An Investigation of the Steady-State Performance of a Pivoted Shoe Journal Bearing with ISO VG 32 and VG 68 Oils

This article presents a report on an investigation into the performance characteristics of a steadily loaded pivoted shoe journal (PSJ) bearing that is lubricated with ISO VG 32 and VG 68 oils. The article describes a testing machine on which the experimental investigation was performed. Measurements of shaft torque, pad temperature distributions, oil inlet and outlet temperatures, oil flow rate, and eccentricity have all been recorded as functions of load and speed. The experimental results from both test oils are presented in graphical form and are compared with theoretical predictions obtained from the author's computer model of the PSJ bearing. These results showed that the thicker ISO VG 68 oil provided thicker oil films. However, it also had higher bearing temperatures and power losses. A good correlation between the theoretical and experimental results has been found. Theoretical analysis of the bearing friction losses indicate that shear losses predominate and churning losses account for approximately 20% of the total losses.     

Effect of Fluid Inertia on Journal Bearing Parameters

In the modeling and analysis of rotordynamic systems with journal bearings, the stiffness and damping parameters are usually obtained from the Reynolds equation of hydrodynamic lubrication. The Reynolds equation is derived from the continuity and momentum equations with several assumptions; the principal one among them being that the inertia terms are negligible since the lubricant flow is viscosity-dominated. Some previous work has shown, however, that the effect of fluid inertia on the static and dynamic properties of a bearing is not negligible in many circumstances.

This paper uses a perturbation approach to present a rigorous derivation of the correction terms to be added to account for the effect of inertia in the case of a journal on a short bearing. The governing equation for pressure correction is derived and the corrected stiffness, damping, and inertia coefficients to the first order are displayed as a function of the equilibrium position.     

Dynamic Stiffness and Damping Characteristics of a High-Temperature Air Foil Journal Bearing

Using a high-temperature optically based displacement measurement system, a foil air bearing s stiffness and damping characteristics were experimentally determined. Results were obtained over a range of modified Sommerfeld Number from 1.5E6 to 1.5E7, and at temperatures from 25° to 538°C.

An Experimental procedure was developed comparing the error in two curve fitting functions to reveal different modes of physical behavior throughout the operating domain. The maximum change in dimensionless stiffness was 3.0E-2 to 6.5E-2 over the Sommerfeld Number range tested. Stiffness decreased with temperature by as much as a factor of two from 25° to 538°C. Dimensionless damping was a stronger function of Sommerfeld Number ranging from 20 to 300. As the temperature is increased, the damping shifts from a viscous type to a frictional type.     

The Static and Dynamic Characteristics of a Two-Lobe Journal Bearing Lubricated with Couple-Stress Fluid

Static and dynamic characteristics of two-lobe journal bearings lubricated with couple-stress fluids are studied. The load-carrying capacity, the stiffness and damping coefficients, the non-dimensional critical mass, and the whirl ratio are determined for various values of the couple stress parameter l. The results obtained are compared with the characteristics of two-lobe bearings lubricated with Newtonian fluids. It is found that the effect of the couple stress parameter is very significant on the performance of the journal bearing. The stability is improved compared to bearings lubricated with Newtonian fluids.     

Test Results Comparing the Effect of Reverse Rotation on Offset Pivot Journal Bearing Pad Temperatures

Abstract

Babbitt temperatures in pivoted shoe bearings can be significantly reduced by offsetting the pad pivots in the direction of rotation. However, reverse rotation can occur in certain types of machinery under temporary or adverse conditions. The offset is then in the wrong direction and it becomes important to know if the bearing can withstand the reverse rotation operating conditions without damage. This paper compares pad temperature data from tests of a 152.4-mm, 60 percent offset bearing in forward and reverse rotation. The data indicate that the offset pivot bearing can run in reverse without damage for the operating conditions tested. Reverse rotation pad temperatures are hotter. Discussions towards the end of the paper address assessment of the data.     

A Study of the Steady-State Performance of a Pressurized Air Wave Bearing at Concentric Position

The steady-state performance of a pressurized air wave bearing in concentric position is predicted using a commercial computational fluid dynamics (CFD) code. This code solves the three-dimensional compressible Navier-Stokes equations in the turbulent regime, taking into account the real geometry of both the bearing fluid film and the supply regions. The code can provide detailed information about the flow (pressure, turbulent kinetic energy distributions, velocity profiles, etc.) in all bearing regions including the supply holes. This approach does not involve a correction of the flow rate with an empirical discharge coefficient. The predicted values of the supply flow rates are compared to the experimental values obtained with a dedicated wave bearing test rig located at NASA Glenn Research Center in Cleveland, Ohio.     

Turbulent Journal Bearings: Dimensionless Steady-State Performance Charts for the Two-Axial Groove Case

Under conditions of high sliding speed, the lubricant film in hydrodynamic bearings becomes turbulent, and large errors can occur if analysis and design are then based on the commonly used laminar theories.

One method of taking into account turbulence in the oil film is to use a modified form of Reynolds equation. Such an equation tins been used to produce dimensionless performance data for journal bearings with two axial grooves.

These data are presented in graphical form in order to give a direct appreciation of the effects of turbulence on dimensionless characteristics and also in tabular form to permit the data to be incorporated into full design procedures.     

Fixed-Geometry,Hydrodynamic Bearing with Enhanced Stability Characteristics

This article presents the results of a successful bearing optimization study aimed at identifying a fixed-geometry, hydro-dynamic journal bearing that does not suffer from the low load instability typical of this class of bearings. This goal was met through optimization of a fairly simple objective function based on the rigid rotor whirl-speed ratio, using a constrained, nonlinear algorithm based on sequential quadratic programming. In the interests of reducing computational time, a two-dimensional isoviscous formulation of the Reynolds equation was used for this work. The equation was solved using a finite element approach.

This article includes a discussion of the optimization approach, the finite element solution approach, the resulting bearing design, and its performance characteristics. It concludes with an application example comparing the optimized bearing's predicted performance to a tilting-pad bearing's predicted performance for a centrifugal compressor-like rotor. The mismatch between shaft and bearing stiffness due to the rigid rotor optimization makes the optimized bearing less desirable from an unbalance response point of view. However, the optimized bearing is shown to have very good stability characteristics, which compare favorably to a tilting-pad bearing.     

Design,Fabrication, and Performance of Open Source Generation I and II Compliant Hydrodynamic Gas Foil Bearings

Foil gas bearings are self-acting hydrodynamic bearings made from sheet metal foils comprised of at least two layers. The innermost “top foil” layer traps a gas pressure film that supports a load while a layer or layers underneath provide an elastic foundation. Foil bearings are used in many lightly loaded, high-speed turbomachines such as compressors used for aircraft pressurization and small microturbines. Foil gas bearings provide a means to eliminate the oil system leading to reduced weight and enhanced temperature capability. The general lack of familiarity of the foil bearing design and manufacturing process has hindered their widespread dissemination. This paper reviews the publicly available literature to demonstrate the design, fabrication, and performance testing of both first- and second-generation bump-style foil bearings. It is anticipated that this paper may serve as an effective starting point for new development activities employing foil bearing technology.     

Experimental Determination of the Dynamic Characteristics of a Two-Axial Groove Journal Bearing

A hydrodynamic bearing test rig was used to experimentally study the steady operating characteristics and dynamic coefficient of a plain two-axial groove journal bearing. Using two electrodynamic shakers to generate synchronous sinusoidal excitations, two small independent elliptical displacement orbits were produced for different static equilibrium positions. Data was measured for two fixed shaft speeds, while the steady load was varied to achieve Sommerfeld numbers ranging from 0.063 to 0.344. The four linearized stiffness and four linearized damping coefficients were determined for each speed-load condition by reducing the orbital data using an average magnitude and phase method. The coefficients are presented in dimensionless form as functions of the Sommerfeld number. Typical average uncertainty was found to be 12 percent for the coefficients and 8 percent for the Sommelfeld number. For the speed, load, and temperature ranges tested herein, the dynamic coefficient results for each speed agreed within the uncertainty of the data, supporting the first order approximation that, for the operating range studied, a coefficient's magnitude is independent of the absolute speed, load, and viscosity so long as the Sommerfeld number is matched. The same conclusion was reached for the steady operating location within the bearing clearance space. The overall consistency of these results also lends confidence as to their reliability. Additional experimental results presented include three sets of continuous circumferential oil film thickness and pressure profiles, and discrete temperatures.     

Severity Estimation of Cracked Shaft Vibrations within Fluid Film Bearings

The equations of motion, with four degrees of freedom, taking into consideration the flexibility, damping and cross coupling of the fluid film bearings are derived for a cracked Jeffcott rotor supported on fluid film bearings.

Dimensionless equations are developed for dynamic radial load, dynamic pressure developed in the fluid film bearings and coefficient of dissipation considering the journal vibrations in two harmonics; bearing fluid film stiffness and damping coefficients. These are applied to a cracked Jeffcott rotor supported on different types of bearings, i.e., cylindrical journal bearings, offset cylindrical bearings, tilting pad journal bearings and three-lobe bearings. Based on the allowable dynamic pressure developed in the fluid bearings, the severity of cracked shaft and allowable crack depths are estimated in this study. Measurement of dynamic pressure and dissipation for monitoring the crack growth is suggested. However, 2x vibration is the best indicator of cracks in the shafts.     

Boundary Conditions of Cavitation Regions in Journal Bearings

The behavior of the oil in a cavitation region is studied. Boundary conditions of the pressure distribution at the inlet and at the outlet border of such a region are given. Calculation of the power loss in a cavitated zone is demonstrated.     

Performance Experiments with a 200 mm,Offset Pivot Journal Pad Bearing

Journal bearings are an important design option, particularly appropriate for high-speed rotating machinery applications. This paper presents results from an extensive program of experimental work with a 200 mm, five-shoe, tilting-pad bearing of this type. The tilting pads were fitted with offset pivots; this is in contrast to most previous work which has concentrated on bearings with pads which have centrally mounted pivots. The new results obtained for the offset pivot pad bearing are compared with recently published, equivalent results for the same bearing filled with center pivot pads. A substantial temperature reduction in bearing temperature is revealed for the offset pivot case.     

Identification of Journal Bearing Force Coefficients under High Dynamic Loading Centered Static Operation

Lightly damped rotor bearing systems experience large amplitudes of vibration when traversing critical speeds. Bearing linearized force coefficients, strictly valid for minute motions about an equilibrium position, may not be reliable for design or troubleshooting in rotordynamics predictive analyses. Experiments assessing the dynamic forced response of a plain journal bearing undergoing large orbital motions due to single-frequency excitation forces were conducted in a test rig. The short test bearing of slenderness ratio L/D = 0.25 has a nominal radial clearance of 0.127 mm (5 mils). Tests were conducted at three rotor speeds (900, 1800, and 2700 rpm), three feed pressures (1, 3, and 6 psig), and three excitation frequencies (15, 30, and 45 Hz). Baseline bearing motions due to shaft runout are recorded and subtracted in the parameter identification procedure. The forces exerted on the bearing induce large orbital motions with peak amplitudes exceeding 50% of the nominal bearing clearance. Identified cross-coupled stiffness and direct damping coefficients fall within value bands predicted by the π and 2π models of the fluid film, even for the largest amplitudes of motion. The bearing whirl frequency ratio approaches the typical 50% value at the highest speed tested. Excitation frequency has a marked influence of the test direct dynamic stiffness coefficients with added mass coefficients at least twice as large as predicted values.     

The Finite Sector Thrust Gas Lubricated Step Bearing

The principal object of this paper is to demonstrate the effect of compressibility of lubricant gas on the performance of a particular type of sector step bearing when the lubricant undergoes an isothermal process.

It is noticed that for small film thickness, deviation from the continuous medium such as the slip flow phenomenon may take place irrespective of the absolute magnitude of the flow density. When the Knudsen number, which is a measure of this phenomenon, is small the flow may still be treated macroscopically.

By assuming a liquid having the same viscosity coefficient, the performance of the bearing for an incompressible lubricant is also evaluated and compared with that for a compressible lubricant over a range of the important physical parameters.     

Aerostatic and Aerodynamic Performance of an In-Pump Spirally Grooved Thrust Bearing: Analysis and Comparisons to Static Load Experiments

The combined effects of external pressurization and in-pump spiral grooves are studied according to the incompressible Whipple analysis; the results are examined in terms of non-dimensional parameters that bring out the interaction between the action of the spiral groove self-pressurization and that of the external pressurization through orifices. It is found that the interaction is significant when the supply pressure level to the orifices is near the peak pressure that can be reached by the spiral grooves alone. An optimized interacting design can improve the bearing stiffness. Away from the optimized interacting design, one of the two actions would dominate and the other one would cause a detraction of the bearing performance. As speed is sufficiently high, the pressurization action of spiral grooves causes the reduction of orifice flow and even its reversal. At such a condition the orifices are merely leakage paths that detract from the self-pressurization action of the spiral grooves. These predicted trends are qualitatively substantiated by tests.     

设计动压向心滑动轴承的膜厚系数法

提出了膜厚系数和温升系数的概念，并给出了它们和长径比、相对偏心率的关系线图。利用这些线图，可以很方便地进行液体摩擦动压向心滑动轴承的设计。     

Laminar Flow in Hydrostatic Circular Step Bearings with Variable Gap

Simplified expressions for calculating pressure, load and adiabatic temperature distributions for laminar flow in hydrostatic circular step bearings have been derived. This derivation takes into account fluid inertia (convective and rotational) and a variable gap as a function of the radial position. Analytical expressions were calculated for the case in which the gap varies linearly, for positive and negative flows. An application to the analysis of the high-pressure seals corresponding to the main circulation pumps at the Atucha 1 nuclear power plant is presented.     

The Design of Externally Pressurized Gas Lubricated Bearings by the Method of Bearing Equivalence

This paper presents the theoretical development and experimental verification of a simplified technique for the design of externally pressurized gas lubricated bearings. The general procedure is to establish an equivalent rectangular bearing which is the performance replica of an arbitrary gas bearing configuration. The resulting equivalent bearing has the same load support, clearance, area, source pressure, entrance losses, and mass flow as the arbitrary bearing which is analyzed. In accomplishing this end, the general rectangular bearing is analyzed, a consistent criterion of equivalence is defined, and theoretical analyses are compared to experimental data.     

Steady-State and Transient Dynamic Simulation of a Continuous Foil Bearing

The objective of this paper is to present an integrated procedure which will analyze the dynamics of a foil hearing on elastic supports. A complete time-dependent Navier-Stokes formulation is used to solve for the interaction between the hydrodynamic effects of the fluid lubricant, the motion of the journal, and the deformable foil boundary. The elastic deformation of the foil and its supports are simulated by a finite-element model. The steady-state, quasi-transient and full transient dynamics of the foil-fluid-journal interaction are examined. For the steady-state simulation of a particular journal position, the fluid lubricant pressures are evaluated by means of a joint iterative scheme until convergence is achieved in both the fluid pressure and the corresponding foil deformation. For the quasi-transient case, the transient motion of the journal is calculated using a numerical integration scheme for the velocity and displacement of the journal. The deformation of the foil is calculated through numerical iteration in the feedback mode in combination with the fluid film pressure generated by the journal motion, until convergence at every time step is achieved. For the full transient simulation, a parallel real-time integration scheme is used, at each time step, to simultaneously evaluate the new journal position and the new deformed shape of the foil.