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. 

Hydropower generators withstand multiple forces from diverse sources during operation. To ensure their stability and safe performance, numerical tools are developed to characterize their dynamic properties. Traditionally, generators are assumed to be rigid in rotordynamic analyses. However, the measurements in power stations challenge this assumption. This article proposes a novel approach to modeling hydropower generators with floating rotor rims using a three-dimensional (3-D) Finite Element Method, aiming to study their dynamic performance and properties, including natural frequencies, the modes of vibrations, and expansion due to centrifugal and electromagnetic forces, with the goal of improving the reliability of modern designs. Both this approach and employing a two-dimensional (2-D) model using curved beams result in similar in-plane natural frequencies and the expansion of the rotor rim due to centrifugal forces. However, the 3-D model can be used to calculate the out-of-plane natural frequencies and modes, to model the dynamics of complex geometries, and to perform stress evaluation and fatigue analysis.

For rotordynamic analysis of hydropower units, the generator is treated as a rotating rigid body. However, previous studies have confirmed that certain designs of generators are elastic, so the complex geometry of generators cannot be considered rigid. This work produced a model of hydropower generators with floating rotor rims, consisting of a rigid hub and a flexible rotor rim coupled with flexible connections. The model takes into account the influence of centrifugal and Coriolis effects, and the electromagnetic interaction between rotor and stator. The model also reproduces the dynamics of the generator with static and dynamic eccentricities. A generator prototype was employed to test the model, showing its different applications. Once validated by empirical data, this model could be used when designing generators.

Modeling the dynamics of hydropower generators has been the aim pursued by many studies, as providing a reliable model would lead to more cost-effective designs. Hydropower generators comprise many parts, tilting-pad bearings, shaft, rotor rim, and stator among them, that contribute to the system's nonlinearities. In this thesis, the dynamics of hydropower generator is studied first by characterizing tilting-pad bearings. Multiple pad bearings are common in the industry; an eight-pad tilting-pad bearing has been studied on vertical rotors. Previous studies have shown that multiple pad bearings display stiffness and damping coefficients dependent on eccentricity and position. A model for eight-pad tilting pad bearings has been proposed and compared to experiments. The effect of cross-coupled phenomena was also investigated.

On the other hand, the generators are not rigid bodies, and the flexibility of either rotor rim or stator influences the distribution of the magnetic field, thus the force distribution. An uneven force distribution endangers the integrity of the machine. This thesis also proposes a model for a generator with flexible rotor rims and rigid stators using Lagrange equations, considering the centrifugal and Coriolis effects, the electromagnetic interaction between rotor and stator, and static and dynamic eccentricities. This model was tried 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.

Dynamic models for hydropower generators treat the rotor part as a rigid body; however, many studies have shown the opposite. The electromagnetic force distribution of deformed rotors is uneven, creating Unbalance Magnetic Pull, causing high forces on generator components leading to a risk of fatigue, therefore shortening the life of machines. Unbalancing masses can worsen the asymmetries of the rotor, which would further increase the effect of the electromagnetic interactions. This paper evaluates the rotor response using different unbalancing masses at the rotor and at the poles to quantify their impact in displacements and exciting frequencies. The model employed in this paper is based on the equation of motion derived using Lagrange equations in both co-rotating and stationary frames of reference, considering the effects of Centrifugal loads, Coriolis, and magnetization of poles. Different unbalancing mass placements affect different variables; extra weights in the poles contribute predominantly to the deformation of the rim, while the unbalance in the shaft affects the position of the shaft; a combination of placements was also studied. The simulations were performed and compared with and without radial electromagnetic forces, showing how the presence of magnetized poles further deforms the shapes of the rotor.

In this paper, the dynamics of tilting pad journal bearings with four and eight pads are studied and compared experimentally and numerically. The experiments are performed on a rigid vertical rotor supported by two identical bearings. Two sets of experiments are carried out under similar test setup. One set is performed on a rigid rotor with two four-pad bearings, while the other is on a rigid rotor with two eight-pad bearings. The dynamic properties of the two bearing types are compared with each other by studying the unbalance response of the system at different rotor speeds. Numerically, the test rig is modeled as a rigid rotor and the bearing coefficients are calculated based on Navier-Stokes equation. A nonlinear bearing model is developed and used in the steady state response simulation. The measured and simulated displacement and force orbits show similar patterns for both bearing types. Compared to the measurement, the simulated mean value and range (peak-to-peak amplitude) of the bearing force deviate with a maximum of 16 % and 38 %, respectively. It is concluded that, unlike the eight-pad TPJB, the four-pad TPJB excite the system at the third and fifth-order frequencies, which are due to the number of pads, and the amplitudes of these frequencies increase with the rotor speed. 

It has been documented that stiffness and damping for a four-pad bearing are dependent not only on the magnitude of the load but also on the position of the rotor in the bearing. However, eight-pad bearings are not commonly employed on horizontal turbines, and the presence of several pads in the bearing will decisively affect the dynamics of the system. This paper evaluates the stiffness and damping coefficients of tilting-pad bearings with eight pads and explores the main frequencies acting on the forced response of a vertical rotor. The bearing properties were modeled as a function of eccentricity and position in the stationary coordinate system by Navier–Stokes equations whose results are taken from commercial software. The simulated unbalanced response is compared to experimental results; the changing position of the shaft produces a periodic stiffness and damping, which is dependent on the number of pads. Cross-coupled coefficients influence is discussed, showing that their absence makes an accurate model for the mean values. The results indicate that simulation of vertical rotors with eight-pad bearings can be simplified which allow more effective simulations and dynamic analysis.