Speakers Information- Controls, Measurement & Calibration Congress
Engine Partial Loads Map for Fuel Economy Analysis Based On 15 Measured Points Marcio Augusto Pereira Pellegrino General Motors do Brasil
ABSTRACT In order to reduce dynamometer test costs and time and be able to predict how an engine should work on a fuel economy cycle before an engine control calibration level capable of running full Partial Loads Map test. The method consists in using only 15 measured points to estimate a full Partial Loads Map that has approximately 450 measured points. Considering similar engines was noticed that partial loads behavior is similar and only three parameters might have significant changes: Fuel Flow Rate, Wide Open Throttle (WOT) Torque and Throttle Opening Percentage. Correction of Fuel Flow Rate is the main focus once the Throttle Opening Percentage will only change if the throttle changes and, considering similar engines, is not common to find significant differences on WOT Torque.
INTRODUCTION Most of the vehicle fuel economy simulation models available base the calculation of fuel consumption on three variables: Engine Speed, Engine Torque or Power and Engine Fuel Flow Rate or Specific Fuel Consumption. For example, the fuel consumption model proposed by Wong (2001) in Eq. (1). đ??š(đ?‘Ą) = đ?œ‡ (
đ?‘˜đ?œ”đ?‘’ (đ?‘Ą)đ?‘‘ 2000
+ đ?‘ƒ(đ?‘Ą))
(1)
F(t) is the fuel consumption rate (l/s) at time t; Âľ is the specific fuel consumption (kg/kJ/s); k is the engine friction in kilopascals (kPa); ωe(t) is the engine speed in revolutions per second (rev/s) at time t; d is the engine displacement (l); and P(t) is the power exerted by the vehicle driveline (kW) at time t. Another approach can be found in the model proposed by Pellegrino and Mello (2013) in Eq. (2) and Eq (3). Where you have the engine speed and torque and interpolate the value of fuel flow rate from an engine partial loads map. đ?œ”đ?‘’ (đ?‘Ą) =
đ?‘Ł(đ?‘Ą)đ?‘–đ?‘”đ?‘’đ?‘Žđ?‘&#x;đ?‘–đ?‘‘đ?‘–đ?‘“đ?‘“
(2)
2đ?œ‹đ?‘&#x;đ?‘‘đ?‘Śđ?‘›
������� (�) =
{[đ?‘š(
đ?‘Ł(đ?‘Ą+1)−đ?‘Ł(đ?‘Ą) )+đ??š0 +đ??š1 đ?‘Ł(đ?‘Ą)+đ??š2 đ?‘Ł(đ?‘Ą)2 ]đ?‘&#x;đ?‘‘đ?‘Śđ?‘› }−đ?‘‡đ?‘Ąđ?‘&#x;đ?‘Žđ?‘›đ?‘ .đ?‘™đ?‘œđ?‘ đ?‘ (đ?‘Ą) ∆đ?‘Ą
đ?‘–đ?‘”đ?‘’đ?‘Žđ?‘&#x; đ?‘–đ?‘‘đ?‘–đ?‘“đ?‘“
+ đ?‘‡đ?‘Žđ?‘?đ?‘? (đ?‘Ą)
(3)
Here v(t) is the vehicle speed at time t; igear is the transmission gear ratio; idiff is the differential gear ratio; rdyn is the dynamic radius of the tire; T engine(t) is the engine torque at time t; m is the vehicle mass; v(t+1) is the vehicle speed at time t+1; Δt is the time step; F0 is the coast down factor (vehicle losses) non related to vehicle speed; F 1 is the coast down factor related to vehicle speed; F2 is the coast down factor related to vehicle speed squared; T trans.loss(t) is the torque lost in transmission at time t; and Tacc(t) is the torque lost to engine accessories (e.g. hydraulic power steering pump). Hence one can estimate an engine behavior on vehicle fuel economy simulation updating the three presented variables. But since we’re using a similar engine as baseline for update, no considerable differences on WOT torque are expected. Adding to this fact the official fuel economy cycles (e.g. FTP-75, HWFET, MVEG, etc) rarely have accelerations that will require the engine to be close or on WOT condition turning this possible calculation deviation negligible. This fact can be seen as example on the FTP cycle presented below on Fig. (1), the HWFET cycle on Fig. (2) and the calculated steps of simulation for the cycles (FTP in green and HWFET in pink) on Fig. (3).
Figure 1 - EPA Federal Test Procedure Speed Profile (http://www.epa.gov)
Figure 2 - Highway Fuel Economy Test Speed Profile (http://www.epa.gov)
Figure 3 - Calculated Steps For FTP (Green) And HWFET (Pink)
This approach of correcting the fuel flow rate for similar engines is based on the combustion efficiency change. Combustion efficiency can be calculated by the Eq. (4) as presented by Heywood (1988). đ?œ‚đ?‘? =
đ??ťđ?‘… (đ?‘‡đ??´ )−đ??ťđ?‘ƒ (đ?‘‡đ??´ )
(4)
đ?‘šđ?‘“ đ?‘„đ??ťđ?‘‰
Ρc is the combustion efficiency; HR is the enthalpy of reactants; HP is the enthalpy of products; T A is the ambient temperature; mf is the fuel mass; and QHV is the fuel heating value. Considering similar engines, same fuel and same ambient temperature, the fuel mass is the only variable that will change combustion efficiency thereafter the torque generated by same amount of fuel.
CALCULATION PROCESS MEASUREMENT DATA Analyzing the Fig. (3) one can conclude that most of the calculation steps for both FTP and HWFET cycles are between 1500-3000 rpm of engine speed and 0-750 kPa of brake mean effective pressure (BMEP). This is consistent throughout different applications considering the vehicle speed is set by the test standards. Considering this common region on engine map noticed through several tests and simulations, 15 standard points for measurement were set as shown on Table 1.
Eng Speed rpm 1000 1000 1000 1500 1500 1500 2000 2000 2000 2500 2500 2500 3500 3500 3500
BMEP kPa 150 350 700 150 350 700 150 350 700 150 350 700 150 350 700
Table 1 - 15 Standard Points For Measurement Data measured for calculation is fuel consumption and it can be received in two formats: fuel flow rate (mass or volume per time unit) or brake specific fuel consumption (BSFC - mass per power unit per time unit). An example of measured data received in BSFC format is shown on Table 2.
Eng Speed rpm 1000 1000 1000 1500 1500 1500 2000 2000 2000 2500 2500 2500 3500 3500 3500
BMEP kPa 150 350 700 150 350 700 150 350 700 150 350 700 150 350 700
BSFC base BSFC target g/kWh g/kWh 233,0 328,0 252,0 219,0 347,0 350,0 336,0 257,0 349,0 263,0 309,0 203,0 296,0 318,0 246,0
213,0 297,0 320,0 299,0 249,0 211,0 252,0 345,0 201,0 343,0 313,0 224,0 214,0 298,0 260,0
Table 2 - Measurement Data Example CORRECTION FACTORS The engine partial loads map will be corrected based on fuel consumption correction factors calculated from measured data. Correction factors are calculated for each measured point using Eq. (5).
đ??śđ?‘œđ?‘&#x;đ?‘&#x;đ?‘’đ?‘?đ?‘Ąđ?‘–đ?‘œđ?‘› đ??šđ?‘Žđ?‘?đ?‘Ąđ?‘œđ?‘&#x;đ??ľđ?‘†đ??šđ??ś =
đ??ľđ?‘†đ??šđ??śđ?‘‡đ?‘Žđ?‘&#x;đ?‘”đ?‘’đ?‘Ą
(5)
đ??ľđ?‘†đ??šđ??śđ??ľđ?‘Žđ?‘ đ?‘’đ?‘™đ?‘–đ?‘›đ?‘’
Resulting on three correction factors for each engine speed as shown on Table 3.
Eng Speed rpm 1000 1000 1000 1500 1500 1500 2000 2000 2000 2500 2500 2500 3500 3500 3500
BMEP kPa 150 350 700 150 350 700 150 350 700 150 350 700 150 350 700
BSFC base BSFC target g/kWh g/kWh 233,0 328,0 252,0 219,0 347,0 350,0 336,0 257,0 349,0 263,0 309,0 203,0 296,0 318,0 246,0
Correction Factor -
213,0 297,0 320,0 299,0 249,0 211,0 252,0 345,0 201,0 343,0 313,0 224,0 214,0 298,0 260,0
Table 3 - Calculated Correction Factors
0,914 0,905 1,270 1,365 0,718 0,603 0,750 1,342 0,576 1,304 1,013 1,103 0,723 0,937 1,057
PARTIAL LOADS MAP CORRECTION In order to correct full map based on only 15 measured points inside engine’s operation, some assumptions were taken.
Each engine speed represent an interval of engine speeds starting and finishing on the average engine speed between selected one and its anterior and posterior respectively (e.g., 1500 rpm correction represents all engine speeds between 1250 rpm and 1750 rpm); For BMEPs below or above the measured ones (100 kPa lower and 750 kPa higher), the correction factor is assumed to be the same as the closer boundary; Is assumed that correction factor have a linear behavior inside BMEP measured interval.
Based on the assumptions, one can linearly interpolate correction factors if inside BMEP measured interval. A comparison with most sophisticated types of regression were made showing no considerable difference on fuel consumption on partial loads map considering the area of interest. A comparison between linearly interpolated map and Kriging regression map can be seen on Fig. (4). Green crosses shows the calculation steps of vehicle fuel economy simulation model running FTP and HWFET cycles; red lines represents regions where linear interpolation has lower fuel consumption and red numbers are the percentage of difference; blue lines represent regions where Kriging regression has lower fuel consumption and blue numbers are the percentage of difference.
Figure 4 - Comparison Between Linear Interpolation And Kriging Regression To consume less resource possible due to easier calculation, linear interpolation was chosen. RESULTS Correlation studies were done first in two different engines but each new job is confirmed with full test as soon as data is available (e.g. final test to deploy engine calibration). These two correlation studies are presented in this work. On the first engine it can be noticed that most of the areas have differences lower than 5% and, if focus on the zone of interest (1500-3500 rpm), most of areas have differences lower than 1% as shown on Fig. (5).
Figure 5 - Engine 1 Comparison Additionally, as this partial loads correction is focused for vehicle fuel economy analysis, the results of an application that uses the engine becomes necessary. A simulation model was used to generate both vehicle fuel economy results to avoid influences from other parameters like vehicle testing equipment precision, production dispersion for different engines, etc. Comparing simulation ran with measured engine and one calculated based on methodology proposed one can find differences lower than 1% in this application as shown on Table 4.
FTP City Highway Combined
Measured Calculated 11.74 km/l 11.67 km/l 16.54 km/l 16.48 km/l 13.50 km/l 13.43 km/l
Diff. 0.60% 0.36% 0.52%
Table 4 - Application 1 Fuel Economy Results Comparison
Second engine analyzed has differences lower than 2% in most of areas also in the interest zone as shown on Fig. (6).
Figure 6 - Engine 2 Comparison Comparing vehicle fuel economy results, the difference is 1.15% on the combined fuel economy (weighted average between urban and highway) but highway fuel economy is a slightly higher with 1.57%. Anyway, even being higher, highway fuel economy is still representative due to difference being lower than average measurement equipment error (~3%).
FTP City Highway Combined
Measured Calculated 15.83 km/l 15.70 km/l 19.76 km/l 19.45 km/l 17.39 km/l 17.19 km/l
Diff. 0.82% 1.57% 1.15%
Table 5 - Application 2 Fuel Economy Results Comparison
CONCLUSION The methodology is solid and can be used to estimate a full engine partial loads map to support vehicle fuel economy analysis as proposed. Resulting in differences close to 1% and lower than 3% the methodology is representing an engine behavior in vehicle fuel economy standard cycles concerning fuel consumed over cycle.
ACKNOWLEDGMENTS Author wants to thank General Motors do Brasil on supporting the development of the work and Alexandre Maykot who coordinated the engine dynamometer work.
REFERENCES 1. Wong, J.Y., 2001. Theory of Ground Vehicles. John Wiley & Sons, Inc. Chichester, UK. 2. Pellegrino, M.A.; Mello, P.E., 2013. Comparison of Powertrain Alternatives for Manual Transmission Vehicles Using One Numerical Model. In Congress of Mechanical Engineering (COBEM), 1467, Ribeir達o Preto, Brazil. 3. Heywood, J.B., 1988. Internal Combustion Engine Fundamentals. McGraw-Hill Book Company. United States.
CONTACT Marcio Augusto Pereira Pellegrino Senior Analysis Engineer General Motors do Brasil Tel: +5511-4234-5794 Email: marcio.pellegrino@gm.com
DEFINITIONS, ACRONYMS, ABBREVIATIONS BMEP: Brake Mean Effective Pressure BSFC: Brake Specific Fuel Consumption EPA: Environmental Protection Agency FTP: Federal Test Procedure HWFET: Highway Fuel Economy Test WOT: Wide Open Throttle