Pressurized Bearings Research Articles

New method of dynamic test for static stiffness of externally pressurized gas bearing

By instancing externally pressurized spherical gas bearing with inherently compensation, equivalent mathematical model of static stiffness, dynamic stiffness and frequency re- sponse function of aerostatic bearing are built. In the presence of mathematic analysis and numerical experiment, the relation between static stiffness, dynamic stiffness and frequency re- sponse function is opened out theoretically. It is indicated that static stiffness in externally pressurized gas bearing at operating point can be acquired by measure amplitude frequency response characteristics of gas film in low frequency. Operating principle of the test apparatus for spherical gas bearing and influence of apparatus’ mechanical modal to test results are introduced. The results show that the new method of static stiffness measure- ment adopted dynamic test technique is correct and feasible. For inherent nonlinear vibration system consist of gas film and loading mass, dynamic stiffness in low frequency is equal to the static stiffness of the bearing at the operating point. On-line automatic testing of bearing static stiffness can be achieved by the new method and testing accuracy and efficiency is increased. After expansion of excitation frequency to the frequency range involved by mechanical system, static stiffness, dynamic stiff- ness and amplitude frequency response characteristics of exter- nally pressurized gas bearing can be obtained at the same time by the new method. It is highly important to the study of stabil- ity and dynamic property of aerostatic bearing and precise shafting, which can be never implemented only by the static testing method of bearing’s stiffness.

Discharge coefficients of orifice-type restrictor for aerostatic bearings

The paper describes an experimental study conducted in order to determine the supply hole discharge coefficients of externally pressurized gas bearings. Tests were carried out on annular orifices and simple orifices with feed pocket. Air consumption and pressure distributions were measured as a function of supply pressure and air gap height for several different orifice and pocket sizes. Discharge coefficients were approximated by an experimental formula based on the Reynolds number and feeding systems geometry.

Comparison of Rotordynamic Analysis Predictions With the Test Response of Simple Gas Hybrid Bearings for Oil Free Turbomachinery

Current applications of gas film bearings in high-speed oil-free microturbomachinery (<0.4 MW) require calibrated predictive tools to successfully deploy their application to mass-produced systems, for example, oil-free turbochargers. The present investigation details the linear rotordynamic analysis of a test rotor supported on externally pressurized gas bearings. Model predictions are compared with the test rotordynamic response determined through comprehensive experiments conducted on a small rotor supported on three lobed hybrid (hydrostatic/hydrodynamic) rigid gas bearings. Predictions for the rotor-bearing system synchronous response to imbalance show good agreement with measurements during rotor coastdowns, and manifest a decrease in damping ratio as the level of external pressurization increases. The rotor-bearing eigenvalue analysis forwards natural frequencies in accordance with the measurements, and null damping ratios evidence the threshold speeds of rotordynamic instability. Estimated whirl frequency ratios are typically 50% of rotor speed, thus predicting subsynchronous instabilities at lower rotor speeds than found experimentally when increasing the magnitude of feed pressurization. Rationale asserting the nature of the discrepancies calls for further analysis.

RESEARCH ON INTERACTION OF SHOCK WAVES WITH BOUNDARY LAYER IN STATIC GAS BEARINGS

The research work on interaction of shock wave with boundary layer in aerodynamics is reviewed, including its general characteristics, theoretical and experimental researches on interaction of shock wave with boundary layer in externally pressurized gas bearings. With the developments of CFD and micro-fluid testing technology, the pressure distribution, velocity distribution, Mach number distribution in the clearance can be simulated by computer with proper turbulence models according to the flow feature in the separate parts of fluid field, and experimentally tested. A deeper research of the theory on interaction of shock wave with boundary layer in externally pressurized gas bearings will be conducted, and further comprehension of its bearing performance of the inlet region, outlet corner region and bearing feature in the clearance will be advanced.

Rotor‐Bearing System Stability Performance Comparing Hybrid versus Conventional Bearings

New closed‐form expressions for calculating the linear stability thresholds for rigid and flexible Jeffcott systems and the imbalance response for a rotor supported on a hybrid bearing are presented. For typical bearings characteristics, expressions yield stability thresholds practically equal to those reported by Lund (1966). The hybrid bearing design has a single injection port whose location is so chosen to stabilize the bearing performance and to reduce the steady equilibrium attitude angle. Rotordynamics coefficients graphs for conventional and pressurized bearings, as functions of bearing equilibrium eccentricity and/or Sommerfeld number, are presented. Using the rotordynamics coefficients into the expressions for the corresponding velocity thresholds and the imbalance response, the system stability and vibration performances are estimated and analyzed. When comparing the Jeffcott flexible shaft supported on two journal bearings of the conventional type with the hybrid type, the results show a clear superiority of the pressurized design as far as stability behavior is concerned. Specifically for cases of flexible shafts with similar characteristics to those used in industry, the analysis shows that this design yields velocity thresholds 25%–40% higher compared to the conventional circular ones. Also this bearing displays nonlinear feeding pressure behavior, and it is capable of reducing the synchronous vibration amplitude in most speed ranges, except around the critical speed; moreover, for certain Jeffcott configurations the amplitude reduction can be substantial.

Water Drive Spindle for Diamond Turning Machine(Advanced machine tool)

A water drive spindle for diamond turning machines is proposed. The spindle uses water flow for driving the rotor by a water drive motor, for supporting the rotor by water hydrostatic pressure bearings, as well as for coolant. As water is not only incompressible and clean but also low viscosity fluid, it is considered that a high-speed and precise rotational motion will be possible in the clean environments for the precision machining. The present paper reports a structure of the spindle as well as the operational principle of the spindle. In the present paper, theoretical equations used for designing the spindle is derived. The characteristics of the spindle are studied theoretically and experimentally. A result of the diamond turning test using the developed water drive spindle is also presented.

Ultra-precision rotating reference based on self-acting external-pressure complex action principle

In order to increase the loading capacity and stiffness of a gas lubricated rotating reference and its anti-disturbance capability, and further improve the rotating precision, this paper puts forward a kind of ultra-precision rotating reference based on a self-acting external pressure complex action principle. First two important parameters were defined, the external pressurized bearing number, and the pressure ratio of the complex action gas bearing. On this basis, the analytical model of this rotating reference was set up completely. This model shows that the loading capacity function of the rotating reference is composed of six items. According to this analytical model, ignoring the self-acting effect, the loading capacity and stiffness increased to 30% higher than the usual in an external pressurized gas lubricated reference.

Modeling and Identification of Gas Journal Bearings: Externally Pressurized Gas Bearing Results

Static and dynamic characteristics of externally pressurized gas journal bearings with four supply orifices positioned at the central cross section for rotating shaft displacements near the bearing center are investigated. Results for transfer functions and for gas-film coefficients derived using the developed mathematical model are compared with the results derived from numerical computations of a nonlinear distributed parameter model of the gas bearings. Averaging and corrective coefficients are elaborated. The results obtained demonstrate that analytical data are in good agreement with the numerical data for the wide range of parameters and the mathematical model developed makes the simple calculation of static and dynamic characteristics of this type of externally pressurized gas bearings possible. Derived analytical relations for transfer functions and for gas-film coefficients of gas bearings provide an efficient means for designing rotor-bearing systems.

Modeling and Identification of Gas Journal Bearings: Self-Acting Gas Bearing Results

A mathematical model is elaborated with analytical relations for transfer functions and for gas-film stiffness and damping coefficients for self-acting and externally pressurized gas journal bearings with four supply orifices positioned at the center plane for rotating shaft displacements near the bearing center. Averaging and corrective coefficients are elaborated. In this paper static and dynamic characteristics of self-acting gas bearings are investigated. Results derived using the developed mathematical model are compared with the results derived from numerical computations of a non-linear distributed parameter model of the gas bearings. The results obtained demonstrate that analytical data are in good agreement with the numerical data for wide range of parameters and the mathematical model developed makes the simple calculation of static and dynamic characteristics of self-acting gas bearings possible. Derived analytical relations for transfer functions and for gas-film coefficients of gas bearings provide an efficient means for designing rotor-bearing systems.

Externally pressurized gas bearings in a mixed configuration

This paper analyses the stabilityof an externally pressurized gas bearing (EPB) in a series-parallel arrangement. This mixed con. guration is an alternative to the rigidly mounted single bearing with no external damping, yielding, as one extreme, a high stiffness, but a low whirl threshold speed. The other extreme is a series bearing arrangement with a full-length externally pressurized sleeve between the journal and the housing, yielding a lower stiffness but a higher whirl threshold speed. The paper shows that a mixed con. guration allows for an increase in whirl threshold speed above that for an equivalent rigidly mounted single bearing but below that for a series arrangement. However, the mixed con. guration is stiffer than the series arrangement.

小径穴内面形状計測装置の開発

Equipment for measuring the shape of a groove with a depth of 3.6-4.5μm and a width of 0.15-0.30 mm inside a kinetic pressure bearing (K.P.B), which is used for magnetic discs, with a length of 8.75 mm and an inner diameter of 3 mm, is developed. The light projected to a specimen through a lens makes a small spot near the inside wall of the specimen. The position of the wall in the specimen is determined by detecting an image of the spot reflected on the wall. A two-dimensional theoretical analysis shows that the depth of the groove can be measured with an error of less than ±0.05μm. An experimental result shows that the depth of the groove can be measured with an amount of scatter less than -0.2 -+0.2 μm. As this scattering is sufficiently small to measure the depth of the groove, this equipment can be used in a production line.

Theoretical Investigation of Fluid Inertia Effects and Stability of Self-Acting Gas Journal Bearings

The journal equation of motion and the complete Reynolds equation of compressible fluid film are numerically solved and a computer program is developed. The formulas are for externally pressurized bearings, but results are shown only for self-acting bearings. For certain cases, the validity of the theoretical results is verified by comparison with the experimental data available from the literature. Through intensive use of the program, journal center trajectories are obtained and effects of fluid inertia are investigated. New stability parameters are presented and stability diagrams are established for bearings with L/D = 0.25, 0.5, 1, 1.5, and 2. The rotor unbalance effects on bearing stability limits are illustrated for several cases.

Numerical Investigation of Compressible Flow within Aerostatic Journal Bearing.

Aerostatic journal bearings are employed in a lot of engineering fields because of the high endurance under severe conditions in current technology. However, it is difficult to investigate the flowfield experimentally, since the flow region of an aerostatic journal bearing is formed by a clearance of micron order. The present study numerically clarifies the flow in a pressurized journal bearing with a circular slot restrictor and the effect of a slit which is used to measure the static pressure. In this study, the flowfield is assumed to be laminar and compressible, and thus the compressible Navier-Stokes equations, equation of continuity and energy equation are solved. The static pressure distributions obtained by our computations are in good agreement with the experimental data, especially under the conditions of small bearing clearances. Furthermore, it is shown that a shock wave is formed around the impinging region at large mass flow rates, and the influence of a static pressure slit should be taken into account to estimate the static pressure reasonably.

An Application of Newton's Method to the Lubrication Analysis of Air-Lubricated Bearings

This study deals with the development of a computational procedure for solving the isothermal compressible Reynolds equation as the governing equation of air-bearing analysis. Newton's method is used to linearize Reynolds equation and an iterative successive relaxation process is adopted to solve for the air film pressure. The optimal value of relaxation factor for the cases studied is suggested in this report for numerical stability and computational efficiency. The model is verified numerically by examining the conservation of mass flow of the lubricant. The dimensional analysis of the governing equation permits the model to be readily applied to any given film geometry. The computer model developed can evaluate the air film pressure distribution, load capacity, frictional force, and mass flow of an air bearing. The proposed computational scheme efficiently analyzes the performance of air-lubricated journal bearings at large eccentricity ratios. A similar procedure can be employed to investigate the performance of highspeed noncircular air bearing or gas-lubrication film under slip-flow conditions. This study gives an analytical basis for the design of orifice-compensated externally pressurized air-lubricated bearing. Presented as a Society of Tribologista and Lubrication Engineers paper at the ASME/STLE Tribology Conference in Toronto, Ontario, Canada, October 26–28, 1998

Comparison between externally pressurized gas thrust bearings with different orifice and porous feeding systems

This paper analyzes the influence of feeding system type on the performance of externally pressurized gas bearings. It compares the optimum characteristics regarding load capacity, stiffness and flow rate of an air thrust bearing which can be obtained by using different kinds of multiple inlets specifically designed with orifices or porous compensation. The investigations have shown that optimum performance may be achieved for each of these different feeding systems, which depend on an optimum number of inlets, position of orifices, or permeability coefficient of the porous material.

Sleeve dampers for externally pressurised gas journal bearings

AbstractAn 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.

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.

Transient Response of Externally Pressurized Fluid Film Bearings©

The transient response of a point-mass rotor supported in turbulent flow, externally pressurized fluid film bearings is presented. The equations of motion are solved numerically with local linearization at each integration time step. The bearing reaction forces are calculated from the numerical solution of unsteady bulk-flow equations including fluid inertia, turbulence, variable fluid properties and thermal energy transport. Examples for the transient response of damper seals and hydrostatic bearings under a variety of external loads are presented. Transient responses based on an approximate model which uses constant rotordynamic force coefficients are also included and shown to compare well with the full nonlinear responses. The nonlinear model needs small time steps with large execution times, while the simple linear model provides reliable results in a minute fraction of time. Presented as a Society of Tribologists and Lubrication Engineers paper at the ASME/STLE Tribology Conference in San Francisco, California, October 13–17, 1996

Estimation of Alignment and Transverse Load inMulti‐Bearing Rotor System

The paper presents a method for estimation of a multi‐bearing machine alignment on the basis of measured eccentricities of the shaft in machine bearings. The method uses a linear FEM model of the rotor and the non‐linear models of machine bearings. In the presented example, the non‐linear models of hydrodynamic bearings are used, but it is shown, that the method could be easily applied to other types of bearings. In addition to the alignment estimation, the method allows to estimate the unknown static load in the transverse direction, reduced to the equivalent load at one or two selected nodes on the shaft. Verification of the method is presented using the model of a machine with vertical shaft supported in three pressurised hydrodynamic bearings. The method is suitable for monitoring of alignment and transverse load during the machine operation.

Pressure-Induced Torque in Unloaded Hybrid Bearings—A Case Study

A pressure-induced torque is emphasized in externally pressurized bearings having deep pockets, due to the pressure buildup by shaft rotation on the downstream vertical side of the recess. A standard simplified analysis is presented for both laminar and turbulent operation, with improved values for parameters kx and kx, which intervene in the pressure differential equation, as well as for the Couette turbulent shear stress; the mentioned values are valid for large Reynolds numbers. Comparison with experimental data for a water-lubricated test bearing exhibits the importance of the pressure-induced effect on the torque acting on the stationary member of the bearing.