Determining cycle-average engine fuel maps.
§ 1036.540 Determining cycle-average engine fuel maps.
(a) Overview. This section describes how to determine an engine's cycle-average fuel maps for model year 2021 and later vehicles with transient cycles. This section may also apply for highway cruise cycles as described in § 1036.510. Vehicle manufacturers may need cycle-average fuel maps for transient duty cycles, highway cruise cycles, or both to demonstrate compliance with emission standards under 40 CFR part 1037. Generating cycle-average engine fuel maps consists of the following steps:
(1) Determine the engine's torque maps as described in § 1036.510(a).
(2) Determine the engine's steady-state fuel map and fuel consumption at idle as described in § 1036.535.
(3) Simulate several different vehicle configurations using GEM (see 40 CFR 1037.520) to create new engine duty cycles, as described in paragraph (c) of this section. The transient vehicle duty cycles for this simulation are in 40 CFR part 1037, appendix I; the highway cruise cycles with grade are in 40 CFR part 1037, appendix IV. Note that GEM simulation relies on vehicle service classes as described in 40 CFR 1037.140.
(4) Test the engines using the new duty cycles to determine fuel consumption, cycle work, and average vehicle speed as described in paragraph (d) of this section and establish GEM inputs for those parameters for further vehicle simulations as described in paragraph (e) of this section.
(b) General test provisions. The following provisions apply for testing under this section:
(1) To perform fuel mapping under this section for hybrid engines, make sure the engine and its hybrid features are appropriately configured to represent the hybrid features in your testing.
(2) Measure NOX emissions for each specified sampling period in grams. You may perform these measurements using a NOX emission-measurement system that meets the requirements of 40 CFR part 1065, subpart J. Include these measured NOX values any time you report to us your fuel consumption values from testing under this section. If a system malfunction prevents you from measuring NOX emissions during a test under this section but the test otherwise gives valid results, you may consider this a valid test and omit the NOX emission measurements; however, we may require you to repeat the test if we determine that you inappropriately voided the test with respect to NOX emission measurement.
(3) This section uses engine parameters and variables that are consistent with 40 CFR part 1065.
(4) For variable-speed gaseous-fueled engines with a single-point fuel injection system, apply all of the following statistical criteria to validate the transient duty cycle in 40 CFR part 1037, appendix I:
Table 1 to § 1036.540
| Parameter | Speed | Torque | Power |
|---|---|---|---|
| Slope, a1 | 0.950 ≤ a1 ≤1.030 | 0.830 ≤ a1 ≤1.030 | 0.830 ≤ a1 ≤1.030. |
| Absolute value of intercept, |a0| | ≤10% of warm idle | ≤3% of maximum mapped torque | ≤2% of maximum mapped power. |
| Standard error of the estimate, SEE | ≤5% of maximum test speed | ≤15% of maximum mapped torque | ≤15% of maximum mapped power. |
| Coefficient of determination, r2 | ≥0.970 | ≥0.700 | ≥0.750. |
(c) Create engine duty cycles. Use GEM to simulate several different vehicle configurations to create transient and highway cruise engine duty cycles corresponding to each vehicle configuration, as follows:
(1) Set up GEM to simulate vehicle operation based on your engine's torque maps, steady-state fuel maps, engine minimum warm-idle speed and fuel consumption at idle as described in paragraphs (a)(1) and (2) of this section, as well as 40 CFR 1065.405(b). For engines without an adjustable warm idle speed replace minimum warm idle speed with warm idle speed, fnidle.
(2) Set up GEM with transmission parameters for different vehicle service classes and vehicle duty cycles as described in Table 2 of this section. For automatic transmissions set neutral idle to “Y” in the vehicle file. These values are based on automatic or automated manual transmissions, but they apply for all transmission types.
Where:
fn[speed] = engine's angular speed as determined in paragraph (c)(3)(ii) or (iii) of this section.
ktopgear = transmission gear ratio in the highest available gear from Table 2 of this section (for powertrain testing use actual top gear ratio).
vref = reference speed. Use 65 mi/hr for the transient cycle and the 65 mi/hr highway cruise cycle, and use 55 mi/hr for the 55 mi/hr highway cruise cycle.
Example for a vocational Light HDV or vocational Medium HDV with a 6-speed automatic transmission at B speed (Test 3 or 4 in Table 3 of this section):
fnrefB = 1870 r/min = 31.17 r/s
kaB = 4.0
ktopgear = 0.61
vref = 65 mi/hr = 29.06 m/s
(ii) Test at least eight different vehicle configurations for engines that will be installed in vocational Light HDV or vocational Medium HDV using vehicles in Table 3 of this section. For example, if your engines will be installed in vocational Medium HDV and vocational Heavy HDV, you might select Tests 2, 4, 6, and 8 of Table 3 of this section to represent vocational Medium HDV and Tests 2, 3, 4, 6, and 9 of Table 4 of this section to represent vocational Heavy HDV. You may test your engine using additional vehicle configurations with different ka and Crr values to represent a wider range of in-use vehicle configurations. For all vehicle configurations set the drive axle configuration to 4×2. For powertrain testing, set Mrotating to 340 kg and Effaxle to 0.955 for all vehicle configurations. Set the axle ratio, ka, and tire size,
for each vehicle configuration based on the corresponding designated engine speed (fnrefA, fnrefB, fnrefC, or fntest) at 65 mi/hr for the transient cycle and the 65 mi/hr highway cruise cycle, and at 55 mi/hr for the 55 mi/hr highway cruise cycle. These vehicle speeds apply equally for engines subject to spark-ignition standards. Use the following settings specific to each vehicle configuration:
(iii) Test nine different vehicle configurations for engines that will be installed in vocational Heavy HDV and for tractors that are not heavy-haul tractors. Test six different vehicle configurations for heavy-haul tractors. You may test your engines for additional configurations with different ka, CdA, and Crr values to represent a wider range of in-use vehicle configurations. Set Crr to 6.9 for all nine defined vehicle configurations. For class 7 and 8 vehicle configurations set the drive axle configuration to 4×2 and 6×4 respectively. For powertrain testing, set Effaxle to 0.955 for all vehicle configurations. Set the axle ratio, ka, and tire size,
for each vehicle configuration based on the corresponding designated engine speed (B, fntest, or the minimum NTE exclusion speed as determined in 40 CFR 86.1370(b)(1)) at 65 mi/hr for the transient duty cycle and the 65 mi/hr highway cruise duty cycle, and at 55 mi/hr for the 55 mi/hr highway cruise duty cycle. Use the settings specific to each vehicle configuration as shown in Table 4 or Table 5 of this section, as appropriate. Engines subject to testing under both Tables 4 and 5 of this section need not repeat overlapping vehicle configurations, so complete fuel mapping requires testing 12 (not 15) vehicle configurations for those engines. However, the preceding sentence does not apply if you choose to create two separate maps from the vehicle configurations defined in Tables 4 and 5 of this section. Note that Mrotating is needed for powertrain testing but not for engine testing. Tables 4 and 5 follow:
(iv) If the engine will be installed in a combination of vehicles defined in paragraphs (c)(3)(ii) and (iii) of this section, use good engineering judgment to select at least nine vehicle configurations from Tables 3 and 4 of this section that best represent the range of vehicles your engine will be sold in. If there are not nine representative configurations you must add vehicles, that you define, to reach a total of at least nine vehicles. For example, if your engines will be installed in vocational Medium HDV and vocational Heavy HDV, select Tests 2, 4, 6 and 8 of Table 3 of this section to represent Medium HDV and Tests 3, 6, and 9 of Table 4 of this section to represent vocational Heavy HDV and add two more vehicles that you define. You may test your engine using additional vehicle configurations with different ka and Crr values to represent a wider range of in-use vehicle configurations.
(v) Use the defined values in Tables 2 through 5 of this section to set up GEM with the correct regulatory subcategory and vehicle weight reduction, if applicable, to achieve the target vehicle mass, M, for each test.
(4) Use the GEM output of instantaneous engine speed and engine flywheel torque for each of the vehicle configurations to generate a 10 Hz transient duty cycle corresponding to each vehicle configuration operating over each vehicle duty cycle.
(d) Test the engine with GEM cycles. Test the engine over each of the transient engine duty cycles generated in paragraph (c) of this section as follows:
(1) Determine the sequence of engine duty cycles (both required and optional) for the cycle-average-fuel-mapping sequence as follows:
(i) Sort the list of engine duty cycles into three separate groups by vehicle duty cycle; transient vehicle duty cycle, 55 mi/hr highway cruise duty cycle, and the 65 mi/hr highway cruise duty cycle.
(ii) Within each group of engine duty cycles derived from the same vehicle duty cycle, order the duty cycles as follows: Select the engine duty cycle with the highest reference cycle work; followed by the cycle with the lowest cycle work; followed by the cycle with next highest cycle work; followed by the cycle with the next lowest cycle work; until all the cycles are selected.
(iii) For each engine duty cycle, preconditioning cycles will be needed to start the cycle-average-fuel-mapping sequence.
(A) For the first and second cycle in each sequence, the two preconditioning cycles are the first cycle in the sequence, the transient vehicle duty cycle with the highest reference cycle work. This cycle is run twice for preconditioning prior to starting the sequence for either of the first two cycles.
(B) For all other cycles, the two preconditioning cycles are the previous two cycles in the sequence.
(2) If the engine has an adjustable warm idle speed setpoint, set it to its minimum value, fnidlemin.
(3) During each test interval, control speed and torque to meet the cycle validation criteria in 40 CFR 1065.514, except as noted in this paragraph (d)(3). Note that 40 CFR part 1065 does not allow subsampling of the 10 Hz GEM generated reference cycle. If the range of reference speeds is less than 10 percent of the mean reference speed, you only need to meet the standard error of the estimate in Table 2 of 40 CFR 1065.514 for the speed regression.
(4) Warm-up the engine as described in 40 CFR 1065.510(b)(2).
(5) Transition between duty cycles as follows:
(i) For transient duty cycles, start the next cycle within 10 seconds after the conclusion of the preceding cycle. Note that this paragraph (d)(5)(i) applies to transitioning from both the preconditioning cycles and tests for record.
(ii) For cruise cycles, linearly ramp to the next cycle over 5 seconds and stabilize for 15 seconds prior to starting the next cycle. Note that this paragraph (d)(5)(ii) applies to transitioning from both the preconditioning cycles and tests for record.
(6) Operate the engine over the engine duty cycle and record measurements using one of the methods described in paragraph (d)(6)(i) or (ii) of this section. You must also measure and report NOX emissions over each test interval as described in paragraph (a)(2) of this section. If you use redundant systems for the determination of fuel consumption, for example combining measurements of dilute and raw emissions when generating your map, follow the requirements of 40 CFR 1065.201(d).
(i) Indirect measurement of fuel flow. Record speed and torque and measure emissions and other inputs needed to run the chemical balance in 40 CFR 1065.655(c) for the test interval defined by the first engine duty cycle; determine the corresponding mean values for the test interval. For dilute sampling of emissions, in addition to the background measurement provisions described in 40 CFR 1065.140, you may do the following:
(A) Measure background as described in § 1036.535(b)(7)(i)(A) but read the background as described in paragraph (d)(9)(i) of this section.
(B) Measure background as described in § 1036.535(b)(7)(i)(B) but read the background as described in paragraph (d)(9)(i) of this section.
(ii) Direct measurement of fuel flow. Record speed and torque and measure fuel consumption with a fuel flow meter for the test interval defined by the first engine duty cycle; determine the corresponding mean values for the test interval.
(7) Repeat the steps in paragraph (d)(6) of this section for all the remaining engine duty cycles.
(8) Repeat the steps in paragraphs (d)(4) through (7) of this section for all the applicable groups of duty cycles (e.g., transient vehicle duty cycle, 55 mi/hr highway cruise duty cycle, and the 65 mi/hr highway cruise duty cycle).
(9) The following provisions apply for interruptions in the cycle-average-fuel-mapping sequence in a way that is intended to produce results equivalent to running the sequence without interruption:
(i) You may pause the cycle-average-fuel-mapping sequence after each test interval to calibrate emission-measurement instrumentation, to read and evacuate background bag samples collected over the course of multiple test intervals, or to sample the dilution air for background emissions. This paragraph (d)(9)(i) requires you to shut-down the engine during the pause. If the pause is longer than 30 minutes, restart the engine and restart the cycle-average-fuel-mapping sequence at the step in paragraph (d)(4) of this section. Otherwise, restart the engine and restart the cycle-average-fuel-mapping sequence at the step in paragraph (d)(5) of this section.
(ii) If an infrequent regeneration event occurs, interrupt the cycle-average-fuel-mapping sequence and allow the regeneration event to finish. You may continue to operate the engine over the engine duty cycle where the event began or, using good engineering judgment, you may transition to another operating condition to reduce the regeneration event duration.
(A) Determine which cycles in the sequence to void as follows:
(1) If the regeneration event began during a test interval, the cycle associated with that test interval must be voided.
(2) If you used dilute sampling to measure emissions and you used batch sampling to measure background emissions that were sampled periodically into the bag over the course of multiple test intervals and you are unable to read the background bag (e.g., sample volume too small), void all cycles associated with that background bag.
(3) If you used dilute sampling to measure emissions and you used the option to sample periodically from the dilution air and you did not meet all the requirements for this option as described in paragraph (d)(6)(i)(B) of this section, void all cycles associated with those background readings.
(4) If the regeneration event began during a non-test-interval period of the sequence and the provisions in paragraphs (d)(9)(ii)(A)(2) and (3) of this section do not apply, you do not need to void any cycles.
(B) Determine the cycle to restart the sequence. Identify the cycle associated with the last valid test interval. The next cycle in the sequence is the cycle to be used to restart the sequence.
(C) Once the regeneration event is finished, restart the sequence at the cycle determined in paragraph (d)(9)(ii)(B) of this section instead of the first cycle of the sequence. If the engine is not already warm, restart the sequence at paragraph (d)(4) of this section. Otherwise, restart at paragraph (d)(5) of this section.
(iii) If the cycle-average-fuel-mapping sequence is interrupted due to test equipment or engine malfunction, correct the malfunction and follow the steps in paragraphs (d)(9)(ii)(A) through (C) of this section to restart the sequence. Treat the detection of the malfunction as the beginning of the regeneration event.
(iv) If any test interval in the cycle-average-fuel-mapping sequence is voided, you must rerun that test interval as described in this paragraph (d)(9)(iv). You may rerun the whole sequence or any contiguous part of the sequence. If you end up with multiple valid test intervals for a given cycle, use the last valid test interval for determining the cycle-average fuel map. If the engine has been shut-down for more than 30 minutes or if it is not already warm, restart the sequence at paragraph (d)(4) of this section. Otherwise, restart at paragraph (d)(5) of this section. Repeat the steps in paragraphs (d)(6) and (7) of this section until you complete the whole sequence or part of the sequence. The following examples illustrate possible scenarios for completing only part of the sequence:
(A) If you voided only the test interval associated with the fourth cycle in the sequence, you may restart the sequence using the second and third cycles as the preconditioning cycles and stop after completing the test interval associated with the fourth cycle.
(B) If you voided the test intervals associated with the fourth and sixth cycles, you may restart the sequence using the second and third cycles as the preconditioning cycles and stop after completing the test interval associated with the sixth cycle. If the test interval associated with the fifth cycle in this sequence was valid, it must be used for determining the cycle-average fuel map instead of the original one.
(10) For plug-in hybrid engines, precondition the battery and then complete all back-to-back tests for each vehicle configuration according to 40 CFR 1066.501 before moving to the next vehicle configuration.
(11) You may send signals to the engine controller during the test, such as current transmission gear and vehicle speed, if that allows engine operation during the test to better represent in-use operation.
(12) For hybrid powertrains with no plug-in capability, correct for the net energy change of the energy storage device as described in 40 CFR 1066.501. For plug-in hybrid engines, follow 40 CFR 1066.501 to determine End-of-Test for charge-depleting operation; to do this, you must get our advance approval for a utility factor curve. We will approve your utility factor curve if you can show that you created it from sufficient in-use data of vehicles in the same application as the vehicles in which the plug-in hybrid electric vehicle (PHEV) engine will be installed.
(13) Calculate the fuel mass flow rate, mfuel, for each duty cycle using one of the following equations:
(i) Determine fuel-consumption rates using emission measurements from the raw or diluted exhaust, calculate the mass of fuel for each duty cycle, mfuel[cycle], as follows:
(A) For calculations that use continuous measurement of emissions and continuous CO2 from urea, calculate mfuel[cycle] using the following equation:
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 1 of 40 CFR 1065.655 to determine α, β, and wC for liquid fuels.
i = an indexing variable that represents one recorded emission value.
N = total number of measurements over the duty cycle.
ṅexh = exhaust molar flow rate from which you measured emissions.
xCcombdry = amount of carbon from fuel and any injected fluids in the exhaust per mole of dry exhaust as determined in 40 CFR 1065.655(c).
xH2Oexhdry = amount of H2O in exhaust per mole of exhaust as determined in 40 CFR 1065.655(c).
Δt = 1/frecord
MCO2 = molar mass of carbon dioxide.
ṁCO2DEFi = mass emission rate of CO2 resulting from diesel exhaust fluid decomposition over the duty cycle as determined from § 1036.535(b)(7). If your engine does not utilize diesel exhaust fluid for emission control, or if you choose not to perform this correction, set ṁCO2DEFi equal to 0.
Example:
MC = 12.0107 g/mol
wCmeas = 0.867
N = 6680
ṅexh1 = 2.876 mol/s
ṅexh2 = 2.224 mol/s
xCcombdry1 = 2.61·10−3 mol/mol
xCcombdry2 = 1.91·10−3 mol/mol
xH2Oexh1 = 3.53·10−2 mol/mol
xH2Oexh2 = 3.13·10−2 mol/mol
frecord = 10 Hz
Δt = 1/10 = 0.1 s
MCO2 = 44.0095 g/mol
ṁCO2DEF1 = 0.0726 g/s
ṁCO2DEF2 = 0.0751 g/s
(ii) Manufacturers may choose to measure fuel mass flow rate. Calculate the mass of fuel for each duty cycle, mfuel[cycle], as follows:
Where:
i = an indexing variable that represents one recorded value.
N = total number of measurements over the duty cycle. For batch fuel mass measurements, set N = 1.
ṁfueli = the fuel mass flow rate, for each point, i, starting from i = 1.
Δt = 1/frecord
frecord = the data recording frequency.
Example:
N = 6680
ṁfuel1 = 1.856 g/s
ṁfuel2 = 1.962 g/s
frecord = 10 Hz
Δt = 1/10 = 0.1 s
mfueltransient = (1.856 + 1.962 + . . . + ṁfuel6680) · 0.1
mfueltransient = 111.95 g
(14) The provisions related to carbon balance error verification in § 1036.543 apply to test intervals in this section.
(15) Correct the measured or calculated fuel mass flow rate, mfuel, for each test result to a mass-specific net energy content of a reference fuel as described in § 1036.535(e), replacing with ṁ̅fuel in Eq. 1036.535-4.
(16) For engines designed for plug-in hybrid electric vehicles, the mass of fuel for each cycle, mfuel[cycle], is the utility factor-weighted fuel mass. This is done by calculating mfuel for the full charge-depleting and charge-sustaining portions of the test and weighting the results, using the following equation:
Where:
mfuel[cycle],CD = total mass of fuel for all the tests in the charge-depleting portion of the test.
UFD,CD = utility factor fraction at distance DCD as determined by interpolating the approved utility factor curve.
mfuel[cycle],CS = total mass of fuel for all the tests in the charge-sustaining portion of the test.
Where:
v = vehicle velocity at each time step. For tests completed under this section, v is the vehicle velocity in the GEM duty-cycle file. For tests under 40 CFR 1037.550, v is the vehicle velocity as determined by Eq. 1037.550-1 of 40 CFR 1037.550. Note that this should include complete and incomplete charge-depleting tests.
(e) Determine GEM inputs. Use the results of engine testing in paragraph (d) of this section to determine the GEM inputs for the transient duty cycle and optionally for each of the highway cruise cycles corresponding to each simulated vehicle configuration as follows:
(1) Your declared fuel mass consumption, mfuel[cycle]. Using the calculated fuel mass consumption values described in paragraph (d) of this section, declare values using the method described in § 1036.535(g).
(2) We will determine mfuel[cycle] values using the method described in § 1036.535(h).
(3) Engine output speed per unit vehicle speed,
by taking the average engine speed measured during the engine test while the vehicle is moving and dividing it by the average vehicle speed provided by GEM. Note that the engine cycle created by GEM has a flag to indicate when the vehicle is moving.
(4) Positive work determined according to 40 CFR part 1065, W[cycle], by using the engine speed and engine torque measured during the engine test while the vehicle is moving. Note that the engine cycle created by GEM has a flag to indicate when the vehicle is moving.
(5) The engine idle speed and torque, by taking the average engine speed and torque measured during the engine test while the vehicle is not moving. Note that the engine cycle created by GEM has a flag to indicate when the vehicle is moving.
(6) The following table illustrates the GEM data inputs corresponding to the different vehicle configurations for a given duty cycle:
[86 FR 34394, June 29, 2021]
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