<p> This thesis addresses itself to one of the most general theoretical problems associated with the art of engineering design. Viewed in its entirety the proposed approach integrates the relation between the design and production engineers through the theory of nonlinear optimization. The conventional optimization problem is extended to include the optimal allocation of the upper and lower limits of the random variables of an engineering system. The approach is illustrated by an example using a sequence of increasingly generalized formulations, while the general mathematical theory is also provided. The method appears to offer a practical technique provided a satisfactory cost function can be defined.</p> <p> The thesis presents an analytical approach to full acceptability design conditions as well as less than full acceptability or scrap design conditions. An important distinction between the design and the manufacturing scrap has been introduced and illustrated through examples.</p> <p> The space regionalization technique is utilized to estimate the system design scrap. Optimization strategies are introduced to the mathematically defined upper and lower limits of the regionalization region. This region is then discretized into a number of cells depending upon the probabilistic characteristic of the system random variables.</p> <p> The analytical approach exhibited does not rely explicitly on evaluation of partial derivatives of either the system cost objective or any of its constraints at any point. Moreover, the technique could be applied to engineering systems with either convex or nonconvex feasible regions. It could also be exercised irrespective of the shape of the probabilistic distributions that describe the random variables variation.</p> <p> Industrially oriented design examples are furnished to justify the applicability of the theory in different engineering disciplines.</p> / Thesis / Doctor of Philosophy (PhD)

A method for allocating tolerances to exactly constrained assemblies is developed. The procedure is established as an optimization subject to constraints. The objective is to minimize the manufacturing cost of the assembly while respecting an acceptable level of performance. This method is particularly interesting for exactly constrained components that should be mass-produced. This thesis presents the different concepts used to develop the method. It describes exact constraint theory, manufacturing variations, optimization concepts, and the related mathematical tools. Then it explains how to relate these different topics in order to perform a tolerance allocation. The developed method is applied on two relevant exactly constrained examples: multi-fiber connectors, and kinematic coupling. Every time a mathematical model of the system and its corresponding manufacturing variations is established. Then an optimization procedure uses this model to minimize the manufacturing cost of the system while respecting its functional requirements. The results of the tolerance allocation are verified with Monte Carlo simulation.

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abstract: Tolerance specification for manufacturing components from 3D models is a tedious task and often requires expertise of “detailers”. The work presented here is a part of a larger ongoing project aimed at automating tolerance specification to aid less experienced designers by producing consistent geometric dimensioning and tolerancing (GD&T). Tolerance specification can be separated into two major tasks; tolerance schema generation and tolerance value specification. This thesis will focus on the latter part of automated tolerance specification, namely tolerance value allocation and analysis. The tolerance schema (sans values) required prior to these tasks have already been generated by the auto-tolerancing software. This information is communicated through a constraint tolerance feature graph file developed previously at Design Automation Lab (DAL) and is consistent with ASME Y14.5 standard. The objective of this research is to allocate tolerance values to ensure that the assemblability conditions are satisfied. Assemblability refers to “the ability to assemble/fit a set of parts in specified configuration given a nominal geometry and its corresponding tolerances”. Assemblability is determined by the clearances between the mating features. These clearances are affected by accumulation of tolerances in tolerance loops and hence, the tolerance loops are extracted first. Once tolerance loops have been identified initial tolerance values are allocated to the contributors in these loops. It is highly unlikely that the initial allocation would satisfice assemblability requirements. Overlapping loops have to be simultaneously satisfied progressively. Hence, tolerances will need to be re-allocated iteratively. This is done with the help of tolerance analysis module. The tolerance allocation and analysis module receives the constraint graph which contains all basic dimensions and mating constraints from the generated schema. The tolerance loops are detected by traversing the constraint graph. The initial allocation distributes the tolerance budget computed from clearance available in the loop, among its contributors in proportion to the associated nominal dimensions. The analysis module subjects the loops to 3D parametric variation analysis and estimates the variation parameters for the clearances. The re-allocation module uses hill climbing heuristics derived from the distribution parameters to select a loop. Re-allocation Of the tolerance values is done using sensitivities and the weights associated with the contributors in the stack. Several test cases have been run with this software and the desired user input acceptance rates are achieved. Three test cases are presented and output of each module is discussed. / Dissertation/Thesis / Masters Thesis Mechanical Engineering 2016

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Tolerances play an important role in product fabrication. Tolerances impact the needs of the designer and the manufacturer. Engineering designers are concerned with the impact of tolerances on the variation of the output, while manufacturers are more concerned with the cost of fitting the parts. Traditional tolerance control methods do not take into account both these needs. In this thesis, the author proposes a framework that overcomes the drawbacks of the traditional tolerance control methods, and reduces subjectivity via fuzzy set theory and decision support systems (DSS). Those factors that affect the manufacturing cost (geometry, material etc) of a part are fuzzy (i.e. subjective) in nature with no numerical measure. Fuzzy comprehensive evaluation (FCE) is utilized in this thesis as a method of quantifying the fuzzy (i.e. subjective) factors. In the FCE process, the weighted importance of each factor affects the manufacturing cost of the part. There is no systematic method of calculating the importance weights. This brings about a need for decision support in the evaluation of the weighted importance of each factor. The combination of FCE and DSS, in the form of Conjoint Analysis (CA), is used to reduce subjectivity in calculation of machining cost. Taguchi's quality loss function is considered in this framework to reduce the variation in the output. The application of the framework is demonstrated with three practical engineering applications. Tolerances are allocated for three assemblies; a friction clutch, an accumulator O-ring seal and a Power Generating Shock Absorber (PGSA) using the proposed framework. The output performances of the PGSA and the clutch are affected by the allocated tolerances. On using the proposed framework, there is seen to be a reduction in variation of output performance for the clutch and the PGSA. The use of CA is also validated by checking efficiency of final tolerance calculation with and without use of CA.

This research effort develops a comprehensive computational framework to support the parametric optimal design of uncertain dynamical systems. Uncertainty comes from various sources, such as: system parameters, initial conditions, sensor and actuator noise, and external forcing. Treatment of uncertainty in design is of paramount practical importance because all real-life systems are affected by it; not accounting for uncertainty may result in poor robustness, sub-optimal performance and higher manufacturing costs. Contemporary methods for the quantification of uncertainty in dynamical systems are computationally intensive which, so far, have made a robust design optimization methodology prohibitive. Some existing algorithms address uncertainty in sensors and actuators during an optimal design; however, a comprehensive design framework that can treat all kinds of uncertainty with diverse distribution characteristics in a unified way is currently unavailable. The computational framework uses Generalized Polynomial Chaos methodology to quantify the effects of various sources of uncertainty found in dynamical systems; a Least-Squares Collocation Method is used to solve the corresponding uncertain differential equations. This technique is significantly faster computationally than traditional sampling methods and makes the construction of a parametric optimal design framework for uncertain systems feasible. The novel framework allows to directly treat uncertainty in the parametric optimal design process. Specifically, the following design problems are addressed: motion planning of fully-actuated and under-actuated systems; multi-objective robust design optimization; and optimal uncertainty apportionment concurrently with robust design optimization. The framework advances the state-of-the-art and enables engineers to produce more robust and optimally performing designs at an optimal manufacturing cost. / Ph. D.

The procedure of joining flexible or nonrigid parts using applied loads is called compliant assembly, and it is widely used in automotive, aerospace, electronics, and appliance manufacturing. Uncontrolled assembly processes may produce geometric errors that can exceed design tolerances and induce an increment of elastic energy in the structure due to the accumulation of internal stresses. This condition might create unexpected deformations and residual stress distributions across the structure that compromise product functionality. This thesis presents a method based on nonlinear Finite Element Analysis (FEA), metamodelling, and optimization techniques to provide accurate and on-time shimming strategies to support the definition of optimum assembly strategies. An example of the method on a typical aerospace wing box structure is demonstrated in the present study. The delivered outputs intend to support the production line by anticipating the response of the structure under a specific assembly condition and presenting alternative assembly strategies that can be applied to address eventual predicted issues on product requirements. / Graduate