Rolling technology can control the thickness precisely. But it isn¡¦t available in width control. FEM software DEFORM 3D is adopted to simulate one stand of the hot finishing rolling process using carbon steel as sheet material. Stress, strain and width spread are discussed. Regression analysis is used to find an empirical equation for rolling load and width spread. Experiment and simulation of cold strip rolling using aluminum as sheet material are conducted,discussing the width spread and detail of width transformation in DEFORM 3D.From the comparisons between analytical and experimental width spread, the analytical model and prediction equation are validated.

The determination of the pressure distribution generated along the arc of contact between the rolls and workpiece during the rolling process has been a subject of interest to researchers for many years. Existing rolling theories make assumptions and include simplifications which are not often substantiated by direct measurement techniques in which pressure transducers are located within the roll surfaces. Such techniques are effective but prohibitively expensive since they render the rolls useless for rolling. A technique has been developed in which the pressure distribution and roll separating load are determined from consideration of the elastic deformation of the rolls during operation. By interrupting a rolling pass before completion, the shapes of the deformed rolls are imparted to the workpiece surface. Accurate measurement of the imparted profiles at several sections across the width of the workpiece allows the extent of the elastic deformation of the roll to be determined. An analytical solution based on solid body contact theory was used to determine the pressure distribution responsible for the elastic deformation along each section. The solution incorporates experimentally determined parameters and functions relating to specific mill-stands and schedules. Initial experimental work was undertaken in which the proposed technique was applied to the quasi-static indentation of flat and inclinedstrip specimens. Having established the basic features of the method relating to these modes of deformation the technique was then applied to the cold rolling process in the form of interrupted rolling passes. Tests were undertaken using a two-high laboratory rolling mill reducing the thickness of mild steel strip workpieces. Comparisons between the predicted pressure profiles using the technique developed and those determined by others using pressure transducers show close similarities. A comparison between the predicted roll separating loads and those determined experimentally show a reasonable correlation.

Abstract The rolling is an efficient and economical approach for the manufacturing of strip or plate metals, it plays an important role because of its versatility and its high production rate in the manufacture of various products with uniform cross-sectional area. Without the knowledge of the influences of the variables such as friction conditions, material properties, and workpiece geometry on the process mechanics, it will not be possible to design and control the equipment adequately, or to predict and prevent the occurrence of failures. According to modeling by numerical has become a major tool in rolling research. By using the proper criterion, de-pending upon the production requirements along with the modeling results, the process efficiency, productivity and quality can be increased and the down time of the mill and cost operation can be reduced. In this study, investigated that it do not consider to work hardening and consider to work hardening during the rolling process from Von Karman theory. We can realize friction coefficient, reduction ratio, rolling force, rolling torque, neutral point, and pressure distribution relation, then from measuring rolling force, torque, neutral point can inverse to solve friction coefficient and pressure distribution. Result that we found the error of direct and inverse solution about rolling friction coefficient was less than 5 %, and the coef-ficient of friction was found to increase with reduction and rolling force and neutral point.

The thesis is focused on lubricants and roll wear in striprolling. Regarding lubricants, the possibility of introducing newones, which are less detrimental towards environment, isstudied in laboratory scale. This is done for cold rolling,both of an Al- alloy and a low carbon steel. The lubricationperformance of such newly developed–water-based–synthetic lubricants is compared with currently used mineraloils and emulsions. By using the experimental method of"forward slip" measurements combined with slab methodcalculations and FE- simulations, friction coefficients areevaluated for different single pass reductions. Lubricantsbearing capacity and the product surface roughness are alsoevaluated. The results are encouraging. A synthetic water-based lubricant, used in the cold rollingof an Al- alloy, showed good lubrication capability, betterthan the mineral oil but worse than the emulsion. The rolledAl- strip finish was found to be finest for the syntheticlubricant followed by the mineral oil and the emulsion. Similarresults were obtained from the steel rolling. Here foursynthetic lubricants were compared with two mineral oils andone emulsion. The best lubricant was found to be one of thewater-based synthetics, showing the lowest value of thefriction coefficient and a smooth product surface. The aim of the wear study is to develop an accurateroll-wear prediction for hot strip finishing mills, which takesmore influential parameters into account. A new model of higheraccuracy is presented. This model is based on a large amount ofproduction campaigns. The strategy of the work is describedbelow. After a comprehensive literature study a promising modelstructure was found. The corresponding equation is tested ontwo hot strip mills. Predicted wear is found to be inqualitative agreement with industrial experience and measuredwear. Thus the structure–taking the influence of back-uprolls into account–was chosen for further development.This was done on behalf of results obtained from one mill builtup by six stands and three different work-roll materials.Campaigns of "mixed" and "similar" strip grades were used. Theobtained model is tested successfully in two other hot stripmills. Contradictory to the currently used on-line model, the newmodel takes the work roll flattening and back-up rolls contactarea into consideration. Also the influence of strip- and workroll grades is included. The model enables increased rolledstrip length and prolonged lifetime of the rolls, because ofimproved process control. Further more, grinding cost and timefor roll changing can be minimized. Of course thesepossibilities should result in considerable energy saving. <b>Keywords:</b>Strip rolling, lubricants, environment, rollwear modeling, production campaigns, regression analysis

<p>The thesis is focused on lubricants and roll wear in striprolling.</p><p>Regarding lubricants, the possibility of introducing newones, which are less detrimental towards environment, isstudied in laboratory scale. This is done for cold rolling,both of an Al- alloy and a low carbon steel. The lubricationperformance of such newly developed–water-based–synthetic lubricants is compared with currently used mineraloils and emulsions. By using the experimental method of"forward slip" measurements combined with slab methodcalculations and FE- simulations, friction coefficients areevaluated for different single pass reductions. Lubricantsbearing capacity and the product surface roughness are alsoevaluated. The results are encouraging.</p><p>A synthetic water-based lubricant, used in the cold rollingof an Al- alloy, showed good lubrication capability, betterthan the mineral oil but worse than the emulsion. The rolledAl- strip finish was found to be finest for the syntheticlubricant followed by the mineral oil and the emulsion. Similarresults were obtained from the steel rolling. Here foursynthetic lubricants were compared with two mineral oils andone emulsion. The best lubricant was found to be one of thewater-based synthetics, showing the lowest value of thefriction coefficient and a smooth product surface.</p><p>The aim of the wear study is to develop an accurateroll-wear prediction for hot strip finishing mills, which takesmore influential parameters into account. A new model of higheraccuracy is presented. This model is based on a large amount ofproduction campaigns. The strategy of the work is describedbelow.</p><p>After a comprehensive literature study a promising modelstructure was found. The corresponding equation is tested ontwo hot strip mills. Predicted wear is found to be inqualitative agreement with industrial experience and measuredwear. Thus the structure–taking the influence of back-uprolls into account–was chosen for further development.This was done on behalf of results obtained from one mill builtup by six stands and three different work-roll materials.Campaigns of "mixed" and "similar" strip grades were used. Theobtained model is tested successfully in two other hot stripmills.</p><p>Contradictory to the currently used on-line model, the newmodel takes the work roll flattening and back-up rolls contactarea into consideration. Also the influence of strip- and workroll grades is included. The model enables increased rolledstrip length and prolonged lifetime of the rolls, because ofimproved process control. Further more, grinding cost and timefor roll changing can be minimized. Of course thesepossibilities should result in considerable energy saving.</p><p><b>Keywords:</b>Strip rolling, lubricants, environment, rollwear modeling, production campaigns, regression analysis</p>

Abstract In today's world, enormous amounts of data are being collected everyday. Thus, the problems of storing, handling, and utilizing the data are faced constantly. As the human mind itself can no longer interpret the vast datasets, methods for extracting useful and novel information from the data are needed and developed. These methods are collectively called knowledge discovery methods. In this thesis, a novel combination of feature selection and data modeling methods is presented in order to help with this task. This combination includes the methods of basic statistical analysis, linear correlation, self-organizing map, parallel coordinates, and k-means clustering. The presented method can be used, first, to select the most relevant features from even hundreds of them and, then, to model the complex inter-correlations within the selected ones. The capability to handle hundreds of features opens up the possibility to study more extensive processes instead of just looking at smaller parts of them. The results of k-nearest-neighbors study show that the presented feature selection procedure is valid and appropriate. A second advantage of the presented method is the possibility to use thousands of samples. Whereas the current rules of selecting appropriate limits for utilizing the methods are theoretically proved only for small sample sizes, especially in the case of linear correlation, this thesis gives the guidelines for feature selection with thousands of samples. A third positive aspect is the nature of the results: given that the outcome of the method is a set of conditional probabilities, the derived model is highly unrestrictive and rather easy to interpret. In order to test the presented method in practice, it was applied to study two different cases of steel manufacturing with hot strip rolling. In the first case, the conditional probabilities for different types of retentions were derived and, in the second case, the rolling conditions for the occurrence of wedge were revealed. The results of both of these studies show that steel manufacturing processes are indeed very complex and highly dependent on the various stages of the manufacturing. This was further confirmed by the fact that with studies of k-nearest-neighbors and C4.5, it was impossible to derive useful models concerning the datasets as a whole. It is believed that the reason for this lies in the nature of these two methods, meaning that they are unable to grasp such manifold inter-correlations in the data. On the contrary, the presented method of conditional probabilities allowed new knowledge to be gained of the studied processes, which will help to better understand these processes and to enhance them.

This dissertation is devoted to the development of new flow-based formulations for the asymmetric traveling salesman problem (ATSP) and to the demonstration of their applicability in effectively solving some scheduling problems. The ATSP is commonly encountered in the areas of manufacturing planning and scheduling, and transportation logistics. The integration of decisions pertaining to production and shipping, in the supply chain context, has given rise to an additional and practical relevance to this problem especially in situations involving sequence-dependent setups and routing of vehicles. Our objective is to develop new ATSP formulations so that algorithms can be built by taking advantage of their relaxations (of integer variables, thereby, resulting in linear programs) to effectively solve large-size problems. In view of our objective, it is essential to have a formulation that is amenable to the development of an effective solution procedure for the underlying problem. One characteristic of a formulation that is helpful in this regard is its tightness. The tightness of a formulation usually refers to the quality of its approximation to the convex hull of integer feasible solutions. Another characteristic is its compactness. The compactness of a formulation is measured by the number of variables and constraints that are used to formulate a given problem. Our formulations for the ATSP and the scheduling problems that we address are both tight and compact. We present a new class of polynomial length formulations for the asymmetric traveling salesman problem (ATSP) by lifting an ordered path-based model using logical restrictions in concert with the Reformulation-Linearization Technique (RLT). We show that a relaxed version of this formulation is equivalent to a flow-based ATSP model, which, in turn, is tighter than the formulation based on the exponential number of Dantzig-Fulkerson-Johnson (DFJ) subtour elimination constraints. The proposed lifting idea is applied to derive a variety of new formulations for the ATSP, and a detailed analysis of these formulations is carried out to show that some of these formulations are the tightest among those presented in the literature. Computational results are presented to exhibit the relative tightness of our formulations and the efficacy of the proposed lifting process.> While the computational results demonstrate the efficacy of employing the proposed theoretical RLT and logical lifting ideas, yet it remains of practical interest to take due advantage of the tightest formulations. The key requirement to accomplish this is the ability to solve the underlying LP relaxations more effectively. One approach, to that end, is to solve these LP relaxations to (near-) optimality by using deflected subgradient methods on Lagrangian dual formulations. We solve the LP relaxation of our tightest formulation, ATSP6, to (near-) optimality by using a deflected subgradient algorithm with average direction strategy (SA_ADS) (see Sherali and Ulular [69]). We also use two nondifferentiable optimization (NDO) methods, namely, the variable target value method (VTVM) presented by Sherali et al. [66] and the trust region target value method (TRTV) presented by Lim and Sherali [46], on the Lagrangian dual formulation of ATSP6. The preliminary results show that the near-optimal values obtained by the VTVM on solving the problem in the canonical format are the closest to the target optimal values. Another approach that we use is to derive a set of strong valid inequalities based on our tighter formulations through a suitable surrogation process for inclusion within the more compact manageable formulations. Our computational results show that, when the dual optimal solution is available, the associated strong valid inequalities generated from our procedure can successfully lift the LP relaxation of a less tight formulation, such as ATSP2R¯, to be as tight as the tightest formulation, such as ATSP6. We extend our new formulations to include precedence constraints in order to enforce a partial order on the sequence of cities to be visited in a tour. The presence of precedence constraints within the ATSP framework is encountered quite often in practice. Examples include: disassembly optimization (see Sarin et al. [62]), and scheduling of wafers/ ICs on automated testing equipments in a semiconductor manufacturing facility (see Chen and Hsia [17]); among others. Our flow-based ATSP formulation can very conveniently capture these precedence constraints. We also present computational results to depict the tightness of our precedence-constrained asymmetric traveling salesman problem (PCATSP) formulations. We, then, apply our formulations to the hot strip rolling scheduling problem, which involves the processing of hot steel slabs, in a pre-specified precedence order, on one or more rollers. The single-roller hot strip rolling scheduling problem can be directly formulated as a PCATSP. We also consider the multiple-roller hot strip rolling scheduling problem. This gives rise to the multiple-asymmetric traveling salesman problem (mATSP). Not many formulations have been presented in the literature for the mATSP, and there are none for the mATSP formulations involving a precedence order among the cities to be visited by the salesmen, which is the case for the multiple-roller hot strip rolling scheduling problem. To begin with, we develop new formulations for the mATSP and show the validity of our formulations, and present computational results to depict their tightness. Then, we extend these mATSP formulations to include a pre-specified, special type of precedence order in which to process the slabs, and designate the resulting formulations as the restricted precedence-constrained multiple-asymmetric traveling salesman problem (rPCmATSP) formulations. We directly formulate the multiple-roller hot strip rolling scheduling problem as a rPCmATSP. Furthermore, we consider the hot strip rolling scheduling problem with slab selection in which not all slabs need to be processed. We model the single-roller hot strip rolling scheduling problem with slab selection as a multiple-asymmetric traveling salesman problem with exactly two traveling salesmen. Similarly, the multiple-roller hot strip rolling scheduling problem with slab selection is modeled as a multiple-asymmetric traveling salesman problem with (m+1) traveling salesmen. A series of computational experiments are conducted to exhibit the effectiveness of our formulations for the solution of hot strip rolling scheduling problems. Furthermore, we develop two mixed-integer programming algorithms to solve our formulations. These are based on Benders&#900; decomposition [13] and are designated Benders&#900; decomposition and Modified Benders&#900; methods. In concert with a special type of precedence order presented in the hot strip rolling scheduling problems, we further introduce an adjustable density ratio of the associated precedence network and we use randomly generated test problems to study the effect of various density ratios in solving these scheduling problems. Our experimentation shows the efficacy of our methods over CPLEX. Finally, we present a compact formulation for the job shop scheduling problem, designated as JSCD (job shop conjunctive-disjunctive) formulation, which is an extension of our ATSP formulations. We use two test problems given in Muth and Thompson [53] to demonstrate the optimal schedule and the lower bound values obtained by solving the LP relaxations of our formulations. However, we observe that the lower bound values obtained by solving the LP relaxations of all variations of our JSCD formulation equal to the maximum total processing time among the jobs in the problem. / Ph. D.

Nesta dissertação de mestrado foram utilizadas duas ligas de alumínio (AA1100 e AA5052) para a produção de uma microestrutura final apresentando tamanho médio de grãos menores que um micrometro. Tal fato foi possível através do processo de Accumulated Roll Bonding (ARB). Tais materiais produzidos por ARB, foram caracterizados conforme propriedades mecânicas (microdureza, limite de escoamento e resistência) e microestruturais (tamanho de grão e macrotextura e composição química dos precipitados). O principal resultado para este trabalho foi a produção de tiras de AA 1100 e AA 5052 com tamanho médio de grão de 0,50 ± 0,04 m e 0,42 ± 0,06 m respectivamente. Tal resultado é coerente em comparação à literatura. Com relação aos resultados de textura, tais amostras apresentaram temperatura de recristalização acima de 473K e componente de textura típicas de cisalhamento (tanto para o material oriundo de fábrica como para o material laminado). Tal fato é esperado já que não se utilizou lubrificação durante ensaios de laminação. A propriedade mecânica de microdureza de AA 1100 ficou coerente com a literatura embora as propriedades de limite de escoamento e de resistência possuíram módulos abaixo da literatura. / The present work is related to the production, in a laboratory scale, of a metallic microstructure having a grain size smaller than one micrometer, through the Accumulated Roll Bonding technique(ARB), for two different aluminum alloys, namely AA 1100 and AA 5052. The strips obtained by the ARB technique have been characterized by their mechanical properties (microhardness, yield and tensile strength), and their microstructure (grain size, macrotexture and precipitates chemical composition). The main result of this work has been the rolling of AA1100 and AA5052 strips with an average grain size of 0.5 ± 0.04 m and 0.42 ± 0.06 m respectively. Such results are consistent with the literature. Relative to the texture, the samples presented a recrystallization temperature higher than 473K and typical shear texture components (due to the dry rolling conditions during the ARB). Microhardness of the AA110 was consistent with literature data; however yield and tensile strength presented values that were lower than those observed in the literature.

Nesta dissertação de mestrado foram utilizadas duas ligas de alumínio (AA1100 e AA5052) para a produção de uma microestrutura final apresentando tamanho médio de grãos menores que um micrometro. Tal fato foi possível através do processo de Accumulated Roll Bonding (ARB). Tais materiais produzidos por ARB, foram caracterizados conforme propriedades mecânicas (microdureza, limite de escoamento e resistência) e microestruturais (tamanho de grão e macrotextura e composição química dos precipitados). O principal resultado para este trabalho foi a produção de tiras de AA 1100 e AA 5052 com tamanho médio de grão de 0,50 ± 0,04 m e 0,42 ± 0,06 m respectivamente. Tal resultado é coerente em comparação à literatura. Com relação aos resultados de textura, tais amostras apresentaram temperatura de recristalização acima de 473K e componente de textura típicas de cisalhamento (tanto para o material oriundo de fábrica como para o material laminado). Tal fato é esperado já que não se utilizou lubrificação durante ensaios de laminação. A propriedade mecânica de microdureza de AA 1100 ficou coerente com a literatura embora as propriedades de limite de escoamento e de resistência possuíram módulos abaixo da literatura. / The present work is related to the production, in a laboratory scale, of a metallic microstructure having a grain size smaller than one micrometer, through the Accumulated Roll Bonding technique(ARB), for two different aluminum alloys, namely AA 1100 and AA 5052. The strips obtained by the ARB technique have been characterized by their mechanical properties (microhardness, yield and tensile strength), and their microstructure (grain size, macrotexture and precipitates chemical composition). The main result of this work has been the rolling of AA1100 and AA5052 strips with an average grain size of 0.5 ± 0.04 m and 0.42 ± 0.06 m respectively. Such results are consistent with the literature. Relative to the texture, the samples presented a recrystallization temperature higher than 473K and typical shear texture components (due to the dry rolling conditions during the ARB). Microhardness of the AA110 was consistent with literature data; however yield and tensile strength presented values that were lower than those observed in the literature.