Influence of the Mechanical Seals on the Dynamic Performance of Rotor–Bearing Systems

In this paper, to consider the effects of mechanical seals, a lumped-mass model and the transfer matrix method are used to establish the equations for the dynamics performance of rotor bearing system. The general inverted iteration method is also used to solve the eigenvalue problem of these equations. To check the response of the rotor bearing system under unbalance motivation, the Gauss method is used to calculate the dynamic response of the constrained vibration. The results, based on the dynamic properties calculation of a typical mechanical spiral seal, such as stiffness coefficients and damping coefficients, exert the influence of the mechanical seal on the rotor bearing system of the high-speed machinery. Meanwhile, some structure parameters that may affect the dynamic performance and forced vibration under unbalance motivation of the rotor bearing system considering mechanical seals are analyzed in the paper. The analysis results show that the mechanical seal more or less has effects on the rotor bearing system. The mechanical seal has much more effects on the flexible rotor bearing system than on the rigid one. For instance, in a certain case, if the effects of the mechanical seal were taken into account, the system s critical speed may increase by 70 80%.     

Numerical techniques for computing nonlinear dynamic characteristic of rotor-seal system

A transient CFD procedure to compute the nonlinear dynamic characteristic of the coupled rotor-seal system was presented in this study. In each time step, the displacement diffusion model was implemented to govern the mesh deformation, and the URANS (Unsteady Reynolds averaged Navier-Stokes) equations were solved to obtain the transient fluid force on the rotor surface for the free vibrations. With the obtained fluid force from the CFD solver, the nonlinear equations of motion for a simplified rotor-seal system were numerically solved on the basis of external user defined routines. During each transient time step, the computed fluid force from the CFD solver and the rotor motion from the user defined routines were transferred to each other timely. The rotor center trajectories, frequency spectrum and projection of Poincaré section were calculated to investigate the nonlinear dynamic performance of the single disk rotor-seal system. The effects of the rotational speed and pressure ratio on the vibration characteristic of the rotor-seal system were analyzed by the bifurcation theorem. The results show that the coupled rotor-seal system experiences a period-one motion, resonance, periodic-doubling motion, quasi-periodic motion, and finally possible chaotic motion as the rotor speed increases. The pressure ratio has pronounced effect on the frequency response of the first-order critical speed; however, it has little influence on the motion state as well as the frequency response of the rotating speed. Although a constant-clearance annular smooth stator seal was selected as the research object in the current paper, the presented transient CFD method is still available for other complex annular seals, such as labyrinth seal, honeycomb seal, pocket damper seal, etc.     

A new transient CFD method for determining the dynamic coefficients of liquid annular seals

Currently, the dynamic characteristics of annular seals are numerically investigated mainly by solving the bulk flow equations using perturbation method, or by simulating the perturbed flow field of annular seal using CFD method. The adopted disturbance way is generally the circular whirling motion of rotor around seal centre with constant speed. Relative to the transient CFD simulation, the quasisteady CFD simulation introducing Moving reference frame (MRF) has been widely used by researchers. Both the dynamic mesh problem and the time-consuming problem suppress the use of transient CFD simulation in annular seal research. In the paper, a new transient CFD method based on rotor’s variable-speed whirl is presented to improve the time-consuming problem and all the (total 20) dynamic coefficients of concentric liquid seal can be obtained by only two transient CFD simulations, one for the variable-speed cylindrical whirl and the other for the variable-speed conical whirl. The results are compared with those from the experiment, the quasi-steady CFD method and the traditional transient CFD method based on constant-speed whirl. The comparisons show that the new transient method can keep the good accuracy of traditional transient method and meantime largely save the computational time.     

间隙环流中同心涡动转子动特性的研究

考虑轴向流动因素的影响，采用紊流整体流动模型和Moody壁面摩擦系数方程，建立间隙环流3D非线性微分方程，运用摄动法和线性振动理论分析求解间隙环流中同心涡动转子动特性系数。实例计算结果表明，间隙环流中同心涡动转子动特性系数与间隙的大于有关，同时分析轴向压差、壁面粗糙度、长径比及入口预旋等参数对大、小间隙环流中同心涡动转子的动特性系数的影响。     

Bulk-Flow Model for the Transition to Turbulence Regime in Annular Pressure Seals

An analysis for the prediction of the dynamic force response for annular seals in the transition regime to flow turbulence is presented. A heuristic curve fit connects the laminar friction factor to Moody's turbulent friction factor curve in the transition regime from laminar to fully developed turbulent flows. A universal friction factor model is provided and included in the bulk-flow equations (zeroth- and first-order) governing the flow for small amplitude rotor motions about an equilibrium position. General equations are presented for the shear coefficients and their derivatives required in the bulk-flow model. Flow rates, drag torque and rotordynamic force coefficients are compared with those from traditional analyses for an annular seal experiencing wear and increased clearances leading to off-design operating conditions. Predicted seal force coefficients show physically sound, smooth variations while passing through the transition zone and demonstrate a marked improvement over simpler models which predict sharp discontinuities.     

离心泵密封口环动力学特性系数计算

本文根据Ｈｉｒｓ的紊流整体流动理论,研究了离心泵间隙密封的动量方程式,在此基础上,推导了计算动力学系数的微分方程组,进行了数值求解并对计算结果进行了分析比较。     

Numerical simulation of rotordynamic coefficients for eccentric annular-type-plain-pump seal using CFD analysis

Annular seals are primarily used to control the leakage in turbomachinery, such as pumps. Consequently, annular seals substantially affect the stability of turbomachinery. Designing the annular seals of high performance pumps require the accurate prediction of the seal’s leakage flow rate and rotordynamic coefficients. The bulk-flow model is the traditional means for leakage flow rate analysis and predictions. Bulk-flow analysis is based on the Hirs’ lubrication equation, which simplifies the Navier-Stokes equation. However, the analysis of the bulk-flow model requires a great amount of time to develop an analysis code. Furthermore, the code possesses many constraints for analyzing seals with complicated shapes. 3D CFD simulations provide faster and less expensive estimates of the flow field for a wide variety of operating parameters and flow conditions. In this study, the flow field and the rotordynamic coefficients of a plain-eccentricannular seal were simulated with circular whirl orbits using 3D CFD code. A relative coordinate system was defined to calculate the 3D velocity profile and the dynamic pressure distribution of the seal clearance for each rotor whirling speed. The rotordynamic coefficients were determined by reaction forces of seal fluid, which were calculated by integrating the dynamic pressures to the whole area of seal. The results from our analyses were compared to existing theoretical calculations as well as compared to results acquired from experiments. The present 3D CFD results of leakage and rotordynamic coefficients of K and C showed better improvement in prediction.     

Influence of the Mechanical Seals on the Dynamic Performance of Rotor-Bearing Systems

In this paper, to consider the effects of mechanical seals, a lumped-mass model and the transfer matrix method are used to establish the equations for the dynamics performance of rotor-bearing system. The general inverted iteration method is also used to solve the eigenvalue problem of these equations. To check the response of the rotor-bearing system under unbalance motivation, the Gauss method is used to calculate the dynamic response of the constrained vibration. The results, based on the dynamic properties calculation of a typical mechanical spiral seal, such as stiffness coefficients and damping coefficients, exert the influence of the mechanical seal on the rotor-bearing system of the high-speed machinery. Meanwhile, some structure parameters that may affect the dynamic performance and forced vibration under unbalance motivation of the rotor-bearing system considering mechanical seals are analyzed in the paper. The analysis results show that the mechanical seal more or less has effects on the rotor-bearing system. The mechanical seal has much more effects on the flexible rotor-bearing system than on the rigid one. For instance, in a certain case, if the effects of the mechanical seal were taken into account, the systems critical speed may increase by 70–80%. Translated from Journal of Xi’an Jiaotong University, 2004, 38(7)     

大间隙环流中刚支转子系统振动特性研究

基于Myklestad传递矩阵法．建立了大间隙环流中转子系统的运动方程，采用数值方法分析转子系统的振动特性。数值计算结果表明，由于大间隙环流的流固耦合作用，使转子系统的固有频率、阻尼临界转速、稳定性和不平衡响应均发生了不同程度的变化。数值计算结果与已有的解析分析和实验结果有较好的一致性。     

A trigonometric series expansion based method for the research of static and dynamic characteristics of eccentric seals

Static and dynamic characteristics of labyrinth seals are important in the prediction of the stability of turbomachinery. The paper presents an effective numerical method to predict the static and dynamic performance characteristics of seals at off-center conditions with different rotor whirling frequency. Modifications are introduced for the traditional turbulent bulk flow model to consider the circumferentially varying flow. A trigonometric series expansion method is used to approximate parameters such as pressure and velocity in seals cavity. Numerical simulations show that 8–10 series terms with 5–10 iterations are enough for the solution of this set of nonlinear equations. The resulting nonlinear algebraic equations can be solved rapidly. The analytical results are verified by comparison with the simulated CFD results. Parametric investigations showing the influence of eccentricity and whirling frequency on seals dynamics are also presented. The results show that the trigonometric series expansion based method gives an effective prediction of the static and dynamic characteristics of the eccentric seals.     

Nonlinear Numerical Prediction of a Rotor–Bearing System Using Damped Flexure Pivot Tilting Pad Gas Bearings

Flexure pivot tilting pad gas bearings with pad radial compliance (FPTPGB-Cs) and metal mesh dampers (MMDs) in parallel (FPTPGB-C-MMDs) have been considered for application to high-speed and high-performance turbomachinery because of their advantages of high effective damping level and adequate compliance with variations in rotor geometry or misalignment. Although the dynamic coefficients of FPTPGB-C-MMDs have been predicted using the linear method, a nonlinear study is urgently needed for their high nonlinear behavior. A nonlinear numerical investigation on the rotor–bearing system supported by FPTPGB-C-MMDs is presented in this study by using the time domain orbit simulation method that couples rotor motion equations, the unsteady Reynolds equation, and pad motion (considering MMDs) equations. The nonlinear predictions are verified by the prediction and experimental results of a published paper.FPTPGB-C-MMDs can effectively suppress the subsynchronous vibrations compared with the rotor system supported by FPTPGB-Cs. The prediction results show that a high damper mesh density has a more positive effect on improving the stability of the rotor system by reducing the subsynchronous vibrations. Investigation shows that MMDs can improve the ability of the rotor system to sustain the effect of destabilizing forces. A high damper mesh density can sustain large destabilizing forces. The simulation results also indicate that low pad radial stiffness or preload leads to high amplitudes of subsynchronous vibrations. A small clearance results in an increase in critical speed and its synchronous amplitude. Moreover, large clearance results in a wide speed range that leads to the occurrence of subsynchronous vibrations with large amplitudes.     

有限长大间隙环流中偏心转子动特性系数的简化分析方法

给出一种分析有限长大间隙环流中偏心转子动特性系数的简化数值分析方法。该方法基于有限长大间隙环流中同心转子的动特性系数计算了三维有限长大间隙环流中偏心转子的动特性系数。数值计算结果表明该方法行之有效。与已有的环压密封的其它数值计算结果和实验结果比较,该方法简单且具有较好的精度。     

转子系统动力特性分析

用传递矩阵法推导转子系统临界转速和动态不平衡响应的计算公式 ,用 MATL AB软件编写了相应的计算程序 ,用一个有理论解的例子对程序进行考核。对一模型悬臂转子进行了比较全面的分析 ,得出了转子系统的临界转速的变化规律。在此基础上对某实际火箭发动机转子系统的动力学特性进行了分析。研究了联轴器刚度、浮动环刚度等对转子特性的影响     

Numerical prediction of rotordynamic coefficients for an annular-type plain-gas seal using 3D CFD analysis

Annular-type gas seals in many types of compressors and turbines are designed to reduce leakage and enhance the vibrational stability of the turbo machinery. Many researchers have attempted precise theoretical evaluation of the leakage and the rotordynamic coefficients from reaction forces of small seal gaps. The Bulk-flow model, which is based on Hirs’ lubrication equation, is a general method with advantages of simplicity and short computing time. However, due to the disadvantage of the long time required to develop analysis code, and constraints from complicated seal shapes, CFD analysis is currently preferred. In the present, the method for determining the rotordynamic coefficients of an annular plain-gas seal, which is the simplest shape of gas seals, is suggested by extending the analysis of an annular plain-pump seal. A relative coordinate system for steady-state simulation is defined to calculate the compressible flow field and dynamic pressure distribution of the seal gap. The present analysis is verified by comparison with results acquired from Bulk-flow analysis code and published experimental results. The 3D CFD rotordynamic coefficients results of direct stiffness(K) and cross coupled stiffness(k) show better improvements in prediction.     

用双控制体模型计算直通式篦齿密封的动特性系数

用双控体模型计算直通式篦齿密封动特性系数,介绍单控体模型。通过理论计算与试验结果的对比,说明采用的双控体模型方法是可行的;分析了密封间隙、转速等对密封动特性系数的影响;用实例比较单控体模型和双控体模型的结果,得出一些有意义的结论。     

密封间隙力对泵转子临界转速的影响分析

随着给水泵的大功率化、高转速化的发展,为保证多级离心泵转子部件的平稳运转,避免其在接近其临界转速时产生共振,需要对设计中的转子进行干态、湿态下的临界转速计算.论文以5级离心给水泵为主要模型,采用有限元法分别计算其在干态、湿态下的临界转速,通过对比,得出密封间隙力对转子临界转速的影响.干态情况下,分别用邓克莱法和有限元法计算给水泵的一阶临界转速;湿态情况下,分别计算密封设计间隙及二倍间隙不同情况下的临界转速,对比结果,表明密封间隙力对泵转子临界转速的影响非常大,并且与密封间隙的大小密切相关.     

锅炉给水泵转子动力学参数的识别

利用摄动传递矩阵法，结合实验室的试验测试，对某电站锅炉给水泵转子的动力学参数进行识别。给出给水泵上的热装叶轮、轴套对转子刚度产生加强作用的具体数据，得到修正的给水泵转子系统动力学计算模型。把由修正模型计算得到的转子系统固有频率与实测的转子系统固有频率进行对比分析，取得了良好的效果。     

Stability analysis of a disk-spindle system supported by coupled journal and thrust bearings considering five degrees of freedom

This paper investigates the stability of a disk-spindle system supported by coupled journal and thrust bearings considering the five degrees of freedom of a rotor-bearing system. The Reynolds equations and their perturbed equations of the coupled bearings were solved by FEM to calculate the stiffness and damping coefficients. The critical mass of the rotor-bearing system was determined by solving the linear equations of motion. As a result, the tilting motion was a major design consideration to determine the stability of the rotor-bearing system. Additionally, the stability without the tilting motion was overestimated, as compared to that with the tilting motion.     

On the Dynamics of Lubricated Cylindrical Roller Bearings,Part II: Linear and Nonlinear Vibration Analysis

This article is the second part of two companion papers. In the first article, curve-fitted relations of stiffness and damping coefficients of a single roller-to-race contact of lubricated roller bearings were developed. In the present work, these relations are applied to a rotor–bearing system. Two cases are studied to investigate the influence of lubricated cylindrical roller bearings on the vibration characteristics of the rotor system. In the first case, lubricated contacts are simulated as a linear spring–damper model. The overall stiffness and damping matrices are calculated by using the dynamic coefficients of individual load sharing rollers. These matrices are used in the finite element analysis of flexible rotor. In the second case, the nonlinear structural vibration of a lubricated cylindrical roller bearing is studied. Equations of motion of bearing elements are derived using the Lagrange equation. A nonlinear load–deflection contact model developed through the derived curve-fitted relations of dynamic coefficients is used in the equations of motion. Equations of motion are solved by a fourth-order Runge-Kutta integration method. The response of bearing elements under free vibration and due to rotating unbalance is studied for damped and undamped cases. Furthermore, results obtained using elastohydrodynamic finite and infinite contact theories are compared.     

短密封动力学分析及计算

参考文献（１,２）利用紊流整体流动理论,考虑了惯性项的影响,对短密封的动特生系数等进行了详细地推导,并研制出计算程序,对短密封动特性系数进行精确计算。