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<p>Maneuver-induced additional acceleration significantly influences asymmetric motions, resulting in behaviors that are periodic, aperiodic, or chaotic. Previous analyses employing a two-degree-of-freedom (2-DOF) model incorporating gravity have revealed complex nonlinear phenomena, such as internal resonance, multiple periodic states, and chaos. However, the effects of unbalance and gravity on nonlinear motions have not been thoroughly investigated for application in high and low pressure rotors in an aero-engine with multiple rotors. In this study, a four-degree-of-freedom (4-DOF) mathematical model, incorporating multiple rotors, is developed using the Lagrangian method to investigate nonlinear motions caused by impacts between a rotor and stator. The Lyapunov exponent is computed to quantify the system’s stability characteristics. Nonlinear impacts between the rotor and stator are incorporated into the model, along with non-dimensional gravity effects. The MATLAB ODE45 solver, combined with an event detection function, is employed to simulate the nonlinear dynamics within the rotating reference frame. Due to the significant influence of non-dimensional gravity on motion asymmetry, parametric studies focus on how additional acceleration modulates nonlinear behaviors. The results indicate that high rotational frequencies induce rich phenomena, including multiple periodic, chaotic, and quasi-periodic motions. Furthermore, the rotor tends to maintain continuous contact with the stator, which increases gravity effects and causes shifts in the forward whirling (FW) and backward whirling (BW) frequencies within the rotating frame.</p>

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Nonlinear motions induced by impacts from a rotor and stator under varying gravity coefficient

  • 期刊论文

  • 发表日期：

    2026年2月24日

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  • Haifei Wang,
  • Kian Meng Lim,
  • Shuai Zhou,
  • Tianyi Ding,
  • XunKai Liang,
  • Tian Zhou,
  • Chao Dong

摘要

Maneuver-induced additional acceleration significantly influences asymmetric motions, resulting in behaviors that are periodic, aperiodic, or chaotic. Previous analyses employing a two-degree-of-freedom (2-DOF) model incorporating gravity have revealed complex nonlinear phenomena, such as internal resonance, multiple periodic states, and chaos. However, the effects of unbalance and gravity on nonlinear motions have not been thoroughly investigated for application in high and low pressure rotors in an aero-engine with multiple rotors. In this study, a four-degree-of-freedom (4-DOF) mathematical model, incorporating multiple rotors, is developed using the Lagrangian method to investigate nonlinear motions caused by impacts between a rotor and stator. The Lyapunov exponent is computed to quantify the system’s stability characteristics. Nonlinear impacts between the rotor and stator are incorporated into the model, along with non-dimensional gravity effects. The MATLAB ODE45 solver, combined with an event detection function, is employed to simulate the nonlinear dynamics within the rotating reference frame. Due to the significant influence of non-dimensional gravity on motion asymmetry, parametric studies focus on how additional acceleration modulates nonlinear behaviors. The results indicate that high rotational frequencies induce rich phenomena, including multiple periodic, chaotic, and quasi-periodic motions. Furthermore, the rotor tends to maintain continuous contact with the stator, which increases gravity effects and causes shifts in the forward whirling (FW) and backward whirling (BW) frequencies within the rotating frame.