Influence of turbulence on the static characteristics of conical journal bearings

Analytical formulas are presented for the static characteristics of conical hydrodynamic and hydrostatic bearings, with variable thermophysical properties and a two-phase lubricant, when turbulence is disregarded or taken into account.     

Steady state and dynamic characteristics of partial journal bearings

The response of the lubricant film of a partial journal bearing to displacements and velocities of its journal for laminar Newtonian flow of the lubricant is presented. The bearing force coefficients (spring and damping coefficients) were evaluated experimentally on a sophisticated test rig, with control over all the essential variables. Test results are presented in non-dimensional form and are applicable to a bearing of 130° arc and with a length-to-diameter ratio of 0.8. Useful design data and a theoretical comparison are given.     

Static and dynamic characteristics of short wavy journal bearings

A general analysis has been done to investigate the static and dynamic performance of short wavy journal bearing. Reynolds equation is solved for both steady‐ and unsteady‐state operations. The steady‐state analysis has been done and compared with circular bearing with respect to their load capacity, flow rate, pressure distribution and friction factor. The unsteady‐state analysis has been used to determine the rotor dynamic coefficients for various eccentricity ratios. These coefficients are used to determine the stability parameters, such as critical mass and whirl ratio, and prove that wave bearing has not only better load carrying capacity but also provides better stability at high speed than circular bearing. Copyright © 2010 John Wiley & Sons, Ltd.     

Lubrication of infinitely long thrust bearings with micropolar fluids

The characteristics of conventional infinitely long thrust bearings were obtained by solving numerically the modified Reynolds equation for the steady laminar flow of an incompressible micropolar fluid that has an increased effective viscosity, especially in thin films. The micropolar fluid pressure and the overall bearing characteristics, as compared with those obtained with a newtonian lubricant, are shown to depend on two groups of micropolar parameters. The bearing performance, in general, is improved by micropolar lubricants.     

A thermohydrodynamic solution for finite journal bearings under dynamic loading conditions

A numerical solution is developed for the equations governing the thermohydrodynamic flow in a finite journal bearing. Both wedge and squeeze pressure contributions are considered. Lubricant viscosity is taken as a function of the temperature distribution in the fluid film. Computer programs are devised to obtain numerical solutions for the prescribed journal centre locus. Thermal effects are shown to be pronounced in laminar flow bearing under dynamic loading conditions.     

Steady state and dynamic characteristics of axial grooved journal bearings

The steady state and dynamic characteristics including whirl instability of oil journal bearings with single axial groove located at the top of the bearing and then at some angular interval from the top from which oil is supplied at constant pressure are obtained theoretically. The Reynolds equation is solved numerically by finite difference method satisfying the appropriate boundary conditions. The dynamic behaviour in terms of stiffness and damping coefficients of fluid film and stability are found using a first-order perturbation method for each location of the groove. It has been shown that both load capacity, end flow is maximum when the feeding groove is at 12° location and thereafter the load capacity falls, stability improves for smaller groove angle and groove length at higher value of eccentricity ratio and speed. The stiffness and damping coefficient magnitude is found to be higher for the bearing with smaller groove angle and groove length, the difference between the hydrodynamic and hydrostatic load increases at 12° groove location.     

Squeeze film characteristics of long partial journal bearings lubricated with couple stress fluids

On the basis of microcontinuum theory, a theoretical analysis of hydrodynamic squeeze film behaviour for long partial journal bearings lubricated by fluids with couple stresses is presented. To take into account the couple stress effects due to the lubricant containing additives or suspended particles, the modified Reynolds equation governing the film pressure is derived by using the Stokes constitutive equations. Various bearing characteristics are then calculated. According to the results obtained, the influence of couple stress effects on the performance of the system is physically apparent and not negligible. Compared with the Newtonian lubricant case, the couple stress effects provide an enhancement in the load-carrying capacity and lengthen the response time of the squeeze film action. On the whole, the presence of couple stresses signifies an improvement in the squeeze film characteristics of the system.     

A study of the dynamic characteristics of synchronously controlled hydrodynamic journal bearings

In this paper, synchronous control of bearing is employed through a control algorithm for an actively controlled hydrodynamic journal bearing in order to suppress whirl instability and to reduce the unbalance response of a rotor-bearing system. Furthermore, a cavitation algorithm, implementing the Jakobsson–Floberg–Olsson boundary condition, is adopted to predict cavitation regions in a fluid film more accurately than the conventional analysis, which uses the Reynolds condition. The unbalance responses and stability characteristics of the rotor-bearing system are investigated for various control gains and phase differences between the bearing and journal motion. It is shown that the unbalance responses of the system can be greatly decreased by synchronous control of the bearing. There is an optimum phase difference, which gives the minimum unbalance response of the system at given operating conditions. It is also found that the stability threshold of the system can be greatly increased by synchronous control of the journal bearing.     

Measurement of friction force and effects of oil fortifier in engine journal bearings under dynamic loading conditions

Commercial base oil and oil fortifier added to this oil are used to investigate the frictional behavior of the engine journal bearings using the theoretical Reynolds equation and experimental test rig. In the theoretical part of the study, the Reynolds equation that states the pressure distribution and friction force with finite width was solved by using the finite difference method. In the experimental part of the study, a new design test rig was conducted to measure the friction force, the lubricant film thickness of the engine journal bearing using base oil under dynamical loaded conditions. The effect of oil fortifier was detected measuring the friction force every three minutes in each 360 crank angle during 15 minutes of experiment. As the theoretical friction results showed similar variation with the experimental measurements of engine bearings, adding oil fortifier to the base oil presented a substantial reduction of friction force during the testing period.     

The cooling effects of supply oil on journal bearings for varying inlet conditions

The cooling effects of the lubricating oil supplied to a full journal bearing through two axial feed grooves each at right angles to the load line are studied. The thermohydrodynamic analysis assumes no heat is removed through either the journal or bush. The results show that the oil temperature distribution along the axial direction of the bearing is usually not uniform. Only if the axial length of the feed grooves approaches the bearing length will the temperature in the high pressure zone be uniformly distributed over its axial length. Both the oil supply pressure and the geometry of the feed grooves control the oil supply rate, which determines the cooling effect of the supply oil. Finally, a formula is suggested for the rate of supply flow     

Effects of oil inlet pressure and inlet position of axially grooved infinitely long journal bearings. Part II: Nonlinear instability analysis

This paper extends the analysis of Part I to investigate the influence of oil inlet pressure and its position on the dynamic characteristics of axially grooved journal bearings. Using the dynamic fluid force derived in Part I, the equations of motion are solved for the locus of the journal center. A trial-and-error method is used to identify the instability threshold speed for a given Sommerfeld number S. The effects of oil inlet pressure (in the range of ) and inlet position (in the range of 0Θ_i90°) on the instability threshold speed of a rotor-bearing system are investigated and discussed. It is shown that the instability threshold speed with oil inlet position Θ_i=0 decreases on increasing the oil inlet pressure from 0 to 1.0 while the influence of oil inlet position on the instability threshold speed depends on the steady state eccentricity ratio ε.     

Performance characteristics of hydrostatic journal bearings with journal rotation by a finite element method

Theoretical studies have been made of a capillary-compensated hydrostatic oil journal bearing supporting a rotating spindle, using a finite element method. Performance data are developed for a four-pocket bearing of $\text{L}\text{D}\text{= 1.0}$. Stiffness and load capacity curves for two significant directions of the line of centres are given for various design parameters and eccentricity ratios. The effects of rotation and the feeding system on the stiffness, load capacity, flow and attitude angle are discussed.     

Numerical calculation and experimental verification of static and dynamic characteristics of aerostatic thrust bearings with small feedholes

In this work, aerostatic annular thrust bearings with feedholes of less than 0.05 mm in diameter are considered, and the static and dynamic characteristics of these bearings are investigated experimentally and numerically. In numerical calculations using the finite difference method (FDM), the discharge coefficients of a small feedhole were determined based on computational fluid dynamics (CFD) software and verified experimentally. In addition, the effect of the bearing surface roughness on the bearing characteristics was analyzed experimentally and numerically. It was confirmed that aerostatic thrust bearings with small feedholes could have larger stiffness and damping coefficient than bearings with compound restrictors.     

Numerical calculation and experimental verification of static and dynamic characteristics of aerostatic thrust bearings with small feedholes

In this work, aerostatic annular thrust bearings with feedholes of less than 0.05 mm in diameter are considered, and the static and dynamic characteristics of these bearings are investigated experimentally and numerically. In numerical calculations using the finite difference method (FDM), the discharge coefficients of a small feedhole were determined based on computational fluid dynamics (CFD) software and verified experimentally. In addition, the effect of the bearing surface roughness on the bearing characteristics was analyzed experimentally and numerically. It was confirmed that aerostatic thrust bearings with small feedholes could have larger stiffness and damping coefficient than bearings with compound restrictors.     

Nonlinear dynamic and bifurcation analysis of short aerodynamic journal bearings

A numerical analysis of a rigid rotor supported by relative short aerodynamic journal bearings is presented for nonlinear dynamic behaviors and bifurcation. The compressible Reynolds' equation is solved by the finite differences method and the successive over relation method and a time-dependent mathematical model for aerodynamic journal bearings is studied. A comparison of the results for the system state trajectory, Poincaré maps, power spectra, and bifurcation diagrams is made and dynamic behavior of the rotor center in the horizontal and vertical directions under different operating conditions is analyzed. The analysis shows how the existence of a complex dynamic behavior comprises periodic and subharmonic response of the rotor center. This paper shows how the dynamic behavior of this type of system varies with changes in bearing number and squeeze number.     

The effect of inlet film boundary conditions on the steady state characteristics of hydrodynamic journal bearings

The well-known solutions for the pressure distribution in the lubricating film of a hydrodynamic journal bearing, satisfying the Reynolds boundary conditions, show a sudden change in the pressure gradient at the position of maximum film thickness, which is possible only if the lubricant is added precisely at this position. Since the pressure develops smoothly because of hydrodynamic action, a correction in the Reynolds boundary conditions is proposed and a new solution for the pressure distribution is obtained. The steady state characteristics of a hydrodynamic journal bearing using the new boundary conditions are compared with the well-known characteristics using the Reynolds boundary conditions.     

Effects of oil inlet pressure and inlet position of axially grooved infinitely long journal bearings. Part I: Analytical solutions and static performance

This paper presents analytical expressions for the dynamic pressure and dynamic fluid force in axially grooved long journal bearings with consideration of oil inlet pressure and inlet position. The effects of oil inlet pressure (in the range of , where the dimensionless oil inlet pressure ) and oil inlet position (in the range of 0Θ_i90°) on the static oil film configuration, pressure distribution, and steady state journal position in axially grooved journal bearings are discussed. In this paper, Reynolds–Floberg–Jakobsson boundary conditions are assumed to account for the appropriate starting position of the cavitation, the reformation of oil film at the end of caviation, and the effect of oil inlet pressure and inlet position.     

Consistency tests for published data on the stiffness characteristics of journal bearings

By considering the flexibility influence coefficients of a journal bearing oil film, this paper shows that, in some published experimental work, static-load loci are inconsistent with corresponding values of displacement coefficients. Consistency tests are described.     

The effect of modified inlet boundary conditions on the stiffness and damping characteristics of finite hydrodynamic journal bearings

The well-known solutions for the pressure distribution in the lubricating film of a hydrodynamic journal bearing, satisfying the Reynolds boundary conditions, show a sudden change in the pressure gradient at the position of maximum film thickness, which is possible only if the lubricant is supplied precisely at this location. Since the pressure develops smoothly because of hydrodynamic action, a correction in the boundary conditions is applied and a modified solution for the pressure distribution is obtained. The stiffness and damping characteristics of a finite hydrodynamic journal bearing using the new boundary conditions are compared with the wellknown characteristics incorporating the Reynolds boundary conditions. There is a significant change in the dynamic characteristics particularly at low values of the eccentricity ratio which can influence the characteristics of rotor-bearing systems.