Vol. 26 No. 1 2024 3 EDITORIAL COUNCIL EDITORIAL BOARD EDITOR-IN-CHIEF: Anatoliy A. Bataev, D.Sc. (Engineering), Professor, Rector, Novosibirsk State Technical University, Novosibirsk, Russian Federation DEPUTIES EDITOR-IN-CHIEF: Vladimir V. Ivancivsky, D.Sc. (Engineering), Associate Professor, Department of Industrial Machinery Design, Novosibirsk State Technical University, Novosibirsk, Russian Federation Vadim Y. Skeeba, Ph.D. (Engineering), Associate Professor, Department of Industrial Machinery Design, Novosibirsk State Technical University, Novosibirsk, Russian Federation Editor of the English translation: Elena A. Lozhkina, Ph.D. (Engineering), Department of Material Science in Mechanical Engineering, Novosibirsk State Technical University, Novosibirsk, Russian Federation The journal is issued since 1999 Publication frequency – 4 numbers a year Data on the journal are published in «Ulrich's Periodical Directory» Journal “Obrabotka Metallov” (“Metal Working and Material Science”) has been Indexed in Clarivate Analytics Services. Novosibirsk State Technical University, Prospekt K. Marksa, 20, Novosibirsk, 630073, Russia Tel.: +7 (383) 346-17-75 http://journals.nstu.ru/obrabotka_metallov E-mail: metal_working@mail.ru; metal_working@corp.nstu.ru Journal “Obrabotka Metallov – Metal Working and Material Science” is indexed in the world's largest abstracting bibliographic and scientometric databases Web of Science and Scopus. Journal “Obrabotka Metallov” (“Metal Working & Material Science”) has entered into an electronic licensing relationship with EBSCO Publishing, the world's leading aggregator of full text journals, magazines and eBooks. The full text of JOURNAL can be found in the EBSCOhost™ databases.
OBRABOTKAMETALLOV Vol. 26 No. 1 2024 4 EDITORIAL COUNCIL EDITORIAL COUNCIL CHAIRMAN: Nikolai V. Pustovoy, D.Sc. (Engineering), Professor, President, Novosibirsk State Technical University, Novosibirsk, Russian Federation MEMBERS: The Federative Republic of Brazil: Alberto Moreira Jorge Junior, Dr.-Ing., Full Professor; Federal University of São Carlos, São Carlos The Federal Republic of Germany: Moniko Greif, Dr.-Ing., Professor, Hochschule RheinMain University of Applied Sciences, Russelsheim Florian Nürnberger, Dr.-Ing., Chief Engineer and Head of the Department “Technology of Materials”, Leibniz Universität Hannover, Garbsen; Thomas Hassel, Dr.-Ing., Head of Underwater Technology Center Hanover, Leibniz Universität Hannover, Garbsen The Spain: Andrey L. Chuvilin, Ph.D. (Physics and Mathematics), Ikerbasque Research Professor, Head of Electron Microscopy Laboratory “CIC nanoGUNE”, San Sebastian The Republic of Belarus: Fyodor I. Panteleenko, D.Sc. (Engineering), Professor, First Vice-Rector, Corresponding Member of National Academy of Sciences of Belarus, Belarusian National Technical University, Minsk The Ukraine: Sergiy V. Kovalevskyy, D.Sc. (Engineering), Professor, Vice Rector for Research and Academic Aff airs, Donbass State Engineering Academy, Kramatorsk The Russian Federation: Vladimir G. Atapin, D.Sc. (Engineering), Professor, Novosibirsk State Technical University, Novosibirsk; Victor P. Balkov, Deputy general director, Research and Development Tooling Institute “VNIIINSTRUMENT”, Moscow; Vladimir A. Bataev, D.Sc. (Engineering), Professor, Novosibirsk State Technical University, Novosibirsk; Vladimir G. Burov, D.Sc. (Engineering), Professor, Novosibirsk State Technical University, Novosibirsk; Aleksandr N. Korotkov, D.Sc. (Engineering), Professor, Kuzbass State Technical University, Kemerovo; Dmitry V. Lobanov, D.Sc. (Engineering), Associate Professor, I.N. Ulianov Chuvash State University, Cheboksary; Aleksey V. Makarov, D.Sc. (Engineering), Corresponding Member of RAS, Head of division, Head of laboratory (Laboratory of Mechanical Properties) M.N. Miheev Institute of Metal Physics, Russian Academy of Sciences (Ural Branch), Yekaterinburg; Aleksandr G. Ovcharenko, D.Sc. (Engineering), Professor, Biysk Technological Institute, Biysk; Yuriy N. Saraev, D.Sc. (Engineering), Professor, V.P. Larionov Institute of the Physical-Technical Problems of the North of the Siberian Branch of the RAS, Yakutsk; Alexander S. Yanyushkin, D.Sc. (Engineering), Professor, I.N. Ulianov Chuvash State University, Cheboksary
Vol. 26 No. 1 2024 5 CONTENTS OBRABOTKAMETALLOV TECHNOLOGY Kuts V.V., Oleshitsky A.V., Grechukhin A.N., Grigorov I.Y. Investigation of changes in geometrical parameters of GMAW surfaced specimens under the infl uence of longitudinal magnetic fi eld on electric arc....................................... 6 Saprykina N.А., Chebodaeva V.V., Saprykin A.А., Sharkeev Y.P., Ibragimov E.А., Guseva T.S. Optimization of selective laser melting modes of powder composition of the AlSiMg system................................................................. 22 Gubin D.S., Kisel’ A.G. Features of calculating the cutting temperature during high-speed milling of aluminum alloys without the use of cutting fl uid............................................................................................................................................. 38 EQUIPMENT. INSTRUMENTS Borisov M.A., Lobanov D.V., Zvorygin A.S., Skeeba V.Y. Adaptation of the CNC system of the machine to the conditions of combined processing...................................................................................................................................... 55 Nosenko V.A., Bagaiskov Y.S., Mirocedi A.E., GorbunovA.S. Elastic hones for polishing tooth profi les of heat-treated spur wheels for special applications..................................................................................................................................... 66 Podgornyj Y.I., Skeeba V.Y., Martynova T.G., Lobanov D.V., Martyushev N.V., Papko S.S., Rozhnov E.E., Yulusov I.S. Synthesis of the heddle drive mechanism....................................................................................................... 80 MATERIAL SCIENCE Ragazin A.A., Aryshenskii V.Y., Konovalov S.V., Aryshenskii E.V., Bakhtegareev I.D. Study of the eff ect of hafnium and erbium content on the formation of microstructure in aluminium alloy 1590 cast into a copper chill mold............................................................................................................................................................................ 99 Zorin I.A., Aryshenskii E.V., Drits A.M., Konovalov S.V. Study of evolution of microstructure and mechanical properties in aluminum alloy 1570 with the addition of 0.5 % hafnium........................................................................... 113 Karlina Y.I., Kononenko R.V., Ivantsivsky V.V., Popov M.A., Deryugin F.F., Byankin V.E. Relationship between microstructure and impact toughness of weld metals in pipe high-strength low-alloy steels (research review)..................... 129 Patil N.G., Saraf A.R., Kulkarni A.P Semi empirical modeling of cutting temperature and surface roughness in turning of engineering materials with TiAlN coated carbide tool................................................................................. 155 Sawant D., Bulakh R., Jatti V., Chinchanikar S., Mishra A., Sefene E.M. Investigation on the electrical discharge machining of cryogenic treated beryllium copper (BeCu) alloys........................................................................................ 175 Karlina A.I., Kondratiev V.V., Sysoev I.A., Kolosov A.D., Konstantinova M.V., Guseva E.A. Study of the eff ect of a combined modifi er from silicon production waste on the properties of gray cast iron................................................. 194 EDITORIALMATERIALS 212 FOUNDERS MATERIALS 223 CONTENTS
OBRABOTKAMETALLOV Vol. 26 No. 1 2024 TECHNOLOGY Features of calculating the cutting temperature during high-speed milling of aluminum alloys without the use of cutting fl uid Dmitry Gubin 1, a, Anton Kisel’ 2, b, * 1 Omsk State Technical University, 11 Prospekt Mira, Omsk, 644050, Russian Federation 2 Kaliningrad State Technical University, 1 Sovetsky Prospekt, Kaliningrad, 236022, Russian Federation a https://orcid.org/0000-0003-1825-1310, gubin.89@list.ru; b https://orcid.org/0000-0002-8014-0550, kisel1988@mail.ru Obrabotka metallov - Metal Working and Material Science Journal homepage: http://journals.nstu.ru/obrabotka_metallov Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science. 2024 vol. 26 no. 1 pp. 38–54 ISSN: 1994-6309 (print) / 2541-819X (online) DOI: 10.17212/1994-6309-2024-26.1-38-54 ART I CLE I NFO Article history: Received: 19 October 2023 Revised: 16 November 2023 Accepted: 22 January 2024 Available online: 15 March 2024 Keywords: Cutting temperature High-speed milling Aluminum alloy Homologous temperature Thermal imager Forecasting Specifi c work Yield strength ABSTRACT Introduction. The calculation of temperature during high-speed milling of aluminum alloys is of interest, since temperature can act as one of the main limiting factors in choosing rational milling modes. This is especially important when milling thin-walled products used in aircraft construction, since its high values can lead to local warping of the structure. It is not possible to control the temperature factor in production conditions, which makes it necessary to develop a mathematical model for calculating temperature. The purpose of the work is to develop a methodology for predicting the cutting temperature during high-speed milling of aluminum alloy workpieces for cutting conditions, in which it is not possible to use cutting fl uid. Methods. This paper presents experimental studies of the cutting temperature during high-speed milling of aluminum alloy workpieces without the use of cutting fl uid using non-contact temperature measurement methods. The results obtained were used to determine the coeffi cients substituted into formulas for calculating temperatures on the front and back surfaces of the cutting blade. Results and discussions. Based on the results of experimental tests and theoretical modeling, a temperature graph is drawn up. A comparison of experimental studies of milling of aluminum alloy D16T, with changing cutting conditions (the cutting speed changed) with theoretical data, gave a satisfactory result. The average relative error when comparing experimental data with theoretical one is 6.05 %. Based on experimental data, it can be concluded that the comparison of experimental data for measuring cutting temperatures is in satisfactory agreement with the proposed method of theoretical calculation of temperatures. The advantage of this technique is that it allows, without time-consuming and costly experimental studies, theoretically calculate (forecast) the temperatures on the front and back surfaces of the cutting blade, as well as the cutting temperature, for those narrow milling conditions, where eff ective heat removal from the cutting zone is impossible. It can also be used for milling aluminum alloys, the mechanical and thermophysical properties of which diff er. For citation: Gubin D.S., Kisel’ A.G. Features of calculating the cutting temperature during high-speed milling of aluminum alloys without the use of cutting fl uid. Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science, 2024, vol. 26, no. 1, pp. 38–54. DOI: 10.17212/1994-6309-2024-26.1-38-54. (In Russian). ______ * Corresponding author Kisel’ Anton G., Ph.D. (Engineering), Associate Professor Kaliningrad State Technical University, 1 Sovetsky Prospekt, 236022, Kaliningrad, Russian Federation Tel.: +7 999 458-08-25, e-mail: kisel1988@mail.ru Introduction The high-speed metal milling process is characterized by a high intensity of heat release. Determining the maximum temperature value and its distribution over the cutting surfaces of the tool is important, since it aff ects the choice of cutting modes, tool durability, and the quality of the machined surface of the part [1, 2, 3]. Thus, the maximum temperature values in determining the processing strategy act as one of the main limiting factors of cutting. The mechanism of heat generation during cutting is quite complex, however, three main factors can be distinguished: plastic deformation of the material, inhomogeneous shear and friction of the chips against the front surface of the tool, as well as friction of the back surface of the tool
OBRABOTKAMETALLOV TECHNOLOGY Vol. 26 No. 1 2024 against the workpiece material being processed. The heat caused by these processes heats the chip material to a temperature of 350–450 °C [4, 5, 6, 7] (this temperature range is typical for milling aluminum alloys). The resulting heat spreads into the workpiece and the tool at a rate that largely depends on the physical characteristics of the material being processed [8, 9]. The heat distribution in the cutting area can be divided into two sections – the temperature on the front surface, depending on the feed, the geometry of the cutting blade (front angle, angle of inclination of the cutting edge, angle in plan, angle of elevation of the screw groove, etc.), and the temperature on the back surface, depending on the number of revolutions, the width of the chamfer in wearing process. The calculation of the contact temperatures on the front and back surfaces of the tool, as well as the cutting temperature of the cutting blade for milling aluminum alloys is based on: – changes in mechanical properties (ultimate strength, percentage of elongation) at increased test temperatures; – taking into account the combined eff ect of processes such as deformation and strain rate on the change in the value of the yield stress; – taking into account the thermal and physical characteristics of the material being processed (heat conduction and thermal diff usivity coeffi cients), as well as the density of the material. The temperature calculations during high-speed milling of aluminum alloys are of interest because temperature is a limiting factor in choosing a processing strategy. For example, when milling a wafer profi le inside a fuel tank for launch vehicles, it is not possible to use cutting fl uid. The thickness of the outer wall of the fuel tank is 2–3 mm [7, 10, 11]. In this milling process, the temperature on the surfaces of the cutting blade acts as a limiting factor, since its high values can lead to local warping of the structure [12, 13, 14]. It is not possible to control the temperature factor at production fi eld. Therefore, it is necessary to calculate rational milling modes in which the cutting temperature does not exceed acceptable values [9, 15]. In connection with the above, there is a necessity to develop a mathematical model for high-speed milling of aluminum alloys, which, as a fi rst approximation, takes into account the combined eff ect of temperature, strain rate and strain magnitude on the change in the yield stress of the processed aluminum alloy. The resulting model will make it possible to calculate temperatures on various surfaces of the cutting tool, as well as the cutting temperature in high-speed milling conditions, for cases where it is not possible to use cutting fl uid. The purpose of this paper is to develop a methodology for calculating the cutting temperature during high-speed milling of aluminum alloy workpieces. To achieve this purpose, it is necessary to solve the following tasks: 1) to create a defi ning equation for the specifi c work of deformation during cutting; 2) to solve the defi ning equation and fi nd its positions of extremum, which are heat sources; 3) to derive theoretical dependencies that allow calculating the temperature in the cutting zone during high-speed milling of aluminum alloy workpieces; 4) to conduct experimental studies to determine the cutting temperature at the specifi ed parameters; 5) to compare the theoretical and experimental data obtained and draw a conclusion about the accuracy of predicting the cutting temperature in a calculated way. Methods The defi ning equation for calculating temperature is the dependence of the change in the ultimate strength of the processed material on three constituent factors that arise during cutting (milling) – temperature, deformation and strain rate. Each of these factors will be considered separately and justifi ed. In conditions of small strain (for example, during tension or compression) andminor changes in temperature and strain rate, the change in yield stress can be described by the law of simple loading [16, 17]: ε σ ε σ ε 0 0 ( ) m T æç ö÷ ÷ = çç ÷ çè ÷ø , (1)
OBRABOTKAMETALLOV Vol. 26 No. 1 2024 TECHNOLOGY where where ε0 is the strain corresponding to the stress σ0; ε is the current value of the strain; m is the coeffi cient of deformation hardening equal to 0.3T ′ (where T ′ is the homological temperature of the processed material). However, equation (1) cannot be used to determine the yield stress for highly dynamic cutting processes (which include high-speed milling), since it does not take into account changes in deformation temperature and strain rate for changes in yield stress. In addition, the deformation temperature and the strain rate have a joint eff ect on the change in the yield stress, and are not free multipliers, as stated in a number of papers [18, 19]. The infl uence of temperature and strain rate in various equations for modeling changes in yield stress is taken into account by introducing appropriate multipliers. In particular, at present, the most popular JohnsonCook plasticity model, which determines the behavior of a material during hardening, takes into account the infl uence of the strain rate on the change in yield stress using the dynamic coeffi cient Kε [17, 20]. However, in the Johnson-Cook equation, the dynamic factor does not depend on temperature changes [21], while experimental data obtained by a number of scientists [16, 22, 23] confi rm the combined eff ect of strain rate and temperature on the dynamic factor (fi gure 1). Fig. 1. Dependence of the Dynamic factor on the Homologous temperature [21, 24] The diagram (fi gure 1) shows empirical results describing the infl uence of such factors as strain rate and homological temperature on the value of the dynamicity coeffi cient, as well as values approximated for the same conditions for the Johnson-Cook plasticity model [21]. In experiments, the strain rate varied by 1,000 and 2,000 times. And the change in homological temperature was achieved due to various processing materials (copper, steel, lead, aluminum). A group of aluminum alloys D16T, AMg6, 2024-T3 was selected for the research because it has similar physical properties and can be used for the manufacture of fuel tanks in the aircraft and rocket industry. The calculations carried out in this research were performed on the basis of the dependences of the change in the actual ultimate strength on temperature during high-temperature tests of aluminum alloys (Table 1) [18, 19]. Based on Table 1, graphs of the change in ultimate strength versus test temperature were plotted (fi gure 2). These graphs were approximated by an exponential curve with an accuracy of 0.9351 for the D16T alloy and 0.9544 for the AMg6M alloy, which gives satisfactory results. Exponential extrapolation was chosen due to the fact that exponential equations are easier to integrate and diff erentiate than, for example, equations with polynomial dependence (although polynomial interpolation is a little more accurate), and linear approximation gives less accurate values for alloy D16T and is 0.8971, and for alloy AMg6M practically does not diff er from exponential and is 0.9318.
OBRABOTKAMETALLOV TECHNOLOGY Vol. 26 No. 1 2024 Ta b l e 1 Strength and temperature characteristics obtained during monotonic tensile tests of aluminum alloy specimens Material (aluminium alloy) Test temperature t, (°C) Ultimate strength σu, (MPa) Ultimate elongation δ, (%) Ultimate true strength Su, (MPa) Homologous temperature increment Ratio of ultimate true strength at room temperature to ultimate true strength at test temperature D16T* 20 460 19 523.6 0.31 1 150 380 19 452.2 0.45 0.86 200 330 11 366.3 0.5 0.7 250 220 13 248.6 0.56 0.47 300 150 13 169.5 0.61 0.32 AMg6M* 20 320 0.24 396.8 0.32 1 100 300 0.3 390 0.4 0.98 150 250 0.37 342.5 0.46 0.97 200 190 0.43 271.7 0.51 0.68 250 160 0.45 232 0.57 0.58 300 130 0.48 192.4 0.62 0.48 20 320 0.24 396.8 0.32 1 100 300 0.3 390 0.4 0.98 * rolled semi-fabricated product (sheets) a b Fig. 2. Changes in the mechanical properties of aluminum alloys D16T (a) and AMg6M (b)
OBRABOTKAMETALLOV Vol. 26 No. 1 2024 TECHNOLOGY For these dependencies, an equation of the infl uence of temperature on the yield stress can be compiled: Δ τ 20 , h T p b S e ¢ - = ⋅ (2) where Sb20° is the value of the actual ultimate strength at room temperature; ∆Т ′ is the increment of the homological temperature; h is the empirical coeffi cient of temperature softening. Taking into account the experience of other researchers and based on experimental data (fi gure 1), it is possible to write the equation for the dynamic coeffi cient, taking into account temperature and strain rate, in the following form: Δ ε ε ε 0 , k T K ¢ æç ö÷ = çç ÷÷ çè ÷ø (3) where ε is the current value of the strain rate; ε 0 is the minimum value of the strain rate; k is an empirical constant. From the above stated, it is possible to make a defi ning equation for the change in yield stress, taking into account the infl uence of deformation, strain rate and temperature: Δ Δ τ ε ε ε ε 0 0 ; m k T p h T u A e S ¢ ¢ - æ ö æ ö ÷ ÷ ç ÷ ç ÷ = ç ÷ ç ÷ ç ÷ ç ÷ ç ç è ø è ø (4) Δ ε τ ε , p m h T p u A K e S ¢ - = (5) where εm p is the multiplier responsible for the deformation hardening of the material; ε K is the dynamic coeffi cient; Δ h T e ¢ - is the multiplier responsible for the temperature softening of the material; A is the deformation coeffi cient; Su is the ultimate true strength. However, in equation (5), deformation, strain rate and temperature act as three independent factors [21]. For example, a variation in the homological temperature can be achieved by heating the material being processed, and a modifi cation of the deformation can be achieved by changing the geometry of the cutting blade (front angle). Therefore, using such a formula will lead to errors. In connection with this, it is necessary to move from the defi ning equation (5) to the specifi c work. Specifi c work for the process of cutting materials in general and in particular for milling aluminum alloys is the most convenient parameter, since it combines the dependence of yield stress and the increment of homological temperature [19, 25]: ε τ ε 0 , u W p p A =ò (6) where τp is the current value of the yield stress; εp is the current value of the deformation; εu is the fi nal value of the deformation. In the mathematical apparatus, it is most convenient to use diff erential equations to approximate calculations, and therefore it is necessary to replace the yield stress in equation (5) with the derivative of the specifi c work on deformation: τ ε . p W u p dA S d = (7) To simplify calculations, we assume that heat transfer conditions close to adiabatic occur in the chip formation zone. Then, taking into account this approximation, the specifi c work of the deformation can be written as:
OBRABOTKAMETALLOV TECHNOLOGY Vol. 26 No. 1 2024 Δ , W v A T c ¢ = (8) where v c is the specifi c thermal capacity of the processed material. By virtue of formula (8), the part of equation (5), which is responsible for the temperature factor, is a function of the specifi c work of deformation. And the following equality is fair for it: ( ) 1 , W hA A W F A e - = (9) where 1 b V melt S A C T = is a dimensionless group. Now that all the parameters responsible for changing the yield stress during milling of aluminum alloys have been determined, it is possible to write the defi ning equation in diff erential form to determine the specifi c work of deformation: εε ε 1 . W m hA A W p p dA AK e d - = (10) The dependence of specifi c work on deformation during milling aluminum alloys allows obtaining an analytical expression for constructing the fl ow curve of these alloys: εε ε 1 . W m hA A W p p A AK e d - = (11) But since aluminum alloys (in particular D16T, AMg6M, 2024–T3) are practically not strengthened during milling, due to the action of such a softening factor as temperature [19], then the construction of an analytical fl ow curve does not make sense. However, it makes sense to determine the maximum values of the yield stress, that is achieved during milling [16, 17, 20, 21]. The front surface during high-speed milling is characterized by homological temperatures above 0.5, and therefore, graphically (fi gure 1, according to Rosenberg-Eremin) the coeffi cient Kq equal to 1.8 was determined. And for the back surface (near the cutting edge) homological temperatures from 0.3 to 0.35 are characteristic; therefore, the dynamic coeffi cient Kε equal to 1.25 was also determined graphically (fi gure 1, according to Rosenberg-Eremin). After compiling a defi ning equation for modeling changes in the properties of the material being processed under high-speed milling conditions, one can proceed to calculating temperatures. However, in this work, the term “temperature” should be applied to the surface of the cutting blade (tooth) on which this temperature occurs. In this regard, it is necessary to distinguish between the temperature that occurs on diff erent parts of the cutting blade, in particular on the front and back surfaces, as well as the temperature that results from these temperatures – the cutting temperature [26]. The cutting temperature is the result of the average temperatures occurring on the front and back surfaces of the cutting blade, related to the value of the coordinates on which these temperatures are distributed. It should be noted that during milling, measuring the temperature on the front and back surfaces of the cutting blade is very diffi cult, since the cutting area is closed in front with chips, and behind with the material (workpiece) being processed. Therefore, all temperature measurements will be compared with the cutting temperature, that is, with the temperature measured by the thermal imager, in order to observe the temperature distribution on the surface under study. To calculate the cutting temperature, a suffi ciently large number of factors should be taken into account. It can be divided into factors that relate to the material being processed, factors that relate to the tool, and factors that are characteristic of the cutting process itself (turning, milling, drilling, etc.). A necessary and obligatory condition for calculating the cutting temperature is the introduction of the mechanical and physical properties of the processed material into the model. These properties and characteristics for the group of aluminum alloys presented in Table 2 [18, 19]:
OBRABOTKAMETALLOV Vol. 26 No. 1 2024 TECHNOLOGY In addition, to simulate the temperature calculation, it is necessary to take into account the geometry of the cutting tool (front angle γ, back angle α, cutting edge inclination λ, peripheral angle ϕ). It is equally important to determine the schematization of the milling process (terminal, cylindrical, end), and also take into account such parameters as the cutting depth e, the ratio of the milling width to the diameter of the cutter and the number of teeth working simultaneously. For example, a changing in the front angle γ leads to a change in the inclination of the conditional shear plane, a change in the ratio of the contact length to the thickness of the cut layer, a change in the deformation, which ultimately aff ects the change in cutting powers [24]. Changing the inclination angle of the cutting edge (angle of elevation of the screw groove) and the angle in plan (peripheral angle) leads to a change in the thickness and width of the cut layer, which also aff ects the cutting powers: ϕ λ ; sin cos t b = ⋅ (12) θ λ sin cos , z m a S = ⋅ (13) where a and b are the thickness and width of the cut layer, accordingly; t is the milling depth; Sz is the feed to the tooth; θm is the angle of contact of the milling tooth with the processed material. To improve the accuracy of calculations, such characteristics as the Peclet – Pe criterion, characterizing the speed of the heat source movement and the Peclet – KPe coeffi cient, taking into account heat exchange with the environment, were added into the model [16, 17, 27]. Changes in the properties of the processed material depending on changes in the cutting temperature were also taken into account (fi gure 3–4). Ta b l e 2 Mechanical and physical properties of aluminum alloys required for temperature calculations Material grade Ultimate strength σu, (MPa) Ultimate elongation δ, (%) Heat conductivity factor λ, (W/m·K) Volumetric specifi c heat СV, (MJ/m3·K) Temperature diff usivity coeffi cient ω, (m2/s) Density ρ, (kg/m3) D16T* 460 16 120 2.56 4.95ˑ10-5 2,800 AMg6M* 320 24 122 2.43 5.44ˑ10-5 2,640 2024–T3* 435 15 121 2.43 5.68ˑ10-5 2,780 * Rolled sheets Fig. 3. Changes in the heat conductivity coeffi cient of the studied group of materials depending on temperature changes
OBRABOTKAMETALLOV TECHNOLOGY Vol. 26 No. 1 2024 To take into account for the heat transfer between the workpiece–environment–tool system, the milling process should be considered quasi-adiabatic. Therefore, the exponent in equation (11) can be written as: Δ 1; Pe W T K A A ¢ = ⋅ ⋅ (14) 1 . u V melt S A C T = (15) Taking into account the equations (14, 15) it is possible to write the defi ning equation of specifi c work for a quasi-adiabatic process: ( ) ε ε ε 1 exp . m W p q W Pe A A K B A A K d = - (16) Now it makes sense to determine the maximum yield stress values achievable with high-speed milling of aluminum alloys for specifi c deformation work. It can be determined after diff erentiating and integrating equation (16) of the specifi c work of deformation: ε τ 0 max ; 1 m u q q q S B A K m ⋅ ⋅ ⋅ ⋅ = + (17) ( ) ε 1 1 max 1 1 . m q q Pe m m J B A A K K + æ ö + ÷ ç ÷ = ç ÷ ç ÷ ç ⋅ ⋅ ⋅ ⋅ ⋅ ÷ çè ø (18) Formulas (17) and (18) are common for both the front and back surfaces of the cutting blade. The diff erence lies in the diff erent values of the dynamic coeffi cient due to the diff erent values of homological temperatures on the contact surfaces of the tooth. For the front surface, the dynamic coeffi cient Kq is accepted as equal to 1.8, and for the back surface it is accepted as equal to 1.25. Taking into account equations (7, 8), dependences (17, 18) can be considered to be heat sources on the front and rear surfaces of the cutting blade [20, 27]. The maximum values of contact temperatures on the front and back surfaces of the cutting blade were calculated numerically from these diff erent heat sources for the back and front surfaces of the cutting blade in the MS Excel software environment. Since the studied group of aluminum alloys obeys the general law of softening for this group (fi gure 2) and can be approximated by an exponential curve with a suffi ciently high accuracy (above 0.93), any of these alloys can be selected to calculate the temperature. So, for example, the calculation performed for milling aluminum alloy D16T. The milling parameters were as follows: a carbide milling cutter with Fig. 4. Changes in Volumetric specifi c heat of the studied group of materials depending on temperature changes
OBRABOTKAMETALLOV Vol. 26 No. 1 2024 TECHNOLOGY a diameter of 10 mm with two teeth, the angle in plan ϕ = 90°, the angle of inclination of the cutting edge λ = 30°, the actual back angle α = 8°. The milling modes were as follows: V = 471 m/min; Sm = 5,490 mm/min; Sz = 0.183 mm/tooth; n = 15,000 rpm; t = 0.5 mm (fi g. 5–6). Fig. 5. Theoretical modeling of the temperature distribution on the front surface of the cutting blade Fig. 6. Theoretical modeling of the temperature distribution on the front surface of the cutting blade At the moment of cutting the cutter into the workpiece, since the pocket was being processed, it worked on both sides, therefore, passing and counter milling was implemented from diff erent sides. On subsequent passes, counter milling was performed in order to eliminate machine backlashes and improve the quality of processing. The cutting temperature was calculated based on the average values of the temperature on the front surface multiplied by the contact length of that face, and the temperature at the back surface multiplied by the width of the wear chamfer: . medium medium FrSur BackSur back cut back ñ h c h ⋅ + ⋅ = + T T T (19) This method of temperatures calculating allows clearly seeing the temperature distribution on the front and back surfaces of the cutting blade. Results and discussion A series of experiments on milling workpieces with a size of 250×40×120 mm made of aluminum alloy D16T was carried out to verify the theoretical calculation of temperatures. The mechanical characteristics and physical properties of this alloy are presented in Table 3. An uncoated end mill of the Hanita 4002 model with a diameter of 10 mm with a fl at end face, with a number of tooth equal to 2 and a cutting edge inclination of 60° was used in the tests (fi gure 7). All tests were carried out without the use of cutting fl uid. The experimental factors were the cutting speed, that is, a one-factor experiment conducted with fi ve levels of factor variation. To record the
OBRABOTKAMETALLOV TECHNOLOGY Vol. 26 No. 1 2024 Ta b l e 3 Mechanical and physical properties of the processed alloy D16T Material grade Ultimate strength σu, (MPa) Ultimate elongation δ, (%) Heat conductivity factor λ, (W/m·K) Volumetric specifi c heat СV, (MJ/m3·K) Temperature diff usivity coeffi cient ω, (m2/s) Density ρ, (kg/m3) D16T 460 10 120 2.43 5.44ˑ10−5 2,800 Fig. 7. Hanita 4002 carbide 2-tooth milling cutter temperature during milling, a non-contact method was used, which allows continuous readings to be taken at a certain distance. The registration of measurements recorded using a Fluke Ti400 thermal imager with a temperature fi eld measurement error of 2 %. In the settings of the thermal imager, the radiation coeffi cient characteristic of aluminum alloys was selected, equal to 0.25. All mechanical processing tests carried out on a multi-axis boring machine 2431SF10 with a DRU with an upgraded spindle, which allows reaching a rotation speed of 18,000 rpm. The experiments were carried out with fi xed feed values per tooth and diff erent values of cutting speed. The experimental system “tool – workpiece – thermal imager” is shown in fi gure 8. Figure 9 shows an example of non-contact temperature measurement for the following cutting modes: a) n = 8,000 rpm; V = 251.2 m/min; Sz = 0.183 mm/tooth; b) n = 10,000 rpm; V = = 314 m/min; Sz = 0.183 mm/tooth. Based on the results of the experimental data, a graph made of the temperature dependence on the change in the factor (in this case, the cutting speed) at all fi ve levels of variation (fi gure 10). To increase the accuracy of cutting temperature calculations, we also took into account the fact that the properties of the material being processed change with changes in the deformation temperature. The test results can be summarized and presented in tabular form, where the average values of the experimental cutting temperature obtained from the results of three tests for each of the fi ve levels of variation in cutting speed are calculated. The ratio errors in comparing the temperature values are also calculated (Table 4). The average cutting temperature was compared with the average temperature of the contact surfaces of the cutting blade (eq. 19) and this result can be represented as a graph (fi gure 10): Based on the results of experimental tests and theoretical modeling, a temperature graph is made (fi gure 11). As a result of the work done, a mathematical model for calculating the temperature for high-speed milling of the studied group of aluminum alloys was developed. This model is based on reference data on high-temperature deformation of aluminum alloys, data on the mechanical and thermal and Fig. 8. Experimental system for temperature measurement
OBRABOTKAMETALLOV Vol. 26 No. 1 2024 TECHNOLOGY a b Fig. 9. An example of temperature measurement for 8,000 rpm (a) and 10,000 rpm (b) with a Fluke Ti400 thermal imager Fig. 10. Experimental values of the cutting temperature physical properties of materials being processed, as well as experimental results on the study of the eff ect of deformation and strain rate on changes in the yield stress of materials during cutting. This model, as a fi rst approximation, allows predicting the temperature values for a fairly wide range of milling parameters. In our case, the cutting speed varied from 251.2 to 562.2 m/min, and the rotation speed varied from 8,000 to 18,000 rpm. The proposed solution for predicting the cutting temperature makes it possible at production fi eld, without using time-consuming and expensive temperature measurement methods, theoretically calculate the temperature value using a computer and MS Excel software environment. Conclusions The evaluation of the results allowed us to draw the following conclusions: 1. Theoretical dependences are derived that allow calculating the temperature in the cutting zone during high-speed milling of aluminum alloy workpieces. 2. Experimental studies are carried out to determine the cutting temperature at the specifi ed milling parameters. 3. Experimental data on measuring cutting temperatures are in satisfactory agreement with the proposed method of theoretical calculation of temperatures. The ratio error in comparing experimental data with theoretical data is 6.05 %.
OBRABOTKAMETALLOV TECHNOLOGY Vol. 26 No. 1 2024 Ta b l e 4 The results of experimental studies on the calculation of the cutting temperature when milling the D16T alloy and the corresponding theoretical calculations Expt. No. Speed (m/min) Texpt., (°С) Texpt., mean value (°С) Tcalc. (°С) Ratio error (%) 1 251.2 166 170.7 160 6.268307 251.2 168 251.2 178 2 314 191 179.7 170 5.397885 314 172 314 176 3 376.8 204 192.3 180 6.396256 376.8 186 376.8 187 4 471 218 208 196 5.769231 471 205 471 201 5 565.2 209 217 203 6.451613 565.2 218 565.2 224 mean value 6.056658 Fig. 11. Comparison of experimental and theoretical values of cutting temperature when milling aluminum alloy D16T The results obtained confi rm the correctness of the calculation formulas and that this technique allows, without time-consuming and costly experimental studies, theoretically calculate (forecast) the temperatures on the front and back surfaces of the cutting blade, as well as the cutting temperature, for those narrow milling conditions where eff ective heat removal from the cutting zone is impossible.
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