Resistance Forces on A Vehicle

P M V SubbaraoProfessor

Mechanical Engineering Department

Estimation of Vehicle Demands….

Resistance Forces on A Vehicle

• The major components of the resisting forces to motion are comprised of :

• Acceleration forces (Faccel = ma & I forces)• Aerodynamic loads (Faero) • Gradeability requirements (Fgrade)• Chassis losses (Froll resist ).

maFFFF grraero

Force System Due to Rolling Resistance

3

Road Conditions

5

Rolling Resistance

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

The magnitude of this force is Approximated as:

Rolling resistance of a vehicle is proportional to the component of weight normal to the surface of travel

gV M C = P rrrr

MgFrr MgCF rrrr

Standard Formula for Rolling Resistance

V M C )10 (2.72 = P

V M C 3600

9.81 = P

rr3-

rr

rrrr

where:

P

= power (kW)

Crr

= coefficient of rolling resistance

M

= mass (kg)

V

= velocity (KpH)

147101.0

VCrr

Contact Type Crr

Steel wheel on rail 0.0002...0.0010

Car tire on road 0.010...0.035

Car tire energy safe 0.006...0.009

Tube 22mm, 8 bar 0.002

Race tyre 23 mm, 7 bar 0.003

Touring 32 mm, 5 bar 0.005

Tyre with leak protection 37 mm, 5 bar / 3 bar

0.007 / 0.01

Typical Values of Coefficient of Rolling Resistance

Effect of Road Condition on Crr

9

Rolling Resistance And Drag Forces Versus Velocity

Grade Resistance

Composed of – Gravitational force acting on the vehicle

gg mgF sin

gg tansin

gg mgF tan

Gg tan

mgGFg

For small angles,

θg mg

θg

Fg

Total Vehicular Resistance at Constant Velocity

     AR = air resistance [N]           RR = rolling resistance [N]

            GR = gradient resistance [N]TR = total resistance [N]

           

Res

ista

nce

Vehicle Speed

Steady State Demand Curve

Vehicle Speed vs. Engine Speed

o

crank

G

irNV

60000

12

V = velocity , km/hr

r = wheel radius, m

Ncrank = crankshaft rpm

i = driveline slippage

GO = Overall gear reduction ratio

Typical Engine Torque-Power Curves @ SS

wheel

EE r

TF

Steady State Demand Vs Available Effort

16

Inertial or Transient Forces

• Transient forces are primarily comprised of acceleration related forces where a change in velocity is required.

• These include:• The rotational inertia requirements (FI ) and • the translational mass (Fma). • If rotational mass is added to a translating vehicle, it adds not

only rotational inertia but also translational inertia.

Inertial Resistance

18

a m = F vehicleeffIR

a m m = F eqvehicleIR

where:FIR = inertia resistance [N]         meff-vehicle = Vehicle mass + Equivalent mass of rotating parts [kg]a = car acceleration [m/s2], (from 0 to 100 km/h in: 6 s (4.63 m/s2), 18 s (1.543 m/s2))mvehicle = Vehicle mass [kg]meq = Equivalent mass of rotating parts [kg]

19

= angular acceleration k = radius of gyration

Equivalent Mass of Rotating Parts

Torque due to any rotating part (ex. Wheel)

wheelwheelwheeli I = dt

d I = T

wheel2

wheel k m =r

a = tire

vehiclewheel

wheels and axles = 78% of total polar inertia propeller shaft = 1.5%Engine = 6%Flywheel and clutch =14.5% 

Therefore the equivalent mass of all rotational parts including losses is represented as:

2

22

2

2

2&

wheel

gbfmtclutchflywheele

wheel

ffpropeller

wheel

axleswheeleq r

GGIII

r

GI

r

Im

Required Torque & Power at Wheels

wheel

vehicledemandwheel

pT

wheel

vehicledemandwheel N

pT

2

60

wheel

mtenginewheel N

pT

2

60

fgb

engine

mtenginewheel

GGN

pT

2

60

fgb

engine

mtenginewheel

GGN

pP

2

60

mtfgbenginewheel GGTT

wheel

mtfgbengine

wheel

wheelTE r

GGT

r

TF

Tractive Effort demanded by a vehicle):

Available Vehicle Tractive Effort (TE):

The minimum of:1. Force generated by the engine, Fe2. Maximum value that is a function of the vehicle’s

weight distribution and road-tire interaction, Fmax

max,mineffort tractiveAvailable FFe

Tractive Effort Relationships

24

MATLAB for Vehicle Torque Requirement

MATLAB Model for Transmission System

Requirements of Vehicle on Road & Engine Power

Urban Driving Cycle

Engine RPM during Urban Driving Cycle

Engine Fuel Consumption During Urban Driving Cycle