Vol.4, No 16, 2004 pp. 55-68
UDC 534:531.8:531.011:517.9:531.381:530.182(043)

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NONLINEAR DYNAMICS OF THE HEAVY GYRO-ROTOR WITH TWO ROTATING AXES
Katica R. (Stevanović) Hedrih, Ljiljana Veljović*
Faculty of Mechanical Engineering University of Niš
Mathematical Institute SANU Belgrade
Serbia and Montenegro, 18000  Niš, Vojvode Tankosica 3/22
Telefax: +381 18 41 663, Mobile +381 63 8 75 75 99
e-mail: katica@masfak.ni.ac.yu, khedrih@eunet.yu
* Faculty of Mechanical Engineering University of Kragujevac
Serbia and Montenegro, 34000 Kragujevac, Sestre Janjić 6

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Abstract. By using an example of the rotor system which rotates around two axes with the section, the scalar equation of the rotor dynamics is derived, as well as the expressions for the kinetic pressure on the rotor system bearings. For the case when the scewlly eccentrical disc rotates around the shaft support axis with constant angular velocity, the nonlinear dynamics around the moveable axis of the proper own rotation  is studied. Nonlinear rotor system dynamics is presented by the phase portrait in the phase plane, with the trigger of the singularities as well as with the homoclinic orbits and homoclinic points of the nonstable saddle and that is done for the different values of eccentricity of the heavy disc as well as of the angle of skewlly disc.

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NELINEARNA DINAMIKA TEŠKOG GIROROTORA
OKO DVE OSE KOJE SE SEKU Za rotor, kao i za disk, koji rotira oko dve ose koje se seku  u nepomičnoj tački, dobijena je diferencijalna jednačina kretanja, kao i izrazi za kinetičke pritiske u ležištima. U slučaju kada ekscentrični okvir-suport diks oko ose konstantnom ugaonom brzinom, proučavaju se nelinearna dinamika obrtanja oko sopstvenoe ose. Svojstva nelinearne dinamike se prikazuju pomo]u faznog portreta u faznoj ravni, homokliničkih trajektorija i singularnih tačaka, a za razne vrednosti koeficijenta ekscentričnosti diska kao i ugla zakošenja istog u odnosu na osu sopstvene rotacije.