Optimum design of hydrostatic journal bearings Part I: Maximum load capacity

The optimization problem is formulated with a view to maximizing the load-carrying capacity of hydrostatic journal bearings. Equations governing the performance of multi-recess hydrostatic journal bearings are summarized. Practical design limits and operational constraints are also defined. The optimization process is based on the well known Rosenbrock method. Results illustrating the effect of area ratio, axial land width and circumferential land width on load capacity, flow rate and power ration are reported. In conclusion precision bearings with small clearances and low pressure ratios are recommended for applications involving low supply pressures, while bearings with large clearances and pressure ratios close to 0.5 are recommended for applications involving high supply pressures     

On the design and development of hybrid journal bearings: a review

This paper presents a comprehensive review of developments in the design and application of hydrostatic and hybrid journal bearing systems during the last few decades. Revolutionary changes have taken place in the applications of hydrostatic and hybrid journal bearings, from very low‐speed radar to very high‐speed turbo‐machinery and ultra‐precision machine tools requiring high stiffness to improve accuracy. Hydrostatic and hybrid bearings are of interest because of their potential at very high operating speed and heavy load‐carrying capacity. This paper also outlines the analyses done of these types of journal bearings in practical application, which has led to improved bearing design. This review critically discusses the parameters that significantly affect the static and dynamic performance of a journal bearing. This review includes coverage of recent publications in the literature pertaining to hydrostatic and hybrid journal bearings focusing on the influence of parameters such as bearing geometry, supply pressure, flow control devices, fluid compressibility, fluid inertia, journal misalignment, bearing flexibility, surface roughness, and thermal effects. Copyright © 2006 John Wiley & Sons, Ltd.     

Performance characteristics of a capillary-compensated hydrostatic journal bearing

Results are presented of an extensive experimental investigation into the performance of a six-pocket hydrostatic journal bearing with pockets of non-uniform depth subjected to a range of static loads. Lubricating oil was supplied, at pressures of up to 8.957 MN m^?2 (1300 Ibf in^?2), to capillarytype restrictors, connected to the six pockets in the bearing. The bearing had an $\text{L}\text{D}$ ratio of unity and operated with a journal rotation ranging from zero to 2000 rev min^?1.The measured load capacity and the stiffness characteristics indicated that bearings of this type had a significant load capacity which was limited by the bending of the shaft. The load capacity increased with speed at low supply pressures, but decreased slightly with increasing speed at higher supply pressures. The stiffness increased with eccentricity ratio except at low supply pressures. Film pressure surveys aided the elucidation of some of the bearing performance characteristics.     

Aspects of the performance of externally pressurized journal bearings

The performance of externally pressurized journal bearings with four and six pockets was investigated experimentally. The influences of supply pressure, rotation and restrictor characteristics on the behaviour of the bearings operating under static loading are examined in the light of available theoretical and design information.Load capacities were found to be generally higher with the greater number of pockets but for both bearings the loads supported at given eccentricities are strongly influenced, in some ways unexpectedly, by restrictor non-linearity and the effects of rotation. At low supply pressures the loads are enhanced by increased rotational speeds whereas at high supply pressures the opposite occurs.     

On the Magnitude of Cavitation Pressure of Steady-State Lubrication

The value of cavitation pressure plays an important role in the implementation of the mass-conservative algorithm. This is particularly crucial in applications that deal with analysis of surface textures. In this paper, published research on cavitation of journal bearing and surface textures are reviewed, and experiments and simulations of textured surface are conducted in order to gain insight into the choice of cavitation pressure for steady-state lubrication. Contrary to the common assertion that cavitation pressure is close to the ambient pressure, both experiments with journal bearings and simulations of surface textures indicate that low cavitation pressure around 30 kPa is possible. Research reveals that the cavitation pressure in steady-state lubrication is affected by the supply of gas dissolved in the oil film. The results of a series of experiments involving the load-carrying capacity of a textured parallel thrust bearing are presented. The comparison between theoretical and experimental results confirms that the value of cavitation pressure could vary depending on the operating conditions.     

Hybrid journal bearings with particular reference to hole-entry configurations

There is a spectrum of pressure-fed journal bearings ranging from the purely hydrostatic bearing characteristics, ie zero speed operation, to the purely hydrodynamic bearing characteristics which depend completely on speed. Between these two extremes, hybrid bearing characteristics rely on mixed modes of external pressurisation and speed-dependent pressurisation. Large high speed hydrodynamic bearings require the lubricant to be pumped under pressure for temperature control. It is therefore attractive to use this external source of pressure to enhance the start-up performance by reducing wear and improving stability. Hybrid bearings offer the possibility of improving on both the zero-speed characteristics of hydrostatic bearings and on the whole range of speed characteristics of hydrodynamic bearings. It is concluded that hole-entry bearings may be particularly effective when compared with other bearing configurations for good load support and low energy consumption, when used in any of the four modes of operation including: zero-speed hydrostatic mode; high-speed hydrodynamic mode; zero and high-speed hybrid mode; and jacking mode where areas are pressurised for start-up. A modification to the procedure for solving the Reynolds equation is introduced to cope with cavitated regions. The technique presented for solving the bearing pressures and cavitation boundaries is efficient and has relevance to any type of liquid film bearing     

Design of multirecess hydrostatic oil journal bearings

This paper presents computer generated design data in terms of load capacity and oil flow for multirecess hydrostatic journal bearings. The Reynolds equation for a finite bearing was solved on a high speed digital computer satisfying appropriate boundary conditions and using the finite difference method. Results for various L/D ratios, recess to bearing area ratios, number of recesses etc are presented for capillary and orifice compensated bearings.     

A study of slot-entry hydrostatic/hybrid journal bearing using the finite element method

A theoretical study concerning the static and dynamic performance of hydrostatic/hybrid journal bearing compensated by slot restrictor has been presented using the finite element method (FEM). Results have been presented for a double row symmetric as well as asymmetric configurations for different values of slot width ratios (SWR) and external load ( ). In order to have a better understanding of their performance vis-à-vis other non-recessed bearing configurations, the performance characteristics of slot-entry journal bearings have been compared with that of similar hole-entry compensated journal bearings using capillary, orifice and constant flow valve restrictors for the same bearing geometric and operating parameters. The comparative study indicates that asymmetric slot-entry journal bearings provide an improved stability threshold speed margin compared with asymmetric hole entry journal bearings compensated by capillary, orifice and constant flow valve restrictors.     

A Porous Hydrostatic Gas Bearing for Use in Miniature Turbomachinery

An analytical program was conducted to establish recommended types of gas-lubricated journal bearings for use in miniature cryogenic turbomachinery. Very high rotative speeds, and the limiting damping properties of gas, indicated that fractional frequency whirl is prevalent, and the most difficult problem to overcome. Of the many journal bearing types investigated, the tilting pad hydro-dynamic and porous hydrostatic journal bearings were suited to the application.

A novel spring mounted, three shoe, porous hydrostatic bearing is discussed in terms of design and experimental results. A 1/2 inch diameter journal bearing is subjected to loading and speeds to 700 grams and 65,000 rpm, respectively. Excellent performance in terms of load capacity, power loss, and flow are indicated. Orbit motions of the floated bearing with respect to the supported shaft demonstrate desirable stability characteristics for the range of tests.     

Calculated load capacity of non-newtonian lubricants in finite width journal bearings

Starting from the most general type of fluid flow equation connecting cubic shear stress to rate of shear for non-Newtonian lubricants, a modified form of Reynolds' equation was derived for steady finite width journal bearings. The finite difference technique with successive over relaxation was used incorporating Reynolds' boundary conditions for pressure to obtain the pressure distribution and hence the load capacity and the attitude angle. It is shown that the flatter pressure profile and higher load capacity at low eccentricity ratios have practical advantages. The apparent viscosity loss at higher rates of shear decreases the load capacity at higher eccentricity ratios but it is expected that the flatter viscosity temperature slope of the polymer thickened non-Newtonian lubricants will compensate for their apparent viscosity decrease.     

Discharge coefficient influence on the performance of aerostatic journal bearings

Aerostatic journal bearings need externally pressurized air. The discharge coefficient is usually assumed constant for sonic and subsonic flow conditions. However, some authors found that it is variable as a function of the pressure ratio, orifice throat discharge and supply pressures. The present study is a theoretical investigation of the discharge coefficient influence on the performance of aerostatic journal bearings. The Reynolds equation for compressible fluids is solved by the finite element method with triangular linear elements. For 0.5 eccentricity ratio, the bearing load carrying capacity difference is 0.5%, although the bearing total mass flow rate difference is 7.4%.     

向心透平发电膨胀机静压气体轴承设计与承载特性分析

为提升有机朗肯循环（organic Rankine cycle,ORC）系统向心透平发电膨胀机静压气体轴承的承载力与刚度,采用表压比法设计了以R245fa为润滑工质的静压气体轴承,分析转子偏心率、供气孔尺寸、进气压力对静压气体轴承承载力与刚度的影响。实验结果表明：在相同供气压力下,轴承承载力与刚度随着转速的增大而增大;在相同转速下,0.7 MPa供气压力相对于其他气体供气压力轴承的承载力与刚度略高;静压气体轴承的偏心率越大承载力越大;相同供气孔直径下,静压气体轴承的承载力与刚度随着转速的升高而升高;随供气孔直径增大,静压气体轴承的承载力和刚度也随之增大。     

Measured Performance of Tilting-Pad Journal Bearings over a Range of Preloads—Part I: Static Operating Conditions

This article presents the measured static characteristics for five tilting-pad journal bearings with a range of preload factors. The bearings had five shoes with static forces applied both on the pad and between pads. The journal diameter was 70 mm, with a length-to-diameter ratio of 0.75, a pivot offset ratio of 0.50, and a nominal assembled radial clearance of 81.3 μm. The rocker-backed pads have nominal radial machined clearances of 176.8, 114.3, 91.4, 73.7, and 61.0 μm. These clearances constitute a range of preloads from ?0.333 to 0.540. Most tilting pad bearings are intentionally designed with positive preloads, although with pivot wear and/or pad and pivot distortion or machining tolerances, bearings can operate with zero or negative preloads. Measured results for bearings with negative preload factors have not previously been available. Measurements reported here were made for a variety of speed-load conditions encompassing a Sommerfeld number of 0.1 to 4.5. The measured parameters are eccentricity magnitude, attitude angle, film thickness, and temperatures sufficient to define thermal boundary conditions. Also measured are oil supply pressure, flow rate, and on-shaft pressure profiles. The focus of the work presented herein is to quantify the influence of preload on film thickness, maximum pad temperature, and eccentricity magnitude and attitude angle. Measurements showed preload had a moderate influence on operating eccentricity but not on attitude angle. Negative preloads resulted in the greatest temperature rise, although all temperature rises were relatively small.     

The Determination of the Characteristics of Hydrostatic Bearings through the use of the Electric Analog Field Plotter

In many applications of hydrostatic lubrication to journal and thrust bearings, determination of flow, load carrying capacity and film thickness is at best an approximation. Anything but the simplest shape is difficult to analyze. The simplified form of Reynolds' equation which applies to hydrostatically lubricated bearings of constant film thickness is analogous to the electric field equation which describes the voltage distribution in a conducting sheet of constant thickness. This analogy suggests the use of the electric analog field plotter to determine the characteristics of hydrostatic bearings.

In this paper the theoretical basis for this method is discussed. In addition, the solution of a journal bearing is presented along with equations for several other useful shapes. Experimental verification of the journal bearing solution is presented, which indicates that this method may be employed with considerable accuracy.     

Modeling of Gas Thermal Effect Based on Energy Equipartition Principle

In the present article, a gas thermal effect is modeled based on the energy equipartition principle. Two new independent state equations for an ideal gas are developed that provide a new way to analyze thermal effects in gas lubrication. Furthermore, the energy equation is derived for gas lubrication and the analysis of thermal effects is carried out on a gas spiral thrust bearing and a gas hydrostatic journal bearing. The results show that gas temperature increases significantly in the lubricated region at high speed for both the thrust and hydrostatic journal bearings, and the thermal effect positively influences the load capacity of the thrust bearing. The gas expansion effect makes the gas temperature decrease in the hydrostatic journal bearing, and the gas temperature decreases with an increase in the inlet pressure.     

Influence of lubricants on the performance of journal bearings – a review

ABSTRACT

The lubricant properties have a significant influence on the static and dynamic performance characteristics of journal bearing such as load-carrying capability, minimum fluid film thickness, maximum pressure, lubricant flow rate, damping coefficients, stiffness coefficients, etc. The present document reviews the behaviour of various lubricants such as power-law lubricants, couple stress lubricants, micropolar lubricants, ionic liquid lubricants and space lubricants. The influence of these lubricants on the performance of hydrostatic, hydrodynamic and hybrid journal bearings is discussed. An effort is made to develop the understanding to choose the suitable lubricant for journal bearings for different journal bearing configurations. Journal bearings operated with non-Newtonian lubricants have shown better performance compared to Newtonian lubricants. Ionic liquid lubricants have shown high potential in vacuum applications and extreme temperature environment such as in bearings of spacecraft moving mechanical assemblies.     

Ferrofluid lubrication of finite journal bearings using Jenkins model

The present study investigates hydrodynamic lubrication by ferrofluids of finite journal bearings using the Jenkins model. A magnetic field created by displaced finite wire is used. A numerical solution for the modified Reynolds equation using the finite difference method is obtained. Static characteristics of finite journal bearings are analyzed using 2 control parameters: magnetic force coefficient and Jenkins viscosity. The obtained results are compared to those from Neurenger‐Rosensweig model. It is shown that pressure, load capacity, attitude angle, and side leakage increase and friction factor decreases when increasing the value of each control parameter at low and medium eccentricity ratios. However, the Jenkins viscosity parameter decreases the load capacity and increases the friction factor at high eccentricity ratios.     

Externally pressurized gas bearings: A comparison between two supply holes configurations

Radial vibration of a vertical rotor with externally pressurized gas bearings is analyzed. The time-dependent Reynolds equation is solved together with the journal equation of motion to obtain the response characteristics of the bearing system. The bearings are supplied with either one or two sets of supply orifices. Stiffness and flow rate are compared for both cases. Stability maps are obtained at different supply pressures and with different supply orifice diameters. The mass range from orbital stability to instability is studied as a function of supply hole downstream pressure level.     

The dynamic behaviour of fluid bearings with grooved lands

In mechanical engineering, grooved mating lands are used for various reasons in a large number of bearing applications. This paper studies the effect of such grooves on the squeeze load characteristics, and hence on the damping capacity, of bearings. A comparison is given between the damping capacity of bearings with grooved lands and that of bearings with equivalent flat lands to give the same pressure flow characteristics. Different bearing configurations, representing thrust and journal applications, are analysed and discussed.     

Approximate Solution of Oil Film Load-carrying Capacity of Turbulent Journal Bearing with Couple Stress Flow

The instability of the rotor dynamic system supported by oil journal bearing is encountered frequently, such as the half-speed whirl of the rotor, which is caused by oil film lubricant with nonlinearity. Currently, more attention is paid to the physical characteristics of oil film due to an oil-lubricated journal bearing being the important supporting component of the bearing-rotor systems and its nonlinear nature. In order to analyze the lubrication characteristics of journal bearings efficiently and save computational efforts, an approximate solution of nonlinear oil film forces of a finite length turbulent journal bearing with couple stress flow is proposed based on Sommerfeld and Ocvirk numbers. Reynolds equation in lubrication of a finite length turbulent journal bearing is solved based on multi-parametric principle. Load-carrying capacity of nonlinear oil film is obtained, and the results obtained by different methods are compared. The validation of the proposed method is verified, meanwhile, the relationships of load-carrying capacity versus eccentricity ratio and width-to-diameter ratio under turbulent and couple stress working conditions are analyzed. The numerical results show that both couple stress flow and eccentricity ratio have obvious influence on oil film pressure distribution, and the proposed method approximates the load-carrying capacity of turbulent journal bearings efficiently with various width-to-diameter ratios. This research proposes an approximate solution of oil film load-carrying capacity of turbulent journal bearings with different width-to-diameter ratios, which are suitable for high eccentricity ratios and heavy loads.