The problems of synthesis and substantiation of elasticity parameters of the resonant vibratory device with electromagnetic drive and one flat spring are considered. At first, the harmonic systems with oscillation frequencies of 50 Hz and 100 Hz were investigated. Then, various asymmetric piecewise linear characteristics of elasticity were carried into effect on one flat spring using auxiliary intermediary fixed cylindrical supports. Due to this, the corresponding vibro-impact operation modes were obtained. The resonant systems characterized by improved functioning efficiency were carried into effect using the new technique of optimization synthesis of elasticity parameters. The resonant systems being investigated were implemented in practice. The basic experimental investigations of their kinematic, dynamic and energetic parameters were carried out. The fundamental result of the investigation consists in confirmation of the improved dynamic efficiency of vibro-impact systems with pulsed electromagnetic excitation designed according to the new technique. The proposed systems may be used in technological processes of materials compaction and screening, of surface treatment of machine parts and in processes associated with nanotechnology.

Multi-frequency vibrators have advantages in bulk materials processing but their design is usually complicated. This article presents the synthesis of design parameters of a two-frequency inertial vibrator according to the specified power characteristics. Based on the developed mathematical model, the parameters of variable periodic force is derived for two angular velocities 157, 314 rad/s and their ratios 0.5 and 2. In the case of the 0.5 ratio, the instant angular velocity of the resulting force vector is 2.0–3.5 times greater than for ratio 2. A dynamical model of vibrating screen with the synthesized inertial drive is considered. It was found that at the ratio of angular velocities 0.5, the second harmonic of acceleration prevails at 50 Hz, while at the ratio of 2, the first harmonic has a greater amplitude at 25 Hz. For the first variant, the power does not depend on the initial angle between unbalances, and at the second variant, it can vary. The angle of rotation of unbalances affects the trajectory of the centre of mass and the phases of the harmonics but does not affect their amplitude. Due to such dynamical features, the two-motor inertial drive allows the vibrating machines to operate at a wider range of frequencies and amplitudes.

The calculation diagrams of oscillating systems and operation features of vibratory finishing machines are considered. The mathematical models of three-mass and four-mass oscillating systems are presented. The amplitude values of the oscillating masses displacements are derived. The functions of inertial and stiffness parameters optimization are formed. The optimization problems are solved with a help of MathCAD software. On the basis of synthesized inertial and stiffness parameters, the amplitude-frequency characteristics of the oscillating systems of vibratory finishing machines are formed and analyzed. In order to verify the validity of the proposed theoretical approaches, the simulation of the mathematical model of the oscillating system motion is carried out by means of numerical solving of the system of differential equations of the oscillating masses motion. The proposed structural diagrams and the operation schemes of the vibratory finishing machine, as well as the derived analytical formulas may be used by designers, researchers and technologists while improving existent and developing new equipment for vibro-finishing treatment.

The paper is aimed at studying the motion conditions of the vibratory compacting machine equipped with the crank excitation mechanism characterized by the changeable geometrical parameters. Unlike numerous scientific publications devoted to similar subject, the novelty of the present research consists in the improved design of the vibro-impact plate compactor and the developed mathematical model describing the motion conditions of the compactor's oscillatory system. It is proposed to use the crank mechanism to excite the oscillations of the impact body acting upon the frame of the compacting plate at a certain angle to the surface being compacted. The main idea of this improvement is to provide the self-propelling locomotion conditions of the compactor and to reduce the pushing force that must be applied by the operator. The research results obtained by means of the numerical modeling in Mathematica software describe the dynamic behavior of the compactor's oscillatory system under different geometrical parameters of the crank excitation mechanism (crank eccentricity, impact gap, etc.). The material of the paper can be of significant practical interest for the designers and engineers dealing with the development of new vibratory compactors and the improvement of compacting technologies.

Автоматизація виробничих процесів у машинобудуванні та приладобудуванні. Вип. 52. 2018 32 УДК 621.923.7 \ I. V. Kuzio, V. M. Zakharov, V. M. Korendiy doi The purpose of the paper. Substantiation of structure (design), parameters and operation modes of the improved vibratory finishing machine. Analysis of dynamical processes which occur during "lap over lap" dressing. Investigation methodology. Mathematical model of motion of the mechanical system of vibratory finishing machine was developed on the basis of Lagrange differential equations of the second order. For the purpose of describing friction between the working surfaces of the laps, the Coulomb friction model was used. Stiffness parameters of all elastic elements were modeled in accordance with the Hooke's law. Energy losses in elastic elements during their tension-compression were taken into account by corresponding coefficients of dissipation (damping). Simulation modelling of motion of the machine's mechanical oscillatory system was carried out in MathCAD software by means of solving the derived differential equations of the system's motion using the numerical methods of Runge-Kutta. Obtained results. Structural and functional peculiarities of the improved vibratory finishing machine for lapping flat surfaces of cylindric and prismatic parts were considered. Design (calculation) diagram of its mechanical oscillatory system was substantiated and differential equations of motion of oscillating masses were derived. Simulation modelling of the laps' motion during their dressing was carried out and the correspondence of the obtained results to the input modelling parameters (operation in near-resonance mode with the given oscillation amplitudes) was analyzed. Scientific novelty. For the first time we obtained following results: spatial design (calculation) diagram of mechanical oscillatory system of the improved vibratory finishing machine was proposed; mathematical model of plane-parallel motion of oscillating masses (with circular trajectories of oscillations) was developed; possibilities of performing the laps dressing using "lap over lap" method were substantiated by means of ensuring their circular oscillations. Practical value. The results of the performed investigations can be used during designing new and improving existing structures of vibratory finishing machines for finishing treatment (lapping) of flat surfaces of cylindric and prismatic parts.

Vibration-driven locomotion systems and mobile robots are widely used in different industries, in particular, for inspecting and monitoring the pipelines. Among the great variety of such robots designs, the ones based on the wheeled chassis and equipped with the vibratory drive are of the most widespread. The novelty of the present paper consists in substantiating the design parameters of the wheeled robot working under the vibro-impact conditions and driven by the crank-slider excitation mechanism. The main goal of this research is maximizing the robot average speed. While simulating the robot dynamic behavior, the numerical methods are used, in particular, the finite-element methods and the Runge-Kutta methods, which are implemented in the SolidWorks and MapleSim software. The obtained results presented in the form of time dependencies of the robot kinematic and dynamic characteristics can be of significant practical interest for the researchers and designers of the similar robotic systems.

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The purpose of research. The main goal of the presented research consists in substantiation of inertial, stiffness and force (excitation) parameters of mechanical oscillatory system of three-mass vibratory conveyer with directed oscillations of the working element in order to provide the highly efficient (high-performance) resonant operation mode. Methodology. The technique of the research is based on fundamental concepts of engineering mechanics and theory of mechanical vibrations. In order to deduce the differential equations of motion of the mechanical oscillatory system of vibratory conveyer the Lagrange equations of the second order were used. The computation modelling of the system's motion caused by periodic excitation forces was carried out using MathCAD software with a help of Runge-Kutta method. Results. The existent structures of vibratory conveyers, as well as the fields and peculiarities of their implementation, are considered. The design of the three-mass vibratory conveyer with electromagnetic drive, directed oscillations of the working element, and resonant operation mode is proposed. The structural diagram of the conveyer's mechanical oscillatory system is developed and its dynamics is investigated. Scientific novelty. The mathematical model of motion of the mechanical oscillatory system of the proposed conveyer is formed. The numerical modelling of motion of the oscillating masses of the vibratory conveyer was carried out for different operation modes. The influence of the excitation parameters (the frequency and amplitude of the excitation force) on the characteristics of oscillations of the conveyer's working element was investigated. Practical value. The results of the carried out investigations can be used while designing and developing various vibratory equipment for conveying, separating and treating of different loose, bulky and piece-wise products.