Pressurized Gas Bearings Research Articles

Rotordynamic Analysis and Operating Test of an Externally Pressurized Gas Bearing Turbo Expander for Cryogenic Applications

This study designed an externally pressurized bearing and analyzed the rotordynamics of a turbo expander for a hydrogen liquefaction plant. The turbo expander, comprising a turbine and compressor wheel assembled to a shaft, lowered the temperature of the helium refrigerant. Its rated speed was 75,000 rpm, and an externally pressurized gas bearing was selected to support the rotor. Pressurized helium was used as the lubricant for the bearing operation. To design the rotor–bearing system, we conducted a bearing performance analysis and rotordynamic characteristic prediction using the developed numerical model. We calculated the bearing stiffness and flow rate of the bearing gas for various feed parameters and selected the appropriate orifice diameter for maximum stiffness. The predicted Campbell diagram showed that the system had a sufficient separation margin with the critical speed, and the predicted critical speed correlated well with the nonlinear orbit simulation. A successful operation was achieved with the manufactured turbo expander within the rated speed. The shaft vibration was monitored during the operation test, and the test results revealed two critical speeds below the rated speed, as predicted by the analytical model. In addition, the shaft vibration was maintained at <3 μm.

Influence of the Refrigerant on the Performance of a Heat Pump with Gas Bearings

Heat pumps have become a potential technology for future thermal management systems in space. However, conventional heat pumps lubricated with oil are currently unfeasible due to the difficulty separating oil in microgravity environments. The oil-refrigerant mixture reduces the heat transfer capacity of heat exchangers, and insufficient separation can damage the compressor. This paper proposes a new heat pump with gas bearings (HPGB) that combines a centrifugal compressor with externally pressurized gas bearings to solve lubrication problems. A numerical model is established to compare performance of the HPGB system with different refrigerants. The results show that the coefficient of performance (COP) of the HPGB system is slightly smaller than those of conventional heat pumps, but higher than those of heat pumps with the impact of an oil concentration of 5%, when evaporator power is 30 kW. The HPGB system is more suitable for high-power conditions because of the higher COP. Ammonia is the best choice for the HPGB system under high-power conditions (above 80 kW). R134a is the best choice under middle-power conditions (from 25 kW up to 80 kW). R1234yf is more suitable with the maximum COP of 2.88 under low-power conditions (below 25 kW).

Unbalance Response Analysis of a Spindle Supported on Gas Bearings: A Comparison between Different Approaches

Gas journal bearings are widely employed in high-speed spindles for the micromachining industry. Compared to their oil and rolling counterparts, gas bearings have a longer life span, lower friction and a lower level of noise. In order to design accurate high-speed spindles supported by externally pressurized gas bearings, it is vital to analyze the characteristics of rotor bearing systems. In this paper, we present an analysis of the unbalance response of a high-speed spindle supported by gas journal bearings. A number of aspects to enhance the accuracy of the system are discussed. We performed the analysis by considering a nonlinear and a linearized numerical model validated through experimental measurements.

Ultra Low Temperature Microturbine for Magic Angle Spinning System

Abstract We investigate the fluid dynamics of a microturbine system that is applied in a device for chemical and biological analysis—a so-called magic angle spinning (MAS) nuclear magnetic resonance (NMR) probe. The present system is utilized in a wide temperature range from 45 K to 293 K. Pressurized air, nitrogen, or helium are used to drive a Pelton type microturbine. This turbine is mounted on a MAS rotor with a diameter between 0.7 mm and 3.2 mm. The rotor system is equipped with a pressurized gas bearing that is operated by the same gas species as the turbine. Computational fluid dynamics (CFD) simulations have been performed and compared with fluid dynamics measurements of the MAS system for different diameters, temperatures, and spinning rates between 23 kHz and 120 kHz. To our knowledge, this work is the first comprehensive CFD and experimental study of such a wide temperature range that has been carried out for microturbines with pressurized gas bearings. The results show good agreement between measurements and CFD simulations with appropriate (real) gas models, i.e., the ideal gas model for air at room temperature, Peng–Robinson model for nitrogen at 105 K, and ideal gas model for helium at 45 K.

Performance prediction of externally pressurized gas bearings for high-speed turbo-expander involving hydrogen, helium and air working fluids

High-speed hydrogen turbo-expander is widely employed in hydrogen liquefaction systems due to its high efficiency. The hydrogen bearings in high-speed turbo-expander are usually applied for low viscosity and pollution-free advantages. Nevertheless, the load capacity of hydrogen bearing is low and the research on maximizing the load capacity is limited by the complicated solution process and danger hydrogen experiment. The purpose of the paper is to easily and quickly acquire the load capacity of high-speed orifice externally pressurized hydrogen journal bearing for optimization of bearing performance. A new simple load capacity predicted model, that is universal for various working fluids involving hydrogen, helium and air, was proposed through the hydrostatic and hydrodynamic analysis. In the model, the evaluation indicators of hydrodynamic and hydrostatic effects were proposed. Based on the model, no numerical analysis and computer programming are needed to calculate the load capacity of journal bearing and numerous key design variables are considered. The results from the predicted model agree very well with those obtained from the finite difference method (FDM) technique. In view of the danger of hydrogen bearing experiment, the load capacity predicted model can be used to design the equivalent experiment of load capacity through substituting air for hydrogen working fluid.

A numerical method for solution of the discharge coefficients in externally pressurized gas bearings with inherent orifice restrictors

To study the discharge coefficients of aerostatic bearings, a new numerical method which combines the method of “separation of variables” for solution of laminar boundary-layer equations and analytical solution of Reynolds equation is proposed. The discharge coefficients are suitable for solution of Reynolds equation. The influences of flow and geometry parameters on discharge coefficients are investigated and the results indicate that there exists parameters insensitive and sensitive regions in discharge coefficient analysis. Further research shows that flow and geometry parameters affect discharge coefficient by influencing the pressure ratio (pr/ps) and discharge coefficient tends to be constant when pressure ratio is approximately less than 0.6, which is the reason that there exists the parameters insensitive and sensitive regions.

Externally Pressurized Gas Bearing which Supplies Gas from Rotor with unbalance

Externally Pressurized Gas Bearing which Supplies Gas from Rotor with unbalance

CFD research on hydrodynamic gas bearings with different styles of grooves

The gas bearing is an appealing technology which is widely used in turbo-machine in large-scale cryogenic systems for its inherent characteristic of oil-free and high-speed capability. The hydrodynamic gas bearings are more effective on cryogenic system but have less load capacity and dynamic stability by comparing with externally pressurized gas bearings. Etching some grooves on shaft or bearing is proved to be effective on improving the static and dynamic performance by experiments. The performance parameters of hydrodynamic gas bearing, such as load capacity and stiffness, are dominated by the styles and the geometric parameters of groove. In this paper, the effect of groove styles and geometric parameters on the performance parameters of hydrodynamic gas bearings is presented. And a novel style of groove is designed which can effectively improve the static and dynamic performance. The results based on the calculation of CFD show that: geometric parameters of the groove do have some influence on static and dynamic performance of hydrodynamic gas bearings, and there is an optimal objective value for each parameter of groove which makes load capacity and stiffness maximum. Compared with the spiral-style and π-style groove, the novel style of groove presented in this paper has better static performance.

Actively compensated aerostatic thrust bearing: design, modelling and experimental validation

Active compensation is an effective method for increasing air bearing static and dynamic performance. This paper describes the design, modelling and experimental validation of an actively compensated externally pressurized gas bearing. The active compensation is obtained through the support compensation strategy. With this strategy, the system’s initial working position is restored by compensating for air gap variations through adjustments to the bearing vertical dimension. The described bearing consists in a conventional thrust bearing which is integrated with a multilayer piezoelectric actuator, a compliant mechanism and a digital controller. Nevertheless the non-linear nature of the air system, a simple linear model results to be an effective choice for neighbour of equilibrium conditions. Results demonstrate the good accuracy of the model and the system’s good capacity of rejecting external force disturbances.

Experimental study of small-size air turbo blower supported by externally pressurized conical gas bearings

This paper describes a several ten thousand rpm class small-size air turbo blower. This has been newly developed using externally pressurized conical gas bearings and blower impeller with centrifugal suction blades on both faces. This bearing can reduce the number of machine parts since it is possible to support the thrust and radial load components in both directions. Calculations of the characteristics were conducted and investigated using the manufactured test bearings. A test rig was manufactured, and the characteristics were experimentally verified. These bearings have a conical bearing surface with diameters of 10mm and 8mm and a length of 15mm. A pair of length is 30mm. The actual bearing clearances are 0.012mm and 0.014mm, respectively. The measured bearing characteristics agreed with the designed values. It was clarified that the proposed calculation method is useful for predicting the characteristics in a relatively simple way. The air turbo blower impeller has a 15mm diameter and a 3mm thickness with centrifugal suction blades on both faces that were made by precision machining. The measured rotational frequency of the rotor exceeds 350Hz (21,000rpm) in the test. The rotor vibration was verified as a forward whirl with a conical mode. The blower characteristics were also investigated. The maximum discharge air flow rate and the pressure were 19.2×10−5m3/s and 1.77kPa, respectively, at the maximum rotational frequency of 350Hz. This may be used as a small-size air supply blower.

Study on the matching performance of a low temperature reverse Brayton air refrigerator

A small reverse Brayton cycle air refrigerator was designed and fabricated. Bump-type air journal foil bearing, pressurized thrust gas bearing and centrifugal blower as brake were employed in the turboexpander. Usually, constant brake inlet pressure is set in a reverse Brayton refrigerator. However, the unchanged brake inlet pressure cannot adapt to the changing temperature and expansion ratio during the cooling down process, which could go against the system performance. In this article, the relationship between the turboexpander operation parameters and brake pressure was disclosed through theoretical analysis. The performance curve was analyzed through numerical simulation using CFX. A matching model was established based on the theoretical analysis and numerical simulation. Brake pressure feedback control was then proposed and applied in the experimental study. Thermal performance of the refrigerator was tested under varied operating conditions (different expansion ratios, temperatures and brake pressures). The results indicated that the appropriate brake pressure facilitated system good thermal performance under both design and off-design conditions, and the theoretical results agreed well with the experimental data.

Experimental Identification of Dynamic Force Coefficients for a 110 MM Compliantly Damped Hybrid Gas Bearing

Compliant hybrid gas bearings (HGBs) combine key enabling features from both fixed geometry externally pressurized gas bearings and compliant foil bearings. The compliant hybrid bearing relies on both hydrostatic and hydrodynamic film pressures to generate load capacity and stiffness to the rotor system, while providing damping through integrally mounted metal mesh bearing support dampers. This paper presents experimentally identified force coefficients for a 110 mm compliantly damped gas bearing using a controlled-motion test rig. Test parameters include hydrostatic inlet pressure, excitation frequency, and rotor speed. The experiments were structured to evaluate the feasibility of implementing these bearings in large size turbomachinery. Dynamic test results indicate weak dependency of equivalent direct stiffness coefficients to most test parameters except for frequency and speed, where higher speeds and excitation frequency decreased equivalent bearing stiffness values. The bearing system equivalent direct damping was negatively impacted by increased inlet pressure and excitation frequency, while the cross-coupled force coefficients showed values an order of magnitude lower than the direct coefficients. The experiments also include orbital excitations to simulate unbalance response representative of a target machine while synchronously traversing a critical speed. The results indicate the gas bearing can accommodate vibration levels larger than the set bore clearance while maintaining satisfactory damping levels.

Application of a forecasting coupling method to the non-linear dynamic analysis of a flexible rotor supported by externally pressurized orifices hybrid gas bearings

The non-linear dynamic characteristics of a flexible rotor supported by externally pressurized hybrid gas bearings are studied in this article. The rotor dynamic equations for the rotor are solved by the Newmark integral method and the gas-lubricated Reynolds equation by the alternating direction implicit method. The multifield coupling algorithm based on the forecasting method is proposed and applied in this article to solve the fluid–structure interaction problem. Also, the non-linear dynamic parameter identification method based on the forecasting orbit method is investigated. It is indicated that the dynamic characteristics of externally pressurized hybrid gas-bearing rotor system and whirling instability of the system reveal the complex behaviour, which could be depicted comprehensively. This would establish the foundation for contributing to a further understanding of the hybrid gas-bearing flexible rotor system.

Externally pressurized gas bearings: A comparison between two supply holes configurations

Radial vibration of a vertical rotor with externally pressurized gas bearings is analyzed. The time-dependent Reynolds equation is solved together with the journal equation of motion to obtain the response characteristics of the bearing system. The bearings are supplied with either one or two sets of supply orifices. Stiffness and flow rate are compared for both cases. Stability maps are obtained at different supply pressures and with different supply orifice diameters. The mass range from orbital stability to instability is studied as a function of supply hole downstream pressure level.

Flexure Pivot Tilting Pad Hybrid Gas Bearings: Operation With Worn Clearances and Two Load-Pad Configurations

Abstract Gas film bearings enable the successful deployment of high-speed microturbomachinery. Foil bearings are in use; however, cost and lack of calibrated predictive tools prevent their widespread application. Other types of bearing configurations, simpler to manufacture and fully engineered, are favored by commercial turbomachinery manufacturers. Externally pressurized tilting pad bearings offer a sound solution for stable rotor support. This paper reports measurements of the rotordynamic response of a rigid rotor, 0.825kg and 28.6mm in diameter, supported on flexure pivot tilting pad hybrid gas bearings. The tests are performed for various imbalances, increasing supply pressures, and under load-on-pad (LOP) and load-between-pad (LBP) configurations. Presently, the initial condition of the test bearings shows sustained wear and dissimilar pad clearances after extensive testing reported earlier, (Zhu, X., and San Andrés, L., 2007, “Rotordynamic Performance of Flexure Pivot Hydrostatic Gas Bearings for Oil-Free Turbomachinery,” ASME J. Eng. Gas Turbines Power, 129, pp. 1020–1027). In the current measurements, there are no noticeable differences in rotor responses for both LOP and LBP configurations due to the light-weight rotor, i.e., small static load acting on each bearing. External pressurization into the bearings increases their direct stiffnesses and reduces their damping, while raising the system critical speeds with a notable reduction in modal damping ratios. The rotor supported on the worn bearings shows an ∼10% drop in first critical speeds and roughly similar modal damping than when tested with pristine bearings. Pressurization into the bearings leads to large times for rotor deceleration, thus demonstrating the little viscous drag typical of gas bearings. Rotor deceleration tests with manually controlled supply pressures eliminate the passage through critical speeds, thus paving a path for rotordynamic performance without large amplitude motions over extended regions of shaft speed. The rotordynamic analysis shows critical speeds and peak amplitudes of motion agreeing very well with the measurements. The synchronous rotor responses for increasing imbalances demonstrate the test system linearity. Superior stability and predictable performance of pressurized flexure pivot gas bearings can further their implementation in high performance oil-free microturbomachinery. More importantly, the measurements show the reliable performance of the worn bearings even when operating with enlarged and uneven clearances.

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.

The Little Engine

This article focuses on research and development works in the field of silicon-gas turbine engines to enable them produce power for portable devices. Alan Epstein, a professor of aeronautics and astronautics at the Massachusetts Institute of Technology, and his team are working on tiny silicon gas-turbine engines that could soon power laptops or cell phones. The group chose pressurized gas bearings, which can hold more weight relative to their size as they get smaller. Thrust bearings with spiral grooves and holes in their centers are self-pumping and keep the rotor in the right position. Epstein’s group considered magnetic bearings early on, but found that in addition to the manufacturing difficulties, the magnetic materials had too Iowa Curie point and would not stay magnetic at the temperatures at which the engine would operate: Instead, they chose pressurized gas bearings, which conveniently can hold more weight relative to their size as they get smaller. Thrust bearings with spiral grooves and holes in their centers are self-pumping and keep the rotor free and in the right position. While there is clearly plenty of room for improving efficiency, the microengine may very well end up as the only significant way to power, say, a laptop, an iPod, or a soldier's thermal weapon sight, to say nothing of a palm-size plane.

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.