Vol. 24 No. 4 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. 4 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. 24 No. 4 2022 5 CONTENTS OBRABOTKAMETALLOV TECHNOLOGY Dyuryagin A.A., Ardashev D.V. A study of the relationship between cutting force and machined surface roughness with the feed per tooth when milling EuTroLoy 16604 material produced by the DMD method...................... 6 Ulakhanov N.S., Tikhonov A.G., Mishigdorzhiyn U.L., Ivancivsky V.V., Vakhrushev N.V. The features of residual stresses investigation in the hardened surface layer of die steels after diffusion boroaluminizing............... 18 Rubtsov V.E., Panfi lov A.O., Knyazhev E.O., Nikolaeva A.V., Cheremnov A.M., Gusarova A.V., Beloborodov V.A., Chumaevskii A.V., Ivanov A.N. Development of plasma cutting technique for C1220 copper, AA2024 aluminum alloy, and Ti-1,5Al-1,0Mn titanium alloy using a plasma torch with reverse polarity................ 33 Amirov A.I., Moskvichev E.N., Ivanov A.N., Chumaevskii A.V, Beloborodov V.A. Formation features of a welding joint of alloy Ti-5Al-3Mo-1V by the friction stir welding using heat-resistant tool from ZhS6 alloy....... 53 EQUIPMENT. INSTRUMENTS Ardashev D.V., Zhukov A.S. Investigation of the relationship between the cutting ability of the tool and the acoustic signal parameters during profi le grinding..................................................................................................... 64 Bataev D. K-S., Goitemirov R. U., Bataeva P. D. Studies of wear resistance and antifriction properties of metalpolymer pairs operating in a sea water simulator........................................................................................................ 84 Zakovorotny V.L., Gvindjiliya V.E., Fesenko E.O. Application of the synergistic concept in determining the CNC program for turning............................................................................................................................................ 98 MATERIAL SCIENCE Sokolov R.A., Novikov V.F., Kovenskij I.M., Muratov K.R., Venediktov A.N., Chaugarova L.Z. The effect of heat treatment on the formation of MnS compound in low-carbon structural steel 09Mn2Si................................ 113 Burkov А.А., Krutikova V.O. Deposition of titanium silicide on stainless steel AISI 304 surface...................... 127 Pugacheva N.B., NikolinYu.V., BykovaT.M., Goruleva L.S. Chemical composition, structure and microhardness of multilayer high-temperature coatings..................................................................................................................... 138 Saprykina N.А., Chebodaeva V.V., Saprykin A.А., Sharkeev Y.P., Ibragimov E.А., Guseva T.S. Synthesis of a three-component aluminum-based alloy by selective laser melting............................................................... 151 Gabets D.A., MarkovA.M., Guryev M.A., Pismenny E.A., NasyrovaA.K. The effect of complex modifi cation on the structure and properties of gray cast iron for tribotechnical application..................................................... 165 Ivanov I.V., Yurgin A.B., Nasennik I.E. Kuper K.E. Residual stress estimation in crystalline phases of highentropy alloys of the AlxCoCrFeNi system........................................................................................................... 181 Korosteleva E.N., Nikolaev I.O., Korzhova V.V. Features of the structure formation of sintered powder materials using waste metal processing of steel workpieces................................................................................. 192 EroshenkoA.Yu., Legostaeva E.V., Glukhov I.A., Uvarkin P.V., TolmachevA.I., Luginin N.A., Bataev V.A., Ivanov I.V., Sharkeev Yu.P. Effect of deformation processing on microstructure and mechanical properties of Ti-42Nb-7Zr alloy............................................................................................................................................. 206 Kutkin O.M., Bataev I.A., Dovzhenko G.D., Bataeva Z.B. The study of characteristics of the structure of metallic alloys using synchrotron radiation computed laminography (Research Review)................................ 219 EDITORIALMATERIALS 243 FOUNDERS MATERIALS 255 CONTENTS
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 4 4 2 Application of the synergistic concept in determining the CNC program for turning Vilor Zakovorotny a, Valery Gvindjiliya b, * , Ellina Fesenko с Don State Technical University, 1 Gagarin square, Rostov-on-Don, 344000, Russian Federation a https://orcid.org/0000-0003-2187-9897, vzakovorotny@dstu.edu.ru, b https://orcid.org/0000-0003-1066-4604, sinedden@yandex.ru, с https://orcid.org/0000-0003-0833-2758, ellinochaa@gmail.com 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. 2022 vol. 24 no. 4 pp. 98–112 ISSN: 1994-6309 (print) / 2541-819X (online) DOI: 10.17212/1994-6309-2022-24.4-98-112 ART I CLE I NFO Article history: Received: 08 September 2022 Revised: 03 October 2022 Accepted: 28 October 2022 Available online: 15 December 2022 Keywords: Controlled cutting system Synergetics of machining Dynamic of the cutting process. Acknowledgements Research were partially conducted at core facility “Structure, mechanical and physical properties of materials”. ABSTRACT Introduction. One of the dynamically developing areas of increasing the effi ciency of CNC machines is associated with the use of the synergetic concept in determining the CNC program. The principle of compressionexpansion of the dimensionality of the state space is used. Subject. On the example of the workpiece machining, the stiffness parameters of which are a function of the toolpath, all stages of control synthesis, which ensures the mutual consistency of dynamic subsystems, including the cutting process, are described in the paper. The aim of the work is to determine asymptotically stable machine actuator toolpath, given by CNC program parameters, from the set of paths, for which the condition of minimum wear intensity is fulfi lled. Method and methodology. Mathematical modeling of the controlled cutting system, which is based on the principle of compression-expansion state space, is presented. When the dimension of the state space is expanded, the model of the dynamic cutting system includes all elements from the CNC system that programs the motion of the actuating elements to the elastic deformations of the tool, which interacts with the workpiece through the connection formed by the cutting process. The dynamic coupling integrates the subsystems into a single coupled control system. In this space, the desired shaping motion path of the tool tip relative to the workpiece is constructed, which should be the attractor of the entire state space. The transformation of the desired motion path into an attractor characterizes the procedure of compressing the dimensionality of the state space. It is supposed that it is possible to control the motion trajectories of the actuators within the bandwidths of the servomotors. Results and Discussion. The analysis of the stability of the cutting process is performed; the example of the effi ciency of a NC program on the basis of the synergetic paradigm is presented. It is shown that by coordinating the external control with the internal dynamics of the system it is possible to increase the effi ciency of a part production up to two times in machine time. For citation: Zakovorotny V.L., Gvindjiliya V.E., Fesenko E.O. Application of the synergistic concept in determining the CNC program for turning. Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science, 2022, vol. 24, no. 4, pp. 98–112. DOI: 10.17212/1994-6309-2022-24.4-98-112. (In Russian). ______ * Corresponding author Gvindjiliya Valery E., Post-graduate Student Don State Technical University, 1 Gagarin square, 344000, Rostov-on-Don, Russian Federation Tel.: +7 (918) 583-23-33, e-mail: sinedden@yandex.ru Introduction Problem Statement. Many problems of the dynamics of technical systems began to be considered taking into account its system-synergetic analysis [3–7] after the publication of the works of H. Haken and I. Prigozhin [1, 2]. The system-synergetic approach has also been used to explain many phenomena in cutting and friction processing [8–10]. At the same time, in the last decade, the scientifi c community pays great attention to the development of a virtual model of machining processes on metal-cutting machines [11–30]. These models are intended for use at the stage of technological preparation of production of parts with a complex geometric profi le. Complex shape parts are defi ned as those that require simultaneous changes in the longitudinal and transverse slide paths, as well as parts that change properties along the paths of the machine’s executive elements (TEE).
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 4 No. 4 2022 The following steps are included in the basis of the structure of the synergistic processing control concept [3–7]. First, the control goal is formulated as the production of a batch of parts of a set quality while minimizing the reduced cost of its production. Secondly, the desired path (3) 0 1,0 2,0 3,0 , , P F F F F L L L L R and the corresponding vector of velocities of forming motion (3) 0 0 1,0 2,0 3,0 , , dt F P F F F F dL V V V V R (3) 1 2 3 and , , dt F P F F F F dL V V V V R are determined, at which the requirements to the quality of parts are satisfi ed while minimizing the intensity of tool wear (Fig. 1, a). b Fig. 1. Controlled dynamic cutting system (a) and drawing of the “basic” part (b) a
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 4 4 2 The space (3) R is defi ned by the directions of TEE motion, which are set by the CNC system. The shaping motion path is understood as the sum of the paths of the TEE, vector (3) 1 2 3 / , , P L L L L R , and the paths of the deformation displacements of the tool – vector (3) 1 2 3 / , , P X X X X R , and the workpiece – vector (3) 1 2 3 / , , P Y Y Y Y R Consequently (F) – – L L X Y . The paths L and (3) 1 2 3 dL , , dt P V Y Y Y R are defi ned by the NC program. The deformation displacements X and Y are considered in the motion coordinate system given by TEE. If X = 0, Y = 0, then (F) L L . The velocities ( ) 1 2 3 , , P x X X X dX v v v v dt and ( ) 1 2 3 , , P Y Y Y Y dY v v v v dt are also considered. Thirdly, such coordination of the terminal path with the paths of the state space is provided, under which L, X, Y are asymptotically stable; – in this case 0 L F is an attractor. The difference between the synergistic paradigm of NC program synthesis and the traditional one is its defi nition based on the mutual agreement of all subsystems and the provision (F) (F) 0 L L of the property of attraction of the entire state space. In addition, the conditions (F) L , dictated by the quality requirements of the parts, should be met. And the dynamics of the system is taken into account as a whole. Therefore, we rely on research in the fi eld of cutting dynamics [24–43] to develop a synergistic approach to the machining processes control. There is a far from complete list of works on the dynamics of cutting. In spite of many works on the dynamics of cutting, it considers some particular models of the representation of cutting forces in the coordinates of an elastic system. The following ones are analyzed: buckling collapse conditions, formation of different attractors of deformation displacements of the tool and workpiece. It is necessary to analyze the dynamic system as a whole when solving the problem of synergistic synthesis, including determination of the desired path (F) (F) L and corresponding paths L(F), X and Y. Here ℵ(F) – is the set of admissible variations of L(F). The paper discusses all the stages of synergistic control of turning parts, the stiffness parameters of which change along the tool path: the methodology of creation (F) 0 L and its asymptotic stability. An analysis of the effectiveness of synergistic control is presented on a specifi c example of manufacturing a “basic” part, the drawing of which is shown in Fig. 1, b. Research methodology Determining the desired path of the forming motion. When analyzing the system, it is advisable to use the principle of motions breaking down into “slow” ones, lying within the bandwidth of the motors of the machine’s executive elements, and “fast” ones, determined by the dynamic properties of the tool and workpiece subsystems. Its use is based on the asymptotic properties of nonlinear differential equations with small parameters in the derivatives [44, 45]. Moreover, the subsystem of “fast” motions is considered in variations with respect to the paths of “slow” motions. If the subsystems are asymptotically stable, the path of the “slow” motions becomes an attractor. Typical for practice is the case when TEE are given and controllable within the servomotor bandwidths. Then we have the following equation of dynamics [40]: 2 ( ) ( ) ( ) (0) 1 1 1 1 2 ( ; ( ) , Y Y Y d Y dY m h c Y F dt dt 2 2 d X dX m h cX F L, V, X, Y) dt dt L, V, X, Y (1)
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 4 No. 4 2022 where m = [ms], ms = m, s = 1, 2, 3 kgs 2/mm; h = [h s,l], kgs 2/mm, c = [c s,l] kg/mm; s,l = 1,2,3 – are symmetric, positively determined matrices of inertial, velocity, and elastic coeffi cients. The subsystem of the workpiece has stiffness in the direction of its rotation axis by an order of magnitude greater than in other directions. In the plane Y1–Y2 it has full symmetry. Therefore, in this plane any orthogonal coordinate system is the main one. Then the force F1 corresponds to the deformations only in the direction Y1 [48]. The force F [4] can be represented in the form (0) 1 2 3 1 2 3 { , , } { , , } F F F F F . It is convenient to consider the following representation of modes (feed SP(p), depth tP(p) and cutting speed VP(p)): 2 2 2 ( ) ( ) ( ) ( ) ; ( ) t P X Y P t T S t V v v d V t 3 2 1 1 1 ( ) ( ); ( ) / 2 ( ), X Y P D v t v t t t D L X Y (2) where T = (Ω)–1 is turnaround time, sec; D – diameter, m. If X = 0, Y = 0, then (0) P S , (0) P t , and (0) 3= D P V V , are traditional modes. Then the model of relation of the force F(0) with the system coordinates has the equation [46, 47]: 3 2 (0) (0) (0) (0) 3 1 1 2 / 1 exp ( ) ( ) ( ) , t X X P t T T dF dt F V v t X Y V v d (3) where ρ – chip pressure on the leading edge of the tool, kg/mm2; μ – dimensionless coeffi cient; ζ – steepness parameter of forces, sec∙m-1; T(0) – chip time constant, sec. If L, V are set, then systems (1)–(3) allow to determine X, Y, and L(F). If (F) (F) L , then L, V determine CNC program. Otherwise, it is necessary to ensure the asymptotic stability of the resulting path and to choose L, V or available variations of the parameters so that the condition (F) (F) L or (F) (F) 0 L L is satisfi ed. To calculate L, V, at which (F) (F) L is provided, let us use the principle of motions breaking down. First, a set of paths (F) (F) L in “slow” time are defi ned; then in this set we choose those for which the trajectories of “fast” motions are asymptotically stable, and among them those for which the wear intensity is minimal. To determine the desired path of the “slow” motions, consider the values L, V averaged over the period of rotation of the workpiece. For this purpose, (1) and (3) are considered in the slow discrete time T = (Ω) – 1: C(iT) Z(iT) = F(iT) (4) where Z(iT) = {X1(iT), X2(iT), X3(iT), Y1(iT)} T; F(iT) = ρ 0tP (0)S P (0)(iT){χ 1,χ2,χ3} T; (0) (0) 1,1 0 1 2,1 3,1 0 1 (0) (0) 1,2 0 2 2,2 3,2 0 2 (0) (0) 1,3 0 3 2,3 3,3 0 3 (0) (0) ( ) 0 1 0 1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0 0 ( ) P P P P P P Y P P c S iT c c S iT c S iT c c S iT iT c S iT c c S iT S iT c S iT Ñ , 0 3 1 exp( ) V In (4) 0 1 i s i iT L (Fig. 1). From (4) 0.5ΔD(iT) = X1(iT) + Y1(iT) is calculated. During processing it is required to ensure the condition ΔD(iT) = const [51–55]. Let us determine ΔD(iT) from (4):
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 4 4 2 (0) (0) ( ) 2 X Y P P D iT t S (5) where (0) (0) 1,1 0 1 2,1 3,1 0 1 (0) (0) 1,2 0 2 2,2 3,2 0 2 (0) (0) 1,3 0 3 2,3 3,3 0 3 (0) (0) ( ) 0 1 0 1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 0 0 ( ) P P P P P P Y P P c S iT c c S iT c S iT c c S iT iT c S iT c c S iT S iT c S iT ; (0) 1 2,1 3,1 0 1 (0) 2 2,2 3,2 0 2 (0) 3 2,3 3,3 0 3 (0) ( ) 1 0 1 ( ) ( ) ( ) ( ) 0 0 ( ) P P X P Y P c c S iT c c S iT iT c c S iT c S iT ; (0) 1,1 0 1 2,1 3,1 1 (0) 1,2 0 2 2,2 3,2 2 (0) 1,3 0 3 2,3 3,3 3 (0) 0 1 1 ( ) ( ) ( ) ( ) ( ) 0 0 P P Y P P c S iT c c c S iT c c iT c S iT c c S iT . An analysis of equation (5) shows that, depending on ΔD(iT), there is a branching of solutions SP (0) (iT). Moreover, there are areas in which there are no real solutions. It all depends on the ratio of stiffness of the workpiece subsystem c(Y), matrix elements c and allowable values ΔD(iT) for given values of the allowance tP (0). In the case if c → ∞ and ΔD(iT) = ΔD 0 = const., then (5) becomes an equation: (0) (0) 0 1 0 (0) ( ) 0 1 ( ) ( ) 2 ( ) ( ) ( ) P P P Y P P V S iT D t c iT V S iT , (6) from which the set of paths SP (0)(iT,V P) is determined, each of which depends on the cutting speed VP = const. Obviously: ( ) (0) 0 (0) 0 1 0 ( ) ( , ) ( ) [ ] Y P P P P D c iT S iT V V t D , (7) SP (0)(iT,V P) – path of the feed per revolution along the slide motion, at which ΔD0 = const. Analysis of the equations (5) and (6) makes it possible to draw some conclusions about the choice of tool parameters and cutting modes to reduce the infl uence of elastic deformations on the part diameter, also known from practice. 1. As the depth of cut decreases, the diameter variations due to changes in stiffness decrease. Therefore, machining a part, the stiffness of which changes along the tool path, is performed in several passes with a successive decrease in the allowance. 2. The value ΔD(iT) is infl uenced by the angular coeffi cient χ1. Angular coeffi cients depend on the tool geometry, fi rst of all, on the back rake angle and the rake angle [56].
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 4 No. 4 2022 3. To reduce the uncertainty ΔD(iT) for variations c, it is reasonable to carry out machining with small feeds. However, at small feeds commensurate with the tool radius at its apex, the stabilizing effect of the motion direction formed on the workpiece is leveled out. Therefore, the magnitude of the feed from below is also limited [57]. These methods do not eliminate the need for matching the CNC program with the law of change of stiffness. If the set of paths SP (0)(iT,V P) is calculated, then it is additionally necessary to select from this set those, for which the condition of minimum wear intensity is satisfi ed. The solution to this problem is described in suffi cient detail in [58]. The paths (7) are calculated under the assumption that the subsystem of “fast” motions is asymptotically stable. Under this condition (7), there is an attractor that has the property of attraction in the entire state space. In this connection, it is additionally necessary to analyze the subsystem of “fast” motions for asymptotic stability. Example of CNC program matching with a change in part stiffness. The problem of matching TEE with changing system properties has a wide range of applications: matching TEE with evolutionary changes in system properties due to the work of forces in the cutting zone; matching TEE with an a priori specifi ed law of changing the stiffness of the workpiece; matching TEE with the development of tool wear, etc. As an example, the longitudinal turning of the fuel pump nozzle fi tting of a diesel engine is considered (length L0 = 144 mm (Fig. 1, b), diameter D = 18 mm, material – hot-rolled bar made of steel 45 (STATE STANDARD 2590-2006) with diameter D = 25 mm. The tools used were tool systems with interchangeable 15 % (WC + TiC) + 6 % Co (HS123) square inserts and MR TNR 2020 K11 toolholders. Tool geometry: back rake angle γ = 15°, cutting edge angle φ = 90°, front clearance angle α = 6o. Parameters of the tool elastic system and dynamic coupling are given in Table 1, Table 2. Generalized mass m = 0.5∙10–3 kg∙s2/mm. To determine the law of variation of the radial stiffness along the axis of the workpiece, we can use the laws of bending vibrations of rods [59]. This information is easier and more accurate to obtain experimentally (Fig. 1, a). The law c(Y)(L 2) should be supplemented by its agreement with the change in the reduced mass along L2. This is due to the fact that the natural frequencies of the bending vibrations of the shaft remain constant at all values of L2 [4–6, 46]. Ta b l e 1 Matrices of velocity coeffi cients and elasticity of the tool subsystem c1,1, kg/mm c2,2, kg/mm c3,3, kg/mm h1,1, kg∙s/mm h2,2, kg∙s/mm h3,3, kg∙s/mm 2,000 1,000 1,000 1.3 1.1 0.8 1,2 2,1, êã/ìì ñ ñ 1,3 3,1, êã/ìì ñ ñ 2,3 3,2, êã/ìì ñ ñ 1,2 2,1, êã ñ/ìì h h 1,3 3,1, êã ñ/ìì h h 2,3 3,2, êã ñ/ìì h h c1,2 = c2,1, kg/mm c1,3 = c3,1, kg/mm c2,3 = c3,2, kg/mm h1,2 = h2,1, kg∙s/mm h1,3 = h3,1, kg∙s/mm h2,3 = h3,2, kg∙s/mm 100 150 80 0.6 0.5 0.4 Ta b l e 2 Dynamic link options ρ, kg/mm2 ζ, (mm/s)–1 T (0), s μ χ 1 χ2 χ3 300 0.1 0.0001–0.0005 0.5 0.7 0.5 0.5
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 4 4 2 The path SP (0)(L 2) in Fig. 2, b corresponds to the speed of longitudinal motions of the slide V2L2 = SP (0) (L2)(T) –1. The paths shown in Fig. 2, c characterize the attracting set of deformational displacement along the whole path of the tool motion in the case when the subsystem of “fast” motions is asymptotically stable. The paths in Fig. 2 are obtained by assuming that V3 = 1.5 m/s = VP = const. Varying V3 and tP (0) will lead to a displacement of the path (Fig. 2). Let us consider the problem of asymptotic stability of deformational displacements for the subsystem of “fast” motions. Quasi-permanent paths of deformational displacements Xs (*)(iT),s = 1,2,3; Y(*)(iT); force F(*,0)(iT) and velocities V 2 (*)(iT) correspond to the curves (Fig. 2). X s (*)(iT), Y(*)(iT), and F(*,0)(iT) are slowly changing state coordinates. Equation in variations with respect to the paths of “slow” motions is obtained after replacing of Xs(t) – Xs (*)(iT) = x s(t); Y(t) – Y (*)(iT) = y(t); and F(0)(t) – F(0,*)(iT) = f(t); Its linearization in the vicinity, Xs (*)(iT),s = 1,2,3; Y(*)(iT); and F(*,0)(iT) leads to a system of linear equations with lagged arguments. The analysis of stability of such systems on the basis of algebraic criteria, as well as the Mikhailov criterion, is not fair [47, 48]. The simulation of forces in state coordinates allows us to interpret the forces as feedbacks in the system. Therefore, Nyquist stability criteria are used, for which c Fig. 2. An example of matching the path of changing the radial stiffness of the workpiece (a) with the value of the feed per revolution (b), changing the diameter variations (c): 1 – complete matching along the path; 2 – processing with a constant feed; 3 – linear interpolation of feed change over four nodal points (A-B-C-D) а б
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 4 No. 4 2022 from (1) taking into account (3) the transfer function WP(p) of the system in the open state is obtained for the linearized system in variations: 1 2 (0) 0 (0) (0) (0) ( ) ( ) 1 exp( ) 1 ( ) 1 exp( ) ( ) 1 exp( ) , P P FX FX FY P P W p S g p Tp T p t g p Tp S g p Tp (8) where 1 1 ( ) / FX X g p ; 2 2 ( ) / FX X g p ; ( ) / FY Y g p ; 1,1 2,1 3,1 1,2 2,2 3,2 1,3 2,3 3,3 ( ) 0 0 0 0 0 0 Y c c c c c c c c c c ; 1 1 2,1 3,1 2 2,2 3,2 3 2,3 3,3 ( ) 1 0 0 0 0 0 X Y c c c c c c c ; 2 1,1 1 3,1 1,2 2 3,2 1,3 3 3,3 ( ) 1 0 0 0 0 0 X Y c c c c c c c ; 1,1 2,1 3,1 1 1,2 2,2 3,2 2 1,3 2,3 3,3 3 1 . 0 0 0 c c c c c c c c c The equation (8) includes technological parameters tP (0) and S P (0), and indirectly V P, because T (0) mainly depends on the cutting speed, and spindle speed. Parameters tP (0), S P (0) and Ω are defi ned by the CNC program. Here is an example of changing the stability area in the plane of two varying parameters “VP – ρ” (Fig. 3). Above the fi gurative lines, the system is unstable. The curves are typical when evaluating the effect of spindle speed on the stability of elastic deformational displacements of the tool and workpiece. Periodic bursts of admissible values ρ explained by the regenerative effect of the integral feed forming operator. Analysis of the properties of the system at t < T shows that the cutting speed primarily changes the parameter T(0). Its increase causes two opposite trends. On the one hand, an increase of T(0) leads to additional phase shifts between forces and strains, which contributes to the loss of stability. On the other hand, an increase of T(0) contributes to an increase in the damping effect of the cutting process on oscillations, which stabilizes the equilibrium. Therefore, there is a minimum when VP is increased. Fig. 3. An example of changing the region of stability in a plane “VP – ”: 1 – с(Y) = 400 kg/mm; 2 – с(Y) = 150 kg/mm
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 4 4 2 If we follow the work [58], as the cutting speed increases, a redistribution of physical interactions in the interface areas of the tool and cutting zone (adhesion, fatigue, abrasion, tribochemical, diffusion, etc.) is observed. Transition from prevailing adhesion to diffusion interactions corresponds to the minimum of wear intensity. This range corresponds to the minimum power of irreversible transformations of the energy input to the cutting [56]. When machining steel 45, the region of this transition is located in the range 1.0–2.0 m/s. In addition, with increasing Ω there is a critical value of Ω, starting from which parametric effects begin to appear, including parametric self-excitation [45]. Therefore, there is a critical value of Ω, exceeding which is unacceptable and it is necessary to take into account the restrictions imposed on the system the peculiarities of its dynamics. Results and discussion One of the currently developing ways to increase the effi ciency of machining parts, the stiffness of which varies along the tool path is the coordination of external control (from the CNC system) with internal control of elastic deformations, determined by the dependence of forces on deformation displacements and TEE. The synergistic problem of interaction between the external control and the internal control [3–7], formed by the dependence of cutting forces on deformation displacements and TEE set by the CNC system, is solved on the basis of matching the external control with the internal dynamics of cutting. To do this, fi rstly, when defi ning the CNC program, a set of desired paths of the forming motions, which include both the TEE and the deformations of the tool tip relative to the workpiece, is constructed. The desired paths are defi ned on the basis of the requirements to the parts quality. All intermediate paths of the dynamical system up to the CNC program are subject to these paths. Thus, the currently existing principle of subordination is replaced by the principle of interaction of subsystems according to the direction of goal achievement. Secondly, from the obtained set of paths obtained at different technological modes, a path is selected, at which the intensity of tool wear is minimal. The depth of cutting is usually set a priori, so when selecting the modes, it is necessary to determine the cutting speed, at which the desired path of the forming motions is asymptotically stable, from the conditions of physical optimality. The performed verifi cation of the effectiveness of the method in the longitudinal turning of the fuel pump nozzle showed that by reducing the number of passes, it is possible to increase the productivity of part manufacturing up to two times in machine time. The increase in productivity is achieved, fi rstly, by reducing the number of passes. According to the basic technology, after drilling the central hole D = 2.5 mm, which is performed on a specialized machine, the workpiece is installed in the centers and the longitudinal turning of the shaft is performed in the beginning for the entire length up to D = 27 mm. Then the main surface of the shaft is turned in three passes with depths of cut tP (0) = 1.5 mm; t P (0) = 0.7 mm; and t P (0) = 0.3 mm. Such transitions provide the required diameter accuracy until the back edge wear reaches 0.6 mm. The cutting modes remain unchanged. When using the synergistic concept due to the coordination of TEE with the changing parameters of the workpiece stiffness along the tool motion coordinates, coordination of TEE with the evolutionary changes in the properties of the dynamic relationship formed by cutting, as well as determining the optimal coordinates of switching (readjustment) of machining cycles, it is possible to reduce the number of passes from four to two. Besides, it is possible to increase the batch of parts before tooling system readjustment by 1.5 times. The optimal switching coordinates were determined according to the method stated by us earlier [59]. It is important to emphasize that the increase in productivity was achieved by software methods, without additional material costs. Conclusion One of the promising directions of manufacturing a batch of parts of a set quality while minimizing the reduced costs is the use of the synergistic principle of matching the external control (CNC program) with the internal dynamics of the system. The given example of manufacturing a part, the stiffness of which
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