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.     

Effect of pressure dependent viscosity on squeeze film characteristics of micropolar fluid in convex curved plates

In this paper, the effect of pressure dependent viscosity on the squeeze film characteristics between convex curved plates of a cosine form is presented. Micropolar fluid theory, which is a possible non-Newtonian model of a suspension of rigid particle additives, is applied to the study of the lubrication of cosine form convex curved plates. The modified Reynolds equation is solved for the fluid film pressure and then the cosine form by considering the exponential relationship in the viscosity variation. For iso-viscous lubricants, the effects of pressure dependent viscosities signify an increase in the values of the squeeze film pressure, the load capacity and the elapsed time. It provides useful information in designing the mechanisms of squeeze film plates for engineering application.     

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.     

Numerical and experimental investigation into porous squeeze films

The paper presents a numerical and experimental investigation into porous squeeze films with a view to application in the printing process. The experimental programme was carried out using targets having different permeability and this work confirmed the dominance of hydrodynamic behaviour associated with the thick film and porous medium flow when the film becomes thin. The numerical model has been implemented via the finite element method and the prediction shows good overall agreement with the data obtained from the experimental investigation. In performing sensitivity calculations, for the physical parameters of practical interest, it was found that the inclusion of slip velocity affects the film thickness decay, but only by a small amount. When the model was applied to the parameters of the actual printing process, it was demonstrated that the volume flowrate of the ink dot which penetrates into the paper and which spreads on it can be obtained from the model, but the penetration component is negligible. In comparing predicted and measured dot gain, initial film thickness was found to be a dominant parameter and the most likely cause of the discrepancy between measured and predicted values.     

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.     

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.     

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.     

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.     

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.     

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。     

Simultaneous monitoring of oil film thickness and temperature in fluid film bearings

This paper reports on the application of an eddy current sensor with an active compensation for changes in sensor temperature to simultaneous monitoring oil film thickness and temperature in a tilting pad thrust bearing. Sensor design, calibration procedure, sensitivity and accuracy are described. Test equipment along with sensor mounting is also presented. Tests were run at different rotational speeds and bearing loads as well as different supplied oil flow rates to evaluate sensor performance in various operating conditions. During the tests film thickness and temperature were simultaneously measured. Temperatures were compared with data from thermocouples installed in the pads and thermistors mounted in the collar. Tests have shown that the sensor can successfully be used to reliably monitor the conditions within the bearing.     

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.     

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.     

Effect of surface roughness on the couple-stress squeeze film between a sphere and a flat plate

In this paper, a theoretical study of the effect of surface roughness on the hydrodynamic lubrication of couple-stress squeeze film between a sphere and a flat plate is presented on the basis of Christensen's stochastic theory for hydrodynamic lubrication of rough surfaces. The modified Reynolds equation accounting for the couple stresses and the surface roughness is mathematically derived. The modified Reynolds equation is solved for the fluid film pressure and the bearing characteristics, such as the load carrying capacity and the time–height relationship, are obtained. It is found that the surface roughness considerably influences the squeeze film characteristics. The load carrying capacity and squeeze film time are found to increase for an azimuthal roughness pattern as compared to the corresponding smooth case, whereas the reverse trend is observed for a radial roughness pattern.     

高压涡轮动叶气膜冷却的数值模拟

为研究旋转造成的非稳定性对高压涡轮动叶气膜冷却的影响,建立了3维涡轮叶栅通道模型,应用周期性边界条件数值模拟了不同转速下涡轮动叶表面气膜冷却效率和换热系数的分布,冷气进口与涡轮前总压比为1.07,温度比为0.5。转速增加,叶片前缘滞止线从压力面移向吸力面,气膜出流从吸力面移向压力面;压力面气膜冷却效率上升,换热系数下降;吸力面冷却效率先上升后降低;换热系数下降。与静止相比,旋转不稳定性增大了叶片表面气膜覆盖面积。     

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.     

Film thickness in point contacts under generalized Newtonian EHL conditions: Numerical and experimental analysis

The current paper contributes to the understanding of the behaviour of a smooth point EHL contact with a generalized Newtonian lubricant under pure rolling. The film thickness distribution was computed using a numerical simulation with measured rheological lubricant properties. The numerical predictions, obtained solving the generalized Reynolds equation were compared with film thicknesses measured in an optical ball-on-disc device. The numerical results correctly predict the absolute film thickness and the film thickness increase with rolling speed.     

EHL line contact central and minimum film thickness equations for lubricants with linear piezoviscous behavior

Full EHL line contact simulations for smooth surfaces are carried out under fully flooded condition to obtain central and minimum film thickness equations pertaining to lubricants with linear piezoviscous response. The present analysis is based upon the assumptions of isothermal condition and Newtonian fluid model. A major drop in the sensitivity of pressure viscosity coefficient (and hence, the material parameter G) is observed. The exponent of the speed parameter U is marginally smaller while that of load parameter is slightly increased. There is close agreement between the simulated and fitted film thickness values.     

Dynamic permeability of highly compressible porous layers under squeeze at constant velocity and under impact

The ability of a highly compressible porous layer (HCPL), imbibed with a Newtonian liquid, to dissipate energy is underlined in recent papers related to ex-poro-hydrodynamic (XPHD) lubrication. The total absorption of energy of a squeeze/impact is due to the hydrodynamic forces generated within the HCPL. Mostly all XPHD processes take place in dynamic conditions, therefore it is essential to know if the permeability determined at constant thickness is adequate for such processes. For this reason, squeeze at constant velocity and impact tests were performed on HCPLs completely saturated with Newtonian liquids, thus the variation of dynamic permeability was determined.