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Non-linear Vibration of Planar Case of Three-blade Bundle with Dry Friction Contacts
Šnábl, Pavel ; Pešek, Luděk ; Půst, Ladislav
Using dry friction couplings (so called tie-bosses) between the blades in turbine rotors can be used to suppress dangerous resonant vibrations of turbine blades and it has been studied on our institute on various models. Experimental setup of three-blade bundle was built along with bladed wheel. The first set-up of the bundle was with blades turned 45 degrees to the disc plane. In that case the deformation of the blades causes turning of the ends of tie-bosses and edge contact together with multi-directional slip occurs. The experimental set-up was simplified herein so that the blades are parallel to the disc plane and in-line slip occurs. Although single electromagnet was used to excite the system, the first mode of vibration with no slip in tie-bosses just occurred. In case of bladed wheel, all blades have coupling through tie-bosses with neighbouring blades which stiffen them and raise their eigenfrequency. In our case, a mistuning by reducing mass of side blades caused similar behaviour. Steel to steel contact pair was used for the first tests.
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Modelling of pulse-triggered running waves on a blade cascade
Šnábl, Pavel ; Pešek, Luděk
An experimental cascade of five NACA 0010 blades with pitch degrees of freedom is excited by a moment pulse to one of the blades. Depending on the flow conditions, such as wind speed and the angle of attack of the wind on the blades, the vibration of the excited blade is transmitted by the wind to the other blades. This can result in a running wave that diminishes over time or in a flutter running wave. A simplified spring-mass-damper model with inter-blade connections and non-linear van der Pol dampers is tuned to match experimentally obtained stability curves and tested to see if it can qualitatively model the response of the cascade to the pulse excitation.\n
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Optimization of Modal Damping of Blades in High Pressure Stages of Steam Turbine
Lošák, Petr ; Zeman,, Vladimír (referee) ; Pešek, Luděk (referee) ; Kellner,, Josef (referee) ; Malenovský, Eduard (advisor)
Steam turbine rotor is a very complicated assembly, typically consists of several rotor rows. Due to design limitations and increasing demands on the efficiency of the steam turbines, it is practically impossible to avoid all of the resonant states. The significant vibrations can occur, for example, due to passing resonance state during turbine start up or run out. In the worst case the turbine operates state is close to the resonance state of the rotor row. This leads to the significant oscillation of the bladed disk, and may results in the blade (or blade to disk joints) high cycle fatigue. These parts are highly loaded components and any cracks are unacceptable. Therefore it is absolutely necessary to damp vibration by using, for example, passive damping elements. The damping element analyzed in this thesis is a strap with an isosceles trapezoidal cross section, which is placed in the circumferential dovetail groove in the blade segmental shrouding. The sliding between the contact surfaces leads to the dissipation of energy which causes decreasing of undesirable vibrations. The main aim is to design the optimal dimensions of the strap cross-section with a view to the most effective damping of vibration for a particular turbine operating state. Considered bladed disk has 54 blades which are coupled in 18 packets by segmental shrouding. The damping element is paced in circumferential dovetail groove created in the shrouding. This type of damping element is suitable especially for damping vibrations in the axial direction and only with the mode shape with the nodal diameters. The modal properties of the bladed disk are influenced by the sliding distance. Since the friction force depends on centrifugal force acting on the damping element and on the angle of the side walls of the strap and groove, the sliding distance can be influenced by the damping element dimensions. During the optimization process the best possible size of middle width, height and angle of damping element cross-section is searched. The strap weight, contact area size and flexural stiffness of damping element can be influenced by these parameters. Their change has also impact on the size of the contact pressure and thus on the size of relative motion as well. As stated previously, the damping efficiency is influenced by the relative motion between the damping element and shrouding. Numerical simulation in time domain is very time-consuming, especially for systems containing nonlinearities. In order to verify dynamic behavior of the computational model with the passive friction element in numerical simulations, the simplified model is created. The model is created in the ANSYS environment. The main requirement imposed on this model is to have as small number of degrees of freedom as possible, so the time needed to perform the simulation is reduced to a minimum. To satisfy this requirement the simplified model is a cantilever beam with rectangular cross section. The dovetail groove is created in this model in longitudinal direction. In this groove is damping element. In addition to damping element dimensions optimization, the influence of each design variable on model dynamic behavior is studied. The results are verified experimentally. Experiment also shows other interesting results that confirm the damping element influence on the modal characteristics. The gained knowledge is used to optimize the dimensions of the damping element in the model of the bladed disk.
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Modal analysis of a rubber-suspended Stadler wheel with two variants of leaf dampers
Šnábl, Pavel ; Pešek, Luděk ; Bula, Vítězslav
The aim of this work was an experimental modal analysis of the Stadler tram wheel for two shock absorber variants: a) standard leaf shocks, b) leaf shear shocks. In the report the measurement methodology is described and the results of the modal analysis are tabulated. The results of the modal behaviour of each damper variant give an assessment of their effectiveness in suppressing significant resonances and the corresponding mode shapes. Standard leaf dampers designed as an open steel-rubber sandwich contributed most to the damping enhancement for the R3 shape, followed by R2. Newly developed leaf shear dampers provided a significant increase in damping for the R2 shape compared to standard dampers.
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Final report on the MIT project no. CZ.01.1.02/0.0/0.0ú20_321/0023673
Zolotarev, Igor ; Pešek, Luděk ; Gabriel, Dušan ; Procházka, Pavel P.
The MIT project entitled Development of a switchgear for severe conditions and reduction of risks of critical infrastructure threat was focused on research, development of optimized design and provision of configuration technology for repeated production of different variants of modular system switchgear for use in severe conditions and reduction of risks of seismic threat, to ensure the reliability of critical infrastructure. The output is to be a prototype seismically robust device with a dynamically lightweight design, high reliability of switchgear and electrical equipment assembly function, and a software application for interactive design and documentation.
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Dynamic tensile experiments of hard rubber on instron test machine under finite deformations
Šulc, Petr ; Pešek, Luděk ; Bula, Vítězslav ; Šnábl, Pavel
This paper deals with the first experimental tests of hard rubbers under tensile harmonic loading on the axial-torsional servohydraulic Instron 8852 test machine. The objective of these experiments on cylindrical rubber specimens on this machine is to obtain stress-strain curves of rubber specimens, first considering uniaxial finite longitudinal strains for a single load cycle. Next, the hysteresis loops and their skeleton curves are compared for two selected strain measures as a function of their conjugate stress. It is shown how to obtain the dependence between elongation in the axial direction and constriction in the radial direction, which is used to determine the Cauchy stress in this configuration.
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