Abstract
Volterra and Wiener theories provide the concepts of linear,bilinear, tri-linear, etc., kernels, which upon convolution with theexcitation force, can be employed to represent the response of anonlinear system. Based on these theories, higher-order frequencyresponse functions (FRFs) are employed to estimate the nonlinearstiffness of rolling element bearings, supporting a rigid rotor. Therotor-bearing assembly is idealized as a single-degree-freedom system,with cubic nonlinearity. The analysis involves a third-order kernelrepresentation of the system response. The first and third-order kerneltransforms are extracted from the measurements of the appliedwhite-noise excitation and the resultant response. A third-order kernelfactor is synthesized from this first-order kernel and is processedalong with the third-order kernel for estimation of the nonlinearparameter. Damping is assumed to be linear in the analysis. Theprocedure is demonstrated through measurements on a laboratory test rig.
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Khan, A.A., Vyas, N.S. Application of Volterra and Wiener Theories for Nonlinear Parameter Estimation in a Rotor-Bearing System. Nonlinear Dynamics 24, 285–304 (2001). https://doi.org/10.1023/A:1008352829782
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DOI: https://doi.org/10.1023/A:1008352829782