PERFORMANCE ET COMPORTEMENT DES VEHICULES · J.Y. Wong. « Theory of Ground Vehicles ». John Wiley...

Vehicle Performance

Pierre DuysinxResearch Center in Sustainable Automotive

Technologies of University of Liege

Academic Year 2018-2019

1

Lesson 1:Tractive efforts and road loads

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Outline

◼ DESCRIPTION OF VEHICLE MOTION

◼ Longitudinal motion

◼ POWER AND TRACTIVE FORCE AT WHEELS

◼ Transmission efficiency

◼ Gear ratio

◼ Expression of power and forces at wheels

◼ Power and forces diagram

◼ VEHICLE RESISTANCE

◼ Aerodynamic

◼ Rolling resistance

◼ Grading resistance

◼ General expression of vehicle resistance forces

3

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. 2nd

Edition. CRC Press.

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Assumptions and definitions

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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

6

Reference frames

Local reference frame oxyz attached to the vehicle body -SAE (Gillespie, fig. 1.4)

XY Z

O

Inertial coordinate system OXYZ

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Reference frames

◼ Inertial reference frame

◼ X direction of initial displacement or reference direction

◼ Y right side travel

◼ Z towards downward vertical direction

◼ Vehicle reference frame (SAE):

◼ x along motion direction and vehicle symmetry plane

◼ Z along vertical direction pointing to the center of the earth

◼ y in the lateral direction on the right hand side of the driver towards the downward vertical direction

◼ o, origin at the center of mass

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Reference frames

z

x

y x

Système SAE

Système ISO

x z

yComparison of conventions of SAE and ISO/DIN reference frames

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Local velocity vectors

◼ Vehicle motion is often studied in car-body local systems◼ u forward speed (+ if in front)

◼ v side speed (+ to the right)

◼ w vertical speed (+ downward)

◼ p rotation speed about a axis (roll speed)

◼ q rotation speed about y (pitch)

◼ r rotation speed about z (yaw)

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Forces

◼ Forces and moments are accounted positively when acting onto the vehicle and the positive direction with respect to the considered frame

◼ Corollary

◼ A positive Fx force is propelling the vehicle forward

◼ The reaction force of the ground onto the wheels is accounted negatively.

◼ Because of the inconveniency of this definition, the SAEJ670e « Vehicle Dynamics Terminology » is naming as normal force a force acting downward while vertical forces are referring to upward forces

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Equilibrium of longitudinal motion

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Longitudinal motion

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Longitudinal equilibrium

◼ Newton-Euler equations

◼ Equilibrium

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◼ Equilibrium along forward x direction

◼ Equation of vehicle longitudinal motion

◼ In energy form

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Force at the hook


◼ Weight under the wheel sets

◼ Solve for Wf

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◼ Solve for Wr:

◼ Generally tractive forces are not known and the acceleration is preferred

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◼ The final expression of the weight under the wheel sets is:

◼ The weight under the front (rear) wheels

◼ Decreases (increases) with the acceleration, the height of the center of gravity, the slope, the aerodynamics loads

◼ Increases (decreases) when breaking or driving down

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◼ Static weight distribution

◼ Low speed weight distribution when accelerating

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◼ Low speed weight distribution when hill climbing

◼ If q is small,

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Application : position of CoG

◼ Horizontal position of CoG: b and c

◼ Measure the weight under front and rear axles in horizontal position

◼ It comes

W f = m g

c

L

W r = m g

b

L

m g = W f + W r

b

L

=

W r

W f + W r

c

L

=

W f

W f + W r

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◼ Vertical position h of CoG:

◼ Measure the weight under the front and rear axles with predefined inclined position

◼ Slope

◼ Relation between the weight Pf and Pr measured under the wheel sets and the effective normal reaction forces Wf and Wr :

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◼ The normal forces, perpendicular to the level plan of the car are given by:

◼ It comes

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◼ The vertical position of the center of gravity is given by

◼ In terms of the measured weight under the axles, it writes:

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Propulsion system architecture

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Propulsion system

Gillespie, Fig 2.327

Layout of transmission

Transversal mounting Longitudinal mounting28

Friction Clutch

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Friction Clutch

Clutch in closed position Clutch in open position

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Torque converter (Hydraulic coupling)

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Hydraulic coupling

◼ Principle: use the 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

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Friction and hydraulic clutches

◼ Clutch efficiency

◼ Friction clutch h=1

◼ Hydraulic coupler: h~0.9

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Manual gear boxes

Gear box principles

Input shaft

Output shaft

Intermediateshaft

Direct transmission

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The gear pairs

◼ Meshed gears behave like two rigid cylinders with equivalent pitch diameters d01 and d02 rolling on each other without any slippage

◼ If there is no slippage, on can write

◼ Thus the reduction ration i

◼ For external meshing, there is an inversion of rotation direction while for internal gear meshes, the gear rotation direction is preserved (like belt and pulleys or chains)

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Manual gear boxes

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Manual gear boxes

Neutral

1st 2nd

3rd

Reverse37

Manual gear boxes

Gear selection38

Manual gear boxes operations

Selection of a gear ratio using rod or cable mechanism

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Power and tractive efforts at wheels

◼ Manual gearbox efficiency:

◼ Efficiency of a pair of gear (good quality) h= 99% to 98.5 %

◼ Gear box: double gear pairs: h = 97.5%

◼ Gear box: direct drive: h = 100%

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Automatic gear boxes

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

Sun = planétaire Planet = satellite Annulus = Couronne41

Automatic gear box

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

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Planetary gear in HEV

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CVT : Van Doorne System

Pulleys with variable radii

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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 actuators and controlled by microprocessors

◼ PERFORMANCES

◼ Variable reduction ratios varying between 4 to 6 (1:0,5→ 2:1) are achieved

◼ Variable efficiency dependent on the input torque and the rotation speed

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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 with one single input torque

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

Output shafts (wheels) 46

Differential

◼ Differential is a device that allows to split the engine power to the two wheel shafts while allowing them to spin at different rotation speeds.

◼ For straight line motion, both wheel spins at the same speed.

◼ In turn, the inner wheel spins at a lower speed than the outer wheel.

Differential system

DIFFERENTIALOPERATION PRINCIPLE

Input shaft (engine)

Output shafts

(wheels)

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Differential system

Working principle of differential system49

Differential system

◼ Efficiency of differential

◼ Longitudinal layout: 90° change of direction (bevel pair) + offset of the shaft (hypoid gear): h = 97,5 %

◼ Transversal layout: no bevel → good quality gear pair: h = 98,75%

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Transfer box

◼ Special differential system for 4-wheel drive vehicle

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

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Power train tractive effort

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Power and tractive effort

POWER AT WHEELS

◼ The power that comes to the wheels is the engine power multiplied by the efficiency of the transmission efficiency h

◼ The driveline efficiency h :

◼ Clutch

◼ Gear box

◼ Differential and transfer box

◼ Kinematic joints

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Gear ratio Longitudinal layout

Transversal layout

Friction clutch Normal 1. 0,975. 0,975 = 0,95

1. 0,975 . 0,985 = 0,96

Direct 1. 1. 0,975 = 0,975

X

Hydraulic coupling

Normal 0,88 . 0,975 . 0,975 = 0,86

0,88 . 0,975 0,985 = 0,865

Direct 0,88 . 1 . 0,975 = 0,88

x

Global efficiency in various situations

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WHEEL TRACTIVE EFFORT

◼ Power at wheels and power at the plant

◼ Gear ratio i>1

◼ Displacement speed and rotation speed of the wheels

◼ Re: effective rolling radius of the tire

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TRACTIVE FORCE

◼ Relation between plant rotation speed and traveling speed

◼ Transmission length R/i

◼ Indicates the travelling speed for a given plant rotation speed.

◼ Generally given in km/h per rpm of the plant

◼ Example 30 km/h per 1000 tr/min

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TRACTIVE FORCES

◼ It follows

◼ Then the tractive force writes

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Tractive force vs vehicle speed

◼ For a given transmission ratio r, one has:

◼ So for a given transmission ratio, one gets the tractive force in terms of the vehicle speed

◼ Plotting the curves requires

◼ Multiplying the speed curve by R/i

◼ Multiplying the tractive force by h i/R v

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v

I

II

III

IV

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◼ To draw the tractive force curve, you have to:

◼ To multiply the speed axis by R/i

◼ To multiple the force axis by h i/R


v

I

II

III

IV

Envelop of the tractive force curves for different gear ratio is defining a constant power (1/v)

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Tractive power vs vehicle speed

Proues(v)

v

h Pmax

I II III IV

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Gillespie, Fig 2.5, 2.6

Effect of automatic transmission and hydraulic clutch

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Vehicle road resistance

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Vehicle road resistance

◼ The vehicle resistance forces include 3 types of forces

◼ Aerodynamic forces (drag force)

◼ Rolling resistance due to energy dissipation in tires, suspensions, shock absorbers, etc.

◼ Grading resistance due to the slope of the road

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Aerodynamic forces and moments

◼ The air flow around the vehicle during its motion creates aerodynamic forces that can become important especially at high speed

◼ The vehicle is a so-called bluff body which generates a lot of vortices and turbulent flows, especially at the level of back of the roof.

◼ The air flow is very complex because of◼ The ground effect that affects deeply the flow◼ The wheel spinning that interact strongly with the vehicle air flow. ◼ The internal aerodynamic flow is necessary to cool the engine

compartment and the air conditioning of the cabin but it introduces a drag penalty

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◼ The aerodynamic forces have two major components:

◼ Shape drag : the shape of the vehicle modifies the air flow creating a pressure distributions giving rise to a net force pointing backward

Because of Mach and Reynolds numbers, the fluid flow is incompressible and non viscous (except in the boundary layers)

Large vortices are present because of the bluff body geometry and the boundary layers are not attached

◼ Skin friction : the viscosity effects, which take place in the boundary layers around the vehicle skin

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Air flow around a car (Gillespie, Fig4.1)

Stagnation pointp = pt

Low pressure / high speedHigh pressure /low speed

CsteVpp st =+= 22/1

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22/1 V

ppc atm

p

−=

Gillespie Fig 4.6 : Pressure distribution along the central line of the car

High pressureFlow separation

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Gillespie Fig 4.7 : Wake systems at the back of the car

Separation zoneImportance of the design:• bakelite• trunk• side rails

3D effects: Air flow is intrinsically 3D which increases the air flow separation at the end of the car

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Estimating the aerodynamic drag

◼ Drag force

◼ Estimating the frontal area

◼ Using CAD system

◼ Using pixel counting

◼ Approximation: Paul Frere formula

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Typical drag coefficient of automobiles

(Wong Table 3.1)

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Typical drag coefficient of automobiles

(Wong Table 3.1)

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Main sources of the drag of passenger car

◼ 65% of drag comes from the body shape (front, back, floor, skin)

◼ Large potential of reduction, especially for the back of the car to control the separation flows

◼ Influence as well of

◼ Wheels (21%)

◼ Details (7%)

◼ Internal aerodynamics (6%)

Gillespie Fig 4.1178

Rolling resistance forces

◼ Under free rolling conditions, it is necessary to apply a torque to maintain the motion and counteract the rolling resistance moment.

◼ The rolling resistance is covering a large number of phenomena of different natures:◼ The energy dissipation in the tire due to the hysteresis of the

material due to alternate motion in the sidewalls and in the tread blocks

◼ Air drag inside and outside the tire

◼ The scrubbing of the tire on the ground

◼ The friction in the driveline

◼ The dissipation of energy in the shock absorber

◼ The misalignment of the tires, the longitudinal and lateral slip

◼ The deformation of the road surface

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◼ Experiments show that generally, the global rolling resistance force are with a very good agreement using a linear model as a function of the vertical force applied onto the tire

The coefficient f is the rolling resistance coefficient

◼ The rolling resistance coefficient, ratio between the rolling resistance force and the normal force encompasses the complicated and interdependent physical properties of the tire and the ground.

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◼ 1st cause: hysteresis of the tire materials (viscoelastic rubber) because of deformation cycle

◼ Other sources:

◼ Frictions during slippage

◼ Air ventilation inside and outside

◼ Example: truck tire at 130 km/h

◼ 90-95 % = hysteresis

◼ 2-10 % friction

◼ 1.5 – 3.5 % aerodynamic dissipation

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◼ The resulting contact force is located in front of the theoretical contact point.

◼ The pressure distribution give rise to a rolling resistance moment that is statically equivalent to a resistance force in the contact patch

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◼ The rolling resistance is influenced by the tire structure: the rolling resistance of bias tire is higher than radial tire

◼ The operating conditions mainly:

◼ The inflating pressure: the rolling resistance is reduced for a higher inflation pressure

◼ The vehicle speed: one observes a slight increase with v at low speed. A dramatic increase after a critical speed because of the development of high-energy standing waves

◼ The longitudinal and lateral slip: the rolling resistance increases as the square of the side slip.

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◼ The rolling resistance is much higher on soft and smooth ground because of the deformation work of the soil

◼ The rolling resistance is also higher on wet ground or in snow

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Evolution of rolling resistance with tire technology development

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fRR


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Estimation of tire rolling resistance

◼ Order of magnitude given by the Automotive handbook (Bosch)

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◼ For instance Wong formula for radial tires:

◼ Influence of inflating pressure and normal load

◼ with V in m/s and p, the inflating pressure in bar

◼ Influence of inflating pressure and normal load

◼ with v in m/s and p, the inflating pressure in bar

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◼ ADVISOR Model developed in collaboration with Michelin

◼ p is the tire pressure in MPa

◼ Fz is the tire load in kg

◼ V is the vehicle speed in m/s

◼ α, β, a, b, and c are coefficients used to fit the experimental rolling resistance data

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Estimation of tire rolling resistance2001 OE Fitments Size alpha beta a b c mass [kg] SMERF [N] SMERF P SMERF Z

Mercury Cougar P205/60R15 -0.4815 1.0051 6.82E-02 2.32E-04 1.20E-06 8.23 24.75 260 4051.5

Kia Optima P205/60R15 -0.4745 0.9552 1.50E-01 4.87E-04 1.18E-06 9.51 35.98 260 4051.5

Mazda 626 P205/60R15 -0.4243 0.9568 1.59E-01 3.44E-04 1.25E-06 10.55 48.63 260 4051.5

Volkswagen Eurovan P205/60R16 -0.4428 0.9036 2.11E-01 6.00E-04 2.17E-06 10.42 40.53 260 4223.1

Honda Accord EX Coupe V6 P205/60R16 -0.3388 0.9375 1.01E-01 1.59E-04 9.93E-07 9.71 43.32 260 4223.1

Dodge Stratus ES

Toyota Camry P205/65R15 -0.3937 0.8901 1.66E-01 3.50E-04 2.09E-06 9.71 37.41 260 4360.3

Honda Accord LX & EX Sedan V6 P205/65R15 -0.3947 0.9468 1.13E-01 1.89E-04 2.24E-06 10.35 40.78 260 4360.3

Hynudai XG300 P205/65R15 -0.3191 0.9076 1.23E-01 1.96E-04 1.52E-06 10.52 47.35 260 4360.3

Lexus ES 300

Nissan Maxima

Saturn L Series

Subaru Outback P225/60R16 -0.4814 0.9463 1.47E-01 3.69E-04 2.38E-06 12.95 38.33 260 5012.7

Ford Crown Victoria P225/60R16 -0.3881 0.9550 1.03E-01 1.46E-04 2.19E-06 11.08 47.21 260 5012.7

Dodge Intrepid P225/60R16 -0.5888 1.0921 7.93E-02 1.18E-04 3.52E-07 15.29 55.69 260 5012.7

Lincoln Town Car

Ford F150 P235/70R16 -0.4704 1.0129 8.49E-02 1.16E-04 2.64E-06 12.86 51.14 260 6180.3

Mazda Tribute LX & ES P235/70R16 -0.4003 0.9315 1.39E-01 2.20E-04 1.90E-06 14.26 57.88 260 6180.3

P235/70R16 -0.4090 0.9765 1.06E-01 1.11E-04 1.52E-06 14.26 61.20 260 6180.3

Ford Explorer P235/75R15 -0.5007 0.9141 2.55E-01 4.69E-04 3.49E-06 13.30 54.08 260 6317.5

Dodge Dakota P235/75R15 -0.4797 0.9464 2.08E-01 2.56E-04 3.94E-06 13.31 65.11 260 6317.5

Chevy Trailblazer P235/75R15 -0.2601 0.8275 2.00E-01 2.50E-05 4.18E-06 13.80 71.30 260 6317.5

Mercury Mountaineer

Mitsubishi Montero Sport ES96

Resistance force due to grading

◼ Expression of grading resistance

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Expression of road load

◼ General form of the vehicle resistance

◼ General formulation

◼ with A, B > 0

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Evolution of road loads with vehicle speed

Wong, Fig 3.3

50 mph = 80 km/h

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◼ For passenger cars, the rolling resistance dominates until a break-event speed of about 80 km/h

◼ For heavy duty vehicle, the rolling resistance is still dominant till max speed.

◼ Grading forces can easily be as large as the aerodynamic drag and the rolling resistance on level road

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PERFORMANCE ET COMPORTEMENT DES VEHICULES · J.Y. Wong. « Theory of Ground Vehicles ». John Wiley...

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