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## Mathematical Programming for Lot Sizing and Production Scheduling in Foundries

### Abstract

The problem considered in the paper is motivated by production planning in a foundry equipped with the furnace and casting line, which provides a variety of castings in various grades of cast iron/steel for a large number of customers. The quantity of molten metal does not exceed the capacity of the furnace, the load is a particular type of metal from which the products are made. The goal is to create the order of the melted metal loads to prevent delays in delivery of goods to customers. This problem is generally considered as a lot-sizing and scheduling problem. The paper describes a mathematical programming model that formally defines the optimization problem and its relaxed version that is based on the conception of rolling-horizon planning
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## The Effect of Pallet Component Geometry on Temperature Gradient During Cooling

### Abstract

The paper discusses the impact of the geometry of foundry pallet components on the value of temperature gradient on the wall crosssection during heat treatment. The gradient is one of the most important factors determining the distribution of thermal stresses in these items. Analysis of quantitative simulation was carried out to detect possible effect of the type of connection between pallet walls and thickness of these walls (ribs) on the interior temperature distribution during rapid cooling. The analysis was performed for five basic designs of wall connections used in pallets. Basing on the results obtained, the conclusions were drawn on the best connection between the ribs in foundry pallets.
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## Production Scheduling for the Furnace - Casting Line System

### Abstract

The problem considered in the paper is motivated by production planning in a foundry equipped with the furnace and casting line, which provides a variety of castings in various grades of cast iron/steel for a large number of customers. The quantity of molten metal does not exceed the capacity of the furnace, the load is a particular type of metal from which the products are made in the automatic casting lines. The goal is to create the order of the melted metal loads to prevent delays in delivery of goods to customers. This problem is generally considered as a lot-sizing and scheduling problem. The paper describes two computational intelligence algorithms for simultaneous grouping and scheduling tasks and presents the results achieved by these algorithms for example test problems.
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## Models and Algorithms for Production Planning and Scheduling in Foundries - Current State and Development Perspectives

### Abstract

Mathematical programming, constraint programming and computational intelligence techniques, presented in the literature in the field of operations research and production management, are generally inadequate for planning real-life production process. These methods are in fact dedicated to solving the standard problems such as shop floor scheduling or lot-sizing, or their simple combinations such as scheduling with batching. Whereas many real-world production planning problems require the simultaneous solution of several problems (in addition to task scheduling and lot-sizing, the problems such as cutting, workforce scheduling, packing and transport issues), including the problems that are difficult to structure. The article presents examples and classification of production planning and scheduling systems in the foundry industry described in the literature, and also outlines the possible development directions of models and algorithms used in such systems.
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## The Use of Formal Knowledge Representation in Operating on Resources Concerning Cast Iron Processing

### Abstract

The problem of materials selection in terms of their mechanical properties during the design of new products is a key issue of design. The complexity of this process is mainly due to a multitude of variants in the previously produced materials and the possibility of their further processing improving the properties. In everyday practice, the problem is solved basing on expert or designer knowledge. The paper is the proposition of a solution using computer-aided analysis of material experimental data, which may be acquired from external data sources. In both cases, taking into account the rapid growth of data, additional tools become increasingly important, mainly those which offer support for adding, viewing, and simple comparison of different experiments. In this paper, the use of formal knowledge representation in the form of an ontology is proposed as a bridge between physical repositories of data in the form of files and user queries, which are usually formulated in natural language. The number and the sophisticated internal structure of attributes or parameters that could be the criteria of the search for the user are an important issue in the traditional data search tools. Ontology, as a formal representation of knowledge, enables taking into account the known relationships between concepts in the field of cast iron, materials used and processing techniques. This allows the user to receive support by searching the results of experiments that relate to a specific material or processing treatment. Automatic presentation of the results which relate to similar materials or similar processing treatments is also possible, which should make the conducted analysis of the selection of materials or processing treatments more comprehensive by including a wider range of possible solutions.
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## Virtual Factory as a Method of Foundry Design and Production Management

### Abstract

The paper outlines the methodology of virtual design of a foundry plant as a system. The most important stage in the procedure involves the development of a model defined as a set of data about the system. Model development involves two stages: defining the model’s architecture and specifying the model data in the form of parameters and input-output relationships. The structure is understood as configuration of machines and transport units, representing the sub-systems and system components. As the main purpose of the simulation procedure is to find the characteristics of the system’s behaviour, the merits of the iterative method involving analysis, synthesis and evaluation of results are fully explored.
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## The Deformation of Wax patterns and Castings in Investment Casting Technology

### Abstract

The dimensional accuracy of a final casting of Inconel 738 LC alloy is affected by many aspects. One of them is the choice of method and time of cooling the wax model for precision investment casting. The main objective of this work was to study the initial deformation of the complex shape of a rotor blades casting. Various approaches have been tested for cooling a wax pattern. When wax models are air cooled and without clamping in the jig for cooling, deviations from the ideal shape of the casting are very noticeable (up to 8 mm) and most are in extreme positions of the model. When the blade is cooled in the fixing jig in a water environment, the resulting deviations compared to those of air cooling are significantly larger, sometimes up to 10 mm. This itself does not mean that the final shape of the casting is dimensionally more accurate with the usage of wax models, which have smaller deviations from the ideal position. Another deformation occurs when the shell mould is produced around the wax pattern and further deformations emerge while cooling the blade casting. This paper demonstrates the first steps in describing the complex process of deformations occurring in Inconel alloy blades produced with investment casting technology by comparing results of thermal imagery, simulations in foundry simulation software ProCAST 2010, and measurements from a CNC scanning system using a Carl Zeiss MC 850. Conclusions are so far not groundbreaking, but it seems that deformations of the wax pattern and deformations of the castings do in some cases cancel each other by having opposite directions. Describing the whole process of deformations will help increase the precision of blade castings so that the models at the beginning and the blades in the end are the same.
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## A Method to Make Classification of the Heat Treatment Processes Performed on Bronze Using Incomplete Knowledge

### Abstract

The article describes the problem of selection of heat treatment parameters to obtain the required mechanical properties in heat- treated bronzes. A methodology for the construction of a classification model based on rough set theory is presented. A model of this type allows the construction of inference rules also in the case when our knowledge of the existing phenomena is incomplete, and this is situation commonly encountered when new materials enter the market. In the case of new test materials, such as the grade of bronze described in this article, we still lack full knowledge and the choice of heat treatment parameters is based on a fragmentary knowledge resulting from experimental studies. The measurement results can be useful in building of a model, this model, however, cannot be deterministic, but can only approximate the stochastic nature of phenomena. The use of rough set theory allows for efficient inference also in areas that are not yet fully explored.
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## The Decision Support System in the Domain of Casting Defects Diagnosis

### Abstract

This article presents a computer system for the identification of casting defects using the methodology of Case-Based Reasoning. The system is a decision support tool in the diagnosis of defects in castings and is designed for small and medium-sized plants, where it is not possible to take advantage of multi-criteria data. Without access to complete process data, the diagnosis of casting defects requires the use of methods which process the information based on the experience and observations of a technologist responsible for the inspection of ready castings. The problem, known and studied for a long time, was decided to be solved with a computer system using a CBR (CaseBased Reasoning) methodology. The CBR methodology not only allows using expert knowledge accumulated in the implementation phase, but also provides the system with an opportunity to "learn" by collecting new cases solved earlier by this system. The authors present a solution to the system of inference based on the accumulated cases, in which the main principle of operation is searching for similarities between the cases observed and cases stored in the knowledge base.
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## Iterated Local Search for Foundry Lotsizing and Scheduling Problem with Setup Costs

### Abstract

The paper presents a novel Iterated Local Search (ILS) algorithm to solve multi-item multi-family capacitated lot-sizing problem with setup costs independent of the family sequence. The model has a direct application to real production planning in foundry industry, where the goal is to create the batches of manufactured castings and the sequence of the melted metal loads to prevent delays in delivery of goods to clients. We extended existing models by introducing minimal utilization of furnace capacity during preparing melted alloy. We developed simple and fast ILS algorithm with problem-specific operators that are responsible for the local search procedure. The computational experiments on ten instances of the problem showed that the presence of minimum furnace utilization constraint has great impact on economic and technological conditions of castings production. For all test instances the proposed heuristic is able to provide the results that are comparable to state-of-the art commercial solver.
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## The Effect of Cooling Agent on Stress and Deformation of Charge-loaded Cast Pallets

### Abstract

The results of research on the effect of the type of cooling agent used during heat treatment and thermal-chemical treatment on the formation of temperature gradient and stress-deformation distribution in cast pallets, which are part of furnace accessories used in this treatment, are disclosed. During operation, pallets are exposed to the effect of the same conditions as the charge they are carrying. Cyclic thermal loads are the main cause of excessive deformations or cracks, which after some time of the cast pallet operation result in its withdrawal due to damage. One of the major causes of this damage are stresses formed under the effect of temperature gradient in the unevenly cooled pallet construction. Studies focused on the analysis of heat flow in a charge-loaded pallet, cooled by various cooling agents characterized by different heat transfer coefficients and temperature. Based on the obtained temperature distribution, the stress distribution and the resulting deformation were examined. The results enabled drawing relevant conclusions about the effect of cooling conditions on stresses formed in the direction of the largest temperature gradient.
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## Numerical Modelling of Fluid Flow and Thermal Phenomena in the Tundish of CSC Machine

### Abstract

The mathematical and numerical simulation model of the liquid steel flow in a tundish is presented in this paper. The problem was treated as a complex and solved by the finite element method. The single-strand slab tundish is used to continuous casting slabs. The internal work space of the tundish was modified by the following flow control devices. The first device was a striker pad situated in the pouring tundish zone. The second device was a baffle with three holes and the third device was a baffle without hole. The main purpose of using these devices was to cause a quiet liquid mixing as well as give directional metal flow upwards which facilitated inclusion floatation. The interaction of flow control devices on hydrodynamic conditions was received from numerical simulation. As a result of the computations carried out, the liquid steel flow and steel temperature fields were obtained. The influence of the tundish modification on velocity fields in the liquid phase of steel was estimated, because these have an essential influence on high quality of a continuous steel cast slab.
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## Case-Based Reasoning System for the Selection of Silumin Alloying Elements

### Abstract

This work presents the project of the application of Case-based reasoning (CBR) methodology to an advisory system. This system should give an assistance by selection of proper alloying additives in order to obtain a material with predetermined mechanical properties. The considered material is silumin EN AC-46000 (hypoeutectic Al-Si alloy) that is modified by the addition of Cr, Mo, V and W elements in the range from 0% to 0.5% in the modified alloy. The projected system should indicate to the user the content of particular additives so that the obtained material is in the chosen range of parameters: tensile strength Rm, yield strength Rp0.2, elongation A and hardness HB. The CBR methodology solves new problems basing on the solutions of similar problems resolved in the past. The advantage of the CBR application is that the advisory system increases knowledge base as the subsequent use of the system. The presented design of the advisory system also considers issues related to the ergonomics of its operation.
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## Introducing Advanced Data Analytics in Perspective of Industry 4.0 in a Die Casting Foundry

### Abstract

The paper presents some aspects of a development project related to Industry 4.0 that was executed at Nemak, a leading manufacturer of the aluminium castings for the automotive industry, in its high pressure die casting foundry in Poland. The developed data analytics system aims at predicting the casting quality basing on the production data. The objective is to use these data for optimizing process parameters to raise the products’ quality as well as to improve the productivity. Characterization of the production data including the recorded process parameters and the role of mechanical properties of the castings as the process outputs is presented. The system incorporates advanced data analytics and computation tools based on the analysis of variance (ANOVA) and applying an MS Excel platform. It enables the foundry engineers and operators finding the most efficient process variables to ensure high mechanical properties of the aluminium engine block castings. The main features of the system are explained and illustrated by appropriate graphs. Chances and threats connected with applications of the data-driven modelling in die casting are discussed.
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## Integrated Analytical and Measurement System for the Evaluation of the Properties of Cast Metals and Alloys

### Abstract

The article presents an integrated analytical and measurement system for evaluation of the properties of cast metals and alloys. The presented platform is an extension of the SLAG - PROP application with new modules, which allow to use information on metallurgical processes in an even more effective way, as well as to evaluate the finished product. In addition, the construction of a measuring station for the analysis of thermal processes taking place in a metal bath allows for precise observation of phenomena together with their appropriate interpretation. The article presents not only the cooling curves of certain copper alloys. The analysis also covered mechanical properties related to hardness, finished products depending on the mold in which the products were cast. In the literature one can find information about the mechanical properties of products in the improved state, usually after plastic or thermal treatment, omitting their properties obtained as a result of a naturally made casting. The article also presents the method of placing information in the database using a convenient graphical tool.
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## Design Options to Decrease the Thermal Stresses in Cast Accessories for Heat and Chemical Treatment Furnaces

### Abstract

By the very nature of their work, castings used in furnaces for heat treatment and thermo-chemical treatment are exposed to the effect of many unfavorable factors causing their deformation and cracking, significantly shortening the lifetime. The main source of damage are the micro- and macro-thermal stresses appearing in each cycle. As the cost of furnace instrumentation forms a significant part of the total furnace cost, in designing this type of tooling it is important to develop solutions that delay the damage formation process and thus extend the casting operation time. In this article, two structural modifications introduced to pallets castings to reduce thermal stresses arising at various stages of the cooling process are proposed. The essence of the first modification consists in making technological recesses in the wall connections, while the aim of the second one is to reduce the stiffness of the pallet by placing expanders in the external walls. Using the results of simulation analyses carried out by the finite element method, the impact of both proposed solutions on the level of thermal stresses was evaluated.
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## Thermal Stresses in the Wall Connections of Cast Grate Structures

### Abstract

The purpose of this study was to establish a relationship between the type of wall connection used in the cast grates, which are part of the equipment operating in furnaces for heat treatment and thermal-chemical treatment, and stresses generated in these grates during the process of rapid cooling. The places where the grate walls are connected to each other are usually characterized by the thickness larger than the remaining parts of walls. Temperature variations in those places are responsible for the formation of hot spots, and in the hot spots temperature changes much more slowly. The type of wall connection shapes the temperature gradient in the joint cross-section, and hence also the value of thermal stresses generated during cooling. In this study, five different designs of the grates were compared; the difference in them was the type of the designed wall connection. The following design variants were adopted in the studies: X connections with and without holes, T connections with and without technological recesses, and R (ring) connection. Numerical analysis was performed to examine how the distribution of temperature changes in the initial phases of the cooling process. The obtained results served next as a tool in studies of the stress distribution in individual structures. The analysis were carried out by FEM in Midas NFX 2014 software. Based on the results obtained, the conclusions were drawn about the impact of different types of wall connections on the formation of thermal stresses in cast grates.
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## Reconstruction of the Casting Technology in the Bronze Age on the Basis of Investigations and Visualisation of Casting Moulds

### Abstract

During excavation of the cremation cemetery of urnfield culture in Legnica at Spokojna Street (Lower Silesia, Poland), dated to 1100-700 BC, the largest - so far in Poland – a collection of casting moulds from the Bronze Age was discovered: three moulds for axes casting made out of stone and five moulds for casting sickles, razors, spearhead and chisels, made out of clay. This archaeological find constituted fittings of foundrymen’s graves. In order to perform the complete analysis of moulds in respect of their application in the Bronze Age casting technology analytical methods, as well as, computer aided methods of technological processes were used. Macroscopic investigations were performed and the X-ray fluorescence spectrometry method was used to analyse the chemical composition and metal elements content in mould cavities. Moulds were subjected to three-dimensional scanning and due to the reverse engineering the geometry of castings produced in these moulds were obtained. The gathered data was used to perform design and research works by means of the MAGMA5 software. Various variants of the pouring process and alloys solidification in these archaeological moulds were simulated. The obtained results were utilised in the interpretation of the Bronze Age casting production in stone and clay moulds, with regard to their quality and possibility of casting defects occurrence being the result of these moulds construction. The reverse engineering, modelling and computer simulation allowed the analysis of moulds and castings. Investigations of casting moulds together with their digitalisation and reconstruction of casting technology, confirm the high advancement degree of production processes in the Bronze Age.
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## Coordinated Production Planning and Scheduling Problem in a Foundry

### Abstract

In the paper, we present a coordinated production planning and scheduling problem for three major shops in a typical alloy casting foundry, i.e. a melting shop, molding shop with automatic line and a core shop. The castings, prepared from different metal, have different weight and different number of cores. Although core preparation does not required as strict coordination with molding plan as metal preparation in furnaces, some cores may have limited shelf life, depending on the material used, or at least it is usually not the best organizational practice to prepare them long in advance. Core shop have limited capacity, so the cores for castings that require multiple cores should be prepared earlier. We present a mixed integer programming model for the coordinated production planning and scheduling problem of the shops. Then we propose a simple Lagrangian relaxation heuristic and evolutionary based heuristic to solve the coordinated problem. The applicability of the proposed solution in industrial practice is verified on large instances of the problem with the data simulating actual production parameters in one of the medium size foundry.
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## Thermal Stresses in the Accessories of Heat Treatment Furnaces vs Cooling Kinetics

### Abstract

Depending on the course of the processes of heat treatment and thermo-chemical treatment, the technological equipment of heat treatment furnaces is exposed to different operating conditions, as the said processes differ among themselves in the temperature of annealing and atmosphere prevailing in the furnace chamber, in the duration of a single work cycle and in the type and temperature of the coolant. These differences affect the magnitude of stresses occurring in each cycle of the operation of furnace accessories, and thus play an important role in fatigue processes leading to the destruction of these accessories. The kinetics of temperature changes during each cooling process plays an important role in the formation of thermal stresses on the cross-section of the cooled parts. It depends on many factors, including the initial cooling temperature, the type and temperature of the cooling medium, or the dimensions and shape of the object. This article presents a numerical analysis of the effect of the initial temperature on the distribution of stresses on the cross-section of the grate ribs, generated in the first few seconds of the cooling process carried out in two cooling media, i.e. hardening oil and water. The analysis was carried out by the finite element method, based on the results of experimental testes of temperature changes in the rib during its cooling.
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## A Study of the Efficiency of Polish Foundries Using Data Envelopment Analysis

### Abstract

The article presents a study on the effectiveness of the foundries using Data Envelopment Analysis (DEA) method. The aim of the article is to analyze the usefulness of DEA method in the study of the relative efficiency of the foundries. DEA is a benchmarking technique based on linear programming to evaluate the effectiveness of the analyzed objects. The research was conducted in four Polish and two foreign plants. Evaluated foundries work in similar markets and have similar production technology. We created a DEA model with two inputs (fixed assets and employment) and one output (operating profit). The model was produced and solved using Microsoft Excel together with its Solver add-in. Moreover, we wrote a short VBA script to perform automating calculations. The results of our study include a benchmark and foundries’ ranking, and directions to improve the efficiency of inefficient units. Our research has shown that DEA can be a very valuable method for evaluating the efficiency of foundries.
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## Production Scheduling under Fuzziness for the Furnace - Casting Line System

### Abstract

The problem considered in the paper is motivated by production planning in a foundry equipped with a furnace and a casting line, which provides a variety of castings in various grades of cast iron/steel for a large number of customers. The goal is to create the order of the melted metal loads to prevent delays in delivery of goods to customers. This problem is generally considered as a lot-sizing and scheduling problem. However, contrary to the classic approach, we assumed the fuzzy nature of the demand set for a given day. The paper describes a genetic algorithm adapted to take into account the fuzzy parameters of simultaneous grouping and scheduling tasks and presents the results achieved by the algorithm for example test problem.
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## Methods of Computational Intelligence in the Context of Quality Assurance in Foundry Products

### Abstract

One way to ensure the required technical characteristics of castings is the strict control of production parameters affecting the quality of the finished products. If the production process is improperly configured, the resulting defects in castings lead to huge losses. Therefore, from the point of view of economics, it is advisable to use the methods of computational intelligence in the field of quality assurance and adjustment of parameters of future production. At the same time, the development of knowledge in the field of metallurgy, aimed to raise the technical level and efficiency of the manufacture of foundry products, should be followed by the development of information systems to support production processes in order to improve their effectiveness and compliance with the increasingly more stringent requirements of ergonomics, occupational safety, environmental protection and quality. This article is a presentation of artificial intelligence methods used in practical applications related to quality assurance. The problem of control of the production process involves the use of tools such as the induction of decision trees, fuzzy logic, rough set theory, artificial neural networks or case-based reasoning.
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## Specificity of SPC Procedures Application in Foundry in Aspect of Data Acquisition and Data Exploration

### Abstract

The paper presents an analysis of SPC (Statistical Process Control) procedures usability in foundry engineering. The authors pay particular attention to the processes complexity and necessity of correct preparation of data acquisition procedures. Integration of SPC systems with existing IT solutions in area of aiding and assistance during the manufacturing process is important. For each particular foundry, methodology of selective SPC application needs to prepare for supervision and control of stability of manufacturing conditions, regarding specificity of data in particular “branches” of foundry production (Sands, Pouring, Metallurgy, Quality).
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## Applicability of Business Rules to Production Management in Foundries

### Abstract

The size and complexity of decision problems in production systems and their impact on the economic results of companies make it necessary to develop new methods of solving these problems. One of the latest methods of decision support is business rules management. This approach can be used for the quantitative and qualitative decision, among them to production management. Our study has shown that the concept of business rules BR can play at most a supporting role in manufacturing management, but alone cannot form a complete solution for production management in foundries.
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