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Computational Analysis Of Dynamic Behaviour Of Journal Bearings
Rak, Vladimír ; Kamenický, Ján (referee) ; Zapoměl, Jaroslav (referee) ; Pochylý, František (referee) ; Malenovský, Eduard (advisor)
This work deals with computational modelling of static and dynamic analyses of journal bearings, with analyses of stability of oil-film motion and analyses of response of the rotor assemblies. At our workplace a new theoretical approach to the modelling of the static and dynamic behaviour of the rigid rotating body in liquid is used. The approach is based on the application of the Navier-Stokes motion eq., equation of continuity and boundary conditions eqs. It is possible to separate the motion of the rigid body and liquid from each other using suitable transformation relations and then it is also possible to separate the stationary and nonstationary motions from each other. A method of control volumes is used for these analyses. The real Bézier body is used for the description of the geometrical configuration and also for the approximation of velocity and pressure functions. Combined the ALE (Arbitrary Lagrange-Euler) method is used, because it´s necessary to generate a new net (to perform new meshing) for a change of the shaft position. The additional effects of the liquid (additional mass, stiffness and damping), which we solved in dynamic analysis, are the function of the single parameter only – the shaft-centre position. There is a large advantage in comparison with the standard approach, which is based on application of the Reynolds liquid eq. Author solving the models of the long and short journal bearing with different geometry, especially the elliptical and cylindrical bearings, with incompressible and compressible journal bearing liquid. If the journal bearing problem is solved, it is possible to include the additional effect of the liquid to the right side of the motion equation of a model rotor assembly. Author analyze a model rotor assemblies with two degrees of freedom, which is supported inside of the two journal bearings on the ends of the rotor (Jeffcott rotor assembly). Author modelling and solveing a response of the model rotor assembly on the forced steady-state vibrations, which was actuating by the unbalanced matter.
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Computational Analysis Of Dynamic Behaviour Of Journal Bearings
Rak, Vladimír ; Kamenický, Ján (referee) ; Pochylý, František (referee) ; Zapoměl, Jaroslav (referee) ; Malenovský, Eduard (advisor)
This work deals with computational modelling of static and dynamic analyses of journal bearings, with analyses of stability of oil-film motion and analyses of response of the rotor assemblies. At our workplace a new theoretical approach to the modelling of the static and dynamic behaviour of the rigid rotating body in liquid is used. The approach is based on the application of the Navier-Stokes motion eq., equation of continuity and boundary conditions eqs. It is possible to separate the motion of the rigid body and liquid from each other using suitable transformation relations and then it is also possible to separate the stationary and nonstationary motions from each other. A method of control volumes is used for these analyses. The real Bézier body is used for the description of the geometrical configuration and also for the approximation of velocity and pressure functions. Combined the ALE (Arbitrary Lagrange-Euler) method is used, because it´s necessary to generate a new net (to perform new meshing) for a change of the shaft position. The additional effects of the liquid (additional mass, stiffness and damping), which we solved in dynamic analysis, are the function of the single parameter only – the shaft-centre position. There is a large advantage in comparison with the standard approach, which is based on application of the Reynolds liquid eq. Author solving the models of the long and short journal bearing with different geometry, especially the elliptical and cylindrical bearings, with incompressible and compressible journal bearing liquid. If the journal bearing problem is solved, it is possible to include the additional effect of the liquid to the right side of the motion equation of a model rotor assembly. Author analyze a model rotor assemblies with two degrees of freedom, which is supported inside of the two journal bearings on the ends of the rotor (Jeffcott rotor assembly). Author modelling and solveing a response of the model rotor assembly on the forced steady-state vibrations, which was actuating by the unbalanced matter.
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Analysis of the lateral vibration of a flexibly supported unbalanced viscoelastic Jeffcott rotor
Ferfecki, P. ; Zapoměl, Jaroslav ; Kozánek, Jan
The behaviour of flexible rotors is significantly influenced by elasticity and damping properties of the shaft. It implies a special attention has to be paid to appropriate choice of a theoretical material to represent the rotors in mathematical models of rotating machines. The procedure developed in this paper concentrates on the investigation of the steady state component of the Jeffcott rotor vibration induced by the disc unbalance and on magnitude of the forces transmitted to the rotor frame. The shaft material is represented by the Zener standard solid material model. The steady state response was determined by application of the trigonometric collocation method. The results of the simulations confirmed the influence of the input oil pressure on the shape of the rotor orbit and on the oscillation amplitude.
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Concepts of reducing the forces transmitted between the rigid rotor and its frame based on magnetorheological damping devices
Zapoměl, Jaroslav ; Ferfecki, Petr ; Kozánek, Jan
A usual technological solution how to reduce forces transmitted between the rotor and its stationary part is to apply a flexible suspension with damping devices placed between the rotor and its casing. Optimum performance of the constraint damping elements can be achieved if their damping effect is controllable. As the control depends only on speed of the rotor rotation that does not vary rapidly the semiactive devices based on utilization of the magnetorheological phenomenon can be used for this purpose. Then the damping force is controlled by the change of electric current generating magnetic flux passing through the layer of the magnetorheological lubricant. Three concepts of their arrangement were studied: magnetorheological dampers with only one layer of the magnetorheological liquid and dampers with two separated layers formed by the normal oil and magnetorheological lubricants in the serial and parallel arrangements.
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The stability investigation of vibrations of flexibly supported rigid rotors damped by hybrid magnetorheological damping elements
Zapoměl, Jaroslav ; Kozánek, Jan ; Ferfecki, Petr
A usual technological solution how to reduce the time varying forces transmitted between the rotor and its casing consists in application of a flexible suspension and in adding the damping devices to the constraint elements. To achieve their optimum performance their damping effect must be controllable. For this purpose a concept of a hybrid damping device working on the principle of squeezing the layers of normal and magnetorheological oils have been developed. Here in this paper, there is investigated influence of the proposed damping element on stability of the rotor vibrations induced by its imbalance during the steady state operating regimes. The stability is evaluated by two approaches: by utilization of a transition matrix and the Floquet theorem and by the evolutive method. The former determines the stability by means of magnitude of the largest eigenvalue of the transition matrix set up over the span of time of one period, the later by time evaluation of eigenvalues of the system linearized in a small neighbourhood of the steady state phase trajectory of the rotor during one period and calculation of the corresponding damping ratio or logarithmic decrement.
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Analýza stability rovnovážné polohy a odezvy rotorů uložených v kapalinných ložiskách a majících kotouč ponořený v nesmáčivé kapalině
Zapoměl, Jaroslav
In a number of technological applications the rotors supported by fluid film bearings have the discs submerged in various liquids. Lateral vibration of such rotors is significantly influenced by their interaction with the medium in the surrounding space. A computer modelling method represents an important tool for investigation of their behaviour. The approach to analysis of vibration of small amplitudes of structures submerged in liquids is based on modification of the Navier Stokes equations leading to the Laplace one. The fluid film bearings are usually implemented into the computational models by means of nonlinear force couplings. The pressure distribution in the full oil film is governed by a Reynolds equation and in cavitated areas the pressure remains constant. The motion of a rotor supported by short hydrodynamic bearings, excited by imbalance forces, and having a disc submerged in inwettable liquid was investigated.
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Postup pro zkoumání stability rovnovážné polohy a nelineární odezvy rotoru uloženého v kapalinných ložiskách a majícím kotouč ponořený v neviskózní, nesmáčivé kapalině
Zapoměl, Jaroslav
Lateral vibration of rotors is significantly influenced by their supports and by their interaction with the medium in the ambient space. If the disc of the rotor is submerged in a liquid and if it vibrates, the pressure field is induced and the liquid acts by a force on the wall of the disc. It is assumed that the disc performs oscillations only with small amplitudes and it enables to describe the produced pressure field by a Laplace's equation and by the relation for the boundary conditions. The liquid is inwettable and it means that it does not lean to the disc surface and therefore no tangential forces acting on the disc are produced. The resulting force is obtained by integration of the pressure distribution around the circumference and along the height of the submerged part of the disc. Its components are proportional to the disc accelerations and it implies that the negatively taken coefficients of proportionality can be considered as additional masses.
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