STABILITY ASSESSMENT OF 30ХНМЛ STEEL MELTING PROCESS IN ELECTRIC ARC FURNACES ON THE BASIS OF TECHNOLOGICAL AUDIT OF SERIAL MELTINGS

The object of research is the process of 30 ХНМЛ steel melting in two electric arc furnaces with a capacity of 6 tons. Technological audit of the process is carried out on existing furnaces in the steel foundry of a machine-building enterprise specializing in the manufacture of large shaped castings for products of transport engineering. The audit is aimed at analyzing the compliance of the performed main technological melting operations with the required regulated technological instructions. On the basis of carrying out serial meltings, a sample of experimental and industrial data is obtained to determine the tensile strength of steel samples 30KhNML. It has been established that according to the actual production data of serial heats it is impossible to postulate the distribution law, in particular, to speak of a normal distribution. Therefore, the use of statistical sampling functions to assess the melting stability is not advisable. It is proposed to use the stability coefficient ( η ), based on the calculation of entropy (H), as a criterion for assessing the melting stability. It is proposed to use a fuzzy description of these values for practical use in assessing the melting stability. In this case, it can be assumed that the calculated values of entropy and melting stability coefficient for each sample separately and the total sample form the left ( α jp ) and right ( β jp ) fuzziness boundary. It is proposed in the fuzzy description to use the membership function of (L–R) type. In a specific case, it can be assumed that α jp =2.63, β jp =2.71 (for a fuzzy number H) and α jp =0.22, β jp =0.24 (for a fuzzy number η ). Thanks to the proposed method for assessing the melting stability, it is possible to obtain objective data without relying on the assumption of a normal distribution law. The proposed method is invariant to the type of technological process in the blank production. These can be metal forming, heat treatment and other metallurgical processes. The importance of the proposed method is related to the fact that the quality of further technological operations for the production of finished parts depends on the inheritance of the quality of blank production as the previous technological stages of production.


Introduction
Steel melting in electric arc furnaces is one of the processes that have significant uncertainty, which mani fests itself in relation to both input and output process variables.The input variables traditionally include the content of elements of the chemical composition of steel, and the output properties are the mechanical proper ties of the finished steel.Uncertainty is twolevel and is manifested in the assessment of the modal value and compactness of the body of uncertainty, knowing that it is possible to solve the clustering problem to obtain the functional dependence of mechanical properties on the chemical composition [1,2].However, it is important to set the left and right boundaries of fuzziness, regarding the choice of which expert opinions may differ.The values of these limits can be determined only on the basis of real data, which are available in the mode of carrying out serial heats.
Therefore, it is relevant to conduct a technological audit of such heats.Due to this, it is possible to obtain a sample of real data for further evaluation of the inac curacy of the description of technological parameters of melting in electric arc furnaces and to assess the stability of this process.

The object of research and its technological audit
The object of research is the process of 30ХНМЛ steel melting in two electric arc furnaces with a capacity of 6 tons.Technological audit of the process is carried out on exis ting furnaces in the steel foundry of a machinebuilding enterprise specializing in the manufacture of large shaped castings for products of transport engineering.The audit is aimed at analyzing the compliance of the performed main technological melting operations with the required regu lated technological instructions.In the course of melting, in accordance with the regulations, samples are taken to determine the mechanical properties of steel 30ХНМЛ.Serial observations are carried out for 120 days.
Based on it, the following is established.ISSN 2226-3780 The first period of melting is carried out at the maximum power of the transformer, the connection of the winding of which is included in the triangle mode.At this point, the first half of the melting consists of almost continuous short circuits and current surges.Melting of the charge begins from the top and as the metal is melted and the electrodes are lowered deep into the mixture, it spreads to the underlying layers.When melted, the metal flows down between the pieces of the charge, heats them and gradually forms a bath of liquid metal at the bottom of the furnace.At the first stage, three wells are melted under each electrode in the charge, which are then connected into one common well.At this stage, the transformer is switched to low power mode, in order to prevent thermal wear of the lining by the opened arcs.
The oxidation period begins with the fact that after the formation of slag, carefully mixing, take the first sample of steel to determine the rapid analysis of the content of carbon, manganese, phosphorus, sulfur and chromium.For deoxidation of liquid steel, direct introduction of deoxidi zers, as well as ferromanganese in the amount of 0.4-0.5 % of the mass of steel is performed, and then in 3-5 minu tes -ferrosilicon.2-3 minutes before steel production, the remaining amount of ferromanganese and aluminum is introduced.Slag deoxidation in the existing conditions of the workshop is carried out until the slag sample after cooling has a light green or blue color at the break.

The aim and objectives of research
The aim of research is determination the stability indicators of 30ХНМЛ steel melting according to the quality criterion «tensile strength» taking into account the uncertainty.
To achieve this aim it is necessary to solve the fol lowing objectives: 1. To obtain a sample of primary data on the determi nation of the tensile strength of 30ХНМЛ steel samples in serial melting.
2. To choose and justify the criteria for assessing the melting stability.
3. To carry out a comparative analysis of the calcula tion of melting stability indicators, justifying the method of its description expedient for practical use.

Research of existing solutions of the problem
The problem of assessing the stability of electric arc melting processes is reduced to the choice of evaluation criteria and the possibilities of their application in ac cordance with the level of technological development in a particular production.Typical solutions in this part are the presentation as priority electrical modes of operation of the furnaces as energy technology complexes integrated into the power grid [3,4] or thermal performance [5].In the first case, the actual modeling and parameter estima tion is replaced by a computer using readymade software packages, for example, in the SIMULINK/MATLAB en vironment [3].In the second case, 3D modeling is used to estimate thermal fields, temperature distribution in the furnace depending on the internal geometry, systems for isolating its individual elements and cooling [5].Such typical approaches are convenient, given the current ca pabilities of software and hardware, but they are focused more on the performance of the metallurgical units them selves, rather than on the products manufactured by them.A certain development of the evaluation criteria of the technological component can be found in [6][7][8].Thus, in [6], the formation of estimated technological parameters is considered from the standpoint of the study of metal lurgical processes occurring in a furnace.And in [7,8], it is proposed to consider economic criteria as criteria for evaluating the melting efficiency.Finally, an approach based on the construction of functional dependences of proper ties on the chemical composition formed at the stages of melting and modifying [9] is also common.Technological priorities in assessing the stability of melting, understood as an analogue of the efficiency of the process, should be organically combined with indicators of metallurgical aggregates.Such mutual integration allows implementing solutions in the field of automated or automatic control of melting [10,11].And also to use the solutions obtained for evaluating measures for the technical reequipment of melting sections of workshops [12].All this allows to conclude about the importance of the choice of performance indicators and criteria for assessing the stability and ef ficiency of melting processes.At the same time, noting the indisputable advantages of modern computer simula tion tools, it should be noted that it is impossible to do without real industrial data and conducting experimental and industrial research in mass production.

Methods of research
The results of determining the strength limit provi ded by the laboratory were processed by the methods of mathematical statistics.The expected value, variance and standard deviation were calculated.To determine the stability of the melting process, the concept of entropy was used, by analogy with that used in information theory.Entropy was calculated as a function of the probability of observing a specific value of the ultimate strength of steel (x i ) in a given melting and the logarithm of the selected basis of the probability of observation [13]: where k -some positive constant; P x i ( ) -probability of observing x i values.
The stability of the melting process when used as an estimate of the entropy was estimated as follows: where Н -the entropy corresponding to a given distribution of the values of the ultimate strength of steel in the ith melting; Н max -the maximum possible entropy corresponding to a uniform distribution; η -stability of the melting process.Formula (2) is applicable in the case of a singlemode distribution of a random variable characterizing the mel ting process.

Research results
The results of determining the strength limit provided by the laboratory for the period of the technological audit are shown in Fig. 1  From Fig. 2 it is possible to see that the distribution of data indicates the probable pre sence of a systematic error, manifested in the presence of more than one vertex.This means that the sample may be heterogeneous.This situation is possible, since the melting is car ried out in two different furnaces and in dif ferent conditions.To verify this, the original sample was artificially divided into two, each of which, presumably, described the distribution of data on the furnaces.Given the complexity of unique identification, expert opinion was used.Fig. 3, a, b are histograms obtained after splitting the initial sample.
The results of the calculations of the entropy and the stability coefficient of melting are given in Table 1.From Fig. 3 it follows that the partitioning of the sample gave the best result in estimating the entropy and melting stability coefficient, and the result for samples No. 1 and No. 2 turned out to be almost the same.
However, the problem in estimating the distribution parameters remained.Therefore, it is impossible to talk about the distribution density and it is more expedient to present the ultimate strength as a fuzzy value.At the same time, the output variable is a fuzzy number F jp , described by membership functions L R − ( ) of the type [1]: where F jp -the measured value of the output variable, in the j th experiment, which is modal for a fuzzy number F jp , j n = 1 2 , ,.Similarly, in the form of (3), the stability coefficient can be represented, which also appears as a fuzzy number.In this case, it can be assumed that the calculated values of entropy and melting stability coefficient for each sample separately and the total sample form the left and right fuzziness boundary in the description (3).In a specific case, it can be assumed that α jp = 2.63, β jp = 2.71 (for a fuzzy number H) and α jp = 0.22, β jp = 0.24 (for a fuzzy number η).

SWOT analysis of research results
Strengths.The strength of this research is the justi fication of the method for assessing the stability of the electric melting of 30ХНМЛ steel.This is due to the im portance of the quality issues of finished products, on which the competitiveness of the manufacturing company fully depends.The inability to ensure the specified indicators of steel quality stability for the selected indicators may be due to the lack of understanding of rational ways to implement the organizational and technological measures of the melting company.In turn, this understanding should be based on sound assessments of quality criteria.Thanks to the proposed assessment methods based on the use of the concepts of entropy and the stability coefficient, this possibility is provided.It should also be noted that the proposed method of assessing the stability indicators is invariant to the type of technological process in the blank production.These can be metal processing, pressure, heat treatment and other metallurgical processes.This is ex plained by the fact that the quality of further technological operations for the production of finished parts depends on the inheritance of the quality of the blank production as the previous technological stages of production.
Weaknesses.The weak points of this research are re lated to the fact that conclusions about the numerical values of the fuzziness boundaries in the description of entropy and the stability coefficient of melting are made from a small sample of data.This can lead to the fact that in the assessment of real data in terms of serial heats inaccuracies are possible.The consequence of this may be an inaccurate assessment of the membership function and overestimated or underestimated melting stability.This, in turn, can lead to erroneous organizational and technological solutions and associated costs.
Opportunities.Additional opportunities when using the above results in an industrial environment are associated with the conduct of serial heats and the accumulation of data to form a more representative sample.The result of this may be a refinement of calculations for the lower and upper boundaries of fuzziness, the modal value and compactness of the body of entropy uncertainty and the coefficient of melting stability.The more accurate values obtained in this way will provide a more accurate descrip tion of the membership function, which can be used to assess the efficiency of the electric arc melting process.It should be noted that the effectiveness here refers to the compliance of the actual entropy indicators and the stability coefficient with the specified values.
Threats.Obvious threats when using the obtained re sults are associated with the requirement of reproducible results.This, in turn, requires the maintenance of strictly regulated values of the content of chemical elements in steel.Attempting to use the research results without a prior technological audit of specific melting conditions in its production can lead to inadequate results.In this case, there will be the problem of estimating the real indica tors of its steelmaking production, which can be either overestimated or underestimated.Elimination of such risks requires prior adaptation of the results obtained in this research to the specific conditions of its production.

Conclusions
1. On the basis of carrying out serial meltings, a sample of experimental and industrial data is obtained to deter mine the tensile strength of 30ХНМЛ steel.As follows from the obtained results, it is impossible to postulate the distribution law, in particular, to speak about the normal distribution.The resulting twovertex histogram suggests that there is heterogeneity of data, in particular, possible systematic error.Therefore, it is advisable to split the sample into two, in accordance with the regulation of melting in two electric furnaces.
2. As a criterion for assessing the melting stability, it is proposed to use a stability coefficient based on the calculation of the entropy and determined on the basis of a sample of data obtained in the serial melting mode.This allows to remove the strict requirement of com pliance with the distribution law to a normal one, on the basis of which the standard deviation can be used as an estimated indicator of melting stability.
3. It is proposed to use fuzzy description of entropy and stability coefficient for practical use in assessing the melting stability.This is justified by the fact that a strict requirement is removed that the distribution law is normal, since the actual distribution density is absent.Despite the fact that this result is obtained for one technology of melting of one steel grade, a similar situation is likely to occur in other industrial conditions.Therefore, it is proposed in the fuzzy description of entropy and melting stability coefficient to use the calculated values of these indicators for the total and divided samples as the lower and upper limits of fuzziness.

Introduction
In the conditions of mass production of special casting types in shops with chill machines or injection casting machines, it is necessary to ensure the specified perfor mance.However, it is difficult to organize the process in such a way as to harmonize the quality requirements of the resulting castings.If the decisions on the organiza tion of the process are wrong, there may be additional costs for the process.For example, the overrun of energy carriers or material resources is possible.Therefore, it is important to develop solutions in the field of control of

Fig. 1 .
Fig. 1.Experimental data on the value of the ultimate strength σ b of 30ХНМЛ steel in serial meltings (the numbers of meltings are indicated on the periphery of the pie chart, the values of σ b , MPa are indicated on the ordinate axis) Fig. 2 shows a histogram of the distribu tion of the σ b value, based on a total sample of experimental industrial data.From Fig.2it is possible to see that the distribution of data indicates the probable pre sence of a systematic error, manifested in the presence of more than one vertex.This means that the sample may be heterogeneous.This situation is possible, since the melting is car ried out in two different furnaces and in dif ferent conditions.To verify this, the original sample was artificially divided into two, each of which, presumably, described the distribution of data on the furnaces.Given the complexity of unique identification, expert opinion was used.Fig.3, a, b are histograms obtained after splitting the initial sample.The results of the calculations of the entropy and the stability coefficient of melting are given in Table1.From Fig.3it follows that the partitioning of the sample gave the best result in estimating the entropy and melting stability coefficient, and the result for samples No. 1 and No. 2 turned out to be almost the same.

Table 1
Fig. 3. σ b distribution when splitting the sample: a -sample No. 1; b -sample No. 2 The results of entropy calculations of the strength limit of steel σ b and the stability coefficient of melting σ b , MPaFig.2. The histogram of the σ b , distribution, built on the total sample