带挤压油膜阻尼器的转子系统动力学建模与非线性研究

MODELING OF A DYNAMIC NONLINEAR ROTOR SYSTEM WITH A SQUEEZE FILM DAMPER

刘一鸣

11849081

硕士

航天工程

任光明

2020-05-28

2020-07-13

哈尔滨工业大学

深圳

转子系统是航空发动机的核心部件之一。在高速工作状态下，较少的不平衡量和外界干扰都会导致转子系统产生较大的不平衡响应。因此，有必要研究转子—支承系统的动力学特性，并且深入地研究非线性支承结构对转子系统的振动影响。挤压油膜阻尼器（Squeeze Film Damper, SFD）是一种振动被动控制结构，也是支承结构的重要组成部分，位于转子系统与机匣之间，用于减振。传统的阻尼器油膜力计算方法是基于经典润滑理论中的雷诺方程，忽略了油膜的惯性效应。但随着转速的增加，雷诺数也随之增加。高速转子系统的雷诺数通常远大于1。因此，在高速运行的转子系统中，对挤压油膜阻尼器进行数值模拟时须考虑油膜惯性的影响，建立更为完备的油膜力计算模型以用于分析系统的不平衡响应。 本文建立了转子系统的动力学模型，采用有限元法对转子系统的运动微分方程进行了推导，基于该方法编写了相应的计算程序，并对编写的转子动力学程序进行了验证。本文还推导了有限长两端非密封挤压油膜阻尼器油膜动压分布和速度分布的表达式，保留了N-S方程中的流体惯性项，引入油膜惯性效应。由此建立了新的油膜压力分布计算模型，考虑油膜惯性效应对油膜力结果的影响，并采用有限差分法进行求解，并分析了压力模型计算的结果。对轴颈表面的压力场进行了数值积分，得到油膜的反作用力。为研究考虑油膜惯性的挤压油膜阻尼器对转子—支承系统的影响，本文建立了考虑油膜惯性效应的转子系统在不平衡质量下的瞬态与稳态响应计算模型。该模型采用Newmark-HHT法将油膜力模型与转子系统动力学计算方法相结合，通过迭代求解转子系统响应，并对结果进行了分析。研究结果表明：小偏心率时，在较小的雷诺数下，粘性力的影响使压力分布更接近正弦曲线，但是在中等和较大的雷诺数下，相位发生变化，压力转换为余弦波形；中等偏心率时，在较小的雷诺数下，结果的差异性主要体现在压力的大小，而压力曲线轮廓的形状和相位则不受影响。但是，在中等雷诺数的情况下，全惯性模型的曲线轮廓和无惯性模型的曲线轮廓依旧相似，相位角有所差别，但时间惯性在曲线轮廓上具有明显差异，说明对流惯性项的影响会极大地影响压力曲线的形状；大偏心率时，即使在较小的雷诺数下，对流惯性效应对压力大小的影响也非常显着，且压力分布对流体惯性较为敏感，雷诺数的变化会对压力分布产生明显的影响；流体惯性效应明显增加了油膜力径向分力的大小，但切向分力基本不受影响；考虑油膜惯性效应的系统不平衡响应振幅与无惯性效应的不平衡响应振幅相比，都有一定程度上的减少，说明惯性效应的增强可以进一步降低系统不平衡响应的幅值。综上所述，在转子高速运转条件下，即大雷诺数情况下：流体惯性对挤压油膜阻尼器的特性影响以及对转子—支承系统的不平衡响应影响都是不能忽视的。

Rotor system is one of the core components of an aero-engine. Rotating at high speed, a small amount of mass unbalance and external interference may lead to greater unbalance response of the rotor system. Therefore, it is necessary to study the dynamic characteristics of a rotor-support system and to investigate the influence of nonlinear support structure on vibration behavior of a rotor system.Squeeze film damper (SFD) is a passive vibration control structure and an important component of the rotor support, which is mounted between the rotor and the casing for damping. In the high-speed operating state, the numerical simulation of squeeze film damper is difficult to ensure accuracy. The conventional calculation method of damper’s oil-film force is deduced from the Reynolds equation based on the classical lubrication theory, ingoring the inertia effect of oil-film. However, with the increase of rotating speed, the Reynolds number increases subsequently. In particular, for high-speed rotor system, it is usually much larger than 1. Therefore, for high-speed rotor system, the influence of oil-film inertia should be considered during numerical simulation of squeeze film damper.A dynamic model of a Jeffcott rotor system is establishd, and the differential motion of equation for the rotor system is deduced using finite element method. On this basis, the calculation algorithm is programmed via Matlab, and verified by the ANSYS results.The expressions of dynamic pressure and velocity distribution of the finite length open-ended oil-film are derived. The fluid inertia terms in Navier-Stokes (N-S) equation are retained, and the oil film inertia effect is introduced. On this basis, a new calculation model of oil-film pressure distribution is established to consider the effect of oil film inertia on oil-film forces, and the results of pressure are analyzed. The pressure distribution is solved by finite difference method. The reaction force of oil-film is obtained by numerical integration of the pressure field on the journal surface. To study the influence of squeeze film damper considering the fluid inertia on the rotor-support system, the calculation model of the rotor system considering the inertia effect of the oil film for transient and steady-state responses is established. In this model, Newmark-Hilber-Hughes-Taylor (Newmark-HHT) method is used to combine the oil-film force model with the dynamic calculation method of the rotor system. The transient responses of the rotor system is solved by iteration, and the results are analyzed.The results indicate that in the case of small eccentricity, the influence of viscous force makes the pressure distribution closer to a sinusoidal curve at a small Reynolds number, but for medium and large Reynolds numbers, the phase changes and the pressure curve is converted into cosine waveform. In the case of medium eccentricity, the difference of the results is mainly reflected in the magnitude of pressure at a small Reynolds number, while the shape and phase of the profile of the pressure curve are not affected. However, the temporal inertia is different in the curve profile, which shows that the convection inertia term will greatly affect the shape of pressure curve. When the eccentricity is large, the effect of convective inertia on the pressure is very significant even at a small Reynolds number, and the pressure distribution is sensitive to the fluid inertia. The change of Reynolds number will have a significant impact on the pressure distribution. The fluid inertia effect increases the radial component of oil-film force, but the tangential component is bascially not affected. The response amplitude considering oil-film inertia effect is reduced to a certain extent when compared with that of the system neglecting inertia effect. In addition, the increase of the inertia effect can reduce the response amplitude further.In conclusion, during high-speed operation with large Reynolds number, the influence of fluid inertia on vibration characteristics of squeeze film damper and the unbalanced response of rotor-support system cannot be ignored.

挤压油膜阻尼器 转子动力学 油膜力 有限元法 有限差分法 不平衡响应

squeeze film damper rotor dynamics oil film force finite element method finite difference method unbalanced response

中文

联合培养

南方科技大学

刘一鸣. 带挤压油膜阻尼器的转子系统动力学建模与非线性研究[D]. 深圳. 哈尔滨工业大学,2020.