Successfully reported this slideshow.
APPROVAL
“I hereby declare that I have read this thesis and in my opinion this thesis is
sufficient in term of scope and q...
DECLARATION
“I hereby, declare this thesis is result of my own research except as cited in the
references”
Signature : ………...
ii
ACKNOWLEDGEMENT
First of all, I would like to thanks ALLAH S.W.T that have given me the
opportunity to complete my „Pro...
iii
ABSTRACT
Car jack is a device used to lift up the cars while changing the tires during an
emergency. Car jacks are ava...
iv
ABSTRAK
Jek kereta merupakan satu alat yang digunakan untuk mengangkat kereta
semasa ingin menukar tayar di waktu kecem...
v
LIST OF CONTENTS
CHAPTER CONTENTS PAGE NUMBER
ACKNOWLEDGEMENT ii
ABSTRACT iii
ABSTRAK iv
LIST OF TABLE viii
LIST OF FIGU...
vi
2.7.1 Characteristic of Ergonomics 14
2.7.2 Cognitive Ergonomics 15
2.7.3 Physical Ergonomics 15
2.7.4 Posture 15
2.7.5...
vii
CHAPTER 5 CONCEPTUAL DESIGN 40
5.1 Product Decomposition 40
5.2 Morphological Chart 41
5.2.1 Advantages of modificatio...
viii
LIST OF TABLE
TABLE TITLE PAGE NUMBER
Table 1 Translation of the customer statement 35
Table 2 Relative important of ...
ix
LIST OF FIGURE
FIGURE TITLE PAGE NUMBER
1 PSM Flow Chart 3
2 Garage Car Jack 5
3 Hydraulic Car Jack 6
4 Scissor Car Jac...
x
18 Components clustering 47
29 Hydraulic concept 49
30 Fulcrum concept diagram 50
31 Fulcrum concept diagram 51
22 a App...
xi
LIST OF SYMBOL / ABBREVIATION
F = Force (N)
𝐹𝑚 = Force produce by men (N)
𝐹𝑤 = Force produce by women (N)
𝑊𝑚 = Weight a...
1
CHAPTER 1
INTRODUCTION
1.1 Car Jack
A jack is mechanical device used to lift heavy loads or apply great
forces. Jacks em...
2
1.2 Problem Statement
Nowadays in this country, most of the cars were equipped with the
scissor car jack. We found that ...
3
as well as project planning. Figure 1 depicts a flow chart for the project
(PSM) from the beginning until the end of the...
4
1.5 Scopes
This project is about the designing and fabricating the car jack. The
types of car jack that we were used in ...
5
CHAPTER 2
LITERATURE STUDY
2.1 Existing Car Jack
The most common form is a car jack, floor jack or garage jack which
lif...
6
stable. When the plunger pulls back, it draws oil out of the reservoir through
a suction check valve into pump chamber. ...
7
Figure 4 Scissor Car Jack
(Photo by http://www.supplierlist.com/products/balmart/shrowroom.htm)
Hydraulic or air-powered...
8
In a Bottle Jack the piston is vertical and directly supports a bearing
pad that contacts the object being lifted. With ...
9
 Do prototype testing in environments where it otherwise would be
undesirable or impossible.
2.4 Structural Analysis
St...
10
2.5 Experimental Methods for Determination of Stress
There are a number of methods that are used for finding the value ...
11
Photoelasticity: this method depends upon the property of certain
transparent solids by which they become doubly refrac...
12
Some of the numerical approaches are
 Finite difference method.
 Finite volume method.
 Boundary element method.
 F...
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Design improvement-of-the-existing-car-jack-design---24-pages

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Design improvement-of-the-existing-car-jack-design---24-pages

  1. 1. APPROVAL “I hereby declare that I have read this thesis and in my opinion this thesis is sufficient in term of scope and quality for the award of Bachelor of Mechanical Engineering (Design & innovation)” Signature : ………………………… Supervisor’s Name : En Mohd Nazim Bin Abd Rahman Date : 22 April 2011
  2. 2. DECLARATION “I hereby, declare this thesis is result of my own research except as cited in the references” Signature : ………………………… Author’s Name : Muhamad Afiq Bin Muhamad Fauzi Date : 22 April 2011
  3. 3. ii ACKNOWLEDGEMENT First of all, I would like to thanks ALLAH S.W.T that have given me the opportunity to complete my „Project Sarjana Muda‟ (PSM). Alhamdulillah, His Willingness has made it possible for me as the author to complete the PSM in time. I worked hard in completing this project within a semester. I would like to take this opportunity to give my special thanks to my dedicated supervisor, En Mohd Nazim Bin Abd Rahman for guiding this project at every stage with clarity, spending much time to discuss and help with this project, and that priceless gift of getting things done by sharing his valuable ideas as well as share his knowledge. I would also like to thank to all UTeM lecturers especially En. Masjuri Bin Musa, En. Razali Md. Tith, Dr. Ir Tan Chee Fai and also the lab technician whom had helped directly or indirectly in completing of this PSM. Not forgotten are my best colleagues for their openhandedly and kindly guided, assisted, and supported and also encouraged me to make this project successful. My heartfelt thanks to my dearest family which always support and pray on me throughout this project. Their blessing gave me the high-spirit and strength to face any problem occurred and to overcome them rightly. The great cooperation, kind heartedness and readiness to share worth experiences that have been shown by them will be always appreciated and treasured by me, thank you.
  4. 4. iii ABSTRACT Car jack is a device used to lift up the cars while changing the tires during an emergency. Car jacks are available at the market has some disadvantages such as requiring more energy to operate, are not suitable for women and cannot be used on the uneven surface. The purpose of this project is to modify the design of the existing car jack in terms of its functionality and also human factors considerations. In this “Projek Sarjana Muda 1”, the scopes of research were on the designing 1.5 - 3 ton maximum lifting capacity of car jack by using optimization concept. To optimize the existing design, the hand lifter has been replaced by the use of pedal lever as it can reduce energy usage. In addition, ergonomic factors are also taken into consideration in order to reduce and simplify how to use a car jack. In the process of obtaining a suitable design, the customer needs will be translate to the engineering characteristic to obtain the concepts that need to be modified and fabricated. From the house of quality, the best concept will be valued based on the weighted rating method. The morphology chart had been used to obtain the best concept solution. After the best concept had been selected using the weighted rating method, next step was to determine the part and component that can be modified by arrange the part into chunks and clustering with the component according to the function or system. From this step, it can be determined which component can be reduced or modified. Then the configuration design was analyzed according the function factor and critical issue so that the design that had been implementing was according to the specification and customer requirement. The last step for this project was parametric design. In this topic, the new design concept will be calculated to obtain the required force and compared with the theoretical calculation in the table of human factor.
  5. 5. iv ABSTRAK Jek kereta merupakan satu alat yang digunakan untuk mengangkat kereta semasa ingin menukar tayar di waktu kecemasan. Jek kereta yang sedia ada di pasaran mempunyai beberapa kelemahan seperti memerlukan banyak tenaga untuk beroperasi, tidak sesuai untuk wanita dan juga tidak boleh di gunakan di atas permukaan yg tidak rata. Tujuan tajuk ini adalah untuk mengubah suai rekabentuk jek kereta yang sedia ada di dalam fungsinya dan juga dari segi pertimbangan faktor manusia. Di dalam Projek Sarjana Muda 1, kajian yang dilakukan adalah untuk mengkaji setiap komponen jek kereta dan pengubahsuaian yang boleh dilakukan oleh jek kereta kapasiti 3 tan maksimum. Untuk mengoptimumkan rekabentuk sedia ada, penggunaan pemijak kaki telah digantikan bagi mengantikan tuil tangan disamping itu dapat mengurangkan tenaga yang digunakan. Selain itu, faktor ergonomik juga di ambil kira supaya dapat mengurangkan serta memudahkan cara untuk menggunakan jek kereta. Di dalam proses untuk mendapatkan rekabentuk yang sesuai, proses yang di ambil kira adalah daripada kehendak pelanggan dan kemudiannya diterjemahakan kepada ciri-ciri kejuruteraan untuk mendapatkan idea dan konsep yang perlu diubahsuai di dalam rumah kualiti. Setelah itu jadual morfologi dibagunkan untuk memperolehi konsep pengubahsuaian yang baru. Konsep terbaik telah dipilih dengan menggunakan kaedah penentu tertimbang. Manakala langkah seterusnya adalah untuk menentukan bahagian-bahagian yang boleh diubahsuai adalah dengan menetapkan bahagian menjadi potongan- potongan dan kluster dengan komponen sesuai dengan fungsi atau sistem. Dari langkah ini, dapat ditentukan dengan komponen dapat dikurangkan atau diubahsuai. Kemudian rekabentuk tersebut dianalisis mengikut fungsi dan isu-isu kritikal sehingga rekabentuk yang telah diubahsuai itu sesuai dengan spesifikasi dan keperluan pelanggan. Langkah terakhir untuk projek ini adalah analisis rekabentuk parametrik. Dalam topik ini, konsep rekabentuk baru akan dinilai dari segi daya yang diperlukan dan akan dibandingkan dengan nilai teori dalam jadual.
  6. 6. v LIST OF CONTENTS CHAPTER CONTENTS PAGE NUMBER ACKNOWLEDGEMENT ii ABSTRACT iii ABSTRAK iv LIST OF TABLE viii LIST OF FIGURE ix LIST OF SYMBOL / ABBREVIATION xi CHAPTER 1 INTRODUCTION 1 1.1 Car Jack 1 1.2 Problem Statement 2 1.3 Objective 2 1.4 PSM Flow Chart 2 1.5 Scope 4 CHAPTER 2 LITERATURE STUDY 5 2.1 Existing Car Jack 5 2.2 Hydraulic System 7 2.3 CATIA Overview 8 2.3.1 CATIA 8 2.4 Structural Analysis 9 2.4.1 Types of Structural Analysis 9 2.5 Experimental Methods for Determination of Stress 10 2.6 Numerical Methods for Analysis 11 2.6.1 Finite Elements method 12 2.7 Ergonomic 13
  7. 7. vi 2.7.1 Characteristic of Ergonomics 14 2.7.2 Cognitive Ergonomics 15 2.7.3 Physical Ergonomics 15 2.7.4 Posture 15 2.7.5 Hunkering Posture 17 2.7.6 Ergonomics Recommendations for Car Jack 18 CHAPTER 3 METHODOLOGY 19 3.1 Introduction 19 3.2 Clarifying Customer Needs 21 3.3 Specifying Customer Needs 21 3.4 Quality Function Deployment 21 3.5 House of Quality 22 3.6 Concept Generation 24 3.6.1 A Five-Step Method 24 CHAPTER 4 ENGINEERING DESIGN SPECIFICATION 26 4.1 Overview 26 4.2 Identifying Customer Needs 26 4.3 Gather raw data from customers 27 4.3.1 Survey method 27 4.4 Analysis result 28 4.4.1 Section A 29 4.4.2 Section B 31 4.4.3 Section C 32 4.5 Interpret the raw data in terms of customer needs 34 4.6 Organized the needs into hierarchy 35 4.6.1 Customer requirement 36 4.6.2 Technical requirement 36 4.6.3 House of Quality 37 4.6.4 QFD Correlation Matrix 38 4.7 Concept Generation 38 4.7.1 Design Improvements 38
  8. 8. vii CHAPTER 5 CONCEPTUAL DESIGN 40 5.1 Product Decomposition 40 5.2 Morphological Chart 41 5.2.1 Advantages of modification 42 5.3 Concept Design 43 5.4 Concept Selected 44 5.4.1 Weighted Rating Method 44 CHAPTER 6 CONFIGURATION DESIGN 46 6.1 Generating Alternative Configurations 46 6.2 Analyzing Configuration Design 48 6.3 Evaluating Configuration Design 48 CHAPTER 7 PARAMETRIC DESIGN 49 7.1 Systematic Parametric Design 49 7.2 Human Factor Design 52 7.3 Simulation analysis 54 7.3.1 New design of foot pedal 55 7.3.2 FEA analysis for the pedal lever new concept 56 CHAPTER 8 DETAIL DESIGN 58 8.1 Assembly drawing 58 8.2 Exploded drawing 61 CHAPTER 9 CONCLUSION AND RECOMMENDATION 62 9.1 Conclusion 62 9.2 Recommendation 62 REFERENCES 64 BIBLIOGRAPHY 66 APPENDIX 67 Appendix 1 : Table of anthropometric estimates for Japanese adults 67 Appendix 2 : Questionnaires 68 Appendix 3 : Drafting Drawing 71
  9. 9. viii LIST OF TABLE TABLE TITLE PAGE NUMBER Table 1 Translation of the customer statement 35 Table 2 Relative important of customer requirement 36 Table 3 Engineering characteristics 37 Table 4 Design improvement 39 Table 5 Morphological chart 41 Table 6 Weighted rating method 45 Table 7 Design factor and critical issues 48 Table 8 Hand and foot-operated control devices and their operational characteristics and control functions 53 Table 9 Assembly View 59 Table 10 Assembly view for after improvement design 60
  10. 10. ix LIST OF FIGURE FIGURE TITLE PAGE NUMBER 1 PSM Flow Chart 3 2 Garage Car Jack 5 3 Hydraulic Car Jack 6 4 Scissor Car Jack 7 5 Hunkering Posture 16 6 Using the Paddle 16 7 The flow chart of the methodology for the PSM I 20 8 Example of the House of Quality 23 9 Five-step concepts 25 10 Pie chart based on gender respondents 29 11 Bar chart on the respondent‟s range of age 29 12 Pie chart for the types of vehicle by respondents 30 13 Class of vehicle bar chart 30 14 Bar chart of the respondent‟s experience on using their vehicle 31 15 Pie chart for the respondent that have change tire by themselves 32 16 Bar chart of the preferred operating system of car jack 32 17 Bar graph on the important criteria for car jack 33 18 Bar graph of the problem that faced by the user 33 19 HOQ of the design 36 20 Product Decomposition 40 21 Ratchet mechanism 42 22 Spring mechanism 42 23 Adding base area 42 24 Concept A 43 25 Concept B 43 26 Concept C 44 27 Schematic diagram 47
  11. 11. x 18 Components clustering 47 29 Hydraulic concept 49 30 Fulcrum concept diagram 50 31 Fulcrum concept diagram 51 22 a Approximate model of the knee and foreleg 52 32 b Analytical model of the knee and foreleg 52 33 Analytical diagrams of the knee and foreleg 53 34 Fulcrum concept diagram 54 35 Factor of safety analysis 55 36 New concept of pedal 55 37 Stress analysis 56 38 Displacement analysis 57 39 Factor of safety analysis 57 40 Assembly drawing 58 41 After improvement design assembly 60 42 Exploded Drawing 61
  12. 12. xi LIST OF SYMBOL / ABBREVIATION F = Force (N) 𝐹𝑚 = Force produce by men (N) 𝐹𝑤 = Force produce by women (N) 𝑊𝑚 = Weight average for men (kg) 𝑊𝑤 = Weight average for women (kg) A = Area (m2 ) m = Mass (kg) P = Pressure (N/m2 ) D = Diameter
  13. 13. 1 CHAPTER 1 INTRODUCTION 1.1 Car Jack A jack is mechanical device used to lift heavy loads or apply great forces. Jacks employ a screw thread or hydraulic cylinder to apply very high linear forces. A mechanical jack is a device which lifts heavy equipment. Car jacks usually use mechanical advantage to allow a human to lift a vehicle by manual force alone. More powerful jacks use hydraulic power to provide more lift over greater distance. The mechanical advantage is the factor by which a mechanism multiplies the force or torque applied to it. An automotive jack is a device used to raise all or part of a vehicle into the air in order to facilitate repairs. Most people are familiar with the basic auto jack that was still included as standard equipment with most new cars. These days, fewer people than ever have had to use a car jack. This is due to the continuing improvements in modern tires that have made “getting a flat” rare. Even so, people who like to rotate their tires themselves or who may install snow tires before the winter and remove them in the spring need to use a jack to perform the job. (http://cotsncots.com/faq-general.html).
  14. 14. 2 1.2 Problem Statement Nowadays in this country, most of the cars were equipped with the scissor car jack. We found that the scissor car jack were very difficult to be used especially by women because this types of jack needed more strength and energy to operate this jack by turning the lead screw. Thus, we want to develop a product based from the problem faced by the users who drive a car regarding to this issue. To overcome this problem, a research has been conducted to find the solution on how to design a car jack for the car using the simplest and cheapest way while it is energy saving. Although there were many ways to solve this problem, we recommend that the design this car jack system is the practical way when we considered all the factors and consequences especially about the analysis to develop this product. During the research, we have found that most of the car user has difficulties in maintaining their vehicles breakdown especially cars in the scope of changing tires. The normal car jack we have in the market is operated using bare hands and it is time consuming. It also requires much energy from the person to rotate the jack. Hence, this report had been prepared to recommend the design of the car jack that is user friendly and easier to operate as do not required too much money to develop this product. 1.3 Objective Design improvement the existing car jack in terms of its functionality and human factor consideration. 1.4 PSM Flow Chart Flow charts are a modelling technique introduced in the 1940/50s and popularized for structured development in the 1970s (Gane and Sarson 1979)
  15. 15. 3 as well as project planning. Figure 1 depicts a flow chart for the project (PSM) from the beginning until the end of the project. There are two basic symbols on this flow chart, squares which represent activities or tasks and arrows which represent flow of control. Figure 1 PSM Flow Chart Determine the Objectives and Scopes Problem analysis Literature review Study on previous research Study on previous research Create new design Analysis of result Problem analysis and solutions Discussion Conclusion Selecting PSM title
  16. 16. 4 1.5 Scopes This project is about the designing and fabricating the car jack. The types of car jack that we were used in this project were hydraulic car jack as it is more reliable and easy to operate. In order to develop new concept of the car jack design, we do some research on by giving questionnaire to car user. The scopes of research were on the designing 3 ton maximum lifting capacity of car jack by using optimization concept. For optimizing the human power, the concepts that will be used in this product were replacing the long arm with the leg pad. By this, the mechanical advantage while lifting can be reducing. In our design we were using CAD to draw out the detailed drawing of each component of our product. Therefore, the deformation, von stress misses, and the factor of safety of pedal lever will be analyzed using the Finite Element Analysis Software. From our analysis, we will propose the best concept of the car jack in terms of friendly user and lower cost in product development.
  17. 17. 5 CHAPTER 2 LITERATURE STUDY 2.1 Existing Car Jack The most common form is a car jack, floor jack or garage jack which lifts vehicles so that maintenance can be performed. Car jacks usually use mechanical advantage to allow a human to lift a vehicle by manual force alone. More powerful jacks use hydraulic power to provide more lift over greater distances. Mechanical jacks are usually rated for a maximum lifting capacity (for example, 1.5 tons or 3 tons). The jack shown in figure 2 is made for a modern vehicle and the notch fits into a hard point on a body. Earlier versions have a platform to lift on the vehicle frame or axle. (http://en.wikipedia. org/wiki/Jack_ (device)) Figure 2 Garage Car Jack (Photo by www.NorthenTool.com) A hydraulic jack uses a fluid, which is incompressible, that is forced into a cylinder by a pump plunger. Oil is used since it is self lubricating and
  18. 18. 6 stable. When the plunger pulls back, it draws oil out of the reservoir through a suction check valve into pump chamber. When the plunger moves forward, it pushes the oil through a discharge check valve into the cylinder. The suction valve ball is within the chamber and opens with each draw of the plunger. The discharge valve ball is outside the chamber and opens when the oil is pushed into the cylinder. At this point the suction ball within the chamber is forced shut and oil pressure builds in the cylinder. (http://hydraulic-equipment-manufacturer.blogspot.com/p/hydraulic- jacks.html) Figure 3 Hydraulic Car Jack (Photo by http://www.manufacturer.com/product/m6509561-Hydraulic+Bottle+Jack.html) These small automotive jacks are of various different types. Bumper jacks have a protuberance that fits into a slot under the vehicle's bumper, providing some security against sudden sideways movement. Scissors jacks and ratchet jacks are other kinds of hand-operated jacks. Any time a small jack is used, it's critical that the vehicle be in a stable position on a flat surface. Be sure that the jack is pushing up against a solid frame member that will support the weight of the vehicle, or else you will need to repair more than your tire. (http://cotsncots.com/faq-general.html)
  19. 19. 7 Figure 4 Scissor Car Jack (Photo by http://www.supplierlist.com/products/balmart/shrowroom.htm) Hydraulic or air-powered jacks are an essential component of modern auto repair shops, and have been fixtures on the auto body repair scene for at least 50 years. They are most often used by professional shops and garages, although there are smaller versions that are made for the home hobbyist as well. Hydraulic jacks operate by pressurizing water in a sealed system, which provides more than enough power to lift a car or small truck into the air. Once the jack has reached its full upward extension, it is locked in position so that the under body of the vehicle is accessible for service and repairs. (http://cotsncots.com/faq-general.html). 2.2 Hydraulic System A hydraulic jack uses a fluid, which is incompressible, that is forced into a cylinder by a pump plunger. Oil is used since it is self lubricating and stable. When the plunger pulls back, it draws oil out of the reservoir through a suction check valve into the pump chamber. When the plunger moves forward, it pushes the oil through a discharge check valve into the cylinder. The suction valve ball is within the chamber and opens with each draw of the plunger. The discharge valve ball is outside the chamber and opens when the oil is pushed into the cylinder. At this point the suction ball within the chamber is forced shut and oil pressure builds in the cylinder.
  20. 20. 8 In a Bottle Jack the piston is vertical and directly supports a bearing pad that contacts the object being lifted. With a single action piston the lift is somewhat less than twice the collapsed height of the jack, making it suitable only for vehicles with a relatively high clearance. For lifting structures such as houses the hydraulic interconnection of multiple vertical jacks through valves enables the even distribution of forces while enabling close control of the lift. (http://en.wikipedia.org/wiki/Jack_(device)) 2.3 CATIA Overview CATIA is a general purpose finite element modelling package for numerically solving a wide variety of mechanical problems. These problems include: Static/Dynamic Structural Analysis (both linear and non-linear), heat transfer and fluid problems, as well as electromagnetic problems. To produce this drawing in this project, we use CATIA Version 5 Release 15 software. Under this software, we were able to use many types of function/features such as line, circle, trim, extrude, edit, polyline, arc, fillet, pad and others. (Dr. R.Ganesan, 2007) 2.3.1 CATIA Finite element analysis software enables engineers to perform the following tasks:  Build computer models or transfer CAD models of structures, products, components, or systems.  Apply operating loads or other design performance conditions.  Study the physical responses, such as stress levels, temperature distributions.  Optimize a design early in the development process to reduce production costs.
  21. 21. 9  Do prototype testing in environments where it otherwise would be undesirable or impossible. 2.4 Structural Analysis Structural analysis is probably the most common application of the finite element method. The term structural (or structure) implies not only civil engineering structures such as bridges and buildings, but also naval, aeronautical, and mechanical structures such as ship hulls, aircraft bodies, and machine housings, as well as mechanical components such as pistons, machine parts, and tools. (Chennakesava R. Alavala, 2009) 2.4.1 Types of Structural Analysis The primary unknown (nodal degrees of freedom) calculated in a structural analysis is displacement. Other quantities, such as strains, stresses, and reaction forces, are then derived from the nodal displacements. Static Analysis used to determine displacements, stresses, etc. under static loading conditions, both linear and nonlinear static analyses. Nonlinearities can include plasticity, stress stiffening, large deflection, large strain, hyper elasticity, contact surfaces, and creep. Transient Dynamic Analysis used to determine the response of a structure to arbitrarily time-varying loads. All nonlinearities mentioned under Static Analysis above are allowed.
  22. 22. 10 2.5 Experimental Methods for Determination of Stress There are a number of methods that are used for finding the value of stress in a part. Some of the methods that are most commonly used are briefly discussed below. Strain Gauges: A strain gauge may be defined as any instrument or device that is employed to measure the linear deformation over a given gauge length, occurring in the material of a structure during the loading of the structure. This definition is quite broad; in fact it covers the range of instruments included between the linear scale and the precise optical and electrical gauges now available. The many types of strain gauges available are quite varied, both in application and in the principles involved in their magnification systems. Depending upon the magnification system, the strain gauges may be classified as follows: 1. Mechanical  Wedge and screw.  Lever-simple and compound.  Rack and pinion.  Combination of lever and rack and pinion.  Dial indicators. 2. Optical. 3. Interferometric type. 4. Electrical.  Inductance.  Capacitance.  Resistance.  Piezoelectric. 5. Magnetic. 6. Acoustical.  Pneumatic.  Scratch type.  Photostress gauge.
  23. 23. 11 Photoelasticity: this method depends upon the property of certain transparent solids by which they become doubly refractive under the action of stress, the magnitude of the optical effect bearing a definite relation to that of the stress. The optical phenomenon, known as Sir David Brewster first discovered the “photo-elastic effect” in 1816 in sheets of stressed glass. Brewster, however, did not succeed in obtaining a uniform stress in his model and was not able to make any quantitative estimate of the relation between the stress and the optical effect produced. In 1820 Biot demonstrated that a strip of glass became doubly reflecting when set into a state of longitudinal vibrations. Fresnel attempted to measure the changes in the velocities of the two oppositely polarized rays in glass without any decisive results. Neumann presented the first theory of the photoelastic effect in 1841 and expressed the velocities of the two waves in terms of the three principal strains in the medium. In 1853, Maxwell presented a theory in which the velocities were related to the principal stresses. Both these theories produced relations of precisely similar form and were equally applicable to an isotropic linear and elastic material under any system of combined stress. (Rao, ‘The finite element methods in Engineering’ Pergamon Press, 1982) 2.6 Numerical Methods for Analysis In engineering analysis a theoretical model was the first choice for researchers and scientists because of accurate and unique solution. But in pragmatic design problem, the theoretical model was scarcely utilized to predict physical response because of the complex geometrical design and path. Therefore powerful numerical method was introduced to engineers to overcome difficulty.
  24. 24. 12 Some of the numerical approaches are  Finite difference method.  Finite volume method.  Boundary element method.  Finite element method. In the design of engineering structures, numerical simulations play an increasingly important role. This can be attributed to the high costs or practical difficulties related to experiments, which have to confront rapid advances in the computational power and the resulting decrease in the costs for computer simulations. 2.6.1 Finite Elements method Finite element method has become a powerful tool for the numerical solution of a wide range of engineering problems. Applications range from deformation and stress analysis to field analysis of heat flux, fluid flow, magnetic flux, seepage and other flow problem. In this method of analysis, a complex region defining a continuum is discredited into simple geometric shapes called Finite Elements. Finite element method solves for forces and displacement over the entire object. Since most visual applications tend to be more interested over the entire object, Finite element method seems promising. Finite element method is used for solving many industrial problems like Automobile frames, optimization of mechanical parts, artificial limbs etc. Rolling mill housing is one of them.

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