Vol. 24 No. 1 2022 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. We sincerely happy to announce that Journal “Obrabotka Metallov” (“Metal Working and Material Science”), ISSN 1994-6309 / E-ISSN 2541-819X is selected for coverage in Clarivate Analytics (formerly Thomson Reuters) products and services started from July 10, 2017. Beginning with No. 1 (74) 2017, this publication will be indexed and abstracted in: Emerging Sources Citation Index. 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. 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
OBRABOTKAMETALLOV Vol. 24 No. 1 2022 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; Sergey V. Kirsanov, D.Sc. (Engineering), Professor, National Research Tomsk Polytechnic University, Tomsk; 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. 23 No. 2 2021 5 CONTENTS OBRABOTKAMETALLOV TECHNOLOGY Kuznetsov V.P., Makarov A.V., Skorobogatov A.S., Skorynina P.A., Luchko S.N., Sirosh V.A., Chekan N.M. Normal force infl uence on smoothing and hardening of steel 03Cr16Ni15Mo3Ti1 surface layer during dry diamond burnishing with spherical indenter............................................................................ 6 Gubin D.S., Kisel’A.G. Calculation of temperatures during fi nishing milling of a nickel based alloys.......... 23 EQUIPMENT. INSTRUMENTS Bratan S.M., Roshchupkin S.I., Chasovitina A.S., Gupta K. The effect of the relative vibrations of the abrasive tool and the workpiece on the probability of material removing during fi nishing grinding................. 33 MATERIAL SCIENCE OzolinA.V., Sokolov E.G. Effect of mechanical activation of tungsten powder on the structure and properties of the sintered Sn-Cu-Co-W material................................................................................................................. 48 Korobov Yu.S., Alwan H.L., Makarov A.V., Kukareko V.A., Sirosh V.A., Filippov M.A., Estemirova S. Kh. Comparative study of cavitation erosion resistance of austenitic steels with different levels of metastability................................................................................................................................................... 61 Vologzanina S.A., IgolkinA.F., PeregudovA.A., Baranov I.V., Martyushev N.V. Effect of the deformation degree at low temperatures on the phase transformations and properties of metastable austenitic steels.......... 73 Filippov A.V., Shamarin N.N., Moskvichev E.N., Novitskaya O.S., Knyazhev E.O., Denisova Yu.A., Leonov A.A., Denisov V.V. Investigation of the structural-phase state and mechanical properties of ZrCrN coatings obtained by plasma-assisted vacuum arc evaporation..................................................................... 87 EDITORIALMATERIALS Guidelines for Writing a Scientifi c Paper ............................................................................................................ 103 Abstract requirements ......................................................................................................................................... 107 Rules for authors ................................................................................................................................................. 111 FOUNDERS MATERIALS 119 CONTENTS
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 4 1 2 The effect of the relative vibrations of the abrasive tool and the workpiece on the probability of material removing during fi nishing grinding Sergey Bratan 1, a,*, Stanislav Roshchupkin 1, b, Anastasia Chasovitina 1, c, Kapil Gupta2, d 1 Sevastopol State University, 33 Universitetskaya str., Sevastopol, 299053, Russian Federation 2 University of Johannesburg, 7225 John Orr Building Doornfontein Campus, Johannesburg, 2028, South Africa a https://orcid.org/0000-0002-9033-1174, serg.bratan@gmail.com, b https://orcid.org/0000-0003-2040-2560, st.roshchupkin@yandex.ru, c https://orcid.org/0000-0001-6800-9392, nastya.chasovitina@mail.ru, d https://orcid.org/0000-0002-1939-894X, kgupta@uj.ac.za Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science. 2022 vol. 24 no. 1 pp. 33–47 ISSN: 1994-6309 (print) / 2541-819X (online) DOI: 10.17212/1994-6309-2022-24.1-33-47 Obrabotka metallov - Metal Working and Material Science Journal homepage: http://journals.nstu.ru/obrabotka_metallov ART I CLE I NFO Article history: Received: 30 December 2021 Revised: 21 January 2022 Accepted: 15 February 2022 Available online: 15 March 2022 Keywords: Grinding of titanium Abrasive grain Microcutting The contact area of the workpiece with the tool Probability of material removing Probability of material not removing Funding The work was carried out with the support of the Priority-2030 program of Sevastopol State University (strategic project No. 2). Acknowledgements Research were conducted at core facility “Structure, mechanical and physical properties of materials”. ABSTRACT Introduction. Grinding remains the most effi cient and effective method of fi nal fi nishing that is indispensable in the production of high-precision parts. The characteristic features of grinding materials are that the removal of the material roughness of the workpiece surface occurs due to the stochastic interaction of the grains of the abrasive material with the surface of the workpiece, in the presence of mutual oscillatory movements of the abrasive tool and the workpiece being processed. During processing workpieces with abrasive tools, the material is removed by a large number of grains that do not have a regular geometry and are randomly located on the working surface. This makes it necessary to apply probability theory and the theory of random processes in mathematical simulation of operations. In real conditions, during grinding, the contact of the wheel with the workpiece is carried out with a periodically changing depth due to machine vibrations, tool shape deviations from roundness, unbalance of the wheel or insuffi cient rigidity of the workpiece. To eliminate the infl uence of vibrations in production, tools with soft ligaments are used, the value of longitudinal and transverse feeds is reduced, but all these measures lead to a decrease in the operation effi ciency, which is extremely undesirable. To avoid cost losses, mathematical models are needed that adequately describe the process, taking into account the infl uence of vibrations on the output indicators of the grinding process. The purpose of the work is to create a theoretical and probabilistic model of material removing during fi nishing and fi ne grinding, which allows, taking into account the relative vibrations of the abrasive tool and the workpiece, to trace the patterns of its removal in the contact zone. The research methods are mathematical and physical simulation using the basic provisions of probability theory, the laws of distribution of random variables, as well as the theory of cutting and the theory of deformable solids. Results and discussion. The developed mathematical models allow tracing the effect on the removal of the material of the superimposition of single sections on each other during the fi nal grinding of materials. The proposed dependencies show the regularity of the stock removal within the arc of contact of the grinding wheel with the workpiece. The considered features of the change in the probability of material removal when the treated surface comes into contact with an abrasive tool in the presence of vibrations, the proposed analytical dependences are valid for a wide range of grinding modes, wheel characteristics and a number of other technological factors. The expressions obtained allow fi nding the amount of material removal also for the schemes of end, profi le, fl at and round external and internal grinding, for which it is necessary to know the magnitude of relative vibrations. However, the parameters of the technological system do not remain constant, but change over time, for example, as a result of wear of the grinding wheel. To assess the state of the technological system, experimental studies are carried out taking into account the above changes over the period of durability of the grinding wheel. For citation: Bratan S.M., Roshchupkin S.I., Chasovitina A.S., Gupta K. The effect of the relative vibrations of the abrasive tool and the workpiece on the probability of material removing during fi nishing grinding. Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science, 2022, vol. 24, no. 1, pp. 33–47. DOI: 10.17212/1994-6309-2022-24.1-33-47. (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
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 4 No. 1 2022 Introduction The development of science and technology sets the task of wide application in the designs of products of electrical engineering, instrumentation engineering, nuclear energy, rocket science, aircraft engineering, space technology, medicine and, more recently, in general engineering, new materials, which are subject to increased requirements for heat resistance, wear resistance, corrosion resistance and chemical resistance. Industrial enterprises are faced with the challenges of effi cient processing of the above materials. In the context of the development of a market economy, the most important factor in the success of an enterprise is the creation of technological processes that ensure the satisfaction of consumer needs. These include reducing the cost of manufacturing range while ensuring high performance characteristics of products, increasing the productivity of creating products with desired properties, for example, in the production of a friction pair, it is necessary to technologically ensure the optimal structure of the surface layer of the working surfaces of parts in the shortest possible time, creating a surface microrelief at the stage of machining parts close to equilibrium. This approach will reduce the running-in stage of the friction pair and increase its service life [1]. An analysis of existing research in the fi eld of material processing shows that, despite the presence of a large number of high-precision processing methods, such as ultrasonic, laser, high-speed milling, and others, grinding remains the most used and effi cient method in the manufacture of high-precision parts [2–6]. Grinding remains the most effi cient and effective method of fi nal fi nishing that is indispensable in the production of high-precision parts. The characteristic features of grinding materials are that the removal of the material roughness of the workpiece surface occurs due to the stochastic interaction of the grains of the abrasive material with the surface of the workpiece, in the presence of mutual oscillatory movements of the abrasive tool and the workpiece being processed. Considerable attention is paid to the study of grinding processes in the works of A.I. Grabchenko, V.L. Dobroskoka, V.I. Kalchenko, F.N. Novikova, M.D. Uzunyan, V.A. Fedorovich, L.N. Filimonova, A.V. Yakimov and other authors who, using various statistical and probabilistic methods, obtained calculated dependencies in relation to specifi c grinding schemes and conditions. The authors have shown that any conclusions about the number of working grains, about its percentage with grains on the surface of the wheel can have real meaning only in relation to specifi c conditions inherent in this process, which is associated with the nonstationarity of grinding operations. The fi rst mathematical models of abrasive-diamond machining, refl ecting the dynamic properties of processes, its stochastic nature, as well as the nonstationarity of the states of technological operations, were obtained and published by Yu.K. Novoselov in 1971. In 1975, publications of A.V. Korolev appeared, which used a similar approach. The above works have made a signifi cant contribution to the development of the theory of shaping of ground surfaces, however, it does not take into account the specifi cs of products processing in the presence of relative vibrations of the wheel and the workpiece on the output indicators of the grinding operation, therefore, it has a limited scope [7–10]. During processing workpieces with abrasive tools, the material is removed by a large number of grains that do not have a regular geometry and are randomly located on the working surface. This makes it necessary to apply probability theory and the theory of random processes in mathematical simulation of operations [11–14]. In real conditions, during grinding, the contact of the wheel with the workpiece is carried out with a periodically changing depth due to machine vibrations, tool shape deviations from roundness, unbalance of the wheel or insuffi cient rigidity of the workpiece. To eliminate the infl uence of vibrations in production, tools with soft ligaments are used, the value of longitudinal and transverse feeds is reduced, but all these measures lead to a decrease in the operation effi ciency, which is extremely undesirable. To avoid cost losses, mathematical models are needed that adequately describe the process, taking into account the infl uence of vibrations on the output indicators of the grinding process [15–19].
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 4 1 2 Based on the above, the purpose of this work is is to create a theoretical and probabilistic model of material removing during fi nishing and fi ne grinding, which allows, taking into account the relative vibrations of the abrasive tool and the workpiece, to trace the patterns of its removal in the contact zone. The research methods The presence of mutual oscillatory movements of the abrasive tool and the workpiece being processed is a characteristic feature of the grinding process. Oscillatory movements arise due to the imbalance of the rotating parts of the machine, vibrations coming from outside, self-oscillations that accompany the cutting process. The frequency of forced oscillations for grinding machines according to P.I. Liashcheritsyn is 150–350 Hz, the frequency of self-oscillations is 300–900 Hz [1]. The presence of relative oscillatory movements of the grinding wheel and the workpiece leads to a change in the size and shape of the contact zone, to a distortion of the trajectories of the relative movement of the tops of abrasive grains in the material being processed, to a change in the current depth of microcutting, Figure 1. Relative displacements in the direction of the center line of the grinding head and the workpiece, regardless of the reasons that caused it, can be described by the equation: cos( ) i i yi i Y A , (1) where i A , i , yi – amplitude, cyclic frequency and initial phase of deviations f t ; – contact time of the surface with the tool. The current value of the microcutting depth z t depends on the radius vectors of the workpiece r and a wheel R, center-to-center distance A (see Fig. 1). For the most protruding grains, it can be determined by the equation: 2 2 ( ) ( ) f f e z D d z t z t t d D D , (2) where D, d are the diameters of the tool and the workpiece, respectively, e D is the equivalent diameter, z is the distance of the workpiece section to the main plane. When the workpiece rotates, the section of the machined surface passes in the contact zone from point A to point B. The depth of cut in the absence of vibrations changes monotonously (line 1) from zero to f t and from f t to zero, the current contact time is determined as u z V . For point A z L , 0 , for point B z L , 2 u L V . Fig.1. Infl uence of vibrations on the depth of microcutting during internal grinding
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 4 No. 1 2022 For a surface section passing through the zone of contact between the workpiece and the wheel, the instantaneous depth of microcutting by single abrasive grains, taking into account (1) and (2), can be described by the function: 2 ( ) cos i i f i yi i e u z z t k t A D V . (3) To describe the patterns of material removing in the contact zone, the authors of [20] proposed the concepts of material removing probability ( ) P M and material not removing probability ( ) P M . The fi rst indicator ( ) P M is determined by the probability of an event in which the material at the point of the treated surface is removed. The second indicator ( ) P M is the probability of an event in which the material is not removed from the treated surface. The sum of the probabilities, as the probabilities of opposite events, is equal to one, and its values depend on the position of the point in the contact zone. For the processing of workpieces with abrasive tools, the probability of material removal is calculated from the dependence: ( ) ( , ) ( ) 1 exp a y a y P M , (4) where ( ) a y is an indicator that determines the probability of material removal at the level y before the surface enters the zone of contact between the workpiece and the wheel; ( , ) a y is an indicator that characterizes the change in the areas of dimples formed by the sum of the profi les of abrasive grains passing through the considered section of the workpiece after the corresponding contacts of the grains with the surface of the workpiece. During time turns through an angle and a section passes through it with an arc length ( ) k u V V or taking into account that u z V we get ( ) k u u z V V V . Of the total number of grains that have passed through the section, the width of the profi le g b will have grains whose vertices are located in the layer of the wheel ( ) k u u V V z u V . The number of such vertices is calculated from the density of its distribution over the depth of the tool ( ) f u ( ) ( ) k u g u V V n f u z u V . (5) In the presence of vibrations, the width of the vertex contour corresponding to a given level is nonstationary, it does not remain constant, but changes over time. Its value can be described by a power dependence [1], which, taking into account the fact that u z V , is calculated by the equation: 2 ( ) ( ) cos m m m g b b b f y e u z z b y C h C t k y u C t y u A D V . (6) To describe the distribution density of the abrasive grains vertices, O. Coyle suggested using a following dependence [17]: 1 ( ) h f u C u 1 ( ) h f u C u , (7) where h C – distribution curve proportionality factor:
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 4 1 2 h u C H , where u H – thickness of the tool working surface layer in contact with the workpiece. Taking into account the above, dependence (7) can be represented as: 1 ( ) u f u u H , (8) where – density function parameter. The change in the parameter ( , ) a y is determined by the increment of the sum of the transverse dimensions of the abrasive grains profi les: ( , ) ( ) ( ) ( ) c g g k u a y K n b f u u V V , (9) where c K – chip formation coeffi cient, which takes into account that not all material is removed from the volume of the scratch mark, but part of it is displaced and forms piles along the edges of the scratch mark. After integrating (9), we obtain an integral equation for calculating the parameter ( , ) a y z in the contact zone ( ) 0 ( , ) ( ) y t k y z k u c g g u L V V a y z K n b f u dudz V , (10) where y L – the distance from the main plane to the intersection of the level with the conventional outer surface of the tool is determined from the equation ( ) yi ki e L t y D . (11) The models of grain tops and densities of its distribution over depth considered above make it possible to establish functional relationships between the probability of material not removing with technological factors. When substituting the obtained expressions g b and ( ) f u from equations (6) and (8) into equation (10), the last one takes the following form: 2 ( ) 1 0 ( ) ( , ) cos y m t k y z c b k u g f y e u L u u K C V V n z z a y z t y u A u dudz D V V H . (12) After integrating the resulting equation with respect to u, we obtain 2 ( 1) ( ) ( ) ( , ) cos ( 1) y m z c b k u g f w y e u L u u m K C V V n z z a y z t y A dz D V m V H , (13) where ( 1) m , ( ) , ( 1) m – corresponding gamma-functions. Дальнейшее интегрирование уравнения (13) возможно только при известных значениях показателей , m и значениях y характеризующих начальную фазу отклонений. Вид зависимостей определяется их суммой. При 1, 5 , 0, 5 m и 2 2 b g C . Further integration of equation (13) is possible only when values of indicators , m, and values y characterizing the initial phase of deviations are known. The type of dependencies is determined by its sum. When For = 1.5 , = 0.5 m and = 2 2 b g C p :
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 4 No. 1 2022 3/2 3 2 ( ) ( , ) 8 y g c g k u u u n K V V a y z V H , (14) where 2 2 cos y y z f y e u L z z t y A dz D V . Denote , y u z V and perform the integration for cases when the initial phase is equal to: 1– 0(2 ) y ; 2– y ; 3.– 2 y ; 4.– 3 2 y 3 3 2 2 5 5 2 2 2 2 2 2( ) ( ) 2( ) 3 2 5 4 ( cos cos ) (sin 2 sin 2 ) 4 f y y f y e e u y u e t y L z z L A t y L z D D AV L z A V D 2 2 2 2 3 2 sin sin 2 2 ( ) (sin sin ) u y u u e f e e AV L z AV V D t y D D , (15) 3 3 2 2 5 5 2 2 2 2 2( ) 2( ) 3 2 5 4 cos cos (sin 2 sin 2 ) 4 f y y f y e e u y u e t y L z z L A t y L z D D AV L z A V D 2 2 2 2 3 2 sin sin 2 2 ( ) (sin sin ) u y u u e f e e AV L z AV V D t y D D , (16) 3 3 2 2 5 5 2 2 2 2 2 2( ) 2( ) 3 2 5 4 sin sin (sin 2 sin 2 ) 4 f y y f y e e u y u e t y L z z L A t y L z D D AV L z A V D 2 2 2 2 3 2 cos cos 2 2 ( ) (cos cos ) u y u u e f e e AV L z AV V D t y D D (17) 3 3 2 2 5 5 3 2 2 2 2 2 2( ) ( ) 2( ) 3 2 5 4 ( sin sin ) (sin 2 sin 2 ) 4 f y y f y e e u y u e t y L z z L A t y L z D D AV L z A V D 2 2 2 2 3 2 cos cos 2 2 ( ) (cos cos ) u y u u e f e e AV L z AV V D t y D D . (18)
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 4 1 2 Results and Discussion The calculation of the probability of material removing in the presence of vibrations in any area of the contact zone with a known initial state of the surface is calculated by substituting the indicator ( , ) a y a from expression (14) into equation (4) taking into account the parameter , for each of the cases when the initial phase is: 0(2 ) y (15); y (16); 0(2 ) y (17); 0(2 ) (18). For clarity of the calculation procedure, let’s consider a numerical example. Let’s calculate the probability of not removing and the probability of removing the material when grinding holes with a diameter of 150 mm in workpieces made of titanium alloy VT3-1 with a tool AW 60 × 25 × 13 63C F90 M 7 BA 35 m/s (at a wheel speed of 35 m/s, a workpiece speed of 0.25 m/s, longitudinal feed – 33 mm/s, transverse feed – 0.005 mm/stroke). From the calculation of the balance of displacements [20], we determine that for the given processing conditions 6 11.54 10 m f t . Based on the research data [20, 21, 22], we accept: = 0.9 m c K ; 6 = 7.31 10 m z ; 2 = 15.86 grains/mm z n . For the considered conditions 4 =3.397 10 m y L , 628 rad/s , 100 Hz . The calculation is performed according to equations (2), (3), (4) for the level 6 10.38 10 m y at 0.8 2 y L z , = 0.2 f A t . Let’s calculate the parameters y u z V and y y u L V for the cases when the initial phase is equal to 0 y : 4 628( 0.136 10 ) = 0= 0.341, 0.25 –4 628 3.397 10 0 0.853 0.25 Отсюда получим sin 0.3344 , cos 0.942 , sin = 0.753 , cos 0.658 , sin2 = 0.63 , sin2 = 0.991 . After substituting the numerical values of the parameters in (15), we obtain: -6 -6 4 3 3 3 4 5 3 5 0 2 2(11.54 10 10.36 10 ) (3.397 10 ) ( 0.136 10 ) (3.397 10 ) ( 0.136 10 ) 3 0.1 5 0.1 Y 2 2 3 4 6 6 6 0.136 10 +3.397 10 2.308 10 +2 11.54 10 10.38 10 2 6 2 6 2 4 3 2 (2.308 10 ) 0.25( 0.63+0.991) 4 2.308 10 0.25 3.397 10 0.942 ( ) ±0.136 10 0.658 4 628 0.1 628 6 2 2 6 6 3 2 2.308 10 0.25 2 0.25 + 0.1 628 11.54 10 10.38 10 ( 0.3344 + 0.753) 0.1 2 ) 6 8 ( 6 4 2 3 2 15 2 2.308 10 0.25 (3.397 10 ) 0.3344 ( 0.136 10 ) 0.753 = 1.22 10 0.1 628 . Then, according to equation (14), we calculate the value of the indicator, taking into account vibrations ( , ) ( , ) a y a y z : 6 6 15 6 3/2 3 3.14 15.866 10 1 2 7.31 10 (35±0.25)1.22 10 ( , ) = 0.282 8 0.25 (11.54 10 ) a y z .
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 4 No. 1 2022 In the absence of vibrations, the indicator ( , ) cm a y z can be calculated according to the dependence [21]: 2 3 5 3/2 3 3 2 ( )( ) 2 8 ( , ) 5 15 8 g c g k u f cm y y y u u n K V V t y z z a y z z L L L V H (19) When substituting the above values of the parameters into expression (19), we obtain the value of the indicator in the absence of vibrations: 6 6 6 6 2 cm 6 3/2 3 3.14 15.86 10 1 2 7.31 10 (35±0.25)(11.54 10 -10.38 10 ) , 8 0 ( ) .25(11.54 10 ) a y z 3 5 3 3 3 4 4 3 4 2 0.136 10 0.136 10 8 0.136 10 3.397 10 = 0.014 15 5 3.397 10 3.397 10 . The absolute error A of calculations is cm , ( , ) 0.014 0.313 0.299, ( ) A a y z a y z and relative error A of calculations is: 0.299 100 % 100 % 95.5 % ( , ) 0.313 A A a y z . Experimental studies were carried out to verify the calculation results. On a Knuth RSM 500 CNC machine, holes with a diameter of 150 mm in workpieces made of titanium alloy VT3-1 with a tool AW 60 × 25 × 13 63C F90 M 7 BA 35 m/s (at a wheel speed of 35 m/s, a workpiece speed of 0.25 m/s, longitudinal feed – 33 mm/s, transverse feed – 0.005 mm/stroke). Profi le diagrams were taken from the prototypes after the grinding operation, according to which the value of the indicator experiment( , ) a y z was estimated (Table 1) and the relative error was determined (Table 2). The probability of an event characterizing removing the surface layer at the level y = 0.004 mm at the value of the indicator a0 = 0.545 is calculated according to the equation by substituting the calculation results ( , ) a y into expression (4): 0 ( , ) 0.545 0.282 ( ) 1 exp 1 exp 0.576. a a y P M The probability of no material removal, as an opposite event, can be determined from the total probability formula: ( ) 1 ( ) 1 0.576 0.424. P M P M Ta b l e 1 The values of the indicator a characterizing the change in the probability of material removing at the considered level The value of the indicator a characterizing the change in the probability of material removing at the considered level Номер опыта 1 2 3 4 5 experiment( , ) a y z 0.392 0.313 0.264 0.4 0.305 cm( , ) a y z 0.014 ( , ) a y z 0.282
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 4 1 2 Ta b l e 2 Relative error of calculations Experimental (actual) values Relative error experiment( 100 %, % , ) A A a y z experiment( , ) a y z cm( , ) a y z ( , ) a y z 0.392 96.4 28.06 0.313 91.05 9.9 0.264 94.6 6.82 0.4 96.5 29.5 0.305 95.4 7.54 The obtained calculations show that the probability of removing at values 0.2 f A t , 0.8 2 y L z , 4 3.397 10 m y L , 6 10.38 10 y m , 6 11,54 10 m f t , 628 rad/s , = 100 Hz is 0.424. This means that 42 % of the material will be removed and 58 % of the processed material will stay on the surface in the form of microroughness. For other levels and values of oscillation frequencies of the considered example, the calculated data on the probability of material removing are shown in Fig. 2 and 3 and in table 3. Fig. 2. Change in the probability of material removing along the contact zone from the value of relative vibrations during internal grinding Fig. 3. Change in the probability of material removing along the contact zone from the level of grain penetration in the workpiece material during internal grinding at a relative vibration value of 100 Hz
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 4 No. 1 2022 Ta b l e 3 The change in the probability of material removing along the contact zone at different levels depends on the values of the relative vibrations of the grinding wheel and the workpiece during grinding holes z, m ( ) P M , Hz 100 200 300 400 = 0.3 , m f y t –0.36 0.925 0.816 0.984 0.973 –0.27 0.977 0.931 0.994 0.992 –0.18 0.995 0.958 0.998 0.997 –0.09 0.999 0.987 0.999 0.999 0 1 0.997 1 1 0.09 1 0.999 1 1 0.18 1 1 1 1 0.27 1 1 1 1 0.36 1 1 1 1 = 0.6 , m f y t –0.27 0.769 0.477 0.623 0.844 –0.20 0.853 0.548 0.652 0.876 –0.14 0.914 0.652 0.699 0.899 –0.07 0.953 0.763 0.769 0.922 0 0.976 0.855 0.843 0.947 0.07 0.988 0.917 0.901 0.963 0.014 0.994 0.954 0.929 0.977 0.20 0.997 0.974 0.961 0.984 0.27 0.999 0.985 0.974 0.989 = 0.9 , m f y t –0.14 0.576 0.488 0.45 0.465 –0.11 0.608 0.515 0.463 0.466 –0.07 0.639 0.546 0.485 0.475 –0.03 0.669 0.579 0.514 0.497 0 0.698 0.612 0.548 0.526 0.03 0.724 0.644 0.581 0.558 0.07 0.749 0.673 0.613 0.587 0.11 0.770 0.699 0.64 0.61 0.14 0.788 0.721 0.661 0.629 The analysis of the data obtained gives a clear illustration of the patterns of material removal along the contact zone at different levels at different frequencies of the relative oscillations of the grinding wheel and the workpiece. The data obtained show that when passing the surface of the contact zone of the wheel with the workpiece, the probability of metal removing increases within the actual depth of cut, and decreases with an increase in the frequency of relative vibrations of the tool and the workpiece at all levels. The probability increases most intensively at the value when the abrasive grains pass through the main plane. This is explained by the fact that during this period the depth of cut is maximum and the largest number of abrasive grains is involved in cutting. Due to the presence of vibrations, the removal still grows intensively even after the grains have passed the level of the main plane.
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 4 1 2 Conclusions The developed mathematical models allow tracing the effect on the removal of the material of the superimposition of single sections on each other during the fi nal grinding of materials. The proposed dependencies show the regularity of the stock removal within the arc of contact of the grinding wheel with the workpiece. The considered features of the change in the probability of material removal when the treated surface comes into contact with an abrasive tool in the presence of vibrations, the proposed analytical dependences are valid for a wide range of grinding modes, wheel characteristics and a number of other technological factors [20–22]. The expressions obtained allow fi nding the amount of material removal also for the schemes of end, profi le, fl at and round external and internal grinding, for which it is necessary to know the magnitude of relative vibrations. However, the parameters of the technological system do not remain constant, but change over time, for example, as a result of wear of the grinding wheel. To assess the state of the technological system, experimental studies are carried out taking into account the above changes over the period of durability of the grinding wheel. One of the ways to determine the parameters of a technological system is a full-scale experiment. Experimental confi rmation of the results was carried out on a CNC grinding machine Knuth RSM 500 CNC in the Common Use Center “Engineering and industrial design” SevGU when processing elements of the experimental system – a pump developed at Sevastopol State University. The design of this product includes parts (leading rotor) made of VT3-1 titanium alloy, the quality parameters of which are ensured only during grinding operations. References 1. Novoselov Y., Bogutsky V., Shron L. Patterns of removing material in workpiece – grinding wheel contact area. Procedia Engineering, 2017, vol. 206, pp. 991–996. DOI: 10.1016/j.proeng.2017.10.583. 2. Kassen G., Werner G. Kinematische Kenngrößen des Schleifvorganges [Kinematic parameters of the grinding process]. Industrie-Anzeiger = Industry Scoreboard, 1969, no. 87, pp. 91–95. (In German). 3. Malkin S., Guo C. Grinding technology: theory and applications of machining with abrasives. New York, Industrial Press, 2008. 372 р. ISBN 978-0-8311-3247-7. 4. Hou Z.B., Komanduri R. On the mechanics of the grinding process. Pt. 1. Stochastic nature of the grinding process. International Journal of Machine Tools and Manufacture, 2003, vol. 43, pp. 1579–1593. DOI: 10.1016/ S0890-6955(03)00186-X. 5. Lajmert P., Sikora V., Ostrowski D. A dynamic model of cylindrical plunge grinding process for chatter phenomena investigation. MATEC Web of Conferences, 2018, vol. 148, pp. 09004–09008. DOI: 10.1051/ matecconf/20181480900. 6. Leonesio M., Parenti P., Cassinari A., Bianchi G., Monn M. A time-domain surface grinding model for dynamic simulation. Procedia CIRP, 2012, vol. 4, pp. 166–171. DOI: 10.1016/j.procir.2012.10.030. 7. Sidorov D., Sazonov S., Revenko D. Building a dynamic model of the internal cylindrical grinding process. Procedia Engineering, 2016, vol. 150, pp. 400–405. DOI: 10.1016/j.proeng.2016.06.739. 8. Zhang N., Kirpitchenko I., Liu D.K. Dynamic model of the grinding process. Journal of Sound and Vibration, 2005, vol. 280, pp. 425–432. DOI: 10.1016/j.jsv.2003.12.006. 9. Ahrens M., Damm J., Dagen M., Denkena B., Ortmaier T. Estimation of dynamic grinding wheel wear in plunge grinding. Procedia CIRP, 2017, vol. 58, pp. 422–427. DOI: 10.1016/j.procir.2017.03.247. 10. Garitaonandia I., Fernandes M.H., Albizuri J. Dynamic model of a centerless grinding machine based on an updated FE model. International Journal of Machine Tools and Manufacture, 2008, vol. 48, pp. 832–840. DOI: 10.1016/j.ijmachtools.2007.12.001. 11. Tawakolia T., Reinecke H., Vesali A. An experimental study on the dynamic behavior of grinding wheels in high effi ciency deep grinding. Procedia CIRP, 2012, vol. 1, pp. 382–387. DOI: 10.1016/j.procir.2012.04.068. 12. Jung J., Kim P., Kim H., Seok J. Dynamic modeling and simulation of a nonlinear, non-autonomous grinding system considering spatially periodic waviness on workpiece surface. Simulation Modeling Practice and Theory, 2015, vol. 57, pp. 88–99. DOI: 10.1016/j.simpat.2015.06.005.
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