Nonlinear dynamic behaviors of high speed rotor supported by rolling element bearings

• Autorzy: Harsha S. P. , Prakash R. , Sandeep K.
• Języki publikacji: EN

Abstrakty

EN

The paper presents a model for investigating structural vibrations in rolling element bearings. The mathematical formulation accounted for tangential motions of rolling elements as well as inner and outer races with the sources of nonlinearity such as the Hertzian contact force, surface waviness and internal radial clearance transition resulting from no contact to contact state between rolling elements and the races. The contacts between the rollers and races are treated as nonlinear springs and the springs act only in compression to simulate the contact deformation and resulting force. The nonlinear stiffness is obtained by using the equations for the Hertzian elastic contact deformation theory. As the nonlinear bearing forces act on the system, a new reduction method and corresponding integration technique is proposed to increase the numerical stability and decrease computer time for system analysis. The effects of various defects of a rotor bearing system in which the rolling element bearings show the periodic, quasi-periodic and chaotic behavior are analyzed. Poincare maps and Fourier spectra are used to elucidate and to illustrate the diversity of the system behavior. It is shown that due to defects such as surface waviness and internal radial clearance the system exhibits an undesirable jump phenomenon with quasi-periodic, subharmonic and chaotic motions.

Słowa kluczowe

EN

nonlinear dynamic response; chaotic vibration; Poincare map; Newmark-β; rolling bearings; Ball pasage frequency

PL

mechanika; łożysko toczne; wibracje

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mechanics and Engineering
• Rocznik: 2003
• Tom: Vol. 8, no 4
• Strony: 705--720
• Opis fizyczny: Bibliogr. 20 poz., rys., wykr.

Twórcy

autor

Harsha S. P.

• Mechanical Engineering Group, Birla Institute of Technology and Science Pilani-333031, INDIA

autor

Prakash R.

• Mechanical Engineering Group, Birla Institute of Technology and Science Pilani-333031, INDIA

autor

Sandeep K.

• Asian Institute of Medicine, Science and Technology, 08000 Sungai Petani, MALAYSIA

Bibliografia

• [1] Akturk N. (1999): The effect of waviness on vibrations associated with ball bearings. - ASME Journal of Tribology, vol.121, pp.667-677.
• [2] Bathe K. and Wilson E. (1990): Numerical Methods in Finite Element Analysis. - New York: Prentice-Hall Englewood Cliffs.
• [3] Childs D. W. and Moyer D.S. (1985): Vibration characteristics of the high pressure oxygen turbopump of the space shuttle main engine. - Journal of Engineering for Gas Turbine and Power, vol.107, pp.152-159.
• [4] Choi Y.S. and Noah S.T. (1987): Nonlinear steady State response of a rotor support system. - Trans. ASME, J. of Vibration, Acoustics, Stress and Reliability in Design, vol.109, pp.255-261.
• [5] Ehrich F.F. (1966): Subharmonic vibration of rotors in bearing clearance. - ASME, Machinę Design paper, Part-I, vol.66, p.281-292.
• [6] Ehrich F.F. (1988): Higher order subharmonic response of high speed rotors in bearing clearance. - ASME Journal of Vibration, Acoustic, Stress and Reliability in Design, vol.110, pp.9-16.
• [7] Ehrich F.F. (1991): Observation of subcritical superharmonic and chaotic response in rotor dynamics. - ASME Journal of Vibration Acoustic Stress and Reliability in Design, vol.114, pp.93-99.
• [8] Ehrich F.F. and O’Connor J.J. (1967): Stator whirl rotors in bearing clearance. - ASME Journal of Engineering for Industry, vol.67, pp.381-389.
• [9] Eschmann P. (1985): Bali and Roller Bearings- Theory, Design and Application. - New York: Willey.
• [10] Gustafson O.G., Tallian T., Olive K. and Martin T. (1963): Research report on study of the vibration characteristics of bearings. - Reg: 585 14: 4223, Dec. 1963; Report: AL 631 023, SKF Ind. Inc.
• [11] Harris T.A. (1991): Rolling Bearing Analysis. - New York: Willey.
• [12] Harsha S.P., Sandeep K. and Prakash R. (2003): Effects of preload and number of balls on nonlinear dynamic behaviors of ball bearing system. - International Journal of Nonlinear Sciences and Numerical Simulation, vol.4, No.3, pp.265-278.
• [13] Kim Y.B. and Noah S.T. (1996): Quasi periodic response and stability analysis for a nonlinear jeffcott rotor. - Journal of Sound and Vibration, vol.190, No.2, pp.239-253.
• [14] Kramer E. (1993): Dynamics of Rotors and Foundations. - New York: Springer Verlag.
• [15] Meyer L.D., Ahlgran F.F. and Weichbrodt B. (1980): An analytical model for ball bearing vibrations to predict vibration response to distributed defects. - ASME Journal of Mechanical Design, vol.102, pp.205-210.
• [16] Rahnejat H. and Gohar R. (1988): Vibration of radial ball bearings. - Proc. IMechE, vol.119, Part C3, pp. 181-193.
• [17] Wardle F.P. (1988): Vibration forces produced by waviness of the rolling surfaces of thrust loaded ball bearings, Part I: Theory. - Proc. IMechE, vol.202, Part C5, pp.305-312.
• [18] Wolf A., Swift J.B., Swinney H.L. and Vastano J.A. (1985): Determining Lyapunov exponents from a time series. - PhysicaD, vol.16, pp.285-317.
• [19] Yamamoto T. (1955): On the vibration of a shaft supported by bearing having radial clearances. - Trans, of JSME, vol.21, pp.182-192.
• [20] Yamauchi S. (1983): The nonlinear vibration of flexible rotors. - Trans, of JSME, vol.49, No.446, pp. 1862-1868.