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Date of Award

3-1995

Degree Type

Thesis

Degree Name

Doctor of Philosophy (PhD)

Department

Mechanical Engineering

Supervisor

Professor H.A. ElMaraghy

Abstract

The increase in quality requirements demands efficient integration of design and manufacturing concerns. This thesis develops a robust design procedure and a novel experimental optimization approach for considering manufacturing tolerances (dimensional and geometric) from both design and manufacturing perspectives. Manufacturing capabilities prohibit the tight control of variations in geometry, dimensions and positions in system components. Two formulations are used where manufacturing tolerances are considered as: i) control variables and ii) noise variables beyond the designer's control. Results indicate the superiority of the developed procedure to detect a design region where system response is robust to sources of variations. Moreover, the procedure overcomes the shortcoming of on-line programming to deal with multi-variable problems and multi-level noisy space. The procedure is applied efficiently and successfully to typical product and process design.

A statistical optimization procedure is developed, implemented and tested to deal with situations where there is no explicit objective functions. The procedure results in a robust design by proper assignment of nominal and tolerance values. Standard matrix decomposition methods and orthogonal search allow obtaining functionally independent designs. The developed procedure and techniques change design specifications from 'acceptable within limits' to 'close-to-target value'. This technique has the advantage of reducing the tolerance optimization problem and minimizing manufacturing costs.

The concept of orthogonal arrays and experimental optimization is used to develop an algorithm for unconstrained and constrained discrete problems. The algorithm employs specially coded designs to form combinatoric search in one and two domains. As a search in one domain, the algorithm uses data from Coordinate Measuring Machines (CMMs) and evaluates the tolerance zones of engineering features such as straightness and roundness (2-Dimensional) and flatness, cylindricity and sphericity (3-Dimensional). The problem of least cost tolerance allocation and optimum process selection is formulated as a discrete optimization problem. The problem is viewed as a search in two domains: the first is tolerance allocation that satisfies the assembly functional requirement; the second is process-selection such that the production cost is minimal. This formulation is based on coupling an inner array (tolerance selection domain) and an outer array (process selection domain). The choice of different structures of orthogonal arrays has a tremendous impact on the resulting minimum production cost and optimum tolerances. Each orthogonal array can be represented by a search graph which can aid the designer in the initial assignment phase. The developed algorithm overcomes one major shortcoming of almost all existing search techniques namely the need for excessive number of function evaluations and provides near-to-global optimum consistently with high reliability.

Finally, the experimental design techniques are used to deal with the problem of linear and nonlinear tolerance analysis of mechanical assemblies. The principal goal was to find a substitute for the expensive Monte Carlo-based simulation technique. Results illustrate the successful application of different orthogonal arrays in yielding a comparable system moments in small finite number of experiments with a sample of 10,000 (linear assembly) and 1,000 (nonlinear assembly).

This dissertation surveys the literature and offers solutions to various design and manufacturing problems. In fact, it proposes unique tools and techniques to tackle problems such as robust product and process design, nominal and tolerance value assignment, form tolerance evaluation, discrete optimization and linear and nonlinear tolerance analysis.

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