The paper expounds the main provisions of original author's devisings devoted to composing of a special information control system for automation of control processes in foundry production, where the problem of quality control of cast products is complicated due to the presence of many uncertain factors of production. To improve the quality of castings, in particular, electric current treatment (ECT) of the melt is used. ECT generates complex electromagnetic and other physical phenomena in the melt that make impossible the direct control of the technological process parameters. Based on the cognitive analysis of the physical content of these phenomena, the main factors influencing the results of treatment are determined. The article presents the innovative information and control system of computer modeling "ITIS", which implements the principles of integration of computing with physical processes of ECT. The algorithmic paradigm of ITIS system involves the formation of simulation models digital twins of ECT modes, especially electromagnetic, that adequately reflect the real physical processes. ITIS de facto embodies the structure and functional scheme of the cyber-physical system (CPS) of "smart casting". The mathematical models and algorithms for calculating the parameters of melt treatment and filling the CPS databases with digital twins of ECT modes to predict its results are presented. Prospects for the application and development of "smart casting" CPS in foundry technologies are discussed.
The trends of technological transformations formed at the current stage of industrial production
development, aimed at achieving higher efficiency and productivity via the applied intelligent
systems of machines and production processes, are embodied in the construction of unmanned
"smart" factories, the creation of "smart" (unmanned) vehicles and other "Industrial Internet of
Things" (IIoT) [
Therefore, these technological advances are successfully implemented in areas where
comprehensive physical, technological and economic information is available, i.e., the certainty of
the manufactured product and the determinacy of the production process [
However, there are a large number of industries in which the characteristics of the final product
depend on many uncertain and even undetected, but significant production factors. A typical
industry of this kind is metallurgy and, in particular, foundry, whose technical assignment is to
produce castings with predictable structural and mechanical quality indicators. The quality of the
resulting castings is determined by the homogeneity and orderliness of the grain structure with a
minimum of impurities and gas inclusions, which is formed spontaneously at the cooling stage and
is revealed only by a posteriori examination of the structure of solidified castings [
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It is ascertained that the quality of the casting structure can be influenced by external physical
impacts on the metal in the liquid state before its solidification, due to the inheritance of physical
features of the melt in the properties of castings [
Achieving these goals provides a significant improvement in the quality of cast products, so
when controlling the process of forming the castings structure, its characteristics, as well as the
normalized operational properties of castings, become the parameters, which are being controlled.
Then the controlling parameters in this technology are external factors that set the melt processing
mode, namely the design of the reactor with the electrode system and the parameters of the electric
current, variations of which determine the possibility of direct influence on the spatial distribution
of the current density. At the same time, parameters of electric current, in particular, amplitude,
frequency, pulse duration, electric current, in particular, amplitude, frequency, pulse duration, and
processing time, set the energy spectrum of effects. This approach is the basis for the concept of a
controlled mode of electric current treatment of melt described in the authors' works [
In such a situation, the high-tech strategy "Industry 4" [
Thus, the tasks of constructing an automated system for the modes control of electric current
melt treatment, which are reflected in the authors' works, fully correspond to the specified content
of CPS. The Integrated Three-Component Information System (ITIS) presented in them is actually a
prototype of CFS, since the procedures for the functioning of the ITIS and its components are fully
identified with the main levels of cyber-physical interaction [
The digital layouts of structure formation specified in clause 4 are used to synthesize prognostic archetypes of the structural properties of castings, on the basis of which the tasks are formed to ascertain the optimal parameters of the ECT mode for specific products.
Thus, the algorithmic paradigm of ITIS functioning [
As a result of such a synthesis, the premises are created for considering the entire set of factors
affecting structure formation and the forming of control influences that should ensure the optimal
mode of melt ECT. That is, virtually, cyber, software and analytical components of the CPS are
developed in detail in the ITIS structure, but its physical component, which is associated with the
managing of processes, which are characterized by a high degree of uncertainty of the physical
processes essence and their technological parameters, requires the use of the most effective methods
of processing great arrays of data, such as Big Data Analyses, neural networks, machine learning,
etc. [
At the same time, the use of this toolkit requires filling the CPS with a sufficient number of identification attributes of the controlled parameters of the modes of technological operation modes for the manufacture of products. So, the objective of this publication is to fill the physical component of the cyber-physical system of "smart casting" with models of the melt ECT process that can be used as digital twins (DT) the simulators of melt processing modes, to identify controllable factors influencing the casting structure formation process to obtain the desired quality indicators. Setting the tasks to form a batch of models simulators of processing modes, obviously, requires specifying the phenomenological content of the processes performed in the melt and the peculiarities of the structural elements of this environment behavior. 2. Cyber-technical: computing and communication equipment with appropriate data exchange protocols for processing and distribution of primary information. 3. Software: software for storing, processing and analyzing the information received from the second component sources. 4. Analytical: algorithms for processing information needed to manage production processes.
analysis of samples after ECT.
casting structure templates and a Data Base of Identified Samples for which quality indicators are determined. 3. CMB & SRB: Data processing algorithms in the computer modeling block and the sample recognition block with a database of template identification cards. 4. DMDB: Algorithms for modeling ECT modes and determining quantitative estimates of the energy intensity of melt treatment and forming a Data Base of Digital Models (layouts) of structure formation.
The cluster model represents a liquid metal as a heterogeneous substance consisting of partially
ordered sibotactic groups and amorphous zones. Sibotaxis is believed to retain the particle placement
inherent in the arrangement of atoms in crystals [
Clusters and disordered zones are thermodynamically unstable systems: the value of the Gibbs
energy for clusters exceeds its level for entire melt, but in disordered zone is lower than it. Clusters
arise and decay due to the shift of atoms through an amorphous zone from one to another. Owing
to this, the microvolume are connected with each other. Nevertheless, the life expectancy of clusters,
cl -9 s. However, it is vastly greater than the period of
thermal oscillations of particles in liquid metals (10-14 s), as well as the duration of elementary acts of
thermal conductivity, and diffusion. In the concept of a microinhomogeneous structure of a metallic
liquid, the number of atoms in a cluster reaches several hundred. However, the size of the clusters is
smaller than the critical size of crystals that can develop into a solid phase at the crystallization
temperature, since the minimum radius of a crystal with an energetically formed surface is
approximately rmcrin 25Å . It is this order that makes up the size of a quasicrystalline formation in
an aluminum (Al) melt, which can act as a nucleus that, under certain conditions, will reach the
critical size rcr. For Al, the radius of a cluster with the number of atoms Ncl rcl
[
The concept of energy-metric levels of interaction of commensurate objects from the deep level of
the substance structure to the inspiration of activity of the structure elements of the upper
hierarchical level, which was introduced in [
described
phenomena creates favorable conditions for the mass formation of crystallization nuclei, which
improve the crystallization ability of the melt. However, there is no comprehensive and
unambiguous understanding of this mechanism. In such circumstances, the use of cognitive analysis
will be a natural approach for solving the problem of determining the factors of targeted control of
ECT process mode [
By the logic of interrelationships of factors that determine the content of physical processes of
ECT, which is displayed on the map (Figure 2), it is necessary to have effective facilities for modeling
the primary electric and magnetic fields, since they have the basic effect on the melt. At the same
time, these fields generate secondary effects that also need to be accounted for in computer models
of ECT for the sake to ascertain CPS reliability and survivability [
Being oriented to the maximum adaptation of mathematical models and computational algorithms
for simulating ECT modes to the IT and CPS format, the authors compiled a taxonomic codifier of
the mentioned tasks and methods for solving them Taxstrum [
The formulation of these DTs is based on structural and procedural patterns, which are unified
abstract forms to compile algorithms for solving specific modeling problems. The mathematical
apparatus, on which the described innovative scheme of computer modeling of ECT modes is
founded, includes a number of traditional and original versions of finite element methods (FEM) and
integral equations (IE). The integral formulation of the mathematical model of the primary electric
field of the ECT process in its general form follows from Green's formula for the internal Dirichlet
problem [
Figure 3 shows an example of an arbitrary region with above conditions. The boundary of the area may consist of mu sites S(u), at which the potential values u0, are given, but the values of the normal component of the electric field strength are unknown, and mE sites S(E), at which the normal component of the electric field strength En0, are given, but the values of the potentials u(b) are unknown. The values u(b) and E(b) are to be determined by solving the given problem. Then the n general expression for the potential at any point M inside the region bounded by the surface S, will have, according to Green's formula, the following form: u(M ) = u(1) (M ) − 1 mu 4 i=1 S(u) En(b,i) rb1,M + ui0 nb rb1,M ds − i
Here rb,M is the radius vector drawn from the point b on the boundary to the point M : rb,M = ( xb − xM )2 + ( yb − yM )2 + ( zb − zM )2 . (1) (2)
The mathematical model (1) (2) covers any boundary conditions, which may be used to calculate the fields in ladles with melt. In most cases, the numerical solution of the IE is carried out with replacing of integrals by finite sums by means of discretization of integration surface (contour) and reducing them to systems of linear algebraic equations (SLAE). For the successful solution of these equations, the primary point of methodological importance is the procedure of rational representation of the geometric parameters of the surfaces, adapted for using in algorithmic procedures the explicit expression of mathematical operations of differentiation and integration on curved surfaces.
For this purpose, a universal geometric platform (GP) is created, based on the approximation of
surface contours with arcs of circles, which provides the possibility to specify various configurations
of boundary surfaces and is fully adapted to the computational operations of integral field equations
according to (1) [
However, in the conducted experiments the ladle with the melt had a simple cylindrical shape, so for the calculation of DTs with proper accuracy it turned out to be sufficient to split the boundary contour just into 4 arcs with a total number of discrete elements not more than 200. In doing so the calculation time of separate DT did not exceed 2 minutes, that makes it quite possible to play out various scenarios of ECT modes on conventional PCs (with 2 4-core processors).
and formation of a database of ECT modes digital twins
The study was carried out by computer modeling of ECT multiphysical processes on simulation models of a reactor with replaceable electrode systems. A long cylindrical vessel with several thin electrodes parallel to the cylinder walls is taken as the main type of the spatial shape of the melt reactor. With regard to the extended length of the reactor, it is reasonable to represent the computational model of such a system as a set of its cross-sections and consider for them the twodimensional problems. Figures 4 shows some results of such calculations for a variant with 2electrode system in a non-insulated and insulated metal ladle, as well as a non-metallic one. Next, in Figure 5 there are shown the results of calculating the flux function lines and equipotentials for 2electrode system in the insulated ladle and a non-metallic ladle. In Figure 6 it is given the results of calculations for 4-electrode system in the non- insulated metal ladle. And Figure 7 show the results of calculating the electric field strength in a non-metallic ladle with four electrodes.
In general, the direct calculation of the magnetic field components H for a given current density its subsequent differentiation: A( P) =
a 4 V ( M ) rPM
dVM ,
rot A = B → H = B / a ,
where а absolute magnetic permeability, rPM radius vector according to (2), and B magnetic
induction. Performing the calculations according to (3) and (4) is a very cumbersome
procedure even in a two-dimensional statement of the problem, as in our version. However,
in the plane-parallel (2D) case, which in our study is taken as the basis for spatial
approximation of the problem, the solution of the outlined task is significantly simplified.
Indeed, if the potential is a function of only х and y, i.e., U = f (х, у), then the induced
magnetic field have only one component Hz = H, and from the equation rotH = = − gradU
follows [
These equations represent the Cauchy-Riemann conditions for harmonically conjugate functions and . Therefore, in the complex plane z = x + jy a complex analytical function W (z) can be introduced as that: W (z) = H (x, y) + j U (x, y) , where the real and imaginary parts characterize the magnetic field strength and electric field potential of plane-parallel systems, respectively. This function is a complete analogue of the same function used to calculate the electric field distribution of the electrode system. Therefore, if the complex potential of the electric field of the spreading currents is known, then the flow function in it is an analogue of the magnetic field, that is, if W (z) V + jU , then V H / . So:
H z = V .
x-component х, which corresponds to this chart. Actually, it's this one that determines the nature of the distribution of the vertical (z-) components of the magnetic field strength formed by the current Hz, the main feature of which is a pronounced unevenness of change δх by coordinate y, which is clearly shown in Figure 8.
It creates an internal pressure p in the medium, and the diagram in Figure 9 (right) explains the occurrence of this pressure. Thus, based on (4) and (6) fem and are determined. Figure 10 clearly illustrates the spatial distribution of these forces. It should be noted that these forces in ECT differ from magnetohydrodynamic (MHD) stresses, because in the MHD process, the current originates from the magnetic field stresses, because in the MHD process, the current originates from the magnetic field when the fluid moves, but in ECT, on the contrary, the current generates a magnetic field, so the physical laws of their influence on the state of the fluid are different from each other.
Determination of the basic electric and magnetic field distribution allows to build models and explore secondary fields and effects associated with them. As an example, Figures 11 shows the results of modeling the thermal field in the volume of the A357 alloy melt during its treatment
The objective of the developed digital twins ECT mode simulators is to identify the zones of their most heterogeneous concentration, which, given the peculiarities of the behavior of the liquid metal structure, are most likely to become places of localization of fluctuations that inevitably arise in a cluster melt medium arise in a cluster melt medium. Based on the analysis of the information obtained, it becomes possible to specify purposefully the configuration of the ECT electrode systems and current parameters, which should synchronize the appearance and ensure the most uniform distribution of fluctuation centers in the melt volume, supposedly triggering the process of selforganization of a favorable casting structure through the formation of crystallization nuclei in these locations.
Thus, in spite of the fact that presented in fig. 4 1 diagrams of the electric field vectors and electromagnetic force density level lines demonstrate the solutions for stationary problems, they explicitly serve as the thermoacoustic waves excited by electric currents that occur at the meso- and submicroscopic levels of the EMLM. With an appropriate intensity of the external energy impact, these fluctuations are capable to initiate the processes of dissipative systems formation at the micro- and macrolevels of the liquid-metal system, which results in the self-organization of a favorable precrystallization state of the melt. The availability of su ECT modes on the formation of the casting crystallization nuclei distribution by varying of the construct data and parameters of electric current in the simulation model of the reactor with an electrode system, which specify the treatment mode, that is, to synthesize a predictive prototype of the proposed structure and properties that corresponds to the given processing options.
Hence, the solutions for stationary problems introduced in the paper as examples of the particular
variant of ECT mode also serve the basis for non-stationary processes modeling. In particular, the
solutions for various types of stationary, harmonic and transient processes obtained by the authors
were introduced in [
1. According to the modern tendencies of AI development in the part related to foundry technologies the concept of filling the physical component of ECT of melt as a subsystem of "Smart mathematical simulation of melt treatment modes has been developed.
2. Based on the analysis of the phenomenological ground of the notion about the ECT content, a cognitive model and a map of the cause-and-effect structuring of information about the processes, that occur in the melt, were developed that determined the logic of algorithmic paradigm of the CPS "smart casting" and the task for creating a database of ECT modes DT. Thus there are established the premises to study CPS from the standpoint of reliability and survivability.
3. The use of a unified mathematical apparatus and a pattern-module scheme of ECT modes DT calculation ensured the representativeness of filling the database of physical components of the CPS "smart casting" and the possibility to build scenarios of the influence of ECT modes on the crystallization nuclei formation in the casting.
4. The conjugation in CPS Big Database of the ITIS information flows, which display the experimental basis, the adequacy of mathematical models and the representativeness of DT, ensures the reliability of the results of electric current effect on the liquid metal system study in a wide range of variations of ECT modes parameters.
5. The relevance and perspective of further work in the direction of the development of the technology of "smart casting" with ECT of melts within the CPS-ITIS algorithmic paradigm framework is determined by the fact that it allows to predict and obtain the specified indicators of the quality of castings with a high degree of probability.