Досліджено коливальну систему, яка моделюється першою змішаною задачею для слабко нелінійного рівняння коливань балки в обмеженій області. Одержано умови існування локального за часовою змінною розв'язку. Особливо виділено коливальний режим із загостренням. Показано можливість застосування до задачі методу Гальоркіна.

Проаналізовано основні типи механізмів регулювання потужності горизонтально-осьових вітроустановок малої потужності. З метою підвищення точності регулювання потужності, ефективності та надійності функціонування вітроустановок у широкому діапазоні швидкостей вітру обгрунтовано необхідність подальшого вдосконалення існуючих механізмів регулювання. Розглянуто перспективи створення комбінованих механічних систем, у яких передбачено можливості одночасного повороту та складання лопатей, повороту (або складання) лопатей і виведення вітроколеса з-під вітру.

Purpose. The aim of the paper is to study dynamic processes in nonlinear oscillatory systems with quasi-zero stiffness and with one or many degrees of freedom, which are widely used in industry for cargo and personnel vibration isolation during transportation. The previous studies of such systems were based only on the numerical approaches. In this paper, we propose to investigate thoroughly the dynamics of the above mentioned systems and the conditions for the occurrence of resonance phenomena in them using the asymptotic methods of nonlinear mechanics and applying the apparatus of special periodic functions. Methodology. The methods of studying resonance oscillations of vibration isolation equipment are based on the asymptotic methods of nonlinear mechanics, wave theory of motion and the use of special Ateb-functions. Findings. In this work, for the nonlinear quasi-zero stiffness vibration isolation systems with one and two degrees of freedom, we analytically obtained conditions of resonance oscillations, threshold values of resonance amplitudes depending on the system parameters. Originality. Scientific novelty lies in the fact that the dynamic processes in systems with concentrated masses and quasi-zero stiffness are analyzed on the basis of analytical approaches for the first time. In contrast to numerical approaches, analytical approaches allow investigating the features of the dynamics of such systems more precisely. Practical value. The proposed method can not only solve the problems of analysis, but also the equally important problem of oscillatory systems synthesis at the design stage, to choose such elastic properties of dynamical systems that prevent resonance phenomena. These modes of equipment operation will allow efficient and safe transportation.

The history and modern tendencies of development of cushioning systems are analyzed in this paper. The development of mathematical modelling as a process is denoted, the methods and means are described and the necessary information of model choosing is presented. It is focused on the development of simulation modelling. The approaches of researchers, recommendations, indexes and specific features of evaluation of motion evenness are described. The works of many scientists are dedicated to analysis of car vibrations, evaluation of motion evenness and vibration-proof features. Many of them are devoted to investigation of vibrations, to optimization of basic design parameters of the cushioning system of cars and to development of new cushioning systems which allow reducing of vibratory overloading of trucks of general purpose. Taking into account the problems of motion evenness from the point of view of vibration of cushioning parts, the works of scientists are based on the linear theory of cushioning and the simplest one-mass car models are considered. It is also established that the drawback of usage of such theory consists in the fact that it is impossible to overview separately the vibrations of cushioning parts, which weight transfers to elastic elements of the suspension, and non-cushioning parts. The overview of scientific works dedicated to investigation of dynamics of wheeled vehicles allows to show the limited possibilities of traditional passive suspension system according to continuously increasing requirements to modern structures and to substantiate the necessity of usage of controlled cushioning systems. Among the existing variants of controlled cushioning systems, the half-controlled systems, which are the most optimal from the point of view of motion evenness increasing, energy consumption, complexity of structural implementation and usage safety, are of the greatest interest nowadays. On the basis of analyzed materials, it may be concluded that there exists a great amount of scientific investigations in the field of motor vehicles vibrations many of which are devoted to improvement of vibration-proof features of cars. Also a number of works are dedicated to investigation of vibratory overloading of industrial, construction and agricultural motor vehicles which are engaged in transportation of cargo of general purpose. However, too small attention is payed to development of techniques of determination of design parameters of cushioning systems of trucks which are engaged in transportation of cargo of special purpose, for example, cars transportation, where essentially greater attention should be payed to vibratory loadings which act upon such cargo during uneven motion.

Purpose. The purpose of the article is to create a viscoelastic dynamic model of flexible axially-moving belt of different mechanisms considering the influence of the material mechanical properties on its dynamic characteristics in case of transverse vibrations. Methodology. Methodology for flexible belt transverse oscillation investigation is based on asymptotical methods of nonlinear mechanics and wave theory of movement. Findings. Analytical relations for amplitude and frequency of transverse vibration definition for flexible viscoelastic axially-moving belts are obtained in the research. The influence of viscous and elastic belt material properties on its frequency response is analyzed. Originality. For the first time, based on a created dynamic model of flexible viscoelastic axially-moving belt, its dynamic performance during the transverse vibrations is identified analytically and the influence of material mechanical properties on these characteristics is studied Practical value. The offered flexible belt transverse oscillation investigation method allows determining the influence of longitudinal movement speed and viscoelastic material properties on the main parameters of dynamic process. Obtained analytical relations can be the basis for engineering calculations of components and mechanisms, part of which are axially-moving flexible belts.

Purpose. Determining the dynamic factor of industrial equipment safety by studying the dynamic processes in a nonlinear compressed shaft type oscillation system, which is widely used in mining industry. Such systems have previously been studied in literature solely based on the numerical modelling approach. In this paper, it is proposed to use asymptotic methods of nonlinear mechanics and the method of special periodic functions for thorough investigation of dynamics of the above systems and the conditions of resonance phenomena occurrence. We also describe the method for determining the dynamic factor of safety for boring equipment. Methodology. The methods for analysing resonant oscillation regimes and determining the factor of safety for industrial equipment elements are based on asymptotic methods of nonlinear mechanics, wave theory of motion and the use of special Ateb-functions. Findings. In this paper, the conditions of resonant oscillations for given nonlinear compressed shaft type systems are analytically obtained depending on system parameters and the method for calculating the dynamic factor of safety for industrial equipment elements is described. Originality. Scientific novelty lies in the fact that, for the first time, the calculation of dynamic processes in compressed shaft type systems is done based on analytical approaches that allow, in contrast to numerical and experimental approaches, investigating the dynamics features of such systems more precisely and avoiding the occurrence of unwanted resonant modes in mining equipment. Practical value. The presented method allows not only solving the problems of analysis, but also solving important problems of oscillation system synthesis at the design stage as well as choosing the elastic characteristics of dynamic systems and calculating the dynamic factor of safety for drilling equipment, taking into account the possible resonance phenomena. These mining machine features allow performing mining operations efficiently and safely.

Індекс рубрикатора НБУВ: О12-01

Рубрики:

Рухомий склад транспорту (засоби сполучення)

Шифр НБУВ: Ж44086 Пошук видання у каталогах НБУВ 

Purpose. To develop a method for determining resonant modes of industrial equipment of elastic shaft type, which is widely used in the mining industry, through the study of mathematical model of nonlinear oscillations. Mathematical models of oscillatory systems previously were studied in the literature mainly based on the numerical and experimental approaches. This paper proposes using a combination of the wave theory of motion and asymptotic methods of nonlinear mechanics using special apparatus of periodic functions to investigate the vibrational dynamics of the system and conditions of resonance phenomena in it, as well as to describe the method for determining the resonance curves to increase the margin of safety of industrial equipment. Methodology. Methods for studying resonance amplitudes and frequencies, determining the strength characteristics of equipment are based on the use of asymptotic methods of nonlinear mechanics, wave motion theory and theory of special Ateb-functions. Findings. In this work the conditions of resonance amplitude and frequency depending on the system parameters were obtained analytically for these nonlinear vibrational systems of elastic shaft and the overall method for determining the resonance curves was described. Originality. For the first time a complete analysis of the impact of physical, mechanical and geometrical factors of the dynamic pricess on the resonant frequency and amplitude in systems such as elastic shaft was conducted on the basis of analytical approaches that allow, in contrast to numerical methods and experimental approaches, exploring features of dynamics of such systems more precisely. Practical value. The proposed technique allows solving important practical problems of developing oscillatory engineering systems at the design stage, selecting the elastic characteristics of shafts, counting modes and screw drilling equipment in view of possible resonance phenomena. Determination of resonance modes of the equipment in turn allows for efficient and safe mining.

Problem statement. Designing and manufacturing of efficient resonant vibratory lapping machines with linear oscillations of laps demand an accurate and detailed calculation of parameters of their elastic systems and electromagnetic drives. Purpose. The main objective of this research consists in derivation of analytical dependencies for calculating the stiffness and excitation parameters of mechanical oscillatory system of vibratory finishing machine in order to ensure its resonance operation mode. Methodology. The technique of the research is based on fundamental concepts of engineering mechanics, strength of materials and theory of mechanical vibrations. Findings (results). The design diagram of mechanical oscillatory system of vibratory finishing machine with linear oscillations of laps is considered and corresponding equations of motion are presented. Analytical dependencies for calculating stiffness and excitation parameters of the system are deduced. The example of parameters calculation is given and time dependencies of the system's motion are constructed. Originality (novelty). The mathematical model of linear oscillations of the three-mass mechanical system of vibratory finishing machine was developed. The possibilities of performing the laps dressing using "lap over lap" method were substantiated. Practical value. The results of the performed investigations can be used during designing new designs and improving existing structures of vibratory finishing machines for lapping flat surfaces of cylindric and prismatic parts. Scopes of further investigations. In further investigations, it is necessary to analyse the influence of the viscous damping on the system's motion. In order to substantiate (justify) the obtained theoretical results, the experimental investigations should be carried out.

Purpose. Determination of dynamic load factors in the links of a two-drum drive of a suspended cable timbertransporting plant equipped with an electric motor and an elastic coupling, taking into account the transient electromechanical processes in the drive motor, variable moments of inertia of drive drums, technological load, as well as changes in the coefficients of longitudinal rigidity of moving cables. Methodology. The developed dynamical model of the drive contains a number of theoretical dependencies, calculation schemes and systems of differential equations that describe the dynamic processes in the two-drum electromechanical drive of the suspended cable timbertransporting plant. The differential equations of the electromagnetic state of the machine, which describe the transient processes in the drive motor, are based on the Park - Goriev equations. Differential equations of mechanical part of the drive motion are developed on the basis of the D'Alembert's method. For the umerical integration of differential equations systems, the modified Euler's method is used. Findings. The simulation model calculates the dynamic forces that are active in mechanical gears and the drive coupling; potentially dangerous operating modes of the drive of suspended cable are determined. The dependence of the load dynamic factor on the structural parameters of the drive is established. The influence of the length of the free part of the movable cable on the magnitude of the dynamic loads in the drive is investigated. Originality. For the first time, a dynamic model of the drive of suspended cable timbertransporting plant was proposed which takes into account: transitional electromechanical processes in the drive motor; variable inertia moments of drive drums; variable load acting on drive drums at each of the stages of the technological cycle of the cable plant work. Calculations of the moment of inertia of the drive drum and the moment of the force of the technological resistance that are variable in time are made taking into account the multilayer winding of the cable on the drive drum, as well as the forces of elastic deformation of moving cables. Practical value. New methods, algorithms and programs have been developed and the existing ones have been improved for calculation of dynamic loads in the coupling and gears of the electromechanical drive of a cable plant with haul-lifting and reversing cables. On the basis of the obtained dependences of load dynamic factor, recommendations for the choice of structural and operational parameters of drives of these plants were developed.

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.

Індекс рубрикатора НБУВ: З252.8

Рубрики:

Сонячні батареї

Шифр НБУВ: Ж44086 Пошук видання у каталогах НБУВ 

The paper considers differential equation of the vibro-impact resonance system with an asymmetric piecewise linear elastic characteristic. The time-instant of switching of elastic characteristic is determined on the basis of equality of oscillation period to average value of the corresponding eigenfrequencies. Then, expansion of the asymmetric piecewise linear elastic characteristic into Fourier series was made. The initial differential equation was reduced to a kind of parametric equations of Hill's andMathieu's type with taking into account the time of elastic characteristic change. Stability analysis of parametric Mathieu equation is shown for the analysis of natural oscillations. For stability analysis of the synthesized by various stiffness coefficients of vibro-impact system, dependencies of Mathieu equations coefficients on the parameter of synthesis are used. The solution of the initial equation with forced oscillations in the form of asymmetric two-frequency vibrations has been obtained by means of Bubnov - Galerkin and Levenberg - Marquardt methods for nonlinear algebraic systems of equations, also amplitude and phase frequency dependence was graphically drawn. The basic equation with an asymmetric elastic response characteristic feature is determined by the fixed natural frequency of oscillations independently of amplitude. Numerical solution of differential equations by means of Runge - Kutta method are presented for comparison. Comparison of the vibro-impact resonance system kinematics characteristics, synthesized by the elastic parameters and solved by the listed methods, is conducted. The feasibility of using nonlinear analysis presented in two harmonics in Fourier series asymmetric elastic characteristic is justified in the article. The suggested approach with Bubnov-Galerkin method for general Hill's equation and correlation analysis of time kinematic characteristics was used. Acceleration frequency spectrum and harmonics are obtained on the basis of Runge - Kutta numerical method simulation of the initial nonlinear differential equation.

Індекс рубрикатора НБУВ: З252.8

Рубрики:

Сонячні батареї

Шифр НБУВ: Ж44086 Пошук видання у каталогах НБУВ 

Індекс рубрикатора НБУВ: И131.111.42

Рубрики:

Електричне буріння свердловин

Шифр НБУВ: Ж16377 Пошук видання у каталогах НБУВ 

Індекс рубрикатора НБУВ: З45-042.2

Шифр НБУВ: Ж44086 Пошук видання у каталогах НБУВ 

Problem statement. The development of energy-efficient and high-performance vibratory lapping machines demands the improvement of their design diagrams and calculation techniques. Purpose. The main objectives of this research consist in detailed analysis of existent design diagrams and mathematical models of vibratory lapping machines; designing the three-mass hanger-type structures of such machines providing circular oscillations of laps; derivation of differential equations describing the motion of their oscillatory systems. Methodology. The technique of the research is based on fundamental concepts of engineering mechanics, strength of materials and theory of mechanical vibrations. Findings (results). The improved design diagrams of vibratory lapping machines with circular oscillations of laps are proposed and the corresponding differential equations describing the motion of the working elements are derived. Originality (novelty). The mathematical model of circular oscillations of the three-mass mechanical oscillatory system of vibratory lapping machine is developed. The possibilities of performing the double-side lapping of cylindrical and prismatic parts are considered. Practical value. The results of the performed investigations can be used during creating new designs and improving existent structures of vibratory finishing machines for lapping flat surfaces of cylindrical and prismatic parts. Scopes of further investigations. In further investigations, it is necessary to perform the numerical modelling of the system's motion using the derived differential equations, and to compare the obtained theoretical results with the results of experimental investigations.

Abstract. Friction treatment refers to surface strengthening (hardening) methods using highly concentrated energy sources. In the course of this processing in the surface layers of the processed surfaces of parts the strengthened layer with nanocrystalline structure is formed. The formed layer has specific physical, mechanical, chemical properties, as well as improved performance properties, which are significantly different from the base metal. A highly concentrated energy source is formed in the contact area of the tool-part due to the high-speed friction (60 - 90 m/s) of the tool on the treatment surface. Frictional treatment of flat parts according to the kinematics of the process is similar to grinding. The strengthening process was carried out on an upgraded surface grinder. The tool is a metal disk made of stainless-steel. Transverse grooves are formed on the working surface of the tool to intensify the process of forming a strengthened (reinforced) layer with a nanocrystalline structure. The grooves form additional shock loads in the contact area of the tool-treatment surface of the part. These shock loads increase the shear deformation of the metal of the parts' surface during treatment, which affects into formation the quality parameters of the parts' surface and surface layer. To study the friction treatment process, the calculation scheme of the elastic system of the machine was developed. A simulation model for the study of dynamic processes that take place during the friction treatment of flat surfaces was built. This model gives possibility to determine the displacements and velocities of the machine table on which the part is fixed and the tool, and to determine their mutual displacement and also calculate the reaction of the machine table.