Volterra series provides a structured analytical platform for modeling and identification of nonlinear systems. The series has been widely used in nonparametric identification through higher order frequency response functions or FRFs. A parametric identification procedure based on recursive evaluation of response harmonic amplitude series is presented here. The procedure is experimentally investigated for a rotor-bearing system supported in rolling element bearings. The estimates of nonlinear bearing stiffness obtained from experimentation have been compared with analytical values and experimental results of previous works.
Issue Section:
Technical Papers
1.
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
.2.
Boyd
, S.
, Tang
, Y. S.
, and Chua
, L. O.
, 1983
, “Measuring Volterra Kernels
,” IEEE Trans. Circuits Syst.
, CAS-30
(8
), pp. 571
–577
.3.
Chua
, L. O.
, and Liao
, Y.
, 1989
, “Measuring Volterra Kernels (II)
,” Int. J. of Circuit Theory and Applications
, 17
, pp. 151
–190
.4.
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
.5.
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
.6.
Lee
, G. M.
, 1997
, “Estimation of Nonlinear System Parameters using Higher Order Frequency Response Functions
,” Mech. Syst. Signal Process.
, 11
(2
), pp. 219
–228
.7.
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.
8.
Harris, T. A., 1984, Rolling Bearing Analysis, Wiley, New York.
9.
Ragulskis, K. M., Jurkauskas A. Y., Atstupenas, V. V., Vitkute, A. Y., and Kulvec, A. P., 1974, Vibration in Bearings, Mintis Publishers, Vilnius.
10.
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
.11.
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
.12.
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
.13.
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
.14.
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
.15.
Ewins, D. J., 1984, Modal Testing: Theory and Practice, Research Studies Press, England.
16.
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
.Copyright © 2003
by ASME
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