Metodología para optimización de sistemas de trasmisión de potencia de engranajes rectos para reducción de vibraciones
ilustraciones, diagramas
- Autores:
-
Torres Molano, Henry Fernando
- Tipo de recurso:
- Fecha de publicación:
- 2023
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/84622
- Palabra clave:
- Engranajes
Frecuencia modulada (radio)-transmisores y transmisión
Radio frequency modulation - Transmitters and transmission
Gearing
Transmisión de potencia
Reducción de vibraciones
Optimización
Error de transmisión
Power transmission
Vibration reduction
Optimization
Transmission error
- Rights
- openAccess
- License
- Atribución-CompartirIgual 4.0 Internacional
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dc.title.spa.fl_str_mv |
Metodología para optimización de sistemas de trasmisión de potencia de engranajes rectos para reducción de vibraciones |
dc.title.translated.eng.fl_str_mv |
Methodology for optimisation of spur gear power transmission systems for vibration reduction |
title |
Metodología para optimización de sistemas de trasmisión de potencia de engranajes rectos para reducción de vibraciones |
spellingShingle |
Metodología para optimización de sistemas de trasmisión de potencia de engranajes rectos para reducción de vibraciones Engranajes Frecuencia modulada (radio)-transmisores y transmisión Radio frequency modulation - Transmitters and transmission Gearing Transmisión de potencia Reducción de vibraciones Optimización Error de transmisión Power transmission Vibration reduction Optimization Transmission error |
title_short |
Metodología para optimización de sistemas de trasmisión de potencia de engranajes rectos para reducción de vibraciones |
title_full |
Metodología para optimización de sistemas de trasmisión de potencia de engranajes rectos para reducción de vibraciones |
title_fullStr |
Metodología para optimización de sistemas de trasmisión de potencia de engranajes rectos para reducción de vibraciones |
title_full_unstemmed |
Metodología para optimización de sistemas de trasmisión de potencia de engranajes rectos para reducción de vibraciones |
title_sort |
Metodología para optimización de sistemas de trasmisión de potencia de engranajes rectos para reducción de vibraciones |
dc.creator.fl_str_mv |
Torres Molano, Henry Fernando |
dc.contributor.advisor.none.fl_str_mv |
Cortés Ramos, Henry Octavio |
dc.contributor.author.none.fl_str_mv |
Torres Molano, Henry Fernando |
dc.contributor.researchgroup.spa.fl_str_mv |
Grupo de modelado y métodos numéricos en ingeniería |
dc.subject.lemb.spa.fl_str_mv |
Engranajes Frecuencia modulada (radio)-transmisores y transmisión Radio frequency modulation - Transmitters and transmission |
topic |
Engranajes Frecuencia modulada (radio)-transmisores y transmisión Radio frequency modulation - Transmitters and transmission Gearing Transmisión de potencia Reducción de vibraciones Optimización Error de transmisión Power transmission Vibration reduction Optimization Transmission error |
dc.subject.lemb.eng.fl_str_mv |
Gearing |
dc.subject.proposal.spa.fl_str_mv |
Transmisión de potencia Reducción de vibraciones Optimización Error de transmisión |
dc.subject.proposal.eng.fl_str_mv |
Power transmission Vibration reduction Optimization Transmission error |
description |
ilustraciones, diagramas |
publishDate |
2023 |
dc.date.accessioned.none.fl_str_mv |
2023-08-31T20:29:56Z |
dc.date.available.none.fl_str_mv |
2023-08-31T20:29:56Z |
dc.date.issued.none.fl_str_mv |
2023-08-31 |
dc.type.spa.fl_str_mv |
Trabajo de grado - Maestría |
dc.type.driver.spa.fl_str_mv |
info:eu-repo/semantics/masterThesis |
dc.type.version.spa.fl_str_mv |
info:eu-repo/semantics/acceptedVersion |
dc.type.content.spa.fl_str_mv |
Text |
dc.type.redcol.spa.fl_str_mv |
http://purl.org/redcol/resource_type/TM |
status_str |
acceptedVersion |
dc.identifier.uri.none.fl_str_mv |
https://repositorio.unal.edu.co/handle/unal/84622 |
dc.identifier.instname.spa.fl_str_mv |
Universidad Nacional de Colombia |
dc.identifier.reponame.spa.fl_str_mv |
Repositorio Institucional Universidad Nacional de Colombia |
dc.identifier.repourl.spa.fl_str_mv |
https://repositorio.unal.edu.co/ |
url |
https://repositorio.unal.edu.co/handle/unal/84622 https://repositorio.unal.edu.co/ |
identifier_str_mv |
Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia |
dc.language.iso.spa.fl_str_mv |
spa |
language |
spa |
dc.relation.references.spa.fl_str_mv |
R. G. Richard G. Budynas, J. Keith. Nisbett, and J. Edward. Shigley, Shigley’s mechanical engineering design. Mcgraw-hill, 2011. S. L. Harris, ‘Dynamic loads on the teeth of spur gears’, Proceedings of the Institution of Mechanical Engineers, Vol. 172, no. 1, pp. 87-112, 1958, doi:10.1243.1958.172.017.02. R. W. Gregory, S. L. Harris, and r. G. Munro, ‘Applied mechanics group dynamic behaviour of spur gears.’, Vol. 178, no. 1, pp. 207-218, 1963, doi:10.1177/002034836317800130. D. James. D. Smith, Gear noise and vibration. Marcel dekker, 2003. A. Kahraman, d. R. Houser professor memasme, and j. J. Zakrajsek memasme, ‘Dynamic analysis of geared rotors by finite elements’, 1992. [online]. Available: http://asme.org/terms A. Kahraman and r. Singh, ‘Non-linear dynamics of a spur gear pair’, Journal of Sound and Vibration, Vol. 142, no. 1, pp. 49-75, 1990, doi: 10.1016/0022- 460X(90)90582-K. h. Nevzat özgüven and d. R. Houser, ‘mathematical models used in gear dynamics—a review’, journal of sound and vibration, vol. 121, no. 3. Academic press, pp. 383–411, 1988. Doi: 10.1016/s0022-460x(88)80365-1. D. Qin and Y. Shao, ‘Power transmissions.’, Crc Press Taylor and Francis Group, 2016. z. Chen, z. Zhu, and y. Shao, ‘fault feature analysis of planetary gear system with tooth root crack and flexible ring gear rim’, eng fail anal, vol. 49, pp. 92– 103, mar. 2015, doi: 10.1016/j.engfailanal.2014.12.014. M. Faggioni, F. Pellicano, a. Andrisano, and G. Bertacchi, ‘Dynamic optimization of spur gears’. [online]. Available: http://www.asme.o W. Schiehlen, ‘Computational Dynamics: theory and applications of multibody systems’, european journal of mechanics, a/solids, vol. 25, no. 4, pp. 566–594, jul. 2006, doi: 10.1016/j.euromechsol.2006.03.004. . Khemili and l. Romdhane, ‘Dynamic analysis of a flexible slider-crank mechanism with clearance’, european journal of mechanics, a/solids, vol. 27, no. 5, pp. 882–898, sep. 2008, doi: 10.1016/j.euromechsol.2007.12.004. I. Khemili and l. Romdhane, ‘Dynamic analysis of a flexible slider – crank mechanism with clearance’, vol. 27, pp. 882–898, 2008, doi: 10.1016/j.euromechsol.2007.12.004. H. Torres, ‘Metodología del análisis del comportamiento dinámico estructural de sistemas multicuerpo con elementos flexibles y su aplicación al manipulador de arquitectura paralela tipo delta de la universidad santo tomas.’, universidad santo tomas, 2017. A. Tuplin, ‘gear tooth stresses at high speed’. Proceedings of the institution of mechanical engineers, vol. 16, pp. 162–167, 1950. A. Tuplin, ‘gear tooth stresses at high speed’. Proceedings of the institution of mechanical engineers, vol. 16, pp. 162–167, 1950. R. Tharmakulasingam, ‘Transmission error in spur gears: static and dynamic finite-element modeling and design optimization’, 2009. G. Kelly, Mechanical engineering, advanced vibration analysis, Crc Press, 2006. H. Nevzat Özgüven, D.R. Houser, ‘Mathematical models used in gear dynamics-a review’, Journal of Sound and Vibration, vol. 121, pp. 383–411, 1988, doi: 10.1016/s0022-460x(88)80365-1 H. D. Nelson, ‘Finite element simulation of rotor bearing systems with internal damping’, no. 76, pp. 1–6, 1976. Z. G. Wang, C. C. Lo, y. C. Chen, and h. C. Liu, ‘Dynamic modelling, optimization and experiment for a high-speed spur gear set’, machines, vol. 10, no. 8, aug. 2022, doi: 10.3390/machines10080653. Z. G. Wang, C. C. Lo, y. C. Chen, and h. C. Liu, ‘Dynamic modelling, optimization and experiment for a high-speed spur gear set’, machines, vol. 10, no. 8, aug. 2022, doi: 10.3390/machines10080653. D. C. H. Y. And Z. S. Sun, ‘A rotary model for spur gear dynamics.’, Asme journal of mechanisms, transmissions and automation in design, vol. 107, no. December, pp. 529 – 535, 1985. T. S. M. Umezawa, ‘Vibration of power transmission helical gears (approximate equation of tooth stiffness)’, bulletin of jsme, vol. 1, no. 4, pp. 197–402, 1958. A. Kahraman, h. Ozguven, and d. R. Houser, ‘Dynamic analysis of geared rotors by finite elements’, journal of mechanical design, vol. 114, no. September 1992, pp. 507–514, 1992, doi: 10.1115/1.2926579. Z. Rao, C. Y. Zhou, Z. H. Deng, and M. Y. Fu, ‘Nonlinear torsional instabilities in two-stage gear systems with flexible shafts’, International Journal of Mechanical Sciences, vol. 82, pp. 60–66, 2014, doi: 10.1016/j.ijmecsci.2014.02.021. Z. Rao, C. Y. Zhou, Z. H. Deng, and M. Y. Fu, ‘Nonlinear torsional instabilities in two-stage gear systems with flexible shafts’, International Journal of Mechanical Sciences, vol. 82, pp. 60–66, 2014, doi: 10.1016/j.ijmecsci.2014.02.021. F. Shakeriaski, M. Mirparizi, F. Sheykhsamani, and M. Alihajabasi, ‘Vibration behavior optimization of planetary gear sets’, propulsion and power research, vol. 3, no. 4, pp. 196–206, dec. 2014, doi: 10.1016/j.jppr.2014.11.002. F. Shakeriaski, M. Mirparizi, F. Sheykhsamani, and M. Alihajabasi, ‘Vibration behavior optimization of planetary gear sets’, propulsion and power research, vol. 3, no. 4, pp. 196–206, dec. 2014, doi: 10.1016/j.jppr.2014.11.002. Z. Chen, Z. Zhu, and Y. Shao, ‘Fault feature analysis of planetary gear system with tooth root crack and flexible ring gear rim’, Engineering Failure Analysis, vol. 49, pp. 92–103, 2015, doi: 10.1016/j.engfailanal.2014.12.014. A. Saxena, A. Parey, and M. Chouksey, ‘Study of modal characteristics of a geared rotor system’, Procedia technology, vol. 23, pp. 225–231, 2016, doi: 10.1016/j.protcy.2016.03.021. A. Saxena, A. Parey, and M. Chouksey, ‘Study of modal characteristics of a geared rotor system’, Procedia technology, vol. 23, pp. 225–231, 2016, doi: 10.1016/j.protcy.2016.03.021. D. Yang, Z. Sun. ‘A Rotary Model for Spur Gear Dynamics.’, ASME, vol. 107, no. 4, pp. 529–535, 1985, doi:10.1115/1.3260759. C. Liu, Z. Fang, and F. Wang, ‘An improved model for dynamic analysis of a double-helical gear reduction unit by hybrid user-defined elements: experimental and numerical validation’, Mechanism and Machine Theory, vol. 127, pp. 96–111, sep. 2018, doi: 10.1016/j.mechmachtheory.2018.04.022. S. P. Radzevich, Dudley’s handbook of practical gear design and manufacture. Crc press, 2021. Doi: 10.1201/9781003126881. A. Vallejo, ‘Dinámica de sistemas multicuerpo rígido-flexibles en coordenadas absolutas’, M.S tesis, Universidad de Sevilla, España, 2006. A. Matamoros, ‘Simulación del comportamiento dinámico de un vehículo de carga utilizando elementos finitos.’, revista ciencia e ingeniería., vol. 28, no. September, p. 2015, 2015. P . Madrid, ‘Análisis dinámico de sistemas multicuerpo’, Universidad Politécnica de Madrid, Pp. 1–54, 2000. S. P. Radzevich, ‘Advances in gear design and manufacture.’ Crc press, 2019. Doi: 10.1201/9781351049832. G. Niemann, and h, winter. ‘General transmisions, gearboxes fundamentals, spur gears.’, band 2: getriebe allgemein, zahnradgetriebe - grundlagen, stirnradgetriebe, springer, 2003. O. D. Mohammed, m. Rantatalo, and j. O. Aidanpää, ‘Dynamic modelling of a one-stage spur gear system and vibration-based tooth crack detection analysis’, Mechanical Systems and Signal Processing, vol. 54, pp. 293–305, mar. 2015, doi: 10.1016/j.ymssp.2014.09.001. O. D. Mohammed, m. Rantatalo, and j. O. Aidanpää, ‘Dynamic modelling of a one-stage spur gear system and vibration-based tooth crack detection analysis’, Mechanical Systems and Signal Processing, vol. 54, pp. 293–305, mar. 2015, doi: 10.1016/j.ymssp.2014.09.001. O. D. Mohammed, ‘dynamic modelling, and vibration analysis for gear tooth crack detection.’, D. thesis, Lulea university Technology, Sweden 2015. O. D. Mohammed, ‘dynamic modelling, and vibration analysis for gear tooth crack detection.’, D. thesis, Lulea university Technology, Sweden 2015. O. D. Mohammed, m. Rantatalo, and j. O. Aidanpää, ‘Dynamic modelling of a one-stage spur gear system and vibration-based tooth crack detection analysis’, Mechanical Systems and Signal Processing, vol. 54, pp. 293–305, mar. 2015, doi: 10.1016/j.ymssp.2014.09.001. Y. Yang, J. Wang, Q. Zhou, Y. Huang, J. Zhu, and W. Yang, ‘Mesh stiffness modeling considering actual tooth profile geometry for a spur gear pair’, Mechanics and industry, vol. 19, no. 3, 2018, doi: 10.1051/meca/2018026. O. D. Mohammed, M. Rantatalo, and J. O. Aidanpää, ‘Dynamic modelling of a one-stage spur gear system and vibration-based tooth crack detection analysis’, Mechanical Systems and Signal Processing, vol. 54, pp. 293–305, mar. 2015, doi: 10.1016/j.ymssp.2014.09.001. Sato, Umezawa, and Ishikawa, ‘Effects of contact ratio and profile correction’, Bull. JSME 26, 1983. d. R. Houser, ‘Optimum profile modifications for the minimization of static transmission errors of spur gears’, Journal of Mechanisms, Transmissions, and Automation in Design, vol. 108, no. 1, pp. 86.94, 1986. doi: 10.1115/1.3260791. V. Simon, ‘Optimal tooth modifications for spur and helical gears’, Journal of Mechanisms, Transmissions, and Automation in Design, vol. 111, no. 1, pp.611-615, 1989, doi: 10.1115/1.3259044. P. Velex, M. Maatar, ‘A mathematical model for analyzing the influence of shape deviations and mounting errors on gear dynamic behaviour’, vol.191, no. 5, pag. 629-660, 1996, doi: 10.1006/jsvi.1996.0148. R. G. Parker, S. M. Vijayakar, and T. Imajo, ‘Non-linear dynamic response of a spur gear pair: modelling and experimental comparisons’, J sound vib, vol. 237, no. 3, pp. 435–455, oct. 2000, doi: 10.1006/jsvi.2000.3067. S. S. Ghosh and G. Chakraborty, ‘On optimal tooth profile modification for reduction of vibration and noise in spur gear pairs’, Mechanism and Machine Theory, vol. 105, pp. 145–163, nov. 2016, doi: 10.1016/j.mechmachtheory.2016.06.008. s. S. Ghosh and g. Chakraborty, ‘on optimal tooth pro fi le modi fi cation for reduction of vibration and noise in spur gear pairs’, vol. 105, pp. 145–163, 2016, doi: 10.1016/j.mechmachtheory.2016.06.008. J. R. Colbourne, ‘The geometry of involute gears.’, Springer new york, 1987. Doi: 10.1007/978-1-4612-4764-7. Y. Yang, J. Wang, Q. Zhou, Y. Huang, J. Zhu, and W. Yang, ‘Mesh stiffness modeling considering actual tooth profile geometry for a spur gear pair’, Mechanics and industry, vol. 19, no. 3, 2018, doi: 10.1051/meca/2018026. G. Bonori, M. Barbieri, and F. Pellicano, ‘Optimum profile modifications of spur gears by means of genetic algorithms’, J sound vib, vol. 313, no. 3–5, pp. 603–616, jun. 2008, doi: 10.1016/j.jsv.2007.12.013. Yang, Lin, ‘Hertzian damping, tooth friction and bending elasticity in gear impact dynamics’, Journal of Mechanisms, Transmissions, and Automation in Design, vol.109, no. 2, pp. 189-196l, 1987, doi: 10.1115/1.3267437. J. Flek, M. Dub, J. Kolář, F. Lopot, and K. Petr, ‘Determination of mesh stiffness of gear analytical approach vs. fem analysis.’, applied sciences, vol. 11, no. 11, pp. 4960,2021, doi: 10.3390/app11114960. Y. Wang, Y. Shao, Z. Chen, M. Du, and H. Xiao, ‘Mesh stiffness calculation of helical gears with profile modification’ International Conference of Fluid Power and Mechatronic Control Engineering, 2018. S. Chul Kim, S. Gon Moon, J. Hyeon sohn, Y. Jun Park, C. Ho Choi, and G. Ho lee, ‘Macro geometry optimization of a helical gear pair for mass, efficiency, and transmission error’, Mechanism and Machine Theory, vol. 144, feb. 2020, doi: 10.1016/j.mechmachtheory.2019.103634. C. Choi, H. Ahn, Y. Jun Park, G. Ho Lee, and S. Chul Kim, ‘Influence of gear tooth addendum and dedendum on the helical gear optimization considering mass, efficiency, and transmission error’, Mechanism and Machine Theory, vol. 166, dec. 2021, doi: 10.1016/j.mechmachtheory.2021.104476. J. Fraczek and M. Wojtyra, ‘multibody dynamics: Computational Methods and Applications’, media, Spring, 2011. D. Andrés and A. Marín, Dinámica elementos finitos (caso lineal). Universidad Nacional, Colombia, 2006. M. Paz, ‘Dinámica estructural, teoría y calculo’. Reverte, 1992. R. Zaradnik, S. Raichman, and A. Mirasso, ‘Comparación de diversas matrices de masas’, vol. Xxviii, pp. 3–6, 2009. R. F. Aguilar, Análisis matricial de estructuras, Espe, Ecuador, 2014. U. Nacional, ‘Matrices de rigidez y masa de elementos continuos’, facultad ingeniería mecánica. X. Tian, ‘Dynamic simulation for system response of gearbox including localized gear faults.’, Library and archives Canada, bibliothèque et archives Canada, 2005. G. Bejarano, ‘Validación experimental del comportamiento dinámico de sistemas flexibles multicuerpo y su aplicación a un robot industrial de arquitectura paralela.’, CIMM, no. 1, pp. 5–8, 2015. |
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Bogotá - Ingeniería - Maestría en Ingeniería - Ingeniería Mecánica |
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Facultad de Ingeniería |
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Bogotá, Colombia |
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Universidad Nacional de Colombia - Sede Bogotá |
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Universidad Nacional de Colombia |
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Atribución-CompartirIgual 4.0 Internacionalhttp://creativecommons.org/licenses/by-sa/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Cortés Ramos, Henry Octavio782ee17357c47b56d872729fdbc34b1dTorres Molano, Henry Fernandod8a75e4894e41c5223f52c4acea9af5fGrupo de modelado y métodos numéricos en ingeniería2023-08-31T20:29:56Z2023-08-31T20:29:56Z2023-08-31https://repositorio.unal.edu.co/handle/unal/84622Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/ilustraciones, diagramasEste trabajo presenta una metodología viable para el desarrollo de análisis de un sistema de transmisión de potencia de engranajes cilíndricos de dientes rectos para la reducción de vibraciones, en base a un caso de estudio científico revisado y estudiado múltiples veces por diferentes investigadores para obtener los parámetros óptimos. Las etapas del proyecto fueron apoyadas por herramientas de MATLAB (solucionador de ecuaciones diferenciales y librerías de optimización). (Texto tomado de la fuente) Inicialmente se realizó un estudio sobre la dinámica de sistemas de transmisión de potencia, revisando tipo de modelos, planteamiento matemático, factores que generan vibraciones y parámetros geométricos del sistema que afectan su masa, rigidez y amortiguamiento. Por otro lado, se realizó una revisión del proceso de optimización para la reducción de vibraciones teniendo en cuenta planteamientos de función objetivo y restricciones. Se planteó un modelo dinámico por medio de parámetros concentrados, teniendo en cuenta todas sus características geométricas, condiciones iniciales y parámetros con el fin de validar la rigidez y desplazamientos con respecto a un caso de estudio. Posteriormente, sobre este modelo se pasó a realizar el proceso de optimización para obtener una reducción en las vibraciones, que se pueden ver expresadas en términos del error de transmisiónThis document presents a viable methodology for the development of analysis of a spur gear power transmission system for vibration reduction, based on a scientific case study reviewed and studied multiple times by different researchers to obtain the optimal parameters. The Project stages were supported by MATLAB tools (differential equation solver and optimization libraries). Initially, a study on the dynamics of power transmission systems was carried out, reviewing the type of models, mathematical approach, factors that generate vibrations and geometric parameters of the system that fail its mass, stiffness, and damping. On the other hand, a review of the optimalization process for vibrations reduction was carried out taking into account objective function approaches and restrictions. A dynamic model was proposed by means of concentrated parameters, considering all its geometric characteristics, initial conditions, and parameters in order to validate the stiffness and displacements with respect to a case study. Subsequently, these results were the conditions to perform the optimization process to obtain a reduction in vibrations, which can be expressed in terms of transmission error.MaestríaMagisterIngeniería de Diseño y Biomecánica88 páginasapplication/pdfspaMetodología para optimización de sistemas de trasmisión de potencia de engranajes rectos para reducción de vibracionesMethodology for optimisation of spur gear power transmission systems for vibration reductionTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMBogotá - Ingeniería - Maestría en Ingeniería - Ingeniería MecánicaFacultad de IngenieríaBogotá, ColombiaUniversidad Nacional de Colombia - Sede BogotáR. G. Richard G. Budynas, J. Keith. Nisbett, and J. Edward. Shigley, Shigley’s mechanical engineering design. Mcgraw-hill, 2011.S. L. Harris, ‘Dynamic loads on the teeth of spur gears’, Proceedings of the Institution of Mechanical Engineers, Vol. 172, no. 1, pp. 87-112, 1958, doi:10.1243.1958.172.017.02.R. W. Gregory, S. L. Harris, and r. G. Munro, ‘Applied mechanics group dynamic behaviour of spur gears.’, Vol. 178, no. 1, pp. 207-218, 1963, doi:10.1177/002034836317800130.D. James. D. Smith, Gear noise and vibration. Marcel dekker, 2003.A. Kahraman, d. R. Houser professor memasme, and j. J. Zakrajsek memasme, ‘Dynamic analysis of geared rotors by finite elements’, 1992. [online]. Available: http://asme.org/termsA. Kahraman and r. Singh, ‘Non-linear dynamics of a spur gear pair’, Journal of Sound and Vibration, Vol. 142, no. 1, pp. 49-75, 1990, doi: 10.1016/0022- 460X(90)90582-K.h. Nevzat özgüven and d. R. Houser, ‘mathematical models used in gear dynamics—a review’, journal of sound and vibration, vol. 121, no. 3. Academic press, pp. 383–411, 1988. Doi: 10.1016/s0022-460x(88)80365-1.D. Qin and Y. Shao, ‘Power transmissions.’, Crc Press Taylor and Francis Group, 2016.z. Chen, z. Zhu, and y. Shao, ‘fault feature analysis of planetary gear system with tooth root crack and flexible ring gear rim’, eng fail anal, vol. 49, pp. 92– 103, mar. 2015, doi: 10.1016/j.engfailanal.2014.12.014.M. Faggioni, F. Pellicano, a. Andrisano, and G. Bertacchi, ‘Dynamic optimization of spur gears’. [online]. Available: http://www.asme.oW. Schiehlen, ‘Computational Dynamics: theory and applications of multibody systems’, european journal of mechanics, a/solids, vol. 25, no. 4, pp. 566–594, jul. 2006, doi: 10.1016/j.euromechsol.2006.03.004.. Khemili and l. 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