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Dynamic Models for Mechanical Analysis of Synchronous Hydropower Generators
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Product and Production Development.ORCID iD: 0000-0002-4185-2395
2024 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

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. 

Place, publisher, year, edition, pages
Luleå: Luleå University of Technology, 2024.
Series
Doctoral thesis / Luleå University of Technology 1 jan 1997 → …, ISSN 1402-1544
Keywords [en]
Rotordynamics, Hydropower, Generator, Curved Beam, Tillting-Pad Bearing
National Category
Applied Mechanics
Research subject
Machine Design
Identifiers
URN: urn:nbn:se:ltu:diva-105169ISBN: 978-91-8048-548-7 (print)ISBN: 978-91-8048-549-4 (electronic)OAI: oai:DiVA.org:ltu-105169DiVA, id: diva2:1852964
Public defence
2024-06-14, B192, Luleå University of Technology, Luleå, 09:00 (English)
Opponent
Supervisors
Available from: 2024-04-22 Created: 2024-04-19 Last updated: 2024-05-16Bibliographically approved
List of papers
1. Rotordynamic Characterization of Tilting-Pad Bearings With Eight Pads in Vertical Rotors 
Open this publication in new window or tab >>Rotordynamic Characterization of Tilting-Pad Bearings With Eight Pads in Vertical Rotors 
2022 (English)In: Journal of energy resources technology, ISSN 0195-0738, E-ISSN 1528-8994, Vol. 144, no 1, article id 010902Article in journal (Refereed) Published
Abstract [en]

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. 

Place, publisher, year, edition, pages
American Society of Mechanical Engineers (ASME), 2022
Keywords
tilting-pad bearing, vertical rotor
National Category
Applied Mechanics
Research subject
Machine Design
Identifiers
urn:nbn:se:ltu:diva-86562 (URN)10.1115/1.4051803 (DOI)000720985000005 ()2-s2.0-85121689564 (Scopus ID)
Funder
Swedish Energy AgencyLuleå University of Technology
Note

Validerad;2022;Nivå 2;2022-01-01 (johcin)

Available from: 2021-08-12 Created: 2021-08-12 Last updated: 2024-04-19Bibliographically approved
2. Dynamic model for hydropower generators with floating rotor rim
Open this publication in new window or tab >>Dynamic model for hydropower generators with floating rotor rim
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2023 (English)In: Mechanical systems and signal processing, ISSN 0888-3270, E-ISSN 1096-1216, Vol. 183, article id 109645Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
Elsevier, 2023
Keywords
Rotordynamics, Magnetic force, Generator model, Hydropower, Dynamic modeling, Curved beam
National Category
Applied Mechanics
Research subject
Machine Design
Identifiers
urn:nbn:se:ltu:diva-88899 (URN)10.1016/j.ymssp.2022.109645 (DOI)000877355300003 ()2-s2.0-85135882306 (Scopus ID)
Projects
Swedish Hydropower Centre - SVC
Funder
Swedish Energy AgencyLuleå University of TechnologyChalmers University of TechnologyUppsala UniversityLund University
Note

Validerad;2022;Nivå 2;2022-08-19 (hanlid);

Funder: Energiforsk, Svenska Kraftnät, KTH Royal Institute of Technology

Available from: 2022-01-24 Created: 2022-01-24 Last updated: 2024-04-19Bibliographically approved
3. Effect of unbalancing mass placement in hydropower generators with floating rotor rim
Open this publication in new window or tab >>Effect of unbalancing mass placement in hydropower generators with floating rotor rim
2022 (English)In: 31st IAHR Symposium on Hydraulic Machinery and Systems 26/06/2022 - 01/07/2022 Trondheim, Norway, Institute of Physics Publishing (IOPP) , 2022, no 1, article id 012094Conference paper, Published paper (Refereed)
Abstract [en]

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.

Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2022
Series
IOP Conference Series: Earth and Environmental Science, ISSN 1755-1307, E-ISSN 1755-1315 ; 1079
National Category
Applied Mechanics
Research subject
Machine Design
Identifiers
urn:nbn:se:ltu:diva-94712 (URN)10.1088/1755-1315/1079/1/012094 (DOI)2-s2.0-85141802042 (Scopus ID)
Conference
31st Symposium on Hydraulic Machinery and Systems (IAHR 2022), Trondheim, Norway, June 26 - July 1, 2022
Projects
Swedish Hydropower Centre - SVC
Funder
Swedish Energy AgencySwedish National GridLuleå University of TechnologyKTH Royal Institute of TechnologyChalmers University of TechnologyUppsala UniversityLund University
Available from: 2022-12-21 Created: 2022-12-21 Last updated: 2024-04-19Bibliographically approved
4. Effects of nonlinear magnetic pole forces on the dynamics of hydropower generators with floating rotor rim
Open this publication in new window or tab >>Effects of nonlinear magnetic pole forces on the dynamics of hydropower generators with floating rotor rim
2023 (English)Conference paper, Published paper (Refereed)
National Category
Applied Mechanics
Research subject
Machine Design
Identifiers
urn:nbn:se:ltu:diva-104995 (URN)
Conference
16th Chaotic Modeling and Simulation International Conference (CHAOS2023), Heraklion, Crete, Greece, June 13-16, 2023
Available from: 2024-04-05 Created: 2024-04-05 Last updated: 2024-04-19
5. Three-Dimensional Modeling for Mechanical Analysis of Hydropower Generators with Floating Rotor Rim
Open this publication in new window or tab >>Three-Dimensional Modeling for Mechanical Analysis of Hydropower Generators with Floating Rotor Rim
Show others...
2024 (English)In: Machines, E-ISSN 2075-1702, Vol. 12, no 4, article id 268Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
MDPI, 2024
Keywords
rotordynamics, FEM, curved beams, hydropower generator, electromagnetic forces, modeling, ring vibration
National Category
Energy Engineering Applied Mechanics
Research subject
Machine Design
Identifiers
urn:nbn:se:ltu:diva-104994 (URN)10.3390/machines12040268 (DOI)
Projects
Swedish Hydropower Centre-SVC
Note

Full text: CC BY License

Available from: 2024-04-05 Created: 2024-04-05 Last updated: 2024-04-30

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