Performance of vehicles

Performance of vehicles

Pierre Duysinx

Research Center in Sustainable Automotive Technologies of University of Liege

Academic Year 2010-2011

Lesson 1:

Power sources and Transmission

Outline

„

MOTORIZATION CHARACTERISTICS

„

Piston engines

„

Torque speed curves

„

Approximation of curves

„

Electric machines

„

POWER AND TRACTIVE FORCE AT WHEELS

„

Transmission efficiency

G ti

References

„ T. 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. 2^nd Edition. CRC Press.

Assumptions and definitions

Assumptions

„

The vehicle is made of several components or subsystems

„

We consider the motion of the system as a whole

„

During acceleration, braking, turn, the vehicle is considered as a rigid body motion and is

characterized by its geometry, its mass and inertia

properties

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.

4 stroke engines: gasoline

„ Stroke 1: Fuel-air mixture introduced into cylinder through intake valve

„ Stroke 2: Fuel-air mixture compressed

„ Stroke 3: Combustion (roughly constant volume) occurs and product gases expand doing work

„ Stroke 4: Product gases pushed out of the cylinder through the exhaust valve

Compression Stroke

Power

Stroke Exhaust

Stroke A

I R

Combustion Products Ignition

Intake Stroke FUEL

Fuel/Air Mixture

4 stroke engines: diesel

„ The Four stroke Compression Ignition (CI) Engine is generally denoted as the Diesel engine

„ The 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.

4 stroke engines: diesel

„ Stroke 1: Air is introduced into cylinder through intake valve

„ Stroke 2: Air is compressed

„ Stroke 3: Combustion (roughly constant pressure) occurs and product gases expand doing work

„ Stroke 4: Product gases pushed out of the cylinder through the exhaust valve

Compression Stroke

Power Stroke

Exhaust Stroke A

I R

Combustion Products

Intake Stroke

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 system

„ The 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.

2-stroke engines

Intake(“Scavenging”)

Compression Ignition Exhaust Expansion

Fuel-air-oil mixture Fuel-air-oil mixture compressed

Crank shaft Check valve

Exhaust port

2-stroke engines

„ Stroke 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

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 T1course =p_moyScourse=p_moy V₁

T

= p

V

n = p

V

t

= t

= k ¼ = !

Torque speed curves of ICE

„ It comes the power curves with respect to rotation speed:

„ The torque speed curve is P = !

k¼pmoyV

C = P

! = 1

k¼pmoyV

P = !

k¼pmoy V C = P

! = 1

k¼pmoyV

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 p p R

d i

d R i d

i

n U A imep n

N V W imep N

V n W V imep W

⋅

⋅

= ⋅

⋅

= ⋅

⋅ →

= ⋅

= 2

Puisque T ∝W_cycle alors imep∝T

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 C

2

b R d

d d R

W C n bmep V

bmep V V n

π

π

⋅

= = ⋅ ⋅ → =

⋅

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 kPa

„ CI engine: 700 – 900 kPa

„ Turbocharged

„ SI engine: 1250 - 1700 kPa

„ CI engine: 1000 - 1200 kPa

„ Two-stroke engines

„ SI engine : idem 4 stroke

„ Large 2-stroke diesel engines (e.g. boat) ~1600 kPa

„ Remark

„ Bmep is maximum at maximum torque and wide open throttle

„ At nominal power, the bmep is lower by 10 to 15%

Brake and indicated mean effective pressure

11.0 12.7

427@5200 492@7000

5.707 V12

Lamborghini Diablo VT

11.4 12.4

398@4500 436@6250

5.474 V12

Ferrari 456 GT

11.6 13.1

268@6000 375@8250

3.496 V8

Ferrari F355 GTS

11.5 12.6

206@3950 190@5300

2.793 L6

BMW 328i

15.7 15.9

210@3500 210@5300

2.255 L4

Turbo Mazda

Millenia S

10.4 11.4

152@4900 150@5700

2.254 L4

Honda Accord EX

9.9 10.8

117@4000 122@6000

1.839 L4

Mazda Protégé LX

BMEP at Rated BP

(bar) BMEP at

Max BT (bar) Max Torque

(lb-ft@rpm) Max Power

(HP@rpm) Displ.

(L) Engine

type 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.

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.

Standard performances of ICE

„ SAE (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

Effect of atmospheric conditions

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

„ Reference atmospheric conditions:

„ T°=15.5°C = 520°R = 60°F

„ p= 101.32 kPa = 14.7 psi = 76 cm Hg

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

„ B_abarometric pressure

„ T the temperature (in °R) at admission pipe

„ B_vvapour pressure to account for the effect of the humidity

Effect of atmospheric conditions

„ For 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)

T T B

B B

P P

0

0

( − )

=

T T B

B B

P P ^{a v 0}

0

0( − )

=

Effect of atmospheric conditions

„ Norm 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

P P

= α

298 / ) (

) ( / 99

6 . 0 2 . 1

K T B

kPa p

A

B A

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 T

= 298 K and dry air pressure p ( ) / 298

= 99 kPa)

) ( / 99

5 . 1 7 . 0

K T B

kPa p

A

B A

p PT a

=

= α =

P

P

= α

Curve fitting of ICE characteristics

„

Two families of curves

„ Fitting to a power function

„ Fitting of a polynomial

„

Data

„ Nominal (maximum) power

„ Maximum torque

P

= P

!

= !

C

= C

!

= !

.

Power approximation

„ On look for a power function of the type

„ Data

„ That is

!1 =!nom P1=Pmax

!2 =!Cm a x P2=Cmax!Cm a x

d C d!

¯¯

¯¯

!2

= 0 P = P¹¡Aj!¡!1j^b b>0

A = P¹¡P²

j!1¡!2j^b

b =

!₁

!₂

¡ 1

P1

P2

¡ 1

Power approximation

„ Maximum power in P₁: OK

„ Maximum torque in ω₂:

„ Given (maximum) torque ω₂:

P(!2) =P²=Cmax!Cm a x

d C d!

¯¯

¯¯_!

2

= d(P=!) d!

¯¯

¯¯_!

2

= 0

a = P¹¡ P²

j!₁¡!₂j^b

P = P

¡ ( P

¡ P

)

¯ ¯

¯ ¯

!

¡ !

!

¡ !

¯ ¯

¯ ¯

b

Power approximation

„ Maximum torque in ω₂:

„ Derivative of the power

„ Leads to the condition d C

d!

¯¯

¯¯_!

2

= !2 dP d!

¯¯

!2¡ P²

!₂² = 0 P²=!2

dP d!

¯¯¯

¯!2

dP d!

¯¯

¯¯

!2

=¡a bj!1¡!2j^b¡1sign(!1¡!2) (¡1) =a b(!1¡!2)^b¡1

P²=!₂ a b(!₁¡!₂)^b¡1=b !₂ P¹¡ P²

!1¡!2

Power approximation

„ Fitted exponent b

„ Fitted approximation

b =

!₁

!₂

¡ 1

P1

P2

¡ 1

P

P¹ = 1¡ µ

1¡P² P¹

¶¯¯

¯¯

¯ 1¡!^!1

1¡^!!²1

¯¯

¯¯

¯

b

C = P=!

Power approximation

„ Example: Peugeot engine XV3 943 cm³

„ One gets

P1 = 33;85kW µa n₁ = 6000tr=min C2 = 67;81kN:m µa n₂ = 3000tr=min

!1= 628;30rad=s

!2= 314;15rad=s P2=C2!2= 21;30kW

P²=P¹ = 0;6293

!2=!1= 0;5

b=

!1

!2 ¡1

P1

P² ¡1 = 2¡1

1;5996¡1 = 1;698

Polynomial approximation

„ Polynomial approximation

„ Power

„ Torque

P(!)=P^max' Xn

i=0

ai(!=!nom)ⁱ

C(!)=C¹' Xn

i=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 e P(!₁) =P^max.

a0= 0

a1+a2+a3= 1

P(!2) =P2=Cmax!Cm a x

d C d!

¯¯

¯¯

!2

= 0

a

n

+ a

n

+ a

n

= P

= P

a

+ 2 a

n

= 0

n₂=!₂=!₁,

Polynomial approximation

„ Polynomial approximation of order 4

„ Identification of the coefficient

„ Same 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+ 2a₂+ 3a₃+ 4a₄ = 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+ 2a2+ 3a3+ 4a4= 0

a1n2+a2n²₂+a3n³₂+a4n⁴₂=P²=P¹ a2+ 2a3n2+ 3a4n²₂ = 0

n₂=!₂=!₁,

Example: 2.0 HDI PSA engine

Example: 2.0 HDI PSA engine

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

0 1 2 3 4 5 6 7 8 9 10

x 10⁴ Caractéristique moteur

Vitesse moteur [min^-1]

Puissance moteur [W]

Cubique Type Puissance

Example: 2.0 HDI PSA engine

0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

0 50 100 150 200 250 300 350

Couple moteur

Vitesse moteur [min^-1]

Couple moteur [N.m]

Cubique Type Puissance

Electric machines

Performance curves of electric machines

Power electronic and control of DC machines

Working principle of a chopper

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

AC motors: induction vs synchronous

AC induction motor AC synchronous motor

Traction motor characteristics

„ At low speed: constant torque

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

„ At high speed: constant power

„ Motor 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

Traction motor characteristics

„ Speed ratio x = ratio between maximum rotation speed to base speed

„ X ~ 2 Permanent Magnet motors

„ X ~ 4 Induction motors

„ X ~ 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

Propulsion system

Gillespie, Fig 2.3

Layout of transmission

Transversal mounting Longitudinal mounting

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 torque

„ The input wheel plays the role of a pump whereas the output wheel acts as a turbine

„ One may add a fixed wheel (stator) to improve the efficiency

Friction and hydraulic clutches

„ Clutch efficiency

„ Friction clutch η=1

„ Hydraulic coupler: η~0.9

Manual gear boxes

Gear box principles

Input shaft

Output shaft

Intermediate shaft

Direct transmission

Manual gear boxes

Manual gear boxes

Neutral

1st 2nd

3rd

Reverse

Manual gear boxes

Gear selection

Manual gear boxes

Gear selection

And selection mechanism

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% à 98.5 %

„ 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%

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 trains and the ratio of teeth of the sun and the annulus

„ Static: Equilibrium of torques

ω

ω

ω

ω

ω

C P

i Z

= Z

( )

C

Z

Z

Z

Z

ω + ω = ω +

(1 ) 1

PS P C

T i T i T

i

= − + = − + (1 )

P

i

i

ω + ω = ω +

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

CVT : Van Doorne System

„ Working principle

„ By modifying the distance between the two conical half shells, one modifies the effective radii of the pulleys and so the reduction ratio

„ Originally the system was based on the centrifugal forces, but nowadays the system is actuated by depression engines and controlled by microprocessors

„ PERFORMANCES

„ Variable reduction ratios varying between 4 to 6 are achieved

„ Variable efficiency variable with the input torque and the rotation speed

Differential system

„ During 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 torque

„ Differential systems can be studied as planetary gears with equal number of teeth for sun and annulus.

Input shaft (engine)

Output shafts (wheels)

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 Ægood quality gear pair: η= 98,75%

Transfer box

„ Special differential system for 4-wheel drive vehicle

„ The transfer box splits the torque between the front and rear axles.