Vol. 25 No. 4 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.
OBRABOTKAMETALLOV Vol. 25 No. 4 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 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, 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. 4 2023 5 CONTENTS OBRABOTKAMETALLOV TECHNOLOGY Akintseva A.V., Pereverzev P.P. Modeling the interrelation of the cutting force with the cutting depth and the volumes of the metal being removed by single grains in fl at grinding........................................................................................................................................ 6 Sharma S.S., Joshi A., Rajpoot Y.S. A systematic review of processing techniques for cellular metallic foam production................. 22 Karlina Yu.I., Kononenko R.V., Ivantsivsky V.V., Popov M.A., Deryugin F.F., Byankin V.E. Review of modern requirements for welding of pipe high-strength low-alloy steels.......................................................................................................................................... 36 Startsev E.A., Bakhmatov P.V. The infl uence of automatic arc welding modes on the geometric parameters of the seam of butt joints made of low-carbon steel, made using experimental fl ux......................................................................................................................... 61 Martyushev N.V., Kozlov V.N., Qi M., Baginskiy A.G., Han Z., Bovkun A.S. Milling martensitic steel blanks obtained using additive technologies................................................................................................................................................................................ 74 Loginov Yu.N., Zamaraeva Yu.V. Evaluation of the bars’ multichannel angular pressing scheme and its potential application in practice................................................................................................................................................................................................... 90 EQUIPMENT. INSTRUMENTS Rajpoot Y.S., SharmaA.K., Mishra V.N., Saxena K., Deepak D., Sharma S.S. Eff ect of tool pin profi le on the tensile characteristics of friction stir welded joints of AA8011.................................................................................................................................................... 105 Chinchanikar S., Gadge M.G. Performance modeling and multi-objective optimization during turning AISI 304 stainless steel using coated and coated-microblasted tools........................................................................................................................................................ 117 Ghule G.S., Sanap S., Chinchanikar S. Ultrasonic vibration-assisted hard turning of AISI 52100 steel: comparative evaluation and modeling using dimensional analysis........................................................................................................................................................ 136 Pivkin P.M., Ershov A.A., Mironov N.E., Nadykto A.B. Infl uence of the shape of the toroidal fl ank surface on the cutting wedge angles and mechanical stresses along the drill cutting edge...................................................................................................................... 151 MATERIAL SCIENCE Sokolov R.A., Muratov K.R., Venediktov A.N., Mamadaliev R.A. Infl uence of internal stresses on the intensity of corrosion processes in structural steel....................................................................................................................................................................... 167 Klimenov V.A., Kolubaev E.A., Han Z., Chumaevskii A.V., Dvilis E.S., Strelkova I.L., Drobyaz E.A., Yaremenko O.B., Kuranov A.E. Elastic modulus and hardness of Ti alloy obtained by wire-feed electron-beam additive manufacturing................... 180 Vorontsov A.V., Filippov A.V., Shamarin N.N., Moskvichev E.N., Novitskaya O.S., Knyazhev E.O., Denisova Yu.A., Leonov A.A., Denisov V.V. In situ crystal lattice analysis of nitride single-component and multilayer ZrN/CrN coatings in the process of thermal cycling.......................................................................................................................................................................................... 202 Rubtsov V.E., Panfi lov A.O., Kniazhev E.O., Nikolaeva A.V., Cheremnov A.M., Gusarova A.V., Beloborodov V.A., Chumaevskii A.V., Grinenko A.V., Kolubaev E.A. Infl uence of high-energy impact during plasma cutting on the structure and properties of surface layers of aluminum and titanium alloys................................................................................................................... 216 Bobylyov E.E., Storojenko I.D., Matorin A.A., Marchenko V.D. Features of the formation of Ni-Cr coatings obtained by diff usion alloying from low-melting liquid metal solutions..................................................................................................................................... 232 Burkov А.А., Konevtsov L.А., Dvornik М.И., Nikolenko S.V., Kulik M.A. Formation and investigation of the properties of FeWCrMoBC metallic glass coatings on carbon steel.......................................................................................................................... 244 Sharma S.S., Khatri R., Joshi A. A synergistic approach to the development of lightweight aluminium-based porous metallic foam using stir casting method........................................................................................................................................................................... 255 Strokach E.A., Kozhevnikov G.D., Pozhidaev A.A., Dobrovolsky S.V. Numerical study of titanium alloy high-velocity solid particle erosion.......................................................................................................................................................................................... 268 EDITORIALMATERIALS 284 FOUNDERS MATERIALS 295 CONTENTS
OBRABOTKAMETALLOV Vol. 25 No. 4 2023 technology Modeling the interrelation of the cutting force with the cutting depth and the volumes of the metal being removed by single grains in flat grinding Alexandra Akintseva a, *, Pavel Pereverzev b South Ural State University, 76 Lenin Ave., Chelyabinsk, 454080, Russian Federation a https://orcid.org/0000-0001-8881-8461, akintsevaav@susu.ru; b https://orcid.org/0000-0002-1416-8918, pereverzevpp@susu.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. 4 pp. 6–21 ISSN: 1994-6309 (print) / 2541-819X (online) DOI: 10.17212/1994-6309-2023-25.4-6-21 ART I CLE I NFO Article history: Received: 20 July 2023 Revised: 01 August 2023 Accepted: 15 August 2023 Available online: 15 December 2023 Keywords: Cutting mode Cutting force Cutting depth Volume of removed metal Flat grinding Cycle Machining error Funding The research was carried out at the expense of the grant of the Russian Science Foundation № 22-29-00792. ABSTRACT Introduction. The model for calculating the cutting force is the basis of the modules of CAM-systems related both to the predicting processing errors on metal-cutting machines for specified grinding conditions, and to the optimizing all parameters of the technological mode (parameters of cutting modes, cutting tools, etc.). However, due to the lack of an adequate model for calculating the cutting force presented in engineering form, such modules have not yet been developed not only for flat grinding operations, but also for all other types of metalworking. It is challenging to obtain an adequate cutting force model for flat grinding operations because it is necessary to establish the interrelation between the machine parameters of the macrocutting modes (feed, cutting speed) of the grinding wheel with the parameters of the microcutting modes — the sets of cutting grains of the wheel associated with the plastic deformation of the metal in the shear zone, microvolumes of the metal being removed and the geometry of the cutting part of the abrasive grains. The purpose of this work is to develop a force model establishing the interrelation of the cutting force with the cutting depth and the volumes of the metal being removed by single grains and the wheel as a whole on the basis of the integration of microvolumes and microforces when metal being removed by the wheel grains. Research methods. The subject of the research is the mathematical modeling of the interrelation between the cutting force and cutting modes with the parameters of microcutting by a group of single grains, based on the equality of work when metal being removed of the same volume. The methodological basis of the research is the connection between the work (energy) spent on the plastic deformation of metal by a single grain, the intensity of stresses, the intensity of deformation rates and the volume of the metal being removed by the wheel as a whole, established by S.N. Korchak. Results and discussion. The result of the study is an analytical model that reliably and adequately establishes the interrelation between the cutting force and the cutting depth, cutting modes, wheel characteristics, physical and mechanical properties of the processing material, and other main technological parameters. The field of application of the results is the possibility of using the cutting force calculation model, presented in this paper, as a basis for the development of a module for a CAM-system (a digital twin of the machining), which would allow to perform the calculation and design of optimal technological parameters of the flat grinding operation, as well as cutting modes testing according to the criterion of processing accuracy of a parts batch, considering the influence of various variable factors and real processing conditions within the manufacturing process. For citation: Akintseva A.V., Pereverzev P.P. Modeling the interrelation of the cutting force with the cutting depth and the volumes of the metal being removed by single grains in flat grinding. Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science, 2023, vol. 25, no. 4, pp. 6–21. DOI: 10.17212/1994-6309-2023-25.4-6-21. (In Russian). ______ * Corresponding author Akintseva Alexandra V., Ph.D. (Engineering), Associate Professor South Ural State University, Lenin Ave., 76, 454080, Chelyabinsk, Russian Federation Tel.: +7 (922) 633-56-57, e-mail: akintsevaav@susu.ru Introduction Flat grinding is a finishing operation subjected to high requirements on the accuracy and quality of machining. These requirements are difficult to satisfy in flat grinding because of the need to control three feeds (fig. 1); the presence of grooves, holes, etc. on machined surfaces; simultaneous machining of several workpieces during the operation; and other factors. The accuracy and quality of the machined surface directly depend on cutting modes. Currently, cutting modes are assigned using a CAM system, which is
OBRABOTKAMETALLOV technology Vol. 25 No. 4 2023 based on digitized reference literature. It is currently impossible to test cutting modes for compliance with the requirements of process design and production charts using CAM systems in a virtual environment. Manufacturers are thus forced to carry out trial processing of workpieces according to the cutting modes set by the process engineer. At the same time, cutting modes are often diminished to a safe level in order to sequentially meet the drawing requirements in the manufacture of a batch of parts, which undoubtedly leads to lost productivity. Experimental verification increases the duration of the preparatory production stage, additional time and material costs. This problem has not yet been solved due to a lack of a wide-range analytical engineering model that reliably establishes the mathematical relationship between cutting force and cutting depth, the volume of metal being removed, cutting modes, the characteristics and geometric parameters of the grinding wheel, the physical and mechanical properties of the material being machined, etc. S.N. Korchak [1] established the relationship between the cutting force of a single grain of an abrasive wheel and the physical and mechanical properties of the material being machined through shear and compression stresses, taking into account the temperature in the cutting zone. Similarly, Yu. M. Zubarev et. al. [2] and Filimonov [3] obtained calculation dependencies to find the cutting force for grinding operations, taking into account friction (internal friction coefficient, friction angle, etc.). The dependences obtained in [1] were used to develop models to calculate the cutting force for flat grinding [4–5]. Several authors have presented force dependences that take into account the processes of blunting and wear of the abrasive grains in models of the cutting force occurring during grinding [6–14]. Others have considered the impact of dynamic loads on the cutting force arising from the “contact stiffness” of manufacturing, the non-stationary nature of abrasive machining, the variable stiffness of manufacturing, etc. [15–23]. In studies by Leonesioa et. al. [15] and Li and Shin [16], the cutting force is calculated with consideration to the rigidity of the technological system and dynamic loads. Patnaik et. al. [17] calculated the cutting force by taking into account the friction coefficient of flat grinding. The papers do not present engineering formulas, which complicates its practical application in mechanical engineering. We can highlight a number of papers on the development of a cutting force model for flat grinding operations. Voronov and Veidun [24] proposed a mathematical model of flat grinding with a disk with abrasive grains distributed over a cylindrical surface with random geometric characteristics. Nosenko et. al. [25] presented a dynamic mathematical cutting force model taking into account the wear of the working wheel surface during flat grinding. Danilenko [26] studied the components of the cutting force that occur during flat grinding for a narrow range of materials (mainly various titanium alloys). Li and Yang [27] experimentally assessed changes in cutting force and roughness for flat grinding of several grades of steel. Liu et. al. [28] experimentally assessed the impact of cutting speed on cutting force and wear of a grinding wheel. An analysis of the literature showed that, despite the abundance of analytical models linking cutting forces to the depth of cutting by single cutting grains, there are still no adequate engineering models for calculating the cutting force for a given cutting depth during grinding for the wheel as a whole. The proposed models calculate a certain cutting depth and force when metal is cut with a single grain of an abrasive wheel, depending on the number of grains and other factors, in the absence of reliable a priori information on the number of cutting grains and the volumes of metal removed. These formulas cannot be used to calculate the cutting depth of a grinding wheel and the resulting cutting force or the allowance to be removed during the operation in several passes. Program depth feed changes tenfold in a stepped cycle of flat grinding (for example, from 0.05 mm/ stroke at the first stage of the cycle to 0.001 mm/min at the last stage). The number of cutting grains and the cutting depth should also be significantly reduced. However, this does not affect the cutting depth by the wheel grains in the considered force models. Considering that there are an excessive number of cutting grains on the working surface of the wheel [29], some grains pass through the contact zone without metal removing. With a tenfold decrease in the depth feed, the number of excess grains increases. There are no available methods for calculating the number of excess grains and the cutting depth with a tenfold decrease in the depth feed. In addition, it is not taken into account that the volume of the metal layer removed
OBRABOTKAMETALLOV Vol. 25 No. 4 2023 technology from the workpiece has a finite value. Models also do not calculate the volume of metal removed during microcutting; the removed metal is not summed and it is unclear when the process of removing a given metal volume will end. A significant omission in the discussed models is that the cutting force does not change depending on the wheel hardness. Thus, there is no scientific approach establishing the relationship of the cutting forces and the depths of the metal cut by a single grain with the stock removal and the cutting force that occurs during grinding with a wheel as a whole. As a result, there is no analytical engineering model, which calculates the relationship between cutting force and cutting depth in flat grinding operations. It is challenging to obtain an adequate cutting force model for flat grinding operations because it is necessary to establish the interrelation between the machine parameters of the macrocutting modes (feed, cutting speed), adjusted on the machine control panel, and parameters of the microabrasive grain cutting conditions, associated with plastic metal deformation in the shear zone, the physical and mechanical properties of the metal being machined, the back rake angle and front clearance of the grain cutting edge, blunting of the cutting edge along the back edge grain surface, cutting speed, the parameters of the contact zone of the cutting tool with the workpiece, etc. For flat grinding in particular, the volume of metal removed from the workpiece and the parameters of the three machine feeds (depth, transverse, longitudinal) should be linked to microcutting parameters: the metal shear angle in the plastic deformation zone; the length and area of contact between the wheel and the workpiece; the variable depth of the metal cut by single grains of the wheel; the stochastic nature of metal being removed by an excess number of wheel grains; the geometry of the cutting grains of the grain cutting edge, the blunting area on the back edge surface; the strength of the metal being machined; as well as the total microvolume of metal removed by all grains. The purpose of this paper is to establish the relationship between the cutting force, the cutting depth, and the volume of metal removed by single grains in flat grinding. Let us consider the main modeling stages for calculating the cutting force in flat grinding based on the equality of the volume of metal removed by a set of single grains and the same volume of metal removed by the grinding wheel as a whole (the equality of the volumes of metal removed). Research methods We will use the model of the cutting force of a single abrasive grain as the foundation for modeling cutting force during flat grinding. Metal is removed by a single grain at energy costs, most often expressed in the form of grinding energy or power. The relationship between energy and power during plastic metal deformation, as established by Korchak are expressed as [1]: ω = σe ω ∫∫∫ A d , (1) ω = = σe ω ∫∫∫ dA N d dt , (2) where А is the energy expended on the deformation of the metal volume ω, N‧m (J); N is the power required to deform the metal ω, N‧m/s (W); σ is the stress intensity in the moving volume of the deformed metal, N/m2; e is the deformation rate intensity, s-1; e is the deformation degree intensity; ω is the volume of deformed metal, m3; t is the deformation time of the metal volume ω, s. The assumptions made by Korchak are not bound to a specific type of grinding; it is also valid for the developed model of the cutting force occurring during flat grinding [1]. Fig. 1 shows the calculation scheme of a metal cutoff by the cutting edge of the abrasive grain of a wheel with a blunting area lj. Korchak adopted a free cutting pattern due to the minor influence of edge effects along the length of the cutting edge, which exceeds a hundredfold the depth of cut by a single grain of a wheel [1]. It is assumed that the shear zone is a parallelogram, since the temperature and speed grinding parameters (cutting speed of 30...60 m/s
OBRABOTKAMETALLOV technology Vol. 25 No. 4 2023 and temperature of 600...1,500 ºС) transform the metal into a state similar to an ideal plastic, and the shear zone is narrowed into a thin strip, rather than a wedge as is seen in other types of cutting. According to Korchak, the thickness m of the shear zone is 1…5 µm [1]. As a result, it is also assumed for free cutting conditions that in the parallelogram shear zone (fig. 1), the stress intensity σ and deformation rate intensity e are constant on average. The metal is sheared in the cutting zone if the abrasive grain is absolutely sharp, when the length of the cutting edge is equal to bj and the length of the blunting area along the rear face is equal to zero, i.e. lj = 0. The area of the shear zone can be described by the thickness m of the zone itself, the cut depth as, and the shear angle β1 (fig. 1). The energy of an absolutely sharp abrasive grain is expended on the plastic deformation of the metal of a volume ωj in the shear zone during the shear time ∆t, when the peak of the sharp grain of the wheel passes the distance hj (see fig. 1, the distance between points O and О1) at a speed of Vk. The volume of chips being removed (fig. 1 and 2, a) consists of a set of volumes ωj. Fig. 1. Calculation model of plastic deformation in the shear zone when cutting with a single grain: 1 – outer metal surface; 2 – cutting grain motion pattern; 3 – cutting grain We transform expression (1) with regard to the shift of the elementary metal volume ωj in the cutting zone made by the j-th grain of the wheel to calculate the energy Аj spent on the plastic deformation of the metal volume ωj (fig. 1): ω = σe ω = σeω ∫∫∫ . j A d . (3) Let us express the power Nj of metal deformation in the shear zone through the increment of the elementary metal volume ωj and the elementary shear time ∆t: ω = = σe = σeω , j j dA d N dt dt (4) given that ω = β1 , sin s j j a mb (5) where as is the thickness of the cutoff made with a sharp single grain (fig. 1 and 2, b), m; m is the thickness of the metal shear zone in the cutting zone, m; β1 is the slope angle of the reference shear plane, deg. (fig. 2, b); bj is the length of the cutting edge of a single abrasive grain, m; Nj is the power of deformation of the metal volume ωj in the shear zone, N‧m/s (W).
OBRABOTKAMETALLOV Vol. 25 No. 4 2023 technology Fig. 2. Flat grinding (a), a cutoff with a single grain, diagram of stresses and force components (b) – view A in fig. 1, a: 1 – grinding wheel; 2 — total volume of chips being removed (shown conditionally); 3 – chips being removed by a single grain; 4 – grain trace; 5 – workpiece; 6 – machined surface; 7 – magnetic table; 8 – stock; 9 – surface being machined; 10 – bond; 11 – pore; 12 – real abrasive grain; 13 – chips cut by a single grain; 14 – ideal abrasive grain а b Then, formula (4) will be written as: = σe β 1 . sin s j j a mb N (6) The plastic deformation of the metal volume ωj in the shear zone results from the action of the tangential component of the cutting force PZSj of an absolutely sharp grain. Therefore, deformation power Nj is equal to the power of the force PZSj. We will use the scheme of a cutoff made by a conditionally sharp grain (Fig. 2, b) to express the power Nj:
OBRABOTKAMETALLOV technology Vol. 25 No. 4 2023 = β = cos , j Sj k ZSj k N R V P V (7) where RSj, PZPj are the resultant and tangential components of the cutting force of the sharp grain, respectively, N; Vk is the wheel speed, m/s; β is the angle between RSj and vector Vk (fig. 2, b), degrees. Let us find the tangential component of the force of cutting with a single grain by equating formulas (6) and (7). = σe β 1 . sin s j ZPj k a mb P V (8) The radial component of the cutting force PYPj with a single grain can be found by the formula: = β = β sin tg , YPj Sj ZPj P R P (9) = σe β β 1 tg . sin s j YPj k a mb P V (10) During grinding, the abrasive grains of the wheel blunt, forming an area lj on the back edge. The blunting area prevents the penetration of abrasive grains into the metal during cutting. An additional radial force PYТj appears, which is necessary to deepen the blunt grain (fig. 2, b), without which metal shear is impossible. During cutting, friction occurs between the grain blunting area along the metal surface, which results in an additional tangential force PZТj. Therefore, it becomes necessary to take into account the influence of the blunting area on the total force, the radial cutting force PYj, and the tangential force PZj. Let us use the model of the cutting force acting on an abrasive grain with a blunting area as the basis (figs. 1 and 2, a). Fig. 2, a shows a kinematic diagram of flat grinding. Many of the elements in fig. 2 are shown conditionally and enlarged in size for clarity (guide marks, abrasive grains, etc.). Let us construct equations to find the components of the force of cutting by the wheel grains (fig. 2, b [1]): = + , Yj YPj YTj P P P (11) = + . Zj ZPj ZTj P P P (12) Let us take into account the influence of the blunting area of the abrasive grain on the components of the cutting forces resulting from the friction force [1]: σ = , 3 YTj j j P b l (13) σ = µ = µ , 3 ZTj Ytj j j P P b l (14) where µ is the coefficient of the abrasive grain friction along the material being machined; lj is the length of the grain blunting area, m. We substitute formulas (9), (10), (13), and (14) into equations (11)–(12) to obtain the following equations: σ = σe β + β 1 tg , sin 3 s j Yj j j k a mb P b l V (15) σ = σe + µ β 1 . sin 3 s j Zj j j k a mb P b l V (16) Formulas (15) and (16) are models for calculating the radial and tangential components of the cutting force during plastic deformation of the metal volume in the shear zone by a single blunt grain.
OBRABOTKAMETALLOV Vol. 25 No. 4 2023 technology In models (15) and (16), the components of the cutting force are expressed not through the parameters of machine modes of cutting by the wheel as a whole (depth feed, axial, longitudinal), but through the parameters of microcutting in the shear zone of the metal and friction of the blunting area of a single grain. The first term in models (15) and (16) determines the cutting force, when the metal is cut with an absolutely sharp grain necessary for plastic deformation of the metal in the shear zone. The addend determines the cutting force needed to overcome the indentation and friction of the blunting area. In flat grinding, metal is simultaneously removed by several grains (a group of single grains) in the contact zone between the wheel and the workpiece, so let us transform the microcutting parameters of many grains into the operating parameters of the wheel as a whole, based on the condition for ensuring the equality of energy expended to remove the same volume of metal by the grains and the wheel as a whole. In other words, let us assume that the volume of metal Wall (allowance) removed during one pass of the table from the workpiece by a set of single abrasive grains is equal to the same volume of metal Wall removed by the grinding wheel as a whole (fig. 3). To perform such a transformation, let us make the following assumptions: 1) the volume of metal Wall being removed from the workpiece is equal to the sum of all volumes Wzone of the metal in the shear zone, i.e. Wall = Wzone (fig. 3). 2) since the volume of the chips being cut consists of many metal shear layers in the cutting zone, the total volume of metal chips is Wchips= Wzone and is also equal to Wall = Wchips = Wzone (fig. 3). * Umax (Ymax) is the maximum possible number of chips (shear zones) Fig. 3. The equality of volumes of metal being removed in shear zones, in the chips, and in the workpiece: 1 – the total volume of metal in the shear zones; 2 – the volume of metal in the shear zone; 3 – the total volume of chips being removed; 4 – the volume of chips cut by a single grain; 5 – the total amount of metal being removed during one pass of the table 3) the metal volume Wall is determined by the length of the workpiece L (mm), the width of the wheel working surface B (mm), and the depth feed Sz,i (mm/pass), i.e. (fig. 3) = = = , . all z i chips zone W S LB W W (17) 4) the sum of cutting forces from all cutting grains that are in contact with the workpiece is equal to the cutting force for the wheel as a whole, i.e.: Σ Σ = = = + = + ∑ ∑ 1 1 , J J Z ZP ZT ZPj ZTj j j P P P P P (18) Σ Σ = = = + = + ∑ ∑ 1 1 , J J Y YP YT YPj YTj j j P P P P P (19)
OBRABOTKAMETALLOV technology Vol. 25 No. 4 2023 where PY, PZ are the radial and tangential components of the cutting force during grinding, respectively; P∑YР, P∑ZР are the radial and tangential components of the cutting force during grinding when all grains are absolutely sharp, respectively; P∑YТ, P∑ZТ are the radial and tangential components of the cutting force from the blunting areas during grinding, respectively. 5) the equality of energy spent on the removal of the same metal volume Wall by a set of single abrasive grains and by the grinding wheel as a whole. Let us establish the relationship of energy on removing the metal volume Wall, separately for a group of grains and the wheel as a whole. According to the structure of model (12) of the cutting force PZj for a single grain, the total energy Aj (Н‧m) expended by the cutting force PZ consists of the energy AРj expended by the force PZРj and the energy AТj expended by the force PZТj, i.e.: = + . j Pj Tj A A A (20) Similarly, the total energy А∑ from the tangential component of the cutting force for the wheel consists of the energy A∑Р expended in total by the forces PZРj from all the cutting grains in the contact zone and the energy A∑Т expended in total by the forces PZТj from all the cutting grains in the contact zone, i.e.: Σ Σ Σ = + . P T A A A (21) Then, the sums of the grinding energy from the cutting forces of single grains are equal to the grinding energy of the wheel from the total cutting force. Let us find the grinding energy expended on plastic metal deformation in the shear zone by the force PZPj at a distance L of the length of the machined surface (fig. 2, a): ω = = σe = σe β 1 sin s j j Pj ZPj k k a mb A P L L L V V , (22) Σ = = = = σe σe σe = = = = ω = β ∑ ∑ ∑ ∑ 1 1 1 1 1 sin J J J J s j P Pj ZPj J k k k j j j j a mb LW L L A A L P V V V ïð , (23) where L is the length of the machined surface, m; ωj is the volume of metal removed during cutting with the j-th single grain, m3. To establish the relationship between the grinding energy А∑P expended by absolutely sharp grains to remove metal, we should find a common energy parameter inherent in single grains and the wheel as a whole. Metal removal rate Q, m3/s is an appropriate parameter for our purposes. When cutting with the j-th single grain, the metal removal rate Qj is equal to the ratio of the metal volume ωj in the shear zone to its deformation time during shear time ∆t, which is equal to a sharp grain moving across a distance hj at a speed of Vk: ω = ∆ j j Q t , (24) at e e = ∆ t , (25) where Qj is the metal removal rate when cutting with the j-th single grain, m3/s; ∆t is the deformation time of the metal volume ωj during the shear time, s. Let us take into account formulas (24) and (25) in the equation: Σ = = σe σe = ω = ∑ ∑ 1 1 J J P J J k k j j L L A Q V V , (26)
OBRABOTKAMETALLOV Vol. 25 No. 4 2023 technology The sum of the metal removal rates by a group of grains in the contact zone is equal to the metal removal rate of the wheel Qw: = = ∑ 1 J w j j Q Q , (27) where Qw is the metal removal rate by the wheel, m3/s. Then formula (4) will be as follows: Σ σe = P w k L A Q V , (28) When metal is removed by the wheel, the metal removal rate Qw is equal to the ratio of the metal volume to the time during which the metal volume Wall is removed at the table speed Vtable. The metal volume Wall is a metal layer with a height equal to the infeed radial feed, a length equal to the length of the machined surface, and a width equal to the grinding width (fig. 3). The grinding width can be equal or less than the height of the grinding wheel. = = = , , z i all w z i table table table S BL W Q S BV t t , (29) or at = table table L t V , = , w z i table Q S BV , (30) where ttable is the table pass time per workpiece length L, s. By substituting expression (29) into equation (28), we obtain Σ σe = , P z i table k L A S BV V . (31) Then, the grinding energy АΣР expended by absolutely sharp grains of the wheel on plastic metal deformation in the cutting zone can be written as: Σ σe = = , P ZP z i table k L A P L S BV V . (32) Let us find the tangential component of the cutting force PZP for an absolutely sharp wheel: σe = , z i table ZP k S BV P V . (33) Let us establish the relationship between the energy expended by the friction forces of blunt grains separately for a single grain and for the wheel as a whole (in which the grains have a blunting area) σ µ = = 3 j j Tj ZTj b l A P L L. (34) After summing the energy of all grains, we obtain the formula for the friction force energy: Σ = = = = σµ σµ σe = = = = = ∑ ∑ ∑ ∑ 1 1 1 1 3 3 J J J J T Tj ZTj j j j fr k j j j j L A A P L L b l L f F V , (35) = = ∑ 1 J fr j j F f , (36) where fj is the blunting area of a single grain, m2; F fr is the sum of the blunting areas of single grains, m2.
OBRABOTKAMETALLOV technology Vol. 25 No. 4 2023 Σ σµ = = η 3 T ZT K A P L BL L, (37) = = ∑ 1 J ZT ZTj j P P , (38) where PZT is the tangential component of the force of cutting with the wheel arising from friction, N; η is the degree of recession of the circle [30]. σµ = η 3 ZT K P BL , (39) = , K z i L DS , (40) where LK is the length of the contact arc for flat grinding, m; D is the diameter of the grinding wheel, m. Then, the tangential component of the cutting force can be calculated as: σe σµη = + , , 3 table z i Z z i k V BS B P DS V . (41) We similarly obtain an expression for the radial component of the cutting force: σe ση = β + , , tg 3 table z i Y z i k V BS B P DS V . (42) In previous studies [30], we proved that tgβ ≈ 0.68 and ε ≈ 2.8. Let us take into account the obtained values in formulas (41) and (42) to obtain: σ σµη = + , , 2,8 3 table z i Z z i k V BS B P DS V , (43) σ η σ = + , , 1, 9 3 table z i Y z i k V BS B P DS V . (44) The adequacy of the above model of the cutting force of flat grinding was experimentally investigated in a university laboratory on a 3L722A flat grinding machine using equipment from KISTLER to record and analyze cutting forces. We measured the radial component of the cutting force as the most significant indicator for processing accuracy (fig. 4). A 3L722A flat grinding machine uses the wheel periphery for machining on a rectangular table, which corresponds to the considered flat grinding type. The technical capacity of the used KISTLER 9257B dynamometer meets the test requirements, while its accuracy is ± 3.5 %, which is sufficient for the measurements. Experimental verification was carried out on 500×20×20 mm (length×width×height) steel 45 (0.45 % C) samples. A sensor receiving signals from two modules was used to measure the cutting force. The received digital signals are then processed on a computer. A wheel with the most common characteristic 25AF40L10V was used. It should be noted that the developed force model makes it possible to take into account circles of various characteristics. Fig. 4 presents the experimental results in graphs reflecting the relationship of the radial component of the cutting force with changes in various parameters of the cutting conditions. The difference between the calculated values and experimental data averaged 10 %. Thus, the adequacy of the presented model for calculating the cutting force for flat grinding is proved.
OBRABOTKAMETALLOV Vol. 25 No. 4 2023 technology Results and discussion The resulting analytic expressions (43) and (44) are presented in engineering form, which makes it possible to practically use to calculate cutting force acting in the process of flat grinding, taking into account the cutting mode, specifications, diameter and width of the wheel, physical and mechanical properties of the workpiece, and many other parameters. The first terms of equations (43) and (44) take into account the cutting force needed for the plastic deformation of metal in the shear zone (to remove the metal). The addends take into account the cutting force needed to overcome the friction force arising from the blunting areas on the grains. The presented force model can serve as the future foundation for an analytical model for calculating cutting depth to predict changes in the technical size and its inaccuracies. The components of the cutting force can be found in two ways. The first is based on the equality of the metal volumes removed in one pass of the workpiece by a set of single cutting grains and by the grinding wheel as a whole (as described above). The second method takes into account the equality of metal cutoff intensities from the grinding wheel and the individual cutting grains making contact with the workpiece. а b c d e f Fig. 4. The relationship between the radial component of the cutting force and the sequential number of the table pass with the workpiece at РХ-ХХ (Vtable = 10m/min and Srad = 0.024 (a), 0.018 (b), 0.011 (c) m/pass) and (Vtable = 10m/min and Srad = 0.024 (d), 0.018 (e), 0.011 (e) m/pass): vertical axis on the graphs is the radial component of the cutting force, N; horizontal axis on the graphs is the sequence number of the table stroke; solid line – calculated values of cutting force; dashed line – experimental values of cutting force
OBRABOTKAMETALLOV technology Vol. 25 No. 4 2023 Both approaches are based on the energy balance proposed by S.N. Korchak on the equality of the energy expended to remove metal from the workpiece surface being machined by single abrasive grains and the grinding wheel as a whole (i.e. the equality of energy in terms of the volume of metal removed and the equality in the rate of stock removal). In a previous study [31], we considered in detail an algorithm of applying the second method to model the cutting force components based on the equal intensity of metal removal by the grinding wheel and the intensity of metal removal by cutting abrasive grains in the zone of contact with the workpiece. The equations of the cutting force model obtained by these two methods are identical. As a result, we can say that these analytical cutting force models, which are built on the assumptions and approaches from S.N. Korchak’s studies on the theory of cutting and plastic deformation of metal, are reliable regardless of the condition of equality of metal removal intensities or volumes. The resulting analytical model for calculating cutting force based on the equality of the removal rate and the volumes of removed metal by the wheel as a whole and by single grains in the zone of contact between the wheel and the workpiece was experimentally confirmed, which indicates its adequacy. Conclusions 1. The lack of adequate analytical models for calculating cutting force and depth for flat grinding in CAM systems from various manufacturers results in the need for manual selection of cutting conditions when an operation is designed. 2. The lack of systems for automatic calculation of cutting conditions for CNC flat grinding operations (digital tool for CAM systems) is a scientific and technical problem leading to the need to develop an analytical model of the cutting force that establishes a relationship between the force and the depth of the metal cut made by single grains with a stock removal and the cutting force that occurs during grinding with a wheel as a whole. 3. An analytical model for calculating the cutting force in flat grinding, which establishes the relationship of the cutting force with the cutting depth and the volumes of metal removed by single grains and the wheel as a whole based on the integration of microvolumes and microforces when the metal is cut by grains is proposed. 4. Mathematical modeling of the relationship between the cutting force and cutting conditions with the parameters of microcutting by a group of single grains was carried out, based on the equality of grinding energy when removing the same volume of metal. 5. The presented model of the cutting force occurring during flat grinding was confirmed experimentally and coincided with a model of cutting force which is also based on S.N. Korchak’s assumptions and the equal intensity of metal removal by the grinding wheel as a whole and by single grains in the contact zone of the wheel with the workpiece. 6. A practical application of the developed cutting force model will be the creation of a digital twin of flat grinding, which can predict the stability of the machined surface accuracy and quality and support optimization of designed operations, requiring the selection of the optimal cycles of cutting conditions and other input parameters (for example, the specifications of the abrasive tool), which is of great practical importance for the digitalization of engineering processes. References 1. Korchak S.N. Proizvoditel’nost’ protsessa shlifovaniya [Productivity of the grinding process]. Moscow, Mashinostroenie Publ., 1974. 280 p. 2. Zubarev Yu.M., Priemyshev A.V. Teoriya i praktika povysheniya effektivnosti shlifovaniya materialov [Theory and practice of improving the efficiency of materials grinding]. St. Petersburg, Lan’ Publ., 2010. 304 p. ISBN 9785-8114-0973-0. 3. Filimonov L.N. Vysokoskorostnoe shlifovanie [High-speed grinding]. Leningrad, Mashinostroenie Publ., 1979. 248 p.
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