Vol. 25 No. 1 2023 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. WEB OF SCIENCE
OBRABOTKAMETALLOV Vol. 25 No. 1 2023 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 Affairs, 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. Gerasenko, Director, Scientifi c and Production company “Mashservispribor”, Novosibirsk; Aleksandr N. Korotkov, D.Sc. (Engineering), Professor, Kuzbass State Technical University, Kemerovo; Evgeniy A. Kudryashov, D.Sc. (Engineering), Professor, Southwest State University, Kursk; 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, Institute of Strength Physics and Materials Science, Russian Academy of Sciences (Siberian Branch), Tomsk; Alexander S. Yanyushkin, D.Sc. (Engineering), Professor, I.N. Ulianov Chuvash State University, Cheboksary
Vol. 25 No. 1 2023 5 CONTENTS OBRABOTKAMETALLOV TECHNOLOGY Ryaboshuk S.V., Kovalev P.V. Analysis of the reasons for the formation of defects in the 12-Cr18-Ni10-Ti steel billets and development of recommendations for its elimination............................................................... 6 Lapshin V.P., Moiseev D.V. Determination of the optimal metal processing mode when analyzing the dynamics of cutting control systems................................................................................................................... 16 Gimadeev M.R., Li A.A., Berkun V.O., Stelmakov V.A. Experimental study of the dynamics of the machining process by ball-end mills.................................................................................................................. 44 Bratan S.M., Chasovitina A.S. Simulation of the relationship between input factors and output indicators of the internal grinding process, considering the mutual vibrations of the tool and the workpiece................... 57 EQUIPMENT. INSTRUMENTS Podgornyj Yu.I., KirillovA.V., Skeeba V.Yu., Martynova T.G., Lobanov D.V., Martyushev N.V. Synthesis of the drive mechanism of the continuous production machine......................................................................... 71 Lobanov D.V., Rafanova O.S. Methodology for criteria analysis of multivariant system................................ 85 MATERIAL SCIENCE Sokolov A.G., Bobylyov E.E., Popov R.A. Diffusion coatings formation features, obtained by complex chemical-thermal treatment on the structural steels............................................................................................ 98 Filippov A.V., Khoroshko E.S., Shamarin N.N., Kolubaev E.A., Tarasov S.Yu. Study of the properties of silicon bronze-based alloys printed using electron beam additive manufacturing technology................... 110 Lysykh S.A., Kornopoltsev V.N., Mishigdorzhiyn U.L., Kharaev Yu.P., Tikhonov A.G., Ivancivsky V.V., Vakhrushev N.V. The effect of borocoppering duration on the composition, microstructure and microhardness of the surface of carbon and alloy steels............................................................................................................. 131 EDITORIALMATERIALS 149 FOUNDERS MATERIALS 159 CONTENTS
OBRABOTKAMETALLOV Vol. 25 No. 1 2023 TECHNOLOGY Simulation of the relationship between input factors and output indicators of the internal grinding process, considering the mutual vibrations of the tool and the workpiece Sergey Bratan a, *, Anastasia Chasovitina b Sevastopol State University, 33 Universitetskaya str., Sevastopol, 299053, Russian Federation a https://orcid.org/0000-0002-9033-1174, serg.bratan@gmail.com, b https://orcid.org/0000-0001-6800-9392, nastya.chasovitina@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. 2023 vol. 25 no. 1 pp. 57–70 ISSN: 1994-6309 (print) / 2541-819X (online) DOI: 10.17212/1994-6309-2023-25.1-57-70 ART I CLE I NFO Article history: Received: 23 December 2022 Revised: 14 January 2023 Accepted: 25 January 2023 Available online: 15 March 2023 Keywords: Grinding of titanium Vibrations Mutual vibrations Pinholes Processing modes Balance of movements in the technological system Acknowledgements Research were conducted at core facility “Structure, mechanical and physical properties of materials”. ABSTRACT Introduction. In real production conditions, the technological modes recommended in the scientific literature do not reflect the declared qualities, due to the fact that it does not take into account many factors inherent in the process of finishing grinding, for example, its stochastic nature, changes in its dynamic properties, an increase in mutual vibrations of the tool and the workpiece that appear due to changes in the state of the technological system, for example, an increase in vibrations machine tool due to uneven tool wear, etc. All previously developed models have a limited scope of application, it does not take into account the fact that the appearance of vibrations leads to fluctuations in the depth of grinding, with accidental contact of grains with the material being processed, where one group of grains cuts off the material, the other gets into the trace of scratches left by previous grains, etc. This leads to changes in the values of material removal, surface roughness and other parameters of the technological system, which directly affects the accuracy of processing and the quality of the machined surfaces. The purpose of the work is to develop mathematical models that establish the relationship between the processing modes and the current parameters of the contact zone during the fine grinding of pinholes, taking into account the mutual vibrations of the tool and the workpiece. The research methods are mathematical simulation using the basic provisions of the theory of abrasive-diamond processing. Results and discussion. The interrelations between the cutting modes and the current input parameters of the contact zone when grinding pinholes are established, taking into account the mutual vibrations of the tool and the workpiece, which make it possible to determine the parameters of the system at the output to avoid cost losses, including reducing the number of defective products and time costs. Non-stationary mathematical dependences are constructed that allow determining the cutting modes during the implementation of the grinding cycle, taking into account the magnitude of relative vibrations and the initial phase. It is established that instead of a steady process, harmonic oscillations are observed caused by deviations in the shape of the circle, the intensity of tool wear and other factors, all of the above has a significant impact on the quality of the machined surface. The obtained models are universal for various characteristics of the tool, however, for a more adequate description of the process, mathematical dependencies are needed that take into account the wear of the tool on various binders, which is the task of further research. For citation: Bratan S.M., Chasovitina A.S. Simulation of the relationship between input factors and output indicators of the internal grinding process, considering the mutual vibrations of the tool and the workpiece. Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science, 2023, vol. 25, no. 1, pp. 57–70. DOI: 10.17212/1994-6309-2023-25.1-57-70. (In Russian). ______ * Corresponding author Bratan Sergey M., D. Sc. (Engineering), Professor Sevastopol State University 33 Universitetskaya str, 299053, Sevastopol, Russian Federation Tel.: +7 (978)7155019, e-mail: serg.bratan@gmail.com Introduction To date, the machine-building industry implements many methods of processing materials with high accuracy, including ultrasonic and laser processing, high-speed milling processes, as well as abrasivediamond processing operations, and specifically the internal grinding process. The grinding process has become widespread due to high efficiency, low costs, along with its accuracy and the quality of the processed surface layer [1–7].
OBRABOTKAMETALLOV technology Vol. 25 No. 1 2023 Despite the wide variety of models describing the processes of abrasive diamond processing, there are practically no scientifically-based recommendations in the modern literature that make it possible to guarantee the receipt of the specified product quality parameters in non-stationary conditions of the technological process [8–12]. Therefore, a comprehensive study of the regularities of the surface geometry generation processes, the development of mathematical models will ensure the creation of highly efficient technological processes and optimal designs of abrasive tools on this basis. The analysis of works in the field of grinding theory allows concluding that all existing models of abrasive-diamond machining processes can be divided into two classes. The first class (pulse models) includes mathematical dependencies that simulate the impact of single abrasive grains on the workpiece. The processed surface is formed as a set of grain traces, which in a section perpendicular to the direction of the cutting speed are identical to the profile of the radius of the vertex of the abrasive grain, for example, mathematical models, developed by I.M. Brozgol, D.V. Korolev, E.N. Maslov, Yu.K. Novoselov, V.A. Nosenko and others [13–17]. The second class (geometric models) includes mathematical dependencies that simulate the effect on the workpiece by a set of elementary cutting profiles. On this basis, work has been carried out on the mechanisms of surface roughness formation, for example, mathematical models developed by Yu.R. Witenberg, Yu.V. Linnik, S.A. Popov, V.A. Shchegolev, A.P. Husu and other scientists [18–23]. In real production conditions, the technological modes, recommended in the above-reviewed works, and reference literature do not reflect the declared qualities, due to the fact that it does not take into account many factors inherent in the process of finishing grinding, for example, its stochastic nature, changes in its dynamic properties, an increase in mutual vibrations of the tool and the workpiece, which appear due to changes in the state of the technological system, for example, an increase in machine vibrations due to uneven tool wear, etc. All previously developed models have a limited scope of application, it does not take into account the fact that the appearance of vibrations leads to fluctuations in the depth of grinding, with accidental grains contact with the material being processed, where one group of grains cuts off the material, the other falls into the trace of scratches left by previous grains, etc. This leads to changes in the values of material removal, surface roughness and other parameters of the technological system, which directly affects the accuracy of processing and the quality of the processed surfaces. To compensate for calculation errors in real production conditions, various technological approaches are used, for example, tools with soft binders are used, feed rates are reduced and other methods are used, which reduce the efficiency of the operation and increases the cost of manufactured products. Advanced approach to problem is to continue research of grinding operations, (in particular internal), in the course of which it is necessary to identify and describe the relationship between input factors and output indicators of the process. Based on the established relationships, it is necessary to build mathematical models that adequately simulate the grinding process, taking into account the mutual vibrations of the tool and the workpiece. To date, one of the most time-consuming technological processes is the grinding operation. The amount of products where internal grinding was used as a finishing machining is not inferior to the amount of products, processed by the external method. However, internal grinding is more difficult due to the heavy flow of the machining process and the lower rigidity of the cutting tools. In connection with the above, the purpose of this paper is to develop mathematical models that establish the relationship between the working modes and the current parameters of the contact zone during fine grinding of precise holes, taking into account the mutual vibrations of the tool and the workpiece. Research methodology The scheme of the finishing process of the hole (internal grinding) is shown in Fig. After inserting a workpiece into a chuck, the tool and the workpiece are set to rotate at a circumferential speed Vu and Vk accordingly. When moving the grinding head in the direction of radial feed Sy, the difference between the radius vectors of the workpiece and the tool becomes less than the center distance Ai, and an area of interpenetration of the tool into the workpiece material – the contact zone – is formed [24].
OBRABOTKAMETALLOV Vol. 25 No. 1 2023 technology In accordance with the dimensional scheme of the internal grinding process, shown in Fig., the displacement balance equation takes the form: 1 i yi fi i i yi A S N t R r A ω - D = + = D - D + D + D , (1) where i A D – current changes in the value of the center-to-center distance, due to the radial feed of the grinding head, m; yi S – radial tool feed, m; N – preload, m; fi t D – changing the actual cutting depth, m; i R D – current tool wear, m; 1 i rω - D – the amount of material removed before the current revolution, m; yi A D – current change in elastic deformations. During internal grinding, an uneven removal of the allowance is observed, a waviness is formed on the surface of the workpiece [25, 26]. Based on this, it can be assumed that not only the removal of the allowance will change according to the harmonic law, but also other parameters included in the balance equation of displacements. For a visual demonstration of this phenomenon, the processing cycle by solving the displacement balance equation will be calculated [27, 28]. Initial data: the material of the workpiece is titanium alloy VT3, d = 150 mm, grinding head AW 60×25×13 63C F90 M 7 B A 35 m/s , circumferential speed of the wheel Vk = 35m/s, workpiece speed Vu = 0.25 m/s, radial feed Sui = 0.005 mm/r, number of grains per unit area ng = 15.86·106 pcs/m2, corner radius the grain vertex r g = 7.31·10 -6 m). Results and its discussion When calculating the parameters of the penetration stage, the values of the transverse feed Sy1 = 5·10 -6 m and preload N = 10×10-6 m are preset, according to the values, given in the reference literature [16]. Let’s perform the calculation of the first revolution: 1) Find the sum of the parameters of preload and cross feed: 6 6 6 1 1 5 10 10 10 15 10 y A S N - - - D = + = ⋅ + ⋅ = ⋅ , m 2) Determine the increment of elastic deformations in accordance with the equation: yi TS y A P D = ω ⋅ D , (2) Internal grinding process scheme
OBRABOTKAMETALLOV technology Vol. 25 No. 1 2023 where ωTS is a system compliance; ωTS = 30·10 -9 m·N; DP y is increment of the normal component of the cutting force; DPy ≥ 0. Let’s assume that there is no increment of the normal component of the cutting force at the first revolution DPy = 0, therefore, after substituting the parameter values into the formula, we get: 1 0 y A D = , m 3) Calculate the depth of micro-cutting. On the previous revolution, there is no radial removal of the material Dr0 = 0. Given the assumption that the wear of the grinding wheel on the first revolution is equal to zero, DR1 = 0, then the equation (1) is defined as: 6 1 1 15 10 f A t - D = D = ⋅ , m From here, the value of the depth of micro-cutting is calculated: 6 6 1 1 1 0 15 10 15 10 f y f t S t - - = + D = + ⋅ = ⋅ , m 4) At the current revolution, the value of the radial removal of the material can be determined by the equation: 2 0,4 7 13 15 3 ( ) fi i u fi c k u g e g t r V t K V V n D ω D = p p + + Y + r , (3) where Kc – chip formation coefficient, Kc = 0.85; Vu – the speed of rotation of the workpiece, m/s; Vk – the speed of rotation of the wheel, m/s; ng – number of grains per unit area, pcs/m2; r g – corner radius the grain vertex, m; De – equivalent diameter, m. The equivalent diameter is calculated by the equation: e D d D D d ⋅ = - , (4) where D – diameter of the grinding wheel, m; d – the diameter of the workpiece, m. After substituting the data into equation (4), we get: 150 60 0.1 150 60 e D ⋅ = = - , m. The value of the variable Y it will be calculated depending on the initial phase of the deviations. For yy = 0×(2p) and yy = p: 2 2 2 3 2 0,5 1,5 3 2 15 2 sin 1 2 15 sin 2 15 sin 15 16 32 2 2 u f u u f e e e A V t A V A V A t D D D ω ω ω ω γ - γ γ Y = + + + ω ω ω or 2 2 2 3 2 0,5 1,5 3 2 15 1 sin ( ) 15 sin 2 15 sin 15 16 32 2 2 u f u u f e e e A V t A V A V A t D D D ω ω ω ω - γ γ γ Y = + + + ω ω ω , If yy = p/2 and yy = 3p/2: 2 2 0,5 15 sin 2 15 16 32 u f e A V A t D ω ω γ Y = - ω ,
OBRABOTKAMETALLOV Vol. 25 No. 1 2023 technology where Aω – amplitude, µm; ω – cyclic frequency, rad/s; yy – the initial phase of vibrations; variable 0,5 0,5 ( ) f e u t y D V ω ⋅ - ⋅ γ = , where y – the level in question. At the initial phase of relative fluctuations yy = 0×(2p) and amplitude Aω = 0.2×tfi, ω = 628 rad/s material removal at the current speed, taking into account vibrations: 6 2 6 1 0,4 6 12 6 6 (15 10 ) 5.89 10 7 13 0, 25 15 10 0.17 10 15 3 0.85(35 0.25)15.866 10 0.1 7.31 10 r - - ω - - - ⋅ D = = ⋅ p p ⋅ + + ⋅ + ⋅ ⋅ ⋅ , m 5) Calculate the thickness of the surface layer, in which the roughness is located, according to: i fi i H t rω = - D , (5) When substituting parameter values into equation (5), we get: 6 6 6 15 10 5.89 10 9.11 10 i fi i H t r - - - ω = - D = ⋅ - ⋅ = ⋅ , m. 6) Calculate the cutting force as follows: max max 1 sin 3 2 0.055 0.061 sin yi k g g g i e i g g s P L n h H D H h b = r + r τ b , (6) where Lk – grinding wheel height, m; hgmax – grain wear, hgmax = 10·10 -6 m; b and b 1 – cutting angles of abrasive material, b = 22° and b1 = 34°; τs – shear stress, N/m2. The shear stress is defined as: 1, 5 s σ τ = , (7) where σ – ultimate strength of the material, σ = 2·109 N/m2, 9 8 2 10 13.33 10 1.5 s ⋅ τ = = ⋅ , N/m2 By substituting the data into equation (6), the cutting force is determined as: 3 6 6 6 6 1 3 2 25 10 15.866 10 7.31 10 10 10 9.11 10 0.1 y P - - - - = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ × 6 6 6 8 0.3746 0.055 9.11 10 0.061 7.31 10 10 10 13.33 10 2.899 0.5591 - - - × ⋅ ⋅ ⋅ + ⋅ ⋅ ⋅ ⋅ ⋅ = , N. 7) Clarify previously obtained calculated values Dtf1, Dr1, Py1. The value of the increment of elastic deformations is determined as: 9 8 1 1 0 ( ) 30 10 (2.899 0) 8.698 10 y TS y TS y y A P P P - - D = ω ⋅ D = ω ⋅ - = ⋅ ⋅ - = ⋅ , m. The micro-cutting depth’ increment and the micro-cutting depth values are calculated, respectively as follows: 6 8 6 1 1 1 15 10 8.698 10 14.91 10 f y t A A - - - D = D - D = ⋅ - ⋅ = ⋅ , m, 6 6 1 0 1 0 14.91 10 14.91 10 f f f t t t - - = + D = + ⋅ = ⋅ , m.
OBRABOTKAMETALLOV technology Vol. 25 No. 1 2023 The amount of material removal will be: 6 2 6 1 0,4 6 12 6 6 (14.91 10 ) 5.844 10 7 13 0.25 14.91 10 0.17 10 15 3 0.85 (35 0.25) 15.866 10 0.1 7.31 10 r - - ω - - - ⋅ D = = ⋅ p p ⋅ + + ⋅ ⋅ + ⋅ ⋅ ⋅ ⋅ , m The thickness of the layer in which the roughness is distributed: 6 6 6 1 1 1 14.91 10 5.844 10 9.069 10 f H t r - - - ω = - D = ⋅ - ⋅ = ⋅ , m The cutting load: 3 6 6 6 6 1 3 2 25 10 15.866 10 7.31 10 10 10 9.069 10 0.1 y P - - - - = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ × 6 6 6 8 0.3746 0.055 9.069 10 0.061 7.31 10 10 10 13.33 10 2.884 0.5591 - - - × ⋅ ⋅ + ⋅ ⋅ ⋅ ⋅ = , N. 8) The distance from the deepest valley to the midline of the profile is calculated according to: 2 fi i mi t r W ω - D = . (8) Insert numeric values into the equation (8): 6 6 6 1 14.91 10 5.844 10 4.535 10 2 m W - - - ⋅ - ⋅ = = ⋅ , m One of the final stages of calculating the parameters of the revolution under consideration is the comparison of the value Wm1 with the amount of Drω1, 1 1 m W rω ≤ D 4.535 × 10–6 ≤ 5.844 · 10–6. Due to the fact that the value of Drω1 exceeds the value of Wm1, then the value of the arithmetic mean length of the profile Ra is determined as: 0.4 0.6 1 0.4 0.4 0.2 0.2 0,4 6 0.6 6 0.4 0.4 6 2 6 2 0.25 ( ) 0.25 0.25 (14.91 10 ) 1.041 10 . 0.85 (0.25 35) (15.866 10 ) 0.1 (7.31 10 ) u f a c u k g e g V t R K V V n D - - - = = + r ⋅ ⋅ = = ⋅ + ⋅ ⋅ ⋅ Second revolution. 1) Find the sum of the parameters of preload and transverse feed: 6 6 6 2 5 10 10 10 15 10 y A S N - - - D = + = ⋅ + ⋅ = ⋅ , m. 2) Determine the depth of micro-cutting: 6 6 6 2 1 5 10 14.91 10 19.91 10 f y f t S t - - - = + = ⋅ + ⋅ = ⋅ , m.
OBRABOTKAMETALLOV Vol. 25 No. 1 2023 technology 3) Calculate the value of the radial removal of the material at the current turn: 6 2 6 2 0.4 6 12 6 6 (19.91 10 ) 8.513 10 7 13 0.25 19.91 10 0.24 10 15 3 0.85(35 0.25)15.866 10 0.1 7.31 10 r - - ω - - - ⋅ D = = ⋅ p p ⋅ + + ⋅ + ⋅ ⋅ ⋅ , m. 4) Calculate the thickness of the layer, in which the roughness is located: 6 6 6 2 2 2 19, 91 10 8, 513 10 11, 4 10 f H t r - - - ω = - D = ⋅ - ⋅ = ⋅ , m. 5) The cutting load at the current speed is equal to: 3 6 6 6 6 2 3 2 25 10 15.866 10 7.31 10 10 10 11.4 10 0.1 y P - - - - = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ × 6 6 6 8 0.3746 0.055 11.4 10 0.061 7.31 10 10 10 13.33 10 3.789 0.5591 - - - × ⋅ ⋅ ⋅ + ⋅ ⋅ ⋅ ⋅ ⋅ = , N. 6) More precise definition of the values of 2 f t D , 2 r D , 2 y P D . Increment of elastic deformations is: 9 8 2 2 1 ( ) 30 10 (3.789 2.884) 2.716 10 y TS y TS y y A P P P - - D = ω ⋅ D = ω ⋅ - = ⋅ ⋅ - = ⋅ , m. Tool wear at the current revolution can be calculated by the equation: 1 0.1 i fi R t - D = ⋅ , (9) After substituting the values into equation (9) we have: 6 7 2 1 0.1 0.1 14.91 10 14.91 10 f R t - - D = ⋅ = ⋅ ⋅ = ⋅ , m. From equation (1) we determine the increment of the depth of micro-cutting: 6 8 7 6 6 2 2 2 2 1 15 10 2.716 10 14.91 10 5.844 10 10.62 10 f y t A A R r - - - - - ω D = D - D + D - D = ⋅ - ⋅ + ⋅ - ⋅ = ⋅ , m Calculate the value of the depth of micro-cutting: 6 6 6 2 1 2 14.91 10 10.62 10 25.53 10 f f f t t t - - - = + D = ⋅ + ⋅ = ⋅ , m Radial material removal: 6 2 6 2 0.4 6 12 6 6 (25.53 10 ) 11.79 10 7 13 0.25 25.53 10 0.28 10 15 3 0.85(35 0.25)15.866 10 0.1 7.31 10 r - - ω - - - ⋅ D = = ⋅ p p ⋅ + + ⋅ + ⋅ ⋅ ⋅ , m. The thickness of the layer, in which the roughness is located, is equal to: 6 6 6 2 2 2 25.53 10 11.79 10 13.74 10 f H t r - - - ω = - D = ⋅ - ⋅ = ⋅ , m The cutting load is: 3 6 6 6 6 2 3 2 25 10 15.866 10 7.31 10 10 10 13.74 10 0.1 y P - - - - = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ × 6 6 6 8 0.3746 0.055 13.74 10 0.061 7.31 10 10 10 13.33 10 4.774 0.5591 - - - × ⋅ ⋅ ⋅ + ⋅ ⋅ ⋅ ⋅ = , N.
OBRABOTKAMETALLOV technology Vol. 25 No. 1 2023 6) The distance from the deepest valley to the midline of the profile: 6 6 2 2 6 2 25.53 10 11.79 10 6.87 10 2 2 f m t r W - - ω - - D ⋅ - ⋅ = = = ⋅ , m. Compare the values Wm2 and Drω2, 2 2 m W rω ≤ D , 6.87 × 10–6 ≤ 11.79 · 10–6, therefore, in the same way as in the previous revolution, we calculate the value of the arithmetic mean length of the profile Ra, m: 0.4 0.6 2 0.4 0.4 0.2 0.2 0.4 6 0.6 6 0.4 0.4 6 2 6 2 0.25 ( ) 0.25 0.25 (25.53 10 ) 1.438 10 . 0.85 (0.25 35) (15.866 10 ) 0.1 (7.31 10 ) u f a c u k g e g V t R K V V n D - - - = = + r ⋅ ⋅ = = ⋅ + ⋅ ⋅ ⋅ For subsequent revolutions of the embedding stage and the steady-state processing mode (Sy = const), the balance of the system is calculated according to the above methodology. No feed mode. There is no transverse feed at this stage Sy = 0 and preload N = 0 [15]. But due to elastic deformations, the grains still cutting-in and, consequently, the metal is being removed tfs > 0. The first turn. 1) The amount of preload and transverse feed is: .1 0 0 0 N À S N D = + = + = , m. 2) Tool wear is: 6 7 .1 _ . 0,1 0.1 35.52 10 35.52 10 N f St R t - - D = ⋅ = ⋅ ⋅ = ⋅ , m. 3) Increment of elastic deformations is: 9 _ .1 _ .10 _ .9 ( ) 30 10 (6.257 6.257) 0 y St TS y TS y St y St A P P P - D = ω ⋅ D = ω ⋅ - = ⋅ ⋅ - = , m. 4) Increment of the micro-cutting depth is: 7 6 6 _ .1 .1 _ .1 .1 _ .10 0 0 35.52 10 18.52 10 14.97 10 f y N St t A A R r - - - ω D = D - D + D - D = - + ⋅ - ⋅ = - ⋅ N N St , m. 5) The depth of micro-cutting is determined as: 6 6 6 _ .1 _ . _ .1 35.52 10 14.97 10 20.55 10 f N f St f N t t t - - - = + D = ⋅ - ⋅ = ⋅ , m. 6) Radial material removal is: _ .1 6 2 6 0.4 6 12 6 6 (20.55 10 ) 8.867 10 7 13 0.25 20.55 10 0.25 10 15 3 0.85(35 0.25)15.866 10 0.1 7.31 10 N r - - ω - - - ⋅ D = = ⋅ p p ⋅ + + ⋅ + ⋅ ⋅ ⋅ , m 7) The thickness of the layer, in which the roughness is located, is equal to: _ .1 6 6 6 .1 _ .1 20.55 10 8.867 10 11.68 10 N N f N H t r - - - ω = - D = ⋅ - ⋅ = ⋅ , m.
OBRABOTKAMETALLOV Vol. 25 No. 1 2023 technology 8) The cutting load is: _ .1 3 6 6 6 6 3 2 25 10 15.866 10 7.31 10 10 10 11.68 10 0.1 N y P - - - - = ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ ⋅ × 6 6 6 8 0.3746 0.055 11.68 10 0.061 7.31 10 10 10 13.33 10 3.902 0.5591 - - - × ⋅ ⋅ ⋅ + ⋅ ⋅ ⋅ ⋅ ⋅ = , N. 9) The value of the distance from the deepest valley to the midline of the profile is: _ .1 6 6 _ .1 _ .1 6 20.55 10 8.867 10 5.84 10 2 2 N f N N m t r W - - ω - - D ⋅ - ⋅ = = = ⋅ , m. Compare the values Wm_N.1 and Dr_N.1, _ .1 N m W ≤ _ .1 N rω D , 5.84 × 10–6 < 8.867 × 10–6. Due to the fact that the value of _ .1 N rω D is more than the value of _ .1 N m W , the value of the arithmetic mean length of the profile Ra, m: 0.4 0.6 1 0.4 0.4 0.2 0.2 0,4 6 0,6 6 0.4 0.4 6 2 6 2 0, 25 ( ) 0, 25 0, 25 (20, 55 10 ) 1.262 10 . 0.85 (0.25 35) (15.866 10 )0.1 (7.31 10 ) u f a c u k g e g V t R K V V n D - - - = = + r ⋅ ⋅ ⋅ = = ⋅ + ⋅ ⋅ The modes calculation continues until the value of the specified roughness Ra = 0.81·10 -6 (m) is reached. The calculated data are given in Table 1: Pl. – plunge mode, St. – steady mode, N. – no feed mode. Ta b l e 1 Calculated data No. fi t D fi t i R D 1 i rω - D yi A D i H 1 2 3 4 5 6 7 Pl. 1 14.91·10–6 14.91·10–6 0 0 8.698·10–8 9.069·10–6 Pl. 2 10.62·10–6 25.53·10–6 1.491·10–6 5.884·10–6 2.716·10–8 13.74·10–6 Pl. 3 5.737·10–6 31.27·10–6 2.553·10–6 11.79·10–6 2.413·10–8 15.78·10–6 Pl. 4 2.617·10–6 33.89·10–6 3.127·10–6 15.49·10–6 1.964·10–8 16.56·10–6 Pl. 5 1.05·10–6 34.94·10–6 3.389·10–6 17.32·10–6 1.595·10–8 16.85·10–6 St. 1 0.389·10–6 35.33·10–6 3.494·10–6 18.09·10–6 1.372·10–8 16.95·10–6 St. 2 0.14·10–6 35.47·10–6 3.53·10–6 18.38·10–6 1.267·10–8 16.98·10–8 St. 3 0.05·10–6 35.52·10–6 3.547·10–6 18.49·10–6 1.225·10–8 16.99·10–6 N.1 -14.97·10–6 20.55·10–6 3.552·10–6 18.52·10–6 0 11.68·10–6 N.2 -6.88·10–6 13.66·10–6 2.055·10–6 8.867·10–6 7.062·10–8 8.451·10–6 N.3 -3.88·10–6 9.78·10–6 1.366·10–6 5.211·10–6 3.737·10–8 6.437·10–6 3.343·10–6
OBRABOTKAMETALLOV technology Vol. 25 No. 1 2023 The data obtained show that at the stage of the steady-state process, the value of the actual depth of micro-cutting varies according to the harmonic law and is not a constant value (Δtfi ≠0) in contrast to what is recommended to be taken in the classical calculation method [16]. The results of the calculations were verified by comparing the calculated and experimental data. Grinding was carried out on a Knuth RSM 500 CNC machine, characterized by increased vibration resistance to external influences. Initial data: the material of the workpiece is titanium alloy VT3, d = 150 mm, grinding head AW 60×25×13 63C F90 M 7 B A 35 m/s , circumferential speed of the wheel Vk = 35m/s, workpiece speed Vu = 0.25 m/s, radial feed Syi = 0.005 mm/r, number of grains per unit area ng = = 15.86·106 pcs/m2, corner radius the grain vertex r g = 7.31·10 -6 m). After processing the profilograms taken from the machined blanks, the relative error of the calculated data with the results of the experiment was calculated. The data are summarized in Table 2. Ta b l e 2 Relative error of calculations No. fi t 1 i rω - D i H Relative error exp 100 % H H H D δ = , % calculated experimental Pl. 1 14.91·10–-6 0 9.069·10–6 8.16·10–6 11.13 Pl. 2 25.53·10–6 5.884·10–6 13.74·10–6 12.53·10–6 9.6 Pl. 3 31.27·10–6 11.79·10–6 15.78·10–6 17.82·10–6 11.45 Pl. 4 33.89·10–6 15.49·10–6 16.56·10–6 18.88·10–6 12.29 Pl. 5 34.94·10–6 17.32·10–6 16.85·10–6 19.87·10–6 15.2 St. 1 35.33·10–6 18.09·10–6 16.95·10–6 19.9·10–6 14.82 St. 2 35.47·10–6 18.38·10–6 16.98·10–8 19.94·10–6 14.84 St. 3 35.52·10–6 18.49·10–6 16.99·10–6 19.97·10–6 14.92 N.1 20.55·10–6 18.52·10–6 11.68·10–6 12.73·10–6 8.25 N.2 13.66·10–6 8.867·10–6 8.451·10–6 9.3·10–6 9.13 N.3 9.78·10–6 5.211·10–6 6.437·10–6 5.73·10–6 12.34 3.343·10–6 A comparison of the calculated and experimental data indicates that the accepted mathematical models provide high accuracy of calculations (the relative error is less than 15 %) and make it possible to analytically determine the values of the output parameters of the internal grinding process, taking into account the influence of the relative vibration oscillations of the grinding wheel and the workpiece. Conclusions The interrelationships of processing modes with the current parameters of the contact zone when grinding precise holes are established, taking into account the mutual fluctuations of the tool and the workpiece, which allow determining the parameters of the system at the output to avoid cost losses, including reducing the number of defective products and time costs. Constructed non-stationary mathematical dependences allow determining cutting modes during the grinding cycle implementation, taking into account the magnitude of relative vibrations and the initial phase. It is established that instead of a steady process, harmonic oscillations are observed caused by deviations in the shape of the wheel, the intensity of tool wear and other factors, all of the above has a significant impact on the quality of the machined surface.
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