Self-acting Gas-lubricated Bearings Research Articles

Stability and nonlinear dynamic analysis of gas-lubricated system with elastomer suspension

This paper presents the dynamic behavior of a rigid rotor supported by a pair of self-acting gas-lubricated bearings which is used in a turbo-expander, the key equipment in a large-scale cryogenic system. In order to restrict the vibration of the rotor relative to bearings, elastomers are mounted between bearings and shell. A finite difference method has been employed to solve the Reynolds equation in time-dependent states. The center orbits of the rotor are got by solving the motion equations. The system state trajectory, Poincare maps, logarithmic spectra maps and bifurcation diagrams are used to analyze the dynamic behavior of the system. The effect of the elastomer suspension to absorb the vibration is verified by comparison with the system with rigid suspension. A set of mass values, damping exponent values and stiffness of elastomer are calculated and compared in this paper. The results show that the rotor center loses its regular behavior gradually with the increase in the rotor mass. The square damping exponent model of the elastomer shows more stability than linear damping suspension model, and the quadratic damping exponent model has a similar motion behavior compared with a linear model. A suitable stiffness of the elastomer is important to the stability of the system. The elastomer with a low stiffness may cause the large amplitude of the vibration, and the system may lose its regular behavior when the stiffness is large enough.

Motion analysis of a rotor supported by self-acting axial groove gas bearing system with double time delays

A rotor system with double time delays supported by the high-speed self-acting gas-lubricated bearings with three-axial grooves is modeled to implement active delay control of the system. The differential transformation method is employed to solve the time-dependent compressible gas Reynolds equation due to its rapid convergence rate and minimal calculation error. Based on the precise integration method, a calculation method is proposed to analyze the dynamic responses of a gas bearing-rotor nonlinear system with time delays. The motion analysis of the self-acting gas-lubricated bearing-rotor system with double time delays is implemented by the orbit diagrams, the time series, and the phase diagrams. The influence of time delays and feedback control gains on the dynamic responses of the bearing-rotor nonlinear system is analyzed. The numerical results show that the amplitude of the responses of the system with time delays control is reduced, the motion is more stable and good control effect is achieved when the chosen feedback control gains match the time delays of the bearing-rotor system.

Nonlinear dynamic analysis of a rotor system with fixed-tilting-pad self-acting gas-lubricated bearings support

Based on the nonlinear theory, the unbalanced responses of a fixed-tilting-pad gas-lubricated journal bearing-rigid rotor system are investigated. A time-dependent mathematical model is established to describe the pressure distribution of gas-lubricated journal bearing with nonlinearity. The rigid rotor supported by a fixed-tilting-pad self-acting gas-lubricated journal bearing is modeled. The differential transformation method has been employed to solve the time-dependent gas-lubricated Reynolds equation, and the dynamic motion equation has been solved by the direct integral method. The unbalanced responses of the rotor system supported by fixed-tilting-pad gas-lubricated journal bearings are analyzed by the orbit diagram, Poincare map, time series, and spectrum diagram. The numerical results reveal periodic, period-3, and quasiperiodic motions of nonlinear behaviors of the system. Finally, the effects of pivot ratio and preload coefficient on the nonlinear dynamic characteristics of the fixed-tilting-pad self-acting gas-lubricated journal bearing-rotor system are investigated.

Fast Numerical Approach for Analyzing Self-Acting Gas-Lubricated Bearings Using a Multigrid Method.

A multigrid method has been introduced as a fast alternative to conventional relaxation methods for obtaining a solution to the Reynolds equation for self-acting gas-lubricated bearings. This paper verifies the procedure applied to both static and time-dependent dynamic analyses of plain-cylindrical journal bearings. The method gives successful results with less computational effort compared with single grid-oriented iterative methods. In addition, the new approach does not require a trial and error process to optimize the overrelaxation parameter unlike a successive overrelaxation method. The nonlinear orbit method which is an accurate but time-consuming transient analysis is expected to be reduced to a handy design tool for a complicated bearing system on incorporating the multigrid technique.

The Effect of Centrifugal Stretching in High-Speed, Self-Acting Gas Bearings Operating under Steady-State Conditions

The study reported in this paper arose from an investigation of methods of achieving oil-free compression of refrigerant vapours. One part of the investigation included a feasibility study of a high-speed rotary machine running in self-acting gas bearings lubricated by the refrigerant. In certain designs of very high-speed rotor-bearing arrangements, centrifugal or radial growth of the journal might disturb the shape and magnitude of the nominal clearance space and thus affect the performance characteristics of the bearing. The nature and magnitude of these changes in bearing performance for uniform and for two forms of non-uniform centrifugal growth have been examined theoretically. Typical gas-film pressure distributions are presented together with design charts showing how attitude angle and load carrying capacity vary with speed. Comparisons are made with the performance of bearings having the same eccentricity ratio on the mid-plane, and guidance is given on the calculation of uniform radial growth at high speeds. It is concluded that changes in lubricating film geometry resulting from centrigual stretching might have a significant effect upon the performance of certain high-speed, self-acting gas-lubricated bearings.

A numerical method and higher approximations for a self-acting gas-lubricated bearing of finite length : H. C. Kao, JOLT, Ser. F, 93 (1) (1971) 87–92; 3 figs., 10 refs.

A numerical method and higher approximations for a self-acting gas-lubricated bearing of finite length : H. C. Kao, JOLT, Ser. F, 93 (1) (1971) 87–92; 3 figs., 10 refs.

Calculation of a self-acting gas-lubricated bearing of finite length

Calculation of a self-acting gas-lubricated bearing of finite length

A Review of the state of the art for the design of self-acting gas-lubricated bearings : D. D. Fuller, JOLT, trans. ASME, ser. F, 91 (1969) 1–16; 37 figs., 95 refs.

A Review of the state of the art for the design of self-acting gas-lubricated bearings : D. D. Fuller, JOLT, trans. ASME, ser. F, 91 (1969) 1–16; 37 figs., 95 refs.

A Review of the State-of-the-Art for the Design of Self-Acting Gas-Lubricated Bearings

This is a review of selected publications over the past eight years, dealing with the analysis and design of self-acting, gas-lubricated bearings. An effort has been made to evaluate the advances made both in the understanding of the basic phenomena involved and in the technical analytical ability to deal with them. Whenever possible, design procedures have been referenced and illustrated.

On Gas Lubrication in Turbulent Regime

This paper analyzes first the transient conditions from laminar to turbulent regime for gas lubricated bearings. Then the pressure equation is deduced for self-acting gas-lubricated bearing by using Prandtl’s mixing length theory. A simple method for determining the pressure and the operating characteristics for bearings operating at high numbers H is given, based on an analogy with the corresponding laminar case. The pressure equation is also given for thrust and journal gas bearings under variable forces and velocities. The last two sections examine the influence of turbulence in externally pressurized gas bearings and the influence of inertia forces, respectively. The results obtained show that the turbulence does not alter qualitatively the operation conditions of gas-lubricated bearings. Moreover, the influence of turbulence in self-acting gas bearings is less important than in the case of liquid-film lubrication and even negligible when the bearing operates at high numbers H.

On Some Secondary Effects in Self-Acting Gas-Lubricated Bearings

Some secondary effects which can influence the operation of self-acting gas-lubricated bearings are analyzed, i.e., effect of the inertia forces, thermal effects, turbulence, and effect of the molecular character of the flow. In order to point out their qualitative influence as well as the conditions in which such influences can be important, the case of infinitely long bearings is considered, but for the computation of quantitative effects, the real case of finite bearings is used. Contributed by the ASLE Technical Committee on Bearings and Bearing Lubrication and presented at the Annual Meeting of the American Society of Lubrication Engineers held in Chicago, Illinois, May, 1964.