Near-critical bifurcating vibration of a rotating shaft with piezoelectric elements

• Autorzy: Przybyłowicz P.M.
• Języki publikacji: EN

Abstrakty

EN

The paper is concerned with problem of active stabilisation of rotating shafts by making use of piezoelectric elements and their effect on non-linear response of such systems, i.e. on bifurcating vibration that appears near the critical threshold. Piezoelectric elements serve in the system as sensors measuring internal bending moment in a given cross-section of the shaft and actuators producing bending moment out of phase with respect to the measured moment and in accordance with a specially devised control strategy. The purpose of incorporating piezoelectric elements is to enlarge domain of stability of rotating shafts; i.e. to increase the critical rotation speed at which dynamic stability is lost and self-excited vibration occurs. Self-excitation observed in shafts, in terms of mathematics, consists in bifurcating of the static equilibrium position into an oscillating state representing in fact either stable or unstable limit cycle. Bifurcation of a static solution into a periodic one is called Hopf`s bifurcation. In rotating shafts, it can appear due to presence of internal friction in material they are made of Internal friction can destabilise such systems when subjected to permanent energy supply maintaining constant rotation speed. It is manifested by occurrence of additional rotary motion of the shaft when the angular velocity becomes sufficiently high. The additional precession can be of soft or hard character, depending on type of bifurcation observed in the system. Application of piezoelectric elements is expected to affect character of the selfexcited vibration, as terms corresponding to their action are present in the non-linear part of equations of motion. The analysis proves that stabilisation method based on piezoelectric elements strongly effects near-critical vibration of rotating shafts as it makes the bifurcation, in vertically rotating shafts always supercritical, subcritical if only gain factor in the control system is great enough.

Słowa kluczowe

EN

piezoelectric elements; bifurcation; vibration; rotating shaft

• Wydawca: Wydawnictwo Politechniki Łódzkiej
• Czasopismo: Mechanics and Mechanical Engineering
• Rocznik: 1999
• Tom: Vol. 3, nr 2
• Strony: 103--112
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Przybyłowicz P.M.

• Warsaw University of Technology Institute of Machine Design Fundamentals ul. Narbutta 84, 02-524 Warszawa Tel. [phone]