Sp
eakers Information
–
Virtual Powertrain Conferences
Deve
lopment of a new way for
optimizing
vehicle performance
calculations
Soares, Ana Cristina
MAN Latin America
Quintiliano, Bibiana
MAN Latin America
Dias, Rogério
MAN Latin America
ABSTRACT
Evaluation of vehicle performance is one of the most important phases of the new
vehicle development.
Start Ability
and
Top Speed
are factors that are noticed by users, therefore are very important to the final product. Vehicle performance
evaluation has been largely benefited from the use of simulation tools. In fact, MAN Latin Ameri
ca (ML) employs
simulation programs to evaluate the performance of its vehicles (trucks and buses) achieving good results. However,
those programs are normally “closed codes” which makes difficult the physical comprehension of results. Altogether, this
art
icle presents
Vehicle Dynamics
, an
Excel
®
macro developed by ML engineering team. The aim of this macro is the
automatic calculation of
Start Ability, Grade Ability, Top Speed
, among other performance parameters. In order to make
Vehicle Dynamics
faster an
d more elegant the macro’s interface was created in
Visual Basic
®,
since it
allows the use of
tools like “Add”, “Replace” and “Select”, among others. Those options allow it to be faster and help adding data as well as
registering several gear boxes, rear a
xle ratios and tires that are used by ML. Hence,
Vehicle Dynamics
enables
immediate and reliable evaluation of new products and as a consequence, the choice of the best powertrain configuration.
Furthermore,
Vehicle Dynamics
was also designed in order to b
e easy and didactic for users who want to have a deeper
unde
rstanding of vehicle behavior.
INTRODUCTION
Vehicle performance evaluation consists in studying in a analytical, numerical or experimental way the performance of a
given vehicle. In other words,
to establish what the maximum velocity that the vehicle will achieve is or the maximum
slope the vehicle will be able to negotiate, among
other performance parameters. Therefore, vehicle performance is
basically the evaluation of a vehicle longitudinal dyn
amics. The aim of this study is quantifying the main forces acting in a
moving vehicle (or even in a vehicle about to move), understanding their nature and, finally, establishing an equation to
relate all those forces.
LONGITUDINAL VEHICLE
DYNAMICS
Ac
cording to Gillespie [1],
determining the axle loading on a vehicle’s under arbitrary conditions is a first simple application
of Newton’s Second Law:
∑
(1)
Where:
F
x
–
Forces in the x

direction,
M
veic
–
Vehicle mass,
–
Acceleration at x direction
In order to
visualize
all the forces acting in a vehicle, a free body diagram can be very useful.
In figure 1,
the mentioned
forces
are
displayed.
Figure 1
–
Arbitrary forces acting in a vehicle [1].
M
v
–
Vehicle mass
Vehicle weight, acting upon front wheels,
Vehicle weight, acting upon rear wheels
F
aer
–
Force due to aerodynamic resistance
F
trat
–
Tractive force
R
xf
, R
xr
–
rolling resistances acting at frontal and rear wheels.
Among the forces presented in figure 1, it can be seen the tractive force which comes from engine torque and that is
responsible for vehicle movement. In contrast, the other forces, like aerodynamics forces and rolling resistance forces, act
against moveme
nt. Since the comprehension of the nature of those forces is vital to understanding vehicle dynamics, a
brief revision of them will be presented.
TRACTIVE FORCE
Engine torque is multiplied by gear
b
ox and rear axle ratio
to
generate the
propulsive
force
.
According to Newton’s Third
Law, a reaction to this force, that is called Tractive Force, will appear:
(2)
Where
:
Tractive force, N.
Torque generated by engine, Nm.
Gear box ratio, non

dimensional.
Rear axle ratio, non

dimensional.
–
Tire dynamic radius, m.
It is important to point out that tractive force is responsible for moving the vehicle; therefore it must be enough to
overcome all resistance fo
rces.
RESISTANCES
As mentioned before, the others forces
showed on figure 1 act against movement and, for that reason, they are called
Resistances. Those forces will be presented from now on.
Rolling resistance
–
this resistance is originated from the interaction between tires and road
surface and it can be
calculated as
:
(
)
(3
)
Where:
Rolling resistance force, N.
Vehicle mass,
kg.
Surface
coefficient
, non

dimensional.
Tire static
coefficient
, non

dimensional
Tire dynamic
coefficient
, non

dimensional.
Gravity acceleration, m/s
2
Slope, º
Aerodynamic Resistance
–
defined as
the resistance caused by
air
to the motion of a solid body moving through it
. It is
calculated as:
(4)
Aerodynamic resitance, N.
Aerodynamic resistance, N.
??
Air density, kg/m
3
.
Front area,
m
2
.
Vehicle velocity, km/h
Grade Resistance
–
On a grade, vehicle weight may have two
components, a cosine component
which is perpendicular to
the road surface and a sine co
mponent parallel to the road. This sine component acts against movement; therefore
it is a
resistance [1]. This force can be calculated by the expression:
(5)
Where:
Vehicle mass, kg.
Gravity acceleration, m/s
2
Slope, º
MOVEMENT EQUATION
Once the main forces acting longitudinally
in a vehicle have been defined, it is possible to apply Newton Second Law in
ord
er to relate them. Then:
∑
(1)
(6)
From equations (2), (3), (4) and (5):
(
)

(7)
VEHICLE PERFORMANCE
CALCULATION
After equation (7)
has been
defined
,
several parameter
s
used to describe vehicle
performance will be
calculated, applying
in each case, the proper boundary condition.
START ABILITY
Star Ability
is defined as the maximum slope that a vehicle is
able to negotiate, once it start
s from rest.
By definition,
Start
Ability
is
calculated at 1000 rpm. B
esides, th
e acceleration is considered to be zero. In doing so, equation (7) becomes:
(
)
(8)
Where:
T
1000
–
Available engine torque at 1000 rpm.
GRADE ABILITY
Grade Ability
is defined as the maximum slope that a vehicle is
able to negotiate, once it start
s
with a velocity different
from zero. Unlike
Start Ability,
which is calculated at 1000 rpm,
Grade Ability
can be calculated over the entire engine
range.
However, in genera
l it is calculated at maximum torque rpm as well as maximum power rpm. Applying the suitable
boundary condition, equation (7) becomes:
(
)
(
)
(9)
POWER SPEED
Defined as the
vehicle speed
that is
calculated at maximum power rpm, taking in account only kinematic factor
s
like gear
bo
x
and rear axle ratios, or in other words, not taking in consideration all resistances
presented previously. Power Speed
is calculate
d like:
(
)
(10)
Where:
TOP SPEED
It is the maximum velocity that a given vehicle can achieve
at a plane road,
after having overcome all vehicle resistances.
Again, it is considered that vehicle acceleration is zero a
nd, by definition, that slope angle is zero. Altogether, equation (7)
becomes:
(
)
(1
1
)
Since torque an
d velocity are func
tion of rpm, it is not possible to
know previously
in which rpm equation (1
1
) will be
verified, as a consequence, the solution is iterative, as it schematically showed in figure 2:
Figure 2
–
Iterative process for calculation Top Speed.
To begin with, a given rpm,
rpm
1
, is chosen and the correspond
ent torque,
T
1
,
and velocity, v
1
, are calculated. Then,
equation (1
1
) is calculated in order to verify if the sum result is zero. If not, another rpm,
rpm
2
, is chosen and all the
process is repeated.
There is only one rpm that verifies equation (1
1
) and to
this specific rpm there is a specific velocity.
This velocity is
Top Speed.
VEHICLE DYNAMCIS MAC
RO
The calculation of the presented parameters
is fundamental to de analytical/numerical evaluation of a vehicle
performance. It is necessary to repeat those calculations every time that a given vehicle powertrain configuration is
modified. For example, when gear box or tires are replaced. Nowadays, na
turally, those calculations are simplified by the
use of electronic macros like
Excel
®.
Even so, it is necessary to type long equations, always taking care to modify a
given parameters every time this appears in an equation. For example, if vehicle mass i
s modified it is necessary to
update equations (2) and (4) therefore,
Start Ability
,
Grade Ability
, and
Top Speed
will be influenced. In face of it, it is
clear that there is a need of an automatic way of calculating those equations, in order to save time
(of typing) as well as
make the calculation itself less prone to errors. This was the main purpose of creating the macro
Vehicle Dynamics
(in
short,
Dynamics
)
,
i.e., to make the principal performance calculations automatic. To the purpose of making the
u
nderstanding of
Vehicle Dynamics
easier, some sheets used to insert data, calculations and results presentations will be
presented.
DATA INSERTION
The first sheet
of
Dynamics
, which will be called
data

sheet
, is used to insert all necessary data to carry
out vehicle
performance evaluatio
n
. The
data

sheet
consists of
three tables, which will be presented in the following.
Figure
3
–
Data

sheet, table 1: insertion of GVW and engine curve.
As it is presented at figure
3, at the first table from
data

s
heet
,
vehicle type, GVW (Gross Vehicle Weight) are informed as
well as engine

torque curve. On figure 4, it is showed table 2, where transmission type can be chosen. By clicking
“Choose New Gear Box”, a new dialog box opens, where several kinds of gear
boxes can be chosen. Additionally, there is
a sheet where it is possible to insert new gear boxes
1
.
Figure 4
–
Data

sheet, table 2: inclusion of gear boxes ratios.
1
Not shown in this paper.
Figure 5
–
Data

sheet, table 2: choosing of desired gear box.
Finally, table 3 is
showed on figure 6. As it can be seen, there are four buttons to select automatically rolling resistance
coefficients, RC
est
and RC
dyn
, tire dimensions, rear axle ratio (RAR), and road type. In the several other fields showed it
can be inserted front area,
aerodynamic resistance coefficient, air density, in short, all vehicle data. Furthermore, on figure
7, it is presented a dialog box for choosing RAR: at first user chooses between single or double axle and then, the rear
axle ratio is chosen.
Figure 6
–
Data

sheet, table 3: insertion of road type, efficiency, front area, etc.
Figure 7
–
Data

sheet: dialog box used for choosing rear axle type as well as its ratios.
AUTOMCATIC CALCULATI
ONS
Once all data ha
s
been inserted, performance calculation is almost automatic.
In
Dynamics
there are 5 sheets, each one
related to one of performance parameters:
Start Ability, Grade Ability, Top Speed, Velocity
and
rpm
.
In each of those
sheets it is possible to visualize which data was used in the calculation. For example, in
Start Ability
sheet, figure 8, it can
be seen GVW, torque at 1000 rpm, gear box and rear axle ratios, among others. This possibility of consulting t
he
calculations allows the user to understand how a given parameter is calculated besides knowing which factors are taken
in account. As a consequence, the user is able to evaluate how to improve that parameter.
For example, in
Start Ability
case, if the
user needs to enhance this factor,
it is clear from figure 8, that the easiest possibilities are choosing a gear
box or rear axle with different ratios. (Of course, it is possible to reduce GVW, but this is not a viable alternative).
Figure 8
–
Start
Ability sheet
There is onl
y one sheet whe
re calculation is not fully automatic
, that is,
Top Speed
, since it was explained before,
Top
S
peed
calculation is iterative.
Because of this,
Top Speed
sheet was created in a way that t
he calculation presented on
equa
tion 10 is perfo
r
med over all
engine rpm
range.
To each pair torque/rpm, the macro calculates automatically the
available tractive force (function of torque/rpm), vehicle velocity (function of rpm) and resistance forces (function of rpm)
.
Then equation
(1
1
) is calculated repeatedly, until it is verified:
(
)
(1
1
)
This
iterat
ive process is showed schematically on figure 9.
Figure 9
–
Top Speed iterative calculation.
RESULTS PRESENTATION
The last sheet of
Dynamics
is the one where all results are presented in a clear and self

understanding way. This sheet,
named
Results
, is showed on figure 10. The presented results are
Start Ability, Grade Ability, Top Speed, Power
Spee
d,
besides
the rpms to achieve the velocities of
60, 70,
80 e 90 km/h
.
Results
sheet is very useful for the user that wants
only to have fast and reliable results, not needing to understand the physics behind them.
Figure 10
–
Results sheet.
EVALUATION OF VEHICL
E DYNAMICS RESULTS
Before starting to use any simulation program it is fundamental that the user can
trust the results generated by this
program. There are basically two ways of achieving a significant grade of confidence in simulation
programs. The first is
comparing simulation results with experimental ones while the other is using another program that is reliable and well
established as a standard. In this paper,
Dynamics
results were compared to a former macro used by ML, whose name
is
Performance
. This macro has been used for several years by ML engineers, with excellent adherence with experimental
results. As a result, the comparison between
Dynamics
and
Performance
was enough to validating the former. It is
important to point out
that both macros,
Dynamics
and
Performance
,
were created based on classical statics and
dynamics equations. Those equations do not need any kind of validation.
What needs validation, after all,
is
Dynamic
macro itself,
beginning with the typing of all presented equations till the automatic fulfillment of
Start Ability, Grade Ability,
Top Speed, velocity
e rpm sheets.
Table 1
–
Comparison between normalized results from Performance and Dynamics. Several products from MA
N Latina America have
been simulated.
Bus
S
tart
Ability
G
rade
Ability
T
op
Speed
Performance
1,0000
1,0000
1,0000
Dynamics
1,0005
1,0000
1,0005
Light Truck
Performance
1,0000
1,0000
1,0000
Dynamics
1,0006
0,9998
0,9988
Medium Truck
Performance
1,0000
1,0000
1,0000
Dynamics
1,0004
1,0020
1,0050
Heavy Truck
Performance
1,0000
1,0000
1,0000
Dynamics
1,0007
0,9998
1,0006
From table 1, it can be seen that the agreement between
Dynamics
and
Performance
was excellent, for buses and trucks.
Based on those results,
Vehicle
Dynamics
was validated, being
used nowadays by ML engineering team.
CONCLUSION
Numerical/analytical evaluation of vehicle performance is based
on
several equations originated from statics and
vehicle
dynamics
. In some cases, those equations are virtually huge besides taking in account several data like vehicle mass,
front area, engine torque, etc. On the other hand, the choice of the best powertrai
n configuration requires the repetitive
evaluation of several gear boxes, rear axle and tires.
Altogether, it is evident that creating a macro able to calculate all
performance parameters in a
n
automatic way is
more than desirable. Consequently, MAN Latin
America engineering
team developed
Vehicle Dynamics,
an Excel macro where parameters like
Start Ability, Grade Ability, Top Speed
and
Power Speed
are automatically calculated.
Vehicle Dynamics
was validated based on analytical results, presenting
excellent
agreement with them.
For this reason,
Vehicle Dynamics
is being used successfully by MAN Latin America
engineering team.
REFERENCES
1.
Gillespie, Thomas D., “Fundamental of Vehicle Dynamics”, Society of Automotive Engineers, Inc.
2.
Azevedo Jr, G., “Apostila
Performance Veicular”, Associação Eduacional Dom Bosco.
CONTACT INFORMATION
Ana Cristina Cosme
Soares
Engenheiro Alan da Costa Batista, 100
Pedra Selada, CPI 4227
Cep 27511

970 Resende, RJ
Telefone: 5524

33811421
e

mail:
ana.soares@volkswagen.com.br
Bibiana Quintiliano
e

mail:
bibianaquintiliano@hotmail.com
ACKNOWLEDGMENTS
Author
s
would like to acknowledge
engineer
Geraldo Azevedo Junior, for support with
Performance
macro
and engineer
Frederico Braz e Silva for technical support. Finally, a
uthor
s
acknowledge
MAN Latin America for general support.
DEFINIÇÕES/ABREVIATU
RA
F
trat
Tractive Force
T
motor
Engine Torque
i
g
Gear box ratio
I
d
Rear axle ratio
R
dyn
Tire dynamics radius
F
rol
Rolling reistance force
M
veic
Vehicle mass
RC
est
Tire rolling resistance, static
RC
dyn
Tire rossling resistance, dynamic
g
Gravity acceleration
Slope angle
F
aer
Aerodynamic force
C
w
Aerodynamic drag coefficient
Air density
v
Vehicle velocity
F
grad
Grade force
GVW
Gross Vehicle Weight
RAR
Rear Axle Ratio
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