determinación de la trayectoria ideal de un vehículo de alto desempeño en una pista pre-definida ...

143 Pages·2010·2.36 MB·Spanish

by  Vinicio Ayala

UNIVERSIDAD CENTROAMÉRICA
“JOSÉ SIMEÓN CAÑAS”

DETERMINACIÓN DE LA TRAYECTORIA IDEAL DE UN
VEHÍCULO DE ALTO DESEMPEÑO EN UNA PISTA
PRE-DEFINIDA CONSIDERANDO RESTRICCIONES
GEOMÉTRICAS Y FÍSICAS

PARA OPTAR AL GRADO DE
INGENIERO MECÁNICO

POR:
RENÉ VINICIO AYALA SARAVIA

OCTUBRE 2010
ANTIGUO CUSCATLÁN, EL SALVADOR, C.A.
RECTOR
JOSÉ MARÍA TOJEIRA, S.J.

SECRETARIO GENERAL
RENÉ ALBERTO ZELAYA

DECANO DE LA FACULTAD DE INGENIERÍA Y ARQUITECTURA
EMILIO JAVIER MORALES QUINTANILLA

COORDINADOR DE LA CARRERA DE INGENIERÍA MECÁNICA
MARIO WILFREDO CHÁVEZ MOLINA

DIRECTOR DEL TRABAJO
MARIO WILFREDO CHÁVEZ MOLINA

LECTOR
AARÓN MARTÍNEZ
THANKS TO

All the persons that made possible the realization of this investigation, but in special to:
My parents, my brothers and all of my family who supported me while realizing the present
investigation.
To the professor Mauro Speranza Neto for the orientation that he gave me during the
realization of the investigation.
To the persons that are involved in the exchange program of the University UCA and the
University PUC, that permitted me to realize this investigation within an exchange program
in the PUC University.
To the professor Mario Chávez, who was my tutor in El Salvador and who was always
orientating my work from there.
To my friends for always being there, supporting me while developing this project and for
encourage me for develop well the present investigation.
To God, for allow me finalize successfully the present investigation and for guiding me
through the whole project.

DEDICATORY

Dedicated to my father and my mother.

EXECUTIVE SUMMARY

In the present investigation it was pursued the develop of a theoretical base of the behavior
of a high performance vehicle in a race-track, considering certain geometrical and physical
restrictions, being these used for establish parameters that was going to be easily used for
whatever race-track that is needed to be evaluated. Parting from this base, it was intended
to develop a program that could be able to determine the best path that could be taken by
the vehicle in the race-track selected, having like a final result the time that the vehicle
needed for covering one lap in the race-track, considering that in each corner it was taken
the biggest arc radius that can fit on it.
By saying that a theoretical base was needed to be created, it means that before defining the
problem of the present investigation it is needed to be defined all of the variables that are
going to affect the behavior of the vehicle in the race-track, to define the kind of segments
that the different race-tracks will count with and the important points within the race-track
for having a behavior that would permit to reach the best time possible within the model
that is being analyzed.
First of all it is important to understand how the vehicle is going to be evaluated within the
investigation, making some simplifications on it for having a mathematical model that
could be easily evaluated for every point in the race-track. The simplifications that were
made to the vehicle are resumed in the one that takes the vehicle like a single particle that is
moving around the race-track, having with this an approximation to the real behavior of the
vehicle, that even so is not the most trustable result that could be expected, for educative
and understanding endings gives an acceptable evaluation of the vehicle and an idea about
how the vehicle should behave within the race-track.
The model of the vehicle that is being evaluated is a high performance vehicle which is
capable to support high amounts and changes of acceleration and velocity and the idea of
the investigation is to try to work within these limits of velocity and acceleration for trying
to reduce the most possible the lap-time of the vehicle. The high performance vehicle
model was capable to cover the selected race-track in a range of velocities between 0 km/
h
and 300 km/ and it was capable to support changes of centripetal acceleration and tangential
h
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acceleration fixed by the Modified Friction Circle limits which is a graphic that delimits the
total acceleration that the vehicle could support in whatever point of the race-track within a
plane where its principal axes are the tangential acceleration (G) vs. the centripetal
acceleration (G) having like a resultant the total acceleration plotted in the GG Diagram.
The graphic that delimits the acceleration of the vehicle is shown in the figure below.
The modified friction circle limits
2
1
0 Centripetal
acceleration
-6 -4 -2 -1 0 2 4 6
-2
-3
-4
-5
Tangential acceleration
Modified friction circle limits for a high performance vehicle

For evaluating the race-track there will be needed to divide it in traces, which will only
depend of the race-track that is being evaluated, where one by one it will be applied a
criteria to follow of the behavior of the velocity of the vehicle through each trace. The three
principal kind of traces in which the track it is going to be divided are the followings:
 The straights that could be taken like straights.
 The straights that could be taken like “S Curves”.
 The corners (Applying the maximum arc radius on each one).
From the last three kinds of traces, the corners are the ones that have the biggest influence
in the lap-time of the vehicle and parting by this idea, these traces should be deeply
analyzed for having a better behave of the vehicle in the entire race-track. So the corners
will have three important points to take in count for having the best behave possible in the
corner and for reaching the higher radius possible in each one, which are (These points are
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shown in the figure below and for each race-track were obtained and designed with the
program Autocad):
 The track-in point.
 The apex point.
 The track-out point.

The three points for making the maximum radius in a corner

And the last limitation at what the vehicle is going to be fixed to, is the geometrical
limitation (which is the same race-track) because it has to be considered that the vehicle
could not abandon the race-track in any moment, so all the design made for constructing the
ideal line that the vehicle should follow it would have to be done considering the fact that
the vehicle should be moving within the limits of the race-track.
After all of the considerations about the vehicle and the race-track have been taken in
count, a program created in Visual Basic for Applications and executed in Microsoft Excel
was used for evaluate each trace of the race-track that is wanted to be analyzed, having like
a final result the curves of “Velocity vs. time”, “Tangential acceleration vs. time”,
“Centripetal acceleration vs. time” and the total time that the vehicle spent for making a
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complete lap in the race-track. The typical graphics that the created program is capable to
generate are like the ones that are shown below.

V vs. t
V (m/s)
80
60
40
20
0
0 5 10 15 20 25 30 35 40 45
t (s)
Velocity of the vehicle vs. time in one lap

a vs. t a vs. t
an (G) n at (G) t
6
2
4
2 1 t (s)
0
0
0 5 10 15 20 25 30 35 40 45
-2 0 5 10 15 20 25 30 35 40 45 -1
-4 -2
-6 -3
t (s)
-4
Centripetal and Tangential acceleration vs. time

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