BEARINGS WITH COMPRESSIBLE FLUID

Abstract

Gas lubrication has interesting and important engineer- ing applications which are the motivating reasons for the expanding research in this area. The gas bearings have the advantage of negligible friction losses, cleanliness and, when air is used, easy availability of lubricant. The wear in gas-lubricated bearings is extremely low, a factor which contributes to their long life. These bearings do not contaminate the surroundings and can very well be employed in the presence of severe radiation. Precisely for these reasons the gas bearings find use in electric motors, machine tools, equipment for gas liquefaction, ultracentrifuges, textile machines, turboco npressors and high precision instru- ments such as inertial guidance system for rockets and space ships.. The gas bearings encounter two familiar shortcomings, low lead carrying capacity and hydrodynamic instability. The problem of instability is more pronounced at lower eccentricities, for example in vertical shafts where load support is not a requirement. The Reynolds ecuation for compressible fluid received a lot of attention from the scientists engaged in theoretical investi- gation in this area. Analytical (closed form) solutions of Reynolds eguation are based on she assumption of infinitely long bearing. Methods such as electrical analogy and analog -iv-' field plotter were used for the solution of externally pressurized gas bearings and only a limited experimental work has been done in studying the performance of gas bearings. The numerical methods, particularly those based on finite differences, have been extensively employed to solve gas bearing flow-fields. limitation of the finite difference method is that for every bearing configuration of interest, a preferred coordinate system for which lubrication boundaries conform with constant coordinate lines, may not exist. In such situations special procedures for the non-conforming boundary segments have to be devised. In addition, where abrupt variations of film thickness exist$ auxiliary conditions, such as continuity of flow have to be invoked: The finite element method has lately been in use for obtaining solutions to lubrication problems comparatively more for incompressible fluids but less so for compressible fluids. The finite element method seems to be the most promising method which can be applied to bearings of any complex geometry; in addition to complete generality with regard to the bearing geometry and lubricant property variations, boundary conditions in terms of pressure and flow are simply, incorporat~.U. The non-linearity of the governing Reynolds equation -V. for compressible fluids requires iterative methods for obtaining the solution for static equilibrium condition. To study the dynarhlic behaviour of journal bearing systems using air or any other gas as lubricant, various pertur-bation techniques including the one by Lund have been suggested. Mathematically; the approach suggested by Lund is somewhat cumbersome and time consuming. Further, the actual journal bearing systems almost invariably have some skew which has not been accounted for in most of the reported literature on gas bearings. In contrast to the wealth of information published on analytical investigations of hydrodynamic (plain journal and tilting pad) and externally pressurized gas bearings9 the amount of published material concerned with the non-circular bearings is small. For self-acting and externally pressurized bearings, the detailed studies of dynamic analysis of translatory as well as conical whirls have not been reported so far. In the present work 9 a general approach using finite element method has been cresented. 'Incremental formulation as suggested by Reddi and Chu has been extended to obtain static equilibrium solutions. Perturbation formulation suggested by Lund has been modified for studying the dynamic properties. The modified perturbation method is simpler and straight forward. An integrated analysis based on -vi.. incremental and perturbation formulations and finite element method has been put forward which can accurately predict the static and dynamic performance characteristics and also the stability behaviour of various types of bearings taking into account the complexities of their geometries and axes misalignment. The studies include the self-acting plain journal, non-circular (elliptical and three-lobe) S and externally pressurized bearings. In all the bearing types analysed; the L/D ratio has been taken as 1.0. In non-circular bearings s both elliptical and three-lobe, the ellipticity ratio has been taken as 0.5. The externally pressurized bearing has been provided with orifice compensation and the air inlet to the bearing clearance is through small holes, spaced in two admission planes. Results have been obtained for beErings operating at different supply pressures and compressibility parameters. Static performance in terms of load capacity, bearing flow and friction power loss has been computed. The effect of skew has been considered for computing the static per-formance of plain journal and non-circular bearings. For any dynamical system, its response to dis-turbance and its stability are very important design considerations. The dynamic response of a journal bearing system can be analytically determined if the system is vii disturbed from its equilibrium position. The response for small perturbations is linearly dependent on stiff-ness and damping coefficients. In the bearings having compressible fluids the stiffness and damping coefficients are whirl frequency dependent. Therefore the stiffness and damping coefficients have to be computed for diff- erent whirling frequencies. Detailed data for different bearing types have been computed for half frequency and synchronous whirl conditions. Since both translatory as well as conical whirl have been considered, sixteen stiff-ness and sixteen damping coefficients have been computed for each case. Effect of skew has been considered for computing these coefficients for plain journal bearing. For selected cases y the stability studies for linearized system (both for lateral and angular whirl) have been carried out by Routh's criteria to compute critical mass and critical inertia. Threshold speeds have been obtained from the computed values of critical