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Ferritic stainless steel is typically used in the automotive industry to fabricate welded tube that is plastically deformed for flanging, bending and necking. The effect of welding parameters during autogenous gastungsten arc welding (GTAW) of thin sheet on the weld metal structure and tensile properties were determined. Two grades of ferritic stainless steels, a titanium-containing Grade 441 and a titanium-free molybdenum-containing Grade 436, were used as base metal. Statistical analysis was used to determine the influence of welding parameters on the microstructure of autogenous GTAW welds. The results of Grade 441 indicated that the welding speed and peak welding current had a statistically significant influence on the amount of equiaxed grains that formed. For Grade 436, the same welding parameters (welding speed and peak welding current) had a statistically significant influence on the grain size of the weld metal grains. The ductility of a tensile test coupon machined parallel to the weld direction, for both base metal grades, was unaffected by the welding parameters or the weld metal microstructure. The elongation was determined by the amount of weld metal in the gauge area of a tensile coupon. The titanium content of the base material seems to have the most significant effect on the formation of equiaxed grains. / Dissertation (MEng)--University of Pretoria, 2019. / Materials Science and Metallurgical Engineering / MEng / Unrestricted

The purpose of this study is to develop a series of response surfaces that define critical outcomes for welding in Al 7075 based on the tool geometry of a convex scrolled shoulder step spiral (CS4) friction stir processing tool. These response surfaces will be used to find critical minimums in forces which will decrease the required power input for the process. A comprehensive parameterization of the tool geometry is defined in this paper. A pilot study was performed to determine the feasibility of varying certain geometric features. Then a screening experiment eliminated those geometric features that were not as significant in determining the response surfaces. A central composite design with the five most important geometric features was used in order to develop response surfaces for nine different response variables. The nine response variables are the longitudinal, lateral and axial forces; the tool temperature, the spindle torque, the amount of flash, the presence of defects, the surface roughness and the ledge size. By using standard regression techniques, response surface equations were developed that will allow the user to optimize tool geometries based on the desired response variables. The five geometric features, the process parameters and several of their interactions were found to be highly significant in the response surfaces.

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.

Within statistical methods, design of experiments (DOE) is well suited to make good inference from a minimal amount of data. Two types of designs within DOE are screening designs and optimization designs. Traditionally, these approaches have been necessarily separated by a gap between the objectives of each design and the methods available. Despite being so separated, in practice these designs are frequently connected by sequential experimentation. In fact, from the genesis of a project, the experimentor often knows that both designs will be necessary to accomplish his objectives. Due to advances in the understanding of experimental designs with complex aliasing and their analysis, a current topic within statistics is how to desegregate these methods into a more unified and economical approach. This project is one treatment of that issue.

Errors of computational simulations in design of a high-speed civil transport (HSCT) are investigated. First, discretization error from a supersonic panel code, WINGDES, is considered. Second, convergence error from a structural optimization procedure using GENESIS is considered along with the Rosenbrock test problem. A grid converge study is performed to estimate the order of the discretization error in the lift coefficient (CL) of the HSCT calculated from WINGDES. A response surface (RS) model using several mesh sizes is applied to reduce the noise magnification problem associated with the Richardson extrapolation. The RS model is shown to be more efficient than Richardson extrapolation via careful use of design of experiments. A programming error caused inaccurate optimization results for the Rosenbrock test function, while inadequate convergence criteria of the structural optimization produced error in wing structural weight of the HSCT. The Weibull distribution is successfully fit to the optimization errors of both problems. The probabilistic model enables us to estimate average errors without performing very accurate optimization runs that can be expensive, by using differences between two sets of results with different optimization control parameters such as initial design points or convergence criteria. Optimization results with large errors, outliers, produced inaccurate RS approximations. A robust regression technique, M-estimation implemented by iteratively reweighted least squares (IRLS), is used to identify the outliers, which are then repaired by higher fidelity optimizations. The IRLS procedure is applied to the results of the Rosenbrock test problem, and wing structural weight from the structural optimization of the HSCT. A nonsymmetric IRLS (NIRLS), utilizing one-sidedness of optimization errors, is more effective than IRLS in identifying outliers. Detection and repair of the outliers improve accuracy of the RS approximations. Finally, configuration optimizations of the HSCT are performed using the improved wing bending material weight RS models. / Ph. D.

Traditional single stage design optimality procedures can be used to efficiently generate data for an assumed model y = f(x^(m),b) + ε. The model assumptions include the form of f, the set of regressors, x^(m) , and the distribution of ε. The nature of the response, y, often provides information about the model form (f) and the error distribution. It is more difficult to know, apriori, the specific set of regressors which will best explain the relationship between the response and a set of design (control) variables x. Misspecification of x^(m) will result in a design which is efficient, but for the wrong model. A Bayesian two stage design approach makes it possible to efficiently design experiments when initial knowledge of x^(m) is poor. This is accomplished by using a Bayesian optimality criterion in the first stage which is robust to model uncertainty. Bayesian analysis of first stage data reduces uncertainty associated with x^(m), enabling the remaining design points (second stage design) to be chosen with greater efficiency. The second stage design is then generated from an optimality procedure which incorporates the improved model knowledge. Using this approach, numerous two stage design procedures have been developed for the normal linear model. Extending this concept, a Bayesian design augmentation procedure has been developed for the purpose of efficiently obtaining data for variance modeling, when initial knowledge of the variance model is poor. / Ph. D.

Impaired reproduction studies with Poisson responses are among a growing class of toxicity studies in the biological and medical realm. In recent years, little effort has been focused on the development of efficient experimental designs for impaired reproduction studies. This research concentrates on two areas: 1) the use of Bayesian techniques to make single regressor designs robust to parameter misspecification and 2) the extension of design optimality methods to the k-regressor model. The standard Poisson model with log link is used. Bayesian designs with priors on the parameters are explored using both the D and F-optimality criteria for the single regressor Poisson exponential model. Since these designs are found via numeric optimization techniques, Bayesian equivalence theory functions are derived to verify the optimality of these designs. Efficient Bayesian designs which provide for lack-of-fit testing are discussed. Characterizations of D, D_s, and interaction optimal designs which are factorial in nature are demonstrated for models involving interaction through k factors. The optimality of these designs is verified using equivalence theory. In addition, augmentations of these designs that result in desirable lack of fit properties are discussed. Also, a structure for fractional factorials is given in which specific points are added one at a time to the main effect design in order to gain estimability of the desired interactions. Robustness properties are addressed as well. Finally, this entire line of research is extended to industrial exponential models where different regressors work to increase and/or decrease a count data response produced by a process. / Ph. D.

In response surface methodology, the central composite design is the most popular choice for fitting a second order model. The choice of the distance for the axial runs, alpha, in a central composite design is very crucial to the performance of the design. In the literature, there are plenty of discussions and recommendations for the choice of alpha, among which a rotatable alpha and an orthogonal blocking alpha receive the greatest attention. Box and Hunter (1957) discuss and calculate the values for alpha that achieve rotatability, which is a way to stabilize prediction variance of the design. They also give the values for alpha that make the design orthogonally blocked, where the estimates of the model coefficients remain the same even when the block effects are added to the model. In the last ten years, people have begun to realize the importance of a split-plot structure in industrial experiments. Constructing response surface designs with a split-plot structure is a hot research area now. In this dissertation, Box and Hunters' choice of alpha for rotatablity and orthogonal blocking is extended to central composite designs with a split-plot structure. By assigning different values to the axial run distances of the whole plot factors and the subplot factors, we propose two-strata rotatable splitplot central composite designs and orthogonally blocked split-plot central composite designs. Since the construction of the two-strata rotatable split-plot central composite design involves an unknown variance components ratio d, we further study the robustness of the two-strata rotatability on d through simulation. Our goal is to provide practical recommendations for the value of the design parameter alpha based on the philosophy of traditional response surface methodology. / Ph. D.

Complex mathematical models are often built to describe a physical process that would otherwise be extremely difficult, too costly or sometimes impossible to analyze. Generally, these models require solutions to many partial differential equations. As a result, the computer codes may take a considerable amount of time to complete a single evaluation. A time tested method of analysis for such models is Monte Carlo simulation. These simulations, however, often require many model evaluations, making this approach too computationally expensive. To limit the number of experimental runs, it is common practice to model the departure as a Gaussian stochastic process (GaSP) to develop an emulator of the computer model. One advantage for using an emulator is that once a GaSP is fit to realized outcomes, the computer model is easy to predict in unsampled regions of the input space. This is an attempt to 'characterize' the overall model of the computer code. Most of the historical work on design and analysis of computer experiments focus on the characterization of the computer model over a large region of interest. However, many practitioners seek other objectives, such as input screening (Welch et al., 1992), mapping a response surface, or optimization (Jones et al., 1998). Only recently have researchers begun to consider these topics in the design and analysis of computer experiments. In this dissertation, we explore a more traditional response surface approach (Myers, Montgomery and Anderson-Cook, 2009) in conjunction with traditional computer experiment methods to search for the optimum response of a process. For global optimization, Jones, Schonlau, and Welch's (1998) Efficient Global Optimization (EGO) algorithm remains a benchmark for subsequent research of computer experiments. We compare the proposed method in this paper to this leading benchmark. Our goal is to show that response surface methods can be effective means towards estimating an optimum response in the computer experiment framework. / Ph. D.