Research on the dynamic characteristics and control mechanism of horizontal vibration induced by structural gap in four-high cold rolling system

Structural clearances in high-speed rolling mills can induce complex nonlinear horizontal vibrations, resulting in strip surface defects and accelerated equipment fatigue. However, how clearance-induced nonlinearities govern chaos onset and stability boundaries remains insufficiently understood. To reveal the underlying mechanisms, a nonlinear horizontal vibration model of a four-high cold rolling mill is established by incorporating gyro-precession and eccentricity effects. Numerical simulations and analytical solutions via the Runge-Kutta and homotopy analysis-averaging methods reveal three key findings: a previously overlooked hysteretic evolution of the critical damping threshold for chaos onset with increasing force fluctuation amplitude; enhanced parametric stiffness markedly enlarges the instability region; and gyro-precession facilitates the transition from period-doubling responses to chaotic motions under strong excitation. To suppress these nonlinear dynamics, a novel bi-variable time-delay control strategy is proposed. Multi-scale analysis shows that properly coordinated control gains and delay parameters effectively mitigate vibration amplitudes and significantly improve system stability. Experimental frequency-sweep and amplitude-sweep tests validate the theoretical predictions, confirming multi-valued jump phenomena and hard-spring nonlinear characteristics. This work establishes an integrated framework for instability prediction, chaos control, and vibration suppression in four-high rolling mills, providing new insights into the dynamic regulation and optimization of high-speed rolling processes.