# Title 40

## SECTION 1065.610

### 1065.610 Duty cycle generation.

§ 1065.610 Duty cycle generation.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, f*ntest. 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 *f*ntest. This is the highest engine speed where an
engine outputs zero torque. For variable-speed engines, determine
*f*ntest as follows:

(1) Develop a measured value for *f*ntest as follows:

(i) Determine maximum power, *P*max, from the engine map
generated according to § 1065.510 and calculate the value for power
equal to 98% of *P*max.

(ii) Determine the lowest and highest engine speeds
corresponding to 98% of *P*max, using linear interpolation,
and no extrapolation, as appropriate.

(iii) Determine the engine speed corresponding to maximum power,
*f*nPmax, by calculating the average of the two speed values
from paragraph (a)(1)(ii) of this section. If there is only one
speed where power is equal to 98% of *P*max, take
*f*nPmax as the speed at which *P*max occurs.

(iv) Transform the map into a normalized power-versus-speed map
by dividing power terms by *P*max and dividing speed terms by
*f*nPmax. Use the following equation to calculate a quantity
representing the sum of squares from the normalized map:

(v) Determine the maximum value for the sum of the squares from the map and multiply that value by 0.98.

(vi) Determine the lowest and highest engine speeds
corresponding to the value calculated in paragraph (a)(1)(v) of
this section, using linear interpolation as appropriate. Calculate
*f*ntest as the average of these two speed values. If there is
only one speed corresponding to the value calculated in paragraph
(a)(1)(v) of this section, take *f*ntest as the speed where
the maximum of the sum of the squares occurs.

(vii) The following example illustrates a calculation of
*f*ntest:

*P*max = 230.0

*f*n1 = 2360,

*P*1 = 222.5,

*f*nnorm1 = 1.002,

*P*norm1 = 0.9675) (

*f*n2 = 2364,

*P*2 = 226.8,

*f*nnorm2 = 1.004,

*P*norm2 = 0.9859) (

*f*n3 = 2369,

*P*3 = 228.6,

*f*nnorm3 = 1.006,

*P*norm3 = 0.9940) (

*f*n4 = 2374,

*P*4 = 218.7,

*f*nnorm4 = 1.008,

*P*norm4 = 0.9508) Sum of squares = (1.002 2 + 0.9675 2) = 1.94 Sum of squares = (1.004 2 + 0.9859 2) = 1.98 Sum of squares = (1.006 2 + 0.9940 2) = 2.00 Sum of squares = (1.008 2 + 0.9508 2) = 1.92

(2) For engines with a high-speed governor that will be subject
to a reference duty cycle that specifies normalized speeds greater
than 100%, calculate an alternate maximum test speed,
*f*ntest,alt, as specified in this paragraph (a)(2). If
*f*ntest,alt is less than the measured maximum test speed,
*f*ntest, determined in paragraph (a)(1) of this section,
replace *f*ntest with *f*ntest,alt. In this case,
*f*ntest,alt becomes the “maximum test speed” for that engine.
Note that § 1065.510 allows you to apply an optional declared
maximum test speed to the final measured maximum test speed
determined as an outcome of the comparison between *f*ntest,
and *f*ntest,alt in this paragraph (a)(2). Determine
*f*ntest,alt as follows:

*f*ntest,alt = alternate maximum test speed

*f*nhi,idle = warm high-idle speed

*f*nidle = warm idle speed

*% speed*max = maximum normalized speed from duty cycle Example:

*f*nhi,idle = 2200 r/min

*f*nidle = 800 r/min

*f*ntest,alt = 2133 r/min

(3) 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 paragraphs (a)(1) and (2) of this section - or use your declared maximum test speed, as allowed in § 1065.510.

(4) 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, T*test. For constant-speed
engines, determine the measured *T*test from the torque and
power-versus-speed maps, generated according to § 1065.510, as
follows:

(1) For constant speed engines mapped using the methods in §
1065.510(d)(5)(i) or (ii), determine *T*test as follows:

(i) Determine maximum power, *P*max, from the engine map
generated according to § 1065.510 and calculate the value for power
equal to 98% of *P*max.

(ii) Determine the lowest and highest engine speeds
corresponding to 98% of *P*max, using linear interpolation,
and no extrapolation, as appropriate.

(iii) Determine the engine speed corresponding to maximum power,
*f*nPmax, by calculating the average of the two speed values
from paragraph (a)(1)(ii) of this section. If there is only one
speed where power is equal to 98% of *P*max, take
*f*nPmax as the speed at which *P*max occurs.

(iv) Transform the map into a normalized power-versus-speed map
by dividing power terms by *P*max and dividing speed terms by
*f*nPmax. Use Eq. 1065.610-1 to calculate a quantity
representing the sum of squares from the normalized map.

(v) Determine the maximum value for the sum of the squares from the map and multiply that value by 0.98.

(vi) Determine the lowest and highest engine speeds
corresponding to the value calculated in paragraph (a)(1)(v) of
this section, using linear interpolation as appropriate. Calculate
*f*ntest as the average of these two speed values. If there is
only one speed corresponding to the value calculated in paragraph
(a)(1)(v) of this section, take *f*ntest as the speed where
the maximum of the sum of the squares occurs.

(vii) The measured *T*test is the mapped torque at
*f*ntest.

(2) For constant-speed engines using the two-point mapping
method in § 1065.510(d)(5)(iii), you may follow paragraph (a)(1) of
this section to determine the measured *T*test, or you may use
the measured torque of the second point as the measured
*T*test directly.

(3) 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 warm idle speed and your maximum test speed
to transform the duty cycle, as follows:

*% speed*= 85% = 0.85

*f*ntest = 2364 r/min

*f*nidle = 650 r/min

*f*nref = 0.85 • (2364−650) + 650

*f*nref = 2107 r/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 *n*lo. Take
*n*lo to be warm idle speed if all power points at speeds
below the maximum power speed are higher than 50% of maximum power.
Also determine the highest speed above maximum power at which 70%
of maximum power occurs. Denote this value as *n*hi. If all
power points at speeds above the maximum power speed are higher
than 70% of maximum power, take *n*hi to be the declared
maximum safe engine speed or the declared maximum representative
engine speed, whichever is lower. Use *n*hi and *n*lo to
calculate reference values for A, B, or C speeds as follows:

*n*lo = 1005 r/min

*n*hi = 2385 r/min

*f*nrefA = 0.25 • (2385−1005) + 1005

*f*nrefB = 0.50 • (2385−1005) + 1005

*f*nrefC = 0.75 • (2385−1005) + 1005

*f*nrefA = 1350 r/min

*f*nrefB = 1695 r/min

*f*nrefC = 2040 r/min

(3) *Intermediate speed.* Based on the map, determine
maximum torque, *T*max, and the corresponding speed,
*f*nTmax, calculated as the average of the lowest and highest
speeds at which torque is equal to 98% of *T*max. Use linear
interpolation between points to determine the speeds where torque
is equal to 98% of *T*max. Identify your reference
intermediate speed as one of the following values:

(i) *f*nTmax if it is between (60 and 75) % of maximum test
speed.

(ii) 60% of maximum test speed if *f*nTmax is less than 60%
of maximum test speed.

(iii) 75% of maximum test speed if *f*nTmax 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. If your engine
is subject to a reference duty cycle that specifies negative torque
values (*i.e.*, engine motoring), use negative torque for
those motoring points (*i.e.*, the motoring torque). If you
map negative torque as allowed under § 1065.510 (c)(2) and the
low-speed governor activates, resulting in positive torques, you
may replace those positive motoring mapped torques with negative
values between zero and the largest negative motoring torque. For
both maximum and motoring torque maps, linearly interpolate mapped
torque values to determine torque between mapped speeds. If the
reference speed is below the minimum mapped speed (*i.e.*, 95%
of idle speed or 95% of lowest required speed, whichever is
higher), use the mapped torque at the minimum mapped speed as the
reference torque. 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.

(3) *Required deviations.* We require the following
deviations for variable-speed engines intended primarily for
propulsion of a vehicle with an automatic transmission where that
engine is subject to a transient duty cycle with idle operation.
These deviations are intended to produce a more representative
transient duty cycle for these applications. For steady-state duty
cycles or transient duty cycles with no idle operation, these
requirements do not apply. Idle points for steady state duty cycles
of such engines are to be run at conditions simulating neutral or
park on the transmission.

(i) Zero-percent speed is the warm idle speed measured according
to § 1065.510(b)(6) with CITT applied, *i.e.*, measured warm
idle speed in drive.

(ii) If the cycle begins with a set of contiguous idle points (zero-percent speed, and zero-percent torque), leave the reference torques set to zero for this initial contiguous idle segment. This is to represent free idle operation with the transmission in neutral or park at the start of the transient duty cycle, after the engine is started. If the initial idle segment is longer than 24 seconds, change the reference torques for the remaining idle points in the initial contiguous idle segment to CITT (i.e., change idle points corresponding to 25 seconds to the end of the initial idle segment to CITT). This is to represent shifting the transmission to drive.

(iii) For all other idle points, change the reference torque to CITT. This is to represent the transmission operating in drive.

(iv) If the engine is intended primarily for automatic
transmissions with a Neutral-When-Stationary feature that
automatically shifts the transmission to neutral after the vehicle
is stopped for a designated time and automatically shifts back to
drive when the operator increases demand (*i.e.*, pushes the
accelerator pedal), change the reference torque back to zero for
idle points in drive after the designated time.

(v) For all points with normalized speed at or below zero percent and reference torque from zero to CITT, set the reference torque to CITT. This is to provide smoother torque references below idle speed.

(vi) For motoring points, make no changes.

(vii) For consecutive points with reference torques from zero to CITT that immediately follow idle points, change their reference torques to CITT. This is to provide smooth torque transition out of idle operation. This does not apply if the Neutral-When-Stationary feature is used and the transmission has shifted to neutral.

(viii) For consecutive points with reference torque from zero to CITT that immediately precede idle points, change their reference torques to CITT. This is to provide smooth torque transition into idle operation.

(4) *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 a
hydrostatic transmission and it has a minimum torque even when all
the driven hydraulic actuators and motors are stationary and the
engine is at idle, then you may use this declared minimum torque as
a reference torque value instead of any reference torque value
generated under paragraph (d)(1) or (2) of this section that is
between zero and this declared minimum torque.

(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.

(1) First transform normalized speed values into reference speed
values. For a given speed point, multiply the corresponding % power
by the mapped power at maximum test speed, *f*ntest, unless
specified otherwise by the standard-setting part. The result is the
reference power for each speed point, *P*ref. Convert these
reference powers to corresponding torques for operator demand and
dynamometer control and for duty cycle validation per 1065.514. Use
the reference speed associated with each reference power point for
this conversion. As with cycles specified with % torque, linearly
interpolate between these reference torque values generated from
cycles with % power.

(2) Permissible deviations for any engine. If your engine does not operate below a certain power under normal in-use conditions, you may use a declared minimum power as the reference value instead of any value denormalized to be less than the declared value. For example, if your engine is directly connected to a propeller, it may have a minimum power called idle power. In this case, you may use this declared minimum power as a reference power value instead of any reference power value generated per paragraph (e)(1) of this section that is from zero to this declared minimum power.

[73 FR 37324, June 30, 2008, as amended at 73 FR 59330, Oct. 8, 2008; 75 FR 23045, Apr. 30, 2010; 76 FR 57453, Sept. 15, 2011; 78 FR 36398, June 17, 2013; 79 FR 23783, Apr. 28, 2014; 80 FR 9118, Feb. 19, 2015; 81 FR 74170, Oct. 25, 2016]