**Streszczenie**

A complex mathematical model of dynamic processes in vibration device on elastic supports with eccentric self-centering unbalanced rotor and induction motor is given. A working chamber of induction motor does a plane motion. The dynamic feature of the electric motor is chosen for descriptions of device starting and a load oscillating character at steady-state modes of the device. Such model allows: to choose the electric motor of necessary power, to study influence of unbalances, to study influence of the rotor eccentricity and other drive parameters at the device starting, movement of characteristic points of its chamber, loads on bearings and the foundation. It has been established that a rational choice of eccentricity lead to the rotor vibrations reduce – realization of the self-centering effect. A visual method for geometric interpretation of the dynamic processes development at the device starting is proposed. Calculations results for the device with specific size are presented. The completed researches are perspective for solve problems of rational parameters choice for the considered class of mechanisms.

**Słowa kluczowe:**

*dynamical process, vibration device, unbalance, eccentric rotor, induction motor.*

**Abstract**

I Przedstawiono model matematyczny procesów dynamicznych w urządzeniu wibracyjnym na elastycznych wspornikach z ekscentrycznym, samocentrującym niezrównoważonym wirnikiem i silnikiem indukcyjnym. Część robocza silnika indukcyjnego wykonuje ruch płaski. Dynamiczna cecha silnika elektrycznego jest wybierana dla opisów urządzenia rozruchowego i charakteru oscylującego obciążenia w trybach stanu ustalonego urządzenia. Model taki pozwala: wybrać silnik elektryczny o wymaganej mocy, zbadać wpływ asymetrii, zbadać wpływ ekscentryczności wirnika i innych parametrów napędu przy uruchomieniu urządzenia, ruch charakterystycznych punktów jego komory, obciążenia na łożyskach i fundamencie. Ustalono, że odpowiedni wybór ekscentryczności prowadzi do zmniejszenia wibracji wirnika - realizacja efektu samocentrującego. Zaproponowano wizualną metodę geometrycznej interpretacji dynamicznego rozwoju procesów przy uruchamianiu urządzenia. Przedstawiono wyniki obliczeń dla urządzenia o określonej wielkości.

**Keywords:**

*proces dynamiczny, urządzenie wibracyjne, niewyważenie, wirnik mimośrodowy, silnik indukcyjny.*

A using of vibration technologies allows intensify production processes, improve the work quality, create materials with new properties, reduce the material and energy intensities of equipments [1]. Vibration machines on elastic supports with an eccentric rotor, unbalances and an induction electric drive have several advantages. The constructions of such mechanisms are simple, but their motion parameters can be determined only by dynamic analysis, since the devices perform oscillations [1, 2]. Additional difficulties are caused with correct description of the dynamic feature of an induction motor (IM) at transient modes and a load with oscillating character [3]. Investigations of dynamical processes simulation, parameters choice, predictions of technological qualities for devices are very significant and urgency. At present, mathematical models of vibration devices are not sufficiently developed. In the papers [4, 5], the motion equations of the simplest mechanism model are obtained at steady-state operating modes and under the assumption that a working chamber performs translational motion. However, in most cases the translational motion conditions are not met. In addition, frequent starts and stops of devices are the characteristic modes of its operations, so the calculations of transient processes are very relevant. The cheap and easy-to-use IM generates additional difficulties associated with the description of its dynamic features at transient modes and a load with oscillating character. The using of linearized static characteristics [6], or linearized differential equations [7], which approximately describe electromagnetic transient processes in electric motors, leads to a significant overestimating of the calculated torque of IM compared with the experimental one [3]. An absence of reliable mathematical models makes it difficult: a choice of motors that provide start-up of devices; a parameters determining of the w [...]

## Prenumerata

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