Basic Vehicle Performance Modeling

8/13/2019 Basic Vehicle Performance Modeling

1/18

ME 379M/397 Prof. R.G. Longoria

Vehicle System Dynamics and ControlDepartment of Mechanical Engineering

The University of Texas at Austin

Basic VehiclePerformance Modeling

Prof. R.G. Longoria

Spring 2004v.1


2/18




Overview

Basic 2 axle vehicle model

Review typical road loads

Example modeling for performance


3/18




Performance Modeling

Performance usually relates to longitudinal motion of a vehicle,

and is constrained by one of two limits.

The first is a power plant limitation, which tends to be especially critical

at high speed. The second limitation is traction, which tends to dominate at low speeds.

In both cases, the impact on acceleration or deceleration is of

particular interest. Some common needs might be:

Finding torque and power for a given application (e.g., to go up a hill,

drawbar)

Selecting a power plant

Development or evaluation of cruise, braking, traction, or engine control


4/18




Basic Model 2 axle vehicle

From Wong, Chapter 3, Fig. 3.1

xx x

dvp m m a F

dt= = =

Along the longitudinal (x) axis:x

z

Tractive force Road LoadsxF =

,

,

tractive effort on front and rear

aerodynamic resistance force

rolling resistance on front and rear

drawbar load

grade resistance sin

x f r a rf rr d g

f r

a

rf rr

d

g s

F F F R R R R R

F

R

R

R

R W

= +

=

=

=

=

= =


5/18




Basic Model 2 axle vehicle

From Wong, Chapter 3, Fig. 3.1

x z

0

0

zz z

y

y y y

dvp m Fdt

dh I T

dt

= = =

= = =

Use equilibrium conditions in thevertical direction and about the y

axis.

Need to:

1. Find loads on the axles2. Use knowledge of road adhesion

and other vehicle parameters to

determine tractive effort (TE)


6/18




Dissipative Loads

Recall, any dissipative forces take the form of effort vs. flow.

For translation: force (F) velocity (V) plots

For rotation: torque (T) (angular) speed () plots

orF T

orV

( or )V forbidden

forbidden


7/18




Aerodynamic Forces and Moments

Aerodynamic effects can affect vehicular dynamics in several

ways.

Refer to Wong, Section 3.2 or Gillespie, Ch. 4, for a detailed discussion of aerodynamic

effects.

From Gillespie (1992)

MomentForceDirection

Yawing

moment

Lift forceVertical,

positive

upward

Pitchingmoment

Side forceLateral,positive right

Rolling

moment

Drag forceLongitudinal,

positive

rearward


8/18




Tire Force and

Moment ConventionsGillespie (1992)

Wong (1993/2001)


9/18




Rolling Resistance Primarily caused by hysteresis in tire materials due to deflection of the

carcass while rolling.

Others factors that might contribute to RR in tires: friction in sliding, air

circulation, fan effect of rolling tire.

Dominant load at low speeds; dependent on speed.

Example: loads on tire at 80-95 mph

(90-95% hysteresis, 2-10% friction, 1.5-3.5% air resistance)

For free-rolling tire, a horizontal force is introduced to balance the rollingresistance moment, which arises when pressure shifts to leading half due to

carcass deflection.

Ratio of rolling resistance to normal load is the coefficient of rolling

resistance, which incorporates all the complicated and interdependent

physical properties of tire and ground.

Aerodynamics become equal to rolling at about 50 or 60 mph.


10/18




Typical Road LoadsFrom Steeds, Mechanics of Road Vehicles (1960)

Generally, we assume that

aerodynamic effects can

be ignored for low groundspeeds.

Rolling resistance and

grade dominate until

about 50 to 60 mph.


11/18




Estimating Rolling Resistance

7 20.0136 0.4 10rf V

= +

Ex. Radial-ply passenger car tires under rated loads and inflation

pressures on a smooth road (Wong, Ch.1),

From Automotive Handbook (SAE)

with V in km/h.

Total force is estimated on all

wheels,r rf rr r F F F f W

= + =

where Wis the total weight on the

vehicle.

In some cases, can approximate with

average values, as given the table

shown.


12/18




Additional Estimates

0.01(1 /100), ( in mph)rf V V= +

Speed dependence of rolling resistance

For low speeds:

At higher speeds: ( )2.5

3.24 , ( in mph)100

basic coefficient

speed coefficient

r o S

o

S

Vf f f V

f

f

= +

=

=

From Automotive Handbook (SAE)


13/18




Vehicle on an Incline 1

From Wong (2001)


14/18





These equations can be

formulated to solve for the 3

unknowns:


15/18





14. 036deg=Ftm axfv( ) W cos ( )

b h frv( )+( )

L h +( ):=Ftmaxrv( ) W cos ( )

a h fr v( )( )

L h ( ):=

atan 1

4

:=

Fa v( ) 1

2 Cd Af v( )

2:=fr v( ) A B v( )

2+:=Fg ( ) W sin ( ):=

r 33 cm:=

b L a:= 0. 8:=

1.23kg

m3

:=

B 0.4 10 7

1

km

hr

2:=a 127 cm:=

mvW

g:=

Cd 0.45:=h 50.8cm:=

A 0.0136:=Af 2.32m

2:=L 279. 4cm:=W 4500lbf :=

Data for Proble m 3.1 from Wong (1993)


16/18





RWD11182674

FWD10574843

RWD6982742FWD6074931

TypeV (m/s)Ftmax (N)Pt.

Check out the power delivery.

Line 2 = 571 kW! (766 hp)

Graphically extracted results

Does this seem reasonable?


17/18




Summary Road Loads

This overview of road loads illustrates the largeamount of information available related to predictingand controlling typical road loads.

Basic analysis can be conducted to determineacceleration performance on grades underaerodynamic loading, including the effect of rolling

resistance. Later, we will examine how power plant and

transmission effects play a role in longitudinal

performance.

First, we will study tire-ground interaction in moredetail to understand braking and traction applications.


18/18




References1. Steeds, W., Mechanics of Road Vehicles, Illiffe and Sons, Ltd., London,

1960.

2. Gillespie, T.D., Fundamentals of Vehicle Dynamics, SAE, Warrendale, PA,

1992.

3. Wong, J.Y., Theory of Ground Vehicles, John Wiley and Sons, Inc., New

York, 1993 (2nd) or 2001 (3rd) edition.

4. W.F. Milliken and D.L. Milliken, Race Car Vehicle Dynamics, SAE,

Warendale, PA.

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