Vol. 26 No. 1 2024 3 EDITORIAL COUNCIL EDITORIAL BOARD EDITOR-IN-CHIEF: Anatoliy A. Bataev, D.Sc. (Engineering), Professor, Rector, Novosibirsk State Technical University, Novosibirsk, Russian Federation DEPUTIES EDITOR-IN-CHIEF: Vladimir V. Ivancivsky, D.Sc. (Engineering), Associate Professor, Department of Industrial Machinery Design, Novosibirsk State Technical University, Novosibirsk, Russian Federation Vadim Y. Skeeba, Ph.D. (Engineering), Associate Professor, Department of Industrial Machinery Design, Novosibirsk State Technical University, Novosibirsk, Russian Federation Editor of the English translation: Elena A. Lozhkina, Ph.D. (Engineering), Department of Material Science in Mechanical Engineering, Novosibirsk State Technical University, Novosibirsk, Russian Federation The journal is issued since 1999 Publication frequency – 4 numbers a year Data on the journal are published in «Ulrich's Periodical Directory» Journal “Obrabotka Metallov” (“Metal Working and Material Science”) has been Indexed in Clarivate Analytics Services. Novosibirsk State Technical University, Prospekt K. Marksa, 20, Novosibirsk, 630073, Russia Tel.: +7 (383) 346-17-75 http://journals.nstu.ru/obrabotka_metallov E-mail: metal_working@mail.ru; metal_working@corp.nstu.ru Journal “Obrabotka Metallov – Metal Working and Material Science” is indexed in the world's largest abstracting bibliographic and scientometric databases Web of Science and Scopus. Journal “Obrabotka Metallov” (“Metal Working & Material Science”) has entered into an electronic licensing relationship with EBSCO Publishing, the world's leading aggregator of full text journals, magazines and eBooks. The full text of JOURNAL can be found in the EBSCOhost™ databases.
OBRABOTKAMETALLOV Vol. 26 No. 1 2024 4 EDITORIAL COUNCIL EDITORIAL COUNCIL CHAIRMAN: Nikolai V. Pustovoy, D.Sc. (Engineering), Professor, President, Novosibirsk State Technical University, Novosibirsk, Russian Federation MEMBERS: The Federative Republic of Brazil: Alberto Moreira Jorge Junior, Dr.-Ing., Full Professor; Federal University of São Carlos, São Carlos The Federal Republic of Germany: Moniko Greif, Dr.-Ing., Professor, Hochschule RheinMain University of Applied Sciences, Russelsheim Florian Nürnberger, Dr.-Ing., Chief Engineer and Head of the Department “Technology of Materials”, Leibniz Universität Hannover, Garbsen; Thomas Hassel, Dr.-Ing., Head of Underwater Technology Center Hanover, Leibniz Universität Hannover, Garbsen The Spain: Andrey L. Chuvilin, Ph.D. (Physics and Mathematics), Ikerbasque Research Professor, Head of Electron Microscopy Laboratory “CIC nanoGUNE”, San Sebastian The Republic of Belarus: Fyodor I. Panteleenko, D.Sc. (Engineering), Professor, First Vice-Rector, Corresponding Member of National Academy of Sciences of Belarus, Belarusian National Technical University, Minsk The Ukraine: Sergiy V. Kovalevskyy, D.Sc. (Engineering), Professor, Vice Rector for Research and Academic Aff airs, Donbass State Engineering Academy, Kramatorsk The Russian Federation: Vladimir G. Atapin, D.Sc. (Engineering), Professor, Novosibirsk State Technical University, Novosibirsk; Victor P. Balkov, Deputy general director, Research and Development Tooling Institute “VNIIINSTRUMENT”, Moscow; Vladimir A. Bataev, D.Sc. (Engineering), Professor, Novosibirsk State Technical University, Novosibirsk; Vladimir G. Burov, D.Sc. (Engineering), Professor, Novosibirsk State Technical University, Novosibirsk; Aleksandr N. Korotkov, D.Sc. (Engineering), Professor, Kuzbass State Technical University, Kemerovo; Dmitry V. Lobanov, D.Sc. (Engineering), Associate Professor, I.N. Ulianov Chuvash State University, Cheboksary; Aleksey V. Makarov, D.Sc. (Engineering), Corresponding Member of RAS, Head of division, Head of laboratory (Laboratory of Mechanical Properties) M.N. Miheev Institute of Metal Physics, Russian Academy of Sciences (Ural Branch), Yekaterinburg; Aleksandr G. Ovcharenko, D.Sc. (Engineering), Professor, Biysk Technological Institute, Biysk; Yuriy N. Saraev, D.Sc. (Engineering), Professor, V.P. Larionov Institute of the Physical-Technical Problems of the North of the Siberian Branch of the RAS, Yakutsk; Alexander S. Yanyushkin, D.Sc. (Engineering), Professor, I.N. Ulianov Chuvash State University, Cheboksary
Vol. 26 No. 1 2024 5 CONTENTS OBRABOTKAMETALLOV TECHNOLOGY Kuts V.V., Oleshitsky A.V., Grechukhin A.N., Grigorov I.Y. Investigation of changes in geometrical parameters of GMAW surfaced specimens under the infl uence of longitudinal magnetic fi eld on electric arc....................................... 6 Saprykina N.А., Chebodaeva V.V., Saprykin A.А., Sharkeev Y.P., Ibragimov E.А., Guseva T.S. Optimization of selective laser melting modes of powder composition of the AlSiMg system................................................................. 22 Gubin D.S., Kisel’ A.G. Features of calculating the cutting temperature during high-speed milling of aluminum alloys without the use of cutting fl uid............................................................................................................................................. 38 EQUIPMENT. INSTRUMENTS Borisov M.A., Lobanov D.V., Zvorygin A.S., Skeeba V.Y. Adaptation of the CNC system of the machine to the conditions of combined processing...................................................................................................................................... 55 Nosenko V.A., Bagaiskov Y.S., Mirocedi A.E., GorbunovA.S. Elastic hones for polishing tooth profi les of heat-treated spur wheels for special applications..................................................................................................................................... 66 Podgornyj Y.I., Skeeba V.Y., Martynova T.G., Lobanov D.V., Martyushev N.V., Papko S.S., Rozhnov E.E., Yulusov I.S. Synthesis of the heddle drive mechanism....................................................................................................... 80 MATERIAL SCIENCE Ragazin A.A., Aryshenskii V.Y., Konovalov S.V., Aryshenskii E.V., Bakhtegareev I.D. Study of the eff ect of hafnium and erbium content on the formation of microstructure in aluminium alloy 1590 cast into a copper chill mold............................................................................................................................................................................ 99 Zorin I.A., Aryshenskii E.V., Drits A.M., Konovalov S.V. Study of evolution of microstructure and mechanical properties in aluminum alloy 1570 with the addition of 0.5 % hafnium........................................................................... 113 Karlina Y.I., Kononenko R.V., Ivantsivsky V.V., Popov M.A., Deryugin F.F., Byankin V.E. Relationship between microstructure and impact toughness of weld metals in pipe high-strength low-alloy steels (research review)..................... 129 Patil N.G., Saraf A.R., Kulkarni A.P Semi empirical modeling of cutting temperature and surface roughness in turning of engineering materials with TiAlN coated carbide tool................................................................................. 155 Sawant D., Bulakh R., Jatti V., Chinchanikar S., Mishra A., Sefene E.M. Investigation on the electrical discharge machining of cryogenic treated beryllium copper (BeCu) alloys........................................................................................ 175 Karlina A.I., Kondratiev V.V., Sysoev I.A., Kolosov A.D., Konstantinova M.V., Guseva E.A. Study of the eff ect of a combined modifi er from silicon production waste on the properties of gray cast iron................................................. 194 EDITORIALMATERIALS 212 FOUNDERS MATERIALS 223 CONTENTS
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 6 1 4 Synthesis of the heddle drive mechanism Yuriy Podgornyj 1, 2, а, *, Vadim Skeeba 1, b, Tatyana Martynova 1, c, Dmitry Lobanov 3, e, Nikita Martyushev 4, f, Semyon Papko 1, f, Egor Rozhnov 1, g, Ivan Yulusov 1, h 1Novosibirsk State Technical University, 20 Prospekt K. Marksa, Novosibirsk, 630073, Russian Federation 2Novosibirsk Technological Institute (branch) A.N. Kosygin Russian State University (Technologies, Design, Art) 35 Krasny prospekt (5 Potaninskayast.), Novosibirsk, 630099, Russian Federation 3 I. N. Ulianov Chuvash State University, 15 Moskovsky Prospekt, Cheboksary, 428015, Russian Federation 4 National Research Tomsk Polytechnic University, 30 Lenin Avenue, Tomsk, 634050, Russian Federation a https://orcid.org/0000-0002-1664-5351, pjui@mail.ru; b https://orcid.org/0000-0002-8242-2295, skeeba_vadim@mail.ru; c https://orcid.org/0000-0002-5811-5519, martynova@corp.nstu.ru; d https://orcid.org/0000-0002-4273-5107, lobanovdv@list.ru; e https://orcid.org/0000-0003-0620-9561, martjushev@tpu.ru; f https://orcid.org/0009-0004-4512-5963, papko.duty@yandex.ru; g https://orcid.org/0009-0003-6779-0553, EgoRozhnov@yandex.ru; h https://orcid.org/0009-0006-7566-6722, yulusov.2017@stud.nstu.ru Obrabotka metallov - Metal Working and Material Science Journal homepage: http://journals.nstu.ru/obrabotka_metallov Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science. 2024 vol. 26 no. 1 pp. 80–98 ISSN: 1994-6309 (print) / 2541-819X (online) DOI: 10.17212/1994-6309-2024-26.1-80-98 ART I CLE I NFO Article history: Received: 12 December 2023 Revised: 08 January 2024 Accepted: 17 February 2024 Available online: 15 March 2024 Keywords: Loom Heddle motion mechanism Warp threads Kinematic chain Structural synthesis of mechanism Assur groups Kinematic scheme Cam mechanism Cam radius Roller Speeds Accelerations Motions Axes Funding This study was supported by a NSTU grant (project No. TP-PTM-1_24). Acknowledgements Research were conducted at core facility “Structure, mechanical and physical properties of materials”. ABSTRACT Introduction. Domestic enterprises in various industries use a variety of process equipment, including weaving machines. Modern weaving machines have several unique features, including a close relationship between technical condition, productivity, and product quality. Weaving machines are widely used in the textile industry in Russia and other countries. To produce cotton, silk, wool, linen, and other types of fabrics, appropriate machines are designed, including shuttle, shuttleless, pneumatic, and hydraulic machines. One of the most crucial parts of the machine is the heddle lifting mechanism, which determines the weave pattern and the quality of the fabric produced. The purpose of the work is to reduce the dimensions of the loom by changing the design parameters of the heddle lifting mechanism. The research methods are based on the theory of machines and mechanisms. They enable the development of a method for synthesizing the heddle lifting mechanism and designing a device with reduced dimensions. The paper presents the synthesis and analysis of the Assur group algorithm, which can determine the kinematic characteristics of the mechanism. Results and discussion. Following the proposed methodology, the mechanism design was modifi ed by removing the fi xing device from the lever mechanism operating area. This allowed for a reduction in interaxial distances and a change in the kinematic scheme. As a result of the new position of the fi xed axes, some levers, the connecting rod, and the angle of the double-arm lever were also altered. The synthesis of the mechanism is proposed to begin with the last Assur group, setting it a specifi c value for the G-point motion equal to 75 mm. (motion of the fourth heddle shaft). As a limitation, the equality of arcs (chords) E′E = F′F was accepted. By assigning these values to the input element for the second-class fi rst-type Assur group and bearing in mind the accepted conditions, the motions for point D were obtained. Thus, the value of the swing angle β of the roller shaft equal to 22.46° was obtained, which is 27.44 mm along the chord. Applying the interpolation principle, we found the initial motion value of 28 mm. Since the loom is planned to produce interlacing fabric patterns using 10 heddles, the design provides for a variable parameter that allows changing the motion of the heddles depending on their location in the depth of the machine. This role was assigned to the lever B03D. A cam pair synthesis was performed after determining the maximum and minimum values of the center of the roller motion. In total, 5 types of laws of motion were considered: straight-line, harmonic, double harmonic, power-law, cycloidal ones. For the center of the roller, the cycloidal law of motion was selected since it better corresponds to the specifi ed conditions. The synthesis's accuracy was confi rmed by the constructed cam profi le and conducted kinematic studies for the Assur groups. For citation: Podgornyj Y.I., Skeeba V.Y., Martynova T.G., Lobanov D.V., Martyushev N.V., Papko S.S., Rozhnov E.E., Yulusov I.S. Synthesis of the heddle drive mechanism. Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science, 2024, vol. 26, no. 1, pp. 80–98. DOI: 10.17212/1994-6309-2024-26.1-80-98. (In Russian). ______ * Corresponding author Podgornyj Yuriy I., D.Sc. (Engineering), Professor Novosibirsk State Technical University, 20 Prospekt K. Marksa, 630073, Novosibirsk, Russian Federation Tel: +7 (383) 346-17-79, e-mail: pjui@mail.ru
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 6 No. 1 2024 Introduction Domestic enterprises in various industries use a variety of process equipment, including weaving machines. Modern weaving machines have several unique features, including a close relationship between technical condition, productivity, and product quality. An essential feature of the process equipment is also the high kinematic complexity of the main mechanisms’ movement and the dynamic intensity of the machines’ operating modes [1–5]. One of the trends in the development of modern mechanical engineering is focused on improving existing and creating new high-performance equipment for weaving production. The increase in dynamic tension combined with that of operating speeds places higher requirements on the design of individual elements and assemblies, including drives that ensure intermittent movements of the machine’s working bodies [1, 6–9]. Currently, the production of a mass assortment of fabrics for consumer needs, including strong ones, is carried out mainly on shuttleless looms [2–18]. Shuttleless looms off er several advantages, including small dimensions, high performance, and automated fabric production processes. They are used to manufacture cotton, silk, wool, linen, technical, and other types of fabrics [3, 4, 9, 19]. One of the most important requirements for modern machines is that the followers are required to perform movements that accurately correspond to a specifi c law. This requirement is sometimes not feasible if simple part connections, such as levers, are being used. Therefore, shuttleless looms use cam links with various contour surfaces obtained using mathematical dependencies in their mechanisms. Compared with other transmission mechanisms, they have a number of advantages. The cam can be shaped to meet the kinematic and dynamic requirements of the developer. This allows for easy adaptation. The design of a cam is simple, allowing for precise execution of the required follower motion [1, 4, 10, 12, 19–25]. However, fabric formation on such machines can present several challenges, including increased vibrations and accelerated wear of mechanisms. These factors reduce the performance and quality of the fabric. In this regard, when designing machine mechanisms, it is important to consider dynamic characteristics, which depend on the smoothness and continuity in the graphs of the followers’ kinematic characteristics [10–12, 19–43]. The industrial use of shuttleless looms indicates that it is not possible to increase performance without considerable changes in defi nite mechanisms. First of all, it is necessary to modernize the mechanisms directly involved in the formation of fabrics. These include a mechanism designed to move the warp threads, i.e., a heddle lifting mechanism. The process of fabric formation on shuttleless looms is similar to that on shuttle looms: shed opening, picking of the weft thread, shed closing, battening of the weft thread to the cloth fell, and then the cycle repeats [40]. In the process of weaving, the warp threads bend around the weft threads and move from one side of the fabric to the other. Each main overlap on one side of the fabric corresponds to a weft overlap on the other. The pattern is created by various interlacing. This function is performed by a heddle lifting mechanism [40, 43]. Signifi cantly, there are a large number of shuttleless looms in the factories of the Russian Federation. Even a small reduction in the size of a machine can allow for more equipment to be placed in the factory, resulting in a signifi cant increase in performance per unit of production area. Consequently, reducing the dimensions of the shuttleless loom by reducing the size of the heddle lifting mechanism is an urgent and practical task. The purpose of the work is to reduce the dimensions of the loom by changing the design parameters of the heddle lifting mechanism. To achieve this goal, the following tasks were solved: – to analyze the possibility of changing the size of the kinematic scheme of the mechanism; – to develop a synthesis technique for the lever mechanism; – to select the necessary parameters for the synthesis of the cam pair and perform the synthesis; – to present the methodology of kinematic analysis and establish criteria for objectively evaluating the proposed solution. Research Methodology Consider the constructive scheme of the mechanism of the remission motion as shown in Fig. 1. It includes drive cams (7), a shaft with rollers (6), a connecting link (10), an eccentric mechanism (11), a double-arm lever (1), and a horizontal rod (9). As can be seen from the diagram, an eccentric
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 6 1 4 mechanism (11) is located inside the lever system. The purpose of this mechanism is to bring the system of levers and rods to a certain position, which contributes to their setting parameters, when installing a set of cams and heddle frames [44]. Relocating the eccentric mechanism (11) from the lever system to the body side is suggested. In this case, it will be possible to change the positions of the fi xed axes and reduce the distances between the axes of the double-arm levers and the roller shaft. Due to the change in these positions, the dimensions of the levers and rods will change, which will require a new synthesis of the lever system. The reduction in the dimensions of the mechanism is due to the removal of the mechanism for fi xing the position of the heddle (eccentric mechanism) from the area of the lever system. This solution allowed for the reduction of the distance between the O2 and O3 axes. As a result of the change in these parameters, the synthesis of the attached structural groups was necessary. Some of the elements, such as the doublearm lever FO4E and the slider G, which is a heddle shaft, will not change their geometric parameters. The fi xed axes of the mechanism’s kinematic scheme are marked in Fig. 2. The O2 axis is at a distance of 151 mm from the origin, the O3 is at a distance of 311 mm from the O1 axis, the dimension of the O2 B lever is 192.5 mm. Due to the new position of the axes, the levers O2B, O3C, and O3 D, as well as the rod BC, should be changed, and their values should be obtained as a result of synthesis. In addition, the angle of the doublearm lever AO2B should be reduced by 35 degrees so that it does not take up much space when defl ected. The lever mechanism is synthesized assuming that it starts from the last link, which is responsible for the stroke provided by the amount of heddle lifting. For instance, the stroke of the fourth heddle shaft should be 75 mm [1, 19]. The symmetry of the heddle stroke relative to the horizontal axis was chosen as the main criterion for synthesis. Thus, for the fourth heddle shaft, it was 37.5 mm. According to the technical documentation, the lever has a size of O4E = 138.5 mm. Then, for the fourth heddle shaft, the value of the angle is μ 1 (see Fig. 2). 1 4 arctan 2 EE O E μ æ ¢ ö÷ ç ÷ = ç ÷ ç ÷ çè ⋅ ø , (1) where EE´= 75 mm. Fig. 1. The design scheme of the heddle motion consists of several components, including a two-arm lever (1), a hub (2), a body (3), a shaft (4), a top arm (5), a roller lever (6), eccentric drive (7), a bottom arm (8), a horizontal rod (9), a connecting rod (10), eccentric mechanism (11)
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 6 No. 1 2024 Fig. 2. Kinematic scheme of the heddle drive mechanism The angle value is μ 1 = 15.15°. Further synthesis of the lever mechanism is carried out on the assumption that the angle of the lever rotation O3DD′ is equal to the angle O4EE′, while the hard angle for the lever CO3D is assumed to be 155°. In this case (see Fig. 2), the angle ξ is determined by: 1 180 ( ( 90 )), ξ μ μ = - - + (2) Here, the angle ξ = 130.15°. To determine the angle ξ 1, it is necessary to consider the triangle O2CO3. First of all, from an oblique triangle, we defi ne the side O21: 2 2 2 1 2 3 3 2 3 3 2 cos , O C O O O C O O O C ξ ¢ ¢ = + - ⋅ ⋅ (3) We received O2C1 = 270.849 mm. Then the angle ξ1 is determined from the expression: 1 1 180 ( (90 )), ξ μ μ = - - - (4) Its values were ξ1 = 99.85°. From the oblique triangle 2 3 O CO¢ , we defi ne the side O 2C′ 2 2 2 2 3 3 2 3 3 1 2 cos , O C O C O C O O O C ξ ¢ ¢ ¢ = + - ⋅ ⋅ ⋅ (5) The side size is O2C′ = 228.832 mm. Similarly, the rod length VS = 225 mm is found from the oblique triangles O2C0O3 and O2B0C0. To determine the angles v1 and v2, consider the expression 3 2 2 arcsin sin O C O C ν ξ æ ¢ ö÷ ç ÷ = ⋅ ç ÷ ç ÷ ç ¢ è ø , (6) The value of this angle is v2 = 23.008°.
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 6 1 4 3 1 1 2 arcsin sin O C O C ν ξ æ ö÷ ç ÷ = ⋅ ç ÷ ç ÷ çè ø , (7) The angle value is v1 = 36.607°. The angles ω1 and ω2 are determined from the triangles O2B′C′ and O2BC: 2 2 2 2 2 1 2 2 arccos 2 O B O C C B O B O C ω æ ö ¢ ¢ ¢ ¢ + - ÷ ç ÷ ç = ÷ ç ÷ ç ¢ ¢ ⋅ ⋅ ÷ çè ø , (8) Then the angle is ɷ1= 55.014 °. 2 2 2 2 2 2 2 2 arccos 2 O B O C CB O B O C ω æ ö + - ÷ ç ÷ ç = ÷ ç ÷ ç ⋅ ⋅ ÷ çè ø , (9) Then ω2 = 63.874°. The swing angle of the roller shaft is determined by: 2 1 1 2 ( ) β ω ν ω ν = + - + , (10) Its value is β = 22.46°. Under such conditions, the stroke of the roller center is 27.44 mm. The dimension of the connecting link DE was determined by the position of the points DE and amounted to 1133 mm for the fourth heddle shaft. Based on the data from the technical documentation of the weaving machine manufacturer (Sibtextilmash plant), the minimum and maximum radius vectors of the cam were rmin = 124.5 mm and rmax = 152.5 mm; in this case, the stroke of the roller center along the chord is 28 mm. In order to leave these parameters unchanged, we changed the dimensions of the lever O3C, and interpolating the values obtained, we found the necessary size for the lever, equal to 142.5 mm, which provided the necessary stroke of the center of the roller (28 mm). The main dimensions of the lever system obtained as a result of synthesis are summarized in Table. Link dimensions Link dimensions, mm АО2 ВО2 ВС СО3 DО3 DE EО4 70 192.5 225 142.5 138.5 1133 138.5 To ensure an interlacing pattern based on 10 heddle shafts, the heddle lifting mechanism must allow for determining the stroke of each shaft [10]. For this purpose, consider the diagram shown in Fig. 3. Where hi is the height of the shed; t is the stroke between the heddle shafts; Δhi is the increments of the shafts stroke; αp is half of the angle of the shed, representing only a part of the shed. In this case, the amount of opening for a full shed (the stroke of heddle shafts) can be determined by the formula: 1 ( ( 1) tan( ) 2 n H h n t α é ù = + - ⋅ ⋅ ⋅ ê ú ë û ð , (11) To implement dependence (11), it is necessary that the dimensions of the lever DO3 correspond to the specifi ed motion of the heddle. Consider the kinematic scheme shown in Fig. 2. The angle μ1 for the arm DO3 is left unchanged, and the chord D0D takes a value equal to half the stroke of the heddle shaft. Taking into account the expression (11), we obtain: ( ) 1 tan 2 n n H L μ = ⋅ , (12)
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 6 No. 1 2024 Fig. 3. A fragment of a half-open shed of a loom where Ln is the dimension of the lever; Hn is the full stroke of the heddle shaft corresponding to its number; μ1 is the angle determining the position of the lever relative to the vertical axis. After determining the required dimensions of the lever system, the synthesis of the cam mechanism becomes possible. The synthesis of the mechanism begins with determining the main parameters and the law of motion for the roller center [10–12, 24–39, 45, 46]. It was necessary to determine the law for the roller center motion because we were only given a table of radius vector values. We considered power-law, straight-line, simple harmonic, double harmonic and cycloidal laws of motion. There is no need to dwell on this in more detail, as it is well described in [10–12, 19, 24–28, 35–38, 45, 46]. The law of motion of the roller center along the cycloid was found to be the most acceptable for the case under consideration. For the synthesis of the cam mechanism, the following calculated data were used: minimum cam radius rmin = 124.5, maximum cam radius rmax = 152.5; roller radius R = 75 mm; phase angles: heddle lifting φ1 = 70°, delay in the upper position – φ2 = 110°, lowering of the heddle – φ3 = 70°, delay in the lower position is φ4 = 110°; the interaxial distance is O1O2 = 151 mm. The coeffi cients for the cycloid calculations are taken from [10–12, 19, 24–28, 35–38, 45, 46]: 1 max 3 max 2 2 1 3 2 2 ; k S k S π π ϕ ϕ = ⋅ = ⋅ . The calculation of acceleration analogues was performed using the formula: ( ) 1 1 1 1 2 1 3 1 2 1 2 3 3 1 2 3 2 sin 0 0 2 sin 0 360 k if if a k if if π ϕ ϕ ϕ φ ϕ ϕ ϕ ϕ ϕ π ϕ ϕ ϕ ϕ ϕ ϕ ϕ φ ϕ ϕ ϕ æ ö÷ ç ÷ ⋅ ⋅ £ £ ç ÷ ç ÷ çè ø £ £ + = æ ö÷ ç ÷ ⋅ ⋅ + £ £ + + ç ÷ ç ÷ çè ø + + £ , (13) To determine the speed of the roller center, we integrated accelerations from 0° to 360° of cam rotation. 0 ( ) ( ) ( ) V a d ϕ ϕ ϕ ϕ =ò , (14) To determine the motion of the roller center, we integrated the speeds from 0° to the 360° cam rotation. 0 ( ) ( ) ( ) S V d ϕ ϕ ϕ ϕ =ò , (15) Graphs of kinematic characteristics for the roller center of the cam mechanism are shown in Fig. 4.
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 6 1 4 To prevent jamming and ensure the strength of the cam pair of the mechanism, it is necessary to know the numerical values of the pressure angles, which in our case should not exceed 45 °. The program developed for this purpose calculated the pressure angle values. Because the determination procedure is cumbersome, it is not presented in the paper. They did not exceed acceptable values in the entire range of studies conducted. To confi rm the accuracy of the selected roller dimension, its value was compared with the actual radius of curvature, determined by the formula: ( ) ( ) 3 2 2 2 2 2 2 i i i i i y y y y y y ρ é ù ê + ú ë û = + ⋅ - ⋅ , (16) where , , , i i i i y y y ρ are the radius vectors of the center profi le of the cam and the derivatives at the i-th point. A program for the mathematical software package was developed for this purpose. The calculation results are shown in Fig. 5. The conditions agree well with the expression: min 0 0, 7 ; 0, 4 r r r ρ £ ⋅ £ ⋅ , (17) where min ρ is the minimum radius of curvature of the cam’s center profi le. The data analysis results suggest that the roller radius choice for the cam mechanism is accurate. Next, the cam profi le (radius vectors of the cam r(i)) was determined using equation (15). The calculation was carried out in a mathematical sotware package; the matrix of values of radius vectors and the shape of the cam profi le are shown in Fig. 6. To confi rm the accuracy of the selected link dimensions, it is necessary to conduct a kinematic analysis for individual Assur groups. If their graphs have smooth and continuous characteristics, we assume that the synthesis was accurate. For kinematic analysis, the dimensions of the links obtained as a result of the lever system synthesis were used (see Table 1). Kinematic analysis began with a fi rst-class fi rst-order mechanism, which was used as a variable radius vector shown in the table (Fig. 6) [10–12, 19, 24–28, 35– a b c Fig. 4. Graphs of kinematic characteristics’ analogs for the center of the roller: (a) acceleration; (b) speed; (c) motion Fig. 5. Pressure angles for the cam mechanism
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 6 No. 1 2024 i:=0deg..5deg..360deg r:= 0deg 10deg 20deg 30deg 40deg 50deg 60deg 70deg 80deg 90deg 100deg 110deg 120deg 130deg 140deg 150deg 160deg 170deg 180deg 190deg 200deg 210deg 220deg 230deg 240deg 250deg 260deg 270deg 280deg 290deg 300deg 310deg 320deg 330deg 340deg 350deg 152.5 152.268 149.728 143.352 135.049 128.351 125.055 124.5 124.5 124.5 124.5 124.5 124.5 124.5 124.5 124.5 124.5 124.5 124.5 125.055 128.351 135.049 143.352 149.728 152.268 152.5 152.5 152.5 152.5 152.5 152.5 152.5 152.5 152.5 152.5 152.5 r:=csort(r, 0) ‹0› ‹1› x:=r y:=r c:=cspline(x, y) r(i):=interp(c, x, y, i) a b Fig. 6. The matrix of values of radius vectors and the shape of the cam profi le: (a) radius vectors of the cam; (b) shape of the cam profi le 38, 45, 46]. Fig. 7 shows a diagram for determining the coordinates of point B. In this case, it is necessary to have the radius vectors of the cam r(i), as well as the lengths of the links AB, BO2, coordinates O1 and O2 (see Table), and a hard angle θ. According to the cosine theorem, we fi nd the angle α (Fig. 8) from the triangle AO1O2 2 2 2 1 2 2 1 2 2 ( ) arccos 2 O O AO r i O O AO α æ ö + - ÷ ç ÷ ç = ÷ ç ÷ ç ⋅ ÷ çè ø , (18) The angle δ is determined by: ( ) δ π α θ = - + . (19) Fig. 7. The second-class fi rst-type Assur group attached to the fi rst-class fi rst-type mechanism
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 6 1 4 Fig. 8. The second-class fi rst-type Assur group The coordinates of point B are found as projections on the X and Y axes: 1 2 2 cos( ) XB O O BO δ = - ⋅ , (20) 2 sin( ) YB BO δ = ⋅ . (21) By determining the coordinates of point B, you can fi nd the resulting value according to the expression: 2 2. B XB YB = + (22) For the second-class fi rst-type Assur group (Fig. 8), the following values are set: coordinates of point B and O3, lengths of links BC, CO3, and CD (Table 1), as well as the angle determining the position of vector B. To determine the coordinates of point D, it is necessary to determine the angle f of the lever DC and the value of the segment BO3 from the triangle BO2O3 according to the cosine theorem. 1 1 3 arctan y f O O x æ ö÷ ç ÷ = ç ÷ ç ÷ ç è - ø , (23) 2 2 3 2 2 3 2 2 3 1 2 cos( ) BO BO O O BO O O f = + - ⋅ ⋅ ⋅ , (24) 2 2 2 3 3 2 3 3 arccos 2 BO CO BC f BO CO æ ö + - ÷ ç ÷ ç = ÷ ç ÷ ç ⋅ ÷ çè ø , (25) 1 2 ( ) f f f π = - + . (26) The coordinates of points C and D are found as projections on the OX and OY axes: 1 3 3 cos( ) XC O O CO f = + ⋅ , (27) 3 sin( ) YC CO f = ⋅ , (28) 1 3 3 cos( ) XD O O DO f = - ⋅ , (29) 3 sin( ) YD DO f = ⋅ . (30) Further, according to the Pythagorean theorem, their resulting values were found: 2 2 C XC YC = + , (31) 2 2 D XD YD = + . (32)
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 6 No. 1 2024 Consider the second Assur group, which is part of the general scheme of the heddle motion mechanism. This is also second-class fi rst-order group (Fig. 9). Fig. 9. The second-class fi rst-type Assur group, which is part of the general scheme of the heddle motion mechanism The following values should be set for this group: the coordinates of points D and O4, the lengths of the links DE, GO4 and the hard angle between EO4 and GO4. From the triangle DEO4, according to the Pythagorean theorem, we determine the hypotenuse DO4 by the formula: ( )2 2 4 1 4 DO O O XD YD = - + . (33) From the triangle DEO4, we fi nd the angle s by the cosine theorem 2 2 2 4 4 4 4 arccos 2 DO EO DE DO EO χ æ ö + - ÷ ç ÷ ç = ÷ ç ÷ ç ⋅ ⋅ ÷ çè ø . (34) The angle ψ is determined by: 4 arcsin YD DO ψ æ ö÷ ç ÷ = ç ÷ ç ÷ çè ø . (35) Then the angle χ1 is found as: 1 χ ψ χ = + . (36) The coordinates of the point E are found as projections on the axes OH and OY: 1 4 4 1 cos( ) XE O O EO χ = - ⋅ , (37) 4 1 sin( ) YE EO χ = ⋅ . (38) The value of motion E is determined by: 2 2 E XE YE = + . (39) The angle of the lever position GO 4 E is found as the angle diff erence: 1 ε χ γ = - . (40) The coordinates and the length of the vector of the point G are defi ned as: 1 4 4 cos( ) XG O O GO ε = - ⋅ , (41) 4 sin( ) YG GO ε = ⋅ . (42)
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 6 1 4 The resultant is determined by: 2 2 G XG YG = + . (43) Consider the last Assur group for our mechanism. It is a second-class second-type group (Fig. 10). The length of the link GF, the x coordinate of the guide along which the slider F moves (in this case, it is zero) are needed to determine the trajectory of the point F. The length of the projection of the GF link on the OX axis is equal to the diff erence between the coordinates of the G point and the guide for the slider. Fig. 10. The second-class second-type Assur group Based on Fig. 10, the value of T is determined by: T XF XG = - . (44) From the GFT triangle, according to the Pythagorean theorem, we defi ne: 2 2 YF GF T = - . (45) Then the total motion of the point F is determined: ( )o YF EG YF = + . (46) Results and discussion The analysis revealed that the heddle fi xing mechanism can be placed outside the heddle frame. As a result, the values of the axial distance O2O3 were reduced by 100 mm. Due to the fact that the heddle shaft stroke is a known value obtained as a result of calculations of the shed geometry [1] (point G in Fig. 2), the methodology of synthesizing the mechanism [9, 29, 35, 36, 45–49] for moving the heddle suggests starting it from the last Assur group. The motion of the fourth heddle shaft equal to 75 mm is accepted as a known parameter [1, 9, 10, 29, 35, 36, 45–49]. The synthesis condition for this group is the equality of chords E′E = F′F relative to the horizontal axis. The angles of rotation of these levers are also equal and amount to μ1 = 15.15°. They were given previously and defi ned by formula (1). Further synthesis was carried out for the fourth second-class fi rst-type Assur group. Signifi cantly, the main condition for synthesis is the equalization of arcs (chords) E′E = D′D, EE0 = DD0 and arm lengths O4E = O3D. Further synthesis of the mechanism consisted of determining the swing angle of the lever with rollers, which is calculated by the formula (10). The swing angle of this lever depends, among other things, on the dimension of the arm O3D. The dimensions of this lever were taken within the range of 138.5–143.5 mm. By interpolating the values of angle β, we determined that β = 22.926°, corresponding to a chord length of 28 mm. We then calculated the length of the arm O3D of the lever O3DC to be 143.5 mm. When tackling the loom for manufacturing a variety of fabrics, up to ten heddles may be used, and their movement is determined by their position within the machine. Therefore, the dimension of one of the levers in the kinematic scheme, which allows the adjustment of the heddles’ stroke, was chosen as a variable parameter. In our case, it was the DO3 lever. Using the analytical dependences (11) and (12), it is possible to calculate the length of the DO3 lever and the value of the heddles’ stroke.
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 6 No. 1 2024 After the synthesis of the lever mechanism, which enabled calculating the motion of the roller center equal to 28 mm, the main parameters for the synthesis of the cammechanismwere determined. The synthesis justifi ed the law of motion of the roller center along the cycloid and determined the radii of curvature (see Fig. 5). This led to the conclusion that a roller radius of 37.5 mm satisfi es condition (17). The calculated pressure angles are within acceptable limits throughout the entire range of rotation of the main shaft, from 0° to 360°. The radius vectors of the cam are shown as a matrix of values (Fig. 6). After processing the tabular values of the radius vectors with splines, we conducted a kinematic analysis of the mechanism for the characteristic points of the Assur groups. The purpose of this analysis was to confi rm the accuracy of the synthesis and the smoothness and continuity of the kinematic parameters graphs of the Assur groups characteristic points. For the latter group, it was necessary to confi rm the value of the heddle shaft stroke for point G, since it was the basis for calculating and constructing the synthesis methodology. Thus, for point B, the kinematic characteristics are shown in Fig. 12, and for point C, in Fig. 11. For point D, the kinematic characteristics are shown in Fig. 13. a b Fig. 12. Kinematic characteristics for point C: (a) velocity; (b) acceleration a b Fig. 11. Kinematic characteristics for point B: (a) velocity; (b) acceleration
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 6 1 4 a b Fig. 13. Kinematic characteristics for point D: (a) velocity; (b) acceleration The analysis showed that the velocities and accelerations for points A, B, C, D, E, G, F have smooth and continuous graphs, which indicates a properly conducted synthesis of the lever system for individual Assur groups. The kinematic characteristics for points G and E are not given in the work. Motion for point F is shown in Fig. 14. a b с Fig.14. Kinematic characteristics for point F: (a) motion; (b) velocity; (c) acceleration The economic eff ect of the proposed solution implementation was determined based on the data of the work [10], where the removal of products from 1 m2 of the production area, adjusted for the rotation frequency of the main shaft equal to 300 min-1, is 1.035 m2/hour. Conclusion The main purpose of the work was to reduce the dimensions of the loom by changing the design parameters of the heddle lifting mechanism. As a result of placing the heddle fi xing mechanism outside of the heddle frame, the dimension of O2O3 was reduced by 100 mm. In this regard, all dimensions for the
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 6 No. 1 2024 elements included in the Assur groups were changed, with the exception of the last one. The presented synthesis methodology assumes that it is carried out in the reverse sequence of their connection. Synthesis for the lever system should be carried out for the fourth heddle shaft, for which a motion of point G was set to be 75 mm. First of all, the swing angle of the lever CO3 D was determined, which was equal to the swing angle of the other lever EO4F. Then the dimension of the CO3 arm was determined, which was 143.5 mm. As a result, the stroke of the center of the roller was equal to 28 mm. Since the stroke of the heddle is diff erent in the depth of the loom, the value of the lever DO3 was chosen as the variable parameter. The variable parameters of the DO3 lever and the heddle stroke were calculated using the analytical dependencies presented in [10] and a mathematical software package of application programs. The results are shown in Fig. 10. As a result of the synthesis, the dimension of the connecting link BC was calculated to be 225 mm, the link O3D was 138.5 mm, and the angle between the arms O3D and CO3 was 155 °. The connecting rod DE assumed the value of 1133 mm. The objectivity of the synthesis is confi rmed by the results of the conducted studies for Assur groups. The kinematic characteristics for individual points of the mechanism are presented in the form of graphs and have smooth, continuous functions, which indicates the quality of the synthesis performed. References 1. Ditskii A.V., Malafeev R.M., Terent’ev V.I., Tuvaeva A.A. Osnovy proektirovaniya mashin tkatskogo proizvodstva [Basics of designing weaving machines]. Moscow, Mashinostroenie Publ., 1983. 320 p. 2. Podgornyj Yu.I., Skeeba V.Yu., Kirillov A.V., Maksimchuk O.V., Lobanov D.V., Gleim V.R., Zhigulev A.K., Sakha O.V. Vybor konstruktivnykh parametrov nesushchikh sistem mashin s uchetom tekhnologicheskoi nagruzki [Selection of form factors of machine carrying systems in reliance on the process duty]. Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science, 2015, no. 4, pp. 51–60. DOI: 10.17212/1994-6309-2015-4-51-60. 3. Podgornyj Yu.I., Skeeba V.Yu., Kirillov A.V., Maksimchuk O.V., Martynova T.G., Lobanov D.V., Filatov I.S., Skeeba P.Yu. Opredelenie zhestkostnykh kharakteristik i energii deformatsii nesushchikh sistem tekhnologicheskikh mashin [Determination of the rigidity and deformation energy of the technological machine load-carrying systems]. Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science, 2016, no. 4 (73), pp. 24–33. DOI: 10.17212/1994-6309-2016-4-24-33. 4. Podgornyj Yu.I., Skeeba V.Yu., Kirillov A.V., Maksimchuk O.V., Skeeba P.Yu. Proektirovanie kulachkovogo mekhanizma s uchetom tekhnologicheskoi nagruzki i energeticheskikh zatrat [Cam mechanism designing with account of the technological load and energy costs]. Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science, 2017, no. 2 (75), pp. 17–27. DOI: 10.17212/1994-6309-2017-2-17-27. 5. Podgornyj Yu.I., Maximchuk O.V., Kirillov A.V., Skeeba V.Yu. Osobennosti tsiklogrammirovaniya mashiny s uchetom vzaimodeistviya zven’ev mekhanizmov s uporami [Features of machine cyclogram optimization with the account of interaction of mechanism links with stops]. Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science, 2018, vol. 20, no. 1, pp. 44–54. DOI 0.17212/1994-6309-2018-20.144-54. 6. Lushnikov S.V., Belyi M.A. Issledovanie vozmozhnosti uravnoveshivaniya sil na glavnom valu tkatskikh stankov STB s ispol’zovaniem kulachkov-razgruzhatelei [Investigation of the possibility of balancing forces on the main shaft of STB looms using fi st-unloaders]. Izvestiya vysshikh uchebnykh zavedenii. Tekhnologiya tekstil’noi promyshlennosti = Proceedings of Higher Educational Institutions. Technology of the textile industry, 2009, no. 2S, pp. 85–88. 7. Gusev V.A., Danilov V.V., Tsvetkov D.M., Smirnov A.B. Razrabotka metodiki otsenki geometricheskoi tochnosti profi lei kulachkov batannogo mekhanizma stanka STB [Development of a methodology for evaluating the geometric accuracy of the cams of the sley mechanism of the STB machine]. Izvestiya vysshikh uchebnykh zavedenii. Tekhnologiya tekstil’noi promyshlennosti = Proceedings of Higher Educational Institutions. Technology of the textile industry, 2007, no. 6S, pp. 92–97. 8. Terekhina A.O., Solov’ev A.B. Modernizirovannyi kulachkovyi privod batannogo mekhanizma tkatskogo stanka tipa STB [Modernized cam drive for the sley mechanism of the STB loom]. Izvestiya vysshikh uchebnykh
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 6 1 4 zavedenii. Tekhnologiya tekstil’noi promyshlennosti = Proceedings of Higher Educational Institutions. Technology of the textile industry, 2004, no. 2, pp. 80–83. 9. Podgornyj Yu.I., Kirillov A.V., Ivancivsky V.V., Lobanov D.V., Maksimchuk О.V. Sintez zakona dvizheniya mekhanizma priboya utochnykh nitei stanka STB s privodom ot kulachkov [Synthesis of the motion law of fi lling threads beat-up mechanisms of the STB loom with cam driven]. Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science, 2019, vol. 21, no. 4, pp. 47–58. DOI: 10.17212/1994-63092019-21.4-47-58. 10. Podgornyj Yu.I., Skeeba V.Yu., Martynova T.G., Maksimchuk O.V Issledovanie i vybor parametrov pri proektirovanii tekhnologicheskikh mashin [Analysis and choice of parameters in designing technological machines]. Novosibirsk, NSTU Publ., 2020. 260 p. ISBN 978-5-7782-4177-0. 11. Vul’fson I.I. Dinamika tsiklovykh mashin [Dynamics of cyclic machines]. St. Petersburg, Politekhnika Publ., 2013. 425 p. ISBN 978-5-7325-1024-9. 12. Podgornyj Yu.I., Martynova T.G., Skeeba V.Yu. Sintez tekhnologicheskikh mashin. Raschet i konstruirovanie [Synthesis of technological machines. calculation and design]. Novosibirsk, NSTU Publ., 2023. 240 p. ISBN 978-57782-4912-7. DOI: 10.17212/978-5-7782-4912-7. 13. Erokhin E.G., Vasil’eva N.M., Sokerin E.F., Kareva T.Y. Kulachkovyi zevoobrazovatel’nyi mekhanizm beschelnochnogo tkatskogo stanka [Cam shedding mechanism of shuttleless loom]. Patent RF, no. 2120508, 1998. 14. Rybakov E.A., Vorob’ev M.I., Shumov G.V. Ustroistvo remiznogo dvizheniya tkatskogo stanka [Loom harness motion]. Patent RF, no. 2176692, 2001. 15. Mshvenieradze A.P. Tekhnologiya i oborudovaniya tkatskogo proizvodstva [Technology and equipment for weaving production]. Moscow, Legkaya i pishchevaya promyshlennost’ Publ., 1984. 362 p. 16. Onikov E.A. Tekhnologiya, oborudovanie i rentabel’nost’ tkatskogo proizvodstva [Technology, equipment and profi tability of weaving production]. Moscow, Tekstil’naya promyshlennost’ Publ., 2003. 320 p. 17. Granovskii T.S., Mshvenieradze A.P. Stroenie i analiz tkanei [Structure and analysis of tissues]. Moscow, Legprombytizdat Publ., 1988. 93 p. 18. Tolubeeva G.I. Osnovy proektirovaniya odnosloinykh remiznykh tkanei [Basics of designing single-ply heald fabrics]. Ivanovo, IGTA Publ., 2005. 200 p. 19. Podgornyi Yu.I. Metody issledovaniya zapravok, ikh sintez i razrabotka kriteriev optimal’nosti uslovii ekspluatatsii tkatskikh stankov pri formirovanii plotnykh tkanei. Diss. dokt. tekhn. nauk [Research methods refi lls, their synthesis and development of criteria of optimality conditions looms in the formation of dense tissue. Dr. eng. sci. diss.]. Kostroma, 1990. 541 p. 20. Flores P., Souto A.P., Marques F. The fi rst fi fty years of the mechanism and machine theory: standing back and looking forward. Mechanism and Machine Theory, 2018, vol. 125, pp. 8–20. DOI: 10.1016/j. mechmachtheory.2017.11.017. 21. Chen K., Wang M., Huo X., Wang P., Sun T. Topology and dimension synchronous optimization design of 5-DoF parallel robots for in-situ machining of large-scale steel components. Mechanism and Machine Theory, 2023, vol. 179, p. 105105. DOI: 10.1016/j.mechmachtheory.2022.105105. 22. Eckhardt H.D. Kinematic design of machines and mechanisms. 1st еd. NewYork, McGraw-Hill, 1998. 620 p. ISBN 0070189536. ISBN 978-0070189539. 23. Erdman A.G., Sandor G.N. Mechanism design: analysis and synthesis. 4th ed. Upper Saddle River, NJ, Pearson, 2001. 688 p. ISBN 0130408727. ISBN 978-0130408723. 24. Hsieh J.-F. Design and analysis of indexing cam mechanism with parallel axes. Mechanism and Machine Theory, 2014, vol. 81, pp. 155–165. DOI: 10.1016/j.mechmachtheory.2014.07.004. 25. Zhu B., Zhang X., Zhang H., Liang J., Zang H., Li H., Wang R. Design of compliant mechanisms using continuum topology optimization: a review. Mechanism and Machine Theory, 2012, vol. 143, p. 103622. DOI: 10.1016/j.mechmachtheory.2019.103622. 26. Faxin L., Xianzhang F. The design of parallel combination for cam mechanism. Procedia Environmental Sciences, 2011, vol. 10, pt. B, pp. 1343–1349. DOI: 10.1016/j.proenv.2011.09.215. 27. Sateesh N., Rao C.S.P., Janardhan Reddy T.A. Optimisation of cam-follower motion using B-splines. International Journal of Computer Integrated Manufacturing, 2009, vol. 22 (6), pp. 515–523. DOI: 10.1080/ 09511920802546814. 28. Rothbart H.A. Cam design handbook. NewYork, McGraw-Hill Professional, 2003. 606 p. ISBN 0071377573. ISBN 978-0875841830.
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 6 No. 1 2024 29. Myszka D.H. Machines & mechanisms: applied kinematic analysis. 4th ed. Upper Saddle River, NJ, Pearson, 2012. 376 p. ISBN 0132157802. ISBN 978-0132157803. 30. Dresig H., Vul’fson I.I. Dynamik der mechanismen. Wien, New York, Springer, 1989. 328 p. ISBN 978-37091-9036-4. DOI: 10.1007/978-3-7091-9035-7. 31. Frolov K.V. Teoriya mekhanizmov i mashin [Theory of mechanisms and machines]. Moscow, Vysshaya shkola Publ., 1987. 496 p. 32. Varbanov H., Yankova T., Kulev K., Lilov S. S&A – Expert system for planar mechanisms design. Expert Systems with Applications, 2006, vol. 31 (3), pp. 558–569. DOI: 10.1016/j.eswa.2005.09.081. 33. Fomin A., Paramonov M. Synthesis of the four-bar double-constraint mechanisms by the application of the Grubler’s method. Procedia Engineering, 2016, vol. 150, pp. 871–877. DOI: 10.1016/j.proeng.2016.07.034. 34. Fomin A., Dvornikov L., Paramonov M., Jahr A. To the theory of mechanisms subfamilies. IOP Conference Series: Materials Science and Engineering, 2016, vol. 124, p. 012055. DOI: 10.1088/1757-899X/124/1/012055. 35. Vulfson I. Dynamics of cyclic machines. Cham, Springer International, 2015. 390 p. ISBN 978-3-319-126333. DOI: 10.1007/978-3-319-12634-0. 36. Ondrášek J. The synthesis of a hook drive cam mechanism. Procedia Engineering, 2014, vol. 92, pp. 320– 329. DOI: 10.1016/j.proeng.2014.12.129. 37. Mott R.L. Machine elements in mechanical design. 5th ed. Upper Saddle River, NJ, Pearson, 2013. 816 p. ISBN 0135077931. ISBN 978-0135077931. 38. Zhoua C., Hua B., Chenb S., Mac L. Design and analysis of high-speed cam mechanism using Fourier series. Mechanism and Machine Theory, 2016, vol. 104, pp. 118–129. DOI: 10.1016/j.mechmachtheory.2016.05.009. 39. Artobolevskii I.I. Teoriya mekhanizmov i mashin: uchebnik dlya vtuzov [Theory of mechanisms and machines]. 4th ed. Moscow, Nauka Publ., 1988. 640 p. ISBN 5-02-013810-X. 40. Levitskii N.I. Teoriya mekhanizmov i mashin [Theory of mechanisms and machine]. 2nd ed. Moscow, Nauka Publ., 1990. 592 p. ISBN 5-02-014188-7. 41. Talavashek O., Svatyi V. Beschelnochnye tkatskie stanki [Shuttleless looms]. Moscow, Legprombytizdat Publ., 1985. 355 p. 42. Bashmetov V.S., Bashmetov A.V. Prokladyvanie utochnykh nitei na tkatskikh stankakh [Laying weft threads on looms]. Vitebsk,VGTU Publ., 2012. 98 p. 43. Tir K.V. Kompleksnyi raschet kulachkovykh mekhanizmov [Complex calculation of cam mechanisms]. Moscow, Mashgiv Publ., 1958. 380 p. 44. Kuzovkin K.S. Opyt raboty na stankakh STB [Experience working on STB machines]. Moscow, Mashinostroenie Publ., 1968. 238 p. 45. Podgornyj Yu.I., Skeeba V.Yu., Martynova T.G., Pechorkina N.S., Skeeba P.Yu. Kinematic analysis of crankcam mechanism of process equipment. IOP Conference Series: Materials Science and Engineering, 2018, vol. 327, p. 042080. DOI: 10.1088/1757-899X/327/4/042080. 46. Yang J., Wu C., Shao N., Liu F., Cao Y., Cao Y., Anwer N. Kinematic accuracy analysis for cam mechanism considering dynamic behavior and formdeviations. PrecisionEngineering, 2024, vol. 88, pp. 109–116. DOI: 10.1016/j. precisioneng.2024.01.023. 47. Podgornyj Yu.I., Skeeba V.Yu., Kirillov A.V., Martynova T.G., Skeeba P.Yu. Motion laws synthesis for cam mechanisms with multiple follower displacement. IOP Conference Series: Materials Science and Engineering, 2018, vol. 327, p. 042079. DOI: 10.1088/1757-899X/327/4/042079. 48. Neklyutin D.A. Optimal’noe proektirovanie kulachkovykh mekhanizmov na EVM [Optimal design of cam mechanisms on a computer]. Moscow, Almata Publ., 1977. 215 p. 49. Tartakovskii I.I. Nekotorye zadachi sinteza optimal’nykh zakonov dvizheniya [Some problems of synthesis of optimal laws of motion]. Mashinostroenie = Mechanical Engineering, 1971, no. 2, pp. 39–43. Confl icts of Interest The authors declare no confl ict of interest. © 2024 The Authors. Published by Novosibirsk State Technical University. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0).
RkJQdWJsaXNoZXIy MTk0ODM1