Analytical study of the effect of a circumferential feeding groove on the unbalance response of a rigid rotor in a squeeze film damper

In recent years, a series of researchers have shown that a circumferential feeding groove of a squeeze film damper (SFD) has an evident effect on the forces of fluid film in SFD. Therefore, the feeding groove also affects the dynamic responses of a rotor in SFD. The present work studies the effect of the feeding groove on the unbalance response of a rigid rotor in a squeeze film damper based on the film force models that include effects of the feeding groove and fluid inertia on dynamic characteristics of the fluid film in SFD. Comparisons with the published work show that the feeding groove increases the orbit radius of rotor whirling and affects the unbalance response of a rotor system. The effect of the feeding groove on the unbalance response is also related to the action of fluid inertia.     

Experimental force response of a grooved squeeze film damper

The effects of a circumferential feeding groove on the dynamic force response of a squeeze film damper are determined experimentally. Open end and sealed damper configurations are tested for different groove depths, Journal orbit radii, whirl frequency and fluid viscosity conditions. Significant levels of dynamic pressures are measured at the groove in dampers with groove depth-to-clearance ratios equal to 5 and 10. These pressures affect considerably the dynamic forces of the dampers tested. Large tangential (damping) forces are produced at the circumferential groove which contribute significantly to the damping characteristics of the test articles. For uncavitated lubricant conditions, radial forces of substantial magnitude are determined at the groove and at the thin film land where the squeeze film Reynolds numbers are typically less than 1.     

Analytical study on effect of a circumferential feeding groove on unbalance response of a flexible rotor in squeeze film damper

Of recent years, a series of researches have shown that a circumferential feeding groove of squeeze film damper (SFD) has evident effect on fluid film forces in SFD. Therefore, the feeding groove also affects dynamic responses of a rotor in SFD. Present work studies the effect of the feeding groove on unbalance response of a flexible rotor in SFD based on new film force models that include effects of the feeding groove and fluid inertia on dynamic characteristics of the fluid film in SFD. Compared with the published work, unbalance responses predicated under considering effect of the feeding groove on the dynamic characteristics in SFD are small, and rotor speed region for unbalance responses with multiple solutions is different, affecting the stability of a rotor system. And the effect of the feeding groove on the unbalance response is related to action of fluid inertia.     

Fluid forces in short squeeze-film damper bearings

This paper has studied influences of fluid inertia on fluid velocity profiles and provided an axial inertia velocity profile for short squeeze film damper bearings (SFDs) using as a starting point a simplified Navier–Stokes equation. The velocity profile reasonably represents influences of fluid inertia on fluid flow. From the inertia velocity profile, present work develops new theoretical models for fluid forces in cylindrical short SFDs. Published experimental work confirms that the new models for fluid forces are better than traditional short-SFD theory, especially for tangential force. The new models show that the damping coefficient for 2π film is related to fluid inertia.     

Force coefficients for a large clearance open ends squeeze film damper with a central feed groove: Experiments and predictions

The paper describes a large load squeeze film damper (SFD) test rig, details measurements of dynamic loads inducing circular orbits conducted on a large clearance (c=0.250 mm) open ends centrally grooved SFD, and presents the identified experimental SFD force coefficients for operation at three static eccentricities. The rig has a bearing cartridge supported atop four elastic rods and a stationary journal, 0.127 mm in diameter. The damper consists of two parallel film lands, 12.7 mm in length, separated by a central groove, 6.35 mm 9.5 mm in depth. In the journal, three equally spaced holes, 120° apart, supply a light lubricant into the central groove and squeeze film lands. The experimental SFD force coefficients are compared to test results obtained earlier for a damper with the same film land lengths but with a smaller clearance (c=0.140 mm) and against predictions obtained from an advanced physical model that accounts for the flow field in the central groove and the interaction with the adjacent film lands. Dynamic pressures in the film lands and in the central groove are (not) surprisingly of the same order of magnitude. The central groove affects the dynamic forced response of the test damper to generate large direct damping coefficients, ~3.5 times those derived from classical lubrication formulas. Experimental added mass coefficients are ~7.4 times the predictive classical values. Predictions from an advanced model correlate well with the test data when using a shallow groove depth. The measurements and analysis advance knowledge on the dynamic forced performance of SFDs, point out to the limited value of simplistic predictive formulas, and validate the accuracy of a modern predictive tool.     

挤压式磁流变液阻尼器--转子系统的动力学特性与控制

用磁流变液代替常规挤压油膜阻尼器的润滑油,可制成阻尼特性受磁场控制的挤压油膜阻尼器,用于转子系统的振动控制。依据Bingham模型推导了磁流变液挤压油膜的雷诺方程及其解的表达式,给出了油膜流速、压力分布、油膜反力和阻尼器内磁拉力等的计算公式;以磁流变液阻尼器—刚性转子系统为例,理论分析了挤压油膜的力学特性和转子系统的不平衡响应特性;设计和制造了一种用于转子振动控制的挤压式磁流变液阻尼器;试验研究了支承在该阻尼器上的单盘偏置柔性转子系统的不平衡响应特性和控制方法。研究表明,磁拉力可降低一阶临界转速和临界振幅;油膜反力可降低转子系统在无阻尼临界转速处的振幅,并使一阶有阻尼临界转速增大;通过开关控制能使阻尼器具有最佳的减振效果,使转子振幅在全转速区达到最小。     

Hydraulic Squeeze Bearing

Prior researchers find that: Where one of two horizontal parallel plates immersed in a fluid is forced to oscillate up and down, a load may be carried, providing the fluid is compressible. Application of Reynolds equation to such a squeeze film bearing supports the condition of compressibility.

However, analysis of the squeeze film bearing, including inertia terms in the Navier-Stokes equations, removes the restriction on compressibility.

Theoretical design of a hydraulic squeeze bearing driven sinusoidally shows that load capacity is improved over a similar gas squeeze bearing under usual design conditions, provided cavitation is prevented. Two cases are considered of a fixed and a free bearing. Torque, work input, and the effects of centrifugal force are analysed.     

Investigation into the effect of piston ring seals on an integrated squeeze film damper model

This research presents an advanced squeeze film damper model that integrates piston ring seal geometry, fluid inertia, and film cavitation to study their combined features. The configuration of the piston ring seal is inspected, and different sealing scenarios are discussed. The flow rate in the seal arrangement is determined on the basis of the pressure gradient according to thin film theory. Moreover, the governing equation for the flow in the film land that considers fluid inertia is solved using the linear complementarity problem method to address the cavitation phenomenon. Validation is performed by comparing the model prediction with long bearing and short bearing models under different seal dimensions. Results show that an oversized gap in the seal grooves and a large frictional coefficient may lock the piston ring seal in the seal groove and thus reduce seal efficiency.

     

On the vibration of rotor-bearing system with squeeze film damper in an energy storage flywheel

The permanent magnetic bearing and the small-sized hydrodynamic spiral groove bearing are utilized as supports for the rotor of the energy storage flywheel system. The hydrodynamic bearing and the squeeze film damper do not need the oil cycle to remove the heat caused by friction because the friction loss is small. The linear dynamics model with four degrees of freedom is built to describe the vibration of the flywheel rotor-bearing system. The squeeze film dampers show good behavior in suppressing the vibration and improving the stability of the rotor-bearing system. The analytical solution of the dynamic characteristic coefficients of the squeeze film is achieved from Reynolds equation after some simplifications are taken. The numerical computation shows that the moment unbalance excites larger vibration of the rotor than the force unbalance. The upper damper plays an important role in helping the rotor pass its critical speed. The damping coefficient of the squeeze film dampers should be selected carefully. The flywheel arrived at the speed of 39,000 rpm and stored the energy of 308 Wh in the experiment. The calculated unbalance response is compared to the test response of the rotor storing quantities of kinetic energy. The comparison indicates that the dynamics model of the rotor-bearing-damper system is appropriate.     

Damping and added mass coefficients for a squeeze film damper using the full 3-D Navier-Stokes equation

Direct and cross-coupled damping coefficients are developed for the 2π-film, π-film (Gumbel cavitation condition) and homogeneous two-phase mixture films in a squeeze film damper. The numerical simulation uses the CFD-ACE+ commercial software, which employs a finite volume method for the discretization of the Navier-Stokes equations (NSE). In order to determine the dynamic coefficients, the NSE is combined with a finite perturbation method applied to the ‘equivalent journal’ of the damper. It was found that for the 2π-film and the Gumbel conditions, the damping coefficients exhibit linear characteristics, while the homogeneous cavitation model yields nonlinear coefficients. Using the CFD-ACE+, the inertia/added mass coefficients are derived for the limiting cases of the short and long dampers, respectively. The first set of forces is calculated by setting the fluid density to its actual value. The second set of forces is calculated when the density of the fluid is set close to zero (1E-10 kg/m³), thus practically eliminating the effects of the inertia terms. Subtracting the two sets of forces from each other, allows the determination of the inertia component contribution and the corresponding inertia coefficients. By varying the density, dynamic viscosity and whirling speed, it was found that the inertia coefficients follow a single curve represented by a function dependent on the modified Reynolds number, Re*. The inertia coefficients presented in this study are compared with the ones reported by other researchers that used the modified Reynolds equation. Some differences were found between the NSE based results and the Reynolds equation based outcomes. This is attributed to the three-dimensional effects introduced by the totality of the terms comprised in the full NSE.     

挤压油膜阻尼器—滑动轴承—刚性转子系统的动力学建模

对挤压油膜阻尼器－滑动轴承－刚性转子系统的动力学模型进行了研究。提出在这一强非线性系统中,对于流体变化较大的挤压油膜层应考虑惯性力的影响,采用紊流短轴理论来分析;对于流体变化较小的滑动轴承油膜层,采用层流长轴理论来分析。文中从运动流体的动量微分方程及其质量连续性方程出发,推导出油膜层考虑惯性力的影响条件下的紊流压力分布函数。在模型的建立过程中,还考虑了旋转机械中出现的外界阻尼力、间隙激励力、外界异频干扰力和外界静态载荷。这对进一步研究系统的动力特性有一定的裨益。     

Synchronous steady state response of an overhung rotor with squeeze film damping

An analytical method is developed for treatment of a typical system in which the outrigger bearing of an overhung rotor is provided with a squeeze film damper supported in a flexible casing. The rotor and stator of multiple degrees-of-freedom are handled with convenience by a “polar receptance matrix” method. A characteristic equation is derived which governs rotor-stator interaction either with dry contact or through a squeeze film damper. For the nonlinear squeeze film action solutions based on “mobility” information of a dynamically loaded journal bearing are obtained facilitating a general approach. A computer programme is written in Fortran for steady state response of the system in terms of whirl, position and force vectors, trial runs of which indicate complex behaviour of a squeeze film damped system.     

A Three-Dimensional Navier-Stokes-Based Numerical Model for Squeeze Film Dampers. Part 2—Effects of Gaseous Cavitation on the Behavior of the Squeeze Film Damper

The damping coefficients for a squeeze film damper (SFD) were determined and discussed in Part 1 using the full Navier-Stokes equations (NSE) coupled with a homogeneous cavitation model. In this continuation, Part 2, article these coefficients are introduced into the governing equations of motion to determine the trajectory of the rotor and its stability. The nonlinear response of the damper predicted by the NSE model is compared to results obtained from the application of the Reynolds equation. The influences of gas mass concentration as well as that of the amount of imbalance on transmissibility and eccentricity of the damper are also investigated.     

Effects of fluid inertia and viscoelasticity on squeeze film bearing forces at large vibration amplitudes

An approximate analytical solution is presented for squeeze film damper forces, which accounts for the effects of fluid inertia and viscoelasticity, in the short bearing case. An earlier “exact” solution for infinitesimal oscillation amplitudes is extended to finite amplitudes using the Rivlin-Ericksen second-order fluid. The governing equations are linearized using an Oseen-type approximation and the resulting partial differential equation is solved by approximating variable coefficient terms to obtain a periodic solution. Although the method is applicable for arbitrary periodic shaft motion, results are computed for the non-cavitating (2π) bearing, in which the shaft performs circular centered orbits. Large discrepancies from lubrication theory are found, particularly with regard to phase-shifting (cross-coupling) behavior between the forces and the imposed motion. Results are presented in terms of the Reynolds and Deborah numbers over ranges which are applicable to many practical lubrication problems.     

Effects of fluid inertia forces on the squeeze film characteristics of conical plates—ferromagnetic fluid model

On the basis of the Shliomis ferromagnetic fluid model, this paper is mainly concerned with the influences of convective fluid inertia forces in magnetic fluid‐based conical squeeze film plates in the presence of external magnetic fields. By applying the averaged momentum principle, a lubrication equation governing the film pressure is derived. Some previous contributions can be obtained from special cases of the present studies. Comparing with the non‐inertia non‐magnetic case, better squeeze film performances are predicted for the magnetic fluid‐based conical plates operating with a larger value of the inertial parameter of fluid inertia forces, the volume concentration of ferrite particles and the strength of applied magnetic fields. Some numerical results with specific cone angles are also provided in tables for engineering applications. Copyright © 2012 John Wiley & Sons, Ltd.     

整体式挤压油膜阻尼器对管道振动抑制试验

针对管道振动现象,设计了一种整体式挤压油膜阻尼器并分析其刚度影响规律。利用SAP2000软件模拟仿真阻尼减振效果。搭建二维门型管道振动试验台,在管道上安装整体式挤压油膜阻尼器,研究整体式挤压油膜阻尼器控制管道振动的影响规律。结果表明：整体式挤压油膜阻尼器安装在激振源处且与激振力平面平行时的减振效果最佳,较原始振动降幅达51.83%;安装在激振源处且与激振力平面垂直时的减振效果最差;安装两个整体式挤压油膜阻尼器减振效果优于安装一个整体式挤压油膜阻尼器;安装在激振源处的减振效果优于安装在远离激振源的效果。     

A Three-Dimensional Navier-Stokes–Based Numerical Model for Squeeze-Film Dampers. Part 1—Effects of Gaseous Cavitation on Pressure Distribution and Damping Coefficients without Consideration of Inertia

Even though most published results detailing damper behavior consider only the liquid phase, the cavitation process in the lubricant film, when it happens, is critical for the damper's performance. A number of modeling approaches, such as the half-Sommerfeld and Elrod models, were proposed in order to account for the effects of cavitation on the pressure generation, without directly simulating the cavitation process. Based on the experimental data, a few other homogeneous cavitation models have also been developed. All these models are based on the classical Reynolds equation. In this article, a three-dimensional numerical model is developed and validated in connection with the operation of a two-phase squeeze-film damper. The full Navier-Stokes equations (NSE), coupled with a homogeneous cavitation model, is solved to simulate the flow of the two-phase lubricant film and the associated pressures. The pressure variation on the journal surface and the gas concentration distribution in the lubricating fluid (cavitated region) will be presented. The damping coefficients predicted by the NSE model are compared to the ones that resulted from the application of the Reynolds equation.     

Evaluation of various fluid-film models for use in the analysis of squeeze film dampers with a central groove

Experimental vibration responses of squeeze film dampers (SFDs) are obtained with four different central groove depths, two types of lubricant and various unbalance levels. Highly non-linear fluid stiffness and damping are observed, the damping being sensitively related to oil viscosity and unbalance. Existing oil film models are applied to predict the SFD behaviour. A special groove-two land model is able to predict the vibration behaviour of a very shallow grooved SFD and the conventional two-land theory is applicable to a SFD with a very deep groove. These observations provide useful guidelines for designing a shallow or deep grooved SFD-rotor assembly.     

Fluid inertia force effects in hydromagnetic sphere-plate squeeze films

This paper investigates the influences of fluid inertia forces in hydromagnetic sphere-plate squeeze films. Applying the averaged inertia principle, a megnetohydrodynamic pressure gradient equation has been derived. From the results obtained, the combined effects of fluid inertia forces and electrical conducting fluids in the presence of external magnetic fields provide better squeeze film characteristics, and lengthen the operating life of the sphere-plate system as compared to the non-inertia non-conducting-fluid case.