Development and Research of Motion Control Algorithms of Elastic Electromechanical Systems Taking into Account the Damping Properties of the Electric Drive

The paper presents the results of studies of the effect of the counter-electromotive force (CEMF) of the dc machine on the parameters of the elastic oscillation control system of a two-mass electromechanical system, synthesized based on of solving the inverse problems of dynamic in accord with prescribed nature of controlled motion. It is shown by the method of numerical simulation that taking into account the CEMF leads to an increase of the damping properties of the electromechanical system and an increase of the gains of the feedbacks on the force in the cable. A method for the selection of these gains is proposed, based on their comparison with the gains obtained in an electromechanical system without taking into account the CEMF and an approximate assessment of its effect on the nature of the transient processes.

Green’s Function of Magnetoelastic Waves

The matrix (5x5) Green's function of magnetoelastic waves in an isotropic magnetoelastic medium taking into account the dipole-dipole interaction has been derived. The imaginary parts of diagonal and off-diagonal elements of the Green's function in the crossing resonance of spin and longitudinal elastic waves has been investigated. It is shown that under changing the angle of wave propagation θ the amplitudes of Green functions change drastically due redistribution of energy between the magnetic and elastic oscillation. Approximate expressions for the dependence of the widths of the gaps in the spectrum on the angle θ have been also derived.

Flutter Amplitude Saturation by Nonlinear Friction Forces: Reduced Model Verification

The computation of the final, friction saturated limit cycle oscillation amplitude of an aerodynamically unstable bladed-disk in a realistic configuration is a formidable numerical task. In spite of the large numerical cost and complexity of the simulations, the output of the system is not that complex: it typically consists of an aeroelastically unstable traveling wave (TW), which oscillates at the elastic modal frequency and exhibits a modulation in a much longer time scale. This slow time modulation over the purely elastic oscillation is due to both the small aerodynamic effects and the small nonlinear friction forces. The correct computation of these two small effects is crucial to determine the final amplitude of the flutter vibration, which basically results from its balance. In this work, we apply asymptotic techniques to consistently derive, from a bladed-disk model, a reduced order model that gives only the time evolution on the slow modulation, filtering out the fast elastic oscillation. This reduced model is numerically integrated with very low computational cost, and we quantitatively compare its results with those from the bladed-disk model. The analysis of the friction saturation of the flutter instability also allows us to conclude that: (i) the final states are always nonlinearly saturated TW; (ii) depending on the initial conditions, there are several different nonlinear TWs that can end up being a final state; and (iii) the possible final TWs are only the more flutter prone ones.

Flutter Amplitude Saturation by Nonlinear Friction Forces: Reduced Model Validation

The computation of the final, friction saturated Limit Cycle Oscillation amplitude of an aerodynamically unstable bladeddisk in a realistic configuration is a formidable numerical task. In spite of the large numerical cost and complexity of the simulations, the output of the system is not that complex: it typically consists of an aeroelastically unstable traveling wave (TW), which oscillates at the elastic modal frequency and exhibits a modulation in a much longer time scale. This slow time modulation over the purely elastic oscillation is due to both, the small aerodynamic effects and the small nonlinear friction forces. The correct computation of these two small effects is crucial to determine the final amplitude of the flutter vibration, which basically results from its balance. In this work we apply asymptotic techniques to consistently derive, from a bladed-disk model, a reduced order model that gives only the time evolution on the slow modulation, filtering out the fast elastic oscillation. This reduced model is numerically integrated with very low CPU cost, and we quantitatively compare its results with those from the bladed-disk model. The analysis of the friction saturation of the flutter instability also allows us to conclude: (i) that the final states are always nonlinearly saturated TW, (ii) that, depending on the initial conditions, there are several different nonlinear TWs that can end up being a final state, and (iii) that the possible final TWs are only the more flutter prone ones.

Flutter Amplitude Saturation by Nonlinear Friction Forces: An Asymptotic Approach

The computation of the friction saturated vibratory response of an aerodynamically unstable bladed-disk in a realistic configuration is a formidable numerical task, even for the simplified case of assuming the aerodynamic forces to be linear. The non-linear friction forces effectively couple different traveling waves modes and, in order to properly capture the dynamics of the system, large time simulations are typically required to reach a final, saturated state. Despite of all the above complications, the output of the system (in the friction microslip regime) is not that complex: it typically consists of a superposition of the aeroelastic unstable traveling waves, which oscillate at the elastic modal frequency and exhibit also a modulation in a much longer time scale. This large time modulation over the purely elastic oscillation is due to both, the small aerodynamic effects and the small nonlinear friction forces. The correct computation of these two small effects (small as compared with the elastic forces) is crucial to determine the final amplitude of the flutter vibration, which basically results from its balance. In this work we apply asymptotic techniques to obtain a new simplified model that gives only the slow time dynamics of the amplitudes of the traveling waves, filtering out the fast elastic oscillation. The resulting asymptotic model is very reduced and extremely cheap to simulate, and it has the advantage that it gives precise information about how the nonlinear friction at the fir-tree actually acts in the process of saturation of the vibration amplitude.