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Speed-Dependent Bearing Models for Dynamic Simulations of Vertical Rotors
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Product and Production Development.ORCID iD: 0009-0000-8078-5036
Vattenfall AB Research and Development, 814 26 Älvkarleby, Sweden.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Product and Production Development.ORCID iD: 0000-0001-6016-6342
2022 (English)In: Machines, E-ISSN 2075-1702, Vol. 10, no 7, article id 556Article in journal (Refereed) Published
Abstract [en]

Many dynamic simulations of a rotor with a journal bearing employ non-linear fluid-film lubrication models and calculate the bearing coefficients at each time step. However, calculating such a simulation is tedious and computationally expensive. This paper presents a simplified dynamic simulation model of a vertical rotor with tilting pad journal bearings under constant and variable (transient) rotor spin speed. The dynamics of a four-shoes tilting pad journal bearing are predefined using polynomial equations prior to the unbalance response simulations of the rotor-bearing system. The Navier–Stokes lubrication model is solved numerically, with the bearing coefficients calculated for six different rotor speeds and nine different eccentricity amplitudes. Using a MATLAB inbuilt function (poly53), the stiffness and damping coefficients are fitted by a two-dimensional polynomial regression and the model is qualitatively evaluated for goodness-of-fit. The percentage relative error (RMSE%) is less than 10%, and the adjusted R-square (R2adj) is greater than 0.99. Prior to the unbalance response simulations, the bearing parameters are defined as a function of rotor speed and journal location. The simulation models are validated with an experiment based on the displacements of the rotor and the forces acting on the bearings. Similar patterns have been observed for both simulated and measured orbits and forces. The resultant response amplitudes increase with the rotor speed and unbalanced magnitude. Both simulation and experimental results follow a similar trend, and the amplitudes agree with slight deviations. The frequency content of the responses from the simulations is similar to those from the experiments. Amplitude peaks, which are associated with the unbalance force (1 × Ω) and the number of pads (3 × Ω and 5 × Ω), appeared in the responses from both simulations and experiments. Furthermore, the suggested simulation model is found to be at least three times faster than a classical simulation procedure that used FEM to solve the Reynolds equation at each time step.

Place, publisher, year, edition, pages
MDPI, 2022. Vol. 10, no 7, article id 556
Keywords [en]
vertical rotor, rotor dynamics, transient, tilting pad journal bearing, bearing coefficient
National Category
Production Engineering, Human Work Science and Ergonomics
Machine Design
Identifiers
ISI: 000832295500001Scopus ID: 2-s2.0-85137216329OAI: oai:DiVA.org:ltu-92529DiVA, id: diva2:1688203
Projects
Swedish Hydropower Centre-SVC
Funder
Swedish Energy AgencyLuleå University of TechnologyChalmers University of TechnologyUppsala UniversityLund University
Note

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

Available from: 2022-08-18 Created: 2022-08-18 Last updated: 2024-04-22Bibliographically approved
In thesis
1. Rotordynamic Modeling and Characterization of Support Elements in Vertical Machines
Open this publication in new window or tab >>Rotordynamic Modeling and Characterization of Support Elements in Vertical Machines
2024 (English)Doctoral thesis, comprehensive summary (Other academic)
Alternative title[sv]
Rotordynamiska Modellering och Karakterisering av Stödelement i Vertikala Maskiner
Abstract [en]

The dynamic properties of rotating machines are highly influenced by supporting elements, such as bearings, seals, damping elements or housings. They play a significant role in regulating the characteristics of the interaction between the rotating and stationary parts of machines. Over the past few years, numerous research studies have been published focusing on the dynamics of such devices across a wide range of applications. The advancement of the research has significantly contributed to enhancing their performance and ensuring the smooth operation of rotating machinery by minimizing excessive vibrations that can lead to catastrophic failure. The research work in this thesis explores the dynamics of supporting elements in vertical rotating machinery, with a particular focus on hydropower applications. In fact, some of the concepts are generic and can be applied to horizontal rotors or any other types of rotating machines. Using numerical simulation and actual measurements, their contribution to the system’s overall performance was investigated. These include the self-induced vibration in vertical application tilting pad journal bearings, and vibration issues observed on a hydropower unit attributed to large bearing clearance. Also, particular attention was given to the influence of the squeeze film damper on the rotor-stator contact dynamics of hydropower units, using tools such as Poincaré maps and bifurcation diagrams.

Moreover, achieving optimal design of such devices requires, among other key aspects, accurate and reliable simulation models to facilitate the prediction and evaluation of their characteristics at any stage in the product development process. In rotordynamic simulations, a common approach for incorporating bearing forces in the system equation is by representing them with stiffness and damping coefficients. For a small vibrational amplitude about a static position, linearized bearing coefficient assumptions can be valid. This is especially applicable for operation under a large radial static load, such as in horizontal rotors, due to the dead weight of the rotor. For vertical rotors, however, the weight of the rotor acts axially, and the radial bearing load is usually low. The bearing coefficients show nonlinearity, making them dependent on the trajectory of the rotor. Therefore, the linear bearing assumption, which is valid for horizontal rotors, does not hold true for vertical rotors. This makes the simulation of a vertical machine more complicated as it typically involves solving the fluid film lubrication model. The classical numerical models can sometimes be computationally demanding and require impractically long computational time. An efficient and fast numerical simulation method which does not significantly affect the accuracy of the result is critical to facilitating the simulation processes effectively. This thesis details the suggested simplifications employed on the bearing models and transformation matrices in the numerical integration procedure. The results from these models were validated using experiments to ensure their reliability.

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
Rotordynamic, Support Element, Bearing, Squeeze Film Damper, Hydropower, Vertical Machine
National Category
Applied Mechanics
Machine Design
Identifiers
urn:nbn:se:ltu:diva-105194 (URN)978-91-8048-552-4 (ISBN)978-91-8048-553-1 (ISBN)
Public defence
2024-06-18, B192, Luleå tekniska universitet, Luleå, 09:00 (English)
Supervisors
Available from: 2024-04-22 Created: 2024-04-22 Last updated: 2024-05-17Bibliographically approved

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Benti, Gudeta BerhanuAidanpää, Jan-Olov

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