Xin Q. Diesel Engine System Design

368 Diesel engine system design

anchor points are connected to form the characteristic curves such as the

gear lines in the engine speed–load domain. Then, at a given vehicle speed,

the vehicle operating point can be visually selected at a preferred gear, and

the corresponding engine speed can be graphically determined. The selected

engine speed is used in the engine speed–load domain to intersect with the

selected gear line. Then the intersection point is the mapped condition of

the running vehicle on the engine map. It should be noted that when the

drivetrain condition changes, the ‘ZWB’ points also change.

A more powerful matching approach is shown in Fig. 5.9 where the vehicle

speed curves, gear lines and for a selected drivetrain or road condition are

computed and superpositioned on various engine performance maps. Figure

5.10 shows the rear axle lines and road grade lines on the engine BSFC

map. The driving points can be conveniently selected on the engine maps by

considering all the performance characteristics, such as BSFC, air–fuel ratio

smoke limit, power reserve for acceleration, emissions, etc. Moreover, it is

noted that the engine map domain may be viewed as a ‘distorted coordinate’

domain of the transmission shift map (i.e., accelerator pedal position vs.

vehicle speed in Fig. 5.11, compared to Fig. 5.9). Once the transmission shift

schedules are visually located on the engine maps based on all the trade-offs,

the transmission shift map can be directly ‘computed’ with mathematical

coordinate transformation conveniently. Such an analytical method of

engine–transmission matching is more advanced than the traditional ‘trial-

and-error’ approach of generating the transmission shift map.

With this advanced analytical technique of engine–vehicle matching,

drivetrain design parameters and engine–transmission matching can be

evaluated as a part of engine system design. The calculated vehicle operating

characteristics marked on the engine maps provide guidance from vehicle

driving requirements to engine design and testing.

5.3 Powertrain/drivetrain dynamics and transient

performance simulation

5.3.1 Theoretical analysis of transient powertrain

dynamics

Transient powertrain simulation is important for both understanding engine

transient behavior and calculating the cycle-composite fuel economy and

emissions of vehicle driving cycles or engine speed–load certication test

cycles. Taking the time derivative of equation 5.6, the engine acceleration

(i.e., dN

E

/dt) can be obtained as a function of vehicle acceleration (i.e.,

dN

v

/dt) and a time derivative of the transient gear ratio (i.e., di

gr

/dt). In the

derivation below, the transient gear ratio effect is neglected for simplicity.

By substituting equations 5.3, 5.8 and the time derivative of 5.6 into 5.1,

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Engine brake torque

Brake power (hp) BSFC (lb/(hp.hr))

This curve is full pedal

Gear 7

Gear 7 Gear 7

Gear 6

Gear 5

Gear 4

Gear 4 Gear 4

Gear 4

80 mph

63 mph

51 mph

Engine speed

Brake speciﬁc soot (g/(hp.hr)) Air–fuel ratio

Engine speed Engine speed

Engine speed 1 mph = 1.609 km/hr

51 mph

200

150

100

50

0.8

0.6

0.4

0.2

0

–0.2

50

40

30

20

–10

2

1.5

1

0.5

This constant power curve is also

basically constant-vehicle speed curve.

Gear 7

5.9 Engine–vehicle matching method with engine performance characteristic maps.

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370 Diesel engine system design

equation 5.20 is derived as an ordinary differential equation to solve for

the transient engine speed N

E

when a transient engine tractive torque J

E

is

produced (see equation 5.3 on how to relate engine brake torque to vehicle

tractive torque):

Engine brake torque

40 mph

level

ground

RAR = 3.70

RAR = 4.11

Engine speed

Rated speed

40 mph

6% uphill

Note: The curves are ﬁrst-

order linear approximation.

BSFC (lb/(hp.hr))

60 mph

6% uphill

Gear 6

Gear 5

Gear 6

1

0.9

0.8

0.7

0.6

0.5

0.4

Gear 6 RAR = 3.70

Gear 6 RAR = 4.11

Gear 5 RAR = 3.70

Gear 5 RAR = 4.11

Gear 4

60 mph

level ground

5.10 Engine–vehicle matching for different road grades.

Accelerator pedal position

Full

load

No

load

Vehicle speed

1 2

2 3

3 4

4 5

3 4 4 5

5.11 Illustration of transmission shift schedule map.

Gear 5

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371Engine–vehicle matching in diesel powertrain system design

I

N

t

rF

FF

Fm

a

E

tir

rF

tir

rF

et

rF

et

rF

er

ac

FF

ac

FF

cb

rr

FF

rr

FF

fa

rrfarr

gl

FF

gl

FF

dr

Fm

dr

Fm

v

d

NdN

d

=

++

FF++FF

FF

er

FF++FF

er

FF

++

FF++FF

cb

++

cb

FF

cb

FF++FF

cb

FF

rr

FF++FF

rr

FF

++

FF++FF

fa

++

fa

FF

fa

FF++FF

fa

FF

+–

Fm+–Fm

Fm

dr

Fm+–Fm

dr

Fm

vvv

dr

iv

e

tir

e

v

gr

tT

vs

tTvstT

lip

I

r

tir

r

tir

a

ii

f

vs

f

vs

–

(

vs

(

vs

1 –

vs

1 –

vs

)

2

Ê

rF

Ê

rF

Ë

rF

Ë

rF

et

Ë

et

rF

et

rF

Ë

rF

et

rF

Á

rF

Ê

rF

Á

rF

Ê

rF

Ë

Á

Ë

rF

Ë

rF

Á

rF

Ë

rF

et

Ë

et

Á

et

Ë

et

rF

et

rF

Ë

rF

et

rF

Á

rF

et

rF

Ë

rF

et

rF

ˆ

¯

˜

ˆ

˜

ˆ

¯

˜

¯

2

ph

gr

ph

gr

ax

ph

ax

ii

ph

ii

gr

ii

gr

ph

gr

ii

gr

h

tT

h

tT

5.20

All the terms in equation 5.20 are in the transient state and can be modeled

in further detail. The tractive force F

t

is produced by engine torque. Transient

engine torque can be modeled in one of the following methods: (1) empirical

formula; (2) model-based formula; (3) mapped engine model; (4) mean-value

cylinder model; or (5) high- delity crank-angle-resolution engine cycle

simulation model. The last two methods may contain a smoke limiter, turbo

lag effect, and transient engine control strategies. Diesel engine transient

torque characteristics are shown in Fig. 5.7. The available transient torque

level depends strongly on how fast the transient event is.

5.3.2 Vehicle driving cycle simulation

In vehicle driving cycle simulations, a vehicle speed schedule as a function

of time is imposed as input, and transient engine torque (or retarding torque

or vehicle braking torque) and engine speed are computed to try to meet the

vehicle speed and load requirements imposed by the vehicle speed schedule

and the gear-shifting schedule, unless the imposed transient change of the

vehicle speed is unrealistic or too fast. Once the engine’s speed and load

state is obtained, fuel consumption and emissions can be calculated either by

using a high- delity engine cycle simulation model or by using the engine

BSFC and emission maps.

Figure 5.12 shows the US EPA FTP emissions certi cation schedule

mapped on the engine map for a heavy-duty diesel engine. It is observed

that for heavy-duty engine certi cations the high speed and high load

engine operation occupies a major portion of the FTP transient cycle. Figure

5.13 shows the vehicle speed schedules of the highway fuel economy test

(HWFET) driving cycle and the HD-UDDS driving cycle. Figure 5.13 also

shows the GT-DRIVE simulation results of a heavy-duty Class-8 truck in

these two driving cycles. It is observed that the truck stays much more

time in the region of medium/high loads in the HWFET cycle than in the

lighter duty HD-UDDS cycle. Obviously, the engine design and calibration

strategies for these two different vehicle applications should be optimized

differently. Figure 5.14 illustrates some other commonly used driving cycles

for heavy-duty and light-duty applications. Figures 5.15–5.17 illustrate the

GT-DRIVE simulation results of a medium-duty truck operating in three

different driving cycles: the city route, the suburban route, and the highway

route. It is observed that the city route application gives the lowest engine

load factors, and the highway route demands the engine operate at high speed

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372 Diesel engine system design

and high load for a long period of time. Again, engine design and calibration

should be optimized differently to suit these different applications for this

medium-duty truck. Figure 5.18 shows the driving cycle transient simulation

of a light-duty truck in the engine speed–load domain. It is observed that,

unlike the heavy-duty applications, the light-duty engine mainly operates at

low speeds/loads due to the low vehicle weight. The rated power condition

is only encountered during fast acceleration or high-road-grade operation in

light-duty applications.

5.3.3 Vehicle acceleration simulation

In vehicle full-pedal acceleration simulations, step-fueling and a transmission

gear shift schedule can be imposed as input. Transient engine speed and

vehicle speed can be computed as a function of time.

Figure 5.19 shows a GT-DRIVE simulation of a light-duty truck during

transient full-pedal acceleration from standstill. The rear axle ratio study in

Fig. 5.19 shows that the larger rear axle ratio gives faster vehicle acceleration.

The vehicle weight effect study in Fig. 5.19 illustrates that the vehicle weight

has a paramount impact on acceleration time.

The effect of engine displacement on powertrain transient acceleration is

illustrated in Fig. 5.20. It is observed that in this light-duty truck example

A speed

B speed

C speed

FTP cycle

Lug curve

13 modes

500 1000 1500 2000 2500 3000

Engine speed (rpm)

Engine brake torque (ft.lb)

700

600

500

400

300

200

100

0

5.12 Illustration of SET and FTP operating points on HD diesel engine

speed–load map.

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HWFET cycle

Target Speed

HD-UDDS cycle

Target Speed

Speed (km/hr)

100

80

60

40

20

0

100

80

60

40

20

0

0 153 306 459 612 765

Time (sec)

0 212 424 636 848 1060

Time (sec)

Time (%)

10

8

6

4

2

0

20

15

10

5

0

Speed (rpm)

Torque (ft.lb)

600

800

1000

1200

1400

1600

1800

1900

1500

1100

700

300

–100

Percentage of time spent during HWFET cycle Percentage of time spent during HD-UDDS cycle

5.13 Heavy-duty Class-8 truck driving cycle simulation.

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Vehicle speed (km/h)Vehicle speed (km/h)Vehicle speed (km/h)

Vehicle speed (km/h) Vehicle speed (km/h)

Vehicle speed (km/h)

150

100

50

0

150

100

50

0

150

100

50

0

150

100

50

0

150

100

50

0

150

100

50

0

City route

Suburban route

Highway route HWFET

(Note: The cycle is repeated for two times.)

US06

(Note: The cycle is repeated for three times.)

FTP 75

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000

Time (second)

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000

Time (second)

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000

Time (second)

0 500 1000 1500 2000

Time (second)

0 500 1000 1500 2000

Time (second)

0 500 1000 1500 2000

Time (second)

5.14 Illustration of commonly used driving cycles.

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375Engine–vehicle matching in diesel powertrain system design

the 8.3% reduction in engine displacement from 4.8 L to 4.4 L makes a

signicant difference on the vehicle acceleration trajectory mapped in the

engine speed–load domain. The 4.4 L diesel engine takes about 0.3 seconds

longer than the 4.8 L engine to reach 30 mph from standstill (i.e., 3.7 seconds

compared to 3.4 seconds) due to its inferior natural aspiration capability at

the beginning of the acceleration.

Engine brake torque (ft.lb)

700

600

500

400

300

200

100

0

–100

–200

These modes should

be calibrated for

better BSFC by

relaxing emissions

constraints

Engine steady state points

13 mode points

Engine lug curve

Engine speed (rpm)

Time history of engine operating points

0 500 1000 1500 2000 2500 3000

Time spent (sec)

600

500

400

300

200

100

0

700

900

1100

1300

1500

1700

1900

2100

2300

2500

Engine speed (rpm)

80

260

440

620

Engine brake

torque (ft.lb)

5.15 Medium-duty truck driving cycle simulation – city route.

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376 Diesel engine system design

5.3.4 Integrated vehicle–engine driving simulation for

system design

Figure 5.21 demonstrates a simulation capability for a long and slow transient

driving route at high altitude uphill climbing coupled with engine coolant-

induced power derating for a heavy-duty truck. Such a vehicle driving

Engine brake torque (ft.lb)

700

600

500

400

300

200

100

0

–100

–200

These modes should

be calibrated for

better BSFC by

relaxing emissions

constraints

Engine steady state points

13 mode points

Engine lug curve

Engine speed (rpm)

Time history of engine operating points

0 500 1000 1500 2000 2500 3000

Time spent (sec)

600

500

400

300

200

100

0

700

900

1100

1300

1500

1700

1900

2100

2300

2500

Engine speed (rpm)

80

260

440

620

Engine brake

torque (ft.lb)

5.16 Medium-duty truck driving cycle simulation – suburban route.

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377Engine–vehicle matching in diesel powertrain system design

simulation coupled with the engine model is a very valuable tool to assess

the engine derating requirement for coolant heat rejection control. Heavy-

duty trucks usually encounter the most severe condition on the radiator

inlet coolant temperature in high-altitude hot-climate operation due to the

deterioration of the vehicle cooling system with the lower-density cooling

Engine brake torque (ft.lb)

700

600

500

400

300

200

100

0

These modes should

be calibrated for

better BSFC if

possible

Engine steady state points

13 mode points

Engine lug curve

Engine speed (rpm)

Time history of engine operating points

0 500 1000 1500 2000 2500 3000

Time spent (sec)

6000

5000

4000

3000

2000

1000

0

700

900

1100

1300

1500

1700

1900

2100

2300

2500

Engine speed (rpm)

80

260

440

620

Engine brake

torque (ft.lb)

5.17 Medium-duty truck driving cycle simulation – highway route.

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Xin Q. Diesel Engine System Design

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