Ante Skoblar

Utjecaj uzdužnog pomaka na nelinearne glavne parametarske rezonancije tračne pile

The transverse vibrations of axially moving Timoshenko beam, as suitable mathematical models for woodworking bandsaws, are investigated. Special attention is paid to the influence of longitudinal displacement effect, as opposed to most models which can be usually encountered in the literature. This influence is introduced through the integro-partial differential equations. The expressions for the mode shapes in the case of hybrid supports with different torsion spring stiffness on the support points are also derived. The influence of mean beam velocity and axial tension on its natural frequencies and mode shapes is also investigated. Based on the nonlinear model, the amplitudes of the steady-state response are calculated for the case of principal parametric resonance. Developed program solution was tested on a number of earlier known examples. Present theoretical considerations, with the help of the program solution, is also used to analyse an example from industrial practice.

Light Rotor-Stator Partial Rub Characterization Using Instantaneous Angular Speed Measurement

Instantaneous angular speed (IAS) measurement is recently recognized as a promising technique for condition monitoring of various rotating machines and their subsystems. There are various approaches considering counting techniques and processing of signal. This paper considers application of analog signals from toothed wheel encoder or zebra tape encoder and acquisition at low to moderate sampling rates. Such a system can experience problems with non-uniformity of encoder segments geometry, thus correction of encoder segment non-uniformity was performed. The rubbing often occurs in rotating machinery at position with small clearances and can sometimes cause catastrophic breakdown of machine. So it is important to develop reliable tools for rub diagnosis. As the rubbing process is nonlinear this paper beside conventional Fourier transform also considered potential of sifting operation of Empirical mode decomposition (EMD) method. EMD was employed to produce intrinsic mode functions (IMFs) and to further improve the detection capabilities of Fourier transform. Developed procedure for IAS measurement was successfully tested on laboratory test rig for rotor to stator contact dynamics investigation at speed transition from no rub to light rotor to stator partial rub condition.

Efficient approach for encoder geometry compensation in time interval measurement of torsional vibration

While it is usually a design goal to avoid torsional natural frequencies, there are systems where resonances will be encountered during normal operation. This paper considers time interval measurement of torsional vibration and problems connected with uneven encoder geometry. Such a problem is usually manifested as high-level order content in frequency spectrum. To prevent mentioned problem an in-situ segment compensation method is proposed that creates a time reference array representative of actual angular segments geometry. The method is experimentally tested on two different encoding devices. First was non-contact eddy current sensor and toothed wheel while the second was optic sensor together with zebra tape. The second encoding device showed better test results and less sensitivity on uneven encoder geometry.

Rotor-Stator Partial Rub Diagnosis Using Hilbert Huang Transform

Rotor–stator rubbing is occasional problem faced by rotating machines especially during startups and shut downs when passing through their critical speeds. The rubbing often occurs in rotating machinery at position with small clearances and can sometimes cause catastrophic breakdown of machine. So it is important to develop reliable tools for rub diagnosis. This paper investigates partial rub occurrence during constant and slightly variable speed operation and try to define vibration diagnosis patterns for its detection with Hilbert Huang Transform (HHT). The HHT is relatively new method which includes Empirical Mode Decomposition (EMD) and the Hilbert Transform. Diagnostic tool is tested on laboratory test rig for rotor to stator contact dynamics research at two different rotor operating conditions i.e. without rotor–stator contact and with partial rotor–stator rub. Measurements were performed with non-contact eddy current displacement sensors. Results are presented in the shape of HHT spectra of Intrinsic Mode Functions (IMF) and are compared to classical FFT spectra and spectrograms based on Short Time Fourier Transform (STFT). Rotor orbits are also presented to additionally verify rubbing condition.

Modeling, design and control of a flexible rotor supported by active magnetic bearings

In this paper an approach to analyze and stabilize a decentralized rotor/AMB system while passing the first critical speed is presented. Since the related difficulties emerge from the sensor/actuator non-collocation a set of finite element calculations and relevant rotordynamic studies are proposed and carried out. In such a way the adequate mechanical configuration of the system is found and proper controllability and observability is ensured. In accordance with the simulation results, the test rig is assembled. Finally, successful run up and run down analyses were carried out, which validated the efficiency of the presented procedure.

Rotor-Stator Partial Rub Detection Based on Teager-Huang Transform

The rubbing between rotor and stator often occurs in rotating machinery at position with small clearances and can cause unexpected machine downtime. Therefore, it is important to develop trustworthy tools for rub detection.

Numerical ill-conditioning in evaluation of the dynamic response of structures with mode superposition method

Dynamic response of structures can be determined by mode superposition method which uses mode shape functions and modal coordinate functions. If the structure can be modelled with a uniform Euler–Bernoulli beam and a combination of clamped, free, pinned or sliding boundary conditions, analytical expressions for mode shape functions and modal coordinate functions are used. If analytical expressions for higher-order mode shapes or analytical expressions for the modal coordinate functions at high value of time are numerically evaluated, errors occur since the programming language cannot recognise the resulting value as a number, due to ill-conditioned analytical expressions. An analytical expression is ill-conditioned if small errors in the data may produce large errors in the solution. In this paper, we present a procedure for the exact numerical evaluation of analytical expressions for modal coordinates at high value of time while existing modified analytical expressions are used for exact calculation of higher-order mode shapes of the Euler–Bernoulli beam. The proposed procedure can be applied in the design of structure elements whose response is calculated with mode superposition method, e.g. for designing of metal frames for sawing machines in woodworking industry.

DETERMINATION OF CRITICAL ROTATIONAL SPEED OF CIRCULAR SAWS FROM NATURAL FREQUENCIES OF ANNULAR PLATE WITH ANALOGOUS DIMENSIONS

It is suitable to reduce thickness of circular saw when trying to enhance usability of wood raw material, but reducing thickness also causes reduction of permissible rotational speed which reduces sawing speed. If one increase circular saw rotational speed over permissible one the quality of machined surfaces will reduce because of enhanced vibrations. Permissible rotational speed can be calculated from critical rotational speed which can be defined from natural frequencies of the saw. In this article critical rotational speeds of standard clamped saws (with flat disk surface and without slots) are calculated by using finite element method and classical theory of thin plates on annular plates. Mode shapes and natural frequencies of annular plates are determined by using Bessel functions and by using polynomial functions. Obtained results suggest that standard clamped circular saws without slots and with relatively small teeth can be determined from classical theory of thin plates for annular plates with accuracy depending on clamping ratio.