Academic literature on the topic 'Steelwork Mathematical models'

Abstract. An analysis of existing methods of power calculation of steelworks under the influence of forced oscillations is performed. When considering the forced oscillations of flat steelworks, two-dimensional models are used, which are complex for wide practical use. Their implementation requires in-depth mathematical training and complex computational tools. The aim of this work is to develop a simplified two-dimensional mathematical model of forced oscillations of flat steelworks with following use of this model in power calculations. The mathematical model proposed in this paper describes oscillations of a weightless steelwork with a point mass of simultaneous action in vertical and horizontal harmonic disturbing forces acting on them. The model is based on the method of forces, establishes a link between the movements of the steelworks and the forces that act on them. Together with the model the dependences for calculating the resonant frequencies of the oscillatory system are obtained. The performed developments allow to determine the dynamic characteristics of the oscillatory process and to calculate a steelwork strength, stiffness and stability.

In this work result of the theoretical analyses, witch the main purpose was modelling of the microstructure change during round bars rolling was presented. To determination of the austenite diameter during numerical modelling of the rolling process it is necessary to assign mathematical models of the microstructure change, relationship making the value of yield stress dependent on deformation parameters, temperature and strain range. Theoretical analysis was made in computer program Forge2008®, based on the finite-element method. An analysis was made for two cases: traditional - without accelerated cooling during rolling process and normalizing with one section of the accelerated cooling during rolling process for the ø26 mm round bars. Modification of the ø26 mm round bars rolling technology with accelerated cooling, affect the reduction of average austenite diameter, which cause improving impact resistance of the final product. Results of the theoretical analysis were verified in industrial conditions, in one of polish steelwork.

The paper presents the main methods of technical-economical analysis of the quality of the metallic material production. The technical - economical analysis of the electric steels quality can be processed both for the product (electric steel) and for the company (electric steelworks). Both the analysis methods for products (A) and the ones for companies (B) are presented in comparison. There are mainly presented and analyzed a specific analysis models for steels elaboration in Electric Arc Furnace (EAF). The main elements specific to the two categories of analysis methods, including mathematical models. The quality of the steels elaborated in the EAF is a very important parameter. From this point of view, there is the need of analyzing the electric steels quality in various methods, including by technical-economical ones. The technical - economical analysis of the electric steels quality can be processed both for the product (electric steel) and for the company (electric steelworks). For the technical - economical analysis for the electric steels quality, we can use two methods: methods of the analysis for the products quality (MAPQ); methods of the analysis for the companys (MACQ).

The paper is devoted to an optimization approach to a problem of statistical modeling of mechanical properties of heavy steel plates during a real industrial manufacturing process. The approach enables the manufacturer to attain a specific set of the final product properties by optimizing the alloying composition within the grade specifications. Because this composition has to stay in the agreement with earlier indicated specifications, it leads to the large system of linear constraints, and the problem itself can be expressed in the form of linear programming (LP) task. It turns out however, that certain of the constraints contain the coefficients which have to be estimated on the base of the data gathered in the production process and as such they are uncertain. Consequently, the initial optimization task should be modeled as so-called Chance Constrained Programming problem (CCP), which is a special class within the stochastic programming problems. The paper presents mathematical models of the optimization problem that result from both approaches and indicates differences which are important for the decision makers in the production practice. Some examples illustrating the differences in solutions resulting from LP and CCP models are presented as well. Although the statistical analysis presented in this paper is based on the data gathered in the ISD Czestochowa Steelworks, the proposed approach can be adopted in any other process of steel production.