This section describes the procedure to measure fuel consumption and create engine fuel maps by testing a powertrain that includes an engine coupled with a transmission, drive axle, and hybrid components or any assembly with one or more of those hardware elements. Engine fuel maps are part of demonstrating compliance with Phase 2 vehicle standards under this part; the powertrain test procedure in this section is one option for generating this fuel-mapping information as described in 40 CFR 1036.505 . Additionally, this powertrain test procedure is one option for certifying hybrids to the engine standards in 40 CFR 1036.108 .
Where:
ka[speed] = drive axle ratio as determined in paragraph (h) of this section. Set ka[speed] equal to 1.0 if torque is measured at the wheel hubs.
vrefi = simulated vehicle reference speed as calculated in paragraph (f)(3) of this section.
r[speed] = tire radius as determined in paragraph (h) of this section.
Where:
ka[speed] = drive axle ratio as determined in paragraph (h) of this section.
vrefi = simulated vehicle reference speed as calculated in paragraph (f)(3) of this section.
r[speed] = tire radius as determined in paragraph (h) of this section.
Where:
i = a time-based counter corresponding to each measurement during the sampling period. Let vref1 = 0; start calculations at i = 2. A 10-minute sampling period will generally involve 60,000 measurements.
T = instantaneous measured torque at the axle input, measured at the wheel hubs, or simulated by the GEM HIL model's transmission submodel.
Effaxle = axle efficiency. Use Effaxle = 0.955 for T [GREATER THAN EQUAL TO]0, and use Effaxle = 1/0.955 for T [LESS THAN]0. Use Effaxle = 1.0 if torque is measured at the wheel hubs.
M = vehicle mass for a vehicle class as determined in paragraph (h) of this section.
g = gravitational constant = 9.80665 m/s2.
Crr = coefficient of rolling resistance for a vehicle class as determined in paragraph (h) of this section.
Gi-1 = the percent grade interpolated at distance, Di-1, from the duty cycle in appendix D to this part corresponding to measurement i-1.
[RHO] = air density at reference conditions. Use [RHO] = 1.1845 kg/m3.
CdA = drag area for a vehicle class as determined in paragraph (h) of this section.
Fbrake,i-1 = instantaneous braking force applied by the driver model.
[DELTA]t = the time interval between measurements. For example, at 100 Hz, [DELTA]t = 0.0100 seconds.
Mrotating = inertial mass of rotating components. Let Mrotating = 340 kg for vocational Light HDV or vocational Medium HDV. See paragraph (h) of this section for tractors and for vocational Heavy HDV.
kaB = 4.0
rB = 0.399 m
T999 = 500.0 N·m
Crr = 7.7 N/kN = 7.7·10-3 N/N
M = 11408 kg
CdA = 5.4 m2
G999 = 0.39% = 0.0039
Fbrake,999 = 0 N
vref,999 = 20.0 m/s
[DELTA]t = 0.0100 s
Mrotating = 340 kg
Where:
vvehicle = measured vehicle speed.
vcycle = reference speed from the test cycle. If vcycle,i-1 [LESS THAN]1.0 m/s, set vcycle,i-1 = vvehicle,i-1.
Table 4 to Paragraph (m) of § 1037.550 -Statistical Criteria for Validating Duty Cycles
Parametera | Speed control |
Slope, a1 | 0.990 [LESS THAN EQUAL TO]a1 [LESS THAN EQUAL TO]1.010. |
Absolute value of intercept, |a0| | [LESS THAN EQUAL TO]2.0% of maximum fnref speed. |
Standard error of the estimate, SEE | [LESS THAN EQUAL TO]2.0% of maximum fnref speed. |
Coefficient of determination, r2 | [GREATER THAN EQUAL TO]0.990. |
a Determine values for specified parameters as described in 40 CFR 1065.514(e) by comparing measured and reference values for fnref,dyno.
Where:
MC = molar mass of carbon.
wCmeas = carbon mass fraction of fuel (or mixture of test fuels) as determined in 40 CFR 1065.655(d) , except that you may not use the default properties in Table 2 of 40 CFR 1065.655 to determine [ALPHA], [BETA], and wC for liquid fuels.
nexh = the mean raw exhaust molar flow rate from which you measured emissions according to 40 CFR 1065.655 .
xCcombdry = the mean concentration of carbon from fuel and any injected fluids in the exhaust per mole of dry exhaust.
xH2Oexhdry = the mean concentration of H2O in exhaust per mole of dry exhaust.
mCO2DEF = the mean CO2 mass emission rate resulting from diesel exhaust fluid decomposition over the duty cycle as determined in 40 CFR 1036.535(b)(9) . If your engine does not use diesel exhaust fluid, or if you choose not to perform this correction, set mCO2DEF equal to 0.
MCO2 = molar mass of carbon dioxide.
Example:
= 12.0107 g/mol
= 0.867
= 25.534 mol/s
= 2.805·10-3 mol/mol
xH2Oexhdry = 3.53·10-2 mol/mol
mCO2DEF = 0.0726 g/s
MCO2 = 44.0095
mfuelidle = 0.405 g/s = 1458.6 g/hr
Where:
i = an indexing variable that represents one test interval.
N = total number of charge-depleting test intervals.
mfuel[cycle]CDi = total mass of fuel in the charge-depleting portion of the test for each test interval, i, starting from i = 1, including the test interval(s) from the transition phase.
UFDCDi = utility factor fraction at distance DCDi from Eq. 1037.505-9 as determined by interpolating the approved utility factor curve for each test interval, i, starting from i = 1. Let UFDCD0 = 0
j = an indexing variable that represents one test interval.
M = total number of charge-sustaining test intervals.
mfuel[cycle]CSj = total mass of fuel over the charge-sustaining portion of the test for each test interval, j, starting from j = 1.
UFRCD = utility factor fraction at the full charge-depleting distance, RCD, as determined by interpolating the approved utility factor curve. RCD is the cumulative distance driven over N charge-depleting test intervals.
Where:
k = an indexing variable that represents one recorded velocity value.
Q = total number of measurements over the test interval.
v = vehicle velocity at each time step, k, starting from k = 1. For tests completed under this section, v is the vehicle velocity as determined by Eq. 1037.550-1. Note that this should include charge-depleting test intervals that start when the engine is not yet operating.
[DELTA]t = 1/frecord
frecord = the record rate.
Example for the 55 mi/hr Cruise Cycle:
Q = 8790
v1 = 55.0 mi/hr
v2 = 55.0 mi/hr
v3 = 55.1 mi/hr
frecord = 10 Hz
[DELTA]t = 1/10 Hz = 0.1 s
DCD2 = 13.4 mi
DCD3 = 13.4 mi
N = 3
UFDCD1 = 0.05
UFDCD2 = 0.11
UFDCD3 = 0.21
mfuel55cruiseCD1 = 0 g
mfuel55cruiseCD2 = 0 g
mfuel55cruiseCD3 = 1675.4 g
M = 1
mfuel55cruiseCS = 4884.1 g
UFRCD = 0.21
mfuelUF55cruise = 4026.0 g
using one of the following methods:
Example:
= 4.0
= 0.399 m
Where:
fnengine = average engine speed when vehicle speed is at or above 0.100 m/s.
vref = average simulated vehicle speed at or above 0.100 m/s.
Example:
fnengine = 1870 r/min = 31.17 r/s
vref = 19.06 m/s
fnpowertrain, and the average powertrain output torque (positive torque only),
Tpowertrain, at vehicle speed at or above 0.100 m/s. (Note: Use all the charge-sustaining and charge-depleting test intervals when determining
fnpowertrain and
Tpowertrain for plug-in hybrid engines and powertrains.)
Table 6 to Paragraph (o)(8)(ii) of § 1037.550 -Generic Example of Output Matrix for Cruise Cycle Vehicle Configurations
Parameter | Configuration | ||||||||
1 | 2 | 3 | 4 | 5 | 6 | 7 | ... | n | |
mfuel[cycle] | |||||||||
fnpowertrain[cycle] | |||||||||
Tpowertrain[cycle] | |||||||||
W[cycle] |
40 C.F.R. §1037.550