<p>To ensure the safe operation and extended service life of rotor-stator systems, this study aims to theoretically derive and numerically reveal their non-smooth frictional dynamics under time-delayed electromagnetic control, as well as to clarify the existence criteria for self-excited oscillations induced by dry friction. Given that electromagnetic forces offer a non-contact means for dynamic balancing, this paper proposes a non-smooth feedback control strategy based on time-delayed electromagnetic dynamic balancing control. Correspondingly, a Filippov-type time-delayed electromagnetic regulation rotor-stator friction model is established to systematically analyze the non-smooth dynamic behaviors under the adjustment of time-delayed electromagnetic forces. Utilizing non-smooth system theory, the existence of subsystem equilibrium points is determined, and the associated conditions for Hopf bifurcation are rigorously derived. By applying the multi-scale method, the tongue-shaped fractal structure and multi-stability motion patterns of the system are elucidated. Subsequently, employing switching flow theory, the necessary and sufficient conditions for the occurrence of time-delayed crossing motion, grazing bifurcation, and sliding motion are strictly established. Numerical simulations demonstrate various typical non-smooth dynamic responses of the rotor mechanical system, highlighting the complex influence of the synergistic effect between time delay and system parameters on the relative sliding time. In particular, based on the critical conditions of sliding motion, this paper presents a method for determining the critical rotational speed and an explicit analytical formula for triggering dry friction backward whirl (DFBW) in the time-delayed electromagnetic regulation system.</p>

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Complex dynamics analysis of non-smooth electromagnetic-controlled rotating mechanical rubbing system with time delay

  • Jiangang Zhang,
  • Zishang Yang,
  • Meijuan He,
  • Xinlei An,
  • Jiayin Liu

摘要

To ensure the safe operation and extended service life of rotor-stator systems, this study aims to theoretically derive and numerically reveal their non-smooth frictional dynamics under time-delayed electromagnetic control, as well as to clarify the existence criteria for self-excited oscillations induced by dry friction. Given that electromagnetic forces offer a non-contact means for dynamic balancing, this paper proposes a non-smooth feedback control strategy based on time-delayed electromagnetic dynamic balancing control. Correspondingly, a Filippov-type time-delayed electromagnetic regulation rotor-stator friction model is established to systematically analyze the non-smooth dynamic behaviors under the adjustment of time-delayed electromagnetic forces. Utilizing non-smooth system theory, the existence of subsystem equilibrium points is determined, and the associated conditions for Hopf bifurcation are rigorously derived. By applying the multi-scale method, the tongue-shaped fractal structure and multi-stability motion patterns of the system are elucidated. Subsequently, employing switching flow theory, the necessary and sufficient conditions for the occurrence of time-delayed crossing motion, grazing bifurcation, and sliding motion are strictly established. Numerical simulations demonstrate various typical non-smooth dynamic responses of the rotor mechanical system, highlighting the complex influence of the synergistic effect between time delay and system parameters on the relative sliding time. In particular, based on the critical conditions of sliding motion, this paper presents a method for determining the critical rotational speed and an explicit analytical formula for triggering dry friction backward whirl (DFBW) in the time-delayed electromagnetic regulation system.