Vehicle Dynamics

Outline1.1. Vehicle dimensioning Vehicle dimensioning 2.2. Resistance in motionResistance in motion3.3. Power for propulsionPower for propulsion4.4. Tractive effort & tractionTractive effort & traction5.5. Road performance curveRoad performance curve

l: wheel base in mmv: vehicle centre of gravity (COG)Bo: body COGUf: front axle COGUr:rear axle COG

Axis of coordinates as per ISO 4130, DIN 70000

Vehicle dimensioning

Centre of Gravity (COG)

v: vehicle CCOGBo: body COGUf: front axle COGUr:rear axle COG

V and Bo are more important ( their distance from both axles and height) for following reasons

1. Braking and acceleration capacity2. Climbing capability3. Vibrational stability4. Driving stability ( straight drive+cornering)5. Mass moment of inertia

Lower is the height, better it is. But ground clearance has to be traded off.

Extreme case of vehicle driving condition

What are the forces acting on the vehicle ?

Resistance

Resistance is defined as the force impeding vehicle motion

1. Aerodynamic resistance2. Rolling resistance3. Inertia force4. Gravitational force (Grade resistance)

fF rF

m

W

aerodynamic resistance in lb (N)

rolling resistance of the front/rear tires in lb (N)

Available tractive effort of the front/rear tires in lb (N)

Total vehicle weight in lb (N)

Angle of the grade in degrees

Vehicle mass in slugs (kg)

Acceleration in ft/s2 (m/s2)a

aF

rlfF rlrF

( neglecting the effect of mass due to rotational effect)

Vector sum of total forces

Aerodynamic Resistance RaIt is sum total of :

1. Form Drag (57%) 2. Lift Drag ( 8%)3. Surface Drag (10%)4. Interference Drag (15%)5. Cooling & Ventilation Drag (10%)

With advanced body design , like smoothening bottom surface, redesigning the front bumper can minimise the lift. This can reduce to be negligible compared to other drags. So , we will neglect for all our study purpose.

v velocity of body relative to fluid A orthographic projected area perpendicular to the flow direction

If RN< 2000, then streamline flow. Otherwise turbulent flow.

For streamline flow (RN <1)FD=-bVb property of fluid+dimension of object

1

2

3

4

5

6

7

8

9

Aerodynamic Resistance Ra

Composed of:1. Turbulent air flow around vehicle body (85%)2. Friction of air over vehicle body (12%)3. Vehicle component resistance, from

radiators and air vents (3%)

V

AC

f

D

air density in slugs/ft3 (kg/m3)

Coefficient of drag

Front area of the vehicle in ft2 (m2)

Speed of the vehicle in ft/m (m/s)

2

2VACR fDa

3

2VACP fDaR

Typical values of air density under specific atmospheric conditions

Ranges of Cd for typical road vehicles

Aerodynamic Resistance RaDrag Coefficient

• Recent vehicles have lower coefficient

• Large personal vehicles have higher coefficient

• Even minor factors like opening window will affect coefficient

Draglift

SpoilerUndertray

Wing

How to reduce Aerodynamic resistance ?

Aerodynamic design

Frontal area of vehicle

Aerodynamic Resistance Ra

Orthographic projection area

most modern road going vehicles.• Smooth vehicle shape, rounded corners • High rake angle for the windscreen• Tapered rear end• Minimized body seams• Optimized rear view mirrors • Substitution of rear view mirrors with cameras• Smooth underbody

Aerodynamic Resistance RaFrontal area of some of the vehicles

Drag area ( Cd x Ft2) Year/ Automobile

4.0 1996 GM EV15.1 1999 Honda Insight5.4 1989 Opel Calibra5.5 1980 Ferrari 308 GTB5.6 1993 Mazda RX-75.6 1993 McLaren F15.6 1991 Opel Calibra5.6 1990 Bugatti EB1105.7 1990 Honda CRX

Rolling resistance

2. < sliding resistance

1. Caused by the deformation of wheel or the road surface or both due to load of the vehicle

4. Rolling resistance leads to heat and sound energy.

Rolling Resistance

3. In an automobile with rubber tyre, it happens mainly due to hysteresis loss ( deformation/ recovery of tyre). Thus it is much higher than that of a steel wheel on train.

Tyres

175/70 R 14 or 185/60 R 15 82 H

Aspect ratio=W/HH=0.5*(ODT-d)

Width (W in mm)

Aspect ratio in %

Radial

Rim dia in inches

Load indexMax speed

Rolling resistance =f( hardness, r, v, W, T, relative micro sliding, matl, temp)

Rolling Resistance

1. If hardness is more, it reduces. Rolling resistance on a concrete road is less than that in sand.

2. Higher the radius of the wheel , lower is the rolling resistance.

3. It has got linear relationship with velocity ( but a low gradient) as frequent deformation / recovery increases temperature and thus rolling resistance.

4. Higher load increases rolling resistance due to same reason as 3.

5. As temperature increases, rolling resistance increases.

6. On a smooth surface ( e.g on wet road ), it is lower….contd

Rolling resistance =f( hardness, r, v, T, relative micro sliding, matl, temp)

Rolling Resistance

7. Softer the material, more is the hysteresis loss and thus more is the rolling resistance. Thus to reduce it many times silane ( silica) replaces the carbon black. Silane is however costlier than the carbon black.

8. Higher inflation pressure reduces the contact area thus reduces rolling resistance. This helps to reduce the hysteresis loss. But excess inflation pressure results in skip and hop of the vehicle which result into loss of traction and problem in braking.

9. Radial tyres reduce rolling resistance ( by >25%) than bias ply tyres due to stiffness of the inserted steel wires. This helps in reduction of the hysteresis loss.

Rolling resistance =f( hardness, r, v, T, relative micro sliding, matl, temp)

Rolling Resistance

10.Higher aspect ratio ( W/H) reduces the rolling resistance.

11. Lower tread thickness reduces rolling resistance.

Rolling Resistance Rrl

Composed primarily of 1. Resistance from tire deformation (90%)2. Tire penetration and surface compression ( 4%)3. Tire slippage and air circulation around wheel ( 6%)4. Wide range of factors affect total rolling resistance

WfWfR rlgrlrl cos

WVfP rlrlR Metric )

..f 1

7344(010 V

rl

V is veh speed (m/s)

( for small gradient)

Crr Description

0.0002 to 0.0010 Railroad steel wheel on steel rail

0.0025 Special racing tires

0.005 Tram rails standard dirty with straights and curves

0.006 to 0.01 Low-resistance car tires on smooth road; truck tires on smooth road

0.010 to 0.015 Ordinary car tires on concrete0.030 to 0.035 Ordinary car tires on tar or asphalt0.055 to 0.065 Ordinary car tires on grass, mud, and sand0.3 Ordinary car tires on sand

Rolling resistance

As speed increases , more heat is generated making the material softer and thus increase in rolling resistance

Grade Resistance Rg

gg WR sin

gg tansin

gg WR tanGg tan

WGRg

For small angles,

θg W

θg

Rg

-Gravitational force acting on the vehicle

G: grade in m/m or in %

Total resistance

Ft=Fa+Fr+Fg+ma Ft=a+bV+CV2

Gradient resistance

Rolling resistance

Air resistance

Total resistance

Velocity ( KMPH)

Res

ista

nce

(N)

For diff gradient find out ?

Propulsion Power Calculation (Tractive Effort)

Fw

Rrlf

Rrlr

mv a

W

Ftf

Ftr

hw

hg

la

lbL

Wf

Wr

Maximum Tractive Effort

mv gcos

mv gsin

Trf

Trr

When accelerating upward, the inertia force is downward

rd

Wf - weight distribution to the front wheel

Wr - weight distribution to the rear wheel

Maximum Tractive ForceFor front wheel drive

It is the multiplied value of coefficient of friction and the normal transferred weight

Ftmax=µ Wf

So,

Ftmax=µ [ ]max

Replace Fr with frl Mvg

Ftmax= µMvg{Lb+fr(hg-rd)}/{(1+µhg/L)L}

Neglecting wheel radius compared to the centre of gravity

Ftmax= µW(Lb+frhg)/{(1+µhg/L)L}

For rear wheel drive

Ftmax= µW(Lb- frhg)/{(1-µhg/L)L}

Maximum Tractive Force

Engine generated Tractive effort

Engine generated Tractive effort reaching the wheels

Engine speed vs wheel speed

Engine speed Gear reduction(Transmission &Differential)

Wheel speed

Lost 5%-25% of total efforts lostd 1

Gear reduction ratio 0

Mechanical efficiency of the drivelined

Gear box+

Final txn

CEE

320

Win

ter 2

006

Urban driving

Highway driving

Engine Generated Tractive Effort

IC engine power is: 10002 ee

enMp

eM

enEngine torque (N-m)

Engine speed in crankshaft revolution per second

Power in kilowatt (KW)IC engine

pe

What about if torque is specified in lb-ft

Engine Generated Tractive Effort

Electric motror driven vehicle

Engine-Generated Tractive Effort

rMF de

e 0

Fe = Engine generated tractive effort reaching wheels (N)

Me = Engine torque (N-m)

ε0 = Gear reduction ratio

ηd = Driveline efficiency (0.75-0.95)

r = Wheel radius (m)

Vehicle Speed vs. Engine Speed

0

12

irnV e

V = velocity (m/s)r = wheel radius (m)

ne = crankshaft rps

i = driveline slippage (2-5%)ε0 = gear reduction ratio

For 5 geared vehicle

• The minimum of:– Force generated by the engine, Fe– Maximum value that is a function of the vehicle’s

weight distribution and road-tire interaction, Fmax

max,mineffort tractiveAvailable FFe

AVAILABLE TRACTIVE EFFORT

Factors affecting are:-

1. Co-eficient of friction2. Gear ratio of driving forces3. Maximum power available to the gear system4. Safe working torque of the gear system

μm (Max tractive effort)

P/v = F ( inverse relationship)

Continuous tractive effort ( force)

Tractive EffortTractive Force (Effort) : Pulling Force exerted by the vehicle

1.0- Maximum Tractive Force 2.0- Engine Generated Tractive Force (P/v)

Maximum force/power beyond which the wheel spins & is a function of weight distribution and road-tyre interaction

The maximum tractive effort is given by: normalW

(Continuous)

1.0-Maximum Tractive Effort1.0-Maximum Tractive Effort :

Tractive Effort Relationships

1st gear

2nd gear

3rd gear

4th gear

w/o gear reduction

F max

Total resistance

Overall drive ratio( final drive+ gear box)

200025.004.0 m

Mr=M*m

Vehicle turning left Vehicle turning left

m=mass of vehv= velocityr=radius of curveF1,F2= Horizontal forces on tyresR1,R2=vertical reaction

F1+F2=mv2/rF1+F2=(R2-R1)*a/h

v= a. r. g/h

So mass plays no role in turning

Rollover dynamics

F1+F2<u * (R1+R2)

Deriving Vskid= u . g . r a/h>u

Skidding case

Home assignmentassignment on derivation !

Slippage is under 2 conditions

-Longitudinal slip- Cornering slip

Accelerate(wheelspin)

Braking(Lockup)

Best at 5 deg, worst at 90 deg

Tyre co-efficient of FrictionTyre co-efficient of FrictionEffect of various parameters on friction

Parameters Condition u

Speed Increase Reduces

Camber angle Increase Reduces

Tyre pressure Increase Reduces

Rain   Reduces

Road surface

Bituminous Highest

Asphalt Low

Cement Lowest

Temperature

Low Higher

High Higher

Optimum Lowest

Traction & Chassis designTraction & Chassis design

Traction : The output of a tyre from it’s handling point of view is it’s traction . In other words , how well it sticks to the ground It determines how fast a car can accelerate , brake and corner

Input for a tyre : Load, Output is Tractionj

So on a lighter car, one can negotiate faster

Traction reduces on positive camber due to lower patch area

Camber & Traction Cirecle of Traction

At acceleration, available traction for cornering is reduced