Application of Volterra and Wiener theories for nonlinear parameter estimation in a rotor-bearing system

Volterra and Wiener theories provide the concepts of linear, bilinear, tri- linear, etc., kernels, which upon convolution with the excitation force, ca n be employed to represent the response of a nonlinear system. Based on the se theories, higher-order frequency response functions (FRFs) are employed to estimate the nonlinear stiffness of rolling element bearings, supporting a rigid rotor. The analysis involves a third-order kernel representation o f the system response. The first and third-order kernel transform are extra cted from the measurements of the applied white-noise excitation and the re sultant response. A third-order kernel factor is synthesized from the first -order kernel and is processed along with the third-order kernel for estima tion of the nonlinear parameter. Damping is assumed to be linear in the ana lysis. The procedure is demonstrated through measurements on the laboratory test rig.