This dissertation introduces a formulation which captures the shape and geometry of drilled surfaces. This formulation is implemented using inverse finite element mapping techniques and parametric mesh generation procedures. The fixturing problem formulation is posed as a constrained optimization problem, in which the physical fixture constraints define the domain, and the desired fixturing variables consisting of locator and clamp positions, and clamping force magnitudes are optimized in accordance with a selected objective function. Six different objective functions capable of describing various geometrical aspects of the machined hole have been developed and tested. The first five functions evaluate the square differences between the simulated and nominal radii and diameter values, minimize the maximum values of the latter quantities, and minimize the deviations of the drilled surface from a perfect cylinder. The remaining objective function is a weighted linear combination of the errors associated with hole roundness, hole center location, and hole dimension. The objective functions are minimized using a Simulated Annealing optimization algorithm which has proven to be effective in the minimization of multi-modal functions.;In the first part of this work, the mathematical model of the drilling process and the optimal fixturing problem formulation are addressed. In the second part, the performance of the five obtained fixture layouts under different drilling conditions is studied. These studies demonstrate that setups and machining time periods result in higher workpiece accuracies. In the second part, simulations addressing drilling through homogeneous plates and drilling through two-layer composite plates are presented. The results show that the optimal fixtures for the four drilling scenarios are different, and that the optimal function values are directly related to the material properties as well as the drilling loads. In the final part of this work, tolerance allocation and objective function selections are discussed. The tolerance study focuses on the scenario in which a single tolerance characteristic of roundness, hole location, or hole dimension is critical, and this study identifies the recommended weights that provide the best results for drilling a hole in the center or at the corner of the plate.;The simulations in this dissertation compare the shape, size, and location of the drilled holes to those of the nominal one. The results of the optimal fixturing simulations suggest that the optimal fixturing model developed herein can lead to appreciable control over the drilling process resulting in significant improvements regarding the quality and accuracy of drilling. The computer simulations further identify optimal fixturing layouts that can be readily implemented in an industrial environment. (Abstract shortened by UMI.).
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