Gas foil bearing rotor (GFBR) systems have received significant interest in the field of rotordynamics and vibration analysis. GFBR systems have a wide range of high-speed turbomachinery ...applications. Due to the high speed, these machines are susceptible to rigorous vibration and instability. Gas foil bearings instigate large amplitude of vibrations at startup and shut down and severe subsynchronous motions during high-speed operations. Over the years, numerous work has been done in the field of high-speed rotors supported on gas foil bearings. Significant improvement has been observed in the stability and feasibility of the GFBR systems. However, accurate model predictions of gas foil bearing still remain a challenge for its widespread usage in high-speed turbomachinery. A comprehensive review needs to be done to study the previous work and pave the way for future research. The current review is majorly divided into three sections. Firstly, various models used for the performance prediction of gas foil bearings are compiled. After that, major causes of instability that manifest during the experiments and practice with gas foil bearing supported rotors is illustrated. Lastly, the developmental attempts made to inhibit the instability is summarised. This paper presents an overall picture of the current engineering scenario and future prospects of the GFBR systems.
Gas foil bearings are gaining popularity for their compliance properties in various high-speed turbomachinery applications such as air cycle machine, turbocompressor, turbocharger, turboexpander etc. ...A modest attempt is made in the current research to study the feasibility of gas foil bearing for a turboexpander rotating at 1,75,000 rpm. The turboexpander rotor with 16 mm diameter and 91 mm length used for experimentation is supported by a pair of gas foil journal bearings and mounted with turbine and compressor wheels at both ends of the rotor. The feasibility study was performed based on comparison of rotodynamic analysis and experimental data for the critical speed of the rotor and unbalance response at bearing locations. The critical speeds and the unbalance response are predicted using the finite element analysis, which takes into account the gyroscopic effect, shear deformation, internal damping, inertia of the rotor and the dynamic coefficients of the gas foil bearing. The predicted and experimental variation of critical speed is found to be within a relative error of 3–6%; similarly, the variation of unbalance response was found with a relative error of 2–9%. The low relative errors suggest that the experiment and prediction methodology are credible. The author believes that the rotodynamic analysis methodology will be quite valuable for researchers working in the area of high-speed rotors supported with gas foil bearings.
Uncertainties in rotating machines are unavoidable, which affect their parameters and dynamic response. So, instead of employing deterministic models, data-driven meta-modeling techniques which ...incorporate unpredictability and randomness are necessary for the response variation analysis of rotating systems. The performance of the meta-model relies heavily on the quality and amount of the training dataset. In reality, however, only a tiny amount of high-fidelity data is obtainable from high-dimensional finite element simulation or experimental investigation, although low-cost low-fidelity data may be numerous. The objective of this paper is to develop a novel neural network model for multi-level response prediction by obtaining a high number of low-fidelity data quickly through model order reduction and a limited amount of high-fidelity data correctly from a full-order model. The accuracy of the meta-model is demonstrated by comparing against a classical deep neural network. Two different types of meta-model are established by using two model reduction techniques: Guyan reduction and modified system equivalent reduction expansion process. The performance of the model is demonstrated by employing frequency response variation characterization of a complex rotor as a case example. The results reveal that the multi-fidelity neural network performs better than the low-fidelity frequency response curves alone, which is observed to have a lot of inaccuracies. The deep neural network, on the other hand, is unable to reflect on the dynamic response of the full model. A regression of more than 90% shows that the meta-model has high effectiveness in properly predicting the frequency responses. The mean squared error values for the meta-model are found to be less than 0.1, which is typically regarded as acceptable. Frequency response curves of four test samples are selected at random for comparison. It is observed that the meta-model frequency response moves much closer to the full model than compared to that of the low-fidelity model reduction. The performance resilience of the model is tested by using five different training runs with random data splits. Minor changes in the values of logarithm mean absolute error and logarithm root mean squared error under different training runs show appropriate curve fitting and signify superior accuracy. It is concluded that the multi-fidelity neural network can reach a higher level of accuracy with a limited amount of high-fidelity data. The model effectively identifies both the linear and complex nonlinear correlation between the high-and low-fidelity data, resulting in enhanced efficacy in contrast to state-of-the-art methods.
Most studies on dynamic coefficients of bearings are focused on evaluation using different analytical methods. Minimal emphasis is given to the level of influence of each geometrical variable, the ...corresponding range of these variables for optimum stiffness and damping and the measure of performance of the analytical method used. The objective of this paper was to study the influence and sensitivity of length-to-diameter ratio, eccentricity ratio, bearing number, whirl ratio, and bearing compliance on the stiffness and damping of gas foil bearing. A numerical model is developed by utilizing the finite difference method to evaluate the dynamic coefficients. The results reveal that the normalized stiffness increases with the bearing number and decreases with increased bearing compliance whereas the normalized damping shows an opposite nature. Further, the stiffness coefficients tend to increase and the damping coefficients tend to decrease corresponding to increase in speed up to 240 krpm. The characteristic data sets obtained from the analysis is used to train an artificial neural network (ANN). Performance of ANN network is evaluated though computation of root-mean-square error (RSME) and regression coefficient (
R
2
) and Mean Absolute Error (MAE). Utilizing the neural network results, a Sobol’s sensitivity test is carried out to identify most effective parameters which have a significant influence on the dynamic coefficients of gas foil bearing. After that, an adaptive neurofuzzy interface system (ANFIS) is established to determine the optimum range of data for which maximum stiffness and damping can be obtained. The results deduce that the neural network shows high efficacy in predicting the output variables correctly with a regression of more than 95%. It is also observed that the variation of dynamic coefficients is the highest for eccentricity ratio whereas lowest for whirl ratio. The maximum stiffness and damping coefficients are also obtained for a wide range of geometrical variables which can help in designing the gas foil bearing.
As a major component of any high rotating turbomachinery to withstand an axial load of the system while providing stability to the rotor, gas foil thrust bearing (axial bearing) should be designed ...and investigated accurately. The article presents sensitivity analysis and provides an optimum range of design parameters of a gas foil thrust bearing for which it has a maximum load-carrying capacity and low power loss using artificial intelligence techniques. The preliminary numerical model is tested by coupling the fluid flow and structural equations to predict the bearing performance. The standard non-dimensional Reynold’s equation is used to predict the pressure distribution of the fluid film. The obtained results from the numerical model are then validated with the experimental results available in the open literature. The article investigates the effect of various parameters like film thickness ratio, minimum film thickness, interface friction coefficients between top foil/bump foil and bump foil/bearing base and bump foil parameters on the load-carrying capacity, frictional torque, side leakage, and power loss. The results conclude four parameters (minimum film thickness, ratio of angular extent at wedging, angular extent of thrust pad, and rotational speed) have a significant effect on load carrying capacity and power loss as compared to others with optimized range. The results highlight the importance of numerical methodology, sensitivity analysis, and prediction capability of the artificial intelligence network.
The use of gas foil bearings in turbomachines such as turbochargers and turboexpanders in recent times comes into picture due to merits of gas foil bearings over simple gas lubricated bearings. The ...high speed leads to various constraints in selection process of the bearings. However, gas foil bearing’s (GFBs) ability to improve the dynamic characteristics (such as stiffness and damping) makes them hot topic to investigate. Usually, gas foil bearings deal with operating conditions such as high speed and low clearance region which further leads to slip-flow condition at solid–fluid interface. The current article investigates the hydrodynamics, thermal characteristics and thermohydrodynamics of the gas foil journal bearing (GFJB) under the impact of slip-flow condition. The mathematical model is formulated by considering first-order velocity slip and thus modifying the Reynold’s equation coupled with the energy equation. The viscosity and density are evaluated as a function of temperature which again substituted in Reynold’s equation to investigate the thermohydrodynamic characteristics of GFJB. The equations are further discretised using finite difference method and solved using successive over relaxation (SOR) methodology. The comparison is drawn between the performance parameters for both no-slip and slip-flow conditions.
Gas foil bearings (GFBs) are often employed in turbomachinery, particularly in high-speed turbochargers and turboexpanders. These bearings operate at very high speed and under very low clearance. On ...account of very low clearance, velocity slip can be observed at the gas–solid-interface. This paper investigates the effect of slip on various performance characteristics of the GFB. A model is put forth to predict the pressure and film thickness of a Gas Foil Journal Bearing (GFJB) used in helium-liquefaction turboexpander operating at 240 krpm. The present model addresses the slip at the gas-foil interface. Modified Reynolds equation, assuming first-order slip, is used along with the structural equation, which illustrates the compliant property of the foil. A numerical model is developed by finite difference approximation and solved by an iterative method. Various performance parameters are assessed for the no-slip and slip flow phenomenon in GFJB. The results are compared and a considerable difference is seen between the two models. The conventional Reynolds equation overestimates the load by approximately 8% at 240 krpm. The load-carrying capacity at different values of Knudsen number is also shown.
High-speed turbomachinery such as cryogenic turboexpander, turbocharger, turbo-compressor, and dental drill machines are prone to rigorous vibration and instability. The rotors of such high-speed ...turbomachinery cannot be analyzed by the fundamental Jeffcott rotor model. This is because, under the conditions of high-speed operation, the flexible rotor experiences many factors such as gyroscopic effect, shear deformation, axial torque, internal friction and viscous damping. These factors can influence catastrophic subsynchronous whirl in the system. Turbomachinery rotors have complex geometries and involve discs, turbine, compressor and bearings. In addition, complex turbomachinery rotors operate in high-speed conditions where tangential forces come in to picture, which further influences the behavior of a rotor and tends to destabilize the turbomachinery. These instabilities can be addressed by the design of a suitable rotor and its supporting bearings. In the present work, a complex turboexpander rotor is designed, which is supported on gas foil bearings, and its modal behavior is studied under high-speed environment. The rotor is small-sized and incorporates a disc, a turbine, a compressor and a pair of gas foil bearings with support structures. Finite element modeling is carried out, and the bearing dynamic coefficients are considered while modeling. The dynamics of the rotor is studied by estimating critical speeds, mode shapes and unbalance response.
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