Resonance Analysis of Horizontal Nonlinear Vibrations of Roll Systems for Cold Rolling Mills under Double-Frequency Excitations

Abstract

In this paper, the fractional order differential terms are introduced into a horizontal nonlinear dynamics model of a cold mill roller system. The resonance characteristics of the roller system under high-frequency and low-frequency excitation signals are investigated. Firstly, the dynamical equation of the roller system with a fractional order is established by replacing the normal damping term with a fractional damping term. Secondly, the fast-slow variable separation method is introduced to solve the dynamical equation. The amplitude frequency response characteristics of the system are analyzed. The study finds that there are three equilibrium points. The characteristics of the three equilibrium points and the critical forces causing the bifurcation are investigated. Due to the different orders of the fractional derivatives, various new resonant phenomena are found in the systems with single-well and double-well potentials. Additionally, the double resonance occurs while p = 0.3 or 1.0, and single resonance occurs while p = 1.8. Unlike integer order systems, the critical resonance amplitude of high-frequency signals in fractional order systems depends on the damping strength and is influenced by the fractional order damping. This study provides a broader picture of the vibration characteristics of the roll system for rolling mills.