Hydropower generators are essential for providing electricity for daily human activities. For that reason, designing and building reliable generators contributes to a sustainable energy supply market. Many studies have sought to model the dynamics of hydropower generators, as providing a reliable model would lead to more cost-effective designs; these models need to consider both operational and faulty conditions. A generator comprises many parts that contribute to its dynamics: tilting-pad bearings, rotor-rim, and stator’s core, which are the ones focused on in this study. Modeling a hydropower generator is a complex endeavor that requires considerable computational resources and is time-consuming. Therefore, this thesis aims to propose models to study and predict the dynamics of hydropower generators, which would be beneficial for manufacturers and operators, reducing the complexity of the design without compromising accuracy. To accomplish this, each mentioned individual part is explored. It starts with characterizing eight-pad tilting-pad bearings on vertical rotors, proposing a model, and comparing the results to experiments. Then it continues by considering the rotor rim in a generator to be flexible and proposing a model for the generator with flexible rotor rims while the stator remains rigid; this is accomplished using Lagrange equations, considering the centrifugal and Coriolis effects, the electromagnetic interaction between rotor and stator, and static and dynamic eccentricities. Reducing the complexity of the rotor rim required assembling 2-D curved beam elements to reproduce its geometry and testing on a generator prototype, discussing the impact of the connecting plates and the magnetic forces on the natural frequencies and the effect of static eccentricity and unbalance. A 3-D Finite Element model of the generator was also proposed, and both simulations focused on the similarities and differences between both approaches.  Furthermore, linear and nonlinear models of the electromagnetic forces acting on the rotor are also considered and applied in the model to study whether the nonlinear behavior in a generator can affect its stability by employing Bifurcation diagrams and Poincaré maps. 

Rotating machinery forms the backbone of modern energy conversion, facilitating the transfer of energy between a fluid and a rotating component, the rotor. Mathematical modeling of rotating machinery has become increasingly sophisticated due to growing demands in modern machine design, primarily driven by the increase of angular momentum sustained by the rotor. Thus, the study of rotating machine dynamics has evolved to improve prediction accuracy and ensure operational stability.

A rotor typically consists of shafts, disks, and blades, supported by bearings that enable rotation relative to a stationary structure. Bearings are tasked to provide both support and energy dissipation. While rotor-bearing models often suffice for dynamic analysis of rotating machinery, stators—such as casings, housings, and foundations—can influence dynamics through rotor-stator interactions. For example, compliant bearing supports may impair bearing function, while generator stators exert significant electromagnetic forces that impact operational stability. The integrated model of these components is known as a rotor-bearing-stator (RBS) system.

While traditional rotor dynamic analysis typically utilizes shaft elements to model the rotor assembly and reduces the stator and bearing to discrete spring elements, a full three-dimensional representation overcomes the kinematic and geometric restrictions of beam theory, enabling the analysis of vastly more complex systems. Furthermore, the increased degrees of freedom lead to greater computational complexity, particularly noticeable for vertical machinery. Unlike horizontal rotors, vertical systems inherently experience large dynamic displacements and lack a stationary point of operation, necessitating the use of nonlinear bearing formulations. Hydropower machinery is generally supported by hydrodynamic journal bearings. This requires tracking the rotor position at each time step and solving equations for fluid-film interaction, further increasing computational demands.

This compilation thesis investigates the dynamics of integrated hydropower systems, with emphasis on how to accurately and efficiently model complex, vertical systems by finite element methods. The thesis constitutes three applied studies of vertical RBS-systems, mostly related to hydropower applications. The first paper focuses on a three-dimensional model of a floating-rim synchronous generator, with emphasis on deformation under electromagnetic and centrifugal loads. The second paper explores the interaction between tilting pad journal bearings and an elastic support frame, exploring the potential implementation of nonlinear journal bearing formulations within a three-dimensional finite element framework. Finally, the third paper investigates the impact of a compliant generator-bearing support on the stability of a hydropower rotor-bearing system.