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

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.

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

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.

Modal analysis of magnetic vibration of induction motor used in household appliances

The paper deals with analysis of vibrational behavior of induction motor using the combined approach linking the finite elements method (FEM) applied to modelling of magnetic and mechanical phenomena in the motor with its modal description in spectral domain. Results of investigations presented in this paper proved that relatively small rotor axis misalignment against stator leads to visible vibration if forces resulted from this effect have frequency close to rotor bending resonance. Paper contains a rigorous description of all steps in analysis with a special attention paid to details of numerical approach both in FEM and in spectral consideration. Results of theoretical investigations were confirmed by measurements.

Wake redirection at higher axial induction

The energy produced by wind plants can be increased by mitigating the negative effects of turbine-wakes interactions. In this context, axial induction control and wake redirection, obtained by intentionally yawing or tilting the rotor axis away from the mean wind direction, have been the subject of extensive investigations. We have recently shown that the combination of static tilt control with static axial over-induction results in significant power gains. However, these early results were based on idealized turbine models where wake-rotation effects, radial force distributions and realistic turbine controller effects were neglected. In this study we therefore compute power gains that can be obtained by operating tilted rotors at higher axial induction for the more realistic native NREL 5-MW turbine model implemented in SOWFA. We then extend this approach to the case of yaw control. We show that power gains obtained by standard wake redirection based on yaw or tilt control are highly enhanced when the yawed or tilted turbines are operated at higher axial induction. These results confirm our early findings for the case of tilt control and extend them to the case of yaw control suggesting an high potential for the practical application of overinductive wake redirection.

SYNCHRONOUS MOTOR WITH INCREASED ROTOR SPEED

Development of the design of a synchronous electric motor with six C-shaped stator teeth, the rotor axis of rotation of which is displaced relative to the axis of rotation of the output shaft. The rotational speed of the output shaft is equal to twice the rotational speed of the stator magnetic flux. Determination of the phase shifts of the supply voltages in time and the spatial position of the stator windings. Visualization of the principle of operation of the electric motor under consideration, namely, step-by-step observation of the position of the rotor in space, when the sinusoidal voltage wave changes by an angle equal to π, with a step of π/6. Mathematical description of the engine under consideration, with all the structural features of the stator-rotor magnetic circuit. In the course of the work, analytical calculation methods were applied. As a result of the study, the basic laws of operation were determined, as well as the design and principle of operation of the considered electric motor with a suspended rotation speed.

Improving the Energy Conversion Efficiency of a Savonius Rotor Using Automatic Valves

Savonius wind turbines are popular for their easy fabrication and high starting capabilities. Nevertheless, they suffer from low power coefficients, which are mainly due to a negative torque resulting from the blade moving against the upcoming wind. Numerous methods have been proposed to alleviate the negative torque, among them are modified blade profiles (twisted blades), adding flow deflectors, and valve-aided blades. In this study, the effects of adding automatic valves to a two-bladed Savonius rotor on its energy conversion efficiency are investigated numerically and experimentally. The valves are placed at three different positions: close to the rotor axis, at the blade center, and at the tip of the rotor. Results show that although adding valves can decrease the negative torque of the returning blade, they can also lead to a considerable reduction in the positive torque of the advancing blade. For the rotors in the current study, the maximum power coefficient is increased 20.8% when the valves are at the tip of the blades, while the two other cases have decreased the power coefficient of the rotor. Adding the valves to the blades does not change the tip speed ratio corresponding to the maximum power coefficient of the rotor.

Ensuring the Vibration Reliability of Rotors Connected by Spline Joints

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.

Design and Testing of a Co-Rotating Vibration Excitation System

A vibration excitation system (VES) in a form of an active coupling is proposed, designed and manufactured. The system is equipped with a set of piezoelectric stack actuators uniformly distributed around the rotor axis and positioned parallel to each other. The actuator arrangement allows an axial displacement of the coupling halves as well as their rotation about any transverse axis. Through the application of the VES an aimed vibration excitation is realised in a co-rotating coordinate system, which enables a non-invasive and precise modal analysis of rotating components. As an example, the VES is applied for the characterisation of the structural dynamic behaviour of a generic steel rotor at different rotational speeds. The first results are promising for both stationary and rotating conditions.