Characterization of Stick–Slip Oscillations in Nonsmooth Rotating Mechanical Systems Modulated by Shape Memory Alloy Controllers

Self-excited Dry Friction Backward Whirling (DFBW) in rotor/stator systems represents one of the most hazardous motion patterns that can occur under extreme operating conditions. It is imperative to comprehend the mechanisms underlying its formation and to develop effective control strategies in the field of engineering. This study proposes a Filippov-type friction model for rotor/stator systems, controlled by shape memory alloy controllers, to investigate the dynamic characteristics of these systems. The tiered research framework employed in this study is a systematic approach to research design, with each tier representing a specific level of analysis. Initially, a parameter analysis systematically examines how the equilibrium points of the subsystems evolve with control parameters, as well as the criteria for their bifurcation. The creation of dual-parameter bifurcation diagrams facilitated the identification of strip-shaped fractal configurations and multistable motion patterns within the system. Subsequently, we employed flow transition theory to derive the necessary and sufficient conditions for crossing, grazing, and sliding motions. Numerical simulations validate the three characteristic nonsmooth motion modes in rotor/stator systems, thereby highlighting the nonlinear regulatory mechanisms of key parameters that govern global dynamics. Consequently, a correlation model is developed, establishing a link between sliding-mode characteristics and the existence boundaries of DFBW. Through a thorough analysis of vector field discontinuities, we formulate criteria for the existence of DFBW that are consistent with established classical theories. This methodology offers a novel approach for predicting and suppressing DFBW in engineering applications. These findings contribute to the advancement of the theory of rotor dynamics and offer practical guidance for mitigating rotor–stator rubbing faults in aero-engines and turbomachinery.