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Identifikace tuhosti a tlumení aerostatických ložisek
Kozánek, Jan ; Šimek, J. ; Steinbauer, P. ; Bílkovský, A.
Paper is a final part of work on subject of dynamic properties identification of aerostatic journal bearings with use of Rotor Kit Bently Nevada, started in 2006. Different bearing types were experimentally investigated and their static and dynamic characteristics were identified. More sophisticated methods of identification were used and spectral and modal properties were calculated. Computer program was revised on the basis of experimental data. The influence of non-diagonal stiffness and damping elements was investigated by numeric simulation.
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Dva způsoby stanovení meze stability
Půst, Ladislav ; Kozánek, Jan
Analysis of two methods used for ascertaining stability of dynamical systems was carried out on a mathematical model of experimental stand of aerodynamic bearings. It was proofed that method of direct eigenvalue calculation gives practically the same results obtained from the solution of equations of motion by means of integral Runge Gutta procedure.
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Dynamické experimenty s aerostatickými ložisky na rotorovém stendu Bently Nevada
Šimek, J. ; Kozánek, Jan ; Steinbauer, P. ; Neusser, Z.
Superstructure of Rotor Kit Bently Nevada was designed for identification of aerostatic journal bearing dynamic properties. The test stand enables to run the test shaft up to 10 000 rpm and to excite test bearing by forces with frequency from 0,1 Hz to about 100 Hz. Up to now measured results show reasonable agreement with calculation as concerns quasi-static stiffness and direct elements of stiffness matrix. The agreement between theory and experiment of main elements of damping matrix is somewhat worse and cross-coupling elements of stiffness and damping have considerable scatter. More sophisticated methods of dynamic coefficients idenification are elaborated to improve credibility of results.
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ANALYTIC FORMULAE FOR THE CONSTRUCTION OF SYMMETRIC DYNAMICAL SYSTEMS
Kozánek, Jan
In this paper the formulae for complex modal matrix and symmetric regular stiffness matrix and symmetric matrix of viscous damping from real, positive definite mass matrix and from diagonal spectral matrix were deduced. Because of the non-unicity of this problem, the solution is based on the fact, that the helping matrix has the same ratio of the eigenvalues as the inversion of given mass matrix. Finally, the resolvent of this symmetric system was expressed in simple additive form.
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ANALYTIC FORMULAE FOR THE CONSTRUCTION OF NON-DIAGONALIZABLE DYNAMICAL SYSTEMS
Kozánek, Jan
In this paper the formulae for regular stiffness matrix and matrix of viscous damping and for complex left modal matrix from regular mass matrix, nondiagonal jordan matrix with one complex eigenvalue of multiplicity 2 and from complex right modal matrix were deduced. Finally, the resolvent of this system was expressed in additive form. The corresponding formulae for dynamical systems with commutative matrix of viscous damping and with real right modal matrix were given, too.
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ANALYTIC FORMULAE FOR THE CONSTRUCTION OF DIAGONALIZABLE DYNAMICAL SYSTEMS
Kozánek, Jan
In this paper the formulae for regular stiffness matrix and matrix of viscous damping and for complex modal matrix of left eigenvectors from regular mass matrix, diagonal spectral matrix and from complex modal matrix of right eiegenvectors was deduced. Finally, the resolvent of this system was expressed in simple additive form. The corresponding formulae for dynamical systems with commutative matrix of viscous damping and with corresponding real modal matrix of right eigenvectors was given, too.
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PROPOSITION OF THE DIFFERENTIAL FEEDBACK CONTROL OF ROTOR’S POSITION FOR CONTACTLESS SUPPORT
Kozánek, Jan ; Synek, L. ; Sýkora, Petr
This paper proposes a differential method for the position control of electromagnetic actuator. The differential method is frequently used by active magnetic bearing in industrial application too. The controller is consisted of position regulator and two current regulators with auxiliary differential part, where is counted a difference between biases current and position current. Thus the controller contains a current feedback and a position feedback. The current feedback is used as current control into exciting coil and the air-gap is measured by an eddy current position sensor. The position stabilization of the contactless rotor is provided by suitable analogue regulator.
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Dynamické vlastnosti plynových ložisek
Kozánek, Jan ; Šimek, J. ; Steinbauer, P. ; Neusser, Z.
The test stand for identification of aerostatic bearing stiffness and damping coefficients was brought into operation and some additional modifications were made to ensure successful dynamical experiments. Dynamic model of the test stand, enabling determination of stiffness and damping coefficients from measured response to harmonic excitation, was devised and programmed. The stiffness and damping coefficients of test bearings were calculated for comparison of theoretical and experimental values. Results of dynamic coefficients calculation are presented together with results of initial identifications on test stand.
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Efect of loading force at aerodynamic
Půst, Ladislav ; Kozánek, Jan
The aerodynamic bearings belong among modern elements of high-speed rotation machinery. Particularly in chemical and food industry, as it excludes the undesirable damage of products by oil. The theoretical solution of bearing dynamic characteristics, including motion of tilting pads, is not yet completely elaborated. This contribution completed the works done in project GACR by a study of influence of loading on dynamic properties and motion of journal at unbalance excitation. Differential equations of motion of the rotor are derived, numerically solved and time histories of journal motion and their plane trajectories are presented.
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Carpe diem – Raymond E.A.C. Paley: life and scientific work (1907-1933)
Zolotarev, Igor ; Žitný, K.
Raymond Edward Alan Christopher Paley, the student of G.H. Hardy and J.E. Littlewood, influenced the progress of harmonic analysis in the 20th century not only through the proper scientific publications about Fourier analysis in the complex domain, lacunary series, trigonometric interpolation and developments in polynomials, but by means of the collaboration with the co-authors J.E. Littlewood, A. Zygmund and N. Wiener, too.
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