Optimisation of slot entry hybrid gas bearings

Optimisation of hybrid gas bearings is considered from the view-point of minimum total power dissipation on load per unit power of the bearing. The optimisation techniques presented in this paper are derived on a varyin clearance basis. The selection of bearing design parameters for the optimum condition varies according to the restraints and constraints of the design. Therefore, the bearing design parameters are related and selected in order to achieve the optimum performance. The optimum design condition for minimum total power dissipation occurs when the friction power is three times the pumping power (K = 3).     

Analysis of orifice compensated externally pressurized gas bearings

Dynamic performance of orifice compensated externally pressurized gas bearings is considered. By adopting the finite element method and modifying the perturbation formulation of Lund, stiffness coefficients, damping coefficients, critical mass and threshold speed for various bearing eccentricities and design parameters have been computed.     

Empirical correlations for the pressure depression in externally pressurized gas bearings

The pressure depression phenomenon, usually observed in the inlet region of externally pressurized gas bearings, is predicated by constructing a simple empirical model. The same sets of experimental data, used previously by other investigators, were used to obtain the empirical equations which formulate the proposed model. Three correlations are proposed. These are the inlet pressure correlation, the minimum pressure correlation, and the position of the minimum pressure within the inlet region. Comparisons between the values obtained using these correlations and available experimental data show good agreement. Further, a comparison between the present model and another previously proposed model shows that the present one gives better results. In addition, comparison between the proposed model and available experimental data shows that the model correctly predicts pressure variations, which occur due to the effect of pressure depression, within the inlet region.     

Static and dynamic characteristics of externally pressurized circular step thrust bearings lubricated with couple stress fluids

The combined effects of couple stresses, fluid inertia and recess volume fluid compressibility on the steady-state performance and the dynamic stiffness and damping characteristics of hydrostatic circular step thrust bearings are presented theoretically. Based on the micro-continuum theory, the modified Reynolds equation and the recess flow continuity equation are derived by using the Stokes constitutive equations to account for the couple stress effect resulting from a lubricant blended with various additives. Using a perturbation technique, results in terms of steady-state load-carrying capacity, oil flow rate, stiffness and damping coefficients are presented. A design example is also illustrated for engineering and industrial applications.     

Static tilt characteristics of aerostatic rectangular double-pad thrust bearings with compound restrictors

Aerostatic rectangular thrust bearings with compound restrictors have often been used in ultra-precision machine tools and precision measuring equipment because high bearing stiffness is easily achieved. Compound restrictors combine a feed-hole restrictor with a groove compensation restrictor. This paper investigates, theoretically and experimentally, the static tilt characteristics of aerostatic rectangular double-pad thrust bearings with compound restrictors, when coupled loads or offset loads are applied. Furthermore, the usefulness of aerostatic thrust bearings with compound restrictors is clarified by comparison with the characteristics of conventional aerostatic thrust bearing with feedhole restrictors.     

Externally pressurized gas journal bearing with slot restrictors arranged in the axial direction

In this study, a novel rectangular slot restriction-type externally pressurized gas journal bearing was developed for use in high-speed rotating machinery, such as medical devices and industrial machines. The proposed bearing has several rectangular slot restrictors arranged in the inner surface of the bearing. To measure the bearing characteristics, a model was developed for the numerical calculation of the pressure distribution in the bearing clearance and the static characteristics of the bearing. The proposed bearing, which consists of two parts, was designed and can be manufactured using appropriate techniques. In this study, a prototype bearing with eight slots in its surface was manufactured as a test piece for fundamental tests. The diameter and length of the test bearing are 30 and 40 mm, respectively. The roundness of the bearing was measured using a three-dimensional coordinate measuring machine, and the results were used in the analysis. The pressure distribution and static characteristics obtained experimentally were found to be in good agreement with the calculated values. In the rotational tests, the rotor speed exceeded 380 Hz (22,800 rpm), and whirl vibration did not occur. During testing, the maximum rotor vibration amplitude was 0.002 mm, corresponding to an eccentricity ratio of 0.3.     

Turbulent lubrication of externally pressurized bearings including convective inertia effects

A numerical solution is developed for the equations governing the turbulent lubrication of externally pressurized circular bearings. The eddy viscosity is based on the nonlinear theory proposed by Elrod and Ng. The effects of fluid convective inertia tobether with these of lubricant acceleration at the recess edge are included in the analysis. Typical graphs showing the influence of recess radius ratio, film thickness ratio, pressure ratio, and method of compensation on the bearing performance—pressure distribution, load, flow rate, power consumption, and stiffness—are presented. Inertia effects are shown to increase or decrease the load factor, flow factor, and power factor, depending upon the values of recess radius ratio and film thickness ratio.     

Analysis of externally pressurized gas bearings with journal rotation

Theoretical studies of rotating externally pressurized gas bearings with multiple pressure sources have been made. The solution is obtained for finite bearings by using pressure perturbation theory. Theoretical results are compared with experimental data. The theory allows good prediction of bearing load capacity, stiffness and attitude angle.     

Sleeve dampers for externally pressurised gas journal bearings

An approximate small eccentricity analysis is presented, for finding the threshold of fractional speed whirl instability of an unloaded double plane admission hybrid gas journal bearing supported by a non-rotating externally pressurised gas journal bearing sleeve damper. A line source is assumed at the feeding planes to the gas film with flow and load correction factors to account for the discreteness of the feed holes (details of these factors are presented in a related publication). The results show that, by careful selection of the design parameters, it is possible almost to remove fractional speed whirl instability from the bearing arrangement. Some practical designs of sleeve dampers are also presented.     

Design of externally pressurized gas bearings for stiffness and damping

A design method for flat, circular thrust bearings is presented in this paper. The design method is based upon a new dynamic model of the bearing and permits the selection of stiffness and damping for applications of bearings in vibrating environments. Application of the design method to the tuning of bearing dynamics is emphasized here, while the development of the dynamic model is discussed in other references. Design constraints are considered in the iterative design procedure and are illustrated in a bearing design example.     

Dynamic behaviour of externally pressurized gas journal bearings with multiple supply holes

A theoretical analysis of the dynamic behaviour of externally pressurized journal bearings using a compressible lubricant is made. Two aspects, (i) “squeeze-film” due to harmonic vibration of a stationary journal and (ii) steady-whirl instability of an unloaded rotating journal were studied. The bearing configuration considered had double plane admission feed holes at quarter station. The effect of recess volume at the downstream of the orifices was considered. The dynamic load and moment were determined for various frequencies, recess volumes and bearing design dimensions. Stability charts of whirl are given for various journal speeds, feed and bearing design parameters.     

Plane vibration characteristics of multired externally pressurized oil journal bearings

Externally pressurised oil journal bearings are often subjected to dynamic loading and vibration. A theoretical analysis of the dynamic behaviour of orifice compensated bearings is presented and a design procedure outlined. The analysis assumes that the journal undergoes plane harmonic vibration about its mean steady state position in the absence of shaft rotation. The lubricant is assumed to be isovicous and incompressible. Stiffness and damping characteristics are presented.     

Experimental study of journal bearings with undulating journal surface

A journal bearing test rig was designed and constructed to test the behaviour of journals with wavy surfaces, the circumferential undulations being varied both in amplitude and in number. Results show that wavy journal surfaces may well enhance the load carrying capacity of a bearing. Moreover, surface undulations are shown to move the journal centre locus closer to the load line, ie cause a lower attitude angle. These effects are found to be more pronounced with larger wave amplitudes, and with higher numbers of waves around the journal circumference. In general, friction is found to be reduced with increase in surface wave amplitude.Good agreement is shown to exist between test results and a computer aided analysis conducted by the authors to predict wavy journals performance¹. It has been established that a wavy journal surface may, under certain conditions, display higher load capacity, lower friction and permit safer running of journal than bearings with perfectly smooth surfaces.     

Dynamic characteristics of gas-lubricated externally pressurized porous bearings with journal rotation II

The dynamic tilt stiffness and damping coefficients of an externally pressurized porous gas bearing with journal rotation have been calculated theoretically. A periodic disturbance (angular displacement) about the transverse axis is imposed on the bearing and the dynamic pressure distribution is determined by small perturbations of the Reynolds equation. Non-dimensional tilt stiffness and damping coefficients for various design conditions are calculated numerically using a digital computer and presented in the form of figures and tables.     

Tilt stiffness and damping of externally pressurized porous gas journal bearings

The dynamic behaviour of an externally pressurized porous gas journal bearing is analysed by assuming one-dimensional flow through the porous bushing. A periodic disturbance (angular displacement) about the transverse axis is imposed on the bearing and the resulting dynamic pressure distribution is determined by small perturbations of the Reynolds equation. A finite difference method is used to determine the dynamic pressure. Design data for tilt stiffness and damping as a function of squeeze number, feeding parameter, supply pressure and porosity parameter are calculated numerically using a digital computer and are presented in tables and figures.     

Dynamic tilt characteristics of aerostatic rectangular double-pad thrust bearings with compound restrictors

Aerostatic rectangular double-pad thrust bearings with compound restrictors have often been used in linear guideway systems of ultra-precision machine tools and precision measuring equipments, because high bearing stiffness is easily achieved in these bearings. However, in actual devices, various dynamic loads as well as static loads are imposed on these aerostatic bearings. Therefore, in this paper, the dynamic stiffness and damping coefficient of this type of bearing for tilt motion of a shaft are investigated, both theoretically and experimentally. It was consequently found that the dynamic tilt characteristics of the aerostatic thrust bearings considered in this paper are greatly influenced not only by design parameters such as the groove position and the groove depth but also by the squeeze effect.     

Dynamic characteristics of gas-lubricated externally pressurized porous bearings with journal rotation: I

The dynamic stiffness and damping coefficients of an externally pressurized porous bearing with journal rotation have been calculated theoretically by assuming one-dimensional flow through the porous wall. A periodic disturbance (displacement) is imposed on the journal around its concentric position and the dynamic pressure distribution is determined by small perturbations of the modified Reynolds equation. Non-dimensional stiffness and damping coefficients for various design conditions are calculated numerically using a digital computer and presented in the form of design charts and tables.     

High-speed stability of a rigid rotor supported by aerostatic journal bearings with compound restrictors

Demands for higher rotational speed and accuracy for effective manufacture of small holes on printed circuit boards and very small precise parts have been increasing remarkably. Aerostatic journal bearings with compound restrictors have greater stiffness than those with conventional inherently compensated restrictors and are one of the most effective candidates to satisfy these demands. In this work, the instability of a rigid rotor supported by aerostatic journal bearings with compound restrictors was investigated numerically and experimentally. It was found that this type of aerostatic bearings showed a much higher threshold speed for instability compared with bearings with inherently compensated restrictors.     

Optimum design of hydrostatic journal bearings Part II. Minimum power

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     

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