Air Bearing Research Articles

Numerical investigations on high-speed turbo-compressor rotor systems with air ring bearings: Nonlinear vibration behavior and optimization

Regarding aerodynamic bearings, mainly two basic types can be distinguished: air bearings with a rigid housing and air foil bearings with an elastic supporting structure. Here, a modified bearing concept -- called air ring bearing -- is investigated, which may be considered as a further development of rigid air bearings or as a combination of the two basic bearing types. The idea of air ring bearings is to insert a ring-shaped bearing bushing between the shaft and the foil structure. Alternatively, a visco-elastic supporting structure (e.g., an elastomer) can be applied to connect the bushing ring with the housing. In the first case, external dissipation is mainly generated by dry friction. In the latter case, viscous damping is used to provide external dissipation. Due to the external friction/damping generated by the ring mounting structure, rotor systems with air ring bearings can be operated above the linear threshold speed of instability so that stable self-excited vibrations with moderate amplitudes can be achieved in the complete speed range. Here, a detailed transient co-simulation model for rotor systems with air ring bearings is presented. The rotor is represented by a multibody model. The air films of the two bearings are represented by two nonlinear time-dependent finite element systems. The multibody model and the two finite element subsystems are solved simultaneously by means of an explicit sequential co-simulation technique. Due to the strong nonlinearities, the system shows interesting vibration and bifurcation effects, which are investigated in detail with the help of run-up simulations.

Effect of Interstage Pipeline on the Performance of Two-Stage Centrifugal Compressors for Automotive Hydrogen Fuel Cells

At present, two-stage centrifugal compressors based on air bearing and high-speed motor technology are widely used in automotive hydrogen fuel cells. The low-pressure stage and high-pressure stage of the compressor are directly connected through an interstage pipeline, thus the structure of the interstage pipeline has an important influence on the aerodynamic performance of the compressor. In this work, a two-stage compressor with three different interstage pipelines were investigated experimentally and numerically. Results show that affected by the interstage pipeline bend section, the flow distortion will be induced at the impeller inlet of the high-pressure stage, and the distortion intensity changes with the pipeline structure. Among the three models, the EPC (elbow pipe change) model induces the most intense total pressure distortion at the condition of 80 kr/min and 130% mass flow rate, resulting in an efficiency reduction of 2 and 1.5 percentage points compared with the SPC (straight pipe change) and the TPC (total pipe change) model, respectively. Further research indicates that the upstream distortion has obvious influence on the downstream rotor blades. As the blade height decreases, the load becomes more uniform on the main blades, while the load extremum migrates to the trailing edge on the splitter blades. Finally, three models are tested, and their performance is compared at three typical rotational speeds., It is recommended that interstage pipelines similar to SPC models should be chosen to improve the two-stage compressor efficiency in the design.

Dynamic Analysis and Machine Learning Prediction of a Nonuniform Slot Air Bearing System

Abstract Nonuniform slot air bearing (NSAB) systems have two major advantages, the external air supply and slot restrictor design, and their inherent multidirectional supporting forces and stiffness that provide excellent rotational stability. However, NSAB systems are prone to vibration from nonperiodic or chaotic motion caused by nonlinear pressure distribution within the gas film, gas supply imbalance, or simply inappropriate design. It is necessary to determine under which conditions these nonperiodic motions arise, and to design a NSAB system that will resist these vibrations. The dynamic behavior of a rotor supported by an NSAB system was studied using spectral response, bifurcation, Poincaré map, and the maximum Lyapunov exponent. The numerical results showed that chaos in an NSAB system occurred within specific ranges of rotor mass and bearing number. For example, the chaotic regions where the maximum Lyapunov exponents were greater than zero occurred in the intervals of rotor mass 20.84 ≦ mf < 24.1 kg with a bearing number of Λ = 3.45. In addition, the coupling effect of rotor mass and bearing number was also investigated. To predict chaotic behavior, ensemble regression, and the back propagation neural network were used to forecast the occurrence of chaos. It was found that ensemble regression using dataset of 26 × 121 gave the best results and most accurate prediction for this NSAB system. The results may make a valuable contribution to the design of NSAB systems for use in a wide variety of industrial applications.

The Partial Derivative Method for Dynamic Stiffness and Damping Coefficients of Supercritical CO2 Foil Bearings

Supercritical CO2 foil bearings are promising bearing technology for supercritical CO2 high-speed turbomachinery. The partial derivative method including complete variable perturbation of the compressible turbulent lubrication Reynolds equation is effective to predict the frequency dependent dynamic stiffness and damping coefficients of supercritical CO2 bearings. In this research, the structural perturbation of foil dynamic model was introduced into this method and then the dynamic coefficients of supercritical CO2 foil bearings were calculated. The results of parametric analysis show that the structural loss factor has little influence on the trend of dynamic coefficients changing with the dimensionless support stiffness but mainly affects the value of stiffness coefficients as well as damping coefficients. Due to the turbulence effect, the bearing number is not able to directly determine the characteristics of supercritical CO2 foil bearings, which is different from air bearings. Compared to the bearing number, the influence of the average Reynolds number on the change of dynamic coefficients with dimensionless support stiffness is more obvious.

Squeeze film air bearing for controlling the shaft positions based on a radial basis function neural network

This study presents a squeeze film air bearing (SFAB) with flexure pivot-tilting pads that can be used to control the shaft positions. As the vibration characteristics and coupling relationship of three pads in the bearings, which determine the position control accuracy, are highly complicated, an intelligence algorithm based on a radial basis function neural network is proposed to forecast the desired pad amplitudes for the shaft reaching target positions. The database of the intelligence algorithm established on the basis of the air lubrication theory model is verified via an experimental test. Different target shaft positions that construct various trajectories are then used as the inputs of the intelligence algorithm. The desired pad amplitudes can be directly outputted from the intelligence algorithm and reused as the initial parameters of the air lubrication theory model to recalculate the shaft positions. The recalculated and target positions are compared and found to be in excellent agreement. This finding proves that the presented SFABs can precisely control the shaft to reach the target positions or move at the intended trajectories with the assistance of an intelligence algorithm.

Fractional-Order Gas Film Model

In this paper, a fractional-order model of the gas film is proposed for the dynamic characteristics of an air bearing. Based on the dynamic characteristics common between gas film and viscoelastic body, the idea of the fractional-order equivalent modeling of the dynamic characteristics of the gas film is presented to improve the modeling accuracy. Four fractional-order gas film (FOGF) models are introduced based on generalization of traditional viscoelastic models. The analysis of the characteristics of the FOGF models shows that the FOGF model can capture more complex dynamic characteristics and fit the real dynamic data of the gas film better than traditional models. A genetic algorithm particle swarm optimization (GA-PSO) method is used for parameter identification of the proposed models. The experimental results tested on the air bearing motion platform show that the FOGF models are superior in accuracy to the traditional equivalent models for the gas film. In particular, the fractional-order Maxwell gas film (FOMGF) model has the best capture accuracy compared to the other FOGF models and traditional models.

A newly treated boundary conditions to enhance accuracy of finite element analysis for orifice-type aerostatic bearings

Although numerical approaches have been extensively employed for solving the Reynolds equation in order to predict the performance of air bearings, we found inappropriate boundary settings can cause significant numerical errors if the grid-dependent condition is ignored. The current scrutiny is focused on crucial procedures for adopting the finite element method to assess the performance of orifice-type aerostatic bearings. To this end, numerical models for a single orifice-type are established and then checked by varying mesh sizes, mesh types, and boundary conditions (BCs). The obtained results reveal that those numerical models with a single-source node are grid-dependent, and the relative error is so large that the results are not credible compared with the analytical solution and becomes worse with denser meshes. This peculiar phenomenon can be mathematically interpreted by a one-dimension finite difference model calculated manually and auxiliary sources have proved to be an effective technique to reduce single-source numerical error to an acceptable level. Additionally, a physical explanation is given based on engineering systems modeling. By this view, rules of setting high pressure on the edge of recess are proposed and three types of grid-independent BC settings are proposed. Stiffness test experiments based on manufacturing a rotary table adopting multi-orifice aerostatic thrust bearings are further carried out to validate these numerical models, and the discrepancy between measured and calculated stiffness is reported to be lower than 5%.

Commissioning NIS 1 kN·m Primary Torque Standard Machine

The presented work shows the design and evaluation of the NIS 1 kN·m primary torque standard machine. The machine covers the range up to 1000 N·m with a very wide range of torque steps thanking different 4 mass stacks. The machine has a double-side lever arm with half-moon ends to provide calibration in the clockwise and anticlockwise directions. An air bearing was used as a fulcrum to provide a low friction coefficient. FEA was used in the design and optimization process of the lever arm. The relative expanded uncertainty of the machine is 0.03% which is proved by recalibration of two reference torque transducers of 200 N·m and 1000 N·m capacity. All En values are less than unity, which reveals the competence of the developed machine.

Dual-modality fluorescence lifetime imaging-optical coherence tomography intravascular catheter system with freeform catheter optics.

.Significance: Intravascular imaging is key to investigations into atherosclerotic plaque pathobiology and cardiovascular diagnostics overall. The development of multimodal imaging devices compatible with intracoronary applications has the potential to address limitations of currently available single-modality systems.Aim: We designed and characterized a robust, high performance multimodal imaging system that combines optical coherence tomography (OCT) and multispectral fluorescence lifetime imaging (FLIm) for intraluminal simultaneous assessment of structural and biochemical properties of coronary arteries.Approach: Several shortcomings of existing FLIm-OCT catheter systems are addressed by adopting key features, namely (1) a custom fiber optic rotary joint based on an air bearing, (2) a broadband catheter using a freeform reflective optics, and (3) integrated solid-state FLIm detectors. Improvements are quantified using a combination of experimental characterization and simulations.Results: Excellent UV and IR coupling efficiencies and stability (IR: , UV: ) are achieved; high FLIm optical performance is obtained (UV beam FWHM: ) contemporaneously with excellent OCT beam quality (IR beam FWHM: ). High-quality FLIm OCT image of a human coronary artery specimen was acquired.Conclusion: The ability of this intravascular imaging system to provide comprehensive structural and biochemical properties will be valuable to further our understanding of plaque pathophysiology and improve cardiovascular diagnostics.

An optimal H 2 controller based on vibration energy minimization for a horizontal vibration isolator supported by air bearings

To suppress various interferences in the active vibration control process simultaneously, an optimal H2 control method based on vibration energy minimization is proposed in this paper. The interference sources mainly include floor vibration interference, direct interference, and sensor noise as well as electrical noise and quantization noise of the analog to digital and digital to analog converters. The interferences are modeled by weighting filters and the load vibration is weighted by a scaling filter, both of which are introduced into the design of the system’s H2 controller. Thus, the load vibration energy is equivalent to the H2 norm of the system. This method can minimize the total impact of external interferences and improve the vibration isolation performance of the system. Compared with the traditional proportional integral derivative control method, it significantly reduces the root-mean-square value of the load vibration. Simulation and experimental results verify the effectiveness of the proposed control method.

Development of a Cryogenic Tester with Air Bearing to Test Sliding-Rolling Contact Friction

This study aimed to test the friction coefficient of cryogenic bearing lubrication materials. A ball-on-disc type friction tester was developed in our lab using air bearings that could simulate the movement of cryogenic bearings under sliding-rolling contact. The tester is equipped with a temperature-controlled chamber to provide a minimum −175 °C low-temperature environment. Using air bearings is an important technique to reduce the base friction of the tester measurement system and ensure the accuracy of the friction coefficient measurement. The friction coefficients of the Ag coating and the PTFE coating were measured at different sliding-rolling velocities on this tester, and the results showed that the friction coefficient curves agreed well with the Gupta sliding model. The developed tester will provide important data for the dynamic analysis and life evaluation of the cryogenic bearings.

Stability and bifurcation analysis of a rotor in rigid and foil air bearings utilized for the identification of the air whirl effect

Stability and bifurcation analyses of holistic rotor-air bearing models are performed. Both, fluid and foils are modeled in a non-linear way, while the model of the latter is validated by measurements. A model order reduction is applied to the fluid film equations to increase computational efficiency. Intentionally, a minimal rotor model is considered in order to isolate the effects of the bearing on the overall system’s behavior. Instead of time integration methods, bifurcation analyses are applied. Thus, different solutions are identified, their stability is assessed and corresponding branch points are determined. The method is applied in order to compare a rigid gas journal bearing with a foil air bearing. In particular for the foil air bearing, parameter studies are performed to investigate the effect of design changes on the rotor stability and the resulting vibrations. The impact of different static rotor unbalances is considered, too. Furthermore, the effect of air whirl – occurring in both bearing types – is identified and explained.

Dynamic performance of a long-stroke fast tool servo system

A fast tool servo (FTS) system can be used to efficiently manufacture optical freeform surfaces. This paper investigates the dynamic performance of an FTS system driven by a voice coil motor and guided by air bearings. A simulation model and testing platform are developed to evaluate the load capacity and stiffness of the air bearings. The mechanical dynamic performance of the designed FTS, including modal and harmonic analyses, is assessed using finite element analysis. A nonlinear relation between air-bearing stiffness and mechanical bandwidth is obtained. The working dynamic performance is tested through system runout, tracking performance, and closed-loop tests. Quantitative relations between air-bearing stiffness and the mechanical and working bandwidths are established and analyzed. Machining experiments verify the feasibility of the FTS system with 31.05 N/μm stiffness air-bearings.

Development of Air Bearing Stage Using Flexure for Yaw Motion Compensation

This paper presents an air bearing stage that uses flexure for yaw motion compensation. The proposed stage realizes motion in three degrees of freedom (DOF), which are the X, Y, and Θz directions. To work with Θz as the rotational motion of the stage, we applied a flexure consisting of four bar linkages. The stage from a previous study in which flexure is applied to compensate for yaw motion error has the limitation of increasing the structural stiffness of the stage due to the rotational stiffness. In this study, we propose a combination of a new stage structure and flexure to ensure the high structural stiffness of the stage and the very low rotational stiffness of the flexure at the same time. Modeling and design optimization were performed to apply adequate flexure to the proposed stage. Experiments were carried out to verify yaw motion error compensation and the performance of the stage. The proposed stage has a maximum yaw motion error of 0.86 arcsec during the scanning motion and 48 ms settling time, while the stepping motion is improved by 34.2% compared to the previous study.

A novel long-stroke fast tool servo system with counterbalance and its application to the ultra-precision machining of microstructured surfaces

This paper presents a novel long-stroke fast tool servo (FTS) system with counterbalance and its application to the diamond machining of microstructured surfaces. The FTS system is driven by a voice coil motor and guided by air bearings. A hybrid control algorithm which combines PID control, sliding mode control and feed-forward control was specifically designed for the system and ensures that it has less than 1% tracking error and achieves ± 1 mm stroke and 105 Hz bandwidth. The counterbalance is achieved by the symmetric arrangement of two of the same FTS systems. System vibration decreased significantly from ± 3 μm to ± 0.145 μm when the counterbalance was working. Machining experiments were conducted using the FTS system on a diamond turning machine. A microstructured surface simulation model was built and information about the workpiece surface tested and collected. When the counterbalance was working, error in the machine axes decreased from micron-level to nano-level and the surface roughness of the microstructured surface was also reduced. The system achieves ± 1 mm (±0.5 mm) stroke at 30 Hz (40 Hz) with 0.35% (0.68%) tracking error during machining processes, and the depth error of the machined microstructured surface was measured at 1.4% (2.3%).

The Influence of Ambient Pressure on the Measured Load Capacity of Bump-Foil and Spiral-Groove Gas Thrust Bearings at Ambient Pressures up to 69 Bar on a Novel High-Pressure Gas Bearing Test Rig

Abstract This paper will show the influence of ambient pressure on the thrust capacity of bump-foil and spiral-groove gas thrust bearings. The bearings were operating in nitrogen at various pressures up to 69 bar and were tested to failure. Failure was detected at various pressures by incrementally increasing the thrust load applied to the thrust bearing until the bearing was no longer thermally stable, or until contact was observed by a temperature spike measured by thermocouples within the bearing. These tests were performed on a novel thrust bearing test rig that was developed to allow thrust testing at pressures up to 207 bar cavity pressure at 260 °C while rotating at speeds up to 120,000 rpm. The test rig floats on hydrostatic air bearings to allow for the direct measurement of applied thrust load through linkages that connect the stationary thrust loader to the rotor housing. Test results on a 65 mm (2.56 in.) bump-foil thrust bearing at 100 krpm show a marked increase in load capacity with gas density, which has not previously been shown experimentally. Results also show that the load capacity of a similarly sized spiral-groove thrust bearing are relatively insensitive to pressure, and supported an order-of-magnitude less load than that observed for the bump-foil thrust bearing. These results are compared with analytical predictions, which agree reasonably with the experimental results. Predicted power loss is also presented for the bump-foil bearing; however, measured power loss was substantially higher.

Dynamics of 5-DOF aerostatic spindle with time-varying coefficients of air bearing

Aerostatic bearing spindle has been widely used in precision machining processes. This paper presents a time-varying dynamic model of aerostatic spindle due to the change of air film thickness under periodic excitation forces. The effects of the magnitude and frequency of the forces on the dynamic coefficients of air bearing and cutting tool deflection are determined quantitatively. The dynamic properties in both translational and rotational directions are considered. The predicted tool vibration with and without considering the time-varying dynamics are compared. Experiments are conducted to measure the cutting tool displacements under stationary and rotational conditions. It is concluded that the variation of the dynamic coefficients plays a significant role in the spindle dynamics when the force magnitude increases beyond a critical value. The effect of unbalance mass on the spindle vibration is investigated based on the proposed model. The results provide guidance in the structure design for the aerostatic spindle and the process planning to improve the dynamic performance of the precision manufacturing process.

An Improved Dynamic Modeling Approach of Aerostatic Thrust Bearing Considering Frequency-Varying Stiffness and Damping of Air Film

Abstract The damped mass-spring model is often used for the dynamic modeling and vibration analysis of aerostatic bearing systems by taking the air film as equivalent springs, especially when the bearing is used as a key component in mechanical equipment. However, the stiffness and damping of the air film are frequency-dependent, making the commonly used approach of taking static stiffness or fixed value as the spring coefficient no longer applicable for a bearing subject to a complex external force containing different frequencies. To address this issue, this paper develops the damped mass-spring model for the aerostatic thrust bearing considering the frequency-varying stiffness and damping by means of the linear superposition method. It indicates that the air bearing is still a linear system under a micro disturbance despite the frequency-dependent character of dynamic coefficients because the bearing vibration satisfies the superposition principle. The improved dynamic modeling approach is able to accurately and efficiently predict the overall dynamic response of the thrust plate with both axial and tilting motion when the plate is subjected to a multi-frequency vibration. In solving the overall dynamic response, the stiffness and damping associated with the responses of the transient part and steady part correspond to the natural vibration frequency and external disturbance frequencies, respectively. The feasibility and accuracy of the improved modeling approach are partly or completely verified by the direct trajectory calculation method, the computational fluid dynamics, dynamic mesh simulation, and a modal test. The proposed modeling method provides an effective way for the vibration analysis of air bearings, and in the meantime avoids the possible numerical errors caused by the traditional modeling approach.

Modified quality loss for the analysis of product quality characteristics considering maintenance cost

ABSTRACT In view of the fact that the product cannot be restored to new for the actual maintenance, and the degradation rate gradually increases after the maintenance. A concept, quality characteristics of products should obey a multi-stage linear variation during service life, is proposed, which can be used to modify the quality loss model. The correlation among maintenance cost, quality loss, and the range of key quality characteristics (KQC) of product is considered, products’ preventive maintenance (PM) schedules are further adjusted to obtain the optimal range of KQC. Failure data of the air bearing of the air conditioner and the piston are used as examples. This paper compares and analyzes the best preventive maintenance of in-service equipment from two dimensions of quality loss and maintenance cost. The results show that the optimal preventive maintenance range can reduce the total operating cost of enterprises. Scientific evaluation of the service life of in-service products, reasonable arrangement of product maintenance and decommissioning work, improved product utilization, and provided a new perspective for product quality research in the whole life cycle.

Experimental Methods for Evaluating Components of Turbomachinery, for Use in Automotive Fuel Cell Applications

This paper describes methods and test beds for components of turbomachinery, for use in automotive fuel cell applications at the Ostfalia University of applied sciences. Turbomachinery for use in fuel cell applications is subject to different requirements than those of conventional turbochargers. Therefore, the turbine and the air bearings of an electrical turbocharger will be subject to evaluation. The different boundary conditions in comparison to conventional turbochargers, with less heat and high humidity from the fuel cell, are especially of interest. Air bearings affect the friction and the vibrations/oscillations of the shaft. The methods and test beds need to fulfill the requirements of these types of turbomachinery. The friction test bed is modified with a new coupling solution, to ensure that the driving electric motor in combination with the shaft of the test component complies with the strict tolerances. For this, a magnetic coupling, for use in high-speed applications, is developed and tested on the friction test bed. The fuel cell turbine was adapted to the hot gas test bed and extended turbine maps are determined. To reach high humidity conditions of a fuel cell application, a water injection system is integrated into the test bed.