Hydrostatic Journal Bearings Research Articles

102 ハイブリッド(水/空気潤滑)静圧ジャーナル軸受に関する研究 : 静的特性(OS3 最新機械要素技術)

102 ハイブリッド(水/空気潤滑)静圧ジャーナル軸受に関する研究 : 静的特性(OS3 最新機械要素技術)

Static and Dynamic Performance Characteristics of Orifice Compensated Hydrostatic Flexible Journal Bearings with Non-Newtonian Lubricants

The combined effect of non-Newtonian lubricant behavior and bearing shell flexibility on the performance of an orifice compensated multirecess hydrostatic/hybrid journal bearing system is studied. The analysis considers the constitutive equations for the flow of a non-Newtonian lubricant through an orifice restrictor, the generalized Reynold's equation governing the flow of lubricant having variable viscosity and 3-D elasticity equations. The computed results demonstrate that loss in bearing performance due to the pseudo-plastic effect of the non-Newtonian lubricant can be mitigated by a proper selection of parameters such as the deformation coefficient (Ȼ4) and non-linearity factor ([Kbar]) or power law index (n).

Numerical Analysis on Dynamic Characteristics of Cryogenic Hydrostatic Journal Bearing

Dynamic characteristics of a two row staggered recess cryogenic hydrostatic journal bearing used in the liquid hydrogen turbopump of rocket engines for space transport systems are numerically analyzed. Effects of the rotational speed and the shaft eccentricity are studied in the analysis. Their effects on the stiffness and damping coefficients and the whirl frequency ratio are clarified. Moreover, effects of the orifice parameter, the distance between two recess rows, and the number of recesses on these dynamic characteristics are investigated.

Erratum: “Step Response Characteristics of Hydrostatic Journal Bearings With Self-Controlled Restrictors Employing a Floating Disk” (Journal of Tribology, 1999, 121, pp. 315–319)

Erratum: “Step Response Characteristics of Hydrostatic Journal Bearings With Self-Controlled Restrictors Employing a Floating Disk” (Journal of Tribology, 1999, 121, pp. 315–319)

Step Response Characteristics of Hydrostatic Journal Bearings With Self-Controlled Restrictors Employing a Floating Disk

This paper describes the step response characteristics of hydrostatic journal bearings with self-controlled restrictors employing a floating disk. This type of bearing can achieve very high static stiffness by controlling the mass flow rate of the fluid entering the bearing clearance using a floating disk. Many design parameters such as supply pressure, viscosity, the magnitude of the step load and the imposed static load affect the step response characteristics of the proposed bearing. Therefore, the influences of each design parameter on the step response characteristics are theoretically investigated in this paper. Furthermore, the theoretical results are compared with the experimental results in order to verify the theoretical predictions. It is subsequently found that the proposed bearing consistently shows a stable step response irrespective of the step-load direction.

Three-Dimensional Flow and Pressure Patterns in a Hydrostatic Journal Bearing Pocket

The laminar flow in a hydrostatic pocket is described by a mathematical model that uses the three-dimensional Navier-Stokes equations written in terms of the primary variables, u, v, w, and p. Using a conservative formulation, a finite volume multiblock method is applied through a collocated, body fitted grid. The flow is simulated in a shallow pocket with a depth/length ratio of 0.02. The flow structures obtained and described by the authors in their previous two dimensional models are made visible in their three dimensional aspect for both the Couette, and the jet dominated flows. It has been found that both flow regimes formed central and secondary vortical cells with three dimensional corkscrew-like structures that lead the fluid on an outward bound path in the axial direction of the pocket. In the Couette dominated flow the position of the central vortical cell center is at the exit region of the capillary restrictor feedline, while in the jet dominated flow a flattened central vortical cell is formed in the downstream part of the pocket. It has also been determined that a fluid turn around zone occupies all the upstream space between the floor of the pocket and the runner, thus preventing any flow exit through the upstream exit of the pocket. The corresponding pressure distribution under the shaft for both flow regimes is presented as well. It was clearly established that both for the Couette, and the jet dominated cases the pressure varies significantly in the pocket in the circumferential direction, while its variation is less pronounced axially.

Misaligned journal effects in liquid hydrostatic non-recessed journal bearings

The performance characteristics of a capillary-compensated hole-entry hybrid misaligned journal bearing have been studied theoretically. The journal of the bearing is allowed to tilt on an axial plane containing the load vector and on a plane perpendicular to an axial plane containing the load vector. The journal misalignment has been accounted for by defining a pair of misalignment parameters σ and δ. The finite element method has been used to solve Reynold's equation governing the lubricant flow field in the clearance space of the journal bearing. Static and dynamic performance characteristics are presented for the different representative values of the journal misalignment parameters for both hydrostatic and hybrid modes of operation of the bearing. The bearing performance characteristics are also compared for the two hole-entry bearing configurations so as to facilitate the selection of a suitable bearing configuration by the designer. The study suggests that the journal misalignment significantly affects the performance of the hole-entry journal bearing, and for a more accurate prediction of the bearing performance it must be considered in the analysis.

フルイドダンパを付加した複合絞り型静圧気体ジャーナル軸受の軸の応答特性

Hydrostatic journal gas bearing with a large pocket in the bearing surface and with fluid damper has high stiffness without causing pneumatic hammer instability. But the settling time cannot be lower than two or three times of natural period time owing to the large pocket volume even if the damping coefficient of fluid damper can be set high. In this paper, the settling time of hybrid restrictor type hydrostatic journal gas bearings is investigated. The stiffness of hybrid type is about 60% less than that of pocket type, and the pocket volume of this type, where pocket depth is about two or three times as deep as bearing clearance, is about 2-5% of the pocket volume of the pocket type. The following conclusion is obtained : the settling time of hybrid type can be set to one natural period time (critical damping) by the use of the appropriate damping coefficients of fluid damper.

Effect of Pressure Difference across Bearing on Characteristics of Cryogenic Hydrostatic Journal Bearing.

The effect of the pressure difference across a bearing on the characteristics of the cryogenic hydrostatic journal bearing used in the liquid fuel turbopump of rocket engines in space transport systems is numerically analyzed. The bearing has many recesses arranged in two rows in a staggered manner. The turbulent lubrication equation is solved under the assumptions that the lubricant is liquid nitrogen and that the temperature change in the bearing is negligible which is in accordance with the experimental results. The effects of rotational speed and the pressure drop at the recess edge are considered in the analysis. Variations in the recess pressure, lubricant flow rate, stiffness coefficients, damping coefficients and whirl frequency ratio with the pressure difference across the bearing and the rotational speed are clarified.

Static and dynamic performance characteristics of an orifice compensated hydrostatic journal bearing with non-Newtonian lubricants

This paper presents a theoretical study of the performance characteristics of hydrostatic rigid orifice compensated multirecess journal bearings using non-Newtonian lubricants. The generalized Reynolds equation governing the flow of lubricant having variable viscosity has been solved using the finite element method and iterative procedure. The static and dynamic performance characteristics are presented for non-Newtonian lubricants of which constitutive equation has been represented by the cubic shear stress law. The non-linearity factor ( K ) in the cubic shear stress law significantly influences the bearing performance characteristics, particularly the dynamic characteristics.

Thermohydrodynamic Analysis of Process-Liquid Hydrostatic Journal Bearings in Turbulent Regime, Part I: The Model and Perturbation Analysis

A bulk-flow thermohydrodynamic (THD) analysis is developed for prediction of the static and dynamic performance characteristics of turbulent-flow, process-liquid, hydrostatic journal bearings (HJBs). Pointwise evaluation of temperature and hence liquid properties is achieved through the solution of the energy equation in the fluid film with insulated boundaries, and justified for fluid film bearings with external pressurization. Fluid inertia within the film lands and at recess edges is preserved in the analysis. Flow turbulence is accounted through turbulence shear parameters based on friction factors derived from Moody’s formulae. The effects of fluid compressibility and temperature variation in the bearing recesses are included. Numerical solution and results are presented in the second part of this work and compared with some limited experimental data for a liquid hydrogen (LH2) bearing.

Thermohydrodynamic Analysis of Process-Liquid Hydrostatic Journal Bearings in Turbulent Regime, Part II: Numerical Solution and Results

A finite difference scheme is implemented to solve the nonlinear differential equations describing the turbulent bulk-flow on the film lands of a hydrostatic journal bearing (HJB). A Newton-Raphson scheme is used to update the recess pressures and to satisfy the mass continuity requirement at each bearing recess. Comparisons of numerical predictions from the thermohydrodynamic (THD) model with experimental measurements of mass flow rate, fluid temperature, and static stiffness coefficient from a LH2 test HJB article show very good agreement. In particular, the exit temperature of the bearing is lower than the supply temperature; i.e., the liquid temperature decreases along the bearing length. Similar values of direct stiffness and damping coefficients are predicted by the adiabatic THD model and other considering isothermal flow characteristics. However, the THD model predicts lower cross-coupled stiffness and whirl frequency ratio (WFR < 0.5). The results show that for the application presented, the LH2 hydrostatic bearing is more stable than previously thought.

Thermohydrodynamic analysis of fluid film bearings for cryogenic applications

A thermohydrodynamic analysis and computer program for prediction of the static and dynamic force response of hydrostatic journal bearings, annular seals, or damping bearings, and fixed arc-pad bearings are presented. The study includes the most important flow characteristics found in cryogenic fluid film bearings such as flow turbulence, fluid inertia, liquid compressibility, and thermal effects. Numerical results detail a comparison of the static performance and dynamic force coefficients for a six-recess hydrostatic bearing and a damping bearingseal for the Space Shuttle Main Engine high-pressure oxidizer turbopump. The calculations indicate that turbulent-flow, externally pressurized bearings support the expected loads with moderate journal center eccentricities and with force coefficients of relevant magnitude for this critical application.

Turbulent-flow hydrostatic bearings: Analysis and experimental results

A bulk-flow thermohydrodynamic (THD) analysis for prediction of the static and dynamic performance characteristics of turbulent-flow, process-liquid hydrostatic journal bearings (HJBs) is presented. The film-averaged momentum transport and energy equations replace the lubrication Reynolds equation, and fluid inertia on film lands and at recess edges are preserved in the analysis. Flow turbulence is accounted through turbulence shear parameters based on friction factors derived from Moody's formulae. Numerical predictions are compared successfully to experimental results from a five-recess, turbulent-flow, water-lubricated hydrostatic bearing operating at a high rotational speed. HJBs operating in a hydrob mode (i.e. with journal rotation) provide no better stability characteristics than hydrodynamic journal bearings and are likely to show half-speed whirl.

Externally Pressurized Oil Bearings with Porous Ceramics Materials.

In the field of hydrostatic bearings, the porous resistor has been adopted only in air bearings. Here, we tried to apply the porous ceramics, the surface of which is not crushed by machining, to hydrostatic journal bearings for incompressible fluid. The equations derived to calculate the bearing performance are effective for bearing types of both with and without axial grooves in the land, and they are also available for both load directions of the center of the pocket and the center of the land. In the calculation, the porous resistor could be treated as being equivalent to the capillary tube resistor. The hydrostatic journal bearings are made with alumina ceramic which has the average porous radius of 85μm. The results of experiment show that the bearing performance of the porous resistor coincides well with the calculated one, and it indicates similar good performance as those of other types of resistors.

Numerical Analysis on Steady Characteristics of Hydrostatic Cryogenic Journal Bearing.

Steady characteristics of a hydrostatic cryogenic journal bearing used for the liquid hydrogen turbopump of rocket engines are numerically analyzed. The bearing has many recesses arranged in two rows in a staggered manner. The turbulent lubrication equation is solved under the assumption that the temperature change in the bearing is negligible in accordance with the experimental results. Effects of the rotational speed, the shaft eccentricity and the pressure drop at the recess edge are considered in the analysis. Their effects on the film pressure distribution, the recess pressures, the total lubricant flow rate and the load carrying capacity are clarified. Moreover, effects of the distance between two recess rows, the orifice parameter, number of recesses and the radial clearance on these characteristics are investigated.

Analysis of Vibration Characteristics for a Rotor‐Bearing System Using Distributed Spring and Damper Model

In this paper, we modelled the journal beatings as distributed springs and dampers to investigate the influence of beating width on the vibration characteristics of a rotor‐beating system. A quadratic function is used as a shape function for hydrodynamic journal bearings. And a trapezoidally or a quadratically distributed model is used as a shape function for hydrostatic journal bearings. A finite element method is applied for analyzing the vibration characteristics of a rotor‐bearing system.Dimensionless governing equations are derived for a uniform rotor supported by two journal bearings, which are modelled as point supported or distributed springs and dampers. For these models, natural frequencies for various beating length ratios and stiffness ratios between the bearing and the shaft are calculated and compared with each other. Then the stability limits of a rotor supported by two cylindrical journal beatings are calculated for the point supported or distributed springs and dampers.

A Test Apparatus and Facility to Identify the Rotordynamic Coefficients of High-Speed Hydrostatic Bearings

A facility and apparatus are described which determine stiffness, damping, and added-mass rotordynamic coefficients plus steady-state operating characteristics of high speed hydrostatic journal bearings. The apparatus has a current top speed of 29800 rpm with a bearing diameter of 7.62 cm (3 in.). Purified warm water, 55°C (130°F), is used as a test fluid to achieve elevated Reynolds numbers during operation. The test-fluid pump yields a bearing maximum inlet pressure of 6.9 Mpa (1000 psi). Static load on the bearing is independently controlled and measured. Orthogonally mounted external shakers are used to excite the test stator in the direction of, and perpendicular to, the static load. The apparatus can independently calculate all rotordynamic coefficients at a given operating condition.

Dynamic Force Response of Spherical Hydrostatic Journal Bearings for Cryogenic Applications

Hydrostatic journal bearings are ideal elements to replace roller bearings as rotor support elements in cryogenic lurbomachinery. These bearings will be used for primary space-power applications due to their long lifetime, low friction and wear, large load capacity, and direct stiffness and damping force coefficients. The performance characteristics of turbulent flow, orifice compensated, spherical hydrostatic journal bearings are presented. These bearings allow tolerance for shaft misalignment without force degradation and are able to support axial loads, thus providing a design configuration which could be used efficiently on high-performance turbomachinery. Bulk-flow mass and momentum equations for the motion of a variable properties liquid on the thin film bearing lands are solved numerically. Predictions of load capacity and force coefficients for a six recess, spherical hydrostatic bearing in a liquid oxygen environment are presented. Fluid film axial forces and dynamic coefficients of a magnitude a...

Theoretical Performance of a Hydrostatic Foil Bearing

The performance of a hydrostatic foil journal bearing operating with an incompressible fluid is discussed. In the configuration considered here, pressurized lubricant fluid is supplied through capillaries to recessed pockets on the surface of the journal. The foil is treated as a perfectly flexible, inextensible shell by a three dimensional finite element model. The pressure distribution is predicted by a finite element formulation of the incompressible Reynolds equation. Results are presented which demonstrate that the foil structure enhances load support while increasing lubricant film thickness. In addition, results indicate that membrane effects are essential in the structural model.