Vol. 27 No. 3 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. 3 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 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. 3 2025 5 CONTENTS OBRABOTKAMETALLOV TECHNOLOGY Kondratiev V.V., Gozbenko V.E., Kononenko R.V., Konstantinova M.V., Guseva E.A. Determination of the main parameters of resistance spot welding of Al-5 Mg aluminum alloy..................................................................................... 6 Gvindjiliya V.E., Fominov E.V., Marchenko A.A., Lavrenova T.V., Debeeva S.A. Infl uence of cutting speed on pulse changes in the temperature of the front cutter surface during turning of heat-resistant steel 0.17 C-Cr-Ni-0.6 Mo-V................................................................................................................................................................ 23 Karelin R.D., Komarov V.S., Cherkasov V.V., OsokinA.A., Sergienko K.V., Yusupov V.S., Andreev V.A. Production of rods and sheets from TiNiHf alloy with high-temperature shape memory eff ect by longitudinal rolling and rotary forging methods.................................................................................................................................................................... 37 EQUIPMENT. INSTRUMENTS Zakovorotny V.L., Gvindjiliya V.E., Kislov K.V. Information properties of vibroacoustic emission in diagnostic systems for cutting tool wear................................................................................................................................................ 50 Zhukov A.S., Ardashev D.V., Batuev V.V., Kulygin V.L., Schuleshko E.I. Modal analysis of various grinding wheel types for the evaluation of their integral elastic parameters...................................................................................... 71 Nishandar S.V., Pise A.T., Bagade P.M. Numerical and experimental investigation of heat transfer augmentation in roughened pipes................................................................................................................................................................ 87 Nosenko V.A., Rivas Perez D.E., Alexandrov A.A., Sarazov A.V. The eff ect of the grinding method on the grain shape coeffi cient of black silicon carbide....................................................................................................................................... 108 MATERIAL SCIENCE Karlina Yu.I., Konyukhov V.Yu., Oparina T.A. Investigation of the process of surface decarburization of steel 20 after cementation and heat treatment.................................................................................................................................. 122 Kovalevskaya Z.G., Liu Y. Eff ect of heat treatment on the structure and properties of high-entropy alloy AlCoCrFeNiNb0.25............................................................................................................................................................. 137 Sirota V.V., Prokhorenkov D.S., Churikov A.S., Podgorny D.S., Alfi mova N.I., Konnov A.V. Corrosion properties of coatings produced from self-fl uxing powders by the detonation spraying method............................................................ 151 Filippov A.V., Shamarin N.N., Tarasov S.Yu., Semenchyuk N.A. The infl uence of structural state on the mechanical and tribological properties of Cu-Al-Si-Mn bronze............................................................................................................. 166 Waheed F., Qayoom A., Shirazi M.F. Fabrication, characterization and performance evaluation of zinc oxide doped nanographite material as a humidity sensor......................................................................................................................... 183 Dolgova S.V., Malikov A.G., Golyshev A.A., Nikulina A.A. Features of the structure of gradient layers «steel - Inconel - steel», obtained by laser direct metal deposition.................................................................................................. 205 Burkov A.A., Dvornik M.A., Kulik M.A., Bytsura A.Yu. The infl uence of tungsten carbide particle size on the characteristics of metalloceramic WC/Fe-Ni-Al coatings.................................................................................................... 221 Patil S., Chinchanikar S. Investigation on the mechanical properties of stir-cast Al7075-T6-based nanocomposites with microstructural and fractographic surface analysis...................................................................................................... 236 EDITORIALMATERIALS 252 FOUNDERS MATERIALS 263 CONTENTS
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 7 5 Modal analysis of various grinding wheel types for the evaluation of their integral elastic parameters Aleksandr Zhukov a, *, Dmitrii Ardashev b, Victor Batuev c, Victor Kulygin d, Egor Schuleshko e South Ural State University, 76 Prospekt Lenina, Chelyabinsk, 454080, Russian Federation a https://orcid.org/0000-0002-9328-7148, zhukovas@susu.ru; b https://orcid.org/0000-0002-8134-2525, ardashevdv@susu.ru; c https://orcid.org/0000-0001-9969-4310, batuevvv@susu.ru; d https://orcid.org/0009-0000-8509-1420, kulyginvl@susu.ru; e https://orcid.org/0000-0002-5709-4285, schuleshko21@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. 3 pp. 71–86 ISSN: 1994-6309 (print) / 2541-819X (online) DOI: 10.17212/1994-6309-2025-27.3-71-86 ART I CLE I NFO Article history: Received: 04 May 2025 Revised: 25 May 2025 Accepted: 05 June 2025 Available online: 15 September 2025 Keywords: Grinding Grinding wheel Grinding wheel natural vibrations Grinding wheel integral elastic indices Modal analysis Participation factor Spectral composition Natural vibrations frequency Computer modelling COMSOL Multiphysics Finite element analysis Funding The study was funded by the Russian Science Foundation grant No. 25-29-20029, https://rscf.ru/en/ project/25-29-20029/ ABSTRACT Introduction. In developing a mathematical model for the sound pressure generated by the grinding process, it became necessary to determine the actual values of the integral elastic parameters of grinding wheels to use as inputs in the model. This will expand the applicability of the model and maximize its practical utility. This paper describes an approach to determining Poisson’s ratios and Young’s moduli for grinding wheels with different characteristics. The elastic properties of the tool are the subject of this study. The purpose is to establish the relationship between actual values of integral elastic parameters and grinding wheel characteristics via modal analysis. The research method combines experimental investigation of natural frequency spectra and modal analysis, implemented via the finite element method in specialized software. Additionally, regression analysis is employed to derive empirical dependencies of the integral elastic parameters of grinding wheels on abrasive grain size and hardness. Results and discussion. The main result of this work is the determination of the actual values of Poisson’s ratios and Young’s moduli for grinding wheels with the studied characteristics. The selection of grinding wheel characteristics allowed for the investigation of the influence of abrasive grain size and hardness on its integral elastic properties. The development of a mathematical model for sound pressure generated by the grinding process, along with a methodology for predicting the service life of grinding wheels based on this model, will improve grinding operation efficiency by reducing the machine-setting time, increasing processing time, reducing consumption of manufacturing resources, and optimizing tool lifespan utilization. For citation: Zhukov A.S., Ardashev D.V., Batuev V.V., Kulygin V.L., Schuleshko E.I. Modal analysis of various grinding wheel types for the evaluation of their integral elastic parameters. Obrabotka metallov (tekhnologiya, oborudovanie, instrumenty) = Metal Working and Material Science, 2025, vol. 27, no. 3, pp. 71–86. DOI: 10.17212/1994-6309-2025-27.3-71-86. (In Russian). ______ * Corresponding author Zhukov Aleksandr S., Ph.D. (Engineering) student South Ural State University, 76 Prospekt Lenina, 454080, Chelyabinsk, Russian Federation Tel.: +7 351 272-32-94, e-mail: zhukovas@susu.ru Introduction Predicting the life of a grinding wheel (GW) by means of the indirect acoustic criterion naturally implies the need to study its dynamic characteristics. The development of a model for the sound pressure generated by the grinding process requires the values of the elastic moduli of the grinding wheel to correctly calculate the modes and frequencies of the natural vibrations which are the source of the acoustic field. According to
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 7 No. 3 2025 the characteristics of such a field, it is possible to predict many output parameters of the grinding process over time: cutting forces, machining quality parameters [1, 2] (roughness, shape deviations of the workpiece, presence of burns, etc.), and stiffness of the technological system. The sequence of manifestation of natural vibration modes of the grinding wheel, inseparably connected with its elastic parameters, determines the nature of the acoustic response of the system during operation, as well as the way it will react to external excitation during grinding. Modal analysis is a powerful method for determining the dynamic characteristics of a mechanical system. In mechanical engineering, this method is used to solve a wide range of problems, from the design and optimization of machine structures, mechanisms, and parts, to the diagnosis and monitoring of equipment condition. The growing need to improve the design of modern metal-cutting machines and tools with respect to vibration resistance, increasing their reliability and rigidity, has led to the emergence of new and effective applications of modal analysis. In [3–8], parametric optimization of both the design of individual elements of machine tools (spindles, beds, etc.) and complex machine tool assemblies is carried out. In particular, designs of numerically controlled machine tools and multi-axis high-precision machine tools are often optimized by means of modal analysis. In [9–13], cutting tools are designed using modal analysis, and existing designs of turning tools, drills, and milling cutters are improved according to criteria of vibration resistance and enhancement of dynamic balance during machining. Calculating the eigenmodes and vibration frequencies of systems whose operation is associated with dynamic vibration loads is necessary at the design, testing, or modernization stages, regardless of the magnitude of the loads. If the system’s operating mode leads to vibrations at the resonance frequency, the design is modified to prevent emergency situations. The complexity and multi-component structure of a grinding wheel make it difficult to determine its elasticity parameters, which are necessary for calculating its natural vibrations. The elastic parameters of abrasive tools are poorly represented in technical literature. There is no systematization, and no correspondence has been established between these parameters and the characteristics of grinding wheels. Reference books do not provide values for the elastic properties of abrasive tools, such as Poisson’s ratio and Young’s modulus. Only isolated experimental references for grinding wheels with specific characteristics can be found. The variety of existing and emerging grinding wheel formulations is extremely large. Depending on the characteristics of the grinding wheel, the proportions of its components (abrasive, bond, and pores) and their properties vary considerably [14]. Exact calculations of the elastic parameters of grinding wheels are extremely laborious, as they require consideration of the properties of each component and how they interact with each other. To simplify the process, modal analysis is proposed to evaluate the elastic properties of the system as a whole without detailing the components. The objective of this study is to determine how the actual values of integral elastic indices depend on grinding wheel characteristics using modal analysis. To achieve this goal, the following tasks must be completed: 1) conduct an experimental study of the frequencies of natural vibrations of grinding wheels with different characteristics; 2) calculate the natural frequencies and mode shapes of grinding wheels for various combinations of elastic and geometric parameters using specialized software and the finite element method; 3) compare and correlate the experimental and calculated natural frequencies of the grinding wheels. 4) determine the actual values of Poisson’s ratio and Young’s modulus for all investigated grinding wheels. Methods Table 1 shows the list of grinding wheel characteristics included in the study of integral elastic performance. The grinding wheels were selected for this study to investigate how changes in granularity, hardness, and abrasive material affect the integral elastic properties of the tool (Fig. 1).
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 7 5 Ta b l e 1 Grinding wheels characteristics according to GOST R 52781-2007 GW No. GW dimensions D × H × d, mm Abrasive material Grit Hardness 1 600×50×305 25А F36 L 2 F46 3 F60 4 F80 5 F120 6 F60 N 7 P 8 500×63×305 S 9 600×50×305 14А L 10 64С 11 600×40×305 92А Fig. 1. Grinding wheels under study The effect of grain size variation on the elastic properties of grinding wheels No. 1, No. 2, No. 3, No. 4, and No. 5 was studied. The grain size ranged from F36 to F120 (H50 to H10 according to GOST 2424-84), with the average grain size ranging from 0.5 to 0.11 mm. Other properties remained unchanged.
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 7 No. 3 2025 The influence of changes in hardness on the elastic properties of grinding wheels No. 3, No. 6, No. 7, and No. 8 was studied. The hardness varied from L to S (CM2 to T2 according to GOST 2424-84). All other formulation characteristics remained unchanged. To study the influence of different abrasives on the elastic properties of grinding wheels, wheels No. 3, No. 9, No. 10, and No. 11 were considered: – 25A white aluminum oxide with 99 % α-Al₂O₃ content. It is used for finishing and profile grinding of hardened steels, as well as sharpening of high-speed tools; – 14A normal electrocorundum with 93 % α-Al₂O₃ content. It is used for rough grinding; – 92A chromotitanium electrocorundum with 60–75 % α-Al₂O₃ content. It is used for grinding hardened steels, machining with large metal removal, and rough grinding; – 64C green silicon carbide with 96–97 % SiC content. It is used for final sharpening and finishing of carbide tools, honing, and superfinishing [14, 15]. The structure of the considered grinding wheels is medium (structure numbers 5, 6, and 7), and the bond is ceramic. Experimental study of natural vibrations of grinding wheels A full-scale experiment was conducted to record the spectrum of natural frequencies of grinding wheel vibrations. The natural oscillations of the grinding wheel were excited by impact, as shown in Fig. 2. The acoustic signal generated by the wheel’s natural vibrations was recorded using the NFM-2 (natural frequency meter) employing a non-contact method. The grinding wheel (GW) was mounted vertically on a carriage. The ICHSK-2 microphone, which serves as the device’s sensitive element, was positioned at an angle of 45° ± 15° relative to the diameter passing through the grinding wheel’s support point. A minimum clearance between the cylindrical surface of the grinding wheel and the microphone must be maintained; contact with the surface is not permitted. The striker (hammer) impacts the grinding wheel at an angle of 45° ± 15° relative to the diameter passing through the support point of the grinding wheel, symmetrical to the microphone’s position. The striker impacts the cylindrical surface of the tested bearing directed toward its center. The force and area of impact are insignificant since the study focuses on the frequencies, not the amplitudes, of natural vibrations. When setting up the device, it is necessary to specify: – type of product – abrasives / blades / other products; – type of abrasive – 14A / 25A / 92A / 64C; – type of bond – bakelite / vulcanite / ceramic; – geometric shape and dimensions of the grit (shape coefficient); – density of the ball; – frequency range of measurements. The experiment involved 10 measurements of the eigenfrequencies of each grinding wheel. Then, the average spectral composition of the natural frequencies of each grinding wheel was determined. Fig. 3 shows an example of a spectrogram of ten measurements of natural frequencies of GW 1 600×50×305 25A F60 L 7 V 50 2kl GOST R 52781-2007 – grinding wheel No. 3. Modal analysis of grinding wheel natural vibrations A computer simulation experiment was conducted using the finite element method in the COMSOL Multiphysics software environment to study natural frequencies and vibration modes. This software is widely used for engineering calculations worldwide and has proven effective in solving acoustic and vibration problems [16–20]. Fig. 2. Scheme of measuring frequencies of GW natural vibrations: 1 – microphone, 2 – hammer, 3 – grinding wheel under study, 4 – base
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 7 5 Amodel of a grinding wheel was developed that allows parametric control over its geometry and elastic parameters. The following equation expresses the relationship between the natural frequencies of a grinding wheel’s vibrations and its geometric dimensions, shape, and elastic parameters: ( , ) i i E f F a = ν ρ where Fi(a, ν) is the shape factor, which depends on the body’s geometrical dimensions and shape (a = f(D, d, H)), Poisson’s ratio (ν), and the mode of oscillation. The model parameters are summarized in Table 2. Fig. 3. Spectral composition of grinding wheel No.3 natural vibrations Ta b l e 2 Grinding wheel model parameters Symbol Description Geometrical model parameters D GW outer diameter d GW inner diameter H GW height Elastic parameters of model material ν Poisson’s ratio Е Young’s modulus ρ density The calculation of eigenmodes and oscillation frequencies was carried out for each variant of the grinding wheel (GW) parameters – D, d, H, ν, E, and ρ – in order to determine the agreement with the experimentally obtained frequencies. The comparison is presented in the section “Comparison of experimental and calculated spectral compositions of grinding wheels”. Results and Discussion Eigenmodes of Grinding Wheel Vibration Computer modeling has shown that the order in which eigenmodes of grinding wheel vibrations manifest remains unchanged over a wide range of values of ν, E, and ρ. The natural frequency values associated
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 7 No. 3 2025 with each mode vary depending on the values and combinations of the elastic parameters. The geometric parameters of grinding wheels have a decisive influence on the shapes of the modes, the sequence of their manifestation, and the corresponding frequencies. Table 3 summarizes the natural frequencies and their corresponding modes in the order of their manifestation for grinding wheel No. 3 – GW 1 600×50×305 25A F60 L 7 V 50 2 class GOST R 52781-2007. Ta b l e 3 Occurrence order of grinding wheel natural oscillations modes* No. 1 2 3 4 5 6 7 f, Hz 544.59 544.62 1187.6 1429.7 1429.71 1451.8 1451.81 Mode Repeated modes Repeated modes Repeated modes No. 8 9 10 11 12 13 14 f, Hz 1983.3 1983.5 2555.5 2555.51 3440.4 3440.8 3503.5 Mode Repeated modes Repeated modes Repeated modes No. 15 16 17 18 19 20 * – GW 1 600×50×305 25А F60 L 7 V 50 2 class GOST Р 52781-2007 f, Hz 3508.8 3508.81 3850.0 3850.1 4503.5 4503.51 Mode Repeated modes Repeated modes Repeated modes Thus, a pair of the lowest modes are bending modes with two nodal diameters, f₁ and f₂ (n = 2, s = 0), followed by the bending mode f₃ with one nodal circle (n = 0, s = 1), called the “umbrella” mode in the literature [21]. This result agrees with the analytical calculations of vibration modes of grinding wheels by B. A. Glagovsky and I. B. Moskovenko [22]. In the study of vibrations of discs with a central axial hole, the letters n and s denote the number of nodal diameters and nodal circles, respectively. The grinding wheels considered in this study belong to this category. The bending modes manifested in pairs f₄ and f₅ (n = 3, s = 0), f₁₀ and f₁₁ (n = 4, s = 0), and f₁₇ and f₁₈ (n = 5, s= 0) are similar and differ only in the number of nodal diameters. The pairs f₈ and f₉ (n = 1,
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 7 5 s = 1) and f₁₂ and f₁₃ (n = 2, s = 1) differ by the presence of a nodal circle and a different number of nodal diameters. The pairs f₆ and f₇ (n = 2, s= 0), f₁₅ and f₁₆ (n = 3, s = 0), f₁₉ and f₂₀ (n = 1, s = 1), and mode f₁₄ (n = 0, s = 1) belong to the class of radial modes. These are characterized by tension-compression stresses, in which oscillations of microvolumes occur in the plane of the grinding wheel. The peculiarity of the pairwise manifestation of modes with nodal diameters (n ≠ 0) is emphasized. These modes are called multiple modes since they are vibration modes with close (or coinciding) natural frequencies, the same mode set but different orientations of nodal lines. Multiple modes appear in pairs and are characterized by the relative displacement of nodal diameters by some angle. Such modes occur in systems with a high degree of symmetry (e.g., circular discs, spherical shells, square plates). Their existence has been confirmed by both experimental studies and analytical calculations [23–26]. The smallest number of nodal lines, whether nodal diameters or nodal circles, are characteristic of the lowest modes, i.e., modes formed at the lowest frequencies characteristic of the “grinding wheel” system. As the number of nodal lines manifested in the vibrational motion of a particular mode increases, the frequency at which this mode occurs also increases. It is well known that the lowest modes are of primary importance in the overall dynamics of the vibrational process of an elastic solid. To describe the contribution of each mode, coefficients of modal participation and modal mass have been introduced. These coefficients will be discussed in more detail in “Modal Participation Coefficients”. Modal participation coefficients The participation coefficient indicates the relative contribution of each mode to the displacement or rotation of the system when excited in a specific direction and manner. Since no rotational modes or angular vibrations of the grinding wheel were identified in the computer simulations, the participation coefficients for rotational directions are not considered in this study. Participation coefficients are calculated when it is necessary to determine the parameters of an external load that could potentially cause undesirable resonance in the system [27]. Such calculations make it possible to assess the significance of each mode participating in the vibration process. These modes are characterized by high vibration energies and sensitivity to specific types of loads. After identifying a significant mode in strength calculations, either the system’s operating modes should be changed or the design modernized to avoid undesirable consequences. Fig. 4 shows the graph of participation coefficients of grinding wheel No. 3 – GW 1 600×50×305 25A F60 L 7 V 50 2 class GOST R 52781-2007 – plotted along three coordinate axes. It demonstrates that the most significant eigenmodes of vibration of the grinding wheel are modes f₁ and f₂, which are most pronounced in the X and Y directions. Regarding the Z axis, the largest contribution in this direction is made by the “umbrella” mode f₃. This mode will be used for acoustic monitoring of the grinding process. When applying boundary conditions, the displacement of the grinding wheel model is restricted – it is rigidly fixed along the seat diameter on the machine spindle. Additionally, a prestressing condition distributed over the volume of the grinding wheel is imposed, resulting from the centrifugal forces during rotation at a speed of 1,590 RPM. Fig. 4. Participation factors of the natural vibration modes of the grinding wheel along the coordinate axes
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 7 No. 3 2025 The order of eigenmodes’ manifestation changes significantly as a result of calculating them under these specified boundary conditions. The bending mode with the highest values of modal participation coefficients and modal masses becomes the lowest and most significant mode, featuring a nodal circle coinciding with the end region — the “umbrella” mode. The participation of this mode in the overall dynamics of the grinding wheel vibrations is much greater (more than 30 times) than that of the others and, accordingly, it generates the most powerful acoustic wave. Comparison of experimental and calculated spectral compositions of grinding wheels In figs. 5, a–k, the black lines show the spectral compositions obtained experimentally using the method described in section “Experimental study of natural vibrations of grinding wheels”. These graphs illustrate the distribution of the natural frequencies of grinding wheels with the studied characteristics. During computer modeling and the modal analysis process, the values of Poisson’s ratio (ν) and Young’s modulus (E) were adjusted to align the calculated frequency values (shown in the graphs as red vertical lines) with the experimental frequencies. The parametric optimization problem was solved using the fitting method. A perfect fit can only be achieved when the real geometric dimensions of the grinding wheels exactly match their modeled counterparts. The frequencies coincide at a satisfactory level. The deviation of the calculated frequencies from the experimental values does not exceed 5 %. Consequently, the values of the integral elastic parameters, ν and E, were obtained for each grinding wheel considered: 1. 25А F36 L – ν = 0.25; Е = 51.25 GPa; 7. 25А F60 P – ν = 0.225; Е = 54 GPa; 2. 25А F46 L – ν = 0.215; Е = 46 GPa; 8. 25А F60 S – ν = 0.2; Е = 67.5 GPa; 3. 25А F60 L – ν = 0.18; Е = 41.5 GPa; 9. 14А F60 L – ν = 0.25; Е = 41.2 GPa; 4. 25А F80 L – ν = 0.17; Е = 40 GPa; 10. 64С F60 L – ν = 0.26; Е = 43 GPa; 5. 25А F120 L – ν = 0.16; Е = 45.5 GPa; 11. 92А F60 L – ν = 0.27; Е = 53 GPa. 6. 25А F60 N – ν = 0.22; Е = 48 GPa; Thus, although labor-intensive, this approach to determining ν and E is recognized as effective. The agreement between the calculated and experimental frequencies allows us to conclude that the simulated values of Poisson’s ratio and Young’s modulus of the grinding wheels correspond to those of their prototypes. Therefore, the main objective of this work has been achieved. Currently, work is underway to develop a mathematical model of the sound pressure generated during grinding and a methodology for predicting the grinding wheel service life based on acoustic indices. This model requires taking into account the actual elasticity parameters of grinding wheels and establishing a relationship between these parameters and the wheels’ characteristics. The values of ν and E obtained during this study were used as parameters to develop a sound pressure model of the grinding process. Preliminary results show the model’s qualitative agreement with, and adequacy to, the experimental acoustic data obtained during the grinding process study. Dependence of integral elastic parameters on grinding wheel characteristics The study of grinding wheels No. 1, No. 2, No. 3, No. 4, and No. 5 determined the influence of abrasive grain size on the elastic parameters, ν and E. Poisson’s ratio decreases as the abrasive grain size decreases. Young’s modulus decreases until the grain size reaches 0.2 mm; thereafter, the trend reverses and begins to increase. However, there is insufficient data to conclude whether the increase in Young’s modulus will continue as the grain size is further reduced. Fig. 6 shows graphs reflecting this dependence in terms of granularity versus Poisson’s ratio and granularity versus Young’s modulus. Next, regression equations and curves were obtained using MS Excel. The regression curves constructed from the experimental data are expressed by second-degree polynomial
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 7 5 a b c d e f g h i j k Fig. 5. Comparison of empirical and calculated spectral compositions of natural vibrations of grinding wheel: a – 25А F36 L; b – 25А F46 L; c – 25А F60 L; d – 25А F80 L; e – 25А F120 L; f – 25А F60 N; g – 25А F60 P; h – 25А F60 S; I – 14А F60 L; j – 92А F60 L; k – 64С F60
OBRABOTKAMETALLOV MATERIAL SCIENCE Том 23 № 3 2021 EQUIPMEN . INSTRUM TS Vol. 7 No. 3 2025 dependencies with approximation reliability levels of R² = 0.949 for the Young’s modulus dependency curve and R² = 0.993 for the Poisson’s ratio dependency curve. This indicates a strong correlation between the values of ν, E and the grain size factor. 2 0 0054 0 054 0 3 . . . x x ν = ⋅ − ⋅ + ; 2 1 75 12 25 62 35 . . . E x x = ⋅ − ⋅ + . It should be noted that the obtained regression relations are not claimed to be universal and can only be applied under the conditions in which they were derived. For instance, the values of ν and E can be determined for a grinding wheel with the following characteristics: an abrasive of white electrocorundum with a hardness grade of L and an average structure number of 6 on a ceramic bond. For a grinding wheel with a grit size of F100 (grit size ranging from 0.15 to 0.11 mm), the values of Poisson’s ratio and Young’s modulus are 0.164 and 42.66 GPa, respectively. Similarly, the effect of hardness on the elastic performance of grinding wheels has been established. An increase in grinding wheel hardness results in higher values of Young’s modulus. Young’s modulus characterizes the stiffness of the system and its ability to resist elastic deformation. This is reflected in the study of natural vibrations of a solid body. Grinding wheels with higher E values exhibit a shift of natural frequencies toward the high-frequency range (see Fig. 5). The change in hardness of grinding wheels with the same structure is due to the redistribution of the proportions of the main components: grain, bond, and pores. An increase in hardness is promoted by a decrease in pore volume and an increase in bond volume. Therefore, it can be concluded that there is a positive correlation between hardness and stiffness, or between the characteristics of plastic and elastic deformation of the grinding wheel, as expressed by Young’s modulus. Poisson’s ratio increases with hardness in the interval from L to P. After reaching a maximum value of 0.23, it begins to decrease. See fig. 7 for the graphs. The obtained regression dependencies have approximation confidence levels close to unity (R² = 0.9913 for the Young’s modulus curve and R² = 0.999 for the Poisson’s ratio curve). Therefore, there is a strong correlation between the values of ν, E, and the hardness factor. 2 0 0162 0 0877 0 109 . . . x x ν = − ⋅ + ⋅ + ; 2 1 75 0 35 40 5 . . . E x x = ⋅ − ⋅ + . These empirical regression models can be used to determine the values of ν and E for white electrocorundum grinding wheels with an F60 grain size and medium structure on a ceramic bond for several hardness grades: K, M, O, R, and T: – 25A F60 K has values ν = 0.148; E = 40.76 GPa; – 25A F60 M has values ν = 0.200; E = 43.91 GPa; Fig. 6. Influence of grinding wheel grit on the value of Poisson’s ratio and Young’s modulus
OBRABOTKAMETALLOV Vol. 23 No. 3 2021 MATERIAL SCIENCE EQUIPMENT. INSTRUMENTS 7 5 Fig. 7. Influence of grinding wheel hardness on the value of Poisson’s ratio and Young’s modulus – 25A F60 O has values ν = 0.227; E = 50.56 GPa; – 25A F60 R has values ν = 0.217; E = 60.713 GPa; – 25A F60 T has values ν = 0.175; E = 74.36 GPa. Values of Poisson’s ratio and Young’s modulus were also obtained for grinding wheels made of normal electrocorundum, white electrocorundum, chromotitanium electrocorundum, and green silicon carbide (see fig. 8). Since the abrasive material of the grinding wheel cannot be quantified, regression analysis and the development of empirical relationships are not applicable in this case, unlike in the study of the effect of grain size and hardness on the elastic parameters of the tool. The values of ν and E in fig. 8 do not permit further applications or insights beyond what is obtained directly. Fig. 8. Influence of abrasive material on the value Poisson’s ratio and Young’s modulus Conclusion 1. The order of appearance of the eigenmodes of grinding wheel vibrations remains unchanged over a wide range of ν and E values. The lowest eigenmodes used for acoustic monitoring of grinding wheels are a pair of bending modes f₁, f₂ (n = 2, s = 0) and the bending mode f₃ (n = 0, s = 1). 2. In the absence of boundary conditions, modes f₁ and f₂ (n = 2, s = 0) contribute most significantly to the dynamics of grinding wheel vibrations along the X and Y coordinate axes. In the Z direction, the largest contribution is made by eigenmode f₃ (n = 0, s = 1); however, this contribution is much smaller than that of f₁ and f₂. 3. The values of Poisson’s ratio and Young’s modulus for the studied grinding wheels were determined by correlating the experimental and calculated spectral compositions of the natural frequency distributions. The values vary within the following ranges: 0.16 < ν < 0.27 and 40 GPa < E < 67.5 GPa. Grinding wheels with significantly different characteristics (e.g., 25A F80 L and 25A F60 S) may have slightly different
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