g/kWh] and overestimate the fuel efficiency [km/L] as the weight to power ratio increases in the urban driving cycle, including under conditions of acceleration and deceleration.

2. The ratio of the measured value of instantaneous fuel consumption under transient conditions and its calculated value obtained from the fuel consumption map by the simulation method can be closely correlated to the rate of change of torque.

3. For the measured and calculated instantaneous fuel consumption values obtained during the arbitrary test cycle, multiple regression analysis was performed using the engine speed and its rate of change and the torque and its rate of change as explanatory variables for each of the following conditions: (a) the rate of engine speed change is positive, and the rate of torque change is positive; (b) the rate of change of engine speed is positive, and the rate of change of torque is negative; (c) the rate of change of engine speed is negative, and the rate of change of torque is positive; and (d) the rate of change of engine speed is negative, and the rate of change of torque is also negative; this yielded a correction factor calculation formula taking into account the engine's transient characteristics for the calculated instantaneous fuel consumption. By multiplying the calculated instantaneous fuel consumption with the correction factor thus obtained, the specific fuel consumption and the fuel efficiency taking into account the engine's transient characteristics could be calculated.

To apply this approach as the test method for fuel consumption of heavy-duty diesel vehicles, findings (2) and (3) must be established for other engine models. Accordingly, further verification using other engine models is necessary.

Norifumi Mizushima, Kyohei Yamaguchi, Daisuke Kawano, Hisakazu Suzuki, and Hajime Ishii

National Traffic Safety and Environment Laboratory

REFERENCES

[1.] "Final Report of the Heavy-duty Vehicles Judgment Subcommittee and Heavy-duty Vehicles Fuel Economy Standard Study Committee, the Energy-saving Standard Committee, The Advisory Committee for Natural Resources and Energy", 2005 (Japanese text only)

[2.] "Study Report on the Approach to Evaluate the Fuel Economy of Heavy-duty Vehicles", Japan Automobile Research Institute, 2003 (Japanese text only)

[3.] Oshima K., et al., "Mode Driving Fuel Economy Simulation and Future Perspective", Text for the Symposium of Society of Automotive Engineers of Japan, Inc., pp.20-26, 1977 (Japanese text only)

[4.] NODA, A., TSUKAMOTO, Y., SATO, T., and YAGI, H., "Evaluation Method for HDV Fuel Economy Performance with PC Simulation and Mapping Procedure," SAE Technical Paper 2003-01-2010, 2003, doi:10.4271/2003-01-2010.

[5.] Noda A., et al., "Vehicle Energy Consumption Efficiency Evaluation Approach and the Testing System", Journal of Society of Automotive Engineers of Japan, Vol.59, no.7, pp.70-76, 2005

[6.] Zhang, H., Sanchez, J., and Spears, M., "Alternative Heavy-Duty Engine Test Procedure for Full Vehicle Certification," SAEInt. J. Commer. Veh. 8(2):364-377, 2015, doi:10.4271/2015-01-2768.

[7.] Newman, K., Dekraker, P., Zhang, H., Sanchez, J. et al., "Development of Greenhouse Gas Emissions Model (GEM) for Heavy- and Medium-Duty Vehicle Compliance," SAE Int. J. Commer Veh. 8(2):388-309, 2015, doi:10.4271/2015-01-2771.

[8.] Fontaras, G., Rexeis, M., Dilara, P., Hausberger, S. et al., "The Development of a Simulation Tool for Monitoring Heavy-Duty Vehicle CO2 Emissions and Fuel Consumption in Europe," SAE Technical Paper 2013-24-0150, 2013, doi:10.4271/2013-24-0150.

[9.] "Development and Validation of a Methodology for Monitoring and Certification of Greenhouse Gas Emissions from Heavy Duty Vehicle Simulation--Final Report -", European Commission, Report No. I 07/14/Rex EM-Iv2012/08 699 from 25.06.2014, 2014

[10.] MLIT Web page http://www.mlit.go.jp/jidosha/jidosha_fr10_000006.html

DEFINITIONS/ABBREVIATIONS

CAN--Controller area network

[dN.sub.e]/dt--Rate of change of engine speed [rpm/s]

[dT.sub.e]/dt,--Rate of change of torque [Nm/s]

DOC--Diesel oxidation catalyst

DPF--Diesel particulate filter

ECU--Engine control unit

EGR--Exhaust gas recirculation

[FC.sub.cal](CAN)--Instantaneous fuel consumption calculated in the
simulation on the basis of the fuel consumption map derived from
the fuel injection quantity obtained from the ECU via CAN [L/h]

[FC.sub.cal](FFM)--Instantaneous fuel consumption calculated in the
simulation on the basis of the fuel consumption map obtained from
the fuel flow meter [L/h]

[FC.sub.cal_w/oTC](FFM)--Instantaneous fuel consumption before
transient correction calculated in the simulation on the basis of
the fuel consumption map obtained from the fuel flow meter [L/h]

[FC.sub.cal_w/TC](F FM)--Instantaneous fuel consumption after
transient correction calculated in the simulation on the basis of
the fuel consumption map obtained from the fuel flow meter [L/h]

[FC.sub.exp](CAN)--Instantaneous fuel consumption measured from the
ECU via CAN under transient operation using engine test cell [L/h]

FE--Fuel efficiency [km/L]

FFM--Fuel flow meter

MLIT--Ministry of Land, Infrastructure, Transport and Tourism

[N.sub.e]--Engine speed [rpm]

SFC--Specific fuel consumption [g/kWh]

TCF--Transient correction factor

[T.sub.e]--Torque [Nm]

WHTC--World-wide harmonized transient cycle

WPR--Weight to power ratio (Weight / Power) [kg/kW]

Table 1. Specifications of test engine

Engine type                Water cooled, In-line 4-cylinder,
                                     4-stroke cycle
Intake system           Two-stage turbocharger with intercooler
Fuel supply system                   Dl Common-rail
Displacement                       2999 [cm.sup.3]
Compression ratio                         17.5
Bore x Stroke                      95.4 mm x 104.9 mm
Maximum power                       110 kW/2800 rpm
Maximum torque                    375 Nm/1400-2800 rpm
Aftertreatment system                   DOC, DPF
Emission regulation       Japanese 2009 (Post new long term)

Table 2. Specifications of virtual test vehicles

No    Height [m]   Width [m]     Vehicle     Max. pay     Number
                               Weight [kg]   load [kg]   of seats

        2.106        1.780        2482         2396         3
2       2.099        1.751        2356         2000         3
3       2.041        1.729        2652         2995         3
4       2.363        2.161        2979         3749         3
5       2.454        2.235        3543         4275         3

No          Transmission gear ratio 1st,         Final     Dynamic
              2nd, 3rd, 4th, 5th, 6th            gear      rolling
                                                 ratio   radius [m]

         5.080, 2.816, 1.587, 1.000, 0.741       5.275      0.343
2        5.315, 2.908, 1.558, 1.000, 0.721       4.555      0.338
3        5.979, 3.434, 1.752, 1.000, 0.795       5.571      0.364
4     5.979, 3.434, 1.862, 1.297, 1.000, 0.759   5.125      0.366
5     5.979, 3.434, 1.862, 1.297, 1.000, 0.759   5.375      0.376

Table 3. Coefficients and intercepts of the TCF formula for each
case: a) [dN.sub.e]/dt > 0 and [dT.sub.e]/dt > 0, b) [dN.sub.e]/dt
> 0 and [dT.sub.e]/dt [less than or equal to] 0, c) [dN.sub.e]/dt
[less than or equal to] 0 and [dT.sub.e]/dt > 0 and d)
[dN.sub.e]/dt [less than or equal to] 0 and [dT.sub.e]/dt [less
than or equal to] 0; Method 1

Case       A [N.sub.e]          B [dN.sub.e]/dt

a)     -2.365 x [10.sup.-5]    1.485 x [10.sup.-5]
b)     -1.212 x [10.sup.-5]    2.411 x [10.sup.-5]
c)     -8.748 x [10.sup.-5]   -5.591 x [10.sup.-4]
d)      2.398 x [10.sup.-5]    1.095 x [10.sup.-6]

Case       C [T.sub.e]         D [dT.sub.e]/dt       E

a)     -1.499 x [10.sup.-4]   1.989 x [10.sup.3]   1.071
b)      2.199 x [10.sup.-4]   1.449 x [10.sup.3]   0.972
c)     -3.129 x [10.sup.-4]   2.360 x [10.sup.3]   1.201
d)      3.683 x [10.sup.-4]   1.806 x [10.sup.3]   0.895

Table 4. Coefficients and intercepts of the TCF formula for each
case: a) [dN.sub.e]/dt > 0 and [dT.sub.e]/dt > 0, b) [dN.sub.e]/dt
> 0 and [dT.sub.e]/dt [less than or equal to] 0, c) [dN.sub.e]/dt
[less than or equal to] 0 and [dT.sub.e]/dt > 0 and d)
[dN.sub.e]/dt < 0 and [dT.sub.e]/dt [less than or equal to] 0;
Method 2

Case     D [dT.sub.e]/dt       E

a)     2.033 x [10.sup.-3]   1.001
b)     1.512 x [10.sup.-3]   0.995
c)     2.829 x [10.sup.-3]   1.027
d)     1.769 x [10.sup.-3]   0.981

Table 5. Coefficients and intercepts of the TCF formula for each
case: a) [dN.sub.e]/dt > 0 and [dT.sub.e]/dt > 0, b) [dN.sub.e]/dt
> 0 and [dT.sub.e]/dt [less than or equal to] 0, c) [dN.sub.e]/dt
[less than or equal to] 0 and [dT.sub.e]/dt > 0 and d)
[dN.sub.e]/dt [less than or equal to] 0 and dT/dt [less than or
equal to] 0; Method 3

Case       A [N.sub.e]          B [dN.sub.e]/dt

a)     -3.269 x [10.sup.-5]   1.341 x [10.sup.-5]
b)
c)
d)

Case       C [T.sub.e]          D [dT.sub.e]/dt       E

a)     -1.182 x [10.sup.-4]   2.044 x [10.sup.-3]   1.075
b)
c)
d)
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Author:Mizushima, Norifumi; Yamaguchi, Kyohei; Kawano, Daisuke; Suzuki, Hisakazu; Ishii, Hajime
Publication:SAE International Journal of Fuels and Lubricants
Article Type:Technical report
Geographic Code:9JAPA
Date:Jun 1, 2016
Words:5507
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