Stability of Stationary Rotation of Rotor Systems with a Liquid in the Case of Anisotropic Fastening of the Rotor Axis

2018 ◽  
Vol 481 (1) ◽  
pp. 35-38
Author(s):  
Dmitrii Derendyaev ◽  
◽  
Nikolai Derendyaev ◽  
Keyword(s):  
Rotor Systems ◽  
Stationary Rotation ◽  
Rotor Axis

scholarly journals DESIGN OF THE BOUNDARIES OF THE STABILITY REGIONS THE STATIONARY ROTATION MODE OF A ROTARY SYSTEM WITH A LIQUID, THE AXLE OF WHICH IS LOCATED IN ANISOTROPIC FIXINGS

2021 ◽  
Vol 83 (3) ◽  
pp. 335-343
Author(s):  
D.N. Derendyaev ◽  
N.V. Derendyaev
Keyword(s):  
Original Method ◽  
Dimensionless Frequency ◽  
Negative Effects ◽  
Stability Regions ◽  
Rotor Systems ◽  
Stationary Rotation ◽  
Opposite Situation ◽  
The Stability ◽  
Permissible Deviation ◽  
Rotor Axis

Earlier, the authors generalized the original method for studying the stability of stationary rotation of rotor systems containing a viscous incompressible fluid, the axis of which is located in isotropic anchors, in the case when the viscoelastic anchors of the axis of the rotor system are anisotropic. The generalization is based on two theorems that say that finding the stability conditions of such systems is associated with the possibility of elliptical precession-type motion, and with such motion there is a special non-inertial reference frame in which the hydrodynamic elements of the system periodically change in time. The study of such movements allows us to construct the boundaries of regions with different degrees of instability, in particular, the boundaries of the stability regions of the stationary rotation regime in the parameter space of the problem. The boundaries of the stability regions are constructed for cases when the anchoring of the rotor axis is anisotropic. In the space of the anchorage parameters, a parametrically defined D-curve is obtained as a function of the dimensionless frequency of the rotor precession. The two most interesting cases are considered – anisotropic stiffness of anchors (damping is isotropic in this case) and the opposite situation: isotropic stiffness of anchors with anisotropic damping. The obtained results are compared with the known results for the case of isotropic anchoring of the rotor axis. It is shown that the anisotropy of anchors, which is always present in real rotary systems due to the imperfection of technologies for the production of anchors, does not lead to negative effects. Moreover, using the obtained D-curves, it is possible to obtain technological tolerances for the production of fasteners, using what is known as the permissible deviation of the stiffness or damping value along the axes.

scholarly journals THE RESEARCH OF STABILITY OF STATIONARY ROTATION A ROTOR SYSTEM WITH A LIQUID, THE AXLE OF WHICH IS LOCATED IN ANISOTROPIC FIXINGS

2021 ◽  
Vol 83 (3) ◽  
pp. 324-334
Author(s):  
D.N. Derendyaev ◽  
N.V. Derendyaev
Keyword(s):  
Liquid Surface ◽  
Original Method ◽  
Rotor System ◽  
Stability Regions ◽  
Stationary Rotation ◽  
Rotation Mode ◽  
The Stability ◽  
Rotation Constant ◽  
Degree Of Instability ◽  
Rotor Axis

Earlier, one of the authors proposed and developed (together with coworkers) an original method to study the stability of stationary rotation of rotary systems containing a viscous liquid and having a drive that maintains the angular velocity of rotation constant. It was assumed that the rotor has axial symmetry, the anchors of its axis are isotropic. The method is based on two theorems, according to which a change in the degree of instability is associated with the possibility of a perturbed motion of the circular precession type. This motion has a remarkable property: the velocity field and the shape of the liquid surface do not depend on time in a specially selected non-inertial reference frame associated with the line of centers. Finding the conditions for the feasibility of circular precession makes it possible to effectively construct the boundaries of the stability regions of the stationary rotation regime in the space of problem parameters. In addition, the study of the occurrence of circular precession allows us to find the conditions under which a subcritical (supercritical) Andronov-Hopf bifurcation takes place in the rotor system and to identify "dangerous" (“safe”) sections of the boundaries of the stability regions. In this paper, the previously proposed method of stability research applies to systems in which the rotor axis is located in anisotropic Laval type anchors. In the study of rotary systems of this type, it is possible to link the change in the degree of instability with the feasibility of perturbed movements of the elliptical precession type. It can be shown that the imaginary characteristic numbers of the equations in deviations from the stationary rotation mode are possible only in the case when there is a perturbed motion in the form of an elliptical precession. An example of a study of the stability of stationary rotation of a typical rotary system is given. Mechanical effects caused by the fact that gyroscopic stabilization becomes impossible with anisotropic fixing of the rotor axis are noted.

scholarly journals Ensuring the Vibration Reliability of Rotors Connected by Spline Joints

2019 ◽  
Vol 6 (2) ◽  
pp. d14-d19 ◽  
Author(s):  
A. Verbovyi ◽  
C. Neamtu ◽  
M. Sieryk ◽  
B. Vashyst ◽  
V. Pavlenko ◽  
...  
Keyword(s):  
Harmonic Analysis ◽  
Intelligent Systems ◽  
High Performance ◽  
Forced Oscillations ◽  
Program Code ◽  
Rotor Systems ◽  
Free And Forced Vibrations ◽  
Methods Of Calculation ◽  
Computational Intelligent ◽  
Rotor Axis

This article is devoted to the development of refined numerical mathematical models of rotor dynamics of high-performance turbomachines having a spline connection. These models consider the dependence of the critical frequencies of the shaft on the angular stiffness of the spline connection, as well as the procedure of virtual balancing. As a result of the complex application of this approach, the methods of calculation of vibration characteristics taking into ac-count variable values of angular rigidity of splined connection are offered. In addition, the method of evaluating the system of initial imbalances with the corresponding displacements of the rotor axis in the correction and calculation sections has also been improved. The proposed approaches, based on the integrated application of CAE software and computational intelligent systems, allow for modal and harmonic analysis and implement virtual balancing with a significant reduction in preparation and machine time without loss of relative accuracy. In addition, the developed mathematical model of free and forced vibrations of rotor systems have been implemented in the program code operational files “Critical Frequencies of the Rotor” and “Forced Oscillations of the Rotor” of the computer algebra system MathCAD that allows improving the dynamic balancing procedure for evaluating primary imbalances. The high accuracy of the proposed approach is confirmed by checking the dynamic deviations of the rotor axis by the system of residual imbalances in accordance with the standards of vibration stability. Keywords: turbomachine, spline connection, angular stiffness, virtual balancing, modal analysis, harmonic analysis.

Reduction of structural vibrations with the piezoelectric stacks ring

2020 ◽  
Vol 64 (1-4) ◽  
pp. 729-736
Author(s):  
Jincheng He ◽  
Xing Tan ◽  
Wang Tao ◽  
Xinhai Wu ◽  
Huan He ◽  
...  
Keyword(s):  
Vibration Control ◽  
Mechanical Energy ◽  
Electrical Energy ◽  
Structural Vibrations ◽  
Rotor Systems ◽  
Fea Model ◽  
Piezoelectric Stacks ◽  
Shunt Damping ◽  
Reduction Effect ◽  
Euler Bernoulli Beam

It is known that piezoelectric material shunted with external circuits can convert mechanical energy to electrical energy, which is so called piezoelectric shunt damping technology. In this paper, a piezoelectric stacks ring (PSR) is designed for vibration control of beams and rotor systems. A relative simple electromechanical model of an Euler Bernoulli beam supported by two piezoelectric stacks shunted with resonant RL circuits is established. The equation of motion of such simplified system has been derived using Hamilton’s principle. A more realistic FEA model is developed. The numerical analysis is carried out using COMSOL® and the simulation results show a significant reduction of vibration amplitude at the specific natural frequencies. Using finite element method, the influence of circuit parameters on lateral vibration control is discussed. A preliminary experiment of a prototype PSR verifies the PSR’s vibration reduction effect.

Effects of Cyclic Pitch on Time Delayed Dynamics in Coaxial Rotor Systems

2021 ◽  
Author(s):  
Ethan S. Genter ◽  
Cory A. Seidel ◽  
David A. Peters
Keyword(s):  
Rotor Systems ◽  
Coaxial Rotor

ACCURACY RATING MEASUREMENT OF VIBRATION ELECTROMECHANICAL DEVICES

2019 ◽  
Vol 1 (7) ◽  
pp. 42-45
Author(s):  
V. A. Golubkov ◽  
V. F. Shishlakov ◽  
A. G. Fedorenko ◽  
E. Yu. Vataeva
Keyword(s):  
Technical Condition ◽  
Rotor System ◽  
Vibration Measurement ◽  
Random Errors ◽  
Mass Ratio ◽  
Signal Flow Graph ◽  
Bond Graphs ◽  
Rotor Systems ◽  
Electromechanical Devices ◽  
Main Components

Electromechanical devices consist mainly of rotor systems. Vibration is the result of the interaction of the elements of the rotor system and is largely determined by the accuracy of manufacturing elements at the production stage and defects arising in the process of operation. The main components of the rotor systems that affect vibration are bearings. To determine the technical condition of the bearings and the service life of the rotor system, it is necessary to accurately measure the unobservable vibrations of the rotor. The article describes the model of the channel for measuring the vibration of an electromechanical system, built using the apparatus of bond graphs. The transfer function is obtained by analyzing the signal flow graph. The systematic and random errors of vibration measurement are analyzed depending on the mass ratio between the system case and the vibration transducer for various sensor masses and attachment rigidity.

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