Dynamic Analysis of Floating-Ring Gas Bearings

The dynamic performances of floating-ring bearing with hydrodynamic/hydrostatic gas lubrication are studied theoretically and some calculated charts of dynamic coefficients are given in the paper. The method of stability analysis is also presented and it is proved that the high speed stability of such bearings is better than other types of gas bearings.

New Start-up Method for a Closed-Cycle Compression System with Gas Bearings and Its Characteristics

Gas bearings,which have the advantages of low frictional resistance and power loss,high rotational speed and high temperature operation,and long life,are more suitable than are traditional liquid lubricated bearings because of their high precision,high rotational speed,and special condition support.However,the problem of starting a closed-cycle compression system with gas bearings still needs to be solved for practical application.Thus,a new start-up method for a closed-cycle compression system with aerostatic gas bearings is proposed in this paper.Further,this paper presents a numerical simulation and experimental investigation of the method’s feasibility and characteristics during the start-up process when the gas tank’s initial pressure is fixed.The results show that the gas tank volume is approximately directly proportional to the start-up time allowable,and a gas tank volume sufficiently small,which not only ensures the feasibility of start-up,but also affects other components only slightly,can be obtained.A perfect combination of radial and axial loads also can be achieved to make the start-up time allowable as long as possible.R134a is a better choice for the working medium than is air,as the start-up time allowable is longer,which leads to a smaller gas tank.This research proposes a new start-up method for a closed-cycle compression system with aerostatic gas bearings which has sufficient load capacity to support system during the start-up method.

Three dimensional discrete element modelling of the conventional compression behavior of gas hydrate bearing coal

To analyze the relationship between macro and meso parameters of the gas hydrate bearing coal(GHBC)and to calibrate the meso-parameters,the numerical tests were conducted to simulate the laboratory triaxial compression tests by PFC3D,with the parallel bond model employed as the particle contact constitutive model.First,twenty simulation tests were conducted to quantify the relationship between the macro–meso parameters.Then,nine orthogonal simulation tests were performed using four meso-mechanical parameters in a three-level to evaluate the sensitivity of the meso-mechanical parameters.Furthermore,the calibration method of the meso-parameters were then proposed.Finally,the contact force chain,the contact force and the contact number were examined to investigate the saturation effect on the meso-mechanical behavior of GHBC.The results show that:(1)The elastic modulus linearly increases with the bonding stiffness ratio and the friction coefficient while exponentially increasing with the normal bonding strength and the bonding radius coefficient.The failure strength increases exponentially with the increase of the friction coefficient,the normal bonding strength and the bonding radius coefficient,and remains constant with the increase of bond stiffness ratio;(2)The friction coefficient and the bond radius coefficient are most sensitive to the elastic modulus and the failure strength;(3)The number of the force chains,the contact force,and the bond strength between particles will increase with the increase of the hydrate saturation,which leads to the larger failure strength.

Computer Aided Analysis of the Performances of a Tilting Pad Gas Journal Bearing

Tilting pad gas journal bearing is one of the most widely used types of aerodynamic bearings due to its inherent excellent stability in high speed applications.A practical method for analyzing and calculating the per- formances of such bearings is presented as well as its rotordynamics based on the computer aided technique.The method of calculation and the philosophy of programming with a microcomputer for the computer aided analysis are highlighted.

Theoretical and experimental research on static stiffness,performance,and lift-off characteristics of multi-layer gas foil thrust bearings

In this study,a new comprehensive fully coupled elastic–hydrodynamic model is developed for a multi-layer gas foil thrust bearing(GFTB).The interaction effects among the top foil,back board,middle foil,and bottom foil,as well as the Coulomb friction effect,are considered.The stiffness and static characteristics obtained by the experimental and theoretical approaches are in good agreement,which verifies the accuracy of the model.The contribution of each foil layer to the overall stiffness and the load-carrying mechanism are analyzed.Interaction effects of the load,preload,and rotational speed on the static performance are investigated comprehensively.Furthermore,start–stop tests are performed to achieve the lift-off speed,start-up torque,and shut-down torque under various operating conditions.

Bifurcation and Chaos Analysis of Nonlinear Rotor System with Axial-grooved Gas-lubricated Journal Bearing Support

Axial-grooved gas-lubricated journal bearings have been widely applied to precision instrument due to their high accuracy, low friction, low noise and high stability. The rotor system with axial-grooved gas-lubricated journal bearing support is a typical nonlinear dynamic system. The nonlinear analysis measures have to be adopted to analyze the behaviors of the axial-grooved gas-lubricated journal bearing-rotor nonlinear system as the linear analysis measures fail. The bifurcation and chaos of nonlinear rotor system with three axial-grooved gas-lubricated journal bearing support are investigated by nonlinear dynamics theory. A time-dependent mathematical model is established to describe the pressure distribution in the axial-grooved compressible gas-lubricated journal bearing. The time-dependent compressible gas-lubricated Reynolds equation is solved by the differential transformation method. The gyroscopic effect of the rotor supported by gas-lubricated journal bearing with three axial grooves is taken into consideration in the model of the system, and the dynamic equation of motion is calculated by the modified Wilson-0-based method. To analyze the unbalanced responses of the rotor system supported by finite length gas-lubricated journal bearings, such as bifurcation and chaos, the bifurcation diagram, the orbit diagram, the Poincar6 map, the time series and the frequency spectrum are employed. The numerical results reveal that the nonlinear gas film forces have a significant influence on the stability of rotor system and there are the rich nonlinear phenomena, such as the periodic, period-doubling, quasi-periodic, period-4 and chaotic motion, and so on. The proposed models and numerical results can provide a theoretical direction to the design of axial-grooved gas-lubricated journal bearing-rotor system.

Experimental study on the infrared precursor characteristics of gas-bearing coal failure under loading

The stress and gas pressure in deep coal seams are very high,and instability and failure rapidly and intensely occur.It is important to study the infrared precursor characteristics of gas-bearing coal instability and failure.In this paper,a self-developed stress-gas coupling failure infrared experimental system was used to analyse the infrared radiation temperature(IRT)and infrared thermal image precursor characteristics of gas-free coal and gas-bearing coal.The changes in the areas of the infrared temperature anomalous precursor regions and the effect of the gas on the infrared precursors were examined.The results show that high-temperature anomalous precursors arise mainly when the gas-free coal fails under loading,whereas the gas-bearing coal has high-temperature and low-temperature anomalous precursors.The area of the high-temperature anomalous precursor is approximately 30%–40%under gasbearing coal unstable failure,which is lower than the 60%–70%of the gas-free coal.The area of the low-temperature abnormal precursor is approximately 3%–6%,which is higher than the 1%–2%of the gas-free coal.With increasing gas pressure,the area of the high-temperature anomalous precursor gradually decreases,and the area of the low-temperature anomalous precursor gradually increases.The highand low-temperature anomalous precursors of gas-bearing coal are mainly caused by gas desorption,volume expansion,and thermal friction.The presence of gas inhibits the increase in IRT on the coal surface and increases the difficulty of infrared radiation(IR)monitoring and early warning for gas-bearing coal.

Fluid-solid coupling model for studying wellbore instability in drilling of gas hydrate bearing sediments

As the oil or gas exploration and development activities in deep and ultra- deep waters become more and more, encountering gas hydrate bearing sediments （HBS） is almost inevitable. The variation in temperature and pressure can destabilize gas hydrate in nearby formation around the borehole, which may reduce the strength of the formation and result in wellbore instability. A non-isothermal, transient, two-phase, and fluid-solid coupling mathematical model is proposed to simulate the complex stability performance of a wellbore drilled in HBS. In the model, the phase transition of hydrate dissociation, the heat exchange between drilling fluid and formation, the change of mechanical and petrophysical properties, the gas-water two-phase seepage, and its interaction with rock deformation are considered. A finite element simulator is developed, and the impact of drilling mud on wellbore instability in HBS is simulated. Results indicate that the re- duction in pressure and the increase in temperature of the drilling fluid can accelerate hydrate decomposition and lead to mechanical properties getting worse tremendously. The cohesion decreases by 25% when the hydrate totally dissociates in HBS. This easily causes the wellbore instability accordingly. In the first two hours after the formation is drilled, the regions of hydrate dissociation and wellbore instability extend quickly. Then, with the soaking time of drilling fluid increasing, the regions enlarge little. Choosing the low temperature drilling fluid and increasing the drilling mud pressure appropriately can benefit the wellbore stability of HBS. The established model turns out to be an efficient tool in numerical studies of the hydrate dissociation behavior and wellbore stability of HBS.

Research on Axial Trail of High-Speed Gas Painting Automizor

The non linear dynamic model is set up of one type of high speed painting automizor with gas supporting system. The stability of motion and dynamic response of the gas painting automizor system are studied over a relatively wide range of rotating speed by numerical analytic method, the critical velocity under working condition is found, and rotate stability and critical condition are discussed in theory. Furthermore, the range of the critical parameter of the system when Hopf bifurcation occurs and the law between axis trace and bearing clearance are acquired, too.

Hydrodynamic Lubrication of Elastic Foil Gas Bearing Using Over Relaxation Iteration Method and Non-Dimensional Equation

The purpose is to accurately predict the performance of foil bearing and achieve accurate results in the design of foil bearing structure.A new type of foil bearing with surface microstructure is used as experimental material.First,the lubrication mechanism of elastic foil gas bearing is analyzed.Then,the numerical solution process of the static bearing capacity and friction torque is analyzed,including the discretization of the governing equation of rarefied gas pressure based on the non-dimensional modified Reynolds equation and the over relaxation iteration method,the grid planning within the calculation range,the static solution of boundary parameters and static solution of the numerical process.Finally,the solution program is analyzed.The experimental data in National Aeronautics and Space Administration(NASA)public literature are compared with the simulation results of this exploration,so as to judge the accuracy of the calculation process.The results show that under the same static load,the difference between the minimum film thickness calculated and the test results is not obvious;when the rotor speed of the bearing is 60000 r/min,the influence of the boundary slip effect increases with the increase of the micro groove depth on the flat foil surface;when the eccentricity or the micro groove depth of the bearing increases,the bearing capacity will be strengthened.When the eccentricity is 6µm and 14µm,the viscous friction torque of the new foil bearing increases significantly with the increase of the depth of the foil micro groove,but when the eccentricity is 22µm,the viscous friction torque does not change with the change of the depth of the foil micro groove.It shows that the bearing capacity and performance of foil bearing are improved.

Study on lift-up speed of aerodynamic compliant foil thrust bearings

Objective The experimental study on the lift-up speed of a new kind of compliant aerodynamic foil thrust bearings was performed on the multifunctional test rig established for testing the performances of foil gas bearings.Methods The lift-up speed of foil gas thrust bearing under given axial load was analyzed through the spectrum of axial displacement response in frequency domain.Results The test results indicated that the difference in the spectrum of axial displacement responses before and after lifting up of the rotor was obvious.After lifting up of the rotor,there were only larger components of rotation frequency and lower harmanic frequencies.If the rotor wasn't lift-up,there were also larger components of other frequencies in the spectrum.Conclusion So by analyzing the spectrum of axial displacement response,the results showed that the lift-up speed was about 1860rpm when the axial load was 31N.

Microscopic pore-fracture configuration and gas-filled mechanism of shale reservoirs in the western Chongqing area,Sichuan Basin,China

Taking the Upper Ordovician Wufeng Formation to Lower Silurian Longmaxi Formation shale reservoirs in western Chongqing area as the study target,the argon ion polishing scanning electron microscope and nuclear magnetic resonance(NMR)experiments of different saturated wetting media were carried out.Based on the image processing technology and the results of gas desorption,the pore-fracture configuration of the shale reservoirs and its influence on gas-filled mechanism were analyzed.(1)The reservoir space includes organic pores,inorganic pores and micro-fractures and there are obvious differences between wells in the development characteristics of micro-fractures;the organic pores adjacent to the micro-fractures are poorly developed,while the inorganic pores are well preserved.(2)According to the type,development degree and contact relationship of organic pore and micro-fracture,the pore-fracture configuration of the shale reservoir is divided into four types.(3)Based on the differences in NMR T_(2) spectra of shale samples saturated with oil and water,an evaluation parameter of pore-fracture configuration was constructed and calculated.The smaller the parameter,the better the pore-fracture configuration is.(4)The shale reservoir with good pore-fracture configuration has well-developed organic pores,high porosity,high permeability and high gas content,while the shale reservoir with poor pore-fracture configuration has micro-fractures developed,which improves the natural gas conductivity and leads to low porosity and gas content of the reservoir.(5)Based on pore-fracture configuration,from the perspective of organic matter generating hydrocarbon,micro-fracture providing migration channel,three types of micro gas-filled models of shale gas were established.

Numerical Analysis on the Static Performance of Gas Journal Bearing by Using Finite Element Method

In this paper,finite element method is used to calculate the static performance of gas journal bearing,in which rotation speed term is introduced into the stiffness matrix of linear triangular element to realize the performance calculation of the bearing with rotation speed.The results indicate that the average gas film thicknesses corresponding to the maximum load capac-ity and stiffness,and the minimum attitude angle increase with the growth of orifice diameter.Load capacity and stiffness significantly improved with the increase of rotation speed,eccentricity ratio and supply pressure when the bearing has thin average gas film thickness.Attitude angle increases with the growth of rotation speed,while the growth rate slows down or even decreases at high speed.The most effective way of reducing attitude angle is to increase supply pressure.It can be found that rotation speed affects attitude angle through changing gas pressure difference between two orifices,while other parameters have the same effect by changing gas pressure at orifice outlet.

Vertical migration through faults and hydrocarbon accumulation patterns in deepwater areas of the Qiongdongnan Basin

In the Qiongdongnan Basin, faults are well developed.Based on the drilling results, the traps controlled two or more faults are oil-rich. However, when only one fault cut through the sand body, there is no sign for hy-drocarbon accumulation in the sandstone. In terms of this phenomenon, the principle of reservoir-forming controlled by fault terrace is proposed, i.e., when the single fault activates, because of the incompressibility of pore water, the resistance of pore and the direction of buoyancy, it is impossible for hydrocarbon to ac-cumulate in sandstone. But when there are two or more faults, one of the faults acts as the spillway so the hydrocarbon could fill in the pore of sandstone through other faults. In total five gas bearing structures and four failure traps are considered, as examples to demonstrate our findings. According to this theory, it is well-advised that south steep slope zone of Baodao-Changchang Depression, south gentle slope zone of Lingshui Depression, north steep slope zone of Lingshui Depression, and north steep slope zone of Baodao Depression are the most favorable step-fault zones, which are the main exploration direction in next stage.

ANALYSIS ON MOTION STABILITY OF A HIGH-SPEED ROTOR-BEARING SYSTEM

A non-linear dynamic model of one type of high-speed rotor system with gassupporting system is set up. The laws between the capacity force and the parameters of bearing, thestatic equilibrium position and rotating speed are studied on the basis of above model. Then, thefailure rotating, speed is given in the working state, and the relation between the minimum failurerotating speed and clearance of bearing is also studied. At last, the stability and failurecondition are discussed in different working conditions.

Study on the Dynamic Performance of the Helium Turboexpander for EAST Subsystems

An increase of the cooling capacities in the liquid helium temperature area is re- quired by Experimental Advanced Superconducting Tokamak （EAST） due to the extension of its subsystems in the near future. Limited by the heat exchangers, cryogenic pipes, and cryogenic valves, it is difficult to enlarge the present EAST helium system. 102 W@4.5 K level helium cryogenic systems are needed in view of feasibility and economy. A turboexpander is the key com- ponent of a helium cryogenic system. In this article, a hydrostatic gas lubricated cryogenic helium turboexpander for a 900 W@4.5 K cryogenic helium system was developed for the EAST updated subsystem by the Institute of Plasma Physics, Chinese Academy of Sciences and the Institute of Cryogenic and Refrigeration of Xi＇an Jiaotong University. The main components, such as gas bearings, expansion wheel, shaft, and brake wheel, were briefly presented. The dynamic perfor- mance of the journal and thrust gas bearings was investigated numerically. The rotordynamic performance of the developed turboexpander was studied experimentally. The results show that the axial and radial load capacities supplied by the journal gas bearing and thrust gas bearing are enough to balance the axial force and radial force of the rotor. A 43% overspeed operation was achieved, which validated the reasonable design of the turboexpander.

An efficient three-dimensional foil structure model for bump-type gas foil bearings considering friction

This paper presents an efficient three-dimensional(3D)structural model for bump-type gas foil bearings(GFBs)developed by considering friction.The foil structures are modeled with a 3D shell finite element model.Using the bump foil mechanical characteristics,the Guyan reduction and component mode synthesis methods are adopted to improve computational efficiency while guaranteeing accurate static responses.A contact model that includes friction and separation behaviors is presented to model the interactions of the bump foil with the top foil and bearing sleeve.The proposed structural model was validated with published analytical and experimental results.The coupled elastohydrodynamics model of GFBs was established by integration of the proposed structural model with data on hydrodynamic films,and it was validated by comparisons with existing experimental results.The performance of a bearing with an angular misalignment was studied numerically,revealing that the reaction torques of the misaligned bearing predicted by GFB models with 2D and 3D foil structure models are quite different.The 3D foil structure model should be used to study GFB misalignment.

Calculation of the Critical Speed and Stability Analysis of Cryogenic Turboexpanders with Different Structures

A modularized code based on the Finite Element QZ （FEQZ） method is developed, for a better estimate of the critical speed and a more convenient method of rotor-dynamic stability analysis for a gas bearing high speed turboexpander rotor system with actual structure and application of a cryogenic turboexpander. This code is then validated by the experimental data of a gas bearing turboexpander, with a rotor diameter of 25 mm and a rated speed of 106,400 rpm. With this code, four rotors with different structures, available to the turboexpander, are parametrically analyzed by the available speed range, vibration modes and logarithmic attenuation rate. The results suggest that the rotor with a structure of two thrust collars on the system exhibits a better performance in the designed conditions.

Rotational Flow in a Narrow Annular Gap Based on Lattice Boltzmann Method

For comprehensive characteristics of flow in a gas bearing,lattice Boltzmann method(LBM)is applied for study of the two-dimensional flow between two eccentric cylinders with the inner one rotating at a high speed.The flow pattern and circumferential pressure distribution are discussed based on critical issues such as eccentricity ranging from 0.2 to 0.9,clearance ratio varying from 0.005 to 0.01 and rotating speed in the range of 3×104—1.8×105 r/min.The analysis and discussion on the circumferential pressure distribution affirmed the quasilinear relation between the extremum pressure and rotating speed.Furthermore,a high eccentricity and small clearance ratio contributes most to the fluctuation of the circumferential pressure distribution.The flow pattern inside the channel exhibits separation vortex under a large eccentricity.The conclusions drawn in this work give rise to prediction of the flow pattern in the gas bearing which is beneficial for evaluating the performance of as well as instructing the design and development.