Influence of leakage flow through labyrinth seals on rotordynamics: numerical calculations and experimental measurements

An extensive investigation of the influence of the leakage flow through a labyrinth seal at supply pressure of 12 bar on the rotordynamics was performed by using numerical calculations and experimental measurements. Toward this end, an experimental rotor setup was established in Shanghai Jiao Tong University. Two labyrinth seals were chosen for comparison, e.g., an interlocking seal and a stepped one. The numerical calculations based on the bulk-flow theory and the perturbation analysis were accomplished. Simultaneous acquisitions of the fluctuating static pressure at the stator wall and the displacement of the whirling rotor were made. The influence of the aerodynamic forcing on the rotor was analyzed in terms of the axial distribution of the mean static pressure, the circumferential distribution of the fluctuating pressure, the fist critical speed and the destabilization rotating speed of the rotor. The experimental results demonstrated that the sinusoidal distribution of the fluctuating static pressure on the stator wall was closely related to the whirling motion of the rotor. The first critical speed of the rotor was reduced by the aerodynamic forcing, resulting in intensified destabilization of the rotor system. Furthermore, the numerical analyses were in good agreement to the experimental measurements.     

高速涡轮泵机械密封端面温度变化规律研究

以高速涡轮泵用机械密封为研究对象,以15#液压油为试验介质,考虑循环冷却量、转速、介质压力以及不同摩擦副配对等因素,采用自行搭建的高速密封试验台开展端面温度变化规律的研究. 结果表明:对于高速机械密封,上述因素均对端面温度产生影响,其中转速对端面温度的影响基本成线性关系,循环冷却量对端面温度的影响存在一个阈值,建议实际设计时取阈值的120%,介质压力对端面温度产生影响较大,但是影响程度不如转速;以尽可能获得低的端面温度值来判断,用作静环时浸渍树脂石墨比普通石墨合适,用作动环时碳化硅比钼合金合适.      

密封环挠性安装形式对干气密封动态追随性的影响

基于气体润滑理论,并通过小扰动法建立了螺旋槽干气密封微扰膜压控制方程,在高速高压条件下获得了气膜动态特性系数;基于动力学相关知识,在考虑转轴轴向振动的情况下,利用气膜轴向动态刚度和阻尼系数分别求解了静环挠性安装、动环挠性安装和两环均挠性安装的干气密封挠性环运动方程.在不同轴向激励振幅、激励频率、挠性环质量、弹簧刚度和辅助密封圈阻尼下分别研究了三种典型结构干气密封动态追随性并进行了对比分析.结果表明:当轴向激励频率较高或挠性环质量较大时,静环挠性安装干气密封在刚受到外界激励时膜厚突变相对严重,动态追随性较差;在轴向激励频率较低且挠性环质量较小时,静环挠性安装干气密封相比动环挠性安装干气密封表现出更好的动态追随性;在三种密封环挠性安装形式中,两环均挠性安装干气密封动态追随性最好,且具有绝对优势.     

Research on the dynamic characteristics of crack damage of a seal-rotor system

Nonlinear Dynamics - In rotor systems, the labyrinth seal system is the core component to suppress fluid leakage between the rotor and the stator. In this paper, based on the finite element method,...     

Nonlinear analysis of orbital motion of a rotor subject to leakage air flow through an interlocking seal

A nonlinear mathematical model for orbital motion of the rotor under the influence of leakage flow through a labyrinth seal was established in the present study. An interlocking seal was chosen for study. The rotor–seal system was modeled as a Jeffcot rotor subject to aerodynamic forcing induced by the leakage flow. Particular attention was placed on the serpentine flow path by spatially separating the aerodynamic force on the rotor surface into two parts, e.g., the seal clearance and the cavity volume. Spatio-temporal variation of the aerodynamic force on the rotor surface in the coverage of the seal clearance and the cavity volume was delineated by using the Muzynska model and perturbation analysis, respectively. The governing equation of rotor dynamics, which was incorporated with the aerodynamic force integrated over all seal clearances and cavity volumes, was solved by using the fourth-order Runge–Kutta method to obtain the orbit of the whirling rotor. Stability of the rotating rotor was inspected using the Liapunov first method. The results convincingly demonstrate that the destabilization speed of the rotor was reduced due to the aerodynamic force induced by the leakage flow through the interlocking seal. The nonlinear analysis method proposed in the present study is readily applied to dynamics of various rotor–seal systems with labyrinth seals.     

迷宫密封转子系统非线性动力稳定性的研究

研究迷宫密封对转子系统动力稳定性的影响，迷宫密封的气动力采用Muszynska非线性力模型，计算了单盘Jeffcott转子非线性动力学特性。对Jacobi矩阵的分析表明，在密封力的影响下，转子达到一定转速后开始失稳，发生Hopf分岔，进入周期涡动状态，涡动幅度随转速的提高而增大，提高到一定程度，密封和转子发生碰摩，采用Runge-Kutta法数值模拟了转子的轴心轨迹。最后分析了迷宫密封的物理和结构参数对系统运动特性的影响。     

The effect of tangential elasticity of the contact layer between stator and rotor in travelling wave ultrasonic motors

In travelling wave ultrasonic motors the elliptical motion of material points of the stator drives the rotor due to frictional mechanisms. The motor characteristic strongly depends on the mechanical properties of the components stator, rotor and contact layer. In order to predict the motor behaviour, a model for the contact between stator and rotor has been developed. The goal of the present paper is to point out the importance of the tangential elasticity of the contact layer which is responsible for the formation of stick zones and also for the amount of friction losses and overall efficiency. Therefore a comparison with a model with a contact layer rigid in tangential direction is given. Based on a visco-elastic foundation model for the contact layer, torque-speed curves as well as torque-efficiency curves are computed. Experimental investigations for identification of parameters, check of assumptions and model validation are carried out. Finally, the model is used to show the results of parameter variations for normal force, vibration amplitude and modulus of elasticity of the contact layer.     

Computation of rotordynamic coefficients associated with leakage steam flow through labyrinth seal

A mathematical model of calculating rotordynamic coefficients associated with leakage steam flow through labyrinth seals was presented. Particular attention was given to incorporating thermal properties of the steam fluid into prediction of leakage flow and subsequent derivation of rotordynamic coefficients, which quantitatively characterize influence of aerodynamic forcing of the leakage steam flow on the rotordynamics. By using perturbation analysis, we determined periodic and analytic solutions of the continuity and circumferential momentum equations for the time-dependent flow induced by non-axisymmetric rotation of the rotor encompassed by a labyrinth seal. Pressure distributions along labyrinth seal cavities and rotordynamic coefficients were compared at the same condition for air and steam flows. Influence of steam flow through the labyrinth seal cavities on rotordynamic coefficients was analyzed in terms of inlet pressure, inlet swirl velocity and rotor speed.     

PEEK旋转密封环密封性能仿真和试验研究

为研究低刚度胀圈型旋转密封环的接触状态和密封性能,以聚醚醚酮(PEEK)材料的无槽环和V形槽环两种密封环为研究对象,基于COMSOL有限元软件建立了旋转密封流固耦合模型,对密封状态进行了模拟分析,并在试验台上测试了密封环的摩擦转矩和漏率. 仿真结果表明:在载荷作用下,密封环的变形显著影响密封面接触压力和流体压力分布. 试验结果表明:由于槽区流体的静压承载作用,V形槽环的摩擦转矩比无槽环小40%左右,但由于端面开槽减小了局部径向密封宽度,V形槽环漏率比无槽环大10%左右. 另外,两种环的摩擦转矩随转速增加均没有下降趋势,说明在试验条件下密封面动压减摩效果不显著. 研究结果有助于进一步认识胀圈型旋转密封环的密封机理,指导新型密封环的设计.      

Influence of steam leakage through vane,gland, and shaft seals on rotordynamics of high-pressure rotor of a 1,000 MW ultra-supercritical steam turbine

A comparative analysis of the influence of steam leakage through vane, gland, and shaft seals on the rotordynamics of the high-pressure rotor of a 1,000 MW ultra-supercritical steam turbine was performed using numerical calculations. The rotordynamic coefficients associated with steam leakage through the three labyrinth seals were calculated using the control-volume method and perturbation analysis. A stability analysis of the rotor system subject to the steam forcing induced by the leakage flow was performed using the finite element method. An analysis of the influence of the labyrinth seal forcing on the rotordynamics was carried out by varying the geometrical parameters pertaining to the tooth number, seal clearance, and inner diameter of the labyrinth seals, along with the thermal parameters with respect to pressures and temperatures. The results demonstrated that the steam forcing with an increase in the length of the blade for the vane seal significantly influences the rotordynamic coefficients. Furthermore, the contribution of steam forcing to the instability of the rotor is decreased and increased with increases in the seal clearance and tooth number, respectively. The comparison of the rotordynamic coefficients associated with steam leakage through the vane seal, gland seal, and shaft seal convincingly disclosed that, although the steam forcing attenuates the stability of the rotor system, the steam turbine is still operating under safe conditions.     

Whirling frequencies and amplitudes due to deviations of generator shape

Earlier measurements in large synchronous generators indicate the existence of backward whirling motion, and also relatively large deviations of shape in both the rotor and the stator. These non-symmetric geometries produce an attraction force between the rotor and the stator, called unbalanced magnetic pull (UMP). The target of this paper is to analyse the whirling frequencies and amplitude of the response for large synchronous generators with a high number of poles, due to deviations of shape in the rotor and stator. A mathematical model is developed to describe the shapes of the rotor and stator, and the corresponding UMP is obtained by using the law of energy conservation. The UMP is analysed due to different deviations of shape. The result gives the average angular frequency and the magnitude of the UMP for certain deviations of shape. From this result, the whirling frequency and the amplitude of the corresponding response can be approximated. Simulations of the response of a Jeffcott rotor model show good agreement with the theoretical results of the UMP for some generator geometries. The conclusion is that different whirling frequencies, both backward and forward whirling, can occur in these machines due to deviations in shape of the generator. Therefore, the shape of the generator can excite resonance vibrations on several other frequencies than the rotation frequency. During maintenance of hydropower generators the shapes of the rotor and stator are frequently measured. The results from this paper can be used to evaluate such measurements and to explain the existence of complicated whirling motion.     

Magnetic field effects on the nonlinear vibration of a rotor

The nonlinear vibration of a rotor operated in a magnetic field with geometric and inertia nonlinearity is investigated. An asymmetric magnetic flux density is generated,resulting in the production of a load on the rotor since the air-gap distribution between the rotor and the stator is not uniform. This electromagnetic load is a nonlinear function of the distance between the geometric centers of the rotor and the stator. The nonlinear equation of motion is obtained by the inclusion of the nonlinearity in the inertia, the curvature, and the electromagnetic load. After discretization of the governing partial differential equations by the Galerkin method, the multiple-scale perturbation method is used to derive the approximate solutions to the equations. In the numerical results, the effects of the electromagnetic parameter load, the damping coefficient, the amplitude of the initial displacement, the mass moment of inertia, and the rotation speed on the linear and nonlinear backward and forward frequencies are investigated. The results show that the magnetic field has significant effects on the nonlinear frequency of oscillation.     

Local convective heat transfer for laminar and turbulent flow in a rotor-stator system

Abstract The aim of this work is to show a better comprehension of the flow structure and thermal transfer in a rotor-stator system with a central opening in the stator and without an airflow imposed. The experimental technique uses infrared thermography to measure the surface temperatures of the rotor and the numerical solution of the steady-state heat equation to determine the local heat transfer coefficients. Analysis of the flow structure between the rotor and the stator is conducted by PIV. Tests are carried out for rotational Reynolds numbers ranging from 5.87×10⁴ to 1.4×10⁶ and for gap ratios ranging from 0.01 to 0.17. Analysis of the experimental results has determined the influence of the rotational Reynolds number, the gap ratio and systems geometry on the flow structure, and the convective exchanges in the gap between the rotor and the stator. Some correlations expressing the local Nusselt number as a function of the rotational Reynolds number and the gap ratio are proposed.     

核主泵用双锥度端面流体静压机械密封热弹流效应研究

针对核主泵用双锥度端面流体静压型机械密封热弹流效应研究在高压和高速条件下,其密封性能易受端面热弹变形影响的特点,提出了收敛型双锥面流体静压型机械密封,并建立了热-流-固耦合数学模型;通过采用有限差分法求解端面温度和端面流体膜压的控制方程组,采用有限元法求解密封环的热、弹变形,对密封进行了流、固、热耦合分析,研究了热弹变形对密封性能的影响,并对单锥面和双锥面2种流体静压型机械密封的密封性能、温度分布进行了对比研究.结果表明:双锥面密封与单锥面密封相比,不仅稳定性更好,而且端面温度分布更均匀,可靠性更高,但是泄漏率略有上升;在泄漏入口处即高压侧,外锥面锥度的大小对开启力影响较大,而在泄漏出口处即低压侧,内锥面锥度的大小对泄漏率影响较大;内锥面宽度比取0.05左右时能获得较大的刚漏比.     

仿特斯拉阀结构新型槽端面干气密封的数值研究

基于特斯拉阀结构的单向导通特性,提出一种集聚点更多和高压区域面积更大的新型(特斯拉阀型)干气密封槽型结构,该结构可获得比经典对数螺旋槽型更佳的密封效果. 通过建立特斯拉阀密封槽型的几何模型和数学模型,采用Fluent软件对不同几何参数和工况参数的密封性能进行系统数值仿真,获得密封开启力、气膜刚度和泄漏量等稳态性性能参数及瞬态膜压波动幅值方差. 分析了主阀道、支阀道和阀槽半径等参数对密封性能的影响规律,对比研究对数螺旋槽与特斯拉阀槽型在不同工况条件下的性能特性. 结果表明:相较于经典对数螺旋槽,同一工况下的特斯拉阀槽型具有更佳的开启力和刚度特性,尤其在高速、高压、小膜厚和大槽深时的开启力提升效果更加显著;在干气密封气膜稳定运行区间(h=3~6 μm),特斯拉阀槽型的气膜刚度较螺旋槽提升近20%;在高转速时(N>30000 r/min),特斯拉阀槽型的稳定性更好,且具有更小的压力波动.      

Non-Linear Dynamics of a Rotor-Bearing-Seal System

The non-linear dynamic behaviors of a rotor-bearing-seal coupled system are investigated by using Muszynska’s non-linear seal fluid dynamic force model and non-linear oil film force, and the result from the numerical analysis is in agreement with the one from the experiment. The bifurcation of the coupled system is analyzed under different operating conditions. It is indicated that the dynamic behavior of the rotor-bearing-seal system depends on the rotation speed, seal clearance and seal pressure of the rotor-bearing-seal system. The system state trajectory, Poincaré maps, frequency spectra and bifurcation diagrams are constructed to analyze the dynamic behavior of the rotor center. Various non-linear phenomena in the coupled system, such as periodic motion and quasi-periodic motion are investigated. The results show that the system has the potential for chaotic motion. The study may contribute to a further understanding of the non-linear dynamics of such a rotor-bearing-seal coupled system.     

Nonlinear dynamics of a Jeffcott rotor with torsional deformations and rotor-stator contact

The dynamics of a modified Jeffcott rotor is studied, including rotor torsional deformation and rotor-stator contact. Conditions are studied under which the rotor undergoes either forward synchronous whirling or self-excited backward whirling motions with continuous stator contact. For forward whirling, the effect on the response is investigated for two commonly used rotor-stator friction models, namely, the simple Coulomb friction and a generalized Coulomb law with cubic dependence on the relative slip velocity. For cases with and without the rotor torsional degree of freedom, analytical estimates and numerical bifurcation analyses are used to map out regions in the space of drive speed and a friction parameter, where rotor-stator contact exists. The nature of the bifurcations in which stability is lost are highlighted. For forward synchronous whirling fold, Hopf, lift-off, and period-doubling bifurcations are encountered. Additionally, for backward whirling, regions of transitions from pure sticking to stick-slip oscillations are numerically delineated.     

非稳态非线性油膜力作用下柔性轴裂纹转子的动力特性分析

分析了在动载轴承非稳态非线性油膜力作用下，具有横向裂纹柔性轴Jeffcott转子在非线性涡动影响下的动力特性。通过数值计算表明，在油膜失稳转速前，随着裂纹轴刚度变化比的增大，系统在低转速区域内具有丰富的非线性动力行为，出现倍周期分叉及混沌现象，涡动振幅随转速升高而减小，直到非稳态非线性油膜失稳，在无裂纹转子油膜临界失稳点处发现了类Hopf分叉现象，系统运动由平衡变为拟周期运动；裂纹转子在油膜临界失稳时的系统运动亦为拟周期运动，裂纹转子轴刚度变化对油膜失稳点及油膜失稳之后转子的运动影响不大，转子系统作拟周期运动。     

非接触式气体润滑密封变形的数值分析

针对离心泵用非接触式螺旋槽气体润滑密封，通过采用有限元法求解描述密封端面间气体流动的雷诺方程，计算了不同约束、不同结构的静密封环和配对动密封环的力变形、端面泄漏量、开启力及气膜刚度等参数，分析了变形对密封特性的影响．结果表明：密封环的力变形使得端面气膜形状大多呈发散型，约束对其变形大小具有重要影响，选择合适的约束可以减小密封面转角、提高气膜刚度、增强密封工作稳定性；变形对密封的开启力影响不大，但变形导致泄漏量增大，并明显改变气膜刚度。     

Stator well flows in axial compressors

This paper reports a study of the flow conditions in spaces often found beneath the stationary blades of modern compressors – stator wells. The design of the stator wells in a modern high-pressure turbofan can be a limiting factor. This study shows good comparison with existing experimental data upon the pressures and velocities in related geometries. The deleterious effects upon machine performance of the flows between the stator well and the mainstream are considered. The purpose of this paper is to show that these effects, especially seal leakage, can be reduced by the incorporation of fins on the rotating component of the downstream well. This works by increasing the tangential velocity in this region, so reducing the pressure there and thus the inter-well leakage for a given radial clearance in the intermediate labyrinth seal and hence the outflow into the mainstream from the upstream well.