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).
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