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.     

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.     

新型挤压油膜阻尼器OSFD的理论研究

将O型环阻尼器与挤压油膜阻尼器组合使用，可以克服SFD设计中固有的缺陷，通过对刚性转子的不平衡响应分析表明，OSFD的设计既可以满足正常设计工况下的小不平衡量，又可以对较大的不平衡量起到良好的减振作用，从而扩大了阻尼器的适用范围，且结构简单，有利于广泛应用。     

Bifurcating behaviour of a rotor on two-lobe wave squeeze film damper

The dynamics of an unbalanced rigid rotor on squeeze film dampers with two-lobe wave bearings was examined by means of a bifurcation analysis based on numerical continuation and on the assumption of the rotor speed as bifurcation parameter. Further parameters in the study were the angular orientation of the bearing, the wave amplitude of the bearing profile and the gravity residual, while single values were given to the static unbalance and the characteristic bearing parameter. The analysis was necessarily restricted, owing to the multiplicity of quantities that affect the system dynamics. Yet, the obtained results put in evidence the way the two-lobe wave geometry influences the bifurcating behaviour of the system, modifying the length of some unstable branches and the whirling periodicity.     

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.     

Optimal design of a squeeze film damper using an enhanced genetic algorithm

This paper represents that an enhanced genetic algorithm (EGA) is applied to optimal design of a squeeze film damper (SFD) to minimize the maximum transmitted load between the bearing and foundation in the operational speed range. A general genetic algorithm (GA) is well known as a useful global optimization technique for complex and nonlinear optimization problems. The EGA consists of the GA to optimize multi-modal functions and the simplex method to search intensively the candidate solutions by the GA for optimal solutions. The performance of the EGA with a benchmark function is compared to them by the IGA (Immune-Genetic Algorithm) and SQP (Sequential Quadratic Programming). The radius, length and radial clearance of the SFD are defined as the design parameters. The objective function is the minimization of a maximum transmitted load of a flexible rotor system with the nonlinear SFDs in the operating speed range. The effectiveness of the EGA for the optimal design of the SFD is discussed from a numerical example.     

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.     

Improved identification of squeeze-film damper models for aeroengine vibration analysis

Numerical solution of the Reynolds equation imposes a prohibitive computational cost on the dynamic analysis of practical squeeze film damped turbomachinery. To surmount this problem, the present paper develops the use of Chebyshev polynomial fits to identify finite difference (FD) solution of the incompressible Reynolds equation. The proposed method manipulates the Reynolds equation to allow efficient and accurate identification in the presence of cavitation, the feed-groove, feed-ports, end-plate seals and supply pressure. The ability of Chebyshev polynomials to rapidly reproduce FD routines is demonstrated. The bearing models developed are experimentally proven to give more accurate results than alternative analytical bearing models.     

Directionally controllable squeeze film damper using liquid crystal

Liquid crystals (LC) are characterized by its phase, which appears as an intermediate state between crystalline solid and isotropic liquid. This intermediate, phase is caused by orientation of molecules, and it can be controlled by an externally applied electric or magnetic field. Subjected to an electric field, the viscosity of the LC varies according to the applied electric field strength, which is called the electroviscous effect. This paper describes an application study of the electroviscous effect of a LC to a controllable squeeze film damper (SFD) for a rotating machine. A prototype controllable SFD using a LC was constructed and its performance was studied. It should be noted that the present SFD can produce anisotropic damping force for a flexible rotor at the supporting position, which enables us to stabilize a flexible rotor in a wide range of its rotating speed.     

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.     

The damping capacity of the squeeze film damper in suppressing vibration of a rotating assembly

A flexible shaft with an overhung disc supported by the squeeze-film damper is investigated theoretically and experimentally. The system is simplified as a three-mass system based on a transfer matrix calculation. Governing equations for both models with and without retainer spring are derived. A fast integration method is used to obtain vibration responses. Both concentric and eccentric responses at the damper are examined. Different imbalances and different supply pressures are supplied to see their influence on the vibration of the system. It is found that for the system with retainer spring, positions of the resonance move between two extremes, one of which is the case with no damping in the system and the other with “full damping” where the SFD is locked-out and the system behaves exactly like one without a retainer spring. Therefore, improvements can be obtained by using a centralizing retainer spring and an accompanying SFD as resonance peaks can be moved to lower frequencies and/or such peaks can be kept down to reasonable limits. Nonlinear subharmonic and superharmonic responses are also found.     

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.     

Inertia effect in squeeze film air contact

The analysis presented in this paper explores the effect of air inertia on the squeeze film air contact operation and assesses the contribution of air inertia to the mechanism of squeeze film formation. Derivation of the Reynolds equation containing inertia term for squeeze film air contact is outlined. An average inertia concept is used in dealing with inertia force across the squeeze film thickness. Numerical iteration is used in solving for the non-linear inertia term in the modified Reynolds equation. Results are compared with the performance of the squeeze film air contact without inertia.     

Load-carrying capacity generation in squeeze film action

The mechanism of squeeze action is explored using results of numerical analyses and physical explanations. The relationship between the mean film force and the load the squeeze film could support is established. It is concluded that the high viscous resistance around the contact boundary is the source of squeeze air film build-up. Repeated compression and expansion of air contribute to the formation of unsymmetric pressure field and load-carrying capacity.     

Dynamic analysis of a rigid rotor supported by three-pad hydrostatic squeeze film damper lubricated with ferrofluid

This work describes an analytical study on the dynamic behaviour of a three-pad hydrostatic journal bearing lubricated with ferrofluids. Each pad is fed with an external pressure through a capillary restrictor-type hydraulic resistance. Ferrofluid or magnetic fluid is a colloidal dispersion of magnetic nano-particles in a carrier liquid. In this study, a non-linear method was performed using Jenkins model in order to investigate the effect of ferrofluids lubrication on the vibrations amplitude and the transmitted forces of hydrostatic squeeze film dampers. The results presented in this paper showed that the ferrofluid lubrication is useful in controlling the bearing vibrations and transmitted forces. The results illustrated in this work are expected to be quite useful to the bearing designers.     

液膜阻尼砂轮主轴运动系统建模

根据达朗贝尔原理建立了带挤压液膜阻尼器的内圆磨床砂轮主轴动力学模型，并对其进行了无量纲处理及便于仿真研究和分析。     

汽车动力传动系双质量飞轮式扭振减振器特性分析

分析几种典型双质量飞轮式扭振减振器的结构,对其工作原理进行详细阐述,着重研究四种典型双质量飞轮式扭振减振器的弹性特性和扭转刚度,对汽车动力传动系双质量飞轮式扭振减振器的选型和设计具有一定的参考价值.     

Optimal design of nonlinear squeeze film damper using hybrid global optimization technique

The optimal design of the squeeze film damper (SFD) for rotor system has been studied in previous researches. However, these researches have not been considering jumping or nonlinear phenomena of a rotor system with SFD. This paper represents an optimization technique for linear and nonlinear response of a simple rotor system with SFDs by using a hybrid GA-SA algorithm which combined enhanced genetic algorithm (GA) with simulated annealing algorithm (SA). The damper design parameters are the radius, length and radial clearance of the damper. The objective function is to minimize the transmitted load between SFD and foundation at the operating and critical speeds of the rotor system with SFD which has linear and nonlinear unbalance responses. The numerical results show that the transmitted load of the SFD is greatly reduced in linear and nonlinear responses for the rotor system.     

Network numerical analysis of hydromagnetic squeeze film flow dynamics between two parallel rotating disks with induced magnetic field effects

We study numerically the hydromagnetic squeeze film between two rotating disks using the numerical network simulation method. The external magnetic field, H, generates an induced magnetic field, B, with radial (B_r), tangential (B_θ) and axial (B_z) components between the two disks, which rotate with different angular velocities, Ω₁ and Ω₂, and at time t are separated by a distance D(1−αt)^1/2. The applied magnetic field at the lower disk is assumed to be zero. The conservation equations for mass, momentum and induced magnetic field are reduced to a set of ordinary differential equations using a series of transformations, in terms of four dependent variables, f (axial velocity), g (azimuthal velocity), m (axial magnetic field component) and n (azimuthal magnetic field component) and a single independent variable, η (dimensionless disk separation), with appropriate boundary conditions. The transformed ordinary differential equations have collective order of 10 and are shown to be controlled by rotational Reynolds number (R₁), squeeze Reynolds number (R₂=Re_m/Bt), dimensionless parameter based on the magnetic force in the axial direction (R₃), dimensionless parameter based on magnetic force strength in the azimuthal (tangential) direction (R₄), magnetic Reynolds number (Re_m), disk rotational velocity ratio (S) and Batchelor number (Bt). In the present study we examine the flow regime at various Batchelor numbers (for the case of unity value of the squeeze Reynolds number, Re_m=Bt). Excellent comparison of NSM solutions is achieved with earlier analytical and shooting solutions. The present study finds applications in hydromagnetic lubrication of braking devices, slider bearings, rotating machinery, etc. Applications also arise in hydraulic shock absorbers employing electrically conducting liquids such as sodium where electro-magnetical braking of streams can be achieved in liquid metal cooled nuclear reactors for arresting control rods. Finally in the context of astronautical vehicles, the present study has applications in electromagnetic braking for potential spacecraft in planetary orbits.     

Effects of surface forces on pure squeeze thin film EHL motion of circular contacts

The pure squeeze thin film elastohydrodynamic lubrication (thin film EHL) motion of circular contacts with effects of surface forces taken into account is explored under constant load conditions. The difference between thin film EHL model and EHL model is apparent as the film thickness is thinner than 5 nm. The oscillation phenomena in pressure and film thickness come mainly from the action of solvation forces. The effects of surface forces become significant as the film thickness becomes thinner. Moreover, the viscosity is oscillatory due to its dependency on the hydrodynamic pressure which is affected by surface forces.