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Publication Date

2009-01-01

Availability

UM campus only

Degree Type

Thesis

Degree Name

Master of Science (MS)

Department

Mechanical Engineering (Engineering)

Date of Defense

2009-05-19

First Committee Member

Dr. Singiresu S. Rao - Committee Chair

Second Committee Member

Dr. Burt Rosenberg - Committee Member

Third Committee Member

Dr. Jizhou Song - Committee Member

Abstract

This thesis is aimed at the optimum design of uncertain mechanical components and systems involving multiple objectives and constraints. There are various mechanical and design problems that are encountered every now and then which require the output that equalize several conflicting objectives. In recent years several methods have been developed to find a solution to multiobjective problems. The most efficient method for obtaining a compromise solution is the game theory method, which is based on the Pareto minimum or optimum solution. A thorough methodology is developed, and subsequently applied to three examples problems. The first problem is to design four helical springs which are further used to support a milling machine. The objective is to minimize the weight of the spring, also to minimize the deflection, and to maximize the natural frequency thus making the problem as a multiobjective problem. Further the subjected constraint is the shear stress constraint. After finding the optimized solution of the deterministic problem, the problem is again solved using Stochastic Nonlinear Programming, and after that it is solved using Interval Analysis. Game theory is used individually in all the three cases. The second problem is to design a gear box where the objectives are defined as the weight of the gear box, stress developed in the shaft 1, and the stress developed in shaft 2. It is subjected to nine constraints which are bending stress in teeth, contact stress of teeth, transverse displacement of shafts 1 and 2, and constraints related to the torque. The third problem is to design a power screw and the objective is to minimize the volume of the screw, and to maximize the critical buckling load and thus making it a multiobjective problem. It is subjected to constraints of being screw to be self locking, then the shear stress in screw thread, and the bearing stress in threads. The results of all the three problems that are achieved using Deterministic, Stochastic Nonlinear Programming, and Interval Analysis Method are tabulated, and the value of each objective achieved using these three methods for each problem at a time are compared to find out the most optimized solution.

Keywords

Interval Analysis; Stochastic Nonlinear Programming; Optimization; Game Theory

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