In today's competitive manufacturing industries, companies strive to reduce manufacturing development costs and lead times in hopes of reducing costs and capturing more market share from early release of their new or redesigned products. Tooling lead time constraints are some of the more significant challenges facing product development of advanced free-form components. This is especially true for complex designs in which large dies, molds or other large forming tools are required. The lead time for tooling, in general, consists of three main components; material acquisition, tool design and engineering, and tool manufacturing. Lead times for material acquisition and tool manufacture are normally a function of vendor/outsourcing constraints, manufacturing techniques and complexity of tooling being produced. The tool design and engineering component is a function of available manpower, engineering expertise, type of design problem (initial design or redesign of tooling), and complexity of the design problem. To reduce the tool design/engineering lead time, many engineering groups have implemented Computer-Aided Design, Engineering, and Manufacturing (CAD/CAE/CAM or CAx) tools as their standard practice for the design and analysis of their products. Although the predictive capabilities are efficient, using CAx tools to expedite advanced die design is time consuming due to the free-form nature and complexity of the desired part geometry. Design iterations can consume large quantities of time and money, thus driving profit margins down or even being infeasible from a cost and schedule standpoint. Any savings based on a reduction in time are desired so long as quality is not sacrificed. This thesis presents an automated tool design methodology that integrates state-of-the-art numerical surface fitting methods with commercially available CAD/CAE/CAM technologies and optimization software. The intent is to virtually create tooling wherein work-piece geometries have been optimized producing products that capture accurate design intent. Results show a significant reduction in design/engineering tool development time. This is due to the integration and automation of associative tooling surfaces automatically derived from the known final design intent geometry. Because this approach extends commercially available CAx tools, this thesis can be used as a blueprint for any automotive or aerospace tooling need to eliminate significant time and costs from the manufacture of complex free-form components.

This paper presents a method for interactive design by means of extending the PDE based approach for surface generation. The governing partial differential equation is generalized to arbitrary order allowing complex shapes to be designed as single patch PDE surfaces. Using this technique a designer has the flexibility of creating and manipulating the geometry of shape that satisfying an arbitrary set of boundary conditions. Both the boundary conditions which are defined as curves in 3-space and the spine of the corresponding PDE are utilized as interactive design tools for creating and manipulating geometry intuitively. In order to facilitate interactive design in real time, a compact analytic solution for the chosen arbitrary order PDE is formulated. This solution scheme even in the case of general boundary conditions satisfies exactly the boundary conditions where the resulting surface has an closed form representation allowing real time shape manipulation. In order to enable users to appreciate the powerful shape design and manipulation capability of the method, we present a set of practical examples.

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The need for increased product variety and improved aesthetics require the manufacturing enterprise to reduce time to market and to increase use of free-form surfaces in the form of the product. These changes lead to problems in the traditional approach for specification and verification of tolerances especially for a free form surfaces. In the case of freeform surfaces, the desired performance of a product depends on its geometry and is often controlled by intrinsic parameters such as curvature. Design intent therefore requires control on variations in these parameters. Ideally therefore, tolerances have to be applied on these parameters to prescribe allowable variations in the geometry of free-form surfaces. Since only the geometry of the product is controlled in manufacturing, tolerance specification has to ensure that the tolerances specified on the part geometry will ensure that the resulting value of the parameter of interest is within the limits prescribed by the designer. Relationship between allowable range in design parameters and that in geometry is not linear. Tolerance specification therefore becomes a trial and error process requiring considerable expertise and time. This thesis provides designers with a tool to automatically derive the corresponding tolerances to be specified to the manufacturing process to realize the final shape, such that the parameters that are used to control shape of the surface are within the prescribed variations. Automation in acquiring inspection data has brought dramatic changes in procedure for tolerance verification too. Optical scanners and similar non-contact devices provide large amount of points on the surface of the part quite rapidly. The unstructured point data are then processed to determine if the part complies with the given tolerance specifications. For freeform surfaces, current methods of verification uses minimum distance criterion between the nominal surface and unstructured point data. This ignores the correspondence between the points in the two data sets and may result in the rejection of good parts and acceptance of bad parts. There are other unresolved such as the singularity at corners of polyhedral shapes and handling datum. A new approach based on the Medial Axis Transform (MAT) has been proposed. It has been shown that reasoning on the MAT of the nominal model and the measured point set respectively enables the identification of corresponding points in the two sets. Verification of the tolerance allocated is therefore free from the problem mentioned above. MAT exhibits dimensional reduction and hence reduces verification time. It also eliminates surface fitting for detected feature. Results of implementation are provided for tolerance specification and verification using MAT.

The objectives of Sensor Based Fixture Design and Verification (SFDV) research are to provide the means for detecting contact failure of the workpiece with fixture locators and for preventing incorrect loading of the workpiece in a fixture. The fixtures that involve complex free-form surfaces especially in the aerospace industries face problems caused by the contact failure of the workpiece with locators. In batch and mass production defects often occur due to incorrect loading of the workpiece in a fixture by an operator due to fatigue or inadvertence. The current fixturing research is focussed on improving the fixture quality and other aspects and do not address these issues. This research is focussed on three areas, to generate algorithms for automatically foolproofing the fixtures, to build locators with embedded sensors that could be used to verify the contact and foolproof the existing fixtures, and to design and experimentally validate fixtures for free-form surfaces with sensors to verify the location. In foolproofing, workpieces were classified into different categories to identify the existence of a solution and the geometry was simplified and used to search for a solution based on symmetry/asymmetry to discover a foolproofing location. The algorithms were implemented in a CAD software and the solutions were verified in 3D space. The locators with inbuilt sensors were designed for foolproofing and location verification purposes and the sensors were used in case studies to establish credibility. A sensor based fixture design method is created for the part location of free-form surfaces using fiber optic sensors. An experimental fixture with sensors incorporated in the locators was used to determine the effects of surface curvature on the sensitivity of the sensors. A new theory on best locations for the sensor based locators by utilizing surface curvature is proposed based on the experimental results. The SFDV implementation may help realize the dream for any manufacturing sys­tem aspiring to move beyond the six sigma levels of quality and achieve zero defects.