Identification of Anisotropic Bearing Non-linearity

  • Published : 2004.12.31


Among other critical conditions in rotor svstems the large non-linearvibration excited by bearing non-linearity causes the rotor failure. For reducing thiscatastrophic failure and predictive analysis of this phenomena the identificationanalysis of bearing non-linearity in an anisotropic rotor system using the higherorder dFRFs are developed and are shown to be theoretically feasible as innon-rotating structures. For the identification of the anisotropic rotor withanisotropic bearing non-linearity expressed by the displacement in polynomial form,the higher order dFRFs based upon the Volterra series are investigated and depicttheir features by using the simple forms of the normal and reverse dFRFs. Theyproduce additional sub-harmonic resonant peaks, which indicate the existence ofhigher order non-linearties, and show the energy transfer such that the modes fornormal and reuerse dFRFs are exchanged, which are the fundamental differencesfrom what we can expect in linear ones.


  1. Lee, C.W., and Joh, C.Y., 'Development of the Use of Directional Frequency Response Functions for the Diagnosis of Anisotropy and Asymmetry in Rotating Machinery: Theory', Mechanical Systems and Signal Processing, Vol. 8, No. 6, 1994, pp. 665-678
  2. Shaw, J. and Shaw, S. W., 'Non-Linear Response of an Unbalanced Rotating Shaft with Internal Damping', Journal of Sound and Vibration, 1991, Vol. 147, pp. 435-451
  3. Vyas, N. S. and Chatterjee, A., 'Non-linear System Identification and Volterra-Wiener Theories', Proceeding of VETOMAC-I, 2000, Oct. Bangalore, India
  4. Zhang, H. and Billings, S. A., 'Analysis Non-Linear Systems in the Frequency-Domain-I. The Transfer Function', Mechanical Systems and Signal Processing, Vol. 7, No. 6, 1993, pp. 5331-550
  5. Tiwari, R. and Vyas, N. S., 'Estimation of Non-Linear Stiffness Parameters of Rolling Element Bearings from Random Response of Rotor-Bearing Systems', Journal of Sound and Vibration, 1995, Vol. 187, pp. 229-239
  6. Liangsheng, Q. and Xiao. L., 'Study and Performance Evaluation of Some Nonlinear Diagonostic Methods for Large Rotating Machinery', Mech. Mach. Theory, 1993, Vol. 28, pp. No. 5, pp699-713
  7. Worden, K. and Manson, G., 'Random Vibrations of a Duffing Oscillator Using the Volterra Series', Journal of Sound and Vibration, 1998, Vol. 217, pp. 781-789
  8. Lin, R. M. and Lim, M. K., 'Identification of Nonlinearity from Analysis of Complex Modal Analysis', International Journal of Analytical and Experimental Modal Analysis, 1993, Vol. 8, pp. 285-299
  9. Ozguven, H. N. and Imregun, M., 'Complex Modes Arising from Linear Identification of Non-linear Systems', nternational Journal of Analytical and Expehmental Modal Analysis, 1993, Vol. 8, pp. 151-164
  10. Worden, K., Manson, G. and Tomlinson. G. R., 'A Harmonic Probing Algorithm for the Multi-Input Volterra Series', Journal of Sound and Vibration, 1997, Vol. 201, pp. 67-84
  11. Bedrosian, E., and Stephen, O. R., 'The Output Properties of Volterra Systems (Nonlinear Systems with Memory) Driven by Harmonic and Gaussian Inputs', Proceedings of IEEE, 1971, Vol. 59, No.l2, pp. 1688-1971
  12. Bendat, J. S., 'Nonlinear System Analysis and Identification from Random Data', John Wiley & Sons, Inc., 1990
  13. Schetzen, M., 'The Volterra and Wiener Theories of Nonlinear Systems', John Wiley & Sons, Inc.. 1990