(continued) (d) Calculating work. Before calculating work values, omit any points recorded during engine cranking and starting. Cranking and starting includes any time when an engine starter is engaged, any time when the engine is motored with a dynamometer for the sole purpose of starting the engine, and any time during operation before reaching idle speed. See §1065.525(a) and (b) for more information about engine cranking. After omitting points recorded during engine cranking and starting, but before omitting any points under paragraph (e) of this section, calculate total work, W, based on the feedback values and reference work, Wref, based on the reference values, as described in §1065.650.
(e) Omitting additional points. Besides engine cranking, you may omit additional points from cycle-validation statistics as described in the following table:
Table 1 of § 1065.514_Permissible Criteria for Omitting Points From Duty-Cycle Regression Statistics
----------------------------------------------------------------------------------------------------------------
When operator demand is at its. . . you may omit. . . if. . .
----------------------------------------------------------------------------------------------------------------
For reference duty cycles that are specified in terms of speed and torque (fnref, Tref).
----------------------------------------------------------------------------------------------------------------
minimum.................................. power and torque............ Tref < 0% (motoring).
minimum.................................. power and speed............. fnref = 0% (idle) and Tref = 0% (idle)
and Tref-(2% · Tmax mapped)
< T < Tref + (2% · Tmax
mapped).
minimum.................................. power and either torque or fn > fnref or T > Tref but not if
speed. fn > fnref and T > Tref.
maximum.................................. power and either torque or fn < fnref or T < Tref but not if
speed. fn < fnef and T < Tref.
----------------------------------------------------------------------------------------------------------------
For reference duty cycles that are specified in terms of speed and power (fnref, Pref).
----------------------------------------------------------------------------------------------------------------
minimum.................................. power and torque............ Pref < 0% (motoring).
minimum.................................. power and speed............. fnref = 0% (idle) and Pref = 0 % (idle)
and Pref - (2% · Pmax mapped)
< P < Pref + (2% · Pmax
mapped).
minimum.................................. power and either torque or fn > fnref or P > Pref but not if
speed. fn > fnref and P > Pref.
maximum.................................. power and either torque or fn < fnref or P < Pref but not if
speed. fn < fnef and P
----------------------------------------------------------------------------------------------------------------
(f) Statistical parameters. Use the remaining points to calculate regression statistics described in §1065.602. Round calculated regression statistics to the same number of significant digits as the criteria to which they are compared. Refer to Table 2 of §1065.514 for the criteria. Calculate the following regression statistics :
(1) Slopes for feedback speed, a1fn, feedback torque, a1T, and feedback power a1P.
(2) Intercepts for feedback speed, a0fn, feedback torque, a0T, and feedback power a0P.
(3) Standard estimates of error for feedback speed, SEEfn, feedback torque, SET, and feedback power SEEP.
(4) Coefficients of determination for feedback speed, r 2 fn, feedback torque, r 2 T, and feedback power r 2 P.
(g) Cycle-validation criteria. Unless the standard-setting part specifies otherwise, use the following criteria to validate a duty cycle:
(1) For variable-speed engines, apply all the statistical criteria in Table 2 of this section.
(2) For constant-speed engines, apply only the statistical criteria for torque in the Table 2 of this section.
Table 2 of § 1065.514_Default Statistical Criteria for Validating Duty Cycles
----------------------------------------------------------------------------------------------------------------
Parameter Speed Torque Power
----------------------------------------------------------------------------------------------------------------
Slope, a1............................ 0.950 [le] a1 [le] 0.830 [le] a1 [le] 0.830 [le] a1 [le]
1.030. 1.030. 1.030.
Absolute value of intercept, [le] 10% of warm idle.. [le] 2.0% of maximum [le] 2.0% of maximum
[bond]a0[bond]. mapped torque. mapped power.
Standard error of estimate, SEE...... [le] 5.0% of maximum [le] 10% of maximum [le] 10% of maximum
test speed. mapped torque. mapped power.
Coefficient of determination, r\2\... >= 0.970............... >= 0.850............... >= 0.910.
----------------------------------------------------------------------------------------------------------------
§ 1065.520 Pre-test verification procedures and pre-test data collection.
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(a) If your engine must comply with a PM standard, follow the procedures for PM sample preconditioning and tare weighing according to §1065.590.
(b) Unless the standard-setting part specifies different values, verify that ambient conditions are within the following tolerances before the test:
(1) Ambient temperature of (20 to 30) °C.
(2) Atmospheric pressure of (80.000 to 103.325) kPa and within ±5% of the value recorded at the time of the last engine map.
(3) Dilution air as specified in §1065.140(b).
(c) You may test engines at any intake-air humidity, and we may test engines at any intake-air humidity.
(d) Verify that auxiliary-work inputs and outputs are configured as they were during engine mapping, as described in§1065.510(a).
(e) You may perform a final calibration of the speed, torque, and proportional-flow control systems, which may include performing practice duty cycles.
(f) You may perform the following recommended procedure to precondition sampling systems:
(1) Start the engine and use good engineering judgment to bring it to 100% torque at any speed above its peak-torque speed.
(2) Operate any dilution systems at their expected flow rates. Prevent aqueous condensation in the dilution systems.
(3) Operate any PM sampling systems at their expected flow rates.
(4) Sample PM for at least 10 min using any sample media. You may change sample media during preconditioning. You may discard preconditioning samples without weighing them.
(5) You may purge any gaseous sampling systems during preconditioning.
(6) You may conduct calibrations or verifications on any idle equipment or analyzers during preconditioning.
(7) Proceed with the test sequence described in §1065.530(a)(1).
(g) After the last practice or preconditioning cycle before an emission test, verify the amount of contamination in the HC sampling system as follows:
(1) Select the HC analyzer range for measuring the flow-weighted mean concentration expected at the HC standard.
(2) Zero the HC analyzer at the analyzer zero or sample port. Note that FID zero and span balance gases may be any combination of purified air or purified nitrogen that meets the specifications of §1065.750. We recommend FID analyzer zero and span gases that contain approximately the flow-weighted mean concentration of O2 expected during testing.
(3) Span the HC analyzer using span gas introduced at the analyzer span or sample port. Span on a carbon number basis of one (C1). For example, if you use a C3H8 span gas of concentration 200 µmol/mol, span the FID to respond with a value of 600 µmol/mol.
(4) Overflow zero gas at the HC probe or into a fitting between the HC probe and its transfer line.
(5) Measure the HC concentration in the sampling system, as follows:
(i) For continuous sampling, record the mean HC concentration as overflow zero air flows.
(ii) For batch sampling, fill the sample medium and record its mean HC concentration.
(6) Record this value as the initial HC concentration, xHCinit, and use it to correct measured values as described in §1065.660.
(7) If xHCinit exceeds the greatest of the following values, determine the source of the contamination and take corrective action, such as purging the system during an additional preconditioning cycle or replacing contaminated portions:
(i) 2% of the flow-weighted mean concentration expected at the standard.
(ii) 2% of the flow-weighted mean concentration measured during testing.
(iii) For any compression-ignition engines, any two-stroke spark ignition engines, or 4-stroke spark-ignition engines that are less than 19 kW, 2 µmol/mol.
(8) If corrective action does not resolve the deficiency, you may request to use the contaminated system as an alternate procedure under §1065.10.
§ 1065.525 Engine starting, restarting, and shutdown.
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(a) Start the engine using one of the following methods:
(1) Start the engine as recommended in the owners manual using a production starter motor and adequately charged battery or a suitable power supply.
(2) Use the dynamometer to start the engine. To do this, motor the engine within ±25% of its typical in-use cranking speed. Stop cranking within 1 second of starting the engine.
(b) If the engine does not start after 15 seconds of cranking, stop cranking and determine why the engine failed to start, unless the owners manual or the service-repair manual describes the longer cranking time as normal.
(c) Respond to engine stalling with the following steps:
(1) If the engine stalls during warm-up before emission sampling begins, restart the engine and continue warm-up.
(2) If the engine stalls during preconditioning before emission sampling begins, restart the engine and restart the preconditioning sequence.
(3) If the engine stalls at any time after emission sampling begins for a transient test or ramped-modal cycle test, the test is void.
(4) If the engine stalls at any time after emission sampling begins for a discrete mode in a discrete-mode duty cycle test, void the test or perform the following steps to continue the test:
(i) Restart the engine.
(ii) Use good engineering judgment to restart the test sequence using the appropriate steps in §1065.530(b)
(iii) Precondition the engine at the previous discrete mode for a similar amount of time compared with how long it was initially run.
(iv) Advance to the mode at which the engine stalled and continue with the duty cycle as specified in the standard-setting part.
(v) Complete the remainder of the test according to the requirements in this subpart.
(d) Shut down the engine according to the manufacturer's specifications.
§ 1065.530 Emission test sequence.
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(a) Time the start of testing as follows:
(1) Perform one of the following if you precondition sampling systems as described in §1065.520(f):
(i) For cold-start duty cycles, shut down the engine. Unless the standard-setting part specifies that you may only perform a natural engine cooldown, you may perform a forced engine cooldown. Use good engineering judgment to set up systems to send cooling air across the engine, to send cool oil through the engine lubrication system, to remove heat from coolant through the engine cooling system, and to remove heat from an exhaust aftertreatment system. In the case of a forced aftertreatment cooldown, good engineering judgment would indicate that you not start flowing cooling air until the aftertreatment system has cooled below its catalytic activation temperature. For platinum-group metal catalysts, this temperature is about 200 °C. Once the aftertreatment system has naturally cooled below its catalytic activation temperature, good engineering judgment would indicate that you use clean air with a temperature of at least 15 °C, and direct the air through the aftertreatment system in the normal direction of exhaust flow. Do not use any cooling procedure that results in unrepresentative emissions (see §1065.10(c)(1)). You may start a cold-start duty cycle when the temperatures of an engine's lubricant, coolant, and aftertreatment systems are all between (20 and 30) °C.
(ii) For hot-start emission measurements, shut down the engine. Start a hot-start duty cycle within 20 min of engine shutdown.
(iii) For testing that involves hot-stabilized emission measurements, such as any steady-state testing, you may continue to operate the engine at fntest and 100% torque if that is the first operating point. Otherwise, operate the engine at warm, idle or the first operating point of the duty cycle. In any case, start the emission test within 10 min after you complete the preconditioning procedure.
(2) For all other testing, perform one of the following:
(i) For cold-start duty cycles, prepare the engine according to paragraph (a)(1)(i) of this section.
(ii) For hot-start emission measurements, first operate the engine at any speed above peak-torque speed and at (65 to 85) % of maximum mapped power until either the engine coolant, block, or head absolute temperature is within ±2% of its mean value for at least 2 min or until the engine thermostat controls engine temperature. Shut down the engine. Start the duty cycle within 20 min of engine shutdown.
(iii) For testing that involves hot-stabilized emission measurements, bring the engine either to warm idle or the first operating point of the duty cycle. Start the test within 10 min of achieving temperature stability. Determine temperature stability either as the point at which the engine coolant, block, or head absolute temperature is within ±2% of its mean value for at least 2 min, or as the point at which the engine thermostat controls engine temperature.
(b) Take the following steps before emission sampling begins:
(1) For batch sampling, connect clean storage media, such as evacuated bags or tare-weighed filters.
(2) Start all measurement instruments according to the instrument manufacturer's instructions and using good engineering judgment.
(3) Start dilution systems, sample pumps, cooling fans, and the data-collection system.
(4) Pre-heat or pre-cool heat exchangers in the sampling system to within their operating temperature tolerances for a test.
(5) Allow heated or cooled components such as sample lines, filters, chillers, and pumps to stabilize at their operating temperatures.
(6) Verify that there are no significant vacuum-side leaks according to §1065.345.
(7) Adjust the sample flow rates to desired levels, using bypass flow, if desired.
(8) Zero or re-zero any electronic integrating devices, before the start of any test interval.
(9) Select gas analyzer ranges. You may use analyzers that automatically switch ranges during a test only if switching is performed by changing the span over which the digital resolution of the instrument is applied. During a test you may not switch the gains of an analyzer's analog operational amplifier(s).
(10) Zero and span all continuous analyzers using NIST-traceable gases that meet the specifications of §1065.750. Span FID analyzers on a carbon number basis of one (1), C1. For example, if you use a C3H8 span gas of concentration 200 µmol/mol, span the FID to respond with a value of 600 µmol/mol.
(11) We recommend that you verify gas analyzer response after zeroing and spanning by flowing a calibration gas that has a concentration near one-half of the span gas concentration. Based on the results and good engineering judgment, you may decide whether or not to re-zero, re-span, or re-calibrate a gas analyzer before starting a test.
(12) If you correct for dilution air background concentrations of engine exhaust constituents, start measuring and recording background concentrations.
(c) Start testing as follows:
(1) If an engine is already running and warmed up, and starting is not part of the duty cycle, perform the following for the various duty cycles.
(i) Transient and steady-state ramped-modal cycles. Simultaneously start running the duty cycle, sampling exhaust gases, recording data, and integrating measured values.
(ii) Steady-state discrete-mode cycles. Control speed and torque to the first mode in the test cycle. Follow the instructions in the standard-setting part to determine how long to stabilize engine operation at each mode and how long to sample emissions at each mode.
(2) If engine starting is part of the duty cycle, initiate data logging, sampling of exhaust gases, and integrating measured values before attempting to start the engine. Initiate the duty cycle when the engine starts.
(d) At the end of the test interval, continue to operate all sampling and dilution systems to allow the sampling system's response time to elapse. Then stop all sampling and recording, including the recording of background samples. Finally, stop any integrating devices and indicate the end of the duty cycle in the recorded data.
(e) Shut down the engine if you have completed testing or if it is part of the duty cycle.
(f) If testing involves another duty cycle after a soak period with the engine off, start a timer when the engine shuts down, and repeat the steps in paragraphs (b) through (e) of this section as needed.
(g) Take the following steps after emission sampling is complete:
(1) For any proportional batch sample, such as a bag sample or PM sample, verify that proportional sampling was maintained according to §1065.545. Void any samples that did not maintain proportional sampling according to §1065.545.
(2) Place any used PM samples into covered or sealed containers and return them to the PM-stabilization environment. Follow the PM sample post-conditioning and total weighing procedures in §1065.595.
(3) As soon as practical after the duty cycle is complete but no later than 30 minutes after the duty cycle is complete, perform the following:
(i) Zero and span all batch gas analyzers.
(ii) Analyze any gaseous batch samples, including background samples.
(4) After quantifying exhaust gases, verify drift as follows:
(i) For batch and continuous gas analyzers, record the mean analyzer value after stabilizing a zero gas to the analyzer. Stabilization may include time to purge the analyzer of any sample gas, plus any additional time to account for analyzer response.
(ii) Record the mean analyzer value after stabilizing the span gas to the analyzer. Stabilization may include time to purge the analyzer of any sample gas, plus any additional time to account for analyzer response.
(iii) Use these data to validate and correct for drift as described in §1065.550.
(h) Determine whether or not the test meets the cycle-validation criteria in §1065.514.
(1) If the criteria void the test, you may retest using the same denormalized duty cycle, or you may re-map the engine, denormalize the reference duty cycle based on the new map and retest the engine using the new denormalized duty cycle.
(2) If the criteria void the test for a constant-speed engine only during commands of maximum test torque, you may do the following:
(i) Determine the first and last feedback speeds at which maximum test torque was commanded.
(ii) If the last speed is greater than or equal to 90% of the first speed, the test is void. You may retest using the same denormalized duty cycle, or you may re-map the engine, denormalize the reference duty cycle based on the new map and retest the engine using the new denormalized duty cycle.
(iii) If the last speed is less than 90% of the first speed, reduce maximum test torque by 5%, and proceed as follows:
(A) Denormalize the entire duty cycle based on the reduced maximum test torque according to §1065.512.
(B) Retest the engine using the denormalized test cycle that is based on the reduced maximum test torque.
(C) If your engine still fails the cycle criteria, reduce the maximum test torque by another 5% of the original maximum test torque.
(D) If your engine fails after repeating this procedure four times, such that your engine still fails after you have reduced the maximum test torque by 20% of the original maximum test torque, notify us and we will consider specifying a more appropriate duty cycle for your engine under the provisions of §1065.10(c).
§ 1065.545 Validation of proportional flow control for batch sampling.
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For any proportional batch sample such as a bag or PM filter, demonstrate that proportional sampling was maintained using one of the following, noting that you may omit up to 5% of the total number of data points as outliers:
(a) For any pair of flow meters, use the 1 Hz (or more frequently) recorded sample and total flow rates with the statistical calculations in §1065.602. Determine the standard error of the estimate, SEE, of the sample flow rate versus the total flow rate. For each test interval, demonstrate that SEE was less than or equal to 3.5% of the mean sample flow rate.
(b) For any pair of flow meters, use the 1 Hz (or more frequently) recorded sample and total flow rates to demonstrate that each flow rate was constant within ±2.5% of its respective mean or target flow rate. You may use the following options instead of recording the respective flow rate of each type of meter:
(1) Critical-flow venturi option. For critical-flow venturis, you may use the 1 Hz (or more frequently) recorded venturi-inlet conditions. Demonstrate that the flow density at the venturi inlet was constant within ±2.5% of the mean or target density over each test interval. For a CVS critical-flow venturi, you may demonstrate this by showing that the absolute temperature at the venturi inlet was constant within ±4% of the mean or target absolute temperature over each test interval.
(2) Positive-displacement pump option. You may use the 1 Hz (or more frequently) recorded pump-inlet conditions. Demonstrate that the density at the pump inlet was constant within ±2.5% of the mean or target density over each test interval. For a CVS pump, you may demonstrate this by showing that the absolute temperature at the pump inlet was constant within ±2% of the mean or target absolute temperature over each test interval.
(c) Using good engineering judgment, demonstrate with an engineering analysis that the proportional-flow control system inherently ensures proportional sampling under all circumstances expected during testing. For example, you might use CFVs for both sample flow and total flow and demonstrate that they always have the same inlet pressures and temperatures and that they always operate under critical-flow conditions.
§ 1065.550 Gas analyzer range validation, drift validation, and drift correction.
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(a) Range validation. If an analyzer operated above 100% of its range at any time during the test, perform the following steps:
(1) For batch sampling, re-analyze the sample using the lowest analyzer range that results in a maximum instrument response below 100%. Report the result from the lowest range from which the analyzer operates below 100% of its range for the entire test.
(2) For continuous sampling, repeat the entire test using the next higher analyzer range. If the analyzer again operates above 100% of its range, repeat the test using the next higher range. Continue to repeat the test until the analyzer operates at less than 100% of its range for the entire test.
(b) Drift validation and drift correction. Calculate two sets of brake-specific emission results. Calculate one set using the data before drift correction and the other set after correcting all the data for drift according to §1065.672. Use the two sets of brake-specific emission results as follows:
(1) If the difference between the corrected and uncorrected brake-specific emissions are within ±4% of the uncorrected results for all regulated emissions, the test is validated for drift. If not, the entire test is void.
(2) If the test is validated for drift, you must use only the drift-corrected emission results when reporting emissions, unless you demonstrate to us that using the drift-corrected results adversely affects your ability to demonstrate whether or not your engine complies with the applicable standards.
§ 1065.590 PM sample preconditioning and tare weighing.
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Before an emission test, take the following steps to prepare PM samples and equipment for PM measurements:
(a) Make sure the balance and PM-stabilization environments meet the periodic verifications in §1065.390.
(b) Visually inspect unused sample media (such as filters) for defects.
(c) To handle PM samples, use electrically grounded tweezers or a grounding strap, as described in §1065.190.
(d) Place unused sample media in one or more containers that are open to the PM-stabilization environment. If you are using filters, you may place them in the bottom half of a filter cassette.
(e) Stabilize sample media in the PM-stabilization environment. Consider an unused sample medium stabilized as long as it has been in the PM-stabilization environment for a minimum of 30 min, during which the PM-stabilization environment has been within the specifications of §1065.190.
(f) Weigh the sample media automatically or manually, as follows:
(1) For automatic weighing, follow the automation system manufacturer's instructions to prepare samples for weighing. This may include placing the samples in a special container.
(2) For manual weighing, use good engineering judgment to determine if substitution weighing is necessary to show that an engine meets the applicable standard. You may follow the substitution weighing procedure in paragraph (j) of this section, or you may develop your own procedure.
(g) Correct the measured weight for buoyancy as described in §1065.690. These buoyancy-corrected values are the tare masses of the PM samples.
(h) You may repeat measurements to determine mean masses. Use good engineering judgment to exclude outliers and calculate mean mass values.
(i) If you use filters as sample media, load unused filters that have been tare-weighed into clean filter cassettes and place the loaded cassettes in a covered or sealed container before taking them to the test cell for sampling. We recommend that you keep filter cassettes clean by periodically washing or wiping them with a compatible solvent applied using a lint-free cloth. Depending upon your cassette material, ethanol (C2H5OH) might be an acceptable solvent. Your cleaning frequency will depend on your engine's level of PM and HC emissions.
(j) Substitution weighing involves measurement of a reference weight before and after each weighing of a PM sample. While substitution weighing requires more measurements, it corrects for a balance's zero-drift and it relies on balance linearity only over a small range. This is most advantageous when quantifying net PM masses that are less than 0.1% of the sample medium's mass. However, it may not be advantageous when net PM masses exceed 1% of the sample medium's mass. The following steps are an example of substitution weighing:
(1) Use electrically grounded tweezers or a grounding strap, as described in §1065.190.
(2) Use a static neutralizer as described in §1065.190 to minimize static electric charge on any object before it is placed on the balance pan.
(3) Place on the balance pan a metal calibration weight that has a similar mass to that of the sample medium and meets the specifications for calibration weights in §1065.790. If you use filters, the weight's mass should be about (80 to 100) mg for typical 47 mm diameter filters.
(4) Record the stable balance reading, then remove the calibration weight.
(5) Weigh an unused sample, record the stable balance reading and record the balance environment's dewpoint, ambient temperature, and atmospheric pressure.
(6) Reweigh the calibration weight and record the stable balance reading.
(7) Calculate the arithmetic mean of the two calibration-weight readings that you recorded immediately before and after weighing the unused sample. Subtract that mean value from the unused sample reading, then add the true mass of the calibration weight as stated on the calibration-weight certificate. Record this result. This is the unused sample's tare weight without correcting for buoyancy.
(8) Repeat these substitution-weighing steps for the remainder of your unused sample media.
(9) Follow the instructions given in paragraphs (g) through (i) of this section.
§ 1065.595 PM sample post-conditioning and total weighing.
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(a) Make sure the weighing and PM-stabilization environments have met the periodic verifications in §1065.390.
(b) In the PM-stabilization environment, remove PM samples from sealed containers. If you use filters, you may remove them from their cassettes before or after stabilization. When you remove a filter from a cassette, separate the top half of the cassette from the bottom half using a cassette separator designed for this purpose.
(c) To handle PM samples, use electrically grounded tweezers or a grounding strap, as described in §1065.190.
(d) Visually inspect PM samples. If PM ever contacts the transport container, cassette assembly, filter-separator tool, tweezers, static neutralizer, balance, or any other surface, void the measurements associated with that sample and clean the surface it contacted.
(e) To stabilize PM samples, place them in one or more containers that are open to the PM-stabilization environment, which is described in §1065.190. A PM sample is stabilized as long as it has been in the PM-stabilization environment for one of the following durations, during which the stabilization environment has been within the specifications of §1065.190:
(1) If you expect that a filter's total surface concentration of PM will be greater than about 0.473 mm/mm 2 , expose the filter to the stabilization environment for at least 60 minutes before weighing.
(2) If you expect that a filter's total surface concentration of PM will be less than about 0.473 mm/mm 2 , expose the filter to the stabilization environment for at least 30 minutes before weighing.
(3) If you are unsure of a filter's total surface concentration of PM, expose the filter to the stabilization environment for at least 60 minutes before weighing.
(f) Repeat the procedures in §1065.590(f) through (i) to weigh used PM samples. Refer to a sample's post-test mass, after correcting for buoyancy, as its total mass.
(g) Subtract each buoyancy-corrected tare mass from its respective buoyancy-corrected total mass. The result is the net PM mass, mPM. Use mPM in emission calculations in §1065.650.
Subpart G—Calculations and Data Requirements
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§ 1065.601 Overview.
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(a) This subpart describes how to—
(1) Use the signals recorded before, during, and after an emission test to calculate brake-specific emissions of each regulated constituent.
(2) Perform calculations for calibrations and performance checks.
(3) Determine statistical values.
(b) You may use data from multiple systems to calculate test results for a single emission test, consistent with good engineering judgment. You may not use test results from multiple emission tests to report emissions. We allow weighted means where appropriate. You may discard statistical outliers, but you must report all results.
(c) You may use any of the following calculations instead of the calculations specified in this subpart G:
(1) Mass-based emission calculations prescribed by the International Organization for Standardization (ISO), according to ISO 8178.
(2) Other calculations that you show are equivalent to within ±0.1% of the brake-specific emission results determined using the calculations specified in this subpart G.
§ 1065.602 Statistics.
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(a) Overview. This section contains equations and example calculations for statistics that are specified in this part. In this section we use the letter “y” to denote a generic measured quantity, the superscript over-bar “-“ to denote an arithmetic mean, and the subscript “ref” to denote the reference quantity being measured.
(b) Arithmetic mean. Calculate an arithmetic mean, y , as follows:
Example:
N = 3
y1 = 10.60
y2 = 11.91
yN = y3 = 11.09
y = 11.20
(c) Standard deviation. Calculate the standard deviation for a non-biased (e.g., N–1) sample, s, as follows:
Example:
N = 3
y1 = 10.60
y2 = 11.91
yN = y3 = 11.09
y = 11.20
sy = 0.6619
(d) Root mean square. Calculate a root mean square, rmsy, as follows:
Example:
N = 3
y1 = 10.60
y2 = 11.91
yN = y3 = 11.09
rmsy = 11.21
(e) Accuracy. Calculate an accuracy, as follows, noting that the y i are arithmetic means, each determined by repeatedly measuring one sample of a single reference quantity, yref:
Example:
yref = 1800.0
N = 10
accuracy = &bond; 1800.0 - 1802.5 &bond;
accuracy = 2.5
(f) t-test. Determine if your data passes a t-test by using the following equations and tables:
(1) For an unpaired t-test, calculate the t statistic and its number of degrees of freedom, ?, as follows:
Example:
y ref = 1205.3
y = 1123.8
sref = 9.399
sy = 10.583
Nref = 11
N= 7
t = 16.63
sref = 9.399
sy = 10.583
Nref = 11
N = 7
? = 11.76
(2) For a paired t-test, calculate the t statistic and its number of degrees of freedom, ?, as follows, noting that the εi are the errors (e.g., differences) between each pair of yrefi and yi:
Example:
ε = -0.12580
N = 16
sε = 0.04837
t = 10.403
? = N - 1
Example:
N = 16
? = 16 - 1
? = 15
(3) Use Table 1 of this section to compare t to the tcrit values tabulated versus the number of degrees of freedom. If t is less than tcrit, then t passes the t-test.
Table 1 of § 1065.602_Critical t Values Versus Number of Degrees of
Freedom, ? \1\
------------------------------------------------------------------------
Confidence
? ---------------------
90% 95%
------------------------------------------------------------------------
1................................................. 6.314 12.706
2................................................. 2.920 4.303
3................................................. 2.353 3.182
4................................................. 2.132 2.776
5................................................. 2.015 2.571
6................................................. 1.943 2.447
7................................................. 1.895 2.365
8................................................. 1.860 2.306
9................................................. 1.833 2.262
10................................................ 1.812 2.228
11................................................ 1.796 2.201
12................................................ 1.782 2.179
13................................................ 1.771 2.160
14................................................ 1.761 2.145
15................................................ 1.753 2.131
16................................................ 1.746 2.120
18................................................ 1.734 2.101
20................................................ 1.725 2.086
22................................................ 1.717 2.074
24................................................ 1.711 2.064
26................................................ 1.706 2.056
28................................................ 1.701 2.048
30................................................ 1.697 2.042
35................................................ 1.690 2.030
40................................................ 1.684 2.021
50................................................ 1.676 2.009
70................................................ 1.667 1.994
100............................................... 1.660 1.984
1000+............................................. 1.645 1.960
------------------------------------------------------------------------
\1\ Use linear interpolation to establish values not shown here.
(g) F-test. Calculate the F statistic as follows:
Example:
F = 1.268
(1) For a 90% confidence F-test, use Table 2 of this section to compare F to the Fcrit90 values tabulated versus (N-1) and (Nref-1). If F is less than Fcrit90, then F passes the F-test at 90% confidence.
(2) For a 95% confidence F-test, use Table 3 of this section to compare F to the Fcrit95 values tabulated versus (N-1) and (Nref-1). If F is less than Fcrit95, then F passes the F-test at 95% confidence.
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View or download PDF
(h) Slope. Calculate a least-squares regression slope, a1y, as follows:
Example:
N = 6000
y1 = 2045.8
y = 1051.1
yref 1 = 2045.0
y ref = 1055.3
a1y = 1.0110
(i) Intercept. Calculate a least-squares regression intercept, a0y, as follows:
Example:
y = 1050.1
a1y = 1.0110
y ref = 1055.3
a0y = 1050.1 - (1.0110 · 1055.3)
a0y = -16.8083
(j) Standard estimate of error. Calculate a standard estimate of error, SEE, as follows:
Example:
N = 6000
y1 = 2045.8
a0y = -16.8083
a1y = 1.0110
yrefi= 2045.0
SEEy = 5.348
(k) Coefficient of determination. Calculate a coefficient of determination, r 2 , as follows:
Example:
N = 6000
y1 = 2045.8
a0y = -16.8083
a1y = 1.0110
yrefi = 2045.0
y = 1480.5
(l) Flow-weighted mean concentration. In some sections of this part, you may need to calculate a flow-weighted mean concentration to determine the applicability of certain provisions. A flow-weighted mean is the mean of a quantity after it is weighted proportional to a corresponding flow rate. For example, if a gas concentration is measured continuously from the raw exhaust of an engine, its flow-weighted mean concentration is the sum of the products of each recorded concentration times its respective exhaust molar flow rate, divided by the sum of the recorded flow rate values. As another example, the bag concentration from a CVS system is the same as the flow-weighted mean concentration because the CVS system itself flow-weights the bag concentration. You might already expect a certain flow-weighted mean concentration of an emission at its standard based on previous testing with similar engines or testing with similar equipment and instruments. If you need to estimate your expected flow-weighted mean concentration of an emission at its standard, we recommend using the following examples as a guide for how to estimate the flow-weighted mean concentration expected at the standard. Note that these examples are not exact and that they contain assumptions that are not always valid. Use good engineering judgement to determine if you can use similar assumptions.
(1) To estimate the flow-weighted mean raw exhaust NOX concentration from a turbocharged heavy-duty compression-ignition engine at a NOX standard of 2.5 g/(kW·hr), you may do the following:
(i) Based on your engine design, approximate a map of maximum torque versus speed and use it with the applicable normalized duty cycle in the standard-setting part to generate a reference duty cycle as described in §1065.610. Calculate the total reference work, Wref, as described in §1065.650. Divide the reference work by the duty cycle's time interval, ?tdutycycle, to determine mean reference power, P ref.
(ii) Based on your engine design, estimate maximum power, Pmax, the design speed at maximum power, fnmax, the design maximum intake manifold boost pressure, pinmax, and temperature, Tinmax. Also, estimate a mean fraction of power that is lost due to friction and pumping, P frict. Use this information along with the engine displacement volume, Vdisp, an approximate volumetric efficiency, ?V, and the number of engine strokes per power stroke (2-stroke or 4-stroke), Nstroke to estimate the maximum raw exhaust molar flow rate, n exhmax.
(iii) Use your estimated values as described in the following example calculation:
Example:
eNOX = 2.5 g/(kW · hr)
Wref = 11.883 kW · hr
MNOX = 46.0055 g/mol = 46.0055 · 10-6 g/µmol
?tdutycycle = 20 min = 1200 s
P ref = 35.65 kW
P frict = 15%
Pmax = 125 kW
pmax = 300 kPa = 300000 Pa
Vdisp = 3.011 = 0.0030 m 3
fnmax = 2800 rev/min = 46.67 rev/s
Nstroke = 4 1/rev
?V = 0.9
R = 8.314472 J/(mol·K)
Tmax = 348.15 K
n exhmax = 6.53 mol/s
x exp = 189.4 µmol/mol
(2) To estimate the flow-weighted mean NMHC concentration in a CVS from a naturally aspirated nonroad spark-ignition engine at an NMHC standard of 0.5 g/(kW·hr), you may do the following:
(i) Based on your engine design, approximate a map of maximum torque versus speed and use it with the applicable normalized duty cycle in the standard-setting part to generate a reference duty cycle as described in §1065.610. Calculate the total reference work, Wref, as described in §1065.650.
(ii) Multiply your CVS total molar flow rate by the time interval of the duty cycle, ?tdutycycle. The result is the total diluted exhaust flow of the ndexh.
(iii) Use your estimated values as described in the following example calculation:
Example:
eNMHC = 1.5 g/(kW·hr)
Wref = 5.389 kW·hr
MNMHC = 13.875389 g/mol = 13.875389 · 10-6 g/µmol
n dexh = 6.021 mol/s
?tdutycycle = 30 min = 1800 s
x NMHC = 53.8 µmol/mol
§ 1065.610 Duty cycle generation.
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This section describes how to generate duty cycles that are specific to your engine, based on the normalized duty cycles in the standard-setting part. During an emission test, use a duty cycle that is specific to your engine to command engine speed, torque, and power, as applicable, using an engine dynamometer and an engine operator demand. Paragraph (a) of this section describes how to “normalize” your engine's map to determine the maximum test speed and torque for your engine. The rest of this section describes how to use these values to “denormalize” the duty cycles in the standard-setting parts, which are all published on a normalized basis. Thus, the term “normalized” in paragraph (a) of this section refers to different values than it does in the rest of the section.
(a) Maximum test speed, fntest. This section generally applies to duty cycles for variable-speed engines. For constant-speed engines subject to duty cycles that specify normalized speed commands, use the no-load governed speed as the measured fntest. This is the highest engine speed where an engine outputs zero torque. For variable-speed engines, determine the measured fntest from the power-versus-speed map, generated according to §1065.510, as follows:
(1) Based on the map, determine maximum power, Pmax, and the speed at which maximum power occurred, fnPmax. Divide every recorded power by Pmax and divide every recorded speed by fnPmax. The result is a normalized power-versus-speed map. Your measured fntest is the speed at which the sum of the squares of normalized speed and power is maximum, as follows:
Where:
fntest = maximum test speed.
i = an indexing variable that represents one recorded value of an engine map.
fnnormi = an engine speed normalized by dividing it by fnPmax.
Pnormi = an engine power normalized by dividing it by Pmax.
Example:
(fnnorm1 = 1.002, Pnorm1 = 0.978, fn1 = 2359.71)
(fnnorm2 = 1.004, Pnorm2 = 0.977, fn2 = 2364.42)
(fnnorm3 = 1.006, Pnorm3 = 0.974, fn3 = 2369.13)
(fnnorm1 2 + Pnorm1 2 ) = (1.002 2 + 0.978 2 ) = 1.960
(fnnorm1 2 + Pnorm1 2 ) = (1.004 2 + 0.977 2 ) = 1.963
(fnnorm1 2 + Pnorm1 2 ) = (1.006 2 + 0.974 2 ) = 1.961
maximum = 1.963 at i = 2
fntest = 2364.42 rev/min
(2) For variable-speed engines, transform normalized speeds to reference speeds according to paragraph (c) of this section by using the measured maximum test speed determined according to paragraph (a)(1) of this section—or use your declared maximum test speed, as allowed in §1065.510.
(3) For constant-speed engines, transform normalized speeds to reference speeds according to paragraph (c) of this section by using the measured no-load governed—speed or use your declared maximum test speed, as allowed in §1065.510.
(b) Maximum test torque, Ttest. For constant-speed engines, determine the measured Ttest from the power-versus-speed map, generated according to §1065.510, as follows:
(1) Based on the map, determine maximum power, Pmax, and the speed at which maximum power occurs, fnPmax. Divide every recorded power by Pmax and divide every recorded speed by fnPmax. The result is a normalized power-versus-speed map. Your measured Ttest is the speed at which the sum of the squares of normalized speed and power is maximum, as follows:
Where:
Ttest = maximum test torque.
Example:
(fnnorm1 = 1.002, Pnorm1 = 0.978, T1 = 722.62 N · m)
(fnnorm2 = 1.004, Pnorm2 = 0.977, T2 = 720.44 N · m)
(fnnorm3 = 1.006, Pnorm3 = 0.974, T3 = 716.80 N · m)
(fnnorm1 2 + Pnorm1 2 ) = (1.0022 + 0.9782) = 1.960
(fnnorm1 2 + Pnorm1 2 ) = (1.004 2 + 0.977 2 ) = 1.963
(fnnorm1 2 + Pnorm1 2 ) = (1.006 2 + 0.974 2 ) = 1.961
maximum = 1.963 at i = 2
Ttest = 720.44 Nm
(2) Transform normalized torques to reference torques according to paragraph (d) of this section by using the measured maximum test torque determined according to paragraph (b)(1) of this section—or use your declared maximum test torque, as allowed in §1065.510.
(c) Generating reference speed values from normalized duty cycle speeds. Transform normalized speed values to reference values as follows:
(1) % speed. If your normalized duty cycle specifies % speed values, use your declared warm idle speed and your maximum test speed to transform the duty cycle, as follows:
Example:
% speed = 85 %
fntest = 2364 rev/min
fnidle = 650 rev/min
fnref = 85 % · (2364 650 ) + 650
fnref = 2107 rev/min
(2) A, B, and C speeds. If your normalized duty cycle specifies speeds as A, B, or C values, use your power-versus-speed curve to determine the lowest speed below maximum power at which 50 % of maximum power occurs. Denote this value as nlo. Also determine the highest speed above maximum power at which 70 % of maximum power occurs. Denote this value as nhi Use nhi and nlo to calculate reference values for A, B, or C speeds as follows:
Example:
nlo = 1005 rev/min
nhi = 2385 rev/min
fnrefA = 0.25 · (2385 1005) + 1005
fnrefB = 0.50 · (2385 1005) + 1005
fnrefC = 0.75 · (2385 1005) + 1005
fnrefA = 1350 rev/min
fnrefB = 1695 rev/min
fnrefC = 2040 rev/min
(3) Intermediate speed. If your normalized duty cycle specifies a speed as “intermediate speed,” use your torque-versus-speed curve to determine the speed at which maximum torque occurs. This is peak torque speed. Identify your reference intermediate speed as one of the following values:
(i) Peak torque speed if it is between (60 and 75) % of maximum test speed.
(ii) 60% of maximum test speed if peak torque speed is less than 60% of maximum test speed.
(iii) 75% of maximum test speed if peak torque speed is greater than 75% of maximum test speed.
(d) Generating reference torques from normalized duty-cycle torques. Transform normalized torques to reference torques using your map of maximum torque versus speed.
(1) Reference torque for variable-speed engines. For a given speed point, multiply the corresponding % torque by the maximum torque at that speed, according to your map. Linearly interpolate mapped torque values to determine torque between mapped speeds. The result is the reference torque for each speed point.
(2) Reference torque for constant-speed engines. Multiply a % torque value by your maximum test torque. The result is the reference torque for each point. Note that if your constant-speed engine is subject to duty cycles that specify normalized speed commands, use the provisions of paragraph (d)(1) of this section to transform your normalized torque values.
(3) Permissible deviations for any engine. If your engine does not operate below a certain minimum torque under normal in-use conditions, you may use a declared minimum torque as the reference value instead of any value denormalized to be less than the declared value. For example, if your engine is connected to an automatic transmission, it may have a minimum torque called curb idle transmission torque (CITT). In this case, at idle conditions (i.e., 0% speed, 0% torque), you may use CITT as a reference value instead of 0 N·m.
(e) Generating reference power values from normalized duty cycle powers. Transform normalized power values to reference speed and power values using your map of maximum power versus speed.
(continued)