Rotor-pala sistemlerinde mil burulma-pala eğilme bağlaşık titreşimleri

Bulut, Gökhan; Turhan, ÖZgür
April 2010
ITU Journal Series D: Engineering;Apr2010, Vol. 9 Issue 2, p40
Academic Journal
Vibrations of rotor-blade systems is an important research topic due to very important applications such as aeroplane and helicopter propellers, compressors, fans, turbo-machines, etc. In those application areas, accurate prediction of vibration characteristics is crucial in the design stage because prototyping and testing costs are exceptionally high and failure is generally disastrous. As the vibratory failures generally occur in the blades, most of the researches are concentrated on the blade vibrations. Bending and torsional vibrations of the shaft are also treated in the literature as other important sources of vibration failure. However, vibrations of different elements are generally considered separately, overlooking thus possible coupling effects, though the few works considering the coupling, pointed to serious interaction between shaft and blade vibrations. The aim of this study is to study the coupling effects between shaft torsional and blade in-plane bending vibrations in single and multi stage rotor-blade systems through an analytical approach. For this purpose, an idealized model, that consists in a torsionally elastic shaft carrying a number of rigid disks, which in turn, carry a number of identical blades modelled as cantilevered, uniform Euler-Bernouilli beams is considered. The equations of this multi body system is derived through a synthetical (elements of the system are considered first), multiframe (the motion of each element is referred to the most appropriate frame) and mixed (each element is modelled by a different method) approach. Thus, the torsionally elastic shaft is modelled by finite element method to obtain a discrete model and the blades are modelled by Galerkin's method to obtain a similar model. The resulting equations of motion are linear in shaft's torsional coordinates, nonlinear in blades' bending coordinates, and include both linear and nonlinear coupling between them. A consistent small vibrations assumption leads to a fully linear model. Then, the resulting linearized equations are brought together into a single hyper-matrix-vector equation whose matrices have repetitive structures owing to the identity of the blades on each stage. The related eigenvalue analysis problem is developed analytically and splitted into two independent sub-problems corresponding to two kinds of possible normal mode motions of the system. These are referred to as coupled shaft torsion-blade bending modes and rigid shaft modes by the authors. …


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