Chapter 3 - Mathematical and Physical Modelling of the Flat Rolling Process

The article provides a substantiation of the conceptual model of the production process of special forms of dumplings. It is the first stage in the development of a model of this process as a control object. The purpose of which is to form an objective basis for the development of an effective system for automatic process control. The development of the conceptual model presupposes the specification and description of the properties of control channels and acting disturbances to the level of their mathematical model, which can be implemented in a simulation environment. Problems of identification of the mathematical model of the process of the production of dumplings, i. e. obtaining a mathematical description of processes based on the results of its purposeful experimental research, due to its complexity as a control object.The experimental approach, in this case, gives much more reliable results on the properties of the process. An attempt to obtain such general properties on the basis of experimental data would inevitably lead to the need for very complex and lengthy multifactorial experiments and nontrivial procedures for their processing. But this will leave open the question of the adequacy of the model for those conditions of the process and types of raw materials that were not covered by the experiments. Fundamentally important is the fact that the mathematical model of the process is developed as a model of the control object.Model can be used in two ways. This is due to the fact that in the closed circuits of the SAC, the discrepancy between the models can be considered as a manifestation of uncontrolled coordinate and parametric disturbances. It is in conditions of this kind of disturbances that the SAC must fulfill its functional purpose. The developed mathematical model of the production process of special forms of dumplings will be used by us only in the direction, when it is of great importance not so much quantitative as its qualitative correspondence to the original object.

Over the past several years Pacific Northwest National Laboratory (PNNL) has been actively involved in supporting the U.S. Department of Energy National Nuclear Security Administration Office of Material Management and Minimization (formerly Global Threat Reduction Initiative). The U.S. High- Power Research Reactor (USHPRR) project is developing alternatives to existing highly enriched uranium alloy fuel to reduce the proliferation threat. One option for a high-density metal fuel is uranium alloyed with 10 wt% molybdenum (U-10Mo). Forming the U-10Mo fuel plates/foils via rolling is an effective technique and is actively being pursued as part of the baseline manufacturing process. The processing of these fuel plates requires systematic investigation/understanding of the pre- and post-rolling microstructure, end-state mechanical properties, residual stresses, and defects, their effect on the mill during processing, and eventually, their in-reactor performance. In the work documented herein, studies were conducted to determine the effect of cold and hot rolling the as-cast and homogenized U-10Mo on its microstructure and hardness. The samples were homogenized at 900°C for 48 h, then later annealed for several durations and temperatures to investigate the effect on the material’s microstructure and hardness. The rolling of the as-cast plate, both hot and cold, was observed to form a molybdenum-rich and -lean banded structure. The cold rolling was ineffective, and in some cases exacerbated the as-cast defects. The grains elongated along the rolling direction and formed a pancake shape, while the carbides fractured perpendicularly to the rolling direction and left porosity between fractured particles of UC. The subsequent annealing of these samples at sub-eutectoid temperatures led to rapid precipitation of the ' lamellar phase, mainly in the molybdenum-lean regions. Annealing the samples above the eutectoid temperature did not refine the grain size or the banded microstructure. However, annealing the samples led to quick recovery in hardness as evidenced by a drop in Vickers hardness of 20%. Hot rolling was performed at 650 and 800°C. The hot-rolling mill loads (load separation force) were approximately 40 to 50% less than the cold-rolling for the same reduction and thickness. It was observed that hot rolling the samples with 50% or more reduction in thickness were responsible for dynamic recrystallization in the hot-rolled samples and led to grain refinement. Unlike the cold-rolled samples, the hot-rolled samples did not fracture the carbides and appeared to heal the casting defects. The recovery phenomenon was similar to the cold-rolled samples above the eutectoid temperatures, but owing to the refined grain size, the precipitation of the lamellar phase was far more rapid in these samples and the hardness increased more rapidly than in the cold rolled sample when heated below the eutectoid temperature. The data generated from these rolling efforts has been used to make the process modeling efforts more robust and applicable to all USHPRR partner rolling mills. The flow stress for cold rolling the samples was determined to be between 170-190 ksi, with frictional forces between 0.2 and 0.4 for the PNNL mill. The measured roll separation forces and those simulated using finite element methods for hot and cold rolling for the PNNL rolling mill were in good agreement.

The underground coal gasification is a continually evolving technology, which converts coal to calorific gas. There are many important parameters in this technology, which are difficult to measure. These parameters include the underground cavity growth, amount gasified coal, and the leakage of input and output gaseous components into the surrounding layers during the coal gasification process. Mathematical modeling of this process is one of the possible alternatives for determining these unknown parameters. In this paper, the structure of the mathematical model of laboratory underground coal gasification process from the material balance aspect is presented. The material balance consists of mass components entering and leaving from the UCG process. The paper shows a material balance in the form of a general mass balance and atomic species balance. The material balance was testing by six UCG laboratory experiments, which were realized in two ex-situ reactors.

The soft cobbing, used in steel’s continuous casting, is widely applying in technologies of rolled metal manufacturing. It is important to know ingot’s stress-strain state and dynamics of ingot’s changes while cobbing, when there is a liquid metal in the centre of section. The complex questions of numerical modeling of soft cobbing process and experimental investigation on physics plasticine models are considered in presented work. The analysis of findings is presented in the article.

When designing a new material for hot rolling rolls, it is necessary to be aware of the conditions in the later utilisation phase. The first step is to quantify stresses, and temperatures the material must tolerate operating in the rolling mills. These characteristics are evaluated by direct measurements and hot rolling simulations. Simulations targeted the identification of the temporal and spatial temperature distribution permeating the roll during the entire rolling process. As a major influence varying cooling conditions had to be accounted for roll temperatures. As an output value the minimum yield stress was identified – the determining factor for the development of a high strength roll material for cast rolls.

This monograph reviews and examines the theoretical background and literature published so far for the mathematical modeling and simulation of the rubber vulcanization process. This work has been organized in the following way. First, an introductory section is given, which provides a brief overview of the topic and the aim and scope of the paper. Then, it goes on to give a comprehensive overview of the historical background up to present state. It is tried here not only to consider rubber vulcanization process, but the curing of other thermoset polymers are examined. The third section presents the mathematical modeling of the curing process and focuses on four key items including heat transfer governing equations, thermal properties of rubbers and their measurements, kinetics of the curing reaction and solution methodology. In this part, the details of the solution methods for the governing equations and also different types of kinetics of curing reactions are studied. The fourth section presents the findings of some research works carried out in this field, which is divided into two subsections as tires and non-tires applications. A brief summary on the presented work and some suggestions for future research are introduced in the fifth section, and finally the bibliography of this review is given.

As part of a research project on El‐hadjar Hot Steel Rolling Mill Plant Annaba Algeria a new Model based control system is suggested to improve the performance of the hot strip rolling mill process. In this paper off‐line model based controllers and a process simulator are described. The process models are based on the laws of physics. these models can predict the future behavior and the stability of the controlled process very reliably. The control scheme consists of a control algorithm. This Model based Control system is evaluated on a simulation model that represents accurately the dynamic of the process. Finally the usefulness to the Steel Industry of the suggested method is highlighted.

The researches of durability in the exploitation of cast-iron rolls define experimentally an important chapter from the thermal fatigue of the organs of machines in the movement of rotation, in variable temperature mediums. The researches on the durability in exploitation of hot rolling mill rolls represent an important scientific and economical issue. This paper presents original experimental equipment by the help of which the durability of hot rolling mills can be studied. This experimental equipment permits the evaluation of exploitation durability for hot rolls by studying the thermal fatigue phenomenon which appears in the case of machine components. The exploitation durability is evaluated through thermal fatigue cycles up to crack point due to thermal fatigue for each condition and each type of studied material. The study represents a detailed approach of the influence of various technological factors on the durability in exploitation of rolling mill rolls made of different steel and pig iron grades and suggests solutions meant to increase the durability of the rolls in exploitation.

Hydroelectric dams may affect anadromous fish survival and recruitment by limiting access to upstream habitats and adversely affecting quality of downstream habitats. In the Manistee River, a tributary to Lake Michigan, two hydroelectric dams potentially limit recruitment of anadromous rainbow trout (steelhead) by increasing tailrace water temperatures to levels that significantly reduce survival of young‐of‐year (YOY) fish. The objectives of this study were to determine whether proposed restoration scenarios (dam removals or a bottom withdrawal retrofit) would alter the Manistee River thermal regime and, consequently, improve wild steelhead survival and recruitment. Physical process models were used to predict Manistee River thermal regimes following each dam alteration scenario. Empirical relationships were derived from historical field surveys to quantify the effect of temperature on YOY production and potential recruitment of Manistee River steelhead. Both dam alteration scenarios lowered summer temperatures and increased steelhead recruitment by between 59% and 129%, but total recruitments were still low compared to other Great Lakes tributaries. Considering only temperature effects, bottom withdrawal provides the greatest promise for increasing natural steelhead recruitment by decreasing the likelihood of year‐class failures in the warmest summers. Results of this study may allow managers to evaluate mitigation alternatives for Manistee River dams during future relicensing negotiations, and illustrate the utility of physical process temperature models in groundwater‐fed rivers. Copyright © 2004 John Wiley & Sons, Ltd.

Results are presented from calculation of the geometry of the deformation zone and the kinematics of plate-rolling. The results were obtained using the program packages DEFORM-3D and Q-FORM. A comparative analysis is made of the data based on the length of the lag and advance zones and the character of the nonuniformity of the stress and strain states during the rolling of plates. The criterion chosen to characterize the nonuniformity of strain inside the deformation zone is the coefficient of variation S/Λav, where Λav is the average shear strain over the height of the plate and S is the standard deviation. The stress state was evaluated on the basis of the stress-state index σ/T. A mathematical model of the plate-rolling process was constructed with allowance for the range of steels rolled on the 5000 mill at the Magnitogorsk Metallurgical Combine and the technological capabilities of the mill's equipment.

Few studies exist which adequately treat the forming of shape rolling, primarily because the process is so difficult to model and control. So, several years ago, the CEMEF developed a computer program, based on the Norton-Hoff model of viscoplastic behavior, to simulate three dimensional flow during the hot rolling process. Since then, the finite element techniques utilized in the program have been modified to account for the geometric deformations, thermal effects, and stresses occurring within the product. In this paper, we review the aforementioned techniques and discuss their successful application to flat rolling and hot shape rolling processes.

High-speed steel (HSS) materials are universally used as work rolls for the hot rolling of stainless steels. Their use has increased the output of the rolling mill and decreased roll material consumption and grinding. Sticking defects often occur, however, during the hot rolling process. In this article, extreme pressure (EP) additives were dropped on the HSS samples at high temperature. Zinc dialkyl dithiophosphate (ZDDP) was chosen as the most effective EP additive by scratch tests on the HSS samples. In order to determine the optimum proportion of ZDDP in the lubricant, two reduction rates were tested on a Hille 100 experimental rolling mill by hot rolling ferritic stainless steel 445J1M at five different concentrations of ZDDP. The mechanism of EP additive action during the hot rolling process was also investigated. By analyzing the deformation behavior of the oxide scale of samples after hot rolling using different proportions of ZDDP, it was found that 20% ZDDP in the lubricant is the preferred concentration for industrial application.

Purpose. When solving practical problems that require the creation and further analysis of the model, an important criterion is the labour intensity of modeling. In this regard, the article is aimed at formalizing the modeling process and using the method of step-by-step modeling for the design of technological processes. This approach allows you to design processes and tasks according to the following stages: physical modeling, mathematical modeling, discrete computer modeling and simulation. Methodology. To solve the problem, a methodology of step-by-step modeling is used. The simulation involves 3 stages and uses the decomposition algorithm, i. e. considers the problem from global to detailed. At the first stage of this implementation, the necessary information is collected for the experiment. This information is presented in the form of statistics. In the second stage, further processing takes place, which is performed by checking the compliance of the input data and the process with the question of how this process should be performed. The last stage is the simulation of passages of this fragment, which is represented by a chain of transitions, obtaining statistics of time efficiency of this process, weaknesses of the process and the ability to compare the results obtained during modeling and in the real process, as well as the ability to predict future results and actions. Findings. The technique can be used to study complex technological processes in the enterprise. It allows modeling of complex processes to obtain information about the time efficiency of the technological operation, finding weaknesses in it and patterns in the occurrence of random events that may affect the operation. Using this approach can be very effective in the systems that require constant real-time monitoring, as this tool can be modified by adding sensor kits that will constantly send information to the system or equip an additional system that will provide ready-made information packets. Originality. The method of step-by-step modeling of representation has been improved, which consists in the simultaneous use of physical, mathematical and simulation modeling of complex processes with a set of stages of their implementation. Practical value. The proposed technique is designed for step-by-step modeling of the technological process with the subsequent construction of simulation programming.

The performance properties of many precision mechanical engineering products manufactured by plastic deformation methods depend significantly on the structural deformation damage of their material. In this regard, methods of mathematical modeling of the complex physical process of structural damage are essential for calculating and predicting reliable operational characteristics of these products. According to systematic experimental data, the damage of metals in large plastic deformations is mainly associated with the formation, growth and coalescence of pores. To formulate the defining relations and determine the material functions included in them, a geometric model of elementary volume (RVE) with stochastically distributedmesoelements (ME) representing a material shell with sometimes is used. For step-by-step calculation of strain increment tensor components at RVE- and ME- levels, their initial (undeformed) and current (deformed) configurations are determined by the metric tensor.Calculation of damage measures based on experimentation, determination and modeling of material functions of plastic dilatancy and deviator deformation of ME depending on deviator deformation of RVE in plastic compression experiments, is given.

The paper deals with the problem of mathematical modeling of the process of thermochemical destruction using the theory of graphs. To synthesize a mathematical model, the Markov chain is used. For the formalization of the model a matrix-graph method of coding is used. It is proposed to consider the process of destruction as a random process, under which the state of the system changes, characterized by the proportion of macromolecules in each fraction of the molecular mass distribution. The intensities of transitions from state to state characterize the corresponding rates of destruction processes for each fraction of the molecular weight distribution (MWD). The processes of crosslinking and polymerization in this work have been neglected, and it is accepted that there is a probability of transition from any state with a lower order index (corresponding to fractions with higher molecular weights) to any state with a higher index (corresponding fractions with lower molecular weights). A computational formula is presented for estimating the number of arcs and model parameters from a given number of fractions of the molecular weight distribution of the polymer. An example of coding in a matrix form of a graph model of the process of degradation of polybutadiene in solution for the case of six fractions of the molecular weight distribution is shown. As the simulation environment, the interactive graphical simulation environment of MathWorks Simulink is used. To evaluate the parameters of the mathematical model, experimental studies of the degradation of polybutadiene in solution were carried out. The chromatography of the polybutadiene solution was used as the initial data for the estimation of the MWD polymer. The considered matrix-graph representation of the structure of the mathematical model of the polymer destruction process makes it possible to simplify the compilation of the model and its software implementation in the case of a large number of vertices of the graph describing the process of destruction