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TECHNICAL PAPERS

Nonlinear Parameter Estimation in Rotor-Bearing System Using Volterra Series and Method of Harmonic Probing

[+] Author and Article Information
Animesh Chatterjee

Department of Mechanical Engineering, Visvesvaraya National Institute of Technology, Nagpur, India-440011e-mail: animeshch@rediffmail.com

Nalinaksh S. Vyas

Department of Mechanical Engineering, Indian Institute of Technology, Kanpur, India-208016e-mail: vyas@iitk.ac.in

J. Vib. Acoust 125(3), 299-306 (Jun 18, 2003) (8 pages) doi:10.1115/1.1547486 History: Received May 01, 2002; Revised October 01, 2002; Online June 18, 2003
Copyright © 2003 by ASME
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References

Bedrosian,  E., and Rice,  S. O., 1971, “The Output Properties of Volterra Systems (Nonlinear System with Memory) Driven by Harmonic and Gaussian Input,” Proc. IEEE, 59(12), pp. 1688–1707.
Boyd,  S., Tang,  Y. S., and Chua,  L. O., 1983, “Measuring Volterra Kernels,” IEEE Trans. Circuits Syst., CAS-30(8), pp. 571–577.
Chua,  L. O., and Liao,  Y., 1989, “Measuring Volterra Kernels (II),” Int. J. of Circuit Theory and Applications, 17, pp. 151–190.
Gifford,  S. J., and Tomlinson,  G. R., 1989, “Recent Advances in the Application of Functional Series to Nonlinear Structures,” J. Sound Vib., 135(2), pp. 289–317.
Chatterjee,  A., and Vyas,  N. S., 2001, “Stiffness Nonlinearity Classification through Structured Response Component Analysis using Volterra Series,” Mech. Syst. Signal Process., 15(2), pp. 323–336.
Lee,  G. M., 1997, “Estimation of Nonlinear System Parameters using Higher Order Frequency Response Functions,” Mech. Syst. Signal Process., 11(2), pp. 219–228.
Chatterjee, A., and Vyas, N. S., 2002, “Nonlinear Parameter Estimation through Volterra Series using Method of Recursive Iteration,” accepted for publication in J. Sound Vib.
Harris, T. A., 1984, Rolling Bearing Analysis, Wiley, New York.
Ragulskis, K. M., Jurkauskas A. Y., Atstupenas, V. V., Vitkute, A. Y., and Kulvec, A. P., 1974, Vibration in Bearings, Mintis Publishers, Vilnius.
Bannister,  R. H., 1976, “A Theoretical And Experimental Investigation Illustrating the Influence of Nonlinearity and Misalignment on the Eight Film Co-efficients,” Proc. Inst. Mech. Eng., 190, pp. 271–278.
Choi,  F. K., Braun,  M. J., and Hu,  Y., 1992, “Nonlinear Transient and Frequency Response Analysis of a Hydrodynamic Bearing,” ASME J. Tribol., 114, pp. 448–454.
Garibaldi,  L., and Tomlinson,  G. R., 1988, “A Procedure for Identifying Non-linearity in Rigid Rotors Supported in Hydrodynamic and Ball/Roller Bearing System,” I. Mech. Proc. on Vibrations in Rotating Machinery, 4, pp. 229–234.
Khan,  A. A., and Vyas,  N. S., 2001, “Application of Volterra and Wiener Theories for Nonlinear Parameter Estimation in a Rotor-Bearing System,” Nonlinear Dyn., 24(3), pp. 285–304.
Chatterjee,  A., and Vyas,  N. S., 2000, “Convergence Analysis of Volterra Series Response of Nonlinear Systems Subjected to Harmonic Excitations,” J. Sound Vib., 236(2), pp. 339–358.
Ewins, D. J., 1984, Modal Testing: Theory and Practice, Research Studies Press, England.
Tiwari,  R., and Vyas,  N. S., 1995, “Estimation of Nonlinear Stiffness Parameters of Rolling Element Bearings from Random Response of Rotor Bearing Systems,” Journal of Sound Vib. 187 (2), pp. 229–239.

Figures

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(a) Experimental set up along with instrumentation (b) Close up view of exciter mounting arrangement and impedance head
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Schematic diagram of rotor bearing test rig and instrumentation
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Response acceleration spectrum from rap test
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Response component spectra for ω=330 Hz
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Excitation level variation, response amplitude, X(ω), and preliminary estimate of H1(ω)
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(a) Typical response spectrum with excitation at ω=330 Hz (b) Measurability of third response harmonic at different excitation levels
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Acceleration response spectra for Case I: Excitation amplitude=4 N
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(a) Iterative estimates of k3, (Case I: Excitation amplitude=4 N) (b) Final estimate of first order kernel transform, H1(ω) (Case I: Excitation amplitude=4 N)
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(a) Iterative estimates of k3, (Case II: Excitation amplitude=3 N) (b) Iterative estimates of k3, (Case III: Excitation amplitude=2 N)
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Variation in sign of real part of X(3ω) around ωn/3
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Schematic diagram of a loaded ball bearing
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Comparison of estimates of stiffness parameters 1–5: Theoretical values with pre-load 0.2, 0.3, 0.4, 0.5 and 0.6 μm respectively. [Harris 8 and Ragulski et al. 9 6,7,8: Present experimental estimates for cases I, II and III respectively. 9: Experimental estimate of Tiwari 16 10: Experimental estimate of Khan 13

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