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Top1. Introduction
The utilization of thermal resources for the energy generation, transportation, and carrying out daily tasks was always considered useful for society. However, due to the concern about Brazilian energy matrix concentrated on water resources, alternative sources of energy generation are increasingly studied (Hamman, 2014; Lamas & Giacaglia, 2013; Lima, Ribeiro, & Perez, 2018). Turbogenerators are closed circuit exothermic rotary motors that convert kinetic energy—produced by water, gas or steam—into mechanical work in the form of torque and rotation speed of rotation (Maia, Faria, Barros, Porto, & Filho, 2017). This generated energy is transferred to a shaft, and it can be used efficiently for the pumps drive, compressors, turbo blowers, propulsion, electric generators, among other several applications. Such efficiency is justified since this type of machine can operate at frequencies an order of magnitude above line frequency, which allows reduce the size of the machines in the same power rating (Rosa, Lima, & Fumagalli, 2017). Currently, great percentage of the world's energy is produced by the turbogenerators. The increase in high-speed machines use was due to the high energy efficiency provided by its operation—62.8%, considering a turbine entry temperature of 1703 K (Paniagua, Iorio, Vinha, & Sousa, 2014)—which is a low cost and low environmental impacts solution.
High-speed machines employed to electrical energy conversion have mechanical coupling, and are supported by mechanical rotational bearings. Amongst the several bearings models, hydrodynamic bearings are widely used in turbomachines because of their ability to withstand high load situations, high rotations and good precision (Machado & Cavalca, 2015; Zhay, Liu, Chen, Xiao, & Wang, 2014). In a simplified way, hydrodynamic bearings can be defined as a mechanical assembly formed by a shaft and a bushing, in which the shaft diameter is very close to the bushing inner diameter, in such a way that the gap between them is very small. This passive lubrication is generated from the bearing rotation upon reaching the hydrodynamic lubrication regime. Hydrodynamic term refers to the thin layer of fluid responsible for bearing loads, a phenomenon possible due to the generation of a pressure field in the oil, and resulting from the movement of the rotor and the construction geometric characteristics. Hydrodynamic pressure depends on several factors such as system rotation, bearing clearance, diameter, bushing length, and applied load (Melconian, 2011).
Knowing the conditions of the system in operation, and the efforts required in its operation are important parameters to define the components sizing and the materials to be applied in study. The static and dynamic behavior analysis of the mechanical assembly rEquires an interaction between practice and theory by the mathematical computational methods. In this way, several researches have been developed around the performance of hydrodynamic bearings used in high-speed machines (Chasalevris, Nikolakopoulos, & Papadopoulos, 2013; Zhay, Luo, Wang, & Liu, 2016; Usman & Park, 2018). Since the finite element methods (FEM) offers obvious modeling advantages, the implementation of simulations for the study of high-speed systems has been the subject of recent publications. The results enable to define the materials to be used, according to its mechanical properties and stresses rEquired of project. Nguyen et al. (2019) simulated the turbulent flow past a vertical axis wind turbine by the Direct Finite Element method in a rotating ALE framework. The simulation results showed good validations against experimental data in parked and rotating conditions. Komori et al. (2018) studied he dynamic characteristics of a high-speed turbine rotor supported by superconducting magnetic bearings. Rezaei (2018) evaluated the dynamics and the aeroelastic effects of geometric nonlinearities in a wind turbine assembly by FEM model. The results revealed that the single-blade models are helpful in demonstrating the overall trends of turbine rotor aeroelasticity. Yao et al. (2018) proposed the identification and optimization of unbalance parameters in a rotor-bearing assembly by the modal expansion technique, in order to provide more accurate predictions of system behavior.