The paper considers a rotor system with a nonlinear characteristic. Its equations of motion are a kind of Duffing class equations with multiple degrees of freedom. The paper shows the advantage of using the method of elliptic functions for solving problems of this type. This method enables us to take into account not only vibrations of the rotor installed in elastic nonlinear supports, but also vibrations of the foundation. A comparative analysis of application of the method of elliptic functions proposed by the authors is carried out by comparing the derived equations of motion of the system, as well as by comparing the obtained amplitude-frequency characteristics with the results obtained by the numerical Runge–Kutta–Fehlberg’s 4-order method and the approximate analytical Van der Pol method. The regions of resonant frequencies for superharmonic oscillations and bifurcation regimes are determined. It is concluded that the method proposed by the authors is a more accurate and general case than the previously used approximate methods.

In this paper is studied a vibratory conveyor that is placed on an elastic base. Using the closed contours method it was determined the system that needs to be solved to obtain graphical representation for the generalized coordinates determining the position of the mechanical system elements. The shaking conveyor represents the chase hanged or supported to the fixed section. The chase commits oscillating motions hereupon the cargo which is in the chase, migrates concerning to the chase. The nature of the flow and its parameters are determined by the nature of the oscillating committed by the chase. Installation causes fluctuations fixed tray. Uniformly distributed load on the tray acts in each element of the mechanism. A proper dynamic model has been developed within MSC ADAMS and Maple 18. Simulation tests have been carried out and results are discussed to validate the proposed design solution.

In this pap er, we study the causes of self-excited oscillations (self-oscillations) and their furtherb ehavior, since these oscillations are the main cause of instability of vertical rotor systemsmounted on sliding b earings. The cause of the self-excited oscillations are hydro dynamic forcesarising from the lubricating layer b etween the b earing and its spike. Based on the classicalmetho ds of the theory of oscillations and the Sommerfeld hyp othesis of a lubricating layer insliding b earings, nonlinear equations of motion of a vertical rotor system were obtained. Theobtained nonlinear differential equations of rotor motion and supp orts do not have an exactsolution. The study is carried out by numerical metho ds. The dep endences of the amplitudes ofthe rotor and b earings on the viscosity of the oil in the b earing, on the size of the gap, on the massof the b earings, on the stiffness and on the damping co efficients are obtained. The results of thestudy of this work allow us to accurately determine and predict all the necessary characteristicsof the working pro cess of this system. The results of the work confirm the physical meaning ofthe pro cess considered in the problem, which can justify the use of this mathematical mo del inthe design of vertical rotor systems on sliding b earings. Берiлген жұмыста сырғу мойынтiректерiнде орналасқан вертикалды роторлық жүйелердi-орнықсыздығының басты себебi болып табылатын өздiгiнен қозатын тербелiстердi-(автотербелiстердiң) пайда болу себептерi және олардың кейiнгi түр өзгерiсi зерттеледi.өздiгiнен қозатын тербелiстердiң себебi ретiнде сырғу мойынтiрегiнiң өзегi менмойынтiрегi арасындағы май қабатының бар болуына байланысты пайда болатынгидродинамикалық күштер болып табылады. Тербелiстер теориясының классикалықәдiстерi мен Зоммерфельдтiң сырғу мойынтiректерiндегi май қабаты туралы гипотезасынегiзiнде вертикал роторлық жүйенiң бейсызық қозғалыс теңдеулерi алынды. Ротор ментiректердiң алынған бейсызық дифференциал теңдеулерiнiң жалпы шешiмi жоқ. Зерттеусандық әдiстер арқылы жүзеге асқан. Ротор мен тiрек амплитудаларының демпферлеукоэффициенттерiнен, қатаңдықтан, тiректер массасынан, саңылау шамасынан жәнемойынтiректегi майдың тұтқырлығынан тәуелдi өрнектерi алынған. Берiлген жұмыстыңзерттеу нәтижелерi жеткiлiктi дәлдiкпен берiлген жүйенiң барлық қажеттi деген жұмысүдерiсiнiң сипаттамаларын анықтап және болжауға мүмкiндiк бередi. Жұмыс есептеқарастырылып жатырған үдерiстiң физикалық мағынасын растауына байланысты,нәтижелер сырғу мойынтiректерiнде орналасқан вертикалды роторлық жүйелердi жобалаукезiнде берiлген математикалық модельдi қолдануға негiздеме болып табылады. В данной работе исследуются причины возникновения самовозбуждающихся колебаний(автоколебаний) и их дальнейшее поведение, так как данные колебания являютсяосновной причиной неустойчивости вертикальных роторных систем, установл енныхна подшипниках скольжения. Причиной возникновения самовозбуждающихся колебанийслужат ги дродинамические силы, возникающие за счет смазочного слоя между подшипникоми его шипом. На основе классических методов теории колебаний и гипотезы Зоммерфельда осмазочном слое в подшипниках скольжения были получены нелинейные уравнения движениявертикальной роторной системы. Полученные нелинейные дифференциальные уравнениядвижения ротора и опор точного решения не имеют. Исследование проводится численнымиметодами. Получены зависимости амплитуд ротора и опор от вязкости масла в подшипнике,от величи ны зазора, от массы опор, от жесткости и от коэффициентов демпфирования.Результаты исследования данной работы позволяют с достаточной точностью определитьи прогнозировать все необходимы е характеристики рабочего процесса данной системы.Результаты работы подтверждают физический смысл процесса, рассматриваемого в з ад аче,что может служит обоснованием...

When the formation flying consists of satellites that are independent from each other and forms a virtual synthetic aperture telescope that replaces a single large telescope with all of its optical elements it is required mutual coordination between the satellites with high accuracy in order to achieve good optical observations. In this paper we consider the problem of developing a control system for a tetrahedral satellite formation flying representing a synthetic aperture telescope in the geostationary orbit for high resolution monitoring of fire in the forest area in infrared spectrum. Synthesizing the image with good quality requires to keep the configuration of formation with µm-class accuracy. Study of dynamics of passive uncontrolled motion of formation flying showed a significant deviation of the configuration from the required shape with a high frequency due to the action of gravitational forces. To keep the configuration in the required form with µm accuracy the analysis of efficiency of various controllers was carried out in the process of numerical simulation. The simulation results made it possible to highlight the features of using various approaches to the development of control system for the satellite formation flying representing a synthetic aperture telescope.

In crank presses, an important role is played by the presence of actuators with dwell, in which, with continuous movement of the input links, the output working link remains stationary at some part of the work. The use of a high-class structural group (fourth class) expands the functionality of the crank press, including it can ensure the link dwell of the working link on a given section of movement during the required period of time. As a result of the conducted numerical research, four variants of actuators of the crank knee press were designed. Due to the rational choice of the positions of racks and crosshead guide, the best layout of the dimensions of the press mechanism has been achieved. Changing the coordinates of the racks accordingly allows for designing a mechanism with upper or lower dwells of the working links. The duration of the dwell of the working link (slider) can be adjusted by selecting the distance between the racks with rotational pairs and a crosshead guide of the mechanism. All this is shown on the basis of a numerical experiment based on kinematic analysis. In addition, the proposed structure of the mechanism makes it possible to ensure the exact link dwell, which cannot be achieved due to the well-known knee presses based on the second-class mechanism.