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Mathematical modelling of srtess-strain behavoir in rolling of the compositions including powder materials
From the analysis of the presented settlement distributions it is possible to draw a conclusion that deformation of a metal substrate begins near the neutral line of rolling. As well as at the time of the beginning of its deformation intensity of growth of normal contact tensions px sharply decreases, and is observed and with intensity of growth of normal tensions ctx, the difference in the size of normal tension of a powder material and a metal substrate is also visible.
In figure 5 settlement distributions of integrated characteristics of process depending on a ratio of powder layers and steel are presented. That is at a fixed thickness of
7 1.0
0.9 0.8 0.7 0.6 0.5
■J
hm/^
jt
/ / -Ji!
/
0
0.74
0.68
0.62
0.56 0.5
0.75 1.50 2.25 3hm/hl
powder - hpol=4 mm and the variable thickness of a metal substrate is hpll=1.2...12 mm. Apparently from the presented settlement distributions than less thickness of a metal substrate of subjects it is more deformed, and powder respectively is less deformed. Also in increasing of a ratio of layers growth of force and the rolling moment, increasing in final relative density of powder composition is observed.
The developed mathematical model allows to determine the rational technological parameters of process excluding deformation of a substrate and raising at the exit of suitable by production of bearings sliding inserts.
0.8 20
1000
P,kH
M.kHm
16 940
12 880
8 820
4 760
0 700
P _- ^
15
13.6
12.2
10.8
9.4
0 .75 1.5 2.25 3 hWhl
a b
Fig. 5. Settlement distributions of integrated characteristics of rolling of composition powder-steel
References
Levkin A.N., Gribkov E.P., Vorobyev Yu.A. Mathematical modeling stressstrain behavior and geometrical characteristics at realization of rolling of bimetallic powder compositions. Kramatorsk, 2000. pp. 360-363. Volkogon G.M., Dmitriev A.M., Dobryakov E.P. etc. Progressive technological processes of stamping of details of powders and equipment. Mos-
cow : Mechanical engineering. 1991, 320 p.
3. Tselikov A.I., Nikitin G.S., Rokotyan S.E. Theory of longitudinal rolling. Moscow : Metallurgy, 1980, 320 p.
4. Potapkin V.F. Levkin A.N., Satonin A.V., Romanov S.M., Vorobyev Yu.A., Gribkov E.P. Stressed state and kinematics in the rolling of powder materials on a metal substrate. Powder Metallurgy and Metal Ceramics, 2000, vol. 39, no. 1-2, pp. 11-17. ISSN 0032-4795.
Tulupov O.N., Moller A.B., Kinzin D.I., Levandovskiy S.A., Ruchinskaya N.A., Nalivaiko A.V., Rychkov S.S., Ishmetyev E.N.
STRUCTURAL-MATRIX MODELS FOR LONG PRODUCT ROLLING PROCESSES: MODELING PRODUCTION TRACEABILITY AND FORMING CONSUMER PROPERTIES OF PRODUCTS
Abstract. The development of rolling production processes towards flexible manufacturing schemes in tightening quality factors makes the search of methods of effective influence on the process, labor management and personnel competence relevant.
To resolve the problems it is expedient to utilise structural matrix of mathematical models based on matrix presentation of long product rolling processes, and on a body of structural matrixes. In order to create mathematical apparatus we proposed to assign a sophisticated structure matrix consisting of units (cells) to each process operation and operation result. These results are identified with a rolling phase, while the process operation - with transformation of the product.
Structural matrix description of a process phase includes blocks that contain data of rolling process factors and parameters. To describe the dynamics of rolling process was presented the relationships between separate process states in a matrix form, e.g. as matrices of technological transformations.
Keywords: long products, rolling processes, structural-matrix models, computer simulation, consumer properties.
Introduction
The main merit of structural-matrix approach is the ability to link various models comprehensively in developing systems to analyze and control long product rolling processes.
Methodological integration of Ishikawa's diagram and structural matrix approach provides science-based solutions of the following problems using databases and IT:
• integrated accounting of the factors that influence the forming, and the forming influence on the process;
• adaptability (various complexity levels of shape rolling process description, on various production sites with no need to change the description structure);
• embedding individual models into an integrated system that links the rolling parameters;
• models compliance with up-to-date requirements for automation systems;
• application of simulators to train technical, technological and management personnel of long product mills and to improve their professional skills.
Examples and results of this approach:
• roll pass designs (for bars, wires, and structural shapes), and operation efficiency of rolls considering wear prediction have been improved;
• the amount of non-conforming products has been cut, the equipment workloads has been reduced, and the strength grades of structural shapes have been increased;
• new decisions to form the mechanical properties have been made;
• an effective system of corrective and preventive actions for long product mills has been created;
• testing, evaluation and flexible training programs on the basis of the above have been developed.
Structural matrix approach and models based on it with reengineering of long product rolling processes allows to solve main issues of traceability of consumer properties. The solutions could be rational for modern challenges of long product rolling technology and quality.
The development of rolling production processes towards flexible manufacturing schemes, while tightening quality factors, makes the search for methods of effective influence on the process, labor management and personnel competence relevant. It also includes the flow control of metal products at the enterprise.
Account should be taken of widespread development and application of automated process control systems and schemes, which require relatively simple, versatile, fast, easily expandable and reliable models meeting the requirements of object-oriented mathematical software. The structure of such models should conform to the principles of decomposition and hierarchical ordering of preserving the unity of mathematical apparatus. Often, embedded systems are highly specialized and do not always agree with each other, poorly adapted to the changing technological conditions of production process, and they forbid rapid analysis of alternative technological schemes. There is also a lack of unity in math approaches: the description of cross-sectional area [1] and the methodology of quality
management of various long products [2, 3]. That hinders the monitoring of product quality factors.
Therefore, the relevant scientific and technical challenge: develop and improve comprehensive, integrated and adaptive long products quality control methods on a unified mathematical basis and unified data representation principles about quality factors.
The adaptive control problem and product traceability should be considered in two aspects:
• adaptability of models and systems to various technological schemes and changing conditions of production;
• adaptability to specific management, engineering and
technical problems.
The proposed modelling approach is based on a few concepts which are listed below.
Methods
First, to resolve process tasks of both the analysis and the control of rolling process patterns for rolled sections of various shapes, a proper mathematical body should be created. Moreover, it should comply with unified concepts of data processing, storage and presentation. In order to create this mathematical body, it is proposed to assign a complex matrix, consisting of blocks (cells), tied to each technological process and to each result of this process. The results are identified with a rolling process phase, while the process itself is identified with technological transformation of the product.
Structural matrix description of a single process phase [A] includes blocks, containing monotype data of rolling process factors and parameters.
To describe rolling process in its dynamics, the relationships between single process states should be represented in the matrix form, i.e. as matrices of technological transformations [H]i = 1...n . Then 'i' process phase is described by the following matrix equation:
[A ]i4x [C], ^[A]i (1.1)
Whereas the rolling process itself is described by the following system containing n number of matrix equations:
i [AL * [Cl ^[A1
[AL x[Cl -+[A1
I KL*[cL-[a]n ,
where [A]o, [A]n are matrices, which describe initial and final technological states respectively; [H]1, [H]n arematrices, which describe the first and the last process operations respectively;
Such form of process presentation is convenient for data processing and computer simulation. Matrices of technological states transformation description [H]i, as well as matrices of technological states [A]i, are complex
Structural-matrix models for long product rolling processes: modeling production traceability and forming consumer properties.
structural matrices consisting of certain finite number of blocks (cells).
Second, structure and contents of the internal blocks are determined by the model purpose and by the type of the problem to be resolved. In general, the following internal blocks are: the block of shape description [®], the block of properties description [C] (i.e. block of mechanical properties description), the block of process parameters description [Q]. These blocks can be block matrices themselves consisting of individual cells.
Data on the shape of rolled section is contained in the shape description block [0]i. For this purpose any complex cross-section is subdivided into finite number of simple elements k, which can be described according to the concept of vector description of simple cross-sections. To render the description coherent and non-ambiguous, a matrix of centres [U,] is introduced. This matrix contains data on the location of centres of simple elements with respect to the common centre of the description. To determine the connection between local and common centres of the description, two values are introduced: distance between the centres, and angle between the vertical line and their connection line. The number of significant vectors [0]i. will depend on the complexity of the cross-section, and the k can be used as an indicator of shape complexity.
Mechanical properties of the feed are contained in the block of properties description [C]. Each matrix [C]i consists of a set of vectors: Ci = 1...p, determining the location of isometric lines of mechanical properties. The choice of p (a number of subdivisions of cross-section plane into isotropic areas of mechanical properties) is determined by specific conditions of each description task, by the required accuracy of consideration of mechanical properties distribution across the cross-section. Besides, the value pi depends on complexity of properties transformation process and can be regarded as an indicator of process sophistication. If average values are sufficient to determine mechanical properties, it is suggested that a block of properties description should be regarded as a degenerated matrix, while values of mechanical properties should be regarded as ctx, S for these particular conditions.
Block of parameters description [n] can comprise sub-blocks: [T] is a matrix of temperature conditions; [M] is a matrix of speeds, [e] is a matrix of boundary conditions; [Hh] is a matrix of tool conditions (wear, etc.); [,3,] is a matrix of tool characteristics. Individual matrixes of process parameters represent a set of finite number of elementary blocks. Data presentation is equal to the one of shape description block, i.e. values of a specific parameter are determined at intersection points of basic radius-vectors with cross-section outline and as such are stored into memory of this parameter to be utilized for data loading into matrix [3,], [Hh], [e], [V].
When it is necessary to know parameter value in any point of cross-section in order to resolve a problem (e.g. temperature field), then data presentation concept in such blocks (e.g., [T]) is identical to the description block [C].
Third, matrices of technological transformation have block structures and block sizes equivalent to those matrices of technological states. Blocks of matrix [H]i can contain vector-type data (a set of figures ordered according to
a certain principle, e.g. matrix of shape deformation -[HO]i), analytical or empirical dependencies (i.e. models). In any case irrespective of method of data presentation, all cells are included in general matrix model.
Structural matrix of the 'i'-th process transformation [H]i includes the blocks [HO]i, [HC]i, [Hn]i, change of section shape, properties and process parameters respectively: [HO]i = [0]i / [0]i.1; [HC]i = [C]i / [C]i_1; [Hn]i = =[n]i / [n]i_1, where i = 1. m.
According to this approach, deformation is described by means of deformation blocks, representing ratio between the matrices «before» and «after» deformation. Deformation block is a diagonal matrix. Its rank is defined by the size of shape description block. The advantage of such interpretation of deformation is essentially in the possibility to computer process the roll pass designs.
Fourth, relations between process parameters at each rolling process phase are logged into the technological transformation matrix (1.3) as lateral components (blocks) of this matrix. These blocks may contain both numerical factors obtained empirically (e.g. relation of tonnage of rolled stock per groove to matrix components that describe roll wear), as well as the entire mathematical models that establish a relation between single parameters (e.g. relation of deformation temperature to speed, relation of steel's tensile strength to spread).
\ n [ ] 3 12 ^1m \[C ]
[C '2 ] = 3 21 [ " 2 ] ■ C ]
ic'm ]_ _ 3m1 3 2 • m2 ■ ["m ]_ _[Cm ]
where:
[Cm] is a matrix that describes initial state of one of the entity's properties;
[C'm] is a matrix that describes final state of one of the entity's properties;
[Hm] is a matrix of state transformation;
3 denotes relations between various variation matrices (e.g. «deformation-temperature» relations).
Therefore, this feature presents an important advantage of structural matrix models, since it allows to comprise and implement the possibilities of other efficient models within the frames of common integrated approach.
Thus, the suggested approach to modelling metal forming processes, and, in particular to modelling shape rolling processes for wire rods, bars, and structural shapes, ensures the following advantages:
• integrated accounting of the factors which have direct impact on the deformation process, and the impact of shape deformation itself on the rolling process aspects;
• versatility (unified method of data interpretation, suitable for computer processing);
• adaptability to metal forming processes (the ability to describe processes of various complexity, on various production sites, with no need to change the description structure);
• adaptability to the tasks of rolling patterns analysis and control to be solved [4, 5, 6];
• embedding individual models into an integrated system that links the rolling parameters;
• accordance with the modern approaches to creation of computer-aided systems of process engineering and control.
Results
Methodological integration of Ishikawa scheme and structural matrix approach using databases and IT provides science-based and effective solutions of the assigned problems.
The developed complex of mathematical models and descriptions of its practical implementation are listed hereinafter.
To control the quality of rolled stock we improved «the uneven deformation ratio» - UDR (the criterion that helps evaluate and compare alternative roll pass designs). As a result, the amount of non-conforming products reduced along with lower equipment loads and higher strength grade of structural shapes.
Instrument was found to form mechanical properties of rebar by defining the boundaries of the magnetic phase sensor values variation and to obtain the required mechanical properties of wire rod using commercial quality steel (C 0.06-0.12%, Mn 0.25-0.50%, Si 0.15-0.30%, S < 0.050%, P < 0.040%, Cr < 0.30%, Ni < 0.30%, Cu < 0.30%) instead of expensive alloyed steel (C 0.20-0.29%, Mn 1.2-1.6%, Si 0.6-0.9%, S < 0.045%, P < 0.040%, Cr < 0.30%, Ni < 0.30%, Cu < 0.30%).
Previously developed matrix evaluation criteria for simple shape gauges transformed into the universal criteria for evaluating structural shapes. Besides, we developed adaptive matrix model of complex productibility, precision, and stability analysis of forming and energy consumption during rolling.
The matrix method of describing the forming process and the principle of least resistance lead to new formulae that calculates power parameters and deformation during section rolling.
A new way was introduced to describe the geometric parameters of axial segregation during billet deformation - a supplement to the bar rolling process modelling using matrix approach and to effectively implement computer modelling of segregation.
«LEAN-production» plays an important role in the quality management strategy. As a part of mathematical apparatus we proposed individual wear index Um, and used it to figure out the schedule of ring rolls and profile changes depending on roll material and diameter (decreased unnecessary supplies, process steps, and changes of expensive ring rolls). Systematization of acquired knowledge eases the development and effective use of section mills, equipped with three-roll RSB stands. Accumulated and generalized experience of using carbide ring rolls could be applied on modern wire-rod mills, equipped with expensive durable rolls in their high-speed finishing blocks.
To assess effectiveness of any pro-
cess, we need measurements to ensure the process to be streamlined and maintained. The extent of regulatory compliance and performance results are usually determined through a comparison of the results to assessment criteria. Using the criteria approach to quality management, based on the development of structural matrices, we developed new indicators of profile conformity, characterized by a deviation of profile distribution (DPD), expressed as a single number - the integral profile deviation (IPD), index of profile match (IPM) of the logical type reflecting compliance deviation allowable range. These indicators and a new tool for maintaining quality - model cards - are used to develop a method for determining the corrective and preventive actions. Experience in creating tables of preventive actions revealed stands affecting the set up of the mill to the greatest degree and to propose criteria that defines their priority. The fewer stands involved in the set up lead to fewer changes of the roll gaps, decreasing overall value of priority coefficient Cpr.
The ability to solve local problems and skills of system analysis by a group of experts - that is the functionality of our instruments to manage the quality rolling system (UDR, U,„, DPD, IPD, IPM, Cpr). Mathematical apparatus created includes new rolling quality indexes and technological personnel competence assessment and it has the potential to produce a synergetic effect to improve product quality at the long product mill.
The use of such models corresponds with the trends of modern management and takes into account a range of factors: reengineering processes (a), adoption of IT (b), product quality control during teaching or retraining the employees (c) and during production process within the framework of traceability and forming consumer properties of products [7, 8].
The further development of the matrix approach and mathematical models, which were listed above, is the methodology of the information model formation [9], which will become the basis for an automated tracking system of metal products. We propose to use the following scheme of information flow that describes the process of passing of semi-finished products through long product mill (see figure).
Information flow scheme at the shape rolling shop of OJSC «MMK»
Structural-matrix models for long product rolling processes: modeling production traceability and forming consumer properties...
Inheritance of technological and organizational measures of previously passed metallurgical conversions as well as follow-up ones takes part in ensuring the required level of consumer properties that will let us predict, monitor and improve the quality of long products.
Created adaptive complex comprises: an information flow scheme (a); new quality indexes of the rolling process (b); methodology to assess and improve the technological competence of personnel (c); methodology of quality control during design, implementation, long products production and improving.
The considered solution of the information model organization correlates well with object-oriented database creation process used in modern automatic process control systems as well as on all CAM systems on all automation levels up to the MES systems and enterprise management systems.
Immutability of the essence of applied mathematical apparatus and the basic principles of its construction to solve technical and technological problems and challenges of quality management makes it possible to adapt and use the developed approach in overlapping technical areas.
References
1. Tulupov O.N. Structure-matrix models for improving the efficiency of rolling grades: Monograph. Magnitogorsk: Nosov Magnitogorsk State Technical University, 2002. 224 p.
2. Tulupov O.N., Ruchinskaya N.A., Moller A.B., Limarev A.S., Lutsenko A.N.Quality management of long products by using rational preventive actions in mill setting Vestnik Magnitogorskogo gosudarstvennogo tehnicheskogo universiteta im. Gl Nosova. [Vestnik of Nosov Magnitogorsk State Technical University]. 2007, no 4, pp. 73-80.
3. Lewandowski S.A. Effectiveness enhancement of section mills by the quality management model improving: PhD Dissertation. Magnitogorsk, 2006.
4. Alekseev A.M., Loginov V.G., Zaitsev A.A., Tulupov O.N., Moller A.B., Rashnikov S.F., Morozov A.A. A method of rod rolling. Patent RUS no. 2148443, 1998.
5. Tulupov O.N., Moller A.B., Kinzin D.I., Lewandowskiy S.A., Limarev A.S., Zavyalov K.A., Richkov S.S., Loginova I.V., Unruh C. J., Nowitskiy R.V. Resistance increasing of the 370 mill roller by cooling system improving. Research report («Magnitogorsk Iron and Steel Works»).
6. Kinzin D.I., Kalugina O.B. Evaluation of values impact of the distortion structure on widening in rolled section Vestnik Magnitogorskogo gosudarstvennogo tehnicheskogo universiteta im. G.I. Nosova. [Vestnik of Nosov Magnitogorsk State Technical University]. 2011, no 4, pp. 21-23.
7. Nalivayko A.V., Steblov A.B., Tulupov O.N., Rychkov S.S. Issledovaniye urovnya mekhanicheskikh svoystv armatury klassa A500S s tsel'yu otsenki vliyaniya osobennostey tekhnologii na pokazateli kachestva. Vestnik Magnitogorskogo gosudarstvennogo tehnicheskogo universiteta im. G.I. Nosova. [Vestnik of Nosov Magnitogorsk State Technical University]. 2010, no. 2, pp. 69-73.
8. Moller A.B., Tulupov O.N., Kinzin D.I., Levandovskiy S.A., Limarev A.S., Zav'yalov K.A., Nazarov D.V., Novitskiy R.V., Rychkov S .S., Loginova I.V. Razrabotka i opytno-promyshlennoye oprobovaniye ekspluatatsii bandazhi-rovannykh valkov v predchistovoy gruppe kletey stana 170 STS OAO «MMK» [Designing and experiment industrial testing of tire rolls running at millstand 170 of «MMK»]. Research report («Magnitogorsk Iron and Steel Works»).
9. Ruchinskaya N.A., Zaytsev O.YU., Tulupov O.N., Lutsenko A.N. Printsipy sozdaniya informatsionnykh modeley upravleniya kachestvom sortovogo prokata. [The principles of creating long products quality management information models]. Proizvodstvo prokata. [Rolling processes]. 2007, no. 8, pp. 33-41.
Logunova O.S., Matsko I.I., Posochov I.A.
INTEGRATED SYSTEM STRUCTURE OF INTELLIGENT MANAGEMENT SUPPORT OF MULTISTAGE METALLURGICAL PROCESSES
Abstract. The necessity to invent a universal technology for creating the intelligent management support of multistage processes, which is able to interface process variables between local loops at each stage of production is determined. The integrated system structure of intelligent management support of multistage metallurgical processes and production stage models are suggested. The improved method of billet macrostructure assessment and block designing technology of intelligent management support of continuous casting billet production are described.
Keywords: control systems, intelligent support, multistage metallurgical processes, continuous cast billet, billet macrostructure assessment.
The actuality of the study
Modern Industries require new systems for multistage process management. These requirements are due to the new priority trends in accordance with Russian state policy. One of these trends is the development of information and telecommunication technologies, which are integrated in automated control systems (ACS) of large industrial enterprise production. The use of new ACS modules for multistage manufacturing processes facilitates unit performance increasing and provides reduced quantity of low-quality products.
From the management point of view, multistage technology of steel products is a complicated process.
Such technologies require the system allowing to monitor output product quality in on-line and providing intelligent decision support of process control.
In developing and implementing new modules, which enlarge already existing ACS, the necessity to use graphic information obtained during quality estimation procedure of finished products and semi-finished products emerges.
The effectiveness of using graphic information and decision-making in ACS production is illustrated by theory and practice.
Methods of image obtaining, processing and segmentation can be found in foreign and Russian scientific pub-
