Quasi-Periodic Oscillations of Roll System in Corrugated Rolling Mill in Resonance

Dongping He,Tao Wang,Zhihua Wang,Huidong Xu

doi:10.3390/math9243201

Abstract

This paper investigates quasi-periodic oscillations of roll system in corrugated rolling mill in resonance. The two-degree of freedom vertical nonlinear mathematical model of roller system is established by considering the nonlinear damping and nonlinear stiffness within corrugated interface of corrugated rolling mill. In order to investigate the quasi-periodic oscillations at the resonance points, the Poincaré map is established by solving the power series solution of dynamic equations. Based on the Poincaré map, the existence and stability of quasi-periodic oscillations from the Neimark-Sacker bifurcation in the case of resonance are analyzed. The numerical simulation further verifies the correctness of the theoretical analysis.

Highlights

The corrugated rolling mill is a multivariable, strongly coupled, multi-constrained and time-varying non-linear system
Johnson and Qi [1] analyzed the influence of the nonlinearity of contact interface between the work roll and the supporting roll on the rolling mill dynamics and found that the nonlinearity could cause high frequency harmonic vibration
Swiatoniowski [2] investigated the dynamic behavior of vertical vibration of rolling system by considering the elastoplastic deformation as nonlinear elastic force

Summary

Introduction

The corrugated rolling mill is a multivariable, strongly coupled, multi-constrained and time-varying non-linear system. Hou et al [7,8] established the torsional vibration equation of the main drive system of the rolling mill by considering the nonlinear factors, such as piecewise nonlinearity, clearance, and nonlinear friction damping of the roll system, and investigated a variety of dynamic behaviors of the system. The main purpose of the present paper is to investigate the quasi-periodic oscillations from the Neimark-Sacker bifurcation in resonance for the roll system of the corrugated rolling mill.

The Mechanical Model and Dynamic Equation of Corrugated Rolling Mill

The Poincaré Map