Analytical Nonlinear Response for a Rotor with the Hertz Contact and Clearance

Abstract

This paper focuses on a nonlinear frequency response of a rotor system with power of Hertz contact and piecewise nonlinearities of bearing clearance. A complex equation of motion for this rotor system was deduced using the Lagrange equation. The natural frequency and phase portraits of the unperturbed rotor system were obtained to demonstrate hardening stiffness characteristics. The amplitude frequency and attraction basins of multiple solutions for the perturbed rotatory system without clearance were investigated. The analytical forms of amplitude frequency of the perturbed system with clearance were analyzed. Through numerical simulation, the correctness of the theoretical formula is verified, and it is in good agreement with the numerical results.