JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN
MECHANICAL ENGINEERING
OPTIMIZATION OF TORSIONAL STIFFNESS OF A
EICHER 11.10 CHESIS USING EVOLUTIONARY
METHODS WITH A HETEROGENEOUS GENOTYPE
REPRESENTATION
1
M. R. GALOLIA, 2 PROF. M. J. PATHAK
1
Lecturer, Department Of Mechanical Engineering, Government Polytechnic,
Junagadh, Gujarat
2 Head, Department Of Automobile Engineering, Sir Bhavsinhji Polytechnic Institute ,
Bhavnagar, Gujarat
mukeshgalolia@yahoo.com
ABSTRACT : Automotive chassis is an important part of an automobile. The chassis serves as an frame work
for supporting the body and different parts of the automobile. Also, it should be rigid enough to withstand the
shock, twist, vibration and other stresses. We present an optimization approach for EICHER 11.10 Chesis a
frame based on evolutionary methods. The optimization objective is to minimize the mass of the frame subject to
a given torsional stiffness and a strength constraint occurring during braking of the vehicle. Further we take
into account different constraints on available sizes, what leads to continuous, discrete or even mixed
optimization variables. The Luego prototype chassis was tested to determine the value of its global optimized
torsional stiffness. This value was calculated to be 1330Nm/deg. This value was to be improved upon by using
Creation of a Finite element baseline validation model, Discussed modification of this model, A design
improvement study and An optimization study
1. INTRODUCTION
For the race-track performance of a vehicle the main
frame, connecting the front wheels via front fork and
steering shaft with the swing arm, is one of the most
crucial parts. Today as in the last decade, there were
two successfully applied concepts for such frames.
One is an aluminum-box frame, typically applied in
Japanese cars. The other one, mainly used by the
Italian builder Ducati, is a steel trellis frame. Both
concepts showed to perform at an equal level during
the last decade of vehicle. In this work we will focus
on the optimization of a tubular steel trellis frame.
Therefore, as a starting point, we use a chesis of the
EICHER 11.10, that has been continously improved
and already rigid enough during the last decade. To
optimize such a frame, one has first to be aware of
what the design objectives. Considering only drive
application, as we do within this work, weight is
always a central issue. Further the stiffness of the
frame between the steering shaft and the swing arm is
a crucial parameter. But it is not maximum stiffness
that designers want to achieve; in fact they want to
have a certain compliance. This compliance depends
on various parameters such as the geometry of the car
or the power deconvolution of the engine. For our
work, we will not discuss this parameter further, we
just assume that a certain stiffness/flexibility has to
be achieved. Experience shows that this stiffness
values are so high, that maximum stresses induced by
a torsional load case are far below critical values. A
second relevant load case is braking. Considering
sport or race bikes, principally the front brake
produces the whole deceleration. Therefore via front
fork and steering shaft a momentum and a
compressive force are introduced into the chassis. For
this load case not stiffness but strength is crucial.
2. TORTIONAL STIFFNESS OF A
CHESIS
The torsional stiffness of a vehicle’s chassis
significantly affects its handling characteristics and
is therefore an important parameter to measure. In
this work a new twist fixture apparatus designed to
measure the torsional stiffness of a Winston Cup
series race car chassis is described. The twist fixture
is relatively light weight,adjustable, and easily
transportable by one person for quick set-up on
different chassis. Measured values of torsional
stiffness are reported for several different chassis.
The fixture applies vertical displacements (using
linear, jack-screw actuators) at the front spring
perches of the chassis while holding the rear perches
fixed. Conventional race car scales located under the
front assembly measure the resulting reaction forces
due to the displacements.
Dial indicators are placed at selected locations along
the chassis to measure deflections. Using the dial
indicator readings, the measured reaction forces and
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the chassis geometry, the torsional stiffness of the
chassis can be calculated.
3.
TORSIONAL LOAD (OR TWISTING
MOMENT)
It is caused due to vertical load when the vehicle
comes across a road bump. The twisting induces a
shear stress in frame. The frame is designed strong
enough to resist torsion by proving

Torque-resisting members

Cross-members

A radius rod
4. BASIC IDEAS OF EVOLUTIONARY
ALGORITHMS
IN
STRUCTURAL
OPTIMIZATION
Evolutionary Algorithms use an analogy with natural
evolution to perform search by evolving solutions to
problems, usually working with large collection of
solutions at a time. The common underlying idea
behind the techniques is to have a given population of
individuals (solutions); the environmental pressure
causes natural selection and hereby the fitness of the
population is growing. From the point of view of
classical optimization, EAs represent a powerful
stochastic zeroth order method and can find the
global optimum of very rough functions. In Structural
Optimization, EAs are used in many different forms.
Commonly they are divided into four categories
However, they are all based on similar evolutionary
principles. Therefore we will use amore modern
terminology also used by and we generally speak
just of Evolutionary Algorithms. All
Fig 1. Basic scheme of an Evolutionary Algorithm
the above listed strategies can be seen as
specializations of general EAs which we will
describe below. EAs use two separate spaces: the
search space and the solution space. The search space
is a space of coded solutions (genotype) to the
problem. The solution space is the space of actual
solutions (phenotype). EAs maintain a population of
P ∈ N individuals. Each individual consists of a
genotype and a corresponding phenotype. A simple
EA works as outlined in Figure 2. A population of a
given number of individuals is initialized randomly.
The fitness of the whole population is evaluated
(Evaluation). A fitness value can be assigned to every
individual by applying the objective function as an
abstract fitness measure. The fitness from the
evaluation is then used to determine how many
copies of each individual are placed into a temporary
area often termed the mating pool. For reproduction
parents are picked from the mating pool by giving
some preference to individuals with better fitness
values (Selection). Offspring are generated by the use
of the crossover operator, which randomly allocates
genes
from each parent’s genotype to each
offspring’s genotype. Mutation is then occasionally
applied to the offspring. A new population is built by
deterministic or stochastic choice of parents and
offspring (Replacement). Then the new individuals of
the population are evaluated. The entire process of
evaluation, reproduction and replacement continues
until a given termination criterion is reached. This
can for example be triggered by with the values of a
time or generation counter or the best fitness of the
population.
5. PROGRAMMING TOOLS
Within our work, we use different C++ software
libraries freely available under a public license as
open source. The evolutionary strategies in this work
are implemented using the EO (Evolving Objects)
library 1 . Fitness evaluations are accomplished using
the FELyX (Finite Element Library eXperiment)
library 2 developed at our chair. Everything was done
under Linux/Unix operating systems and compiled
with GNU gcc compilers 3 . As pre- and
postprocessor for the Finite Element model of the
frame, we used the commercial Finite Element
software ANSYS4 . 3.1 EO - The Evolvable Objects
Library
EO - the Evolvable Objects library allows to evolve
any data structure (object) that provides the necessary
operators
for
the
according
evolutionary
programming paradigm. Basically EO just provides
the building blocks to perform any kind
of
evolutionary strategy within the field of evolutionary
computing. Nevertheless common paradigms like
Genetic Algorithms, Evolutionary Strategies,
Evolutionary Programming, or Genetic Programming
are already implemented in the actual release of EO.
The design improvement study performed resulted in
a optimum torsional stiffness of 6448Nm/deg, an
increase of 377% over the baseline model. A
maximum increase in efficiency of 286% to
23g/Nm/deg for a mass of 148.3Kg accompanied this
increase in torsional stiffness resulting optimizing
parameter.
Material of the “C” channel is taken as : St 52
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6. ASSEMBLY
Just as we can combine features into parts, we can
also combine parts into assemblies. Assembly mode
in Pro/ENGINEER enables we to place component
parts and sub assemblies together to form assemblies, as
well as to design parts based on how they should fit
together. We can then modify, analyze, or reorient
the resulting assemblies.
The test procedure is the same as that used with the
chassis except the maximum twist value is much
larger.
The standard is twisted in increments of ±0.100” up
to a maximum value of ±1.000” measured with the
front dial indicators placed 32” apart.Based on beam
theory to predict the deflection of the square beams,
simple torsion for the circular tube, and with ball
joints (free rotations) at each end of the standard, the
vertical reactions at the front are equal and opposite
with magnitude, where
Az = Right-front reaction force
Bz = Left-front reaction force
G = Modulus of rigidity of steel
J = Second polar moment of area of circular tube
d = Twist fixture jack-screw displacement
l = Longitudinal distance between front and rear
supports
d = Lateral distance between left and right supports
E = Modulus of elasticity of steel
I = Second moment of area of square sections
From the applied twist angle
q = 2d/d, the torsional stiffness predicted by the
analysis is,
Figure 3 : Assembly of Chassis elements
At present time the problem of enhancing optimized
stiffness is very actual for the world automotive
industry and chassis is the backbone of the
automotive system. Day by day modification has
been done in existing system to increase strength and
durability with minimum possible cost. Here is the
one approach presented.
This work presents to study the optimized stiffness of
automobile chassis. When different parts are mounted
o n it at that time no. of stresses are produce in
chassis. First Design stress is calculated then it was
compare with the stress result of Finite element
Analysis report by using pro-Mechanica tool. Then
the model is then optimized for said parameter.
7. CONCLUSION
We introduced an universal genotype for
optimization of heterogeneous parameter lists and
applied it successfully to different optimization
problem formulations in context of a CHASSIS OF
EICHER 11.10. Further we used normalized function
formulation for the different terms contributing to the
fitness function. This made it quite easy and
understandable to find adequate coefficients for the
different terms of the fitness function. Surprisingly,
this frame design, intensively developed during one
decade, still shows quite some potential for
improvement. We could reduce the weight by 20.8%
while preserving the originally desired mechanical
properties. This also demonstrates the potential of
using this optimization not only for weight reduction,
but to easily realize specific mechanical properties of
a structure in a very efficient way.
8.
REFERENCES
Figure 2 : Middle Frame
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JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN
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[1]
Former Ford And Chrysler Chief Engineer
Unveils New Way To Design Vehicles At Sae World
Congress
[2]
P. Hajela, Stochastic Search In Structural
Optimization: Genetic Algorithms And
Simulated
Annealing, In: Structural Optimization: Status And
Promise, Vol. 150,
Progress In Astronautics And
Aeronautics, 1992, Pp. 611–637.
[3]
L. Fogel, A. Owens, M. Walsh, Artificial
Intelligence Through Simulated
Evolution, John
Wiley, New York, 1966.
[4]
D. Goldberg, Genetic Algorithms In Search,
Optimization And Machine Learning,
AddisonWesley Publishing Company, Inc., Reading,
Massachusetts, 1989.
[5]
P. Soni, “Effects Of Chassis Flexibility On
Roll Stiffness Of A Winston Cup Stock
Car Using
The Finite Element Method”,Masters Thesis,
Department Of
Mechanical Engineering, Clemson
University, May 1998.
[6]
Analysis Of Torsional Stiffness And Design
Improvement Study Of A Kit Car Chassis Prototype,
By Wesley Linton, M.Sc. Thesis, Cranfield
Niversity,School Of Industrial And Manufacturing
Science Motorsport Engineering And Management
2001-2
[7]
Automotive Chassis-Brake, Suspension,
Steering – By Lane Eichhen.
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