Xin Q. Diesel Engine System Design

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358 Diesel engine system design

(2000), Millo et al. (2000), McManus and Anderson (2001), Regner et al.

(2002), Callahan et al. (2003), Giannelli et al. (2005), Montazeri-Gh et al.

(2005), Wehrwein and Mourelatos (2005), and Pagerit et al. (2006).

5.2.2 Drivability and drivetrain design parameters

The application scope of the vehicle application determines the design limits

of the drivetrain. The vehicle tractive power requirements (



WF =WF

) are

best explained in Fig. 5.1. The entire domain is formed by a family of

constant-power curves. The ideal characteristic is a constant power over the

full vehicle speed range because it provides the vehicle with a high tractive

force at a low speed where the demands for grade climbing and acceleration

are high. To achieve superior vehicle performance, fuel economy, and

emissions, the drivetrain parameters must be optimized together with the

engine torque curve.

Final drive gears are used in driven axles and transaxles to transmit torque

from the gearbox output shaft to the driven wheels through a constant gear

reduction in order to keep the wheel size practical. The  nal drive ratio

(also known as the drive axle ratio) is de ned as the ratio of the number of

teeth on the crown wheel of the bevel drive to the number of teeth on the

bevel pinion. The drive axle ratio is determined based on the best trade-off

between acceleration time and vehicle fuel economy. The minimum drivetrain

transfer ratio (i

)

min

at the highest (top) transmission gear and the engine

torque J

should be designed together to ensure the combined term J

can overcome the minimum resistance forces at the maximum vehicle

design speed. It should be noted that only rolling friction and aerodynamic

resistance are considered when the vehicle is on level ground. The (i

)

min

is determined mainly by the drive axle ratio. From a power perspective, once

the maximum vehicle speed target is speci ed, the required engine power can

be calculated using equation 5.15. The selection of the minimum drivetrain

ratio is based on an optimized compromise between the engine speed and the

torque at a  xed power (



WJ =WJ

). The choice of engine speed depends

on engine design factors such as mechanical friction and diesel combustion

quality at high speeds. The maximum vehicle speed target should be high

enough to ensure the vehicle can have certain power in reserve to climb an

upgrade or accelerate at a lower normal driving speed in the highest gear.

Another important analysis in the selection of the rear axle ratio is to conduct

a sensitivity calculation to analyze its effect on vehicle fuel economy and

acceleration ability, then choose the best trade-off from the so-called ‘C

shape’ curve (Chana et al., 1977; Wong and Clemens, 1979).

The engine speed at the maximum vehicle speed depends on the drivetrain

matching strategy. The traditional strategy is to match the engine speed at

the right side of the engine rated speed (i.e., where the rated or the maximum

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359Engine–vehicle matching in diesel powertrain system design

power occurs, Fig. 5.5) in order to favor a power reserve at the expense of

fuel consumption. Alternatively, the engine speed can be matched to locate

at the left side of the engine rated speed in order to reduce fuel consumption

but sacrice the power reserve. A third option is to match the engine speed

just at the rated speed. Engine rated power is determined from the above

drivetrain-matching considerations. The diesel engine’s maximum speed is

determined by three factors: (1) mechanical limitations such as valvetrain

separation and the high reciprocating inertia forces of the heavy components;

(2) the rapidly increasing friction at high speeds; and (3) the time required

to complete the combustion process of the diesel fuel. High-speed governors

are used to rapidly reduce the fueling amount in order to steeply reduce the

brake torque from a speed slightly above the rated speed to the high-idle

speed.

Engine rated power requirement is determined by the maximum vehicle

speed at an acceptable uphill road grade. If the road grade is set at zero, it is

the special case of level ground mentioned above. In the drivetrain matching

for light-weight cars, level ground analysis is commonly used. However, for

heavy trucks, certain uphill road grade target is usually used to determine

the engine rated power requirement.

Engine rated speed is determined by the following considerations. A

higher rated speed provides a wider span of the engine speed range from peak

torque to rated power so that fewer transmission gears can be used to cover

a vehicle speed range for better drivability. Vehicle acceleration can also be

Engine lug curve at top gear with RAR = 3.11

Engine lug curve at top gear with RAR = 3.41

Engine lug curve at top gear with RAR = 3.93

At an uphill road grade,

the vehicle resistance

curve moves up, and

higher engine rated

power is required.

Total vehicle resistance

power (rolling friction

plus aerodynamic

resistance)

Power

reserve

Vehicle power

0 10 20 30 40 50 60 70 80 90 100 110

Vehicle speed (mph)

5.5 Integrated design of engine and drivetrain for rated power/speed

matching.

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360 Diesel engine system design

faster, as reected by a smaller area enveloped under the ‘1/a curve’ shown

in Fig. 5.2. On the other hand, a lower rated speed generally enables lower

emissions on the heavy-duty FTP transient cycle, lower BSFC and lower

engine noise at high speeds. Engine brake specic soot emission is usually

much higher and more difcult to control at the ‘C speed’ (the higher speed

in the 13-mode test, see Fig. 5.12 later) than the A and B speeds (the lower

speeds) in the US SET emission modes. The engine dynamometer speed

schedule in some heavy-duty emissions certications is practically proportional

to the declared rated speed. For example, a higher rated speed may center

the FTP cycle close to the C speed rather than the B speed compared to the

case of using a lower rated speed. A C-speed centered FTP cycle usually

produces higher emissions in both NO

and PM than a B-speed centered

cycle. Although lowering the declared rated speed for emissions certication

in heavy-duty FTP transient cycle can effectively lower emissions results,

the allowable declared rated speed is dependent on the shape of the curve

of engine power vs. engine speed. New emission regulations may change

the way engine dynamometer speed schedule is calculated for an emissions

transient test cycle, for example, changing from using the rated speed to a

‘maximum test speed’ encountered in the cycle. This may impact the design

decisions related to the shape of the engine torque curve and the governed

engine speed from an emissions perspective.

The maximum drivetrain transfer ratio (i

)

max

and the engine torque

should be selected together to ensure the combined term J

can

overcome the maximum resistance forces (including uphill climbing or

acceleration) at a minimum required vehicle speed. The (i

)

max

is achieved

by combining the nal drive ratio and the maximum transmission gear ratio.

Again, from a power perspective, once the minimum required vehicle speed

target is specied, the required engine power can be calculated using equation

5.15. The (i

)

max

can be calculated using equation 5.6. The selection of

the maximum drivetrain ratio should be based on an optimized trade-off

between the engine speed and the peak torque at a xed power requirement.

The choice of engine peak torque speed depends on the desirable speed range

between peak torque and rated power for torque backup and acceleration. The

peak torque speed is limited by the engine’s ability to breathe sufcient air

in order to produce high peak torque. Usually, it is desirable to have a low

peak-torque speed and a high torque level for better drivability and faster

acceleration. Note again that the acceleration time is related to the area under

the curve of ‘1/a

vs. vehicle speed’ as shown in Fig. 5.2. Moreover, the

engine peak torque should not exceed the durability limit of the drivetrain.

Also note that the maximum tractive force should not exceed the tire–road

adhesion force in order to avoid tire spinning or slipping. The traction control

system provides exible ring or braking torque to prevent the tire from

spinning during acceleration or on a slippery road. A design approach to

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361Engine–vehicle matching in diesel powertrain system design

determine the minimum required vehicle speed, the maximum transmission

gear ratio, the engine speed and the torque is illustrated in Fig. 5.6. A proper

maximum drivetrain ratio is also required to ensure sufcient startability for

vehicles on level ground.

Diesel engines are characterized by high torque due to turbocharging.

During fast transient acceleration the steady-state full-load condition cannot be

achieved because of turbocharger lag and a minimum required air–fuel ratio

to avoid excessive smoke. Vehicle acceleration is limited by engine transient

torque characteristics (the curves shown in Fig. 5.7). Figure 5.7 also shows

the vehicle driving characteristic curves and the engine derating curve. It

is worth noting that the design decision on the shape of the modern engine

torque curve is also affected by the requirement to meet emission regulations

for heavy-duty diesel engines, as explained earlier in the discussion about

the rated speed.

Engine torque

Engine speed

Engine torque

Max vehicle tractive force

Smoke limit

Engine speed Minimum required vehicle speed

Exhaust

temperature

limit

Higher

torque

backup

Constant

power

Design point

gr,max

= 11

gr,max

= 11

Road grade = 4%

gr,max

= 8

gr,max

= 8 Road grade = 8%

gr,max

= 5

gr,max

= 5

Road grade = 12%

Design point

Road adhesion force

Minimum required vehicle speed Minimum required vehicle speed

Constant engine power at each

minimum vehicle speed

Different required engine power

at each vehicle speed

5.6 Integrated design of maximum drivetrain transfer ratio for engine

peak torque.

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362 Diesel engine system design

In the earlier discussions, torque curve shape and torque backup were

mentioned. The advantages of a large torque backup coefcient, which

is dened as the ratio of peak torque to the torque at rated power, can be

summarized as follows.

1. A high torque backup makes the ‘tractive force vs. vehicle speed’

curve closer to the ideal constant power curve. It allows the vehicle to

accelerate or climb a steep upgrade from a low speed with a high torque.

It may reduce the number of gears and gear changes required during

driving. High torque backup allows the engine to stably respond to a

load increase (e.g., climbing a hill) when operating under the full-load

condition. The higher the torque backup, the less rapidly the engine speed

decreases when going uphill. In contrast, if the engine runs along the

lug curve below the peak torque speed where engine torque decreases

with a falling speed, a sudden load increase may stall the engine. A

lower peak torque speed is desirable because the gear-changing speed

needs to be higher than the peak torque speed in order to prevent the

engine from stalling. When operating in the region of low engine speed

Engine brake torqueEngine brake power

Fueling de-

rating due to

high oil or

coolant

temperature

and high

altitude

limitations

Engine speed

Diesel transient torque at

1000 rpm/sec raise rate

Gasoline engine lug

Diesel engine steady state lug curve

Deﬁne and match

vehicle frequent

operating region in

engine speed load

domain

20 mph, 5%

uphill grade

20 mph, 7%

uphill grade

Diesel transient torque

at 250 rpm/sec raise

rate

Required power

for 30 mph, 5%

uphill grade

Gear 7

20 mph

Gear 6

20 mph

Gear 5

20 mph

5.7 Diesel full-load lug curve and transient torque.

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363Engine–vehicle matching in diesel powertrain system design

and high brake torque, a large torque backup requires no or less gear

down-shifting when climbing hills or accelerating. This provides driving

convenience.

2. A high torque backup provides less vehicle acceleration time as shown

by the smaller area under the curve of ‘1/a

vs. vehicle speed’ in Fig.

5.2. This results in a higher overall vehicle speed and associated better

fuel economy in driving cycles because of the higher acceleration and

faster attainment of the higher speed.

3. As a result of less downshifting to low gears, there is less chance to

operate in the region of high engine speed, low brake torque and high

BSFC. This results in better fuel economy.

4. A high coef cient of speed reserve, which is de ned as the ratio of rated

power speed to peak torque speed, can increase gradeability and defer the

required gear downshift. The coef cient of adaptability (de ned as the

torque backup coef cient multiplied by the coef cient of speed reserve)

and gear ratios determine how often the driver must shift gears.

A variation of drivetrain transfer ratio between the minimum and the

maximum enables the vehicle to be driven properly at various conditions

of load, speed, and road surface. The ratio change can be a discrete change

in several gear ratios such as in a traditional transmission, or it can be a

continuous change with variable ratios. The number of transmission gears

depends on the ratio span between (i

)

max

and (i

)

min

, and directly

affects the vehicle’s acceleration performance and fuel economy. A larger

number of gears enables the vehicle to operate near the maximum power and

enhances the acceleration and hill-climbing capabilities. With a continuously

variable transmission (CVT) the vehicle can operate in the region of low

fuel consumption (i.e., the region of high load and low speed) on the engine

speed–load map when vehicle power requirements change during driving.

The gear ratios are designed based on the usage frequency of each gear and

also based on a rule that the engine should be operated within a similar speed

range in each gear. The ratios, usually less than 1.7–1.8, generally follow a

pattern similar to a geometric progression:

gr12gr

gr23gr

≥

◊◊◊

()

n()n

– 1() – 1

5.19

Properly selecting the transmission gear number and ratios can make the

curves of vehicle tractive force close to the ideal constant-power shape, hence

maximizing the vehicle acceleration capability. A detailed introduction to

drivetrain mechanical structure was provided by Nunney (1998).

Drivability is comprehensively discussed by Everett (1971), Yonekawa

et al. (1984), Naruse et al. (1993), Ciesla and Jennings (1995), List and

Schoeggl (1998), Dorey and Holmes (1999), Balfour et al. (2000), Schoeggl

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364 Diesel engine system design

et al. (2001), Sutton et al. (2001), Dorey et al. (2001), Hayat et al. (2003),

and D’Anna et al. (2005). The reader may nd useful information in these

studies.

For CVT, the reader is referred to SAE J1618 (2000), Kluger and Fussner

(1997), Kluger and Long (1999), Soltic and Guzzella (2001), Osamura et

al. (2001), Frijlink et al. (2001), Min et al. (2003), and Lee et al. (2004).

5.2.3 Powertrain matching and vehicle fuel economy

The goal of system integration analysis is to seek the optimum combination

of the engine and the drivetrain through sensitivity analysis. The optimum is

usually the best compromise between vehicle fuel economy and acceleration

time. The design options to improve vehicle fuel economy include the

following:

1. Design proper engine displacement and higher BMEP level or higher

load factor for driving cycles, possibly by downsizing the engine. High

BMEP operation provides higher thermal efciency for the engine and a

lower proportion of mechanical friction. But the requirements for vehicle

launch or off-idle responsiveness (i.e., basically starting with naturally

aspirated conditions) and engine rated power may set limitations on

displacement reduction.

2. Reduce engine BSFC and extend the low BSFC region as much as possible

in the engine speed–load map. The desirable shape of the constant low

BSFC contours from a vehicle driving perspective can be determined

by matching (plotting) the frequently encountered vehicle driving cycles

on the BSFC map.

3. Increase torque backup and the coefcient of speed reserve to improve

the shape of the engine torque curve.

4. Reduce engine and vehicle weight, aerodynamic resistance, tire rolling

friction, and accessory power loss. The aerodynamic resistance force is

proportional to the square of the vehicle speed. Excessively reducing

the rolling friction coefcient in tire design may result in losses in road

adhesion and driving smoothness, especially on wet roads. A detailed

discussion of fuel consumption and design trade-offs is provided by

Steinberg and Goblau (2004).

5. Improve drivetrain efciency (e.g., using torque converter lockup to

prevent slip and efciency loss in automatic transmissions). Increase

the number of transmission gears to make the engine operate in the low

BSFC region more often. Identify the frequent operating conditions of

vehicle speed and resistance power, and then map these conditions to a

region in the engine speed–load domain and try to match the region close

to the low BSFC area by adjusting the rear axle ratio, the transmission

gear ratios and the shift schedule.

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365Engine–vehicle matching in diesel powertrain system design

6. As shown in equation 5.17, the fuel rate consumed depends on BSFC,

engine power and vehicle speed. At a low vehicle speed, although the

power consumption is low, the BSFC is high. At a high vehicle speed, a

high engine power is needed to overcome the fast increasing aerodynamic

resistance, but the BSFC is low due to the high BMEP level. In fact,

the lowest fuel consumption occurs at a medium vehicle speed.

7. Steady-state cruising at constant vehicle speed (or essentially constant

engine power consumption) by using a higher gear gives a lower engine

speed, higher engine torque, higher load factor and hence lower BSFC.

An extreme case of this type of driving is to use the overdrive gear which

has an even smaller gear ratio than the top gear. However, the torque

reserve or power reserve for uphill climbing and acceleration becomes

less.

5.2.4 Analytical engine–drivetrain matching with engine

characteristic maps

In analytical engine–vehicle matching, the vehicle characteristics are mapped

on engine performance maps. The vehicle characteristics include vehicle

speed contours, gear lines, road grade lines, and typical vehicle acceleration

contours. The engine performance characteristics consist of the contours of

ring power, BSFC, NO

, soot, air–fuel ratio, EGR rate, transient torque

smoke limit, etc., as discussed in Chapter 4 and Section 5.2.2. The matching

quality and parametric sensitivity can be viewed conveniently, and the

best trade-off between drivability and fuel economy can be selected. The

analytical formulas presented in Section 5.1.2 are used to construct the

vehicle characteristic curves graphically. The scope of the analytical matching

approach includes the following:

∑ Conduct a vehicle force balance to predict the engine power required and

the load factor for various vehicle operating conditions in order to better

design the engine and its air system for real-world driving scenarios.

∑ Select the drive axle ratio, the transmission gear number, the gear ratios,

and design the transmission shift schedule based on the best trade-

offs.

∑ Simulate transient driving cycles and calculate the cycle composite fuel

economy and emissions.

An analytical matching approach is proposed in Fig. 5.8 to map the vehicle

operating point to the engine speed–load domain. A concept of ‘ZWB’ (zero-

wheel-braking) is introduced in the approach. The ‘ZWB’ points on each

gear are calculated by using the vehicle force balance for a given vehicle

weight, drivetrain ratio and road condition in both the ‘engine speed vs.

vehicle speed’ domain and the ‘engine speed vs. torque’ domain. The ‘ZWB’

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Vehicle speed (mph)

140

130

120

110

100

Notes: ‘ZWB’ refers to zero-wheel-braking (i.e.,

the driver does not use wheel brake). The

further away from ZWB curve at left side, the

faster the vehicle accelerates. The further away

from ZWB curve at right side, the faster the

vehicle decelerates. On ZWB curve, the vehicle

runs at constant speed. 1 mph = 1.609 km/hr

65 mph line

Engine speed (rpm)

Running on gear 1

Running on gear 2

Running on gear 3

Running on gear 4

Running on gear 5

Running on gear 6

Running on gear 7

ZWB of 100% brake torque

ZWB of 80% brake torque

ZWB of 60% brake torque

ZWB of 40% brake torque

ZWB of 20% brake torque

Rated speed line

Maximum over-speed line

5.8 Illustration of engine–vehicle matching method with the ‘ZWB’ concept.

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100% ﬁring load

80% ﬁring load

60% ﬁring load

40% ﬁring load

20% ﬁring load

ZWB of 100% brake torque

ZWB of 80% brake torque

ZWB of 60% brake torque

ZWB of 40% brake torque

ZWB of 20% brake torque

Rated speed line

Maximum over-speed line

On level ground,

without using

wheel brake

Engine ﬁring brake torque

Gear 7

Gear 6

Gear 5

Gear 4

Gear 3

Engine speed (rpm)

5.8 Continued

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