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Keywords = symmetric infinitesimal motion

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27 pages, 8871 KB  
Article
A Comparative Study of Theoretical and Experimental Analysis on Balanced and Unbalanced Rotors Supported by Oil- and Water-Lubricated Journal Bearings
by Omar Ahmed, Tamer A. El-Sayed and Hussein Sayed
Machines 2024, 12(10), 675; https://doi.org/10.3390/machines12100675 - 26 Sep 2024
Cited by 4 | Viewed by 2826
Abstract
Studying rotor-bearing systems involving fluid film bearings is essential for designing and assessing the dynamic responses and performance of rotating machinery. They are involved in many applications such as pumps, turbines, and engines. Water-lubricated bearings are often used in many applications where the [...] Read more.
Studying rotor-bearing systems involving fluid film bearings is essential for designing and assessing the dynamic responses and performance of rotating machinery. They are involved in many applications such as pumps, turbines, and engines. Water-lubricated bearings are often used in many applications where the use of oil-based lubricants is not desirable, such as in environmentally sensitive areas such as water desalination. In this study, dynamic analysis is performed to identify the stability regions that prevent the application of water-lubricated journal bearings. This is achieved by solving the system equations of motion and then using an infinitesimal perturbation method to evaluate the second-order bearing coefficients of a journal bearing. In this paper, a steel shaft supported by two symmetrical journal bearings was used to investigate the system stability analysis. A test rig is designed and manufactured to examine the rotor’s dynamic behavior and verify the theoretical outcomes of the FE model, utilizing the bearing coefficients based on second-order analysis. Furthermore, this study compares the two fluids, both theoretically and experimentally, investigating their impact on the rotor-bearing system at different rotational speeds. The theoretical findings indicate that the threshold speed for journal bearings is significantly higher when using water as the lubricant fluid film compared to using oil as the lubricant fluid. Additionally, because of the low viscosity of water, water-lubricated bearings are susceptible to significant wear and noise in operating conditions. Our experiments show that an oil lubricant provides less response than a water lubricant for unbalanced rotors within the tested speed range. Full article
(This article belongs to the Section Machine Design and Theory)
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12 pages, 549 KB  
Article
Halo Orbits under Some Perturbations in cr3bp
by Abdulrahman B. Albidah and Abdullah
Symmetry 2023, 15(2), 481; https://doi.org/10.3390/sym15020481 - 11 Feb 2023
Cited by 8 | Viewed by 3317
Abstract
The general idea of this paper is to study the effect of mass variation of a test particle on periodic orbits in the restricted three-body model. In the circular restricted three-body problem (cr3bp), two bigger bodies (known as primary and secondary or sometime [...] Read more.
The general idea of this paper is to study the effect of mass variation of a test particle on periodic orbits in the restricted three-body model. In the circular restricted three-body problem (cr3bp), two bigger bodies (known as primary and secondary or sometime only primaries) are placed at either side of the origin on abscissa while moving in circular orbits around their common center of mass (here origin), while the third body (known as smallest body or infinitesimal body or test particle) is moving in space and varies its mass according to Jeans law. Using the Lindstedt–Poincaré method, we determine equations of motion and their solutions under various perturbations. The time-series and halo orbits around one of the collinear critical points of this model are drawn under the effects of the solar radiation pressure of the primary and the oblateness of the secondary. In general, these two dynamical properties are symmetrical. Full article
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35 pages, 1266 KB  
Article
Symmetry Adapted Assur Decompositions
by Anthony Nixon, Bernd Schulze, Adnan Sljoka and Walter Whiteley
Symmetry 2014, 6(3), 516-550; https://doi.org/10.3390/sym6030516 - 27 Jun 2014
Cited by 5 | Viewed by 8337
Abstract
Assur graphs are a tool originally developed by mechanical engineers to decompose mechanisms for simpler analysis and synthesis. Recent work has connected these graphs to strongly directed graphs and decompositions of the pinned rigidity matrix. Many mechanisms have initial configurations, which are symmetric, [...] Read more.
Assur graphs are a tool originally developed by mechanical engineers to decompose mechanisms for simpler analysis and synthesis. Recent work has connected these graphs to strongly directed graphs and decompositions of the pinned rigidity matrix. Many mechanisms have initial configurations, which are symmetric, and other recent work has exploited the orbit matrix as a symmetry adapted form of the rigidity matrix. This paper explores how the decomposition and analysis of symmetric frameworks and their symmetric motions can be supported by the new symmetry adapted tools. Full article
(This article belongs to the Special Issue Rigidity and Symmetry)
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