航空发动机转子系统碰摩的非线性动力学研究
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摘要
近年来，为了提高航空发动机的推重比和效率，旋转部件与静止部件之间的间隙被设计得越来越小，从而使得系统发生碰摩的可能性越来越大。严重的碰摩可能导致叶片断裂、转子失稳，造成严重的运行事故。
本文对航空发动机转子系统碰摩的非线性动力学进行研究，以期为航空发动机转子系统的设计提供一定的理论依据，主要工作如下：
考虑具有非线性刚度的单盘转子的碰摩，将约束分岔理论首次应用到转子同步全周碰摩的研究中，讨论了参数对系统在升降速过程中的跳跃现象的影响，给出了对应不同分岔形式的参数域；对同步全周碰摩运动的稳定性进行分析，给出了参数平面上同步全周碰摩运动的稳定区域和分岔边界；并讨论了同步全周碰摩失稳后系统可能出现的动力学行为。
研究了非线性转子系统的反向全周碰摩，通过数值计算结果和国外实验结果的对比说明了在反向全周碰摩研究中考虑转子系统非线性刚度的必要性；给出了非线性转子反向全周碰摩的解析解，利用Floquet理论分析了反向全周碰摩解的稳定性；讨论了系统参数对反向全周碰摩振幅、频率、存在性和发生的临界条件的影响，给出了系统参数-转速平面上不同动力学行为的转迁；发现非线性转子系统不仅存在由摩擦力方向改变引起的反向全周碰摩，同时转子的非线性刚度也会导致系统出现一种新的反向全周碰摩运动，这种新的反向全周碰摩运动是稳定的周期运动。研究了非线性转子系统突加不平衡的瞬态响应和稳态响应；给出了参数-转速平面上系统稳态响应的转迁和系统在突加不平衡之后降速过程中不发生失稳的参数域。
根据航空发动机转子的特点，将航空发动机转子简化为弹性支承的刚性偏置转子，利用拉格朗日方程建立了系统的运动方程，采用两状态变量约束分岔理论和李雅普诺夫稳定性理论研究了系统同步全周碰摩的分岔和稳定性。研究了弹性支承的刚性偏置转子的反向全周碰摩，讨论了系统参数对反向全周碰摩振幅和频率的影响。
考虑航空发动机的主要结构特点，包括双转子-中介轴承结构、非线性的弹性支承、结构不对称引起的陀螺效应、空心转轴，建立了航空发动机双转子-机匣耦合系统动力学模型；求解了系统的临界转速和振型，讨论了支承参数和转速比对临界转速和振型的影响。计算了双转子-机匣耦合系统的碰摩响应，发现系统在轻微碰摩时振幅会出现多次跳跃现象；双转子同向旋转轻微碰摩时，系统的响应中将出现双转子转动频率的组合频率成分，而双转子反向旋转时则不会出现频率成分的组合；在严重碰摩时，系统可能出现反向全周碰摩响应，双转子系统的反向全周碰摩从运动形式上看和单转子系统是相同的；研究了不平衡量对工作转速下振幅的影响，发现双转子反向旋转较同向旋转更容易发生自激振动失稳。计算了双转子-机匣耦合系统的突加不平衡响应，给出了系统稳态响应随突加不平衡量变化的分岔图；发现同向旋转时系统的稳态响应形式有：周期运动、概周期运动和自激振动失稳，而反向旋转时系统不会发生自激振动失稳。
To increase the efficiency and thrust-weight ratio of aero engines, theclearance between rotor and stator has been designed to be smaller and smaller,however, which leads a larger possibility of impact-rub. Rubbing may induce therotor’s dynamic instability, blade break, and other serious accidents.
In this thesis, rubbing dynamics of aero rotor system is investigated to givesome theoretical references for the design of aero engine. The main contents areas follows:
SFARM (synchronous full annular rub motion) of a single-disc rotor withnonlinear stiffness is considered. The constraint bifurcation theory is firstlyapplied to discuss the influence of parameters on the jump phenomena at therotor’s run-up and run-down. The stability of SFARM is analyzed and the stableregion on the parameter plane is obtained. The possible dynamical behaviorsafter the Hopf bifurcation are also studied.
Reverse full annular rub of nonlinear rotor system is studied analyticallyand numerically, which shows the necessity to consider the nonlinearity of rotorcompared with earlier test results. Analytical solution of reverse full annular rubis calculated and then its stability is discussed by Floquet theory. Influences ofparameters on the response and existence region, as well as the onset of reversefull annular rub are discussed. The results show that besides the dry frictionwhirl resulting from the change of direction of friction, another reverse fullannular rubbing motion caused by the rotor’s nonlinearity also exists. And thiskind of reverse full annular rub is a stable periodic motion. Transient andsteady-state responses of the sudden imbalance of the nonlinear rotors system areinvestigated. The transitions of steady-state response on the parameters-rotationspeed plane are given.
Aero engine rotor system is simplified as an unsymmetrical-rigid-rotor withnonlinear-elastic-support based on its characteristics. Governing equations of therubbing system are solved by averaging method to obtain the bifurcationequations. Then bifurcation and stability of SFARM are analyzed according tothe two-dimensional constraint bifurcation theory and Lyapunov stability theory.Reverse full annular rub of the elastic-support rigid-rotor system is studied todiscuss the influences of parameters on the amplitude and frequency.
The dynamical model of a dual rotor-casing coupled system is establishedconsidering the main characteristics of aero engine including dual rotor-intermediary bearing structure, nonlinear supports, gyroscopic effect, and hollow rotating shaft. The critical speeds and modes are solved and the influences ofsupport stiffness and rotating speed ratio are discussed. Rubbing response of thedual rotor-casing coupled system is calculated. The results show that jumpphenomena may happen for many times in light rubs. And co-rotating of the dualrotors may lead the combination of rotating frequencies, however,counter-rotating may not. Reverse full annular rub which is the same as the oneof single rotor system may happen in heavy rubs. The influence of massimbalance on the amplitude at the operating condition is discussed, which showsthe self-excited instability is easier to happen with the rotors’ counter-rotating.Sudden imbalance response of the dual rotor-casing coupled system is solved,and bifurcation diagrams of steady-state response with the variation of suddenimbalance are given. It shows that periodic motions, quasi-periodic motions andself-excited instability may appear in the co-rotating system, however, incounter-rotating system self-excited instability may not happen.
本文对航空发动机转子系统碰摩的非线性动力学进行研究，以期为航空发动机转子系统的设计提供一定的理论依据，主要工作如下：
考虑具有非线性刚度的单盘转子的碰摩，将约束分岔理论首次应用到转子同步全周碰摩的研究中，讨论了参数对系统在升降速过程中的跳跃现象的影响，给出了对应不同分岔形式的参数域；对同步全周碰摩运动的稳定性进行分析，给出了参数平面上同步全周碰摩运动的稳定区域和分岔边界；并讨论了同步全周碰摩失稳后系统可能出现的动力学行为。
研究了非线性转子系统的反向全周碰摩，通过数值计算结果和国外实验结果的对比说明了在反向全周碰摩研究中考虑转子系统非线性刚度的必要性；给出了非线性转子反向全周碰摩的解析解，利用Floquet理论分析了反向全周碰摩解的稳定性；讨论了系统参数对反向全周碰摩振幅、频率、存在性和发生的临界条件的影响，给出了系统参数-转速平面上不同动力学行为的转迁；发现非线性转子系统不仅存在由摩擦力方向改变引起的反向全周碰摩，同时转子的非线性刚度也会导致系统出现一种新的反向全周碰摩运动，这种新的反向全周碰摩运动是稳定的周期运动。研究了非线性转子系统突加不平衡的瞬态响应和稳态响应；给出了参数-转速平面上系统稳态响应的转迁和系统在突加不平衡之后降速过程中不发生失稳的参数域。
根据航空发动机转子的特点，将航空发动机转子简化为弹性支承的刚性偏置转子，利用拉格朗日方程建立了系统的运动方程，采用两状态变量约束分岔理论和李雅普诺夫稳定性理论研究了系统同步全周碰摩的分岔和稳定性。研究了弹性支承的刚性偏置转子的反向全周碰摩，讨论了系统参数对反向全周碰摩振幅和频率的影响。
考虑航空发动机的主要结构特点，包括双转子-中介轴承结构、非线性的弹性支承、结构不对称引起的陀螺效应、空心转轴，建立了航空发动机双转子-机匣耦合系统动力学模型；求解了系统的临界转速和振型，讨论了支承参数和转速比对临界转速和振型的影响。计算了双转子-机匣耦合系统的碰摩响应，发现系统在轻微碰摩时振幅会出现多次跳跃现象；双转子同向旋转轻微碰摩时，系统的响应中将出现双转子转动频率的组合频率成分，而双转子反向旋转时则不会出现频率成分的组合；在严重碰摩时，系统可能出现反向全周碰摩响应，双转子系统的反向全周碰摩从运动形式上看和单转子系统是相同的；研究了不平衡量对工作转速下振幅的影响，发现双转子反向旋转较同向旋转更容易发生自激振动失稳。计算了双转子-机匣耦合系统的突加不平衡响应，给出了系统稳态响应随突加不平衡量变化的分岔图；发现同向旋转时系统的稳态响应形式有：周期运动、概周期运动和自激振动失稳，而反向旋转时系统不会发生自激振动失稳。
To increase the efficiency and thrust-weight ratio of aero engines, theclearance between rotor and stator has been designed to be smaller and smaller,however, which leads a larger possibility of impact-rub. Rubbing may induce therotor’s dynamic instability, blade break, and other serious accidents.
In this thesis, rubbing dynamics of aero rotor system is investigated to givesome theoretical references for the design of aero engine. The main contents areas follows:
SFARM (synchronous full annular rub motion) of a single-disc rotor withnonlinear stiffness is considered. The constraint bifurcation theory is firstlyapplied to discuss the influence of parameters on the jump phenomena at therotor’s run-up and run-down. The stability of SFARM is analyzed and the stableregion on the parameter plane is obtained. The possible dynamical behaviorsafter the Hopf bifurcation are also studied.
Reverse full annular rub of nonlinear rotor system is studied analyticallyand numerically, which shows the necessity to consider the nonlinearity of rotorcompared with earlier test results. Analytical solution of reverse full annular rubis calculated and then its stability is discussed by Floquet theory. Influences ofparameters on the response and existence region, as well as the onset of reversefull annular rub are discussed. The results show that besides the dry frictionwhirl resulting from the change of direction of friction, another reverse fullannular rubbing motion caused by the rotor’s nonlinearity also exists. And thiskind of reverse full annular rub is a stable periodic motion. Transient andsteady-state responses of the sudden imbalance of the nonlinear rotors system areinvestigated. The transitions of steady-state response on the parameters-rotationspeed plane are given.
Aero engine rotor system is simplified as an unsymmetrical-rigid-rotor withnonlinear-elastic-support based on its characteristics. Governing equations of therubbing system are solved by averaging method to obtain the bifurcationequations. Then bifurcation and stability of SFARM are analyzed according tothe two-dimensional constraint bifurcation theory and Lyapunov stability theory.Reverse full annular rub of the elastic-support rigid-rotor system is studied todiscuss the influences of parameters on the amplitude and frequency.
The dynamical model of a dual rotor-casing coupled system is establishedconsidering the main characteristics of aero engine including dual rotor-intermediary bearing structure, nonlinear supports, gyroscopic effect, and hollow rotating shaft. The critical speeds and modes are solved and the influences ofsupport stiffness and rotating speed ratio are discussed. Rubbing response of thedual rotor-casing coupled system is calculated. The results show that jumpphenomena may happen for many times in light rubs. And co-rotating of the dualrotors may lead the combination of rotating frequencies, however,counter-rotating may not. Reverse full annular rub which is the same as the oneof single rotor system may happen in heavy rubs. The influence of massimbalance on the amplitude at the operating condition is discussed, which showsthe self-excited instability is easier to happen with the rotors’ counter-rotating.Sudden imbalance response of the dual rotor-casing coupled system is solved,and bifurcation diagrams of steady-state response with the variation of suddenimbalance are given. It shows that periodic motions, quasi-periodic motions andself-excited instability may appear in the co-rotating system, however, incounter-rotating system self-excited instability may not happen.
引文
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