For mechanical engineering and other branches of industry the most progressive and economic technological processes permitting to increase wear resistance, corrosion resistance and other properties of the working surface of the produced machines are technological processes of gas-thermal coating evaporation. In the paper there is considered the scheme of gas-thermal coating evaporation and selected the optimum technological modes of gasthermal evaporation. There is developed a mathematical model defining relations between the evaporation distance, the angle of the melted particles dispersion, the speed of the part rotation, the speed of the burner movement and the evaporated coating thickness

G. Zhetessova

O. Zharkevich

T. Buzauova

V. Yurchenko

Ye. Platonova

Ye. Pleshakova

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Building mathematical model for gas-thermal process of coating evaporation

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63METALURGIJA 55 (2016) 1, 63-66G. ZHETESSOVA, O. ZHARKEVICH, YE. PLESHAKOVA, V. YURCHENKO, YE. PLATONOVA, T. BUZAUOVABUILDING MATHEMATICAL MODEL FOR GAS-THERMAL PROCESS OF COATING EVAPORATIONReceived – Primljeno: 2014-12-14Accepted – Prihvaćeno: 2015-06-19Preliminary Note – Prethodno priopćenjeISSN 0543-5846METABK 55(1) 63-66 (2016)UDC – UDK 621.795.66.095:542.4:537.717:51.086.5=111G. Zhetessova, O. Zharkevich, V. Yurchenko, Ye. Platonova, T. Buza-uova, Karaganda State Technical University, Karaganda, KazakhstanYe. Pleshakova, Karaganda State Industrial University, Temirtau, Ka-zakhstanFor mechanical engineering and other branches of industry the most progressive and economic technological pro-cesses permitting to increase wear resistance, corrosion resistance and other properties of the working surface of the produced machines are technological processes of gas-thermal coating evaporation. In the paper there is con-sidered the scheme of gas-thermal coating evaporation and selected the optimum technological modes of gas-thermal evaporation. There is developed a mathematical model defining relations between the evaporation dis-tance, the angle of the melted particles dispersion, the speed of the part rotation, the speed of the burner move-ment and the evaporated coating thickness.Key words: coating, gas-thermal evaporation, mathematical model, dependence speed, thickness.INTRODUCTIONAt present the matters of essential increase of wear resistance of machine parts are mainly solved by intro-ducing to the technology of their production the addi-tional labor-consuming operations for hardening the part outer zone. An urgent task is searching for such strengthening processes which would combine the pos-sibility of obtaining the surface roughness with high parameters and needed accuracy with simultaneous hardening of the outer zone. Gas-thermal technologies of evaporated coating strengthening meet these condi-tions [1].At present in mechanical engineering there is a set of problems connected with the hydraulic equipment protection against corrosion impact [2].In this connection gas-thermal coating evaporation on the elements of equipment gives a possibility to use materials without changing their properties.The coatings can be multilayered that permits to use properties of various materials and to obtain coatings with the set properties including multipurpose or so-called pseudo-alloy coatings [3].Pseudo-alloy coatings represent a separate type of composite coatings consisting of the materials which are not forming solid solutions and compounds in the liquid and solid state and differing in the melting tem-perature. The coatings obtained from materials like pseudo-alloys possess a number of properties: a combi-nation of high values of melting temperature and evapo-ration to the mechanical durability, hardness, damping ability, wear resistance, ability to self-greasing in the conditions of dry friction, as well as high level electro- and heat conductivity [4].The analysis of methods of pseudo-alloy coating evaporation showed that the most economic and simple is the gas-thermal evaporation.In gas-thermal evaporation it is needed to take a set of factors into account: sizes and form of particles of the evaporated powder, the wire or bar diameter; density, specific heat, heat conductivity of evaporated materials, evaporation distance, speed of the burner movement, speed of the wire feeding, the angle of the melted parti-cles dispersion [5 - 7].MATHEMATICAL MODEL OF GAS-THERMAL COATING EVAPORATIONThe most important factor of designing and control-ling the processes of coating evaporation by the method of electric arc spraying is the existence of an adequate mathematical model of the spaying process. The tech-nological scheme of gas-thermal evaporation of a coat-ing is given in Figure 1.For building the gas-thermal coating evaporation mathematical model let us write down the evaporated material consumption:  /  m3/s (1)where V1 is the evaporation speed / m/s;π is the mathematical constant value (π = 3,1415...); d is the burner nozzle diameter / m.The evaporated coating width can be determined by the formula:64G. ZHETESSOVA et al.: BUILDING MATHEMATICAL MODEL FOR GAS-THERMAL PROCESS OF COATING... METALURGIJA 55 (2016) 1, 63-66  / m (2)where h is the evaporation distance/ m;tg α is the melted particles dispersion angle/ degree.Linear speed V2 is determined from the expression:  / m/s (3)where D is the part diameter/ m;ω is the angular speed or the part rotation speed/ 1/s.From here we obtain that the evaporation volume is equal:  / m3 (4)where Δ is the evaporated layer thickness/ m;l is the coating width/ m;SH is the evaporation area/ m2, determined by the for-mula: SH = l / m2 (5)The volume velocity or the speed of evaporation flow can be expressed through the volume of the evapo-rated coating Q2: / m3/s (6)where t is the time of operation/ s.The same value can be expressed in:  (7)where R is the part radius/ m.Substituting equation (3) into equation (7)  it is ex-pressed the volume consumption of evaporation Q2:  (8)The total consumption of the evaporated material is:  / m3 (9)where L is the width of the evaporated coating on the entire shaft length/ m.The volume consumption of the evaporated material Q3 can be expressed through the total material consump-tion Q:   / m3/s (10)Q3 can be also expressed through the burner move-ment speed V3:   (11)At last, equal in equations (1), (8), and (11) it is ob-tained  the kinematic characteristic conformance:   (12)  NANO CALC PROGRAMBased on the presented mathematical model there was developed a program of technological process of evaporation which permits to calculate more precisely the technological parameters with a margin error to 2 %.This mathematical model permits to calculate the tech-nological process parameters of evaporation taking into account the time and changing the evaporation angle.There was developed a special computer Nano Calc program containing the above mathematical model for the selection of the optimum technological parameters of the gas-thermal process of coating evaporation (Figure 2).This technique and the developed program permit to calculate the technological data of the evaporation pro-cess for diametrical parts with various overall dimen-sions, with different basic data. In this program it is also possible to select various materials for evaporation.Thus, the use of this program and the method of cal-culating the technological process of the gas-thermal evaporation permits to calculate the technological pa-rameters taking into account the set basic data and on the basis of these calculations to issue the optimum de-cisions and graphic dependences.The following data are reflected in this program: se-lection of parameters, optimum decision, the course of the decision, building dependences, evaporation dia-Figure 1  Gas-thermal evaporation scheme:  h – evaporation distance; d – burner nozzle diameter; D – part diameter; L – evaporated coating width on the entire shaft length; l –  coating width; Δ – evaporated layer thickness;  ω –angular speed; α – melted particles dispersion angle; V1 – evaporation speed ; V2 – linear speed; V3 – burner movement speed65G. ZHETESSOVA et al.: BUILDING MATHEMATICAL MODEL FOR GAS-THERMAL PROCESS OF COATING...METALURGIJA 55 (2016) 1, 63-66gram, as well as the possibility to add the data with various evaporation materials for making graphs and dependences.DISCUSSION OF THE RESULTS When developing a mathematical model and a pro-gram of calculating the technological parameters there were considered the modes of evaporation and charac-teristics of the material. The thickness of the evaporated layer is defined depending on the evaporation speed, the evaporation  distance, and other parameters.For calculation of the technological parameters of gas-thermal evaporation we will take the following ba-sic data:- diameter of the burner nozzle d - 7 mm; - diameter of the part D - 160 mm; -  the width of the evaporated coating on the entire shaft length L - 936 mm; - evaporation speed V1 – 5,6 m/s.The experimental data are presented in Table 1.Table 1 Results of the technological calculationPara-meter nameVariables valueΔ×10-3/ m2 2,5 3 3,5 4 4,5 5ω / rpm800 850 900 950 1000 1050 1100h /m 0,1365 0,1385 0,1145 0,118 0,1055 0,1295 0,1065V2 / m/s 1,067 1,133 1,2 1,267 1,333 1,4 1,467V3/ m/s 0,214 0,172 0,143 0,123 0,107 0,095 0,086α / 0 19 14 13 10 9 6 6Figure 2  Optimization of the technological process of electric arc metallizingFigure 3 Dependence of the coating  thickness  on speed V2Figure 4  Dependence of the coating thickness  on speed V3Figure 5  Dependence of the coating thickness  on the set h eighthBy the results of calculation there were obtained the following dependences:-  dependence of the coating thickness Δ on the speed V2 (Figure 3);-  dependence of the coating thickness Δ on the speed V3 (Figure 4);-  dependence of the coating thickness Δ on the set height h (Figure 5);-  dependence of the coating thickness Δ on the rota-tion speed ω (Figure 6);Figure 6  Dependence of the coating thickness  on the rotation speed  66G. ZHETESSOVA et al.: BUILDING MATHEMATICAL MODEL FOR GAS-THERMAL PROCESS OF COATING... METALURGIJA 55 (2016) 1, 63-66-  dependence of the coating thickness Δ on the melt-ed particles dispersion angle α (Figure 7).The analysis of the obtained graphic dependences of the gas-thermal evaporation shows that:-  the coating thickness Δ linearly depends on V2 speed, therefore with the speed increasing the coat-ing thickness increases (Figure 3);-  the speed of the burner movement V3 significantly effects the process efficiency and the coating thickness (Δ), i.e. the less is the burner movement speed, the thicker is the coating,  and it lays down unevenly (Figure 4);-  with increasing the evaporation distance h the loss of the evaporated coating increases and so porosity does (Figure 5);-  with increasing the speed of the part rotation the coating thickness Δ increases (Figure 6);-  the angle of the melted particles dispersion α ef-fects the formation of the evaporated particles flow and the coating thickness Δ. At small angles there is formed the greatest coating thickness, and at big angles the thickness of the evaporated coating de-creases to minimum owing to the losses of the evaporated material (Figure 7).The method of calculation of the evaporation tech-nological process yields satisfactory results for any set parameters.Using the obtained mathematical model in the de-veloped program, it is possible to define the rational modes of the gas-thermal evaporation which reduce the time for the number of experiments for their selection.CONCLUSIONSThe most saving and simple way of placing pseudo-alloy coatings is the gas-thermal evaporation. The mathematical model of gas-thermal coating evaporation considers the evaporation distance h, linear speed V2, the speed of the burner movement V3, the melted particles dispersion angle α, the rotation speed ω and permits to determine the coating thickness Δ.The developed Nano Calc program gives an evident idea of dependences of the  mathematical model param-eters of the gas-thermal coating evaporation.REFERENCES[1]  Askinazi B. Hardening and restoration of parts by electro-mechanical processing. - L.: Mechanical engineering, 1977, 124-128.[2]  Solod G. I. Increasing durability of mining machines.  – M: Mechanical engineering, 1976,  212-220.[3]  Baldayev L. Kh. Gas-thermal evaporation.  – M:DS mar-ket, 2007,  147-158.[4]  Encyclopedia of inorganic materials. (Ukr. Sov.Enc., Kiev), T2. 1977, 345-360.[5]  Ilyushchenko A. F., Okovity VA. Forming gas-thermal co-atings: theory and practice. – Minsk: Bestprint, 2002, 268-275.[6]  Ilyushchenko A. F., Shevtsov A. I., Okovity VA., Gromyko G. F. Processes of forming gas-thermal coatings and their modeling. - Minsk Belarus: Navuka, 2011, 145-150. [7]  Khassui L., Morigaki O. Weld deposition and evaporation. – M: Mechanical engineering, 1985, 171-115.Note: The translation of the N.M. Drag, Karaganda, KazakhstanFigure 7  Dependence of the coating thickness  on the melted particles dispersion angle 

Building mathematical model for gas-thermal process of coating evaporation

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