INVESTIGATION OF A HYDRO-IMPULSE SYSTEM WITH A NONLINEAR SPRING ELEMENT

  • V. G. Gorodetskyi National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”
Keywords: single-mass model, system of differential equations, external action, dissipation coefficient, periodic function

Abstract

We investigated the dynamic characteristics of a single-mass model of a hydraulic pulse system using the example of a hydraulic hammer with real parameters. When designing such systems, it is important to forecast the nature of the oscillation processes, which in turn affect equipment characteristics such as efficiency, noise and vibration, and more. In the initial stages of research and design, single-mass models may be sufficiently effective for some types of equipment.

The model is a non-autonomous system of ordinary differential equations with a sinusoidal external action in one of the equations. The study revealed the dependence of the modes of operation of the hammer on the values of the parameters of its mathematical model. It is revealed that at nominal parameters the hydro-impulse system operates in almost-periodic mode, when the higher harmonics of oscillations are not multiples of the basic harmonic component. When the coefficient of dissipation increases, the dynamics of the device is periodic, when the frequency of oscillations in the system coincides with the frequency of external action. When the coefficient of dissipation is reduced, bifurcation of the doubling of th eperiod is observed. Also, an important feature of this system is the possibility of a mode of deterministic chaos at certain values​​ of the coefficient of dissipation. As the study showed, when the value of the consolidated mass changes, the system operates in periodic mode or in double period mode, or it operates in almost periodic mode. Also, studies have found that increasing nonlinear stiffness causes the system to operate periodically.

All these features of the system are illustrated by the time series of the variables, phase portraits and spectra, which give a clear representation of the behavior of the hydro hammer. The above mentioned characteristics of the model can be useful for the design of hydro-pulse systems and for the choice of modes of their operation.

References

1. Льюнг Л. Идентификация систем. Теория для пользователя. Москва: Наука, 1991. 432 с.
2. Martcheva Maia. A non-autonomous multi-strain SIS epidemic model. Journal of Biological Dynamics. 2009. Vol. 3, No. 2–3. P. 235–251.
3. Кременецкий И. А., Сальников Н. Н. Нестохастический подход к определению размерности и параметров линейных авторегрессионных моделей по результатам измерения входных и выходных переменных. Проблемы управления и информатики. 2010. № 1. С. 63–75.
4. Sauer T. Detection of periodic driving in nonautonomous difference equations. Advanced Studies in Pure Mathematics. 2009. Vol. 53. P. 301–309.
5. Сліденко В. М., Шевчук С. П., Замараєва О. В., Лістовщик Л. К. Адаптивне функціону-вання імпульсних виконавчих органів гірничих машин. Київ: НТУУ «КПІ», 2013. 180 с.
6. Сліденко В. М., Сліденко О. М. Математичне моделювання ударно-хвильових процесів гідроімпульсних систем гірничих машин. Київ, 2017. 220 с.
7. Быховский И. И., Гольдштейн Б. Г. Основы конструирования вибробезопасных ручных машин. Москва: Машиностроение, 1982. 224 с.
8. Левитан Б. М. Почти-периодические функции. Москва: Гостехиздат, 1953. 396 с.
9. Мун Ф. Хаотические колебания. Москва: Мир, 1990. 312 с.
10. Лоскутов А. Ю., Михайлов А. С. Введение в синергетику. Москва: Наука. Гл. ред. физ.-мат. лит., 1990. 272 с.
11. Кузнецов С. П. Динамический хаос. Москва: Изд-во Физ.-мат. лит-ры, 2001. 296 с.
12. Shvets A. Yu., Makaseyev A. M. Chaotic Oscillations of Nonideal Plane Pendulum Systems. Chaotic Modeling and Simulation (CMSIM) Journal. 2012. № 1. Р. 195–204.
13. Shvets A. Yu., Sirenko V. O. Peculiarities of Transition to Chaos in Nonideal Hydrodynamics Systems. Chaotic Modeling and Simulation (CMSIM) Journal. 2012. № 2. Р. 303–310.
Published
2020-03-02
How to Cite
Gorodetskyi, V. G. (2020). INVESTIGATION OF A HYDRO-IMPULSE SYSTEM WITH A NONLINEAR SPRING ELEMENT. Bulletin of Zaporizhzhia National University. Physical and Mathematical Sciences, (2), 29-37. Retrieved from http://journalsofznu.zp.ua/index.php/phys-math/article/view/223