Nonlinear dynamics and stability analysis of horizontal vibration for rolling system with gyro-precession and eccentricity effects

This paper investigates the nonlinear dynamics and stability of the rolling system with gyro-precession and eccentricity effects. Based on the d’Alembert principle, considering the influence of the roll’s elastic deformation as well as the coupling effects of gyro-precession and eccentricity, it is proposed that the nonlinear dynamic model for the horizontal vibration of rolling system. Firstly, a codimension two-bifurcation characteristic is deduced by combining with the multi-scale method and singularity theory under the condition of nonautonomy. Secondly, according to Runge-Kutta method, the chaos threshold of the dissipative system is obtained through the abrupt change point of the phase trajectory topology structure. By taking the force fluctuation amplitude above the chaotic critical threshold, it is analyzed the systematic bifurcation and maximum Lyapunov exponent to explore the systematic stability in the unstable state space, which reveal the effect of parameters variation on the nonlinear dynamic behavior of systematic horizontal vibration. Finally, the graph-cell mapping program was developed to explore the systematic global motion characteristics, it is revealed that the dynamic transition mechanism of the nonlinear horizontal vibration system under both local and global motion characteristics. The research results provide a theoretical basis for the determination of process parameters and the vibration suppression. • A codimension two-bifurcation characteristic is deduced by combining with the multi-scale method and singularity theory. • Constructing pseudo-Hamiltonian system, the topology of dynamic motion is able to distinguish whether the system is in chaos. • Constraint set of objective parameters is constructed when chaos occurs in nonlinear horizontal vibration of rolling system. • The collision of the chaotic attractor and unstable periodic orbit on the boundary of its attraction domain caused systematic sudden instability.