Convergent Wedge Research Articles

Structural Design and Lubrication Properties under Different Eccentricity of Magnetic Fluid Bearings

As a lubricant, the viscosity of the magnetic fluid changes with the external magnetic field, which improves the bearing capacity of the oil film and hence the lubrication effect, and has a promising application in bearings. Based on the Roelands viscosity theory, the Shliomis model is used to derive the viscous temperature, viscous pressure, and magnetic viscosity characteristics of magnetic fluids under the influence of an applied magnetic field, and further proposes a structural model of magnetic fluid lubricated bearings to investigate the pressure, temperature and magnetic intensity distribution of magnetic fluids under different eccentricity conditions. The results show that the viscosity of the magnetic fluid decreases exponentially with increasing temperature, rises linearly with increasing pressure, and increases and stabilizes with increasing magnetic induction strength. Because the minimum film thickness point is the dividing point between the convergent wedge and the dispersed wedge, the pressure distribution of the lubricant film separates high pressure from low pressure at the minimum film thickness, and the differential pressure increases with the increase in eccentricity. The temperature distribution of the high-temperature zone is mainly distributed in the middle of the film, and the minimum film thickness zone and the maximum temperature increases with the increase in eccentricity. The magnetic intensity distribution of the strong magnetic field is mainly concentrated in the minimum film thickness zone, and the magnetic induction intensity increases with the increase in eccentricity. The results of this study have certain research significance for solving the problem of the poor lubrication effect of bearing lubricant due to high temperature.

Comparison of measured and calculated water film thickness of a water-lubricated elastically supported tilting pad thrust bearing

A xenon induced fluorescence technique is used to measure the water film thickness of a rubber-supported water-lubricated tilting pad thrust bearing (RWTB). Film thickness maps are obtained over a range of speeds and loads. Based on a Thermo-Elasto-Hydrodynamic lubrication model, the calculated film thickness is compared with the measured one. The measurement shows that the lubrication regime of the RWTB can be observed and it can form a convergent wedge of lubricant. The calculated results are on par with the experimental results at low speed condition (200 r · min−1). Generally, the calculated film thickness is larger and the discrepancy between them increases respecting to the speed. The RWTB is in the hydrodynamic lubrication regime when the speed is over 200 r · min−1 and the load is less than 0.25 MPa. The comparison between the measurements and calculations verifies that the fluorescence technique can be used to measure the film thickness of water-lubricated thrust bearings.

Texture shape effects on hydrodynamic journal bearing performances using mass-conserving numerical approach

ABSTRACTIt is a known fact that incorporating textures in the contact surfaces can significantly enhance bearing performances. The purpose of this paper is to outline the effects of texture bottom profiles and contour geometries on the performances of hydrodynamic textured journal bearings. The analysis was conducted using computational approach to test eight texture shapes: rectangular, cylindrical, spherical, triangular (TR, T1, T2, T3) and chevron. The steady-state Reynolds equation for modelling the hydrodynamic behaviour of thin viscous film was solved using finite difference technique and mass conservation algorithm (JFO boundary conditions), taking into account the presence of textures on both full film and cavitation regions. The comparison with the benchmark data shows good consistency and an enhancement in bearing performances (load carrying capacity and friction). The results clearly show that the mechanisms of wedge effect and micro-step bearing for the full/partial texturing feature are the main crucial parameters, where the convergent wedge effect present in T2 triangular texture shape can significantly enhance the load-carrying capacity, while the divergent wedge action causes a net load loss. Considering the right arrangement of textures on the contact surface, their surface contours can have a significant impact on the performance of hydrodynamic journal bearings at high eccentricity ratios.

Investigation of the effect of cavitation and journal whirl on static and dynamic characteristics of journal bearing

The cavitation phenomenon in journal bearing and journal whirl are considered to evaluate the static and dynamic characteristics of journal bearing, to be more consistent with the actual operating conditions of journal bearing. With a 3D CFD method, the cavitation and journal whirl are simulated by adopting mesh deformation technique and mixture phase-change model. By comparing the results with those of the traditional Reynolds equation, we observe that first, the phenomena of cavitation and journal whirl are very consistent with the actual operating conditions of journal bearing. Moreover, for single-phase and two-phase flow models, the distribution features of oil film pressure are similar in convergent wedge zone while largely different in divergent part of the gap. The oil film pressure and vapor phase volume fraction notably vary on different whirl positions of the journal. We also observe that as whirl frequency increases, the oil film force gradually increases and the stability of journal bearing decreases rapidly before reaching a plateau. The efforts of this paper provide an efficient method to accurately evaluate the static and dynamic characteristics of journal bearing and offer a useful insight into the accurate analysis and design of journal bearing.

Analysis of Oil Film Characteristics of Two-Axial Groove Sleeve Bearings

Abstract Based on the finite finite difference method, the Reynolds equation, the flow equilibrium relationship of oil film gradient, and the oil film thickness equation are solved for different groove locations and depths in two-axial groove sleeve bearings. The oil film pressure, extent of the cavitation zone, and carrying capacity of two-axial groove sleeve bearings are computed at different oil groove locations and depths. With the increase of oil groove depth, the oil film pressure of two-axial groove sleeve bearings decreases noticeably, and the bearing capacity decreases gradually. It can be concluded that the maximum oil film pressure and bearing capacity of two-axial groove sleeve bearings are lower than that of the common sleeve bearing. With the groove position moving along the circumferential direction, the oil film pressure peak heights and bearing capacities decrease and then increase. The oil film pressure peak heights and load capacities reach maximum when the position of the two-axial oil groove is about 20° and 200°. It has been proven that different positions of oil grooves show different influences on the extent of the cavitation zone. The first oil groove is always located in the full oil film region, and the second oil groove may be located in the full oil film region or the cavitation region because of the change of distance from the convergent wedge of the bearing. The cavitation area firstly decreases and then increases with the movement of the groove in the circumferential direction.

Influence of Donut-Shaped Bump on the Hydrodynamic Lubrication of Textured Parallel Sliders

The influence of donut-shaped bump texture on the hydrodynamic lubrication performance for parallel surfaces is presented in this paper. A mathematical equation has been applied to express the shape of three-dimensional donut-shaped bump texture. Numerical simulation of the pressure distribution of lubricant between a textured slider and a smooth, moving slider has been performed to analyze the geometrical parameters' influence on the hydrodynamic performance for textured surfaces. The numerical results show that the convex of the donut-shaped bump provides a microstep slider, which can form a convergent wedge and build up hydrodynamic pressure. Optimum values of horizontal spacing and bump height are obtained to maximize the hydrodynamic pressure. It is also noted that the average pressure increases monotonically with the increase of bump radius, but decreases with the increase of vertical spacing and dimple depth, respectively.

Cartilage and Joint Lubrication: New Insights Into the Role of Hydrodynamics

Cartilage is slippery when hydrated but it loses hydration and lubricity during loading. However, dehydrated cartilage regains lubricity during high-speed sliding in the stationary contact area; this result is often interpreted as experimental evidence of fluid film lubrication based on theoretical predictions that pre-equilibrated cartilage remains equilibrated during sliding in this testing configuration. In-situ compression measurements were made during variable speed stationary contact area experiments with fully and partially equilibrated osteochondral cores under saline lubrication to test this prediction. Reduced friction coefficients and compression were observed during high speed sliding, at near-physiological speeds. The results suggest that the marked friction reductions observed during high-speed sliding following equilibration were likely consequences of interstitial fluid recovery, a mechanism we term tribological rehydration, rather than the formation of a hydrodynamic fluid film. The results also suggest that hydrodynamic pressurization was the likely driving force underlying the tribological rehydration phenomenon. We propose that external hydrodynamic pressures in the convergent wedge near the leading edge of contact pushed fluid into the porous surface to restore hydration, thickness, mechanical stiffness, and lubrication following periods of static exudation.

Jeffery-Hamel flow of non-Newtonian fluid with nonlinear viscosity and wall friction

A Jeffery-Hamel (J-H) flow model of the non-Newtonian fluid type inside a convergent wedge (inclined walls) with a wall friction is derived by a nonlinear ordinary differential equation with appropriate boundary conditions based on similarity relationships. Unlike the usual power law model, this paper develops nonlinear viscosity based only on a tangential coordinate function due to the radial geometry shape. Two kinds of solutions are developed, i.e., analytical and semi-analytical (numerical) solutions with suitable assumptions. As a result of the parametric examination, it has been found that the Newtonian normalized velocity gradually decreases with the tangential direction progress. Also, an increase in the friction coefficient leads to a decrease in the normalized Newtonian velocity profile values. However, an increase in the Reynolds number causes an increase in the normalized velocity function values. Additionally, for the small values of wedge semi-angle, the present solutions are in good agreement with the previous results in the literature.

Study on Performance and Wall Slip Behavior of Visco-plastic Hydrodynamic Lubrication in Convergent Wedge

According to the rheological behavior of visco-plastic fluid lubricants in convergent wedge at high-speed and high-pressure, the visco-plastic hydrodynamic lubrication equation considering boundary slip is extracted by selecting the Smith rheological model. And for the hydrodynamic lubrication with constant viscosity and incompressible lubricants at isothermal condition, the initial boundary slip position, the development process and distribution of boundary slip field are determined in the light of shear stress distribution and maximum shear stress position of lubricants. The performance and wall slip behavior of visco-plastic hydrodynamic lubrication in various film thickness ratio convergent wedge at different moving lubrication surface speed are also analyzed and contrasted with the solutions at traditional hydrodynamic lubrication by means of solving visco-plastic hydrodynamic lubrication equations at different fields together, results indicate significant influences of film thickness ratio and moving lubrication surface speed on visco-plastic hydrodynamic lubrication performance and boundary slip behavior.

Analysis of Mechanical Seal Leakage within Hydrostatic on Nuclear Reactor Coolant Pump

According to the fluid hydrodynamic lubrication theory, and the structural characteristics of the convergence gap seal is combined, the effect of differential pressure and centrifugal force should be considered, then the convergent wedge gap mechanical seals flow field numerical model is established and the influence of the leakage factors are researched, including the geometric parameters and operating parameters. Research has shown that the amount of leakage and the seal clearance were positively correlated. And the larger turning Angle is, the bigger correlation becomes, however, it is negatively correlated with speed and turning radius, the seal leakage is impeded by the centrifugal force and the larger turning radius is, the smaller leakage becomes.

Thermal Deformation in a Dry Gas Seal

In order to know thoroughly the thermal deformation characteristics of the dry gas seal in the synthesis gas compressor, the physical model and the thermal equilibrium model of the seal pair are established on its structural and thermal analysis. Based on finite element analysis software ANSYS, separation method are applied to resolve and analyze the temperature field and thermal-structural coupling deformation of the seal pair. The analyzed results show that the temperature of the rotating ring decreases gradually from the end face to the back face, and decreases gradually from the inner radius to the outer radius. The maximum of the temperature gradient of the rotating ring locates at the outer radius of the end face.The deformation of the stationary ring is negative conicity, the deformation of the rotating ring is positive conicity, and the later is the major reason of seal failure. Because of the thermal deformation, the end faces will form a convergent wedge. The convergent wedge favors the formation of a gaseous film, but it will lead to a increase in leakage quantity.

An Investigation of Lubricant Film Thickness in Sliding Compliant Contacts

An optical interferometric technique has been used to investigate fluid film thickness in sliding, isoviscous elastohydrodynamic contacts (I-EHL). Monochromatic two-beam interferometry has been employed to map lubricant film thickness across a range of applied loads and entrainment speeds. The contact was formed between an elastomer sphere and plain glass disc, illuminated under red light, λ= 630 nm. Experimental work has employed sunflower oil and glycerol/water solutions as the test lubricants, due to their similar refractive indices and varying viscosity. A black-and-white-image-intensified camera has been employed to capture interference images and a computer processing technique used to analyse these images, pixel by pixel, and create film thickness maps based on their gray-scale intensity representations. Comparison of film thickness results to theoretical models shows reasonable qualitative agreement. Experimental results show both a reduced horseshoe, which is limited to the rear of the contact, and wedge-shaped film thickness profile within the Hertzian contact region. This is unlike conventional hard EHL contacts where the horseshoe-shaped pressure constriction extends around the contact toward the inlet. Experimental results suggest that film thickness profiles take on a convergent wedge shape similar to that used in many hydrodynamic bearings. It is likely that this wedge is largely responsible for generating fluid pressure and therefore the load-carrying capacity of the contact.

Shock focusing in a planar convergent geometry: experiment and simulation

The behaviour of an initially planar shock wave propagating into a linearly convergent wedge is investigated experimentally and numerically. In the experiment, a 25° internal wedge is mounted asymmetrically in a pressure-driven shock tube. Shock waves with incident Mach numbers in the ranges of 1.4–1.6 and 2.4–2.6 are generated in nitrogen and carbon dioxide. During each run, the full pressure history is recorded at fourteen locations along the wedge faces and schlieren images are produced. Numerical simulations performed based on the compressible Euler equations are validated against the experiment. The simulations are then used as an additional tool in the investigation.The linearly convergent geometry strengthens the incoming shock repeatedly, as waves reflected from the wedge faces cross the interior of the wedge. This investigation shows that aspects of this structure persist through multiple reflections and influence the nature of the shock-wave focusing. The shock focusing resulting from the distributed reflected waves of the Mach 1.5 case is distinctly different from the stepwise focusing at the higher incoming shock Mach number. Further experiments using CO2 instead of N2 elucidate some relevant real-gas effects and suggest that the presence or absence of a weak leading shock on the distributed reflections is not a controlling factor for focusing.

Low Friction and High Load Support Capacity of Slider Bearing With a Mixed Slip Surface

The classical Reynolds theory reveals that a converging gap is the first necessary condition to generate a hydrodynamic pressure in a viscous fluid film confined between two solid surfaces with a relative sliding/rolling motion. For hundreds of years, the classical lubrication mechanics has been based on the frame of the Reynolds theory with no slip assumption. Recent studies show that a large boundary slip occurs on an ultrahydrophobic surface, which results in a very small friction drag. Unfortunately, such a slip surface also produces a small hydrodynamic pressure in a fluid film between two solid surfaces. This paper studies the lubrication behavior of infinite width slider bearings involving a mixed slip surface (MSS). The results of the study indicate that any geometrical wedges (gaps), i.e., a convergent wedge, a parallel gap, and even a divergent wedge, can generate hydrodynamic pressure in an infinite slider bearing with a mixed slip surface. It is found that with an MSS, the maximum fluid load support capacity occurs at a slightly divergent wedge (roughly parallel sliding gap) for an infinite width slider bearing, but not at a converging gap as what the classical Reynolds theory predicts. Surface optimization of a parallel sliding gap with a slip surface can double the hydrodynamic load support and reduce the friction drag by half of what the Reynolds theory predicts for an optimal wedge of a traditional slider bearing.

Rheological Properties and Shear Induced Texture Development of Thermotopic Liquid Crystalline Polymer Melts

AbstractThe flow behavior of two commercial liquid crystalline polymers (LCPs), trade name Vectra B 950 and Vectra L 950 supplied by Ticona, was investigated using a capillary rheometer with a special double slit die. The pressure drops in convergent and divergent wedge passage between the two slit sections, which are influenced by the curvature strains in nematic melts, were determined and compared with the pressure drops of a conventional polystyrene (PS) with flexible polymer chains. Furthermore the extensional viscositiy was determined from the pressure drop in convergent wedge passage. The development of the shear induced texture as a function of shear rate was investigated by use of a rapidly coolable double slit die with the same gap design as the double slit die used for viscosity measurement. The structural analysis was performed using polarized light microscopy.

Analysis of Gas Lubricated Foil Thrust Bearings Using Coupled Finite Element and Finite Difference Methods

Load performance of gas lubricated, compliant surface foil thrust bearings has an interlocking relationship with the compliance of the bearing and hydrodynamics of convergent wedge surface. Compliance of the bearing consists of supporting spring elements (elastic foundation) and a smooth elastic top foil. In this paper, a class of gas lubricated foil thrust bearings has been investigated analytically utilizing a novel approach which combines Finite Difference (FD) and Finite Element (FE) methods. Solution of the governing hydrodynamic equations dealing with compressible fluid is coupled with the structural resiliency of the foil bearing surfaces. FD method is utilized for hydrodynamic analysis while FE is used to model structural resiliency. Influence coefficients were generated to address the elasticity effects of combined top foil and elastic foundation on the hydrodynamics of thrust bearing, and were used to expedite the numerical solution. Within 2 to 3 iterations the convergence criterion was reached. The overall program logic proved to be an efficient technique to deal with the complex structural compliance of various foil bearing. Case study has been conducted and sample solutions are provided. Unlike prior analytical investigations, the essential effect of the top foil on the performance of the bearing has been elucidated. [S0742-4787(00)02501-7]

Contribution of ductile flow to exhumation of low‐temperature, high‐pressure metamorphic rocks: San Juan‐Cascade nappes, NW Washington State

The San Juan‐Cascade (SJC) nappes were subducted to a depth of ∼18 km, metamorphosed under low‐temperature, high‐pressure conditions, and then exhumed, all within ∼16 m.y. During exhumation, penetrative deformation by solution mass transfer (SMT) resulted in a widespread spaced cleavage. Strain directions were determined for 27 sandstone samples, and absolute strain measurements for a subset of 19 samples. Z directions generally plunge moderately to the NE, and X and Y directions are scattered in the plane perpendicular to Z. SMT deformation is constrictional at the local scale, but the tensor average indicates plane‐strain uniaxial shortening at the regional scale, with Sx, Sy, and Sz equaling 1.01, 0.91, and 0.58, respectively. The average flattening plane (XY) dips 30° to the NE, and the average X direction plunges 20° to the north. The large shortening in Z was compensated by a mass‐loss volume strain of ∼47%. We present a simple one‐dimensional model that illustrates the relationship between finite strain and ductile exhumation for a steady state convergent wedge. Assuming depth‐dependent ductile flow and no reversal of principal strain rates with depth, this model indicates that ductile thinning of the SJC nappes accomplished only 13% of the total exhumation, despite a vertical shortening strain of 36%. There is no evidence that normal faulting contributed significantly to exhumation. We conclude that erosion operating at an average rate of ∼1.1 km m.y.−1 was the dominant exhumation process.

A Lubrication Analysis of a Swing-Pad Journal Bearing

A steady-state performance analysis has been conducted for a radially loaded swing-pad journal bearing with given initial clearance and normal load. The analysis consists of equilibrium determination of journal center displacements, pad tilting position, elastic deflections, pad load distribution, effective temperature, as well as operating clearances in bearings. Using values of statically measured shear and radial stiffness for the laminate, numerical results have been calculated for an oil-lubricated 12-pad swing-pad bearing which show that there is sufficient moment about the curvature center of the laminate, caused by various hydrodynamic forces, to swing the pad to produce a convergent lubricant wedge between the pad surface and the journal. The calculated film ratio which characterizes the lubricant-wedge-forming action is found to increase with pad load. The examples yield values of coefficient of friction in good agreement with those obtained from measured torque values in experiments conducted a...

Inverse Hydrodynamic Methods Applied to Mr. Beauchamp Tower’s Experiments of 1885

The experiments of Mr. Beauchamp Tower and their subsequent interpretation by Professor Osborne Reynolds form the basis of all hydrodynamic lubrication theory. In the experiments described in his second report, Tower made nine pressure tappings in a 157 deg partial arc bearing. Reynolds assumed that the film shape corresponded to a circular bearing and analyzed the results on this assumption. Inverse hydrodynamic theory allows the calculation of the actual film shape from this measured pressure distribution. It is found that the film was a slightly convergent wedge which does not correspond to a fitted bearing as assumed by Tower and certainly not to the clearance bearing assumed by Reynolds. Existing methods of inverse hydrodynamic analysis require the second differential of the pressure profile (or its equivalent in the two-dimensional case) to become zero at some point in the film. The film thickness can be found directly at this point and then elsewhere by the solution of a cubic equation. Two separate and more general methods are developed in this paper in which this requirement for the second differential is unnecessary.