w4 section 3 driveline dynamics

8/3/2019 W4 Section 3 Driveline Dynamics

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Vehicle Dynamics

Section 3

DrivelineDynamics

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Performance of a car

The maximum achievable acceleration of a

vehicle is limited by two factors:

maximum torque at driving wheels:

depends on engine and transmission performance

maximum traction force at tire prints

depends on tire-road friction. In this chapter

we examine

engine and transmission performance.


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Power of an Engine

The maximum attainable power Pe of an IC

engine is a function of

the engine angular velocity (e).

must be determined experimentally.

The function Pe = Pe (e),

called the power performance function,

can be estimated by a third-order polynomial

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Power and Torque performance of aspark ignition engine

PM = 50kW at

M = 586 rad/ s

5600 rpm.

The curve begins

at an angular

velocity at which

the engine startsrunning

smoothly.


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Maximum attainable power Pe, Pe(e)

a third-order polynomial

(M) to indicate the angular

velocity, measured in [rad/s],

at which the engine power

reaches the maximum value PM ,

measured in [Watt = Nm/s],

for spark ignition engines weuse

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Maximum attainable power Pe, Pe(e)

For indirect

injection Diesel

engines we use

for direct injection

Diesel engines

we use


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The driving torque of the engine Te

The driving torque of

the engine Te is the

torque that provides

Pe

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Example (R10, p166)


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Porsche 911 engine

The power performance equation for the

Porsche 911 engine has the coefficients

and, its power performance function is

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Corvette Z06


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Corvette Z06 engine

The power performance equation for the

engine of Corvette Z06 has the coefficients

and, its power performance function is

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The resulting Pe

no limit for developinga powerful engine

any engine with poweraround 100 hp wouldbe enough for streetcars with normalapplications.

It seems that engineswith 600 hp reach thelimit of application forstreet cars.


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Street Cars vs. Race Cars

For street cars No design limitation for power

No design limitation for physical properties

For race cars (Formula 1, F1) It must be a four-stroke engine,

less than 3000 cm3 (3 lt) swept volume

no more than ten cylinders

no more than five valves per cylinder

but there is no limit for power.

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Engine efficiency curves

Engines convert chemical energy of fuel, into mechanical energy at the engine

output shaft

Conversion happens at a specific efficiency

Constant efficiency contours can be added to theperformance map

Hence, every point under the curve Pe = Pe (e) can bean operating condition at a specific efficiency.

The maximum efficiency around the angular velocity corresponding to the maximum

torque

when the throttle is almost wide open.


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Power performance of a spark ignition

engine with constant efficiency contour

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Power Units

There are many different units for expressing

power. The metric unit for power is Watt [W].

Horsepower [ hp] is also used in vehicledynamics.


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Fuel Consumption

Consider a vehicle moving straight at a constant

speed vx.

The energy required to travel can be calculated by

multiplying the power at the drive wheels by time

d is the distance travelled

E is the needed energy toturn the wheels

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Fuel Consumption

To find the actual energy needed to run the wholevehicle include the coefficients of efficiencies. e for engine efficiency,

H for thermal value of fuel

f for density of the fuel.

Vehicle moves at constant speed, the traction force Fx is equal to the resistance forces. Therefore,

the fuel consumption per unit distance, q, is

(m3/m)


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Ideal Engine Performance

It is said that an ideal engine is one thatproduces a constant power (Po) regardless ofspeed.

For this kind of ideal engine we have

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Ideal Engine

Power and

Torque

performance

curves for an

ideal engine.

Po = 50 kW

Not realistic


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Lets optimise to operate at high power

we introduce a gearbox

to keep the engine running at the maximum power

or in a working range around the maximum power

practically aim is to

achieve the power of the engine efficiently

the power at wheels constant at max. value.

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An ideal engine!?

However, internalcombustionengines do notwork like an idealengine.

Figure on the leftillustrates such anideal performancefor Ce = 0.14539.


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Maximum power and torque at same M

Ideal performance for an engine would behaving maximum power and maximumtorque at the same angular velocity M.

However, it is impossible because the maximum torque TM of a spark

ignition engine occurs at

half of the speed at

which the power is

maximum.

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Maximum power and torque at same M

When the torque is maximum, the power is at

When the power is maximum at e = M, the

torque is


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Performance curves of an ideal engine having a

linear torque-speed relationship Te = 0.14539 e

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Driveline (transmission) and efficiency

the systems and devices that transfer torque and power

from the engine to the drive wheels of a vehicle

Most vehicles use one of two common transmission types: manual gear transmission

automatic transmission with torque converter.

A driveline includes the engine

Clutch Gearbox

propeller shaft

differential

drive shafts

drive wheels


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Driveline

The engine: power source The output from the engine is an engine torque Te and engine speed e.

The clutch connects and disconnects the engine to the rest of thedriveline

when the vehicle is equipped with a manual gearbox. The gearbox can be used to change the transmission ratio between the engine

and the drive wheels.

The propeller shaft connects the gearbox to the differential. The propeller shaft does not exist in front-engined front-wheel-drive and rear-

engined rear-wheel-drive vehicles. In those vehicles, the differential isintegrated with the gearbox in a unit that is called the transaxle.

The differential is a constant transmission ratio gearbox that allows thedrive wheels to have different speeds. So, they can handle the car in acurve.

The drive shafts connect the differential to the drive wheels.

The drive wheels transform the engine torque to a traction force on theroad.

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Driveline @


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Power transmission on driveline

The available power at the

drive wheels is (P)

< 1 indicates the overall

efficiency between the engine

and the drive wheels

c < 1 is the converter

efficiency and t < 1 is thetransmission efficiency.

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The relationship between theangular velocity of the engineand the velocity of thevehicle is

where ng is the transmission ratio of

the gearbox, nd is the transmission ratio of

the differential,

e is the engine angularvelocity,

R

is the effective tire radius.

Gear

BoxDifferential

Tire

e

ng

nd

Rw

Engine


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Transmission ratio or gear

reduction ratio of a gearing

device, n, is the ratio of the

input velocity to the output

velocity

while the speed ratio r is the

ratio of the output velocity tothe input velocity.

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The input and output torque and angularvelocity of each driveline components


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Torque at the wheel

The power at the wheel is P

= Pe, and the

angular velocity at the wheel is

w = e/ (ng nd).

P = T , the available torque at the wheel, Tw, is

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Volumetric, thermal, and mechanicalefficiencies

There is an efficiency between the attainable

power in fuel and the power available at the

engines output shaft

V is the engine volumetric efficiency, T is

the thermal efficiency, and M is the

mechanical efficiency.


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Efficiencies

Volumetric efficiency V identifies how much

fuelled air gets into the cylinder. (%80-100)

Thermal efficiency T identifies how much of

the fuel is converted to usable power(%26 -

%34)

Mechanical efficiency M identifies how much

power is consumed by the engine to run itself(system dependent!?)

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Front or rear-engined, front or rear drive

The engine may be installed in front : front-engined

back : rear-engined

The driving wheels may be: the front

the rear

all wheels .

6 six combinations

Most common combinations are front-engined front-wheeldrive

front-engined rear-wheel-drive

front-engined all-wheel-drive vehicles

A few manufacturers make cars with rear-engined rear-wheel-drive.

However, there is no rear-engined front-wheel-drive vehicle.


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Gearbox and Clutch Dynamics

The internal combustion engine can not operate below a minimum engine speedmin.

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Gearbox and Clutch Dynamics

Consider a vehicle with only one drive wheel forward velocity vx of the vehicle

proportional to the angular velocity of the engine e tire traction force Fx is

proportional to the engine torque Te

Rw is the effective tire radius,

nd is the differential transmission ratio, ni is the gearbox transmission

ratio in gear number i,

is the overall driveline efficiency

e eq. is called the speed equation,

Te eq. is called the traction equation.


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Available torque at the wheel, Tw, is

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R10 - Page 180


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42


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A Sample Calculation for

1 1

2 2

1 1 1

2 2 2

10.875

3.827 10 /

2.36 24 /

10.875 10.875 3.827 10 416.19 rad/s

10.875 10.875 2.36 24 615.96 rad/s

e i x

x

x

e x

e x

n v

n v m s

n v m s

n v

n v

=

= =

= =

= = =

= = =

e

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A sample of a gear-speed plot for

a gearbox.

e2

e1


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A Sample Calculation

2 3 2 2

1

2 3 2 2

5.7405 10 3.7588 246.13

17 /

3.827

5.7405 10 (3.827) (17) 3.7588 (3.827) (17) 246.13 (3.827)

947.93 mN

w i d e

w i x i x i

x

w

w

T n n T

T n v n v n

v m s

n

T

T

=

= + +

=

=

= + +

=

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Wheel torque-speed Equation

(4.77) at each gear ni of a gearbox,and the envelope curve simulatingan ideal engine behaviour.


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Summary

Driveline system is presented

Engine performance curves discussed

Related properties are presented

Homework: (R10)

Revising: 164 - 181 Reading: 182 - 206

Exercises 207 -217:

w4 section 3 driveline dynamics

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