This study determines the energy of a fatigue-loaded shaft of circular cross-section, in stable equilibrium, deflecting during rotation even in the absence of external loads. The shaft is subjected to completely reversed stresses as well as torsion and bending stresses varying with rotation and introducing fatigue loading problems. The research was conducted in order to establish equilibrium condition at which a shaft subjected to fatigue loading can operate without axial vibration problems, divergence buckling, and instability at critical or above critical speeds. When inertia slows the shaft to rest, where the energy goes usually causes the shaft to rattle. At rest, kinetic energy is zero at that point while potential energy is maximum. The stability status of the shaft can eliminate rattling. The energy method is used, in this study, to develop force-displacement relations. It is also used to show that the total potential energy is minimum in the rotating shaft. Invoking the principle of minimum potential energy is a way to more easily derive the shaft energy related characteristics. The principle is used to analyze displacement and end points boundary conditions. Boundary conditions give prescription of displacements. The principle of virtual displacements and that of the minimum potential energy give the so-called stiffness (or displacement) method. The primary unknowns in that are the nodal displacements instead of the nodal forces. The strain-energy-density factor represents the strength of the elastic energy field in the vicinity of a crack-tip (with stress singularity) developed in the shaft. It was found that the energy which is a source of fluctuation in motion during shaft rotation was minimum when the total energy transferred to the shaft is minimum.
| Published in | International Journal of Mechanical Engineering and Applications (Volume 11, Issue 3) |
| DOI | 10.11648/j.ijmea.20231103.11 |
| Page(s) | 60-65 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2024. Published by Science Publishing Group |
Stiffness, Strain Energy, Minimum Potential Energy, Fatigue, Torsion
| [1] | Bagci, C. (2007). Computer-Aided fatigue Design of Power Transmission Shafts Using Tree-Dimensional Finite Shaft Element and Updated Mean Stress Diagram. Journal of Mechanical Design 12 (79), 10-12. |
| [2] | Bannantine, J., Comer, J., & Handrock, J. (2021). Fundamentals of Metal Fatigue Analysis. Eaglewood Cliffs, NJ: Prentice. |
| [3] | Boulenouar, A., Benseddiq, M., Mohamed, M., Benamara, N., & Mazari, M. (2016). A strain energy density theory for mixed mode crackpropagation. Journal of Theoreticaland Applied Mechanics, 54 (4), 17–31. |
| [4] | Cook, R., Malkus, D., & Plesha, M. (2009). Concepts and Applications of Finite Element Analysis. New York: John Wiley. |
| [5] | Ginsberg, J. (2019). Mechanical andStructural Vibrations Theory and Applications. New York: John Wiley. |
| [6] | Hayes, J. (2019). Fatigue Analysis and Fail-Safe Design of Vehicle Structures, (2nd. Ed.) Cincinnati, Ohio: E. F. Bruhn Educational. |
| [7] | Kolsky, H. (2003). Stress Waves in Solids. New York: Dover. |
| [8] | Langston, L. (2013). The Adaptable Gas Turbine. [e-book]. Retrieved fromhttp://books.google.co.nz. 23/09/2022 |
| [9] | Neal-Sturgess, C. (2017). (p. 1). A direct derivation of the Griffith – Irwin relationship using a crack tip unloading stress wave model. Retrieved from http://www.google.com.Fatigue. |
| [10] | Reifsnider, K., & Talug, A. (2020). Analysis of Fatigue Damage in Composite Laminates. International Journal of Fatigue 2 (1), 456-500. |
| [11] | Sanford, R. (2013). Principles of Fracture Mechanics. Upper Saddle River: Prentice Hall. |
| [12] | Shigley, J., & Mitchell, L. (1993): Mechanical engineering design. (6th. Ed.), New York: McGraw-Hill. |
| [13] | Sokolnikoff, I. (2016). Mathematical theory of elasticity, (2nd Ed.). New York: McGraw-Hill. |
| [14] | Yongsheng, R., Qiyi, D., & Xingqi, Z. (2018). Modeling and dynamicanalysis of rotating composite shaft. Journal of Vibroengineering 15 (4), 1790-1806. |
| [15] | Yoon, K., & Rao, S. (1993). Cam motion synthesis using cubic splines. Journal of Mechanical Design 8 (3), 15-41. |
APA Style
Steven Odi-Owei, Kenny Ayoka. (2023). Stable Equilibrium of a Mechanical Energy Storage Device. International Journal of Mechanical Engineering and Applications, 11(3), 60-65. https://doi.org/10.11648/j.ijmea.20231103.11
ACS Style
Steven Odi-Owei; Kenny Ayoka. Stable Equilibrium of a Mechanical Energy Storage Device. Int. J. Mech. Eng. Appl. 2023, 11(3), 60-65. doi: 10.11648/j.ijmea.20231103.11
AMA Style
Steven Odi-Owei, Kenny Ayoka. Stable Equilibrium of a Mechanical Energy Storage Device. Int J Mech Eng Appl. 2023;11(3):60-65. doi: 10.11648/j.ijmea.20231103.11
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Download@article{10.11648/j.ijmea.20231103.11,
author = {Steven Odi-Owei and Kenny Ayoka},
title = {Stable Equilibrium of a Mechanical Energy Storage Device},
journal = {International Journal of Mechanical Engineering and Applications},
volume = {11},
number = {3},
pages = {60-65},
doi = {10.11648/j.ijmea.20231103.11},
url = {https://doi.org/10.11648/j.ijmea.20231103.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmea.20231103.11},
abstract = {This study determines the energy of a fatigue-loaded shaft of circular cross-section, in stable equilibrium, deflecting during rotation even in the absence of external loads. The shaft is subjected to completely reversed stresses as well as torsion and bending stresses varying with rotation and introducing fatigue loading problems. The research was conducted in order to establish equilibrium condition at which a shaft subjected to fatigue loading can operate without axial vibration problems, divergence buckling, and instability at critical or above critical speeds. When inertia slows the shaft to rest, where the energy goes usually causes the shaft to rattle. At rest, kinetic energy is zero at that point while potential energy is maximum. The stability status of the shaft can eliminate rattling. The energy method is used, in this study, to develop force-displacement relations. It is also used to show that the total potential energy is minimum in the rotating shaft. Invoking the principle of minimum potential energy is a way to more easily derive the shaft energy related characteristics. The principle is used to analyze displacement and end points boundary conditions. Boundary conditions give prescription of displacements. The principle of virtual displacements and that of the minimum potential energy give the so-called stiffness (or displacement) method. The primary unknowns in that are the nodal displacements instead of the nodal forces. The strain-energy-density factor represents the strength of the elastic energy field in the vicinity of a crack-tip (with stress singularity) developed in the shaft. It was found that the energy which is a source of fluctuation in motion during shaft rotation was minimum when the total energy transferred to the shaft is minimum.},
year = {2023}
}
TY - JOUR T1 - Stable Equilibrium of a Mechanical Energy Storage Device AU - Steven Odi-Owei AU - Kenny Ayoka Y1 - 2023/07/26 PY - 2023 N1 - https://doi.org/10.11648/j.ijmea.20231103.11 DO - 10.11648/j.ijmea.20231103.11 T2 - International Journal of Mechanical Engineering and Applications JF - International Journal of Mechanical Engineering and Applications JO - International Journal of Mechanical Engineering and Applications SP - 60 EP - 65 PB - Science Publishing Group SN - 2330-0248 UR - https://doi.org/10.11648/j.ijmea.20231103.11 AB - This study determines the energy of a fatigue-loaded shaft of circular cross-section, in stable equilibrium, deflecting during rotation even in the absence of external loads. The shaft is subjected to completely reversed stresses as well as torsion and bending stresses varying with rotation and introducing fatigue loading problems. The research was conducted in order to establish equilibrium condition at which a shaft subjected to fatigue loading can operate without axial vibration problems, divergence buckling, and instability at critical or above critical speeds. When inertia slows the shaft to rest, where the energy goes usually causes the shaft to rattle. At rest, kinetic energy is zero at that point while potential energy is maximum. The stability status of the shaft can eliminate rattling. The energy method is used, in this study, to develop force-displacement relations. It is also used to show that the total potential energy is minimum in the rotating shaft. Invoking the principle of minimum potential energy is a way to more easily derive the shaft energy related characteristics. The principle is used to analyze displacement and end points boundary conditions. Boundary conditions give prescription of displacements. The principle of virtual displacements and that of the minimum potential energy give the so-called stiffness (or displacement) method. The primary unknowns in that are the nodal displacements instead of the nodal forces. The strain-energy-density factor represents the strength of the elastic energy field in the vicinity of a crack-tip (with stress singularity) developed in the shaft. It was found that the energy which is a source of fluctuation in motion during shaft rotation was minimum when the total energy transferred to the shaft is minimum. VL - 11 IS - 3 ER -
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