Accuracy and precision assesment of stochastic simulation tools for springback variation

The sheet forming industry is plagued by inherent variations in its many input variables, making quality control and improvements a major hurdle. This is particularly poignant for Advanced High Strength Steels (AHSS), which exhibit a large degree of property variability. Current FE-based simulation packages are successful at predicting the manufacturability of a particular sheet metal components, however, due to their numerical deterministic nature are inherently unable to predict the performance of a real-life production process. Though they are now beginning to incorporate the stochastic nature of production in their codes. This work investigates the accuracy and precision of a current stochastic simulation package, AutoForm Sigma v4.1, by developing an experimental data set where all main sources of variation are captured through precise measurements and standard tensile tests. Using a Dual Phase 600Mpa grade steel a series of semi-cylindrical channels are formed at two Blank Holder Pressure levels where the response metric is the variation in springback determined by the flange angle. The process is replicated in AutoForm Sigma and an assessment of accuracy and precision of the predictions are performed. Results indicate a very good correspondence to the experimental trials, with mean springback response predicted to within 1 ° of the flange angle and the interquartile spread of results to within 0.22°.

Towards development of a quality cost model for automotive stamping

The current work used discrete event simulation techniques to model the economics of quality within an actual automotive stamping plant. Automotive stamping is a complex, capital intensive process requiring part-specific tooling and specialised machinery. Quality control and quality improvement is difficult in the stamping environment due to the general lack of process understanding and the large number to interacting variables. These factors have prevented the widespread use of statistical process control. In this work, a model of the quality control techniques used at the Ford Geelong Stamping plant is developed and indirectly validated against results from production. To date, most discrete event models are of systems where the quality control process is clearly defined by the rules of statistical process control. However, the quality control technique used within the stamping plant is for the operator to perform a 100% visual inspection while unloading the finished panels. In the developed model, control is enacted after a cumulative count of defective items is observed, thereby approximating the operator who allows a number of defective panels to accumulate before resetting the line. Analysis of this model found that the cost sensitivity to inspection error is dependent upon the level of control and that the level of control determines line utilisation. Additional analysis of this model demonstrated that additional inspection processes would lead to more stable cost structures but these structures many not necessarily be lower cost. The model was subsequently applied to investigate the economics of quality improvement. The quality problem of panel blemishes, induced by slivers (small metal fragments), was chosen as a case stuffy. Errors of 20-30% were observed during direct validation of the cost model and it was concluded that the use of discrete event simulation models for applications requiring high accuracy would not be possible unless the production system was of low complexity. However, the model could be used to evaluate the sensitivity of input factors and investigating the effects of a number of potential improvement opportunities. Therefore, the research concluded that it is possible to use discrete event simulation to determine the quality economics of an actual stamping plant. However, limitations imposed by inability of the model to consider a number of external factors, such as continuous improvement, operator working conditions or wear and the lack of reliable quality data, result in low cost accuracy. Despite this, it still can be demonstrated that discrete event simulation has significant benefits over the alternate modelling methods.

Elastic behaviour in mechanical draw presses

This thesis explores the elastic behaviour of the mechanical double action press and draw die system commonly used to draw sheet metal components in the automotive industry. High process variability in production and excessive time spent in die try-out are significant problems in automotive stamping. It has previously been suggested that the elastic behaviour of the system may contribute to these problems. However, the mechanical principles that cause the press system to affect the forming process have not been documented in detail. Due to a poor understanding of these problems in industry, the elasticity of the press and tools is currently not considered during the die design. The aim of this work was to explore the physical principles of press system elasticity and determine the extent to which it contributes to problems in try-out and production. On the basis of this analysis methods were developed for controlling or accounting for problems during the design process. The application of frictional restraining force to the edges of the blank during forming depends on the distribution and magnitude of the clamping force between the binders surfaces of the draw die. This is an important control parameter for the deep drawing process. It has been demonstrated in this work that the elasticity of the press and draw die can affect clamping force in two ways. The response of the press system, to the forces produced in the press during forming, causes the magnitude of clamping force to change during the stroke. This was demonstrated using measured data from a production press. A simple linear elastic model of the press system was developed to illustrate a definite link between the measured force variation and the elasticity of the press and tools. The simple model was extended into a finite element model of the complete press system, which was used to control a forming simulation. It was demonstrated that stiffness variation within the system could influence the final strains in a drawn part. At the conclusion of this investigation a method is proposed for assessing the sensitivity of a part to clamping force variation in the press during die design. A means of reducing variation in the press through the addition of a simple linear spring element is also discussed. The second part of the work assessed the influence of tool structure on the distribution of frictional restraining forces to the blank. A forming simulation showed that tool stiffness affects the distribution of clamping pressure between the binders. This was also shown to affect the final strains in a drawn part. However, the most significant influence on restraining force was the tendency of the blank to increase in thickness between the binders during forming. Using a finite element approximation of the try-out process it was shown that the structure of the tool would also contribute to the problems currently experienced in try-out where uneven contact pressure distributions are addressed by manually adjusting the tool surfaces. Finally a generalised approach to designing draw die structures was developed. Simple analysis methods were combined with finite element based topology optimisation techniques to develop a set of basic design guidelines. The aim of the guidelines was to produce a structure with uniform stiffness response to a pressure applied at the binder surface. The work concludes with a recommendation for introducing the methods developed in this thesis into the standard production process.

Two dynamic discrete choice estimation problems and simulation method solutions

This paper considers two problems that frequently arise in dynamic discrete choice problems but have not received much attention with regard to simulation methods. The first problem is how to simulate unbiased simulators of probabilities conditional on past history. The second is simulating a discrete transition probability model when the underlying dependent variable is really continuous. Both methods work well relative to reasonable alternatives in the application discussed. However, in both cases, for this application, simpler methods also provide reasonably good results.

Research methods for social work

The book considers

Caracterização experimental e modelação numérica de espumas metálicas

As espumas de alumínio são materiais ultraleves, o que as torna atractivas para um largo espectro de aplicações comerciais na área da defesa, na indústria automóvel e aeroespacial, entre outras. Actualmente, há um grande interesse na utilização de espumas de alumínio em componentes estruturais ultraleves, incorporados em sistemas de absorção de energia para protecção contra o impacto. O recurso à simulação numérica para resolver problemas de engenharia em várias áreas é cada vez mais comum. A modelação numérica dos materiais assume vital importância quando o problema envolve a análise de processos tecnológicos como, por exemplo, a conformação plástica de materiais, ou a análise de estruturas. Deste modo, torna-se imprescindível garantir que a modelação dos materiais é de tal forma rigorosa que permite simular o melhor possível o seu comportamento real nas condições concretas da análise a realizar. A forma mais comum de garantir o rigor dos modelos utilizados é a validação dos modelos numéricos tendo por base resultados experimentais. Neste trabalho, fez-se a caracterização do comportamento mecânico das espumas de alumínio com nome comercial ALPORAS!, obtidas pelo processo de fabrico denominado expansão directa do metal fundido por adição de um agente expansor. Esta caracterização consistiu num conjunto de ensaios experimentais quer no regime quasi-estático, quer no regime dinâmico. No regime quasi-estático realizaram-se ensaios de compressão uniaxial e de compressão multiaxial. Para a caracterização no regime dinâmico foram realizados ensaios em barras de Hopkinson de polimetil-metacrilato (PMMA). Com base nos resultados experimentais obtidos determinaram-se os parâmetros dos dois modelos constitutivos para espumas metálicas implementados no programa comercial Abaqus™/Explicit. Estes modelos, e os respectivos parâmetros determinados, foram validados reproduzindo numericamente alguns ensaios experimentais quasi-estáticos e dinâmicos. Assim, verificou-se a adequabilidade dos modelos em diversas condições quer em termos de esforços quer em termos de regime de taxa de deformação Por último, desenvolveu-se uma estrutura inovadora para absorção de energia durante um impacto, constituída por componentes perfilados em liga de alumínio e por componentes em espumas de alumínio. Esta estrutura foi testada exclusivamente com recurso à simulação numérica, utilizando os modelos constitutivos validados anteriormente.

Adaptive MCMC methods with applications in environmental and geophysical models

This work presents new, efficient Markov chain Monte Carlo (MCMC) simulation methods for statistical analysis in various modelling applications. When using MCMC methods, the model is simulated repeatedly to explore the probability distribution describing the uncertainties in model parameters and predictions. In adaptive MCMC methods based on the Metropolis-Hastings algorithm, the proposal distribution needed by the algorithm learns from the target distribution as the simulation proceeds. Adaptive MCMC methods have been subject of intensive research lately, as they open a way for essentially easier use of the methodology. The lack of user-friendly computer programs has been a main obstacle for wider acceptance of the methods. This work provides two new adaptive MCMC methods: DRAM and AARJ. The DRAM method has been built especially to work in high dimensional and non-linear problems. The AARJ method is an extension to DRAM for model selection problems, where the mathematical formulation of the model is uncertain and we want simultaneously to fit several different models to the same observations. The methods were developed while keeping in mind the needs of modelling applications typical in environmental sciences. The development work has been pursued while working with several application projects. The applications presented in this work are: a winter time oxygen concentration model for Lake Tuusulanjärvi and adaptive control of the aerator; a nutrition model for Lake Pyhäjärvi and lake management planning; validation of the algorithms of the GOMOS ozone remote sensing instrument on board the Envisat satellite of European Space Agency and the study of the effects of aerosol model selection on the GOMOS algorithm.

Testing Mean-Variance Efficiency in CAPM with Possibly Non-Gaussian Errors : An Exact Simulation-Based Approach

In this paper we propose exact likelihood-based mean-variance efficiency tests of the market portfolio in the context of Capital Asset Pricing Model (CAPM), allowing for a wide class of error distributions which include normality as a special case. These tests are developed in the frame-work of multivariate linear regressions (MLR). It is well known however that despite their simple statistical structure, standard asymptotically justified MLR-based tests are unreliable. In financial econometrics, exact tests have been proposed for a few specific hypotheses [Jobson and Korkie (Journal of Financial Economics, 1982), MacKinlay (Journal of Financial Economics, 1987), Gib-bons, Ross and Shanken (Econometrica, 1989), Zhou (Journal of Finance 1993)], most of which depend on normality. For the gaussian model, our tests correspond to Gibbons, Ross and Shanken’s mean-variance efficiency tests. In non-gaussian contexts, we reconsider mean-variance efficiency tests allowing for multivariate Student-t and gaussian mixture errors. Our framework allows to cast more evidence on whether the normality assumption is too restrictive when testing the CAPM. We also propose exact multivariate diagnostic checks (including tests for multivariate GARCH and mul-tivariate generalization of the well known variance ratio tests) and goodness of fit tests as well as a set estimate for the intervening nuisance parameters. Our results [over five-year subperiods] show the following: (i) multivariate normality is rejected in most subperiods, (ii) residual checks reveal no significant departures from the multivariate i.i.d. assumption, and (iii) mean-variance efficiency tests of the market portfolio is not rejected as frequently once it is allowed for the possibility of non-normal errors.

The Kineticist's Workbench: Combining Symbolic and Numerical Methods in the Simulation of Chemical Reaction Mechanisms

The Kineticist's Workbench is a program that simulates chemical reaction mechanisms by predicting, generating, and interpreting numerical data. Prior to simulation, it analyzes a given mechanism to predict that mechanism's behavior; it then simulates the mechanism numerically; and afterward, it interprets and summarizes the data it has generated. In performing these tasks, the Workbench uses a variety of techniques: graph- theoretic algorithms (for analyzing mechanisms), traditional numerical simulation methods, and algorithms that examine simulation results and reinterpret them in qualitative terms. The Workbench thus serves as a prototype for a new class of scientific computational tools---tools that provide symbiotic collaborations between qualitative and quantitative methods.

Effect of membrane stress on surface roughness changes in sheet forming

Friction plays an important role in sheet metal forming (SMF) and the roughness of the surface of the sheet is a major factor that influences friction. In finite element method (FEM) models of metal forming, the roughness has usually been assumed to be constant; even though it is commonly observed that sheet drawn under tension over a tool radius results in the surface becoming shiny, indicating a major change in surface morphology. An elastic–plastic FEM model for micro-contact between a flat surface and a single roughness peak has been developed. The model was used to investigate the effect of the membrane stress in the sheet on the deformation of an artificial roughness peak. From the simulation results, the change in asperity, or deformation of the local peak, for a given nominal tool contact stress is significantly influenced by the local substrate stress. The height of the asperity decreases with increasing substrate stress and the local pressure is much higher than the nominal pressure. In addition, the local contact stress decreases with an increase in the substrate stress levels.

Determination of drawbead contacts with variable bead penetration

In stamping operations, the sliding of the sheet metal over the drawbeads is of great importance. The geometry of the drawbead and the degree of penetration both influence material flow and alter the frictional effects between the work and the tool. The effect of drawbead penetration over drawbeads has been studied using the Drawbead Simulator (DBS) test. The contact phenomenon between the sheet and drawbeads was analysed by examining deformed samples with an image fitting technique. The results were compared with an FE simulation and with an approximate geometric analysis. The results give a useful relationship between the rates of change of the contact angle with increasing bead penetration.

Improving stamping tryout using variational analysis, FE simulations and robustness

The tryout process at an automotive sheet metal production plant is outlined and analysed with the aim of augmenting the process to improve robustness through an understanding of variation using Finite Element (FE) analysis and other tools. The result is tryout can produce a more robust stamping process.

Using the solid-shell element to model the roll forming of large radii profiles

Roll forming is an incremental bending process for forming metal sheet, strip or coiled stock. Although Finite Element Analysis (FEA) is a standard tool for metal forming simulation, it is only now being increasingly used for the analysis of the roll forming process. This is because of the excessive computational time due to the long strip length and the multiple numbers of stands that have to be modelled. Typically a single solid element is used through the thickness of the sheet for roll forming simulations. Recent investigations have shown that residual stresses introduced during steel processing may affect the roll forming process and therefore need to be included in roll forming simulations. These residual stresses vary in intensity through the thickness and this cannot be accounted for by using only one solid element through the material thickness, in this work a solid-shell element with an arbitrary number of integration points has been used to simulate the roll forming process. The system modelled is that of roll forming a V-channel with dual phase DP780 sheet steel. In addition, the influence of other modelling parameters, such as friction, on CPU time is further investigated. The numerical results are compared to experimental data and a good correlation has been observed. Additionally the numerical results show that the CPU time is reduced in the model without friction and that considering friction does not have a significant effect on springback prediction in the numerical analysis of the roll forming process.