QC 351 A7 no. 61 / In an attempt to design a three -mirror aspheric camera, a procedure was developed to arrive at a design with a minimum obscuration ratio. It was found that, in some cases, the sky baffling became the diffracting obscuration rather than the obscuration caused by the secondary. The procedure allowed for this and was able to select a system with the smallest diffracting obscuration in the pupil. Initially, two designs were selected and optimized through the use of aspheric surfaces. The designs represented two extremes in that one had much faster surfaces than the other. The fast mirror system was easier to optimize, performed better, and had the shorter over -all length. Further, evaluation of manufacturing errors on the fast mirror design showed that an acceptable level of performance could be expected if the errors were kept small. The maximum errors are spacing errors ±0.0005 in. tilt of surface errors ±0.001 /D in. radii of curvature errors ±0.125 in. where D is the diameter of the mirror surface.

Reliability evaluation by analytic modelling constitute an important issue of designing a reliable multiprocessor system. In this thesis, a model for reliability and fault tolerance analysis of the interconnection network is presented, based on graph theory. Reliability and fault tolerance are considered as deterministic and probabilistic measures of connectivity. Exact techniques for reliability evaluation fail for large multiprocessor systems because of the enormous computational resources required. Therefore, approximation techniques have to be used. Three approaches are proposed, the first by simplifying the symbolic expression of reliability; the other two by applying a hierarchical decomposition to the system. All these methods give results close to those obtained by exact techniques.

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The thesis introduces an approach for obtaining higher level decision support information using electromagnetic transient (EMT) simulation programs. In this approach, a suite of higher level driver programs (decision support tools) control the simulator to gain important information about the system being simulated. These tools conduct a sequence of simulation runs, in each of which the study parameters are carefully selected based on the observations of the earlier runs in the sequence. In this research two such tools have been developed in conjunction with the PSCAD/EMTDC electromagnetic transient simulation program. The first tool is an improved optimization algorithm, which is used for automatic optimization of the system parameters to achieve a desired performance. This algorithm improves the capabilities of the previously reported method of optimization-enabled electromagnetic transient simulation by using an enhanced gradient-based optimization algorithm with constraint handling techniques. In addition to allow handling of design problems with more than one objective the thesis proposes to augment the optimization tool with the technique of Pareto optimality. A sequence of optimization runs are conducted to obtain the Pareto frontier, which quantifies the tradeoffs between the design objectives. The frontier can be used by the designer for decision making process. The second tool developed in this research helps the designer to study the effects of uncertainties in a design. By using a similar multiple-run approach this sensitivity analysis tool provides surrogate models of the system, which are simple mathematical functions that represent different aspects of the system performance. These models allow the designer to analyze the effects of uncertainties on system performance without having to conduct any further time-consuming EMT simulations. In this research it has been also proposed to add probabilistic analysis capabilities to the developed sensitivity analysis tool. Since probabilistic analysis of a system using conventional techniques (e.g. Monte-Carlo simulations) normally requires a large number of EMT simulation runs, using surrogate models instead of the actual simulation runs yields significant savings in terms of shortened simulation time. A number of examples have been used throughout the thesis to demonstrate the application and usefulness of the proposed tools.

The thesis introduces an approach for obtaining higher level decision support information using electromagnetic transient (EMT) simulation programs. In this approach, a suite of higher level driver programs (decision support tools) control the simulator to gain important information about the system being simulated. These tools conduct a sequence of simulation runs, in each of which the study parameters are carefully selected based on the observations of the earlier runs in the sequence. In this research two such tools have been developed in conjunction with the PSCAD/EMTDC electromagnetic transient simulation program. The first tool is an improved optimization algorithm, which is used for automatic optimization of the system parameters to achieve a desired performance. This algorithm improves the capabilities of the previously reported method of optimization-enabled electromagnetic transient simulation by using an enhanced gradient-based optimization algorithm with constraint handling techniques. In addition to allow handling of design problems with more than one objective the thesis proposes to augment the optimization tool with the technique of Pareto optimality. A sequence of optimization runs are conducted to obtain the Pareto frontier, which quantifies the tradeoffs between the design objectives. The frontier can be used by the designer for decision making process. The second tool developed in this research helps the designer to study the effects of uncertainties in a design. By using a similar multiple-run approach this sensitivity analysis tool provides surrogate models of the system, which are simple mathematical functions that represent different aspects of the system performance. These models allow the designer to analyze the effects of uncertainties on system performance without having to conduct any further time-consuming EMT simulations. In this research it has been also proposed to add probabilistic analysis capabilities to the developed sensitivity analysis tool. Since probabilistic analysis of a system using conventional techniques (e.g. Monte-Carlo simulations) normally requires a large number of EMT simulation runs, using surrogate models instead of the actual simulation runs yields significant savings in terms of shortened simulation time. A number of examples have been used throughout the thesis to demonstrate the application and usefulness of the proposed tools.

abstract: Geometrical tolerances define allowable manufacturing variations in the features of mechanical parts. For a given feature (planar face, cylindrical hole) the variations may be modeled with a T-Map, a hyper solid in 6D small displacement coordinate space. A general method for constructing T-Maps is to decompose a feature into points, identify the variational limits to these points allowed by the feature tolerance zone, represent these limits using linear halfspaces, transform these to the central local reference frame and intersect these to form the T-Map for the entire feature. The method is explained and validated for existing T-Map models. The method is further used to model manufacturing variations for the positions of axes in patterns of cylindrical features. When parts are assembled together, feature level manufacturing variations accumulate (stack up) to cause variations in one or more critical dimensions, e.g. one or more clearances. When the T-Maps model is applied to complex assemblies it is possible to obtain as many as six dimensional stack up relation, instead of the one or two typical of 1D or 2D charts. The sensitivity of the critical assembly dimension to the manufacturing variations at each feature can be evaluated by fitting a functional T-Map over a kinematically transformed T-Map of the feature. By considering individual features and the tolerance specifications, one by one, the sensitivity of each tolerance on variations of a critical assembly level dimension can be evaluated. The sum of products of tolerance values and respective sensitivities gives value of worst case functional variation. The same sensitivity equation can be used for statistical tolerance analysis by fitting a Gaussian normal distribution function to each tolerance range and forming an equation of variances from all the contributors. The method for evaluating sensitivities and variances for each contributing feature is explained with engineering examples. The overall objective of this research is to develop method for automation friendly and efficient T-Map generation and statistical tolerance analysis. / Dissertation/Thesis / Masters Thesis Mechanical Engineering 2018

abstract: 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. / Dissertation/Thesis / M.S. Mechanical Engineering 2012

Ever since the design and manufacture of products moved from the craftsman era where individual craftsman designed and manufactured the entire product, to the mass production era, where skilled laborers were crafting interchangeable parts or in some cases single features on interchangeable parts, variation in assemblies has been a major concern to designers, manufacturers, and in a more subtle way, customers. Variation, in the end, affects quality, performance and the cost of products. One particular type of design that is particularly robust to variation is an exactly constrained design. Several researchers have recently explored the topic of exact constraint design. An exactly constrained design is one in which each degree of freedom is constrained by a single constraint until the desired degrees of freedom for the design is attained. One attractive advantage of exactly constrained designs is that they are robust to variation. However, exactly constrained designs often require nesting forces to maintain the configuration of the design. This research develops a method for designing features that will supply robust nesting forces such that the advantages of the exactly constrained design are preserved. The method developed in this work takes advantage of a proven method for tolerance analysis and enhances this method to include the analysis of these features that supply nesting forces. Along with the enhancement, principles are developed that aid this analysis. All the examples provided in this work are verified using comparisons to Monte Carlo simulations. The comparisons show good results, typically less than 2% difference from the Monte Carlo simulations, verifying that this method accurately predicts variation and allows for the robust design of features that supply the nesting forces in exactly constrained assemblies.

Surface micromachining of micro-electro-mechanical systems (MEMS), like all other fabrication processes, has inherent variation that leads to uncertain material and dimensional parameters. To obtain accurate and reliable predictions of mechanism behavior, the effects of these variations need to be analyzed. This thesis expands already existing tolerance and uncertainty analysis methods to apply to micro compliant mechanisms. For simple compliant members, explicit equations can be used in uncertainty analysis. However, for a nonlinear implicit system of equations, the direct linearization method may be used to obtain sensitivities of output parameters to small changes in known variables. This is done by including static equilibrium equations and pseudo-rigid-body model relationships with the kinematic vector loop equations. Examples are used to show a comparison of this method to other deterministic and probabilistic methods and finite element analysis.