Tolerances on line profiles are used to control cross-sectional shapes of parts, such as turbine blades. A full life cycle for many mechanical devices depends (i) on a wise assignment of tolerances during design and (ii) on careful quality control of the manufacturing process to ensure adherence to the specified tolerances. This thesis describes a new method for quality control of a manufacturing process by improving the method used to convert measured points on a part to a geometric entity that can be compared directly with tolerance specifications. The focus of this paper is the development of a new computational method for obtaining the least-squares fit of a set of points that have been measured with a coordinate measurement machine along a line-profile. The pseudo-inverse of a rectangular matrix is used to convert the measured points to the least-squares fit of the profile. Numerical examples are included for convex and concave line-profiles, that are formed from line- and circular arc-segments.

This thesis concerns the role of geometric imperfections on assemblies in which the location of a target part is dependent on supports at two features. In some applications, such as a turbo-machine rotor that is supported by a series of parts at each bearing, it is the interference or clearance at a functional target feature, such as at the blades that must be controlled. The first part of this thesis relates the limits of location for the target part to geometric imperfections of other parts when stacked-up in parallel paths. In this section parts are considered to be rigid (non-deformable). By understanding how much of variation from the supporting parts contribute to variations of the target feature, a designer can better utilize the tolerance budget when assigning values to individual tolerances. In this work, the T-Map®, a spatial math model is used to model the tolerance accumulation in parallel assemblies. In other applications where parts are flexible, deformations are induced when parts in parallel are clamped together during assembly. Presuming that perfectly manufactured parts have been designed to fit perfectly together and produce zero deformations, the clamping-induced deformations result entirely from the imperfect geometry that is produced during manufacture. The magnitudes and types of these deformations are a function of part dimensions and material stiffnesses, and they are limited by design tolerances that control manufacturing variations. These manufacturing variations, if uncontrolled, may produce high enough stresses when the parts are assembled that premature failure can occur before the design life. The last part of the thesis relates the limits on the largest von Mises stress in one part to functional tolerance limits that must be set at the beginning of a tolerance analysis of parts in such an assembly.

The main objective of this project was to create a framework for holistic ideation and research about the technical issues involved in creating a holistic approach. Towards that goal, we explored different components of ideation (both logical and intuitive), characterized ideation states, and found new ideation blocks with strategies used to overcome them. One of the major contributions of this research is the method by which easy traversal between different ideation methods with different components were facilitated, to support both creativity and functional quality. Another important part of the framework is the sensing of ideation states (blocks/ unfettered ideation) and investigation of matching ideation strategies most likely to facilitate progress. Some of the ideation methods embedded in the initial holistic test bed are Physical effects catalog, working principles catalog, TRIZ, Bio-TRIZ and Artifacts catalog. Repositories were created for each of those. This framework will also be used as a research tool to collect large amount of data from designers about their choice of ideation strategies used, and their effectiveness. Effective documentation of design ideation paths is also facilitated using this holistic approach. A computer tool facilitating holistic ideation was developed. Case studies were run on different designers to document their ideation states and their choice of ideation strategies to come up with a good solution to solve the same design problem.

The essence of this research is the reconciliation and standardization of feature fitting algorithms used in Coordinate Measuring Machine (CMM) software and the development of Inspection Maps (i-Maps) for representing geometric tolerances in the inspection stage based on these standardized algorithms. The i-Map is a hypothetical point-space that represents the substitute feature evaluated for an actual part in the inspection stage. The first step in this research is to investigate the algorithms used for evaluating substitute features in current CMM software. For this, a survey of feature fitting algorithms available in the literature was performed and then a case study was done to reverse engineer the feature fitting algorithms used in commercial CMM software. The experiments proved that algorithms based on least squares technique are mostly used for GD&T; inspection and this wrong choice of fitting algorithm results in errors and deficiency in the inspection process. Based on the results, a standardization of fitting algorithms is proposed in light of the definition provided in the ASME Y14.5 standard and an interpretation of manual inspection practices. Standardized algorithms for evaluating substitute features from CMM data, consistent with the ASME Y14.5 standard and manual inspection practices for each tolerance type applicable to planar features are developed. Second, these standardized algorithms developed for substitute feature fitting are then used to develop i-Maps for size, orientation and flatness tolerances that apply to their respective feature types. Third, a methodology for Statistical Process Control (SPC) using the I-Maps is proposed by direct fitting of i-Maps into the parent T-Maps. Different methods of computing i-Maps, namely, finding mean, computing the convex hull and principal component analysis are explored. The control limits for the process are derived from inspection samples and a framework for statistical control of the process is developed. This also includes computation of basic SPC and process capability metrics.

Current trends in the Computer Aided Engineering (CAE) involve the integration of legacy mesh-based finite element software with newer solid-modeling kernels or full CAD systems in order to simplify laborious or highly specialized tasks in engineering analysis. In particular, mesh generation is becoming increasingly automated. In addition, emphasis is increasingly placed on full assembly (multi-part) models, which in turn necessitates an automated approach to contact analysis. This task is challenging due to increases in algebraic system size, as well as increases in the number of distorted elements - both of which necessitate manual intervention to maintain accuracy and conserve computer resources. In this investigation, it is demonstrated that the use of a mesh-free B-Spline finite element basis for structural contact problems results in significantly smaller algebraic systems than mesh-based approaches for similar grid spacings. The relative error in calculated contact pressure is evaluated for simple two dimensional smooth domains at discrete points within the contact zone and compared to the analytical Hertz solution, as well as traditional mesh-based finite element solutions for similar grid spacings. For smooth curved domains, the relative error in contact pressure is shown to be less than for bi-quadratic Serendipity elements. The finite element formulation draws on some recent innovations, in which the domain to be analyzed is integrated with the use of transformed Gauss points within the domain, and boundary conditions are applied via distance functions (R-functions). However, the basis is stabilized through a novel selective normalization procedure. In addition, a novel contact algorithm is presented in which the B-Spline support grid is re-used for contact detection. The algorithm is demonstrated for two simple 2-dimensional assemblies. Finally, a modified Penalty Method is demonstrated for connecting elements with incompatible bases.