Vol. 27 No. 1 2025 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. 27 No. 1 2025 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. 27 No. 1 2025 5 CONTENTS OBRABOTKAMETALLOV TECHNOLOGY Umerov E.D., Skakun V.V., Dzhemalyadinov R.M., Egorov Y.A. Investigation of the eff ect of oil-based MWFs with enhanced tribological properties on cutting forces and roughness of the processed surfaces.............................................. 6 Manikanta J.E., Ambhore N., Thellaputta G.R. Investigation of vegetable oil-based cutting fl uids enhanced with nanoparticle additions in turning operations........................................................................................................................ 20 Shlykov E.S., Ablyaz T.R., Blokhin V.B., Muratov K.R. Improvement the manufacturing quality of new generation heat-resistant nickel alloy products using wire electrical discharge machining................................................................... 34 Ablyaz T.R., Osinnikov I.V., Shlykov E.S., Kamenskikh A.A., Gorohov A.Yu., Kropanev N.A., Muratov K.R. Prediction of changes in the surface layer during copy-piercing electrical discharge machining....................................... 48 Martyushev N.V., Kozlov V.N., Boltrushevich A.E., Kuznetsova Yu.S., Bovkun A.S. Milling of Inconel 625 blanks fabricated by wire arc additive manufacturing (WAAM)..................................................................................................... 61 Fatyukhin D.S., Nigmetzyanov R.I., Prikhodko V.M., Sundukov S.K., Sukhov A.V. Infl uence of the oscillating systems inclination angle on the surface properties of steel 45 during ultrasonic surface plastic deformation................... 77 EQUIPMENT. INSTRUMENTS Borisov M.A., Lobanov D.V., Skeeba V.Y., Nadezhdina O.A. Development of a device for studying and simulating the electrochemical grinding process................................................................................................................................... 93 Lapshin V.P., Gubanova A.A., Dudinov I.O. Predicting machined surface quality under conditions of increasing tool wear............................................................................................................................................................................... 106 Podgornyj Y.I., Skeeba V.Y., Martynova T.G., Sadykin A.V., Martyushev N.V., Lobanov D.V., Pelemeshko A.K., Popkov A.S. Designing the homogenization mechanism.................................................................................................... 129 MATERIAL SCIENCE Usanova O.Yu., Ryazantseva A.V., Vakhrusheva M.Yu., Modina M.A., Kuznetsova Yu.S. Improving the performance characteristics of grey cast iron parts via ion implantation.......................................................................... 143 Abdelaziz K., Saber D. Fabrication and characterization of Al-7Si alloy matrix nanocomposite by stir casting technique using multi-wall thickness steel mold................................................................................................................ 155 Dama Y.B., Jogi B.F., Pawade R., Pal S., Gaikwad Y.M. DLP 3D printing and characterization of PEEK-acrylate composite biomaterials for hip-joint implants....................................................................................................................... 172 Prudnikov A.N., Galachieva S.V., Absadykov B.N., Sharipzyanova G.Kh., Tsyganko E.N., Ivancivsky V.V. Eff ect of deformation thermocyclic treatment and normalizing on the mechanical properties of sheet Steel 10.......................... 192 Bhanavase V., Jogi B.F., Dama Y.B. Wear behavior study of glass fi ber and organic clay reinforced poly-phenylenesulfi de (PPS) composites material........................................................................................................................................ 203 EDITORIALMATERIALS 218 FOUNDERS MATERIALS 227 CONTENTS
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 7 1 5 Designing the homogenization mechanism Yuriy Podgornyj1, 2, а, *, Vadim Skeeba 1, b, Tatyana Martynova 1, c, Artur Sadykin 1, d, Nikita Martyushev 3, e, Dmitry Lobanov 4, f, Arina Pelemeshko 1, g, Andrey Popkov 1, h 1 Novosibirsk State Technical University, 20 Prospekt K. Marksa, Novosibirsk, 630073, Russian Federation 2 Novosibirsk Technological Institute (branch) A.N. Kosygin Russian State University (Technologies. Design. Art), 35 Krasny prospekt (5 Potaninskayast.), Novosibirsk, 630099, Russian Federation 3 National Research Tomsk Polytechnic University, 30 Lenin Avenue, Tomsk, 634050, Russian Federation 4 I. N. Ulianov Chuvash State University, 15 Moskovsky Prospekt, Cheboksary, 428015, 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/0009-0002-2061-650X, artur060779@gmail.com; e https://orcid.org/0000-0003-0620-9561, martjushev@tpu.ru; f https://orcid.org/0000-0002-4273-5107, lobanovdv@list.ru; g https://orcid.org/0009-0004-5916-6782, pyatkova.arina@gmail.com; h https://orcid.org/0009-0006-5587-9990, andrej.popkov.2013@mail.ru Obrabotka metallov - Metal Working and Material Science Journal homepage: http://journals.nstu.ru/obrabotka_metallov Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science. 2025 vol. 27 no. 1 pp. 129–142 ISSN: 1994-6309 (print) / 2541-819X (online) DOI: 10.17212/1994-6309-2025-27.1-129-142 ART I CLE I NFO Article history: Received: 14 December 2024 Revised: 09 January 2025 Accepted: 31 January 2025 Available online: 15 March 2025 Keywords: Homogenization Cycle diagram of operation Kinematic scheme Cam mechanism Pusher Roller Speed Accelerations Motions Cam profile Funding This study was supported by a NSTU grant (project No. TP-PTM-1_25). Acknowledgements The research was carried out at the equipment of the Engineering Center “Design and Production of High-Tech Equipment”. ABSTRACT Introduction. The primary goal of food processing equipment manufacturing is to create highly efficient process equipment that can increase labor productivity while reducing energy costs. Improving existing and creating new high-performance equipment for food production is one of the main trends in the development of modern mechanical engineering. The term “homogenization” literally means “increasing uniformity”. In the context of emulsions, homogenization refers to the process of treating emulsions, which leads to the fragmentation of the dispersed phase. Homogenization is the process of grinding liquid or mashed foods by passing it at high speed and pressure through narrow annular slots. The authors propose to use cam-type mechanisms for homogenization. Cam-type mechanisms allow for a more efficient allocation of the time for the product suction and injection. The homogenization process benefits from the potential to reduce the speed during product injection. The purpose of the work is to reduce power consumption during homogenization. The research methods are based on the theory of machines and mechanisms. These methods enabled developing a methodology for synthesizing the homogenizer drive mechanism and designing a machine that ensures its operation in accordance with the proposed cycle diagram. Results and discussion. The synthesis of mechanisms is executed with consideration for the workload, which was calculated for existing domestic machines in the production of processed cheese. Thus, with a given production capacity of 550 l/h and a plunger diameter of 28 mm, the technological force is F = 12315 N. In accordance with the authors’ proposals, the design of the homogenizer is modified by introducing cam mechanisms. In the design of this drive, a novel cycle diagram is proposed, enabling an increase in product injection time and a reduction in suction time. According to the novel cycle diagram, 280° is proposed for product injection and 80° for suction. In this case, the power on the drive shaft is equal to P = 2.5 kW instead of 3.5 kW for the existing design, driven by a crank mechanism. The power consumption is decreased by 26 %. For citation: Podgornyj Y.I., Skeeba V.Y., Martynova T.G., Sadykin A.V., Martyushev N.V., Lobanov D.V., Pelemeshko A.K., Popkov A.S. Designing the homogenization mechanism. Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science, 2025, vol. 27, no. 1, pp. 129–142. DOI: 10.17212/1994-6309-2025-27.1-129-142. (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. 7 No. 1 2025 Introduction The primary goal of food processing equipment manufacturing is to create highly efficient processing equipment that can increase labor productivity while reducing energy costs. Homogenization machines are among the many types of process equipment used in food industry enterprises [1–9]. Among the many critical features of contemporary processing machines, the equipment’s performance, technical condition, and product quality are the most important [10–19]. Enhancing existing and developing novel, high-performance equipment for food production is a key trend in modern mechanical engineering. As dynamic stresses and operating speeds increase, more stringent demands are placed on the design of individual components and assemblies, such as the drives that ensure intermittent motion of the machine’s working parts [7, 12–14, 16–22]. A significant requirement for modern machines is that the follower movements accurately correspond to a specific motion profile. Therefore, the use of cam-type mechanisms is proposed for food processing machines, as they allow for efficient control of the timing for product suction and injection. The motion profiles of cam mechanisms can be synthesized in a wide variety of ways, making them easily adaptable to the kinematic and dynamic requirements specified by the developer. Furthermore, the technology for obtaining the required cam profile as been firmly established ensuring accurate follower motion [23-35]. The homogenization process can benefit from the ability to reduce speed during product injection [36, 37]. The term “homogenization” literally means “increasing uniformity”. In the context of emulsions, homogenization refers to the process of treating emulsions that results in the fragmentation of the dispersed phase. More specifically, homogenization is the process of grinding liquid or mashed foods by passing them at high speed and pressure through narrow annular slots. The homogenization process is widely used in the food industry, particularly in the dairy industry, for example, in the manufacture of processed cheese. Processed cheese is a food product that has undergone melting and homogeneous distribution of its components. It is produced from specific mixtures formulated with a clear, specific recipe that details the ingredients: the components of milk, cream, butter, cheeses, melting salts, stabilizers, as well as flavors and additives. The technology for manufacturing processed cheese includes several stages. First, the cheese or cottage cheese is crushed and mixed. The mixture is then melted and emulsified, and special additives that aid in achieving the product’s desired consistency and texture, such as structurizers or emulsifying salts, may be used. According to analysis, homogenizer designs most frequently utilize crank mechanisms. Preliminary research [1–7, 12, 13, 36] suggests that laminar flow invariably results in a threefold increase in the degree of dispersion of fat globules compared to turbulent flow. Cheese is produced using specialized machines called homogenizing machines, and their indicator diagrams can be viewed in detail in [36]. The constituent elements of the diagram include the moments of product suction and injection through the annular slot. Product suction occurs at a pressure lower than atmospheric one, while injection through an annular slot occurs at a pressure of 20 MPa or higher. In conventional designs, the operation of the crank mechanism is divided into two sections: the first section is suction, which takes up half the distance traveled by the crank, and the second section provides injection, taking the second half of the distance. The disadvantage of such designs is their high power consumption. Therefore, we believe that replacing the crank mechanism with a cam mechanism is a promising, relevant, and timely task. The purpose of the work is to reduce power consumption during product homogenization To achieve this purpose, the following tasks were addressed: – the technological load during homogenization was determined; – the feasibility of replacing the crank mechanism with a cam mechanism was analyzed; – the necessary parameters for synthesizing of the cam pair were selected, and the synthesis was performed; – a novel cycle diagram of the device operation was proposed;
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 7 1 5 – the resistance forces torque has been determined, both for each camshaft individually and for the total torque; – the power required for homogenization with the proposed new drive was determined. Research methodology The first step in this research involved determining the technological load during the homogenization process in processed cheese manufacturing. According to [37], the operating pressure in the cylinder cavity at the moment of liquid injection is 20 MPa. With a plunger diameter of d = 28 mm and a production capacity of 550 L/h, and a main shaft rotation speed of n = 180 min−¹, the required force exerted by the plunger on the liquid in the homogenizing head’s passage section was determined to be F = 12,315 N. Kinetostatic analysis of this mechanism indicated that the required power consumption for this case is 3.8 kW. The details of the cam-driven homogenizer design proposed by the authors are presented below. Fig. 1 illustrates the locations of the drive cams and pushers driving the plungers. Functionally, all other elements operate in the same manner as in drives with crank mechanisms. Detailed information about the design of the homogenizer can be found in [37]. Fig. 1. The proposed design of a cam-driven homogenizer Numerous motion laws are applicable to cam mechanisms in mechanics. To select an motion law, we propose considering three common types: – simple harmonic motion law; – double harmonic motion law; – cycloidal motion laws [7, 12, 13–27, 31–35, 38–41]. The design scheme for the cammechanism is shown in Fig. 2. The following parameters were considered as variables: profile angles β; phase angles of motion for ascent and descent – φ1, φ2, φ3, φ4; the maximum displacement of the pusher is Smax; current value of the cam rotation angle φ. Due to the fact that all calculations were performed using a mathematical software package, the following notation was adopted for clarity: displacement s(φ); velocity v1(φ); acceleration a1(φ);and torques on the working shaft M1(φ), M2(φ), M3(φ), corresponding to the three cams involved in the design; coefficients for the harmonic motion law max 1 2 S k = , 3 max 2 3 6 k S = − ϕ ; workload forces during product injection and suction, F1, F2, which were assumed to be F1 = 12,315 N and F2 = 2,500 N, respectively.
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 7 No. 1 2025 Fig. 2. Cam mechanism of the homogenizer The results of this study indicated that simple harmonic motion law is the most suitable one, as its maximum velocity values were 25 % and 30 % lower than those of double harmonic and cycloidal motion laws, respectively. The analytical expression for simple harmonic motion law is given by: max ( ) 1 cos , 2 S s φ φ = ⋅ − π ⋅ β (1) The kinematic characteristics for simple harmonic motion law were calculated using the Mathcad software package, with the listing shown in Fig. 3. a(φ) := ( ) 1 1 1 2 1 2 3 1 2 1 2 3 3 1 2 3 cos 0 1 1 1 0 1 2 0 360 deg, k if if k if if π φ ⋅ ⋅ π ⋅ ≤ φ ≤ φ φ φ φ ≤ φ ≤ φ + φ φ − φ + φ ⋅ − ⋅ φ + φ ≤ φ ≤ φ + φ + φ φ φ + φ + φ ≤ φ ≤ (2) The speed is defined as: v(φ) = ( ) ( ) 1 1 1 3 1 2 3 sin 0 0 0 360 deg, k if if k if 1 1 1 2 1 1 2 1 2 1 2 1 2 3 3 π π ⋅ φ − ⋅ ⋅ ≤ φ ≤ φ φ φ φ ≤ φ ≤ φ + φ φ − φ + φ ⋅ φ − φ + φ ⋅ 1 − φ + φ ≤ φ ≤ φ + φ + φ φ φ + φ + φ ≤ φ ≤ if (3) Fig. 3. Listing of a program for determining kinematic characteristics Displacement was calculated as the integral function of the velocities, using Equation (3): ( ) ( ) . 0 s v d φ ϕ = φ ⋅ φ ∫ (4) The torque acting on the first cam was determined using a program developed within the mathematical software package. The program listing is shown in Fig. 4.
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 7 1 5 The torques for the second and third cams can be expressed as follows: 2 1 2 3 1 3 ( ) ( ), ( ) ( ), Ì M Ì M φ = φ + ψ φ = φ + ψ (6) where M2 and M3 are the torques for the second and third cams; ψ1, ψ2 are the phase displacement angles for the cams on the drive shaft. The torques on the drive shaft (cam) were determined based on the phase shift magnitudes of the angles ψi and profile angles βᵢ. The total torque Mc on the drive shaft was determined as the sum of the component torques Mᵢ, of which there are three in this case: 3 1 c i i M M = = ∑ . (7) The power consumption applied to the drive shaft can be expressed as [34]: c P = M ω max , (8) where Mcmax is the maximum value of the total torque. The profile angles β were determined iteratively using the programs shown in Figs. 3 and 5. As a result, by identifying the minimum velocity value from the family of curves, we selected simple harmonic motion law with profile angles β₁ = 280° and β₂ = 80° and initiated the design of the cam mechanism according to the specified parameters [12]. Furthermore, the pressure angles were determined using the following Equation: ( ) 1 ( ) tan ( ) v e a sh s φ + δ φ = + φ . (9) To achieve this, it was necessary to find the cam’s minimum radius, Rmin. A graph was constructed in v(s) coordinates using the calculated position functions s(φ) and velocity analogs v(φ) (Fig. 6) during the ascent and descent phases. The only difference in this process was the use of numerical velocity values. The resulting scheme is shown in Fig. 7. The velocity vectors are indicated by points from A0 to As. The ascent phase is represented by points from A0 to A4, and the descent phase, from A5 to As. The minimum cam radius vector was determined to be Rmin = 90 mm. The next step in determining the design parameters of the mechanism is to determine the roller radius. This can be found using an algorithm that calculates the radii of curvature for the cam profile based on its rotation angle. The curvature radius values, ρcur, can be calculated using a general formula applicable to any cam type [23]: 2 3/2 2 2 2 2 2 , 2 cur d d d d d d ρ ρ + β ρ = ρ ρ ρ + − ρ β β (10) where p is the radius vector of the theoretical profile; β is the profile angle. Fig. 4. Listing of the program for determining the torque on the cam shaft 1 3 2 1 sin 0 0 1 0 ( 360 deg k F if if k F if if 1 1 1 1 2 1 2 1 2 1 2 1 2 3 3 1 2 3 π φ ⋅ ⋅ π ⋅ ⋅ ≤ φ ≤ φ φ φ φ ≤ φ ≤ φ + φ φ − φ + φ φ − φ + φ ⋅ − ⋅ φ + φ ≤ φ ≤ φ + φ + φ φ φ + φ + φ ) ≤ φ ≤ v(φ) = (5)
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 7 No. 1 2025 ( ) 1 1 1 1 1 1max 1max : 0.5..180 : 1 1 180 : 1 : max( 1) 1 1 i i i Discrete angle values Conversion of angles from degrees to radians in section Velocity analog in section Maximum velocity analog in sec i f i v tio v f v n v v = − π = ⋅ − = − = − ;90 1 1 1 1 1max 1 1 90 0.01 0.019 : ( 1 ) : (90 deg) 1 i i Velocity analog value in section Maximum velocity analog value in section at Displacement of the driv v s s f s s en link in section Maximum displacement of = − = − = − = ϕ = − 1max 2 3 1 0.01 1 2 5 3max 1max : tan 1max 3max : 2 2 the driven link in section Maximum displacement value of the driven link in section Angle value in se s s s a v v dop ction Angle value in sect = − − ε = − − π ε = − δ + ε − ( ) 1 1 3 : 2 : 31 sin ( 1max) : 31 cos( ) 1max 3 1 1 0.014 : 180..360 h h ion Angle value in section Eccentricity in section Roller center displacement Roller center displacement value Discret dop e l dop v s l dop s s i e ε = ⋅ δ − = ⋅ δ − − ⋅ δ − − = − = − 3 3 3 3 3 3max 3max 3 : 3 180 : ( 3 ) : max( 3 3 ) 0.01 3 4 i i i angle values Conversion of angles from degrees to radians in section Velocity analog in section Velocity analog valu f i v v f e i v v n section Maximum vel v π = ⋅ − = − = − − = − − ;70 3 3 3 3 3max 0.014 : ( 3 3 ) : 3 (270 deg 70 3 ) i i ocity analog value in section Velocity analog value in section at Displ v s acement of the driven link in section Maximum displacement of the driven s f s s = = = − − ϕ = − 3max 34 4 0.015 1max 3max : cos( 3 2) : 2 3 3 1 link in section Maximum displacement value of the driven link in section Difference between maximum velocity values in section of the profile s v v l do = − − = − ε π ε = − δ − 31 31 4 3 1 3 2 sin( 4) : 34 sin( 1) 0. 3 1 03 Angle value in section Difference between maximum velocity values in section of the profile Difference value between velocity analogs p l l in section l − ε − ε = ⋅ − ε = − − − Fig. 5. Listing of a program for determining pressure angles δ Fig. 6. Graph of analog speeds of the cam mechanism’s roller center
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 7 1 5 Fig. 7. Diagram of determining the minimum radius vector for a mechanism with a pusher When writing a program to determine the minimum curvature radius, it is necessary to consider the interpolation of the radius vector values for the displacements of the cam mechanism’s roller center [12]. A listing of the program for determining the cam surface curvature is shown in Fig. 8. Fig. 8. Listing of a program for determining the curvature of the cam surface : 0..360 deg : 18 0 : ( ) : ( ) k k k x k th h k y t Discrete angle values Conversion of angle from degrees to radians Ve k f k v f locity analog in the k section along the x axis Velocity analog in the k section alo v f n = − π = ⋅ − = β − = ρ − − : ( , ) ( ) : int ( , , ) ( ) : ( ) it it i i t t R cspline vx vy f x erp R vx g the y axis Spline processing of the velocity analog value array Inter vy d df x f x d polation of the radius vector R array value First derivativ x e of the f = − − − = = − ( ) ( ) ( ) 2 2 1.5 2 2 2 2 1 2 ( ) : ( ) ( ) ( ) ( ) : ( ) 2 ( ) 2 ( ) ( ) : 0..28 it it it it cur it it i i t t t i x function ond derivative of the f x function Formula defining the radii of curvatur d d f x e of t f x dx f x df x x f x d he cam f x d f x f profi x l i e = − + ρ = − + ⋅ − ⋅ = Sec 1 1 1 1 1 1 1 1 0 deg : 180 : ( ) min( ) 0 1 .03 i i i cur cur cur Discrete angle values Conversion of angle from degrees to radians Radius of cu f i f rvature of the cam profile in section Minimum radius of curvature of − π = ⋅ − ρ = ρ − ρ = − 1 the profile in section Results and Discussions Analyzing the obtained power consumption values, we concluded that it is 3.8 kWfor a crankmechanism. For a simple harmonic motion law, it is 3.8 kW; for cycloidal and double harmonic motion law, it is 4.5 kW and 4.3 kW, respectively. These values were calculated at equal profile angles β = 180°. The authors suggest that the new cycle diagram of the cam drive operation should provide a significant reduction in torque for
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 7 No. 1 2025 Ta b l e 1 Options for investigating pressure angles No. Phase angles Values of maximum pressure angles, degrees φ, degrees (suction) φ, degrees (injection) 1 200 160 32 2 220 140 33 3 240 120 32 4 260 100 31 5 280 80 25 the follower and, consequently, lead to a decrease in power consumption. Using the calculation algorithms shown in Figs. 4, 5, and 8, and setting the phase angles for suction and injection in 20° increments, we obtained values for the pressure angles. One calculation option is presented below. Option 1. The phase angle for the injection and suction moment is 180°. The graphs for this option are shown in Fig. 9. Fig. 9. Graph of pressure angle variations As can be seen from the graph, the pressure angle values at 70° and 310° exceed acceptable limits. Therefore, this option is not viable for the homogenizer design. Subsequently, five more options were proposed (Table 1). Of the family of curves presented in Table 1, only one satisfies the requirement: the pressure angles throughout a full rotation (360°) do not exceed the permissible value of 30°. This curve has phase angles of 280° for the injection period and 80° for the suction period. Subsequently, using these parameters as a basis, we initiated the cam synthesis. For preliminary calculations during synthesis, the following cycle diagram parameters were used: 80° was allocated for suction, and 280° of the full cam rotation was allocated for liquid injection. Formula (5) was used to determine the torque on the cam. The numerical values of the forces at the injection and suction moments were assumed to be F1 = 12,315 N and F2 = 2,500 N, respectively. For one variant, graphs of the torques at phase displacement angles ψ1 = 170° and ψ2 = 340° are shown in Fig. 10. The total torque acting on the drive shaft is indicated in purple. The data for the remaining options are summarized in Table 2. Only Option 5 (also depicted in Fig. 10) exhibits the lowest total torque value on the camshaft, as evident from the table above. Following a thorough analysis of the available options, the cam mechanism synthesis can begin with the following specifications: 280° and 80° for injection and suction, based on the cycle diagram; a pusher stroke of 30 mm; and a minimum curvature radius of 90 mm.
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 7 1 5 Fig. 10. Graphs of torques with a phase displacement angle ψ1 = 170 and ψ2 = 340: – total torque on the drive shaft; – torque for the first cam; – torque for the second cam; – torque for the third cam Ta b l e 2 Torque values on the drive shaft No. Phase angles Torque values on the drive shaft, N·m φ, degrees (suction) φ, degrees (injection) 1 120 240 185 2 140 260 186 3 160 280 185 4 180 300 186 5 170 340 137 The displacements and velocities were determined according to the listing in Fig. 3 and Equation 4. The displacements are shown in Fig. 11, and the cam profile is shown in Fig. 12. Fig. 11. Graph of displacement variations
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 7 No. 1 2025 Fig. 12. Cam profile Conclusion The primary objective of this research was to reduce the power consumption of the homogenizer. Using the analytical relationships (1–4) and setting specific numerical values for the cam mechanism parameters, we selected the most efficient pusher motion law in the form of a simple harmonic curve. This law exhibits the minimum velocity values among the considered family of mathematical curves. The amplitude values of the velocity analogs were 0.012 m in the positive region and −0.03 m in the negative region. The pressure angles for this curve do not exceed the permissible value of δ = 30° across the entire studied angle range. The presented torque dependencies on the drive shaft indicate the appropriateness of setting their displacement angles to ψ1 = 170° and ψ2 = 340°. In this configuration, the total torque was 137 N·m, and the power on the drive shaft was P = 2.5 kW, compared to 3.8 kW for the existing design driven by a crank mechanism. This represents a 34 % decrease in power consumption. References 1. Inguva P., Grasselli S., Heng P.W.S. High pressure homogenization –An update on its usage and understanding. Chemical Engineering Research and Design, 2024, vol. 202, pp. 284–302. DOI: 10.1016/j.cherd.2023.12.026. 2. Chen X., Liang L., Xu X. Advances in converting of meat protein into functional ingredient via engineering modification of high pressure homogenization. Trends in Food Science & Technology, 2020, vol. 106, pp. 12–29. DOI: 10.1016/j.tifs.2020.09.032. 3. Chevalier-Lucia D., Picart-Palmade L. High-pressure homogenization in food processing. Green food processing techniques. Ed. by F. Chemat, E. Vorobiev. Elsevier, Academic Press, 2019, pp. 139–157. DOI: 10.1016/ B978-0-12-815353-6.00005-7. 4. Luo D., Fan J., Jin M., Zhang X., Wang J., Rao H., Xue W. The influence mechanism of pH and polyphenol structures on the formation, structure, and digestibility of pea starch-polyphenol complexes via high-pressure homogenization. Food Research International, 2024, vol. 194, p. 114913. DOI: 10.1016/j.foodres.2024.114913. 5. Mehmood T., Ahmad A., Ahmed A., Ahmed Z. Optimization of olive oil based O/W nanoemulsions prepared through ultrasonic homogenization: a response surface methodology approach. Food Chemistry, 2017, vol. 229, pp. 790–796. DOI: 10.1016/j.foodchem.2017.03.023. 6. Ma Z., Zhao Y., Khalid N., Shu G., Neves M.A., Kobayashi I., Nakajima M. Comparative study of oil-in-water emulsions encapsulating fucoxanthin formulated by microchannel emulsification and high-pressure homogenization. Food Hydrocolloids, 2020, vol. 108, p. 105977. DOI: 10.1016/j.foodhyd.2020.105977.
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