ON STABILIZATION OF UNSTABLE ROTATION IN THE RESISTING MEDIUM OF THE LAGRANGE GYROSCOPE USING THE SECOND GYROSCOPE AND ELASTIC HINGES

The possibility of stabilizing an unstable uniform rotation in a resisting medium of a "sleeping" Lagrange gyroscope using a rotating second gyroscope and elastic spherical hinges is considered. The "sleeping" gyroscope rotates around a fixed point with an elastic recovery spherical hinge, and the second gyroscope is located above it. The gyroscopes are also connected by an elastic spherical restorative hinge and their rotation is supported by constant moments directed along their axes of rotation. It is shown that stabilization will be impossible in the absence of elasticity in the common joint and the coincidence of the center of mass of the second gyroscope with its center. With the help of the kinetic moment of the second gyroscope and the elasticity coefficients of the hinges, on the basis of an alternative approach, the stabilization conditions obtained in the form of a system of three inequalities and the conditions found on the elasticity coefficients at which the leading coefficients of these inequalities are positive. It is shown that stabilization will always be possible at a sufficiently large angular velocity of rotation of the second gyroscope under the assumption that the center of mass of the second gyroscope and the mechanical system are below the fixed point. The possibility of stabilizing the unstable uniform rotation of the "sleeping" Lagrange gyroscope using the second gyroscope and elastic spherical joints in the absence of dissipation is also considered. The "sleeping" gyroscope rotates at an angular velocity that does not meet the Mayevsky criterion. It is shown that stabilization will be impossible in the absence of elasticity in the common joint and the coincidence of the center of mass of the second gyroscope with its center. On the basis of the innovation approach, stabilization conditions were obtained in the form of a system of three irregularities using the kinetic moment of the second gyroscope and the elastic coefficients of the hinges. The condition for the angular momentum of the first gyroscope and the elastic coefficients at which the leading coefficients of these inequalities are positive are found. It is shown that if the condition for the angular momentum of the first gyroscope is fulfilled, stabilization will always be possible at a sufficiently large angular velocity of rotation of the second gyroscope, and in this case the center of mass of the second gyroscope can be located above the fixed point.

Numerical studies of the effect of the temperature drop in the crucible - melt - cooled disk system on the shapes of crystallization fronts

The crystallization process on a cooled disk located on the free surface of a water layer is studied numerically. The influence of thermal gravitational-capillary and mixed convection on the shape of the crystallization front is investigated. In mixed convection modes, the speed of uniform rotation of the disk is set. The calculations were carried out in an axisymmetric formulation of the problem by the finite element method using an adaptive triangular grid and taking into account the latent heat of crystallization and the inverse dependence of density on temperature.

ANALYTICAL STUDY OF FRICTIONAL AUTO-VIBRATIONS IN SYSTEMS WITH TWO DEGREES OF FREEDOM

Purpose of the study is to study the properties of frictional self-oscillations in systems with two degrees of freedom. As a research method, the asymptotic method of N.N. Bogolyubov and Y.A. Metropolitan. Research methods. The methodological basis of the work is the generalization and analysis of the known scientific results of the dynamics of systems in resonance modes and the use of a systematic approach. The analytical method and comparative analysis were used to form a scientific problem, goal and formulation of research objectives. When developing empirical models, the main provisions of the theory of stability of systems, methodology of system analysis and research of functions were used. The results of the study. A system with two degrees of freedom is considered, assuming that the friction function is approximated by a cubic polynomial in the sliding velocity, and friction is applied only to one of the masses. The exclusion of uniform rotation, corresponding to the third degree of freedom, leads to consideration not of the frictional moment, but the difference between the frictional moment and the moment of the moving forces. From the analysis of the results of the solutions of the equation, we can conclude that, with an accuracy up to the first approximation, inclusive, self-oscillations occur with constant frequencies equal to the natural frequencies of the system. This is consistent with the conclusions of other authors obtained using other methods. Stationary values of the amplitudes are found. The following four cases are possible: trivial solution corresponding to uniform rotation of the system without oscillations; single frequency oscillations with the first frequency; single frequency oscillations with a second frequency; two-frequency oscillatory mode. Conclusions. G. Boyadzhiev's method can be applied to study multi-mass self-oscillating systems and gives their general solution in the form of asymptotic expansions to any degree of accuracy. The obtained conditions for the stability of stationary regimes confirm the experimental results that in multi-mass systems, self-oscillations are possible only in the falling sections of the friction characteristics. The nature of the developing vibrations - their frequency and the ratio of the amplitudes of the constituent harmonics - is completely determined by the structure of the system, its elastic and inertial properties.

Rotating frame effects and potential on a relativistic scalar particle in Kaluza–Klein theory

The effects of uniform rotation on a relativistic scalar particle that interacts with a Cornell-type potential in background space–time described by the Kaluza–Klein theory are analyzed and the gravitational analogue of the Aharonov–Bohm effect is observed. Furthermore, linear confinement of a relativistic scalar particle was also discussed. We see a coupling between the angular velocity of the rotating frame [Formula: see text] and the angular momentum eigenvalue [Formula: see text] which shows the Sagnac-type effect.

Mathematical Modelling of Water-Based Fe3O4 Nanofluid Due to Rotating Disc and Comparison with Similarity Solution

The current research demonstrates the revolving flow of water-based Fe3O4 nanofluid due to the uniform rotation of the disc. This flow of nanofluid is investigated using CFD Module in COMSOL Multiphysics. However, the similarity solution for this flow is also obtained after transforming the given equation into a non-dimensional form. In the CFD Module, streamlines and surface plots are compared with the similarity solution for the magnitude of the velocity, radial velocity, tangential velocity, and axial velocity. The results from the direct simulation in the CFD Module and the solution of dimensionless equations represent a similar solution of velocity distribution. The derived results show that increasing the volume concentration of nanoparticles and effective magnetic parameters decrease the velocity distribution in the flow. Results in the CFD Module are important for monitoring the real-time particle tracing in the flow and, on the other hand, the dimensionless solution is also significant for the physical interpretation of the problem. Both methods of solution empower each other and present the physical model without sacrificing the relevant physical phenomena.

Stability Analysis in Couple-Stress Rotatory Fluid

The aim of the present research was to study the effect of uniform rotation on the layer of a couple-stress fluid heated from below in porous medium. Following the linearized stability theory, Boussinesq approximation and normal mode analysis, the dispersion relation is obtained. The stationary convection, stability of the system and oscillatory modes are discussed. For the case of stationary convection, it is found that rotation has a stabilizing effect, whereas the couple-stress parameter and medium permeability have both stabilizing and destabilizing effects on the system. It is found that the presence of rotation introduces oscillatory modes in the system which were non-existent in its absence. A sufficient condition for the non-existent of overstability is also obtained.

Simulation of Constant-Volume Removal Rate Machining of Middle-Convex and Varying Ellipse Piston

One kind of constant-volume removal rate machining method of the middle-convex and varying ellipse piston is proposed in this paper. By analyzing the structure and movement relationship of the middle-convex and varying ellipse piston machine, the NC machining model is built. And, the constant-volume removal rate machining model is also built by superposing the variable rotation satisfying the dynamic performance constraints on the uniform rotation of the spindle of the CNC piston lathe. Then, the instantaneous position parameters of each axis of the CNC piston lathe are obtained and turned into NC code. The functional feasibility of the method finally is verified by simulation machining.

RESEARCH OF NON-UNIFORM ROTATION OF SHIP POWER PLANT ELEMENTS DRIVE

This article contains the results of studies of the rotation unevenness parameters of the ship power plants elements drive. Theoretical prerequisites of such analysis are described and an example of calculation of parameters of torsional-oscillating system of high-pressure fuel pump drive and speed controller is given in the article. Calculations have shown that at the nominal crankshaft speed of the internal combustion engine, the possibility of resonant oscillations of the camshaft of the fuel pump is not excluded. Design features, faults, violation of adjustments or operating rules can contribute to the operation of elements of power plants at resonant frequencies and cause operational failures. Analysis of rotation unevenness of elements drive and additional equipment of ship's power plants is an appropriate technical measure that allows to increase the reliability of ship's power plants.