optimization of weight of flywheel

1 Optimization Of Weight Of Flywheel

CHAPTER 1

INTRODUCTION

1.1 INTRODUCTION Design optimization can be defined as the process of finding the maximum or minimum of some

parameters which may call the objective function and it must also satisfy a certain set of

specified requirements called constraints. Many methods have been developed and are in use for

design optimization. All these methods use mathematical programming techniques for solutions.

In these cases it is difficult to apply traditional optimization techniques. Non-conventional

techniques are applied to such cases. These are potential search and optimization techniques for

complex engineering problems. Genetic algorithms are found to have a better global perspective

than the traditional methods.

Genetic Algorithms have good potential as optimization techniques for complex

problems and have been successfully applied in the area of Mechanical Engineering. Popular

applications include machine elements design, heat transfer, scheduling, vehicle routing, etc.

1.2 FLYWHEEL

INTRODUCTION

Flywheel is a rotating disk that stores energy as kinetic energy. The faster the flywheel spins the

more kinetic energy it stores. The flywheel rotates with a connecting rod, known as the shaft. The

shaft is where the energy moves in and out of the flywheel.

Fig 1.1 A flywheel


When more kinetic energy can be stored in a flywheel, the less energy needs to come from the main

power source. This increases the efficiency of the mechanism’s energy output. Because a flywheel

can be used in such a variety of mechanisms, the amount of energy stored in the flywheel varies.

There are two factors that control the amount of energy the flywheel stores: the moment of inertia and

the rotational speed of the flywheel.

BENEFITS:

Energy moving in and out of the flywheel can be used to provide temporary and constant power.

A flywheel’s greatest benefit is in mechanisms where the main power source is provided in

unsteady bursts. By using conservation of energy, the flywheel stores energy as it is being

released from the main power source in a surge or burst. As the main source of energy decreases,

the energy stored in the flywheel is released. Mechanisms will receive an uninterrupted supply of

energy. Currently, flywheels are used in electrical grids to level out power surges and in cars to

smooth the rapid explosions from the engine that provide power.

With modern materials flywheels are smaller, weigh less, and can spin more quickly, therefore

they can store more energy. One of the most promising areas where flywheels are being applied

is the automobile industry. Williams, a Formula 1 racing team, is currently researching the use of

flywheel hybrid car systems. These flywheel systems would replace current electric hybrid

systems. In a hybrid system, a flywheel stores energy from the motion of the car as the car

breaks. To accelerate after slowing down or stopping, the car uses the energy stored in the

flywheel instead of using the engine and more fuel. Unlike a battery, a flywheel will never lose

its ability to charge and discharge energy. They would be cheaper, more efficient, and better for

the environment.


CHAPTER 2

GENETIC ALGORITHM

2.1 INTRODUCTIONDefinition

GAs are special AI techniques which has a large space of potential solutions and whose search

methods model some natural phenomena such as :

Genetic inheritance.

Darwinian strife for survival.

GAs are search methods based on the mechanics of natural selection and natural genetics.They

combine survival of the fittest string structures with a structured yet randomized

information.They exchange to form a search algorithm with some of innovative flair of human

search.In every generation, a new set of artificial creatures(or strings) is produced.

Terms used in G.A:

Chromosomes are made of genes (features, charactersor decoders).

A gene is said to be in several states called alleles.

Every gene controls the inheritance of one or several characters and are located on certain

places of the chromosomes called loci.

Genetic operators:

Crossover: It combines the feature of two parents’ chromosomes to form two similar offspring's

by swapping corresponding segments of the parents. e.g.

P1:(a1 b1 c1 d1 e1)

P2:(a2 b2 c2 d2 e2)


Crossing after 2nd gene yields the offsprings:

O1:(a1 b1 c2 d2 e2)

O2:(a2 b2 c1 d1 e1)

Mutation: It arbitrarily alters one or more genes of a selected chromosomes for introducing

some extra variability into the population.

Let the chromosomes be:

P1:(0 1 1 1 0 1)

Mutating the 2nd & 5th gene yields the offsprings:

O1:(0 0 1 1 1 1)

Reproduction:

For selecting the new population w.r.t. the probability distribution based on the “fitness value”

Reproduction is used with the use of a ROULETTE WHEEL with slots sized according to fitness

is used.


2.2 PROBLEM FORMULATIONThe objectives in a design problem and the associated design parameters vary from product to

product. Different techniques are to be used in different problems. The purpose of the

formulation procedure is to create a mathematical model of the optimal design problem, which

then can be solved using an optimization algorithm.

The formulation of optimal design problems requires other considerations such as

constraints, objective function, and variable bounds.

OBJECTIVE FUNCTION

The objective function is to minimize the weight of the flywheel (WF) which is the sum of the weights of rim (WR), hub (WH) and spokes (WS).

f=W F=W R+W H+s .W S

The objective function is simplified by considering the weight of hub and spokes to be one-eighth of the weight of the rim concentrated at the mean radius of the rim.

W H+sW S=.125W R

Therefore the simplified objective function is:

CONSTRAINTS:

Rim stresses:

The rim stresses have been developed due to combined effect of hoop tension and bending

stresses. The rim is subject to high bending stresses. The maximum combined stress at the rim of

the flywheel having six spokes is given by:


CHAPTER 3

OPTIMIZATION ANALYSIS

3.1 METHODOLOGY For solving the problem I used Genetic Algorithm.

3.2 MATLAB TOOLBOX

In this the optimization is performed using and GENETIC ALGORITHM which is a

component of the MATLAB optimization toolbox.

STEPS FOR USING MATLAB TOOLBOX:

STEP 1: PROBLEM SETUP

1. At first I defined my objective function in editor of matlab and saved it as objfun.m file.

The objective function was defined as:

2. Then I defined the constraints in editor of matlab and saved it as simple_constraint.m

file.

3. Then I opened the optimization toolbox by typing optimtool in the command window.

4. In the toolbox I selected genetic algorithm.

function[c, ceq] = simple_constraint(x)

a=1;

n=1500;

s=300*10^6;

sr=400*10^6;


5. In the fitness function column I called my objective function by typing @objfun

6. Then I selected the no. of variables for my problem as 3.

7. Then I defined the lower bound and upper bound for the five variables as:

Lower bound=[0.8 .1 .1]

Upper bound=[1.2 .2 .15]

The optimization toolbox will appear as:

Fig. 3.1 optimization toolbox


STEP 2: RUN SOLVER AND VIEW RESULTS

Then I selected the graphs that that I wanted to plot and clicked on start option. The algorithm

started and after some iterations it stopped and gave the desired result and displayed the graphs.

The procedure is shown in the following figure:

fig 3.2: Showing The Results


3.3 RESULTS

The results obtained after 100 iterations are:

Radius (r) Breadth (b) Thickness (t) F(x)

800 100 100.07 554.87

Various plot obtained by performing genetic algorithm is shown below:

fig 3.3: Various Plot Obtained By Performing Genetic Algorithm


CHAPTER 4

CONCLUSIONS

In this report, I have done minimization the weight of flywheel with the help of genetic algorithm toolbox in MATLAB. Operation in Engineering Design is the past aimed at a Design problem with single objective function with single variable and with or without constraints. But here the code is used for the optimization of flywheel to minimize the weight. It is found that the results obtained by genetic algorithms are better, search space is wide and it aims at global optimum than that the local optimum as in a traditional method for the same input parameters.


CHAPTER 5REFERENCE

1.Singiresu.S.Rao., 1984, "Optimization Theory and applications", Wiley Eastern, New Delhi.

2. Kalylanmoy Deb., 1995, "optimization for engineering design algorithms and examples", prentice-hall of india private limited, New Delhi.

3.Maley, michael. Flywheel generated in solidworks. 17 apr 2009.

optimization of weight of flywheel

Documents