Luděk Pešek

VIBRATION OF CIRCULAR BLADED DISK WITH IMPERFECTIONS

The steady state response of a model of circular bladed disk with imperfection is investigated. Disk imperfection results from additional two groups of damping heads fixed on opposite ends of one diameter. These damping heads are introduced into the computing model as additional point mass, damping and stiffness. Such type of imperfection causes the bifurcation of double eigenfrequencies into pairs of close eigenfrequencies. The effect of imperfection is examined both numerically on three-dimensional nonrotating FE-model and analytically on a simplified split 2DOF model of rotating disk excited by single point harmonic force. Nonlinear friction connection is analyzed and equivalent linear damping coefficient is derived and used in the calculation procedure. It is shown that nonproportional distribution of damping strongly influences the high of resonance peaks. Some examples of response curves illustrate the dynamic properties of stationary and rotating disks with mass-damping-stiffness imperfection.

Pre-stressed rubber material constant estimation for resilient wheel application

Abstract This paper describes the methodology and results of the complex modulus estimation of rubber segments pressed between the disk and the rim of a rubber-damped railway wheel. The solution comes out from the method proposed and validated at rubber constant identification on the case of the steel beam with rubber layer. In the vicinity of eigenfrequency its dependence to Young modulus is quasilinear and can be solved effectively by the gradient method. The similar behavior showed itself also for dependence of the modal damping constant on the damping coefficient. The ascertained results of tuned rubber material constants, i.e. the modulus of elasticity and a loss factor, of the rail rubber segments are very valuable for prediction of modal behavior of the new resilient wheels and they are qualitatively in accordance with the behavior of hard synthetic rubbers.

Stiffening Effect and Dry-Friction Damping of Bladed Wheel Model with “Tie-Boss” Couplings - Numerical and Experimental Investigation

Bladed wheel model with tie-boss couplings for numerical and experimental investigation of stiffening and friction damping between tie-bosses is introduced. The modal behavior of FE numerical models of the wheel for two contact limit states, i.e. open and bonded contacts, was ascertained. The experimental modal analysis of the wheel both for open and pre-stressed contacts were performed, too. For detail stiffening and damping effect investigation the physical model of three-blade-bundle was elaborated. The experiments were performed for different excitation forces, excitation frequencies and contact pre-stresses. The dynamics of the bundle with respect to different contact states was evaluated from vibration attenuation after short resonant excitation. It was observed that if the macroslips arise in contacts that eigen-frequencies of the bundle are very close to the eigen-frequencies of open contact model bundle and high damping effect is achieved. If the microslips arise in contacts the eigen-frequencies are close to eigen-frequencies of the bond contact model and low damping is achieved. Hence the stiffening effect is high only in the case of microslips. The slip transition is conditioned by the level of adhesion that must be exceeded by excitation force. The FE model of the wheel and blade triple model with dynamic frictional contacts in the tie-boss couplings were developed and calculated results are compared with experiment.

Torsion dissipated energy of hard rubbers as function of hyperelastic deformation energy of the Yeoh model

In this paper, we are proposing a new formulation of dissipated energy of hard rubbers as a function of the deformation energy expressed by the Yeoh hyperelastic model. Torsion deformation is considered as a planar deformation of a simple shear on the surface of a cylinder. Thus the deformation energy is dependent only on the first invariant of strain. Based on the experiment, a “hyperelastic proportional damping” (HPD) is proposed for hard rubbers under finite strains. Such damping is analogical to the model of proportional damping in the linear theory of viscoelasticity, i.e. the dissipated energy is proportional to the deformation energymultiplied by the frequency of dynamic harmonic loading. To obtain the experimental data, samples of hard EPDM rubbers of different harnesses were dynamically tested on a torsional test rig for different frequencies and amplitudes. The Yeoh model is chosen since the deformation function is dependent only on the first strain invariant for the description of the simple shear of a surface cylinder. The Yeoh constants are evaluated by curve fitting of the analytical stress function to the experimental torsion stress-deformation curve. The constants are used to express the deformation energy of the Yeoh model for specific cases of tested rubbers. The coefficients of hyperelastic proportional damping are evaluated on the basis of experimental results.

Amplitude-Temperature Analysis of Hard Rubber by Torsional Vibration

This paper deals with an experimental analysis of hard rubber dynamic tests under finite torsion deformations. The experimental test rig was designed and composed for torsion loading of rubber under defined amplitudes, frequencies and temperatures. The present paper brings an amplitude-temperature analysis of isoprene-butadiene rubber ascertained by the use of the test rig. The mathematical rheological model of rubber was designed for phenomenological description and parametric identification of rubber.

Dynamics of Simple Gearing Model with Flexible Planetary Pins

The influence of flexible pins of planet gears on the dynamic properties of planetary gearing box is investigated by means of a general analysis with some alternative values of parameters. For discovering of basic dynamic behaviour of planetary gear system the simplest planetary gear set with neglected compliance of teeth contacts, fixed axes of central sun wheel and fixed planetary carrier, etc is used One mode of free vibration with eigenfrequency Ω proportional to and zero frequency mode Ω→0 corresponding to the rotation with constant angular velocity were analysed. Forced vibrations, analysed by means of response curves, were oriented on ascertaining of influence of driving aggregate characteristic on frequency spectrum of the whole set.

Basic Optimization Methodology for the Design of Friction Damping in Blade Shrouds

This paper is focused on the optimization of friction element parameters in blade shrouds for various types of excitation. In order to create and validate a proper modelling methodology an experimental stand and a numerical simulation of blades interaction by means of a friction element placed in the shrouds were prepared. Mathematical models are based on the finite element method combined with rigid bodies. The interaction of the friction element and blades is described by normal contact and tangential friction forces derived for particular geometrical parameters of the studied mechanical system. The models can be analyzed both in frequency domain (by the harmonic balance method) or in time domain (by the numerical integration). The results of the optimization of friction element parameters with respect to the bending vibration suppression are documented in the paper. Another contact modelling approach intended for more complex contact surfaces is based on the decomposition of a contact surface into a set of elementary areas and on the expression of contact and friction forces between these areas. All methodologies are implemented in the MATLAB system and the results for the chosen test cases are compared with the results obtained by a measurement or by the ANSYS software.© 2013 ASME