Tribological design of tilting pad thrust bearings in various lubrication regimes with the application of numerical and machine learning techniques
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Date
2023-07-26
Authors
Κατσαρός, Κωνσταντίνος
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Abstract
Hydrodynamic Tilting Pad Thrust Bearings are machine elements that were designed in order to support the thrust load of rotating machinery. These bearings constitute of sectors, also called pads, which are able to rotate freely around a pivot. During operation a fluid film is dragged inside the mechanism due to the relevant motion of the rotor to the stationary pad. At the same time the tilt of the pad to the rotor’s surface leads to the development of a pressure distribution that makes it possible for the bearing to withhold the axial load of the machine. Normally, during operation the two friction surfaces are separated from the lubricant film. However, there are conditions under which the thrust bearing may be designed or forced to operate under incomplete or mixed lubrication. The phenomena that are developed during these states can have severe impact in the performance of the bearing and lead to accelerating deterioration or even failure. In our days, thrust bearings have been used in a wide range of applications from large industrial turbines or compressors, to ship propellers, car engine turbines and water pumps. These bearings must be designed to be compact in size, yet efficient in maximum load carrying capacity with minimum energy losses, in order to meet the challenging demands of modern industry and world economy. Thus, many investigators have studied and proposed improvements on a variety of the thrust bearing’s configurations. These improvements include different surface profiles, texturing, tailor made lubricants as well as coatings. Nevertheless, especially in the areas of incomplete and mixed lubrication there are many opportunities for improvements, making such investigations crucial for modern hydrodynamic thrust bearing designs.
The hydrodynamic lubrication of thrust bearings is governed by the Navier-Stokes equations of mass and momentum continuity. A simplification of these equations is the Reynolds equation that is most commonly applied during the investigations. The Reynolds equation is a differential equation that can be solved analytically (when many constrains and simplifications are applied for a specific problem) or numerically. The most common methods applied for the numerical solution of the Reynolds equation include the finite difference, the finite volume and the finite elements. Even though the Reynolds equation has been widely applied in order to calculate the tribological characteristics of thrust bearings, its application is limited to the hydrodynamic lubrication regime. When the thrust bearing operates in mixed lubrication regime the Reynolds equation must be improved in order to include the effect of the asperities of the two friction surfaces on the flow of the lubricant inside the mechanism. As a result a more detailed model such as the one proposed by Patir and Cheng must be applied in the numerical calculations in order to properly approach the hydrodynamic forces developed inside the bearing during operation. To add to that, the contact forces that are developed due to direct asperity interaction have a significant impact on the bearing’s performance and must be taken into consideration. To do so, stochastic models have been developed and widely used from investigators initially from Greenwood and Williamson and later from Greenwood and Tripp in order to calculate the boundary forces in the asperity contact regions. The combination of such models can lead to detailed and robust numerical algorithms that are able to calculate the tribological characteristics of a hydrodynamic thrust bearing in great detail and accuracy.
The last decade the 4th Industrial Revolution has introduced many groundbreaking innovations that were initially applied in the field of computer science but have gradually expanded in every aspect of engineering, including Mechanical Engineering. Internet of Things (IoT), Artificial Intelligence (AI) and Machine Learning (ML) applications have started to become more and more popular within the scientific community, since their limitless potentials have brought new ways to approach engineering investigations. In Tribology, the application of such methods is yet raw. However, the combination of robust numerical algorithms with Machine Learning techniques will bring a new era in the field and is assumed to be the most important contribution and innovation of the current Doctoral Thesis.
In summary, for the current investigation the 2D Reynolds equation is solved numerically using the finite difference method in order to calculate the tribological characteristics of a tilting pad thrust bearing. The study focuses on the hydrodynamic lubrication, the incomplete oil film lubrication as well as the mixed lubrication regime. In order to improve the results of the original algorithm for the investigation in the mixed lubrication regime the Average Reynolds equation from the model of Patir and Cheng is applied. To add to that, the stochastic model of Greenwood and Tripp is used in order to calculate the boundary loads developed inside the mechanism due to direct asperity contact. In order to avoid the computational cost of an extra algorithm that would solve the energy equation, the concept of ‘Effective Temperature’ is applied and combined with the Sutherland law in order to calculate the viscosity of the lubricant. Moreover, the balance of the pad is determined by applying an iterative algorithm based on the Newton-Raphson methodology. During the investigation different lubricants as well as coatings are examined and compared in terms of optimum bearing’s performance. In addition, a Multi-Variable, Quadratic, Polynomial Regression Machine Learning algorithm is developed and trained with the data gathered from the numerical simulations. Finally, Quadratic Support Vector Machines models as well as a Regression Tree models are developed with the same datasets in order to be compared with the originally developed ML algorithm in terms of better fitting to the numerical data and the ability to predict the performance of the thrust bearing in various operating conditions and configurations. All in all, the current Doctoral Thesis focuses on the combination of numerical and machine learning techniques in order to predict performance and design characteristics of a tilting pad thrust bearing in various lubrication regimes. At the moment, no similar work can be found in literature, constituting the current Thesis as innovative and with a significant contribution to the field.
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Keywords
Tribology, Thrust bearings, Machine learning