Static characteristics of aerostatic porous rectangular thrust bearings

A theoretical analysis of the steady state performance of aerostatic rectangular thrust bearings with porous pads is presented. The equations governing the gas flow through the porous pad and the bearing clearance are solved simultaneously using a finite-difference method to obtain the pressure distribution in the bearing clearance. The load capacity, the mass rate of flow and the static stiffness are calculated numerically for different bearing dimensions and operating pressures and are presented in graphical form. The load capacity predicted for a square bearing correlates with previous results.     

Dynamic behaviour of aerostatic rectangular thrust bearings

A theoretical study to determine the dynamic stiffness and damping characteristics of an aerostatic rectangular thrust bearing is presented. The governing non-linear partial differential equation of film pressure is linearized using a first-order perturbation method. The perturbed equations are solved numerically to determine the dynamic load, which in turn gives the stiffness and damping characteristics. The effect of various parameters on stiffness and damping is also investigated.     

Analysis of aerostatic porous annular thrust bearings with tilt

A theoretical analysis is presented in order to predict the static characteristics of an aerostatic porous annular thrust bearing with a tilted runner pad. The flow through the porous matrix is assumed to be axial because the thickness of the pad is small compared with its radius. After the pressure in the porous matrix is obtained, the modified Reynolds equation is solved numerically using a finite-difference technique for the pressure distribution in the bearing clearance. The theoretical results are computed numerically in dimensionless form for the load capacity, mass rate of flow and static stiffness for various bearing dimensions and supply conditions. The results are presented in the form of design charts as a function of the feeding parameter. The effect of tilt is to improve the load capacity and the mass rate of flow.     

A simplified method for the correction of velocity slip and inertia effects in porous aerostatic thrust bearings

Inertia effects in porous material, as well as velocity slip at the porous bearing surface, have hindered the use of simple mathematical models for the analyses of porous aerostatic bearings. Experimental evidence indicated that velocity slip at the porous surface did not obey the Beavers model, but could be approximated by an added equivalent clearance. This experimentally determined clearance value did not bear any direct relationship with the surface roughness of the test specimen. Good agreement between theoretical and experimental results of static load capacity of a porous ceramic test bearing, however, demonstrated the use of this equivalent clearance method, in conjunction with a proposed approximation to correct for inertia effects, as an effective modification to the simple one-dimensional model by Sheinberg.     

A tolerancing procedure for inherently compensated, rectangular aerostatic thrust bearings

Manufacturing errors on aerostatic bearing surfaces and orifice geometry are known to impair performance. Theoretical analyses were carried out on a rectangular thrust bearing for the most common form of gap non-uniformities — tilt, concavity, convexity and waviness at various spatial wavelengths, as well as changes in orifice diameter and position from the bearing edge. The results illustrate the sensitivity of both static load and stiffness to various forms of manufacturing error. A tolerancing procedure is recommended to limit changes in static load and stiffness to 10%.     

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.     

Numerical and experimental analysis of aerostatic thrust bearings with porous restrictors

The finite element method is used to predict the performance of aerostatic thrust bearings with a complete porous surface. Results obtained by a 1D and 3D source flow model derived from D’Arcy’s law are compared for rectangular porous bearings having an infinite width. It turns out that the 1D source flow model is adequate for practical design parameters. For a circular aerostatic porous thrust bearing results calculated with several mathematical models for the source flow and slip flow are compared with experimental results. A relatively simple model incorporating unflatness and deformation of the bearing surface correlates well with the experimentally determined bearing performance.     

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.     

Static tilt characteristics of aerostatic rectangular double-pad thrust bearings with double row admissions

Aerostatic thrust bearings have been used in linear guideway systems of various precision measuring apparatus by reasons of low friction, non-hysteresis and high accuracy of motion. In such a case that the measuring systems do not satisfy the Abbé principle, the accuracy of linear guideway systems is greatly influenced by the tilt characteristics in pitch, roll and yaw directions of aerostatic thrust bearings. This paper proposes the application of aerostatic rectangular double-pad thrust bearings with double row admissions of compound restrictors to the linear guideway systems subjected to tilt moments in both pitch and roll directions, and investigates, theoretically and experimentally, the static tilt characteristics of these aerostatic thrust bearings.     

Effects of velocity slip,anisotropy and tilt on the steady state performance of aerostatic porous annular thrust bearings

The analysis predicts the steady state performance characteristics of externally pressurized annular porous gas thrust bearings of finite pad thickness. The modified Reynolds equation, governing the flow in the bearing clearance, is derived from the Navier-Stokes equations using the Beavers-Joseph slip velocity condition at the porous interface. The anisotropy of the porous matrix and the tilt of the bearing are also taken into account. The dimensionless load capacity, the mass rate of flow and the static stiffness are computed numerically and presented in the form of charts for various operating parameters and bearing dimensions. The effect of slip is to reduce the load capacity and to increase the mass rate of flow for all values of the feeding parameter.     

Analysis of aerostatic porous journal bearings using the slip velocity boundary conditions

A theoretical analysis of the static characteristics of aerostatic porous journal bearings is presented using the slip velocity boundary condition at the interface of the lubricating film and porous surface of the bearing. With thin wall bearings, the pressure in the porous bushing is obtained in closed form and the modified Reynolds equation is solved numerically using the finite difference method. The load capacity and the mass rate of flow are expressed non-dimensionally and are calculated numerically for different operating conditions. Variation in $\text{W}\text{?}$ and $\text{G}\text{?}$ with the feeding parameter and other parameters is shown graphically. The effect of velocity slip on $\text{W}\text{?}$ and $\text{G}\text{?}$ for different operating conditions was studied. The theoretical results are compared with a similar available solution using a three-dimensional flow model in the bushing. There is near-perfect agreement.     

The effects of velocity slip on externally pressurized gas porous thrust bearings

A numerical analysis is presented for the velocity slip on an externally pressurized gas porous bearing consisting of a circular pad with a central partially gas-supplied area and sealed circumferential area. Non-axial flow is assumed in the porous matrix. The modified Beavers-Joseph boundary condition of velocity slip is applied at the interface of the porous matrix and lubricating film. The result shows that the solution with the consideration of velocity slip on porous surface tends to agree with the experimental data for increasingly higher values of bearing number.     

CFD investigation of pressure depressions in aerostatic circular thrust bearings

Under certain operating conditions, the pressure distributions of aerostatic thrust bearings experience an undesirable pressure depression which decreases their load carrying capacity. Many investigators reasoned this phenomenon to the occurrence of shock waves in the bearing clearance. Recently, some investigators reasoned this phenomenon to the transition from laminar to turbulent flow and claimed that no shock wave is generated at the boundary between supersonic and subsonic flows. As such, there is a contradiction between these two opinions. In this paper, the rationale of the pressure depression phenomenon in aerostatic thrust bearings is investigated using computational fluid dynamics (CFD) simulations. The turbulent full Navier-Stokes equations for steady, three-dimensional, compressible flows are numerically solved in this study. Two circular bearing configurations are analyzed. The obtained results showed that the predicted pressure distributions along the fluid film compare well with the corresponding experimental data of other investigators. The present computational methodology allowed a clear capturing of the coherent structures of the flowfield in the bearing inlet region which include the coalescing of compression waves into shock waves and the region of shock/boundary layer interaction (pseudo-shock). The thorough understanding of this phenomenon is the first step towards the development of its appropriate control methods.     

Effect of velocity slip in axially undefined porous bearings

A theoretical analysis of the performance characteristics of axially undefined journal bearings was carried out. The analysis takes into account the velocity slip at the surface of the porous medium by using the Beavers-Joseph criterion. Results are presented for various bearing characteristics and compared with earlier results obtained by using the no-slip condition.     

Static behavior and dynamic stability analysis of grooved rectangular aerostatic thrust bearings by modified resistance network method

This paper begins with the development of the resistance network method (RNM) for designing an aerostatic rectangular bearing with X-shaped grooves. The Newmark integration method and the modified RNM, which takes into account the equilibrium of the mass flow rate and the squeeze film effect, are used to analyze the time-dependent dynamic behaviors at each time step.Finally, the stability properties as well as impulse responses of this type of bearing, which simulates variation in film gap caused by imperfect guideway geometry, are demonstrated in the current paper.     

Non-parallel operation of rectangular hydrostatic thrust bearings

A theoretical study of the behaviour of capillary-compensated rectangular hydrostatic thrust bearings with tilt and sliding was made. The influence of the aspect ratio on the load-carrying capacity, flow and stiffness and damping characteristics is discussed.     

Effect of velocity slip on squeeze films in porous bearings

The performance of squeeze films in porous journal bearings was analysed using the Beavers-Joseph criterion of velocity slip at a porous boundary. Closed-form expressions were obtained for the pressure distribution in an infinitely long bearing and also in an infinitely narrow bearing. Numerical results evaluated from these expressions are presented in graphical form to illustrate the influence of velocity slip.     

Magnetohydrodynamic externally pressurized porous thrust bearings

The characteristics of externally pressurized porous thrust bearings in the presence of a transverse applied magnetic field have been studied. It was found that the load capacity increases as the supply pressure, permeability and strength of the magnetic field increase. The time of approach also increases as the strength of the magnetic field increases for a prescribed porosity parameter.     

Inertia effects in magnetohydrodynamic porous conducting thrust bearings

The effects of fluid inertia in an externally pressurized porous conducting thrust bearing in the presence of a transversely applied magnetic field are theoretically analysed. The load capacity increases and the flow flux decreases as the fluid inertia term, the applied magnetic field or the conductivity of the plate increases. Both the load capacity and the flow flux increase with increasing permeability of the plate.     

Effect of velocity slip in an externally pressurized porous circular thrust bearing

Modified expressions for the characteristics of an externally pressurized circular porous thrust bearing have been obtained by using the appropriate conditions given by Beavers and Joseph. The expressions were obtained in closed form by assuming that the flow in the bearing matrix is predominantly axial. The results obtained are in good agreement with experimental observations.