Oleksii Lanets

Problem statement. Considering the prospects of using discrete-continuous vibration machines, there is a need to study the properties of continuous sections, which are elastic plates, in a wide range of frequencies. Purpose. It consists of studying the frequency response of continuous sections of various shapes and sizes from the harmonic disturbance force and identifying the frequency ranges in which the maximum stresses will be observed. Methodology. A schematic diagram of a discrete-continuous oscillating system is given. A set of necessary parameters is selected, which the studied samples of continuous sections should possess. Rectangular, diamond-shaped, X-shaped, parabolic convex and parabolic convex plates of different thicknesses corresponding to the given parameters were designed. Control point arrays were selected to investigate stresses in the plates. For each of the plates, a linear dynamic analysis was carried out with the help of simulation modeling. The dependence of the maximum stresses at the control points of the investigated plates on the frequency of the harmonic disturbance was determined. Findings (results) and originality (novelty). A linear dynamic analysis of continuous sections of various shapes and thicknesses was performed for the first time. The results obtained from the conducted research, in general, indicate the presence of stress amplifications occurring in plates of various shapes and sizes at certain frequencies of harmonic disturbance. In all investigated types of plates, stress amplification was found at the first and third natural frequencies of oscillations. It was determined that the largest stresses occur in the parabolic convex plate and the smallest - in the parabolic convex. Practical value. Frequency ranges have been established in which, with harmonic disturbance of continuous sections, it is possible to obtain significant dynamic amplification of oscillations of discrete-continuous vibrating machines with an electromagnetic drive. Recommendations for choosing the optimal geometric parameters of the plates as continuous sections of vibration machines, in which they could be operated for an infinite number of load cycles, are described. Scopes of further investigations. The reaction of continuous sections with various shapes and dimensions to the simultaneous interaction of several forces with different frequencies and amplitudes of disturbance requires further research.

Goal. It consists of studying the influence of the frequency of harmonic disturbance of a continuous section in the form of a rectangular plate on its maximum stresses, deflections, and acceleration, and in identifying frequency ranges in which there is a significant amplification of the oscillations of continuous sections. Significance. In known designs of discrete-continuous vibrating machines, only the first natural frequency of oscillations of the continuous section is used to implement energy-efficient modes of operation. Conducting a dynamic analysis of a continuous section on a wide range of frequencies would allow the formation of new ideas for the realization of the dynamic potential of such vibrating equipment. Method. A continuous section in the form of a rectangular plate hinged in the intermediate mass of the vibrating machine is considered. For the plate, taking into account the fastening conditions, the natural frequencies of oscillations are determined. The calculation scheme of the plate is formed. Control points on the surface of the plate were selected, for which the maximum stresses, deflections, and resulting accelerations were determined using simulation modeling. Results. When conducting a dynamic analysis of a continuous section in the form of a rectangular plate, it was found that the maximum stresses, deflections, and accelerations are observed during its harmonic disturbance at frequencies, close in value to the first, third, and seventh natural frequencies. Scientific novelty. For the first time, the linear dynamic analysis of a continuous section in the form of a rectangular plate hinged in the intermediate mass of a discrete-continuous vibrating table with an electromagnetic drive, was carried out. Practical significance. Based on the conducted research, ideas were formed for the implementation of new, more energy-efficient modes of operation of discrete-continuous vibrating machines.

Goal. It consists in substantiating the rational design of the vibroconveyor as a component of the vibroconveyor line of length , which will provide the necessary technological parameters for the transportation of artificial cargoes. The difficulty of this task is that the speed of transporting goods by mass should be at least . Topicality. The need for these studies is due to the fact that the vibration machine interacts with the parameters of the oscillation system, the main of which are inertial, rigid and power. If they are correctly calculated and implemented in the design of a vibration machine, it will be robust. Failure to consider one type of parameters causes an error in the calculation. Method. The refinement of analytical expressions is carried out using the classical approaches for linear vibrational systems with harmonic perturbation. For this the physical model of the two-mass resonance oscillation system is considered and its mathematical model is developed as a system of linear differential equations. On the basis of this the solution is formed (the values of the amplitudes of oscillations). Unknown parameters remain rigid, provided that the inertia is constructed. Therefore, using the determinants of the matrix of coefficients for unknowns, the necessary mathematical operations are performed that satisfy the imposed conditions for the establishment of rigid parameters. Results. In the paper a series of analytical expressions are obtained that examine the mutual influence of rigid parameters in the system. A comparison of the obtained results according to the specified expressions with classical analytical expressions is made. It is established that the values according to the proposed expressions do not differ significantly from the classical approaches, and therefore, in the case of in-energy calculations, it is sufficient to use existing expressions. The proposed expressions are more precise and therefore recommended for scientific research. Scientific novelty. For the first time, we succeeded in synthesizing analytical expressions for the establishment of inertia-rigid parameters that allow more accurate calculation of two-mass resonance oscillation systems. It is established that for the correct choice of resonant alignments in the system, the mutual influence of rigid parameters in the system is not significant, and therefore it is scientifically grounded to use classical approaches. Practical significance. Established analytical expressions can be widely used in the design of vibration process equipment. The transparency of the output and the relative simplicity of the proposed analytical expressions allows for their widespread use in practice.

Problem statement. To ensure highly efficient inter-resonance modes of operation of vibrating equipment, the oscillating masses of the system must have certain inertia-rigid parameters, as well as a certain frequency of natural oscillations. The disadvantage of highly efficient inter-resonance oscillatory systems is that the third reactive mass must be small, and therefore the use of complex and large structures is impossible. Therefore, it is best to use the reactive mass as a continuous section. The continuous section, which is a flexible body, optimally combines inertial and rigid parameters. Scientific works have already considered the design of the vibrating table, in which the continuous section is an ordinary rectangular plate hinged in the intermediate mass. This decision looks quite promising. However, likely, the rectangular shape of the plate is not the best option to ensure maximum energy efficiency. Purpose. Extend the method of calculating the natural frequency of oscillations of the plates by the approximate Rayleigh-Ritz method using the general hyperboloid equation to plates with variable cross-section for the proposed types of plates and check the results with the calculation in Ansys software. Methodology. The calculations of the plates were performed using the basic principles of the theory of oscillations, in particular the Rayleigh-Ritz method in the software product MathCAD. Findings (results) and originality (novelty). Two types of elastic plates with variable cross-sections are considered. In the first case, the shape of the plate was given by quadratic functions, in the second case, it was described by trigonometric functions of cosine. In both cases, the same conditions of attachment in the intermediate mass were observed. The calculation of the first natural frequency of oscillations of the considered plates was performed using the approximate Rayleigh-Ritz method with the assumption that the deflection of the plates occurs on the surface of the hyperboloid. The reliability of the obtained results was verified by numerical calculation in the software product Ansys. Practical value. It is assumed that the proposed types of plates can increase the dynamic potential of the vibrating machine. Scopes of further investigations. For further study of the considered types of plates as a continuous section of the inter-resonance vibrating machine, it is necessary to calculate their deflections at forced oscillations.

Goal. It consists in substantiating the inertial-rigid and force parameters of a high-efficient discrete three- mass inter-resonance oscillation system of a vibratory machine with an electromagnetic drive and in forming its mathematical model taking into account the drive. Significance. Despite the widespread use of one- and two-mass vibratory machines in the industry, their three-mass analogs in the inter-resonance oscillation zone have significant dynamic potential. New approaches to the calculation and design of three-mass inter-resonance vibratory machines would facilitate their mass introduction in enterprises of various industries as technological equipment. Method. A mathematical model of a three-mass inter-resonance oscillatory system of a vibrating machine with an electromagnetic drive in the form of a system of linear differential equations is considered. Based on it, dependencies are formed to determine the required inertial-rigid and force parameters of a highly efficient vibratory machine. Based on the already known power parameters of the system is a technique for establishing the necessary parameters for the design of the vibratory machine electromagnetic drive. The above parameters are embedded in the mathematical model of the vibratory machine. The time dependences of the motion of oscillating masses are investigated taking into account the processes occurring in the electromagnetic vibrator. Results. Inertial-rigid, force parameters of the oscillatory system are substantiated. A mathematical model of a three-mass inter-resonance oscillatory system is formed, which takes into account electromagnetic processes in the drive. Scientific novelty. A mathematical model of a three-mass inter-resonance oscillatory system of a vibratory machine is formed, taking into account the processes occurring in the electromagnetic drive, where the force action of the electromagnet is formed through the current in the coil of the vibrating exciter. Practical significance. The proposed method of calculations of three-mass inter- resonance vibratory machines with electromagnetic drive can be used in the design of high-efficiency vibratory process equipment.

Problem statement. While designing vibration isolators, the essential attention should be paid to the safety factors such as the levels of vibration and noise, as well as to the material and the structure of isolators. In major vibratory technological equipment, there are used full-metal vibration isolators, which can be designed in the form of coil (cylindrical, conical, helico-spiral) or flat (leaf-type, disc-type) springs. The problems of stress-strain analysis of metal springs used for vibration isolation of various vibratory equipment are of urgent interest among the designers and researcher. The engineering techniques of step-by-step calculation of full-metal vibration isolators of different types of vibratory technological machines are not thoroughly presented in the modern information resources. Purpose. The present paper is aimed at developing and implementing the detailed algorithm of determining the stiffness parameters of the metal coil springs used for vibration isolation of large-scale vibratory machines. Methodology. The investigations are carried out using the basic laws and principles of solid mechanics and theory of vibrations. The calculations were conducted using MathCAD software; the computer simulation of the spring’s stress-strain state was performed using SolidWorks software. Findings (results) and originality (novelty). The improved design of the vibratory conveyer-separator is considered. The engineering technique of calculating the passive vibration isolators of various vibratory equipment designed in the form of metal coil springs is developed. The proposed technique is implemented while designing the vibration isolation system of the vibratory conveyer-separator. The system’s operational characteristics are determined, and the computer simulation of the springs stress-strain state is carried out. Practical value. The proposed design of the vibratory conveyer-separator can be implemented in various industries (machine-building, chemical, pharmaceutical, food-processing, construction, mining, metallurgy, textile industries etc.) for conveying different loose, bulky and piecewise products, and separating them into fractions of different sizes. Scopes of further investigations. While carrying out further investigations, it is necessary to analyse the influence of the proposed design of vibratory conveyer-separator on the foundation during its operation, and to consider the necessary of applying the additional fixation systems.

Problem statement. The three-mass vibratory system can be defined by five basic parameters: inertial parameters of the masses and stiffness parameters of two spring sets. Unlike the classical discrete system, the discrete-and-continual one consists of two rigid bodies connected by one spring set that form the discrete subsystem, and of the reactive mass considered as deformable (elastic) body characterized by certain stiffness and inertial parameters, which are related with one another. Purpose. The main objective of the paper consists in determining the first natural frequency of the continual subsystem of the three-mass discrete-and-continual vibratory machine. Methodology. While carrying out the investigations, it is used the classical theory of oscillations of straight elastic rods. Findings (results). The engineering technique of determining the first natural frequency of the continual subsystem of the three-mass vibratory machine is developed and approved by means of analytical calculations and numerical simulation. Originality (novelty). The optimal diagram of supporting the continual subsystem (elastic rod) is substantiated. The possibilities of exciting the vibrations of the three-mass discrete-and-continual mechanical system using the eccentric drive are considered. Practical value. The obtained research results and the developed calculation techniques can be used be engineers and designers dealing with various technological and manufacturing equipment that use vibratory drive. Scopes of further investigations. While carrying out further investigations, it is necessary to develop the model of combined discrete-and-continual system of three-mass vibratory machine, and to carry out the numerical simulation of the system’s motion under different operational conditions.