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, can be employed to represent the response of a nonlinear system. Based on these theories, higher-order frequency response functions (FRFs) are employed to estimate the nonlinear stiffness of rolling element bearings, supporting a rigid rotor. The rotor-bearing assembly is idealized as a single-degreefreedom system, with cubic nonlinearity. The analysis involves a third-order kernel representation of the system response. The first and third-order kernel transforms are extracted from the measurements of the applied whitenoise excitation and the resultant response. A third-order kernel factor is synthesized from this first-order kernel and is processed along with the third-order kernel for estimation of the nonlinear parameter. Damping is assumed to be linear in the analysis. The procedure is demonstrated through measurements on a laboratory test rig.