Nonlinear Modeling and Chaos Analysis in AMB-Rotor System with time delay

Active magnetic bearings (AMBs) are critical in high-speed machinery due to their contactless support and rapid active vibration control. However, this reliance on high response speed makes them highly susceptible to instability induced by time delays. To address the limitations of linearized models in explaining complex experimental phenomena, this work investigates the interplay between time delays and intrinsic nonlinearities. First, a nonlinear electromagnetic force model is derived via coupled Finite Element Analysis and multivariate polynomial regression, explicitly incorporating magnetic flux saturation and geometric nonlinearities. Subsequently, a dynamic model for a four-degree-of-freedom AMB rotor system incorporating multiple time delay sources is developed. To quantify the stability boundary, an analytical criterion based on Hassard's theorem is implemented, precisely determining the critical time delay. To accurately solve the nonlinear dynamics, a co-simulation strategy combining multibody dynamics and control is implemented. Both numerical simulations and experimental validations demonstrate that increasing time delay induces a bifurcation route from stable periodic motion to quasi-periodic and ultimately bounded chaotic motions. The results confirm that the proposed nonlinear model successfully captures the destabilizing mechanism of time delays, which was underestimated by linear theories, providing a predictive framework for bifurcation control in high-speed AMB applications.