Rotordynamics of High-Speed Rotors Supported on Gas Foil Bearings

Abstract

High-speed rotor-bearing systems have received significant interest in the field of rotordynamics and vibration analysis. These systems are used in a wide range of turbomachinery applications such as turboexpanders, turbo compressors, turbo generators, turbochargers, etc. Due to the high speed, these machines are susceptible to rigorous vibration and instability. These instabilities can be addressed by the design of a suitable rotor and its supporting bearings. In many cases, such systems need oil-free bearing technology to address the issues of contamination and high friction. One of the suitable approaches to overcome these limitations is to use gas bearings. These bearings have become increasingly popular over the last few decades due to their advantages, such as low frictional losses, low power consumption, the ability to operate at high temperatures, and low noise. However, a downside of simple gas bearings is that they have low stiffness and damping properties. Therefore, gas foil bearings have been proved to be an appropriate candidate for such a high-speed system due to their compliant behavior and higher load-carrying capacity. In the present work, a numerical model of the gas foil bearing is developed by utilizing the perturbation approach to predict the stiffness and damping coefficients of bearings. The behavior of the normalized stiffness and damping is obtained with respect to the bearing number and compliance number. The results are utilized, and Sobol's sensitivity test is conducted to estimate the most effective parameters among the length-to-diameter ratio, eccentricity ratio, bearing number, whirl ratio, and compliance number. After that, the characteristic data sets obtained from the analysis are used to train an artificial neural network (ANN) for a wide range of bearing parameters. Additionally, an adaptive neuro fuzzy interface system (ANFIS) is established to determine the optimum range of data for which maximum stiffness and damping can be obtained. In the next phase of research, the modal behavior of a high-speed rotor-bearing system is estimated for a turboexpander. The finite element (FE) modeling of the high-speed rotor is carried out, which takes into account the gyroscopic effect, shear deformation, internal damping, inertia of the rotor, and the dynamic coefficients of the gas foil bearing. Further, the thesis attempts to reduce the finite element model by gradually discarding the rotational as well as translational displacements for the rotor and investigating its effect on the response of the rotor while maintaining a tradeoff between the accuracy and computational time of the reduced models. A set of recommendations are suggested for careful selection of the degrees of freedom at important locations, which influence the reduction success chances. The reductions are applied to the high-speed rotor-bearing model, and a comparative analysis was presented via four robust model reduction techniques: Guyan, improved reduced system (IRS), component mode synthesis (CMS), and modified system equivalent reduction expansion process (Modified SEREP). Additionally, a novel meta-modeling approach is suggested where a neural network model is developed for multi-level response prediction. The implementation of artificial intelligence in rotordynamics is absolutely important as is that it enables data-driven meta-modeling. This technique incorporates unpredictability and randomness which are necessary for the response variation analysis of rotating systems. In this meta-model, a large number of low-fidelity data from the reduction model and a limited number of high-fidelity data from the FE model are used. The performance of the model is demonstrated by employing frequency response characterization of the high-speed rotor-bearing system. Further, the experimental investigation is presented in the current dissertation to study the vibrational behavior of the high-speed rotor supported on gas foil bearings. The fabrication methodology of the rotor, gas foil bearings, housing, and all the associated parts of a turboexpander is presented. The rotor is dynamically balanced, and all the components are assembled. Additionally, the test setup is also developed to test the performance of the high-speed rotor. The high-speed rotor-bearing system is attached to the DAQ (data acquisition system) and vibration card. The various sensors and equipment like an oscilloscope, proximity probes, piezoelectric accelerometers, a digital tachometer, and a high-pressure compressor air facility are used to fully develop the experimental test facility. The feasibility study was performed based on a comparison of rotordynamic analysis and experimental data for the critical speed of the rotor and unbalance response at bearing locations. Overall, the thesis highlights the importance of using a model reduction method and artificial neural network instead of using only a FE method to predict the rotordynamics of the high-speed rotor-bearing system. For the gas foil bearing design, the most influential parameters are identified, and the range of these parameters for maximum stiffness and damping are determined. The results also conclude that the classical recurrent neural network underestimates the frequency response of high-speed rotor-bearing systems, and thus, a multi-fidelity neural network should be used for prediction. Finally, the experimental investigation is carried out to validate the numerical models formulated in the thesis.