Некоторые аспекты динамики переходных процессов поворотного рабочего элемента под воздействием упругих и вязкоупругих сил

Abstract

Получена математическая модель динамики поворотного рабочего элемента, работающего на высоких скоростях с ускорениями, и выполняющего при этом высокоточную координатную ориентацию. Поворотный рабочий элемент рассмотрен как звено системы автоматического регулирования.

Отримано математичну модель динаміки поворотного робочого елемента, який працює на високих швидкостях з прискоренням. Елемент виконує високоточну координатну орієнтацію. Поворотний робочий елемент розглянуто як ланку системи автоматичного регулювання.

Background. The necessity to create the mathematical model of the dynamic behavior of the rotary operating element, which is under the influence of the inertial forces (friction, elastic and viscoelastic) for using the model in robotics, manipulators, etc. Statement. Due to the created mathematical model of the rotary operating element, working, as a rule, with the high angular and linear velocities and accelerations, performing herewith high-precision coordinate orientation, we are able to examine the dynamics of its behavior (movement) in acceleration and deceleration modes. This moving may be realized either by an exponential law, or under the law of damped harmonic oscillations. The rotary working element is considered as a link of the automatic control system (ACS). In this case, the rotary working element can be represented either by the 2nd order link and this link can be replaced by the two series-connected inertial links or as an oscillating link. Research methodology. These results are achieved due to the resulting inhomogeneous differential equation of 2nd order. Depending on the structure of the roots of the characteristic equation (real or complex roots) transients can be carried out either by an exponential law (real roots), or under the law of damped harmonic oscillations (complex roots). Moreover, the rotary operating element is considered as a link of ACS, that has been made possible by solving the differential equation, which was presented in a symbolic way by which amplitude-frequency, phase-frequency and amplitude-phase characteristics of the rotary operating element were obtained as a link of the ACS. Conclusion. The conclusions enable the practical use of the results.