=Paper=
{{Paper
|id=Vol-2843/shortpaper015
|storemode=property
|title=The use of information technology and mathematical modeling in the development of modes of aluminum alloy (short paper)
|pdfUrl=https://ceur-ws.org/Vol-2843/shortpaper015.pdf
|volume=Vol-2843
|authors=Anastasia S. Samoylova,Valentina V. Britvina,Ekaterina O. Bobrova,Galina P. Konyukhova,Alexey V. Altukhov
}}
==The use of information technology and mathematical modeling in the development of modes of aluminum alloy (short paper)==
https://ceur-ws.org/Vol-2843/shortpaper015.pdf
The use of information technology and mathematical
modeling in the development of modes of aluminum
alloy*
Anastasia S. Samoylova1, Valentina V. Britvina1, Ekaterina O. Bobrova1,2, Galina P.
Konyukhova3 and Alexey V. Altukhov2
1
Moscow Polytechnic University, 38, st. Bolshaya Semyonovskaya, Moscow, 107023, Russia
2
Lomonosov Moscow State University, 1, Leninskie Gory, Moscow, 119991, Russia
3
Moscow State Technical University "Stankin", 1, Vadkovsky per., Moscow, 127994, Russia
saaturn2015@mail.ru
Abstract. The work is devoted to the application of the correlation analysis
method for the study of aluminum cast alloys; or rather, the relationship be-
tween the density of a substance and the concentration of chemical elements in
it. The purpose of the work is to study the dependence of the density and con-
centration of chemical elements in aluminum alloys to establish patterns of
growth and decrease in material density. The objective of the work is to deter-
mine by the correlation method t he presence of a relationship between the den-
sity and concentration of elements of chemical composition. The study was per-
formed by the method of correlation analysis using modern software tools, with
the help of which the dependencies between the physical parameters of alloys
and their chemical properties were searched. The study made a number of im-
portant assumptions, detailed in the publication. As a result of the analysis, it
was revealed for which metals in the alloys the values can be processed by the
correlation method, and the corresponding point diagrams of the values were
constructed. Additionally, the accuracy of the research results was determined
by using manual and automatic methods. The study concluded that the density
of aluminum alloys depends on the concentration of magnesium. It is shown
that using the applied methodology it is possible to establish the accuracy corre-
lation between variables and determine the priority of certain additives in the
material. The publication is equipped with the necessary tables and figures, as
well as detailed explanations for each stage of the study.
Keywords: Correlation, Dependence, Aluminum alloys, Calibration, Concen-
tration, Physical properties, Chemical properties.
*
Copyright © 2021 for this paper by its authors. Use permitted under Creative Commons License Attribu-
tion 4.0 International (CC BY 4.0).
1 Introduction
When researching materials, their properties and characteristics are distinguished by
parameters, without values of which their use will be useless. There are many differ-
ent factors that determine such qualities as ductility, ductility, weldability, brittleness,
hardness, hardenability and much more. However, the systematization of this knowl-
edge is not feasible and without any certainty I parameters associated with the aggre-
gate as a whole body condition. This article will focus on the physical properties of
metals and their alloys.
The physical properties of the body are basic and determine the state of the mate-
rial or element in a given period of time. The future shape of a particular machine, as
well as the reaction to environmental influences, depend on their values, so it is im-
portant to remember that when studying the material on the physical properties of a,
the accuracy of the calculations is necessary.
Physical properties include many different measurements: from magnetic proper-
ties to measurements related to body weight and systematize physical processes in a
general structural approach [1-3]. In this article, we shall discuss only one physical
parameter - is the density of matter, which expresses the ratio of body mass to its
volume.
The aim of this work is to study the dependence of the physical parameter (density)
and chemical parameters (concentration of chemical elements) of aluminum alloys in
order to establish the pattern of growth and decrease in the density of the material.
The objective of the work is to determine the existence of a relationship between the
density and concentrations of elements of the chemical composition by the correlation
method .Please note that the first paragraph of a section or subsection is not indented.
The first paragraphs that follows a table, figure, equation etc. does not have an indent,
either.
2 Materials and methods
To begin with, when studying the dependence of density on other factors, we made
the following assumption with respect to volume: this parameter will be taken as a
constant, and the mass, in turn, will change its parameters due to changes in the basic
chemical properties [4-6].
To study the relationship between the main properties, 14 aluminum alloys with
different density indices were taken and their chemical compositions were painted
(Table 1).
Using the Exel 2007 program , sorting was performed according to the Density
column in ascending order, as a result of which the concentrations of chemical ele-
ments occupied the corresponding positions (Figure 1).
The chemical compositions of each alloy are subject to differences due to a variety
of mining methods and locations. In this regard, one more assumption was made re-
garding the frequency of the element encountered: the more often the element occurs
in alloys, the more accurate the correlation calculations between the main properties
will be (Table 2).
Table 1. The chemical composition of aluminum alloys.
No. Alloy Density Fe Si Al Cu Mg Zn Ti Mn Zr
1 AL 1 2.75 0.4 0.35 91.575 4.125 1.5 0.05 0 0 0
2 AL 2 2.65 0.75 11.5 86.9 0.3 0.05 0.15 0.05 0.25 0.05
3 AL3 2.7 0.8 5 90.025 2.25 0.475 0.15 0 0.75 0.25
4 AL 4 2.65 0.5 9.25 89.48 0.05 0.235 0.1 0 0.35 0
5 AL5 2.68 0.75 5 91.92 1.25 0.475 0.15 0.075 0.25 0.075
6 AL 7 2.8 0.5 0.6 94.075 4.5 0.015 0.1 0.1 0.05 0.05
7 AL8 2.55 0.15 0.15 89.63 0.05 9.75 0.05 0.035 0.05 0.1
8 AL 9 2.66 0.75 7 91.37 0.1 0.3 0.15 0 0.25 0
9 AL11 2.94 0.75 7 82 0.3 0.2 9.5 0 0.25 0
10 AL13 2.6 0.75 1.05 92.725 0.05 5 0.1 0 0.25 0.075
11 AL21 2.83 0.3 0.25 89.5 5.3 1.05 0.15 0 0.2 0
12 AL22 2.5 0.6 1 86.35 0 11.75 0.05 0.1 0 0.1
13 AL24 2.74 0.25 0.15 93.15 0.1 1.75 4 0.15 0.35 0.05
14 AL25 2.72 0.4 12 82.265 2.25 1.05 0.25 0.125 0.45 0
Source: compiled by the author according to open sources [2].
Fig. 1. Sorting data by increasing density.
Table 2. Calculation of the accuracy of the correlation.
The percentage
of concentrations that entered Accuracy Decryption
the area
Accuracy with a very gross er-
5 qualifica-
10-20% ror. Indicates no dependence due to a
tions
false indicator .
Accuracy with a gross error. Generally
4 qualifica- indicates the absence of dependence due to a
21-40%
tions false indicator, but allows some exceptions:
in some situations, this dependence will exist
The accuracy of the calculations is nor-
3 qualifica- mal. Indicates a controversial relationship
41-60%
tions between variables, allows for both
the absence and the presence of dependence.
Good calculation accuracy. Generally in-
dicates a strong dependence between vari-
2 qualifica-
61-80% ables, however, an exception is allowed: in
tions
some situations, this dependence will not
exist
Reference accuracy of calcula-
81-100% 1 quality tions. Indicates a strong relationship between
variables.
Source: compiled by the author according to open sources [3].
As a result of the analysis, it was found that the processing of values by the corre-
lation method [7-8] can be performed for iron, silicon, copper, magnesium, zinc a,
titanium a, manganese, and zirconium , since for these parameters the error value is
less than 50% of all data.
The error value is the ratio of data whose significance is absent, i.e. equal but zero,
for all their number. For the most obvious picture, this ratio is multiplied by 100%
and a result is obtained that is processed using Table 2. If the error value exceeds
50%, then the calculation of correlation will be less than 50% reliable.
As a result of the selection, the elements that are most likely to be processed are
determined by accuracy. Typically, when sorting e values and parameter setting accu-
racy analyzing workload can with krato in the range from 30 to 45 %. In this case, the
workload was reduced by 40 %, since the values of chromium, beryllium, cesium, tin,
nickel, and lead have a low accuracy level.
We construct point diagrams of values for elements: iron, silicon, copper, magne-
sium, zinc, titanium, manganese, zirconium in Microsoft Word 2007. The obtained
result must be analyzed from the point of view of the parameter of point concentra-
tions in the diagram area [8-9]. A prerequisite for calculating the relationship between
the variables is the accuracy of determining the I correlation area. For this, it is neces-
sary and sufficient to find a region of the diagram that is formed by the largest num-
ber of points (Figure 2).
Fig. 2. Determination of the correlation region for metals: a) iron b) silicon c) magnesium, d)
titanium, e) zinc, e) copper
After the area has been determined, it is necessary to calculate the correlation in-
dex. Its value can be calculated in the following way.
The first step is to determine the area of the ellipse with the highest concentration
of points [7]. Inserted elliptical figure in the diagram using calculations region "in-
sert" and then using the editor is invoked m region figures and via points draw axis by
a straight line (Figure 3).
Fig. 3. Determination of the correlation value - the first method.
The constructed ellipse in the diagram area allows finding the value of one or an-
other correlation. To do this, find the ratio of the major and minor axes of the ellipse.
Upon completion and calculations, you need to choose the most convenient calibra-
tion of the results on a five, ten or stobal scale. After this scale, it is necessary to di-
vide into five intervals and determine the degree of correlation (Table 3).
Table 3. The degree of correlation for the graphical method.
Correlation value Degree of correlation Decryption
There is no correlation.
9-10 5 qualifications Dependence does not exist.
Correlation is generally absent. Dependence may
8-7 4 qualifications
or may not exist.
Correlation with controversial nature. Dependence
5-6 3 qualifications may or may not exist.
Correlation exists, but allows some exceptions.
4-3 2 qualifications The dependency will mainly exist, in some cases it
will be absent
Correlation exists and shows the strongest depend-
2-0 1 quality ence.
3 Results
The result will be positive, if the calibration is, results to determine the same results.
Otherwise, there are several reasons:
─ Inaccurate determination of the point concentration region;
─ Incorrect determination of the axes of the ellipse;
─ Error in the mathematical calculation.
When processing data on density and concentrations using an automated and man-
ual method, no errors were detected. The result was the following conclusion: the
density of aluminum alloys is strongly affected by the concentration of magnesium
and zinc, and to a lesser extent, the concentration of copper (Table 4).
It is known that aluminum and its alloys require a special approach to heat treat-
ment [9]. The thickness of its oxide film is 1-3 nanometers [10], which is not allowed
to correctly distribute the temperature on the surface of the alloy. To determine the
cause of the increased oxide concentration in the alloy and its reduced density, we use
the results of the obtained correlation.
4 Discussion
From table 5 it is seen that the concentration of magnesium has the most pronounced
dependence on the density. The curious fact is that a pure magnesium alloy does not
exist. It is this alloy that carries a large concentration of oxygen. Confirmation of the
reason for the increased oxygen concentration is also the color of metals: with an
increased concentration of oxide, the metal loses its luster. In the physical properties
of magnesium, it is noted that this alloy in its pure form does not have a luster, as well
as aluminum (Figure 4).
Table 4. Results of determining correlation by manual and automated method.
Source: compiled by the author.
Fig. 4. Aluminum and magnesium alloy.
An additional question in the study of correlation analysis was the determination of
the accuracy of the method [7-8]. Since the largest number of points in the range was
taken as the basis of the method in this study, it can rightly be suggested that there
may be several such clusters throughout the diagram; therefore, the analysis method
by determining the ratio of the ellipse axes may not be accurate.
Also, the most striking evidence of the fact that the physical properties of alumi-
num alloys greatly affects the concentration of magnesium , is obtained by us correla-
tion. From the results obtained it can be concluded that aluminum with melting
AK7ch grade with a density of 2.66 g / cm3 has a magnesium concentration of 0.3%
in a difference game and from alloy grade AK8 with density w 2.8 g / cm3 and a mag-
nesium concentration of 0.5% [9]. For completeness of the study will analyze and the
remaining two impurities - zinc and copper. Considering copper can be noted the
color and ductility, i.e. when a strong correlation can be noted that the alloy with a
certain concentration of copper color is slightly yellowish (when mixed with silver
and serami shades alloys) and have a high ductility, but the color of aluminum has
only light gray shades.
Zinc is a silver-colored metal with increased brittleness, the alloys of which con-
tain a minimum percentage of oxygen and have an expressive metallic luster. As is
known, aluminum is not a brittle material, but has a thick oxide film and has an aver-
age gloss differences in e from zinc.
5 Conclusion
According to the results of the study it can be concluded that the density of aluminum
alloys depends on the magnesium concentration dependence retrograde expressed that
this material provides ductility, and difficult processing.
In addition, the Performan study may be mentioned rapid processing of data man-
ual method. Using the methodology used by us, it is possible to establish the quality
of correlation accuracy between variables, as well as determine the priority of certain
additives in the material.
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