Development of a new way for optimizing vehicle performance calculations

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16 Νοε 2013 (πριν από 3 χρόνια και 8 μήνες)

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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