1

Performance of vehicles

Pierre DuysinxResearch Center in Sustainable Automotive

Technologies of University of LiegeAcademic Year 2010-2011

Lesson 1:Power sources and Transmission

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Outline

MOTORIZATION CHARACTERISTICSPiston engines

Torque speed curvesApproximation of curves

Electric machines

POWER AND TRACTIVE FORCE AT WHEELS

Transmission efficiencyG ti

ReferencesT. Gillespie. « Fundamentals of vehicle Dynamics », 1992, Society of Automotive Engineers (SAE)R. Bosch. « Automotive Handbook ». 5th edition. 2002. Society of Automotive Engineers (SAE)J.Y. Wong. « Theory of Ground Vehicles ». John Wiley & sons. 1993 (2nd edition) 2001 (3rd edition).W.H. Hucho. « Aerodynamics of Road Vehicles ». 4th edition. SAE International. 1998.M. Eshani, Y. Gao & A. Emadi. Modern Electric, Hybrid Electric and Fuel Cell Vehicles. Fundamentals, Theory and Design. 2nd

Edition. CRC Press.

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Assumptions and definitions

Assumptions

The vehicle is made of several components or subsystems We consider the motion of the system as a wholeDuring acceleration, braking, turn, the vehicle is considered as a rigid body motion and is characterized by its geometry, its mass and inertia properties

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Piston engines

4 stroke engines: gasoline

In 1862, Beau de Rochas developed a operation sequence that is still now the basis of any piston engine operations

The 4-stroke engine requires to 2 crankshaft revolutions to accomplish one thermodynamic cycles, which means 2 compression and expansion motions of the piston.

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4 stroke engines: gasolineStroke 1: Fuel-air mixture introduced into cylinder through intake valve Stroke 2: Fuel-air mixture compressedStroke 3: Combustion (roughly constant volume) occurs and

product gases expand doing workStroke 4: Product gases pushed out of the cylinder through the exhaust valve

CompressionStroke

PowerStroke

ExhaustStroke

AI

R

CombustionProducts

Ignition

IntakeStroke

FUEL

Fuel/AirMixture

4 stroke engines: diesel

The Four stroke Compression Ignition (CI) Engine is generally denoted as the Diesel engineThe cycle is similar to Otto cycle albeit that it requires a high compression ratio and a low dilution (air fuel) ratio.Air is admitted in the chamber and then compressed. The temperature rises the ignition point and then the fuel is injected at high pressure. It can inflame spontaneously.There is no need for a spark and so stochoemetric air fuel ration is not necessary.

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4 stroke engines: dieselStroke 1: Air is introduced into cylinder through intake valve Stroke 2: Air is compressedStroke 3: Combustion (roughly constant pressure) occurs and product gases expand doing workStroke 4: Product gases pushed out of the cylinder through the exhaust valve

CompressionStroke

PowerStroke

ExhaustStroke

AI

R

CombustionProducts

IntakeStroke

Air

Fuel Injector

2-stroke engines

Dugald Clerk has invented the 2-stroke engine in 1878 in order to increase the power to weight ratio for a equal volume.The 2-stroke engines is also simpler with regards to valve systemThe 2-stroke principle is applicable to both spark ignition engine and compression ignition engine. It is however more usual with spark ignition engines.The 2-stroke engine involves two strokes and the cycle is carried out during one single crankshaft revolution.

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2-stroke engines

Intake (“Scavenging”)

Compression Ignition

ExhaustExpansion

Fuel-air-oilmixture

Fuel-air-oilmixture compressed

Crankshaft

Checkvalve

Exhaustport

2-stroke enginesStroke 1: Fuel-air mixture is introduced into the cylinder and

is then compressed, combustion initiated at the end of the stroke

Stroke 2: Combustion products expand doing work and then exhausted

* Power delivered to the crankshaft on every revolution

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Troque-speed curves of ICE engines

Torque speed curves of ICE

Suppose that the gas pressure is remaining constant along the power stroke, its work is given by:

The work of the n pistons over the cycle is:

For an k-stroke engine the duration of the cycle is given by

T 1 c o u r s e = p m o y S c o u r s e = p m o y V 1

T1 cycle = pmoy V1 n = pmoy V

t 1 c y c l e = t k = 2 t o u r s = k ¼ = !

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Torque speed curves of ICE

It comes the power curves with respect to rotation speed:

The torque speed curve is

P =

!

k ¼

p m o y V

C =

P

!

=

1

k ¼

p m o y V

P =

!

k ¼

p m o y V

C =

P

!

=

1

k ¼

p m o y V

ω ω

Indicated mean effective pressure

The indicated mean effective pressure imep is a fictitious constant pressure that would produce the same work per cycle if it acted on the piston during the power stroke

imep does not depend on engine speed,

R

pp

R

di

d

Ri

d

in

UAimepn

NVimepWNVnW

VWimep

⋅

⋅⋅=

⋅⋅=→

⋅⋅

==2

Puisque alors imepcycleT W T∝ ∝

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Brake mean effective pressure

The brake mean effective pressure(bmep) is defined similary to the indicated mean effective pressure as a fictitious constant pressure that would produce the same brake work per cycle if it acted on the piston during the power stroke

2 C2

b dR

d d R

W bmep VC nbmepV V n

ππ

⋅⋅ ⋅= = → =

⋅

Brake and indicated mean effective pressure

Order of magnitude of the brake mean effective pressure of modern engines:

Four-stroke engines: Atmospheric

SI engine: 850 – 1050 kPaCI engine: 700 – 900 kPa

TurbochargedSI engine: 1250 - 1700 kPaCI engine: 1000 - 1200 kPa

Two-stroke enginesSI engine : idem 4 strokeLarge 2-stroke diesel engines (e.g. boat) ~1600 kPa

RemarkBmep is maximum at maximum torque and wide open throttleAt nominal power, the bmep is lower by 10 to 15%

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Brake and indicated mean effective pressure

11.012.7427@5200492@70005.707V12LamborghiniDiablo VT

11.412.4398@4500436@62505.474V12Ferrari456 GT

11.613.1268@6000375@82503.496V8FerrariF355 GTS

11.512.6206@3950190@53002.793L6BMW328i

15.715.9210@3500210@53002.255L4Turbo

Mazda Millenia S

10.411.4152@4900150@57002.254L4Honda Accord EX

9.910.8117@4000122@60001.839L4MazdaProtégé LX

BMEP atRated BP

(bar)

BMEP atMax BT(bar)

Max Torque(lb-ft@rpm)

Max Power(HP@rpm)

Displ.(L)

Enginetype

Vehicle

Piston engines characteristics

Good combustion properties (and so the maximum torque) are obtained for a medium (design) rotation speed.For increasing rotation speed, the admission pressure drop and the engine frictions are increasing and the brake mean effective (and the torque) pressure is dropping.Power = torque x speed is still increasing till the torque drops is so high than power is falling as well. A low regimes, the dilution is high and the combustion is deteriorated, while heat transfer to piston and walls is becoming more important. It comes that the mean effective pressure and the torque is also reduced.

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Piston engines characteristics

Gillespie, Fig. 2.1

Standard performances of ICE

Torque-curves provided by the manufacturer are giving the basic power of the engine

Basic power = performance with requirement equipment to insure the normal conditions: ventilator, water pump, oil pump, exhaust pie, air filter

Pay attention to the multiplication of accessories and auxiliary equipments (air conditioned, steering wheel assistance, braking systems, electric generator) reduce the power available at the wheels by a significant part.

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Standard performances of ICESAE (Society of Automotive Engineers, USA): the power of the engine without its auxiliaries, with parameters adapted to each regimes (ignition advance, carburetor). Ideal maximum power.

DIN (Deutsche Industrie Normen) and CE. The engine has to provide the power necessary to operate all its needed auxiliaries while the parameters settings are the standard ones.

CUNA. Italian system that is in between DIN and CAE: no accessories but standard settings.

Power consumption of auxiliaries

The power consumption of the accessories is increasing and has a significant impact on the output power available for the propulsion especially for the small engines and the electric motors

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Effect of atmospheric conditions

The atmospheric conditions (temperature, pressure, hygrometry) affects the engine performances.

Reference atmospheric conditions:T°=15.5°C = 520°R = 60°Fp= 101.32 kPa = 14.7 psi = 76 cm Hg

Wong is referring to the correction formulae proposed by Taborek (1956):

Ba barometric pressureT the temperature (in °R) at admission pipeBv vapour pressure to account for the effect of the humidity

Effect of atmospheric conditionsFor SI engines (gasoline)

For CI engines (diesel) the effect of atmospheric pressures is more complex:

The atmospheric conditions may impact significantly tje engine performances (Wong Fig. 3.24)

TT

BBBP

P va 0

0

0 )( −=

TT

BBBP

P va 0

0

0 )( −=

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Effect of atmospheric conditionsNorm EEC 80/1269 – ISO 1585 – JIS D 1001 – SAE J1349 for SI engines (gasoline)Standards conditions (temperature T0= 298 K and dry air pressure p0= 99 kPa)

Corrected power

PP aα=0

298/)()(/99

6.02.1

KTBkPapA

BA

p

PT

a

===α

Effect of atmospheric conditions

Norm EEC 80/1269 – ISO 1585 – JIS D 1001 – SAE J1349 for CI engines (diesel)Standards conditions (temperature T0= 298 K and dry air pressure p0= 99 kPa)298/)(

)(/99

5.17.0

KTBkPapA

BA

p

PT

a

===α

PP aα=0

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Curve fitting of ICE characteristics

Two families of curvesFitting to a power functionFitting of a polynomial

DataNominal (maximum) power

Maximum torque

P1 = Pmax!1 = !nom

C2 = Cmax!2 = !Cmax .

Power approximationOn look for a power function of the type

Data

That is

!1 = !nom P1 = Pmax

!2 = !Cm ax P2 = Cmax!Cmaxd C

d!

¯̄̄̄!2

= 0

P = P 1 ¡ A j ! ¡ ! 1 j b b > 0

A =

P 1 ¡ P 2

j ! 1 ¡ ! 2 j b

b =

! 1

! 2 ¡ 1

P 1

P 2 ¡ 1

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Power approximationMaximum power in P1: OKMaximum torque in ω2:

Given (maximum) torque ω2 :

P(!2) = P2 = Cmax !Cmaxd C

d!

¯̄̄̄!2

=d (P=!)d!

¯̄̄̄!2

= 0

a =P1 ¡ P2j!1 ¡ !2jb P = P1 ¡ (P1 ¡P2)

¯̄̄̄!1 ¡ !!1 ¡ !2

¯̄̄̄b

Power approximationMaximum torque in ω2:

Derivative of the power

Leads to the condition

d C

d!

¯̄̄̄!2

=!2

dPd!

¯̄!2¡ P2

!22= 0 P2 = !2

dPd!

¯̄̄̄!2

dPd!

¯̄̄̄!2

= ¡a b j!1 ¡ !2jb¡1 sign(!1 ¡ !2) (¡1) = a b (!1 ¡ !2)b¡1

P2 = !2 a b (!1 ¡ !2)b¡1 = b !2P1 ¡P2!1 ¡ !2

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Power approximationFitted exponent b

Fitted approximation

b =

! 1

! 2 ¡ 1

P 1

P 2 ¡ 1

P

P 1

= 1 ¡

µ

1 ¡

P 2

P 1

¶ ¯ ¯ ¯ ¯ ¯

1 ¡ !

! 1

1 ¡ ! 2

! 1

¯ ¯ ¯ ¯ ¯

b

C = P = !

Power approximationExample: Peugeot engine XV3 943 cm³

One gets

P1 = 33; 85 kW µa n1 = 6000 tr=min

C2 = 67; 81 kN:m µa n2 = 3000 tr=min

!1 = 628; 30 rad=s

!2 = 314; 15 rad=s

P2 = C2 !2 = 21; 30 kW

P2=P1 = 0; 6293!2=!1 = 0;5

b =!1!2¡ 1

P1P2 ¡ 1

=2¡ 1

1; 5996¡ 1 = 1; 698

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Polynomial approximation

Polynomial approximationPower

Torque

P(!)=Pmax 'nXi=0

ai (!=!nom)i

C(!)=C1 'nXi=0

ai (!=!nom)i¡1

Polynomial approximation

Polynomial approximation of order 3

Identification of the coefficients

P(!)=P1 = a0 + a1 (!=!1) + a2 (!=!1)2 + a3 (!=!1)3

P(0) = 0 eP(!1) = Pmax.

a0 = 0

a1 + a2 + a3 = 1

P(!2) = P2 = Cmax !Cmaxd C

d!

¯̄̄̄!2

= 0

a1 n2 + a2 n22 + a3 n

32 = P2=P1

a2 + 2 a3 n2 = 0

n2 = !2=!1,

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Polynomial approximation

Polynomial approximation of order 4

Identification of the coefficientSame as polynomial of order 3 + new condition on the maximum power in ω1:

P(!)=P1 = a0 + a1 (!=!1) + a2 (!=!1)2 + a3 (!=!1)

3

+ a4 (!=!1)4

a1 + 2 a2 + 3 a3 + 4 a4 = 0

Polynomial approximation

Polynomial approximation of order 4

Value of the coefficients

P(!)=P1 = a0 + a1 (!=!1) + a2 (!=!1)2 + a3 (!=!1)

3

+ a4 (!=!1)4

a1 + a2 + a3 + a4 = 1

a1 + 2 a2 + 3 a3 + 4 a4 = 0

a1 n2 + a2 n22 + a3 n

32 + a4 n

42 = P2=P1

a2 + 2 a3 n2 + 3 a4 n22 = 0

n2 = !2=!1,

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Example: 2.0 HDI PSA engine

Example: 2.0 HDI PSA engine

0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000

1

2

3

4

5

6

7

8

9

10

x 104 Caractéristique moteur

Vitesse moteur [min-1]

Pui

ssan

ce m

oteu

r [W

]

CubiqueType Puissance

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Example: 2.0 HDI PSA engine

0 500 1000 1500 2000 2500 3000 3500 4000 4500 50000

50

100

150

200

250

300

350

Couple moteur

Vitesse moteur [min-1]

Cou

ple

mot

eur [

N.m

]

CubiqueType Puissance

Electric machines

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Performance curves of electric machines

Power electronic and control of DC machines

Working principle of a chopper

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Power electronic and control of AC machines

Working principle of an inverter

DC motor: series and separated excitation

DC series motor DC motor with separated excitation

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AC motors: induction vs synchronous

AC induction motor AC synchronous motor

Traction motor characteristicsAt low speed: constant torque

Voltage supply increases with rotation speed through electronic converter while flux is kept constant

At high speed: constant powerMotor voltage is kept constant while flux is weakened, reduced hyperbolically with the rotation speed

Base speed: transition speed from constant torque to constant power regime

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Traction motor characteristicsSpeed ratio x = ratio between maximum rotation speed to base speed

X ~ 2 Permanent Magnet motorsX ~ 4 Induction motorsX ~ 6 Switched Reluctance motors

For a given power, a long constant power region (large x) gives rise to an important constant torque, and so high vehicle acceleration and gradeability. Thus the transmission can be simplified.

Propulsion system architecture

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Propulsion system

Gillespie, Fig 2.3

Layout of transmission

Transversal mounting Longitudinal mounting

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Friction Clutch

Clutch in closed position Clutch in open position

Hydraulic coupling

Principle: use hydro kinetic energy of the fluid to transfer smoothly the power from the source to the load while amplifying the output torqueThe input wheel plays the role of a pump whereas the output wheel acts as a turbineOne may add a fixed wheel (stator) to improve the efficiency

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Friction and hydraulic clutches

Clutch efficiencyFriction clutch η=1Hydraulic coupler: η~0.9

Manual gear boxes

Gear box principles

Input shaft

Output shaft

Intermediateshaft

Direct transmission

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Manual gear boxes

Manual gear boxes

Neutral

1st 2nd

3rdReverse

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Manual gear boxes

Gear selection

Manual gear boxes

Gear selectionAnd selection mechanism

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Power and tractive efforts at wheels

Power and tractive efforts at wheels

Manual gearbox efficiency:Efficiency of a pair of gear (good quality) η= 99% à98.5 %Gear box: double gear pairs: η = 97.5%Gear box: direct drive: η = 100%

Differential efficiency:Longitudinal engine layout: axis offset and change of direction with hypoid gears: η = 97,5 %Transverse engine layout (no change of direction): regular gears : η = 98,75%

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Automatic gear boxes

The basic element of automatic gear boxes is the planetary gear train

Sun = planétaire Planet = satellite Annulus = Couronne

Planetary gear pair

Kinematics: Willys formula

Relation between the rotation speed of the different gear trainsand the ratio of teeth of the sun and the annulusStatic: Equilibrium of torques

ωCωCωPS

ωSωP

C

P

ZiZ

=( )C C P P PS C PZ Z Z Zω ω ω+ = +

1(1 )PS P CiT i T T

i+

= − + = −

(1 )P C PSi iω ω ω+ = +

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Automatic gear box

Principle of an automatic gear box based on double planetary gear trains

Mèmetaux Fig 5.9

CVT : Van Doorne System

Pulleys with variable radii

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CVT : Van Doorne System

Working principleBy modifying the distance between the two conical half shells, one modifies the effective radii of the pulleys and so the reduction ratioOriginally the system was based on the centrifugal forces, but nowadays the system is actuated by depression engines and controlled by microprocessors

PERFORMANCESVariable reduction ratios varying between 4 to 6 are achievedVariable efficiency variable with the input torque and the rotation speed

Differential systemDuring turn, the inner and outer wheels have different rotation speeds because of different radii.Differential systems allow a different speed in left / right wheels while one single input torqueDifferential systems can be studied as planetary gears with equal number of teeth for sun and annulus.

Input shaft (engine)

Output shafts (wheels)

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Differential system

Working principle of differential system

Differential system

Efficiency of differential

Longitudinal layout: 90 change of direction (bevel pair) + offset of the shaft (hypoïd gear): η = 97,5 %Transversal layout: no bevel good quality gear pair: η = 98,75%

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Transfer box

Special differential system for 4-wheel drive vehicleThe transfer box splits the torque between the front and rear axles.