Spherical Gas Bearings Research Articles

Research on dynamic characteristics of gas film of spherical hybrid gas bearings based on computational fluid dynamics

A realizable k–ε turbulence model for spherical spiral groove hybrid gas bearing films was established based on computational fluid dynamics (CFD). A six degrees of freedom passive grid was used to calculate the gas film pressure distribution, bearing capacity, and dynamic characteristic coefficients numerically. The gas flow field dynamic and static pressure coupling mechanism was studied. The effects of the rotation speed, gas film thickness eccentricity ratio, and gas supply pressure on the dynamic and static pressure bearing capacity, and dynamic characteristic coefficients during operation were analyzed as a method of research into the mechanical mechanisms of gas bearing stability. The CFD calculation analysis can simulate the complex gas flow in the transient flow field of the gas film and determine reasonable operation parameters to optimize the dynamic and static pressure coupling effects, which can improve the gas film bearing capacity, dynamic characteristics, and operational stability of gas bearings.

A High-Precision Random Forest-Based Maximum Lyapunov Exponent Prediction Model for Spherical Porous Gas Bearing Systems

Spherical porous air bearing (SPAB) systems have been extensively used in various mechanical engineering applications. SPABs are promising materials in high-rotational speed, high-precision, and high-stiffness instruments. In SPAB systems, a rotor is supported by gas bearings, which provides higher rotational speed and lower heat generation environment than oil bearings do. Furthermore, SPAB does not cause deformation. Although, the supporting force of gas bearings is less, their stability is better than that of oil films. However, because the pressure distribution in the gas films is nonlinear, they are prone to failure at specific critical speeds, rotor imbalances, or inappropriate operations, which results in nonperiodic or chaotic motion and causes structural fatigue to the system. To understand and control the operating conditions of the SPAB systems during the nonperiodic motion, first, the governing equations of the SPAB system were solved to obtain the dynamic behavior of the rotor center. Then, the performance of the SPAB system were examined under different operating conditions by generating the maximum Lyapunov exponents (MLEs). However, the calculation process of MLE is extremely time consuming and complex. To solve this problem efficiently, a high-precision machine learning (ML)-based MLE prediction model was proposed in this study. The results show that the training process can be finished within few minutes, and the prediction process is able to be completed within few seconds. Meanwhile, the results demonstrate the merit of using the machine learning method for solving the MLE prediction problem and shorten the calculation time significantly. The proposed prediction model achieves excellent prediction outcome and it is more efficient and precise than traditional iteration scheme for the calculation of MLE. The feasibility of the proposed model is validated and the results also are the major contribution of this study.

Study on dynamic characteristics of gas films of spherical spiral groove hybrid gas bearings

According to the gas film force variation law, when the bearing axis is slightly displaced from the static equilibrium position, displacement and velocity disturbance relation expressions for the gas film force increment are constructed. Moreover, combined with the bearing rotor system motion equation, calculation model equations for the gas film stiffness and damping coefficients are established. The axial and radial vibration and velocity of the gas bearings during operation are collected. The instantaneous stiffness and damping coefficients of the gas film are calculated by the rolling iteration algorithm using MATLAB. The dynamic changes in the gas film stiffness and damping under different motion states are analyzed, and the mechanism of the gas film vortex and oscillation is studied. The results demonstrate the following: (1) When the gas bearing is running in the linear steady state in cycle 1, the dynamic pressure effect is enhanced and the stability is improved by increasing the eccentricity; when the gas supply pressure is increased, the static pressure effect is enhanced and the gas film vortex is reduced, but the oscillation is strengthened. (2) With the increase in rotational speed, the gas film vortex force gradually exceeds the gas film damping force, and the stability gradually worsens, causing a fluctuation in the gas film stiffness and damping, following which singularity occurs and a half-speed vortex is formed. Meanwhile, the gas film oscillation is intensified, and the rotor enters the nonlinear stable cycle 2 state operation. (3) As the fluctuation of the film force increases, the instantaneous stiffness and damping oscillation of the film intensifies, most of the stiffness and damping coefficients exhibit distortion, and the rotor operation will enter a chaotic or unstable state. Therefore, the gas bearing stiffness and damping variation characteristics can be used to study and predict the gas bearing operating state. Finally, measures for reducing the vortex and oscillation of the gas film and improving the stability of the gas bearing operation are proposed.

Flow field calculation and dynamic characteristic analysis of spherical hybrid gas bearings based on passive grid

In order to research the spherical spiral groove hybrid gas bearings, the Realizable k − e turbulence model of gas film was established based on FLUENT. The simulation calculation method of 6-degrees of freedom passive grid was used, which can simulate the lubrication characteristics of the gas film transient flow field accurately. And the gas film pressure distribution and dynamic characteristic coefficients are numerically calculated. The dynamic and static pressure coupling effects of the gas flow field were analyzed, and the axis motion trajectory was simulated. The effect of rotation speed, gas supply pressure and tangential angle on the dynamic characteristic coefficients during bearing operation was analyzed. And the stability of the gas bearing was studied. The conclusion from the analysis shows that different rotation speed and gas supply pressure will change the pressure distribution of the gas bearing during the operation. The dynamic characteristics of the gas film can be changed by reasonably optimizing the operation parameters, which can change the whirl characteristics of the gas film and improve the stability. Through calculation and analysis, the tangential angle is selected between 55° and 60°, to ensure that the gas film has a high stiffness, while it also can obtain the larger damping. The simulation results and the experimental results are compared and analyzed to verify the correctness and effectiveness of the simulation method. At the same time, the research of this paper provided a theoretical basis for optimizing the bearing structure and operating parameters, improving the dynamic characteristics of gas bearings and improving the operation stability.

Nonlinear Analysis of Stability and Unbalanced Response on Spherical Spiral-Grooved Gas Bearings

ABSTRACTThis study conducts a nonlinear numerical analysis of the stability and the unbalance response of spherical spiral-grooved bearings (SSGBs) using a nonlinear orbit simulation method. This method is more accurate than the linear method, especially at high bearing loads. Parametric analyses are also performed with respect to nominal clearance and groove depth to optimize groove parameters. Shaft trajectories reflect the nonlinear characters of SSGBs when mass unbalance increases. Fast Fourier transform analyses of rotor orbit responses facilitate identification of the subsynchronous whirling and unbalance response in rotor vibration behavior. Results show that optimum dimensionless groove depths vary for different nominal clearances or rotational speeds. The static performance and stability characteristics of spherical bearings can be significantly influenced by the spiral grooves on the journal surface.

Analysis of dynamic characteristics and stability prediction of gas bearings

PurposeThe prediction model to estimate the stability of a rotor-bearing system is established, which can predict the stability of gas bearings by applying Routh–Hurwitz stability criterion. This paper aims to provide the theoretical foundation for controlling actively the bearing running stiffness and damping and stemming the instability of a gas film.Design/methodology/approachThe nonlinear dynamic lubrication analysis mathematical model of spherical hybrid gas bearings is established. Perturbation control equation is derived by the partial derivative method. The finite difference method is used to discrete the perturbation control equation in generalized coordinate system, and the difference expression of perturbation pressure is derived. The relational expression which involves the relationship between the dynamic characteristic coefficients of HSGHGB systems and perturbation pressure is deduced. So, the transient perturbation pressure distribution of a three-dimensional micro gas film, nonlinear gas film force, dynamic stiffness and dynamic damping coefficients of bearings are numerically computed using VC++6.0 programs.FindingsThe results show that the influence of supply pressure, speed and eccentricity on the dynamic characteristics of bearings is significant.Originality/valueThe influence law of supply pressure, speed and eccentricity ratio on the dynamic stiffness and damping coefficients of HSGHGB systems is researched. The prediction model to estimate the stability of rotor-bearing system is established, which can predict the stability of gas bearings by applying the Routh–Hurwitz stability criterion.

Dynamic Stability Prediction of Spherical Spiral Groove Hybrid Gas Bearings Rotor System

Taking the hemisphere spiral groove hybrid gas bearings (HSGHGB) as the research object, the nonlinear dynamic lubrication analysis mathematical model of spherical hybrid gas bearings is established with the axis instantaneous position and instantaneous displacement speed as the parameters. The perturbation pressure control equation is solved by means of the finite difference method in generalized coordinate system. The calculation program is prepared based on VC++6.0, and the transient perturbation pressure distribution of three-dimensional (3D) gas film, nonlinear gas film force, and dynamic stiffness and damping coefficients are numerically calculated. The influences of different speeds, eccentricity ratios, and gas supply pressures on the dynamic characteristic coefficients of gas film are studied. The results show that the influence of bearing's supply pressure, speed, and eccentricity on the dynamic characteristics of gas film is significant. The dynamic equations of rotor-bearing system containing the gas film dynamic stiffness and the damping coefficients are established, and the stability of the gas film is predicted based on the Routh–Hurwitz stability criterion. The research provides the theoretical foundation for actively controlling the bearing running stiffness and damping and stemming the instability of gas film.

The Development of Spherical Gas Bearings for the 3DRW Operated by a Small Air Supplier

The Development of Spherical Gas Bearings for the 3DRW Operated by a Small Air Supplier

Study on the dynamic characteristics of a new type externally pressurized spherical gas bearing with slot–orifice double restrictors

This study proposes a new type externally pressurized spherical gas bearing with slot–orifice double restricted restrictors, used in a new type gas gyroscope. Based on the spherical Reynolds equation and cylindrical Reynolds equation, small perturbation theory is employed to analyze the dynamic characteristics of the new type externally pressurized spherical gas bearing. The slot gas film and the spherical film are united by means of compatibility condition and a weak solution formula, based on Galerkin residual method, is erected. The nonlinear coupled weak solution equations are solved with FEM and the dynamic coefficients are obtained. Numerical simulation is operated and the change laws that the dynamic coefficients change with dimensionless perturbation frequency f, eccentricity ratio E h and other structure parameters are analyzed. This paper provides a reference and preparation for analysis on the dynamic characteristics of the similar gas bearings.

Bifurcation and nonlinear analysis of a flexible rotor supported by a relative short spherical gas bearing system

This paper employs a hybrid numerical method combining the differential transformation method and the finite difference method to study the bifurcation and nonlinear dynamic behavior of a flexible rotor supported by a relative short spherical gas bearing (RSSGB) system. The analytical results reveal a complex dynamic behavior comprising periodic, sub-harmonic, quasi-periodic, and chaotic responses of the rotor center and the journal center. Furthermore, the results reveal the changes which take place in the dynamic behavior of the bearing system as the rotor mass and bearing number are increased. The current analytical results are found to be in good agreement with those of other numerical methods. Therefore, the proposed method provides an effective means of gaining insights into the nonlinear dynamics of RSSGB systems.

Modeling and Simulation of a Externally Pressurized Spherical Gas Bearing

Because of many advantages that other kinds of bearings can not match, for example high precision and high speed, gas lubricated bearing has been used widely in areas such as ultra-precision machine tool and inertia apparatus. The paper introduced an orifice restrictor externally pressurized spherical gas bearing, which is easily shaped and has bigger stiffness in both axial and radial directions. The paper also introduced a bearing force calculation model based on finite partition of the bearing, in which the influence of the uniform pressure slot also considered.

Load Performances Analysis of Orifice Compensated High-Speed Externally Pressurized Spherical Gas Bearing

The influence of parameters to load performances of a high-speed externally pressurized spherical gas bearing compensated by two-rows of orifices has been studied numerically based on finite element method (FEM). Reynolds equation governing the flow field in the clearance space in spherical coordinates system is transformed into a analogous style in Descartesian coordinates by parameter substitution, and Galerkin weighted residual method is applied to reduce the order of derivatives of the transformed equation. Pressure distribution on the gas-film is obtained by solving of the equation. On the basis of theories, influences of rotating speed, nominal gas-film thickness and supplying pressure to load carrying capacity and stiffness are analyzed. Comparison of performances between hydrostatic and hybrid state of the bearing has also presented.

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.

Minitact gyroscope-the low cost alternative

The allure of the solid state optical gyros is being challenged by the invention of a new spinning mass device, providing superior low noise drift performance, high reliability at a very low cost. The Minitact is a unique two axis gyroscope advancing the technology of spinning mass devices to set new low cost standards. Minitact provides all the low noise performance benefits of tuned rotor gyroscopes without the vagaries of fixture suspension systems. The Minitact design integrates together the advantages of a spherical hydrodynamic gas bearing and a three axis permanent magnet DC commutated, motor and torquer, into miniature two aids gyroscope with a dynamic range of greater than 10/sup -7/. The design is described and performance data presented illustrating the capability of this low cost next generation rate gyroscope. The Minitact is the result of Integrated Product Development (IPD) and Design to Unit Production Cost (DTUPC) design processes and is expected to become the tactical performance benchmark.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Performance of Spherical Gas Bearings in Axisymmetric Operation

Performance of Spherical Gas Bearings in Axisymmetric Operation

Choked flow in externally pressurized spherical gas bearings

The flow in an externally pressurized fitted-type spherical gas bearing was investigated under choking conditions. The effects of geometrical and flow parameters on the pressure distribution along the bearing flow were considered. The choked flow, which is accompanied by shock wave formation in the bearing clearance, was found to have a detrimental effect on the pressure distribution and consequently on the bearing performance. The limiting design conditions required to avoid the presence of a shock wave in the bearing clearance were determined using a mathematical model.

Design data for externally pressurised spherical gas bearings

Radial and thrust loading characteristics are given for both single row entry and double row entry bearings. The design data presented gives a basis for comparison of the two bearing configurations. The paper shows that the double entry configuration reduces the negative stiffness regions which occur in single entry bearings. Finally a procedure is given to enable the designer to select a bearing to meet his particular requirements.

A Spherical Gas Bearing for Airborne Application

A spherical gas bearing is analyzed and tested for an airborne application. The externally pressurized bearing supports an inertially stabilized 36-in aperture, infrared telescope. The bearing provides the isolation of rotary motion from the aircraft and also serves as a seal between the aircraft cabin and cavity condition at 50,000 ft altitude. The accompanying temperature gradient of 135 F across the 16-in.-diam bearing created special design and manufacturing considerations. Test data on the static load under temperature and vacuum environment are presented in support of the analysis.

Analysis of externally-pressurized spherical gas bearings employing slot restrictors

Radial and thrust load characteristics for partial sphere configurations are presented. The nature of static instability under certain loadings is explained in terms of variable film thickness and the position of the feed slots. Charts are derived which show the interaction between loading in one direction and the deflection in a normal direction. The conditions of optimum design are discussed for the bearing geometry and pressure ratio.

Investigation of the Spherical Hydrostatic Gas Bearing for Two-Axis Gyros

Investigation shows that spherical hydrostatic gas bearings can be manufactured by coining of precision dimensions in aluminum die castings. The paper also shows that the goals of low competitive costs and high reliability can be achieved with commercial balls, filters, and gas cartridges. Load support of a spherical hydrostatic gas bearing can be 40 percent of the supply pressure times the projected ball area. Gas consumption for a bearing ball size of 1.0-2.0 in. can be low (1.0 SCFM). Bearing noise can be less than 5.0 dyne-cm. These observations are from work on a family of two-axis gyros and a two-axis wind tunnel model pivot.