Исследование динамической устойчивости регулятора давления с пневматическим управлением при учете колебаний столбов газа в трубопроводах

Abstract

Составлена дискретно-континуальная нелинейная модель и выведено трансцендентное характеристическое уравнение для исследования свободных колебаний регулятора пневмосистемы запуска ракетного двигателя. Разработан метод нахождения границы динамической устойчивости системы и критерий устойчивости ее предельного цикла. Описан порядок настройки системы на автоколебания малой амплитуды.The discrete-continual nonlinear dynamic model of the liquid rocketengine pneumatic starting system is developed. The model describes steady oscillations atcompressed helium supply from a gas tank through the pipelines and pressure regulator with pneumatic control. By using the harmonic linearization method the formulae have been derived for calculation of the gas flowrate oscillations in the throttle and throttling gap as well as collar friction forces. The calculation method of mechanical impedance has been developed for gas columns’ oscillations of the control unit’s piping system and formulae have been obtained for impedance of the cavities contacting with the regulator. The transcendental characteristic equation for frequencies and amplitudes of the regulator and pneumatic system free oscillations has been derived and methods of its solution have been developed. The graphic-analytical method of the dynamic stability system limit determination has been proposed as well as the new stability criterion for corresponding limit cycles has been obtained. It is shown that stability and oscillation depend on the pipes dimensions and control orifice diameter. The system adjusting sequence for self-oscillations of small amplitude is described.