Consideration of Whirl Frequency Ratio and Effective Damping Coefficient of Seal

Abstract

Seal stability is often evaluated by Whirl frequency ratio (WFR) and Effective damping coefficient (C eff) calculated on the assumption of synchronous whirl. However, the natural frequency of the rotor system must be used for calculation of WFR and C eff when determining self-excited vibration. This paper discusses the evaluation of seal stability using WFR and C eff. First, the stability analysis is performed by FEM for a simply supported Jeffcott rotor model, having a seal near the disk. Next, WFR and C eff are calculated for the following two frequencies; (1) the natural frequency of the rotor system, (2) rotational frequency. As the reference of stability, the logarithmic decrement is used for comparing with WFR and C eff. Effective damping coefficient (C eff) calculated using the natural frequency of the rotor correctly estimates the seal stability. Whirl frequency ratio (WFR) for the natural frequency of the rotor can judge the rotor stability, but cannot evaluate how good the seal is. Both C eff and WFR calculated by using the rotational frequency cannot give correct criterion for the rotor stability.

Investigations of the static and dynamic performances of an annular seal with a tilted rotor by transient CFD methods with dynamic mesh

“…To better illustrate dynamic behavior of annular seals, the whirl-frequency ratio f is commonly used to weigh the stability of rotor systems, which should be as small as possible to guarantee the safe operation of the systems. The whirl-frequency ratio consists of the two key coefficients of cross-coupled stiffness and direct damping, and is often estimated under the assumption of synchronous whirl (Iwatsubo and Ishimaru, 2010). It is observed from Figure 9 that the whirl-frequency ratios under the three pressure differences increase with the increasing L/D ratio.…”

Leakage and rotordynamic characteristics of labyrinth seal and hole-pattern damping seal with special-shaped 3D cavity

“…The rotor whirls in a circular vibration trajectory about the centered position of rotor can be characterized as equation (2): where e is the rotor eccentricity, Ω is whirl angular velocity, among which Ω > 0 and Ω < 0 correspond to forward and backward whirls, respectively (Iwatsubo and Ishimaru, 2010). After one revolution of rotor whirling, the work of seal reaction force on rotor system is defined as equation (3): …”

Study on the Critical Stable State of the Labyrinth Seal

“…着节能降耗的关键作用 [1] 。 随着机组容量及工质参 数的不断提高，密封引起的气流激振问题日益突 出，密封气流激振已经成为发展高性能透平机械 * 国家自然科学基金资助项目(51875361， 51575105， 51676131)。 20190606 收到初稿，20190925 收到修改稿 的瓶颈 [2][3][4] 。密封的稳定性研究对进一步提升透平 机械可靠性具有重要意义。 钟明磊等 [5] 采用数值模拟方法建立了涡动转 子-迷宫密封三维模型，计算分析了不同结构高低 式迷宫密封气流激振力特点。 张万福等 [6] 建立了气 缸-密封系统动力学分析模型，提出一种新的密封 气流力及刚度系数识别方法，并应用双控制体模 型对偏心密封腔内压力分布及切向气流力产生机 理进行分析，并阐述了转速、进气压力、偏心、 密封间隙等因素对切向气流力的影响。 王庆峰等 [7] 基于稳态计算流体力学方法研究了压差对旋转直 通式迷宫气封泄漏、流场和流场力的影响，研究 结果表明：随着压差的增大，泄漏量、径向流体 压力、轴向流体压力、总流体压力和总流体粘滞 力均增大。 马文生等 [8] 采用数值方法计算得到迷宫 密封在五种偏心率与转速下的压力分布、密封力 的变化情况，并对影响泄漏量与动力学参数的因 素进行分析。 孙丹等 [9] 研究了偏心率对迷宫密封动 力特性及转子稳定性的影响，并提出新型浮式自 同心密封结构。 高性能计算机的不断发展，进一步推动了计算 流体力学的应用。从早期基于有限差分、有限体积 等方法的小规模编程计算 [10][11] ，到目前以大型商业 计算软件为主的 CFD 三维湍流模拟。 密封流场计算 方法主要有如下两种： 瞬态涡动法： 该方法基于 CFD 非稳态求解及动 网格方法，对密封内流场进行计算 [12][13][14] 。如果在固 定坐标系下求解，计算域参数属于非稳态，则需要 采用动网格技术对密封流场进行非定常求解，具有 较高的计算难度。 旋转坐标系法：该方法应用旋转坐标系将转子 实际的非稳态涡动问题转变为准稳态模型，计算速 度较快 [15][16] [18] 。 在(x, y)坐标系中，设转子轴心涡动轨迹方程为 cos( ) sin( )…”

“…进气接口 7. 进气孔 3.1 密封静态稳定性分析 交叉刚度系数表征切向气流力效果，是衡量静 态转子-密封系统稳定性的主要指标，当交叉刚度系 数 k 为正值，将降低转子-密封系统稳定性[18] 。 图 7 给出 5 种齿数迷宫密封密封段转子所受静 态切向气流力随转速变化趋势， 进口压力为 2.9 bar。图 7 切向力 F t 随转速变化情况 图 8 给出 5 种齿数迷宫密封转子段静态切向 气流力随进口压力变化曲线(转速 60 000 r/min)。 与图 7 所示气流力随转速变化趋势相似，随着进 口压力的增加气流力不断变大，即交叉刚度绝对 值随进口压力增加而变大。5 齿与 10 齿模型交叉…”