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
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
ISSN 0975 –668X| NOV 10 TO OCT 11 | VOLUME – 01, ISSUE - 02Page 1
JOURNAL OF INFORMATION, KNOWLEDGE AND RESEARCH IN
MECHANICAL ENGINEERING
- 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.
- 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 the chassis geometry, the torsional stiffness of the chassis can be calculated.
- 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
- 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.
- 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
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 2 : Middle Frame
- 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.
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.
- 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.
- REFERENCES
[1]Former Ford And Chrysler Chief Engineer Unveils New WayTo 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, Addison-Wesley 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.
ISSN 0975 –668X| NOV 10 TO OCT 11 | VOLUME – 01, ISSUE - 02Page 1