Introduction to optimization
- 1. Introduction to Optimization in Engineering Applications Dr.S.Padmanabhan Associate Professor Vel Tech, Avadi
- 2. Contents.. Definition Engineering Applications Optimization Problem Design Optimization Gear Design – Case Study Genetic Algorithm
- 3. Optimization Definition Optimization - finding better among different possible solutions with the measure of the quality of those solutions. The procedure or procedures used to make a system or design as effective or functional as possible, especially the mathematical techniques involved.
- 4. ENGINEERING OPTIMIZATION- OPTIMIZATION ALGORITHM An Optimization Algorithm is a procedure which is executed iteratively by comparing various results till the optimum or a satisfactory solution is found. Optimization algorithms provide systematic and efficient ways of creating and comparing new design solutions in order to achieve an optimal design. Design optimization is the application of numerical algorithms and techniques in engineering design to improving the system's performance, weight, reliability, and cost. 4
- 5. Engineering applications of optimization Some typical applications in different engineering disciplines are given below. Design of aircraft and aerospace structure for minimum weight Finding the optimal trajectories of space vehicles. Design of civil engineering structures such as frames, foundations, bridges, towers, chimneys and dams for minimum cost. Designed of minimum weight structures for earth quake, wind and other types of random loading.
- 6. Optimum design of linkages, cams, gears, machine tools, and other mechanical components. Selection of machining conditions in metal-cutting processes for minimizing the product cost. Design of material handling equipment such as conveyors, trucks and cranes for minimizing cost. Design of pumps, turbines and heat transfer equipment for maximum efficiency. Optimal production planning, controlling and scheduling. Optimum design of electrical machinery such as motors, generators and transformers. Designing the shortest route to be taken by a salesperson to visit various cities in a single tour.
- 7. Optimization Problem A farmer has 2400 ft of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. What are the dimensions of the field that has the largest area?
- 8. Mathematical model: Maximize: A = xy Constraint: 2x + y = 2400
- 12. Max – Min functions Want to minimize f. Smaller = better (Cost, Weight, Time etc.) What about maximization? Bigger = better (Efficiency, System Life, High Salary etc) How to solve optimization problem? ◦ Analytically ◦ Numerically
- 13. Development of an optimization model Development of an optimization model can be divided into five major phases. Collection of data Problem definition and formulation Model development Model validation and evaluation or performance Model application and interpretation of
- 14. DESIGN OPTIMIZATION Designing is the process where the product are made attractive, suitable, highly efficient but there are certain difficulties in making the perfect, best, desired product. An engineering design involves large numbers of design variables, and it requires knowledge, experience, and decision to specify these variables. Mechanical design can be defined as the selection of materials and geometry, which satisfies, specified and implied functional requirements. 14
- 15. The conventional design procedures aim at finding an acceptable or adequate design which merely satisfies the functional and other requirements of the problem. In general, there will be more than one acceptable design, and the purpose of optimization is to choose the best one of the many acceptable designs available. Thus a criterion has to be chosen for comparing the different alternative acceptable designs and for selecting the best one. The criterion with respect to which the design is optimized, when expressed as a function of the design variables, is known as the objective function.
- 16. 16 INTRODUCTION - Contd… Gears are the most common of machine elements. Gears may be defined as a class of mechanical elements, which are used for transmitting controlled relative motion between shafts. Gears are used to change the speed, power, and direction between an input and output shaft. Gears are used in various filed like Automobiles, Machine Tools, Marine and Aerospace etc.
- 17. 17 Gears are generally categorized into three distinct types: Transmitting power and motion between parallel shafts - Spur and Helical Gears Shafts with intersecting axes, the angle between the shafts being generally 90° - Bevel gears The shafts are neither parallel nor intersecting, the axes generally making 90° (or some other angle) to each other but in different planes - Worm and Worm-wheel CLASSIFICATION OF GEARS
- 18. 18 Spur Gear Helical Gear Bevel Gear Worm and Worm Gear
- 19. 19 NEED FOR GEAR DESIGN In recent times, the gear design has become a highly complicated and comprehensive subject. A designer of a modern gear drive system must remember that the main objective of a gear drive is to transmit higher power. The need for designing a gear drives has been increasing with the increasing application of gear drives in high speed with small space. With comparatively smaller overall dimensions of the driving system which can be produced with minimum possible manufacturing cost.
- 20. To survive in this environment, gearbox designer’s main objective is to transmit higher power with comparatively lesser weight, maximum efficiency and minimum distance between shafts. Gear Optimization involves Gear drive optimization and Gear Box optimization. Gear Optimization is problem involves design variables which can be both integer value, discrete value and real value. The problem of gear design optimization is difficult to solve because it involves multiple objectives and large number of variables. 20
- 21. Motive or Objective of Gear Drive Gear drives with Maximizes the Power, Efficiency , Gear life etc. Minimizes the overall Weight, Centre distance, Gear noise, Vibration etc.
- 22. Flowchart
- 23. Design Variables
- 24. Bicycle Problem, Production rate of race and mountain bikes are design or control variables. i.e, x1 and x2. For Gear Design, Power (P), Thickness(b), No. of Teeth(Z) and module(m) are design variables.
- 25. DESIGN CONTROL VARIABLES Power, Gear Thickness, Module, Number teeth on Pinion are considered as control variables. Power (P) directly used as Power transmitted. Gear Thickness (b) directly influences the gear drive weight or volume. Module (m) which influences the gear drive weight or volume and center distance. Number of Teeth on pinion (Z) which also influences the gear drive weight or volume and efficiency and center distance. 25
- 26. Constraints
- 29. Bicycle Problem, For Gear Design, Bending Stress, Compressive Stress, Minimum module and Minimum centre distance
- 32. 32 Gear Design Objectives, Multi-Objectives like, Maximizing Power Maximizing Efficiency Minimizing Weight or Volume Minimizing Centre distance are considered in Combined Objective Function (COF). Design Constraints Objectives should satisfies with the design constraints of allowable bending stress, allowable compressive stress, minimum module and minimum centre distance, gear ratio etc.