MODELING AND ANALYSIS OF A BALL AND BEAM SYSTEM INCLUDING IMPACTS AND DRY FRICTION
Autor(a) principal: | |
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Data de Publicação: | 2014 |
Outros Autores: | , , , |
Tipo de documento: | Artigo de conferência |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://hdl.handle.net/11449/184798 |
Resumo: | The Ball and Beam system is a common didactical plant that presents a complex nonlinear dynamics. This comes from the fact that the ball rolls over the beam, which rotates around its barycenter. In order to deduce the system's equations, composition of movement must be applied, using a non-inertial reference frame attached to the beam. In the Literature, a common hypothesis is to suppose that the ball rolls without slipping. If a viscous friction is supposed to be present, a simpler situation is obtained, where Lagrangean mechanics can be applied, and no contact force is known. Even then, the dynamics is very nonlinear: However; this model does not include all the relevant phenomena, such as ball's slipping at higher beam's inclination angles, dry friction between the ball and the beam, and impacts between: 1) the ball and the ends of the beam, and 2) the beam and the base (ground). These additions to the model impose the necessity to calculate, in a simulation setting, the contact forces, and the Newton's approach to determine the system's equations becomes more convenient. Also, discontinuities in the model are introduced, and the simpler mathematical object for model such systems are the differential inclusion systems. In this work, we deduce the Ball and Beam differential inclusion system, including dry friction and the impact between the ball and beam. We also present simulation results for the corresponding differential inclusion system in a typical situation. |
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MODELING AND ANALYSIS OF A BALL AND BEAM SYSTEM INCLUDING IMPACTS AND DRY FRICTIONThe Ball and Beam system is a common didactical plant that presents a complex nonlinear dynamics. This comes from the fact that the ball rolls over the beam, which rotates around its barycenter. In order to deduce the system's equations, composition of movement must be applied, using a non-inertial reference frame attached to the beam. In the Literature, a common hypothesis is to suppose that the ball rolls without slipping. If a viscous friction is supposed to be present, a simpler situation is obtained, where Lagrangean mechanics can be applied, and no contact force is known. Even then, the dynamics is very nonlinear: However; this model does not include all the relevant phenomena, such as ball's slipping at higher beam's inclination angles, dry friction between the ball and the beam, and impacts between: 1) the ball and the ends of the beam, and 2) the beam and the base (ground). These additions to the model impose the necessity to calculate, in a simulation setting, the contact forces, and the Newton's approach to determine the system's equations becomes more convenient. Also, discontinuities in the model are introduced, and the simpler mathematical object for model such systems are the differential inclusion systems. In this work, we deduce the Ball and Beam differential inclusion system, including dry friction and the impact between the ball and beam. We also present simulation results for the corresponding differential inclusion system in a typical situation.Univ Sao Paulo, Polytech Sch, LAC PTC, Av Prof Luciano Gualberto,Trav 3,158, BR-05508900 Sao Paulo, SP, BrazilSao Paulo State Univ, UNESP, GASI, BR-18087180 Sorocaba, SP, BrazilSao Paulo State Univ, UNESP, DEMAC, BR-13506900 Rio Claro, SP, BrazilSao Paulo State Univ, UNESP, GASI, BR-18087180 Sorocaba, SP, BrazilSao Paulo State Univ, UNESP, DEMAC, BR-13506900 Rio Claro, SP, BrazilAmer Soc Mechanical EngineersUniversidade de São Paulo (USP)Universidade Estadual Paulista (Unesp)Colon, DiegoBueno, Atila Madureira [UNESP]Diniz, Ivando S. [UNESP]Balthazar, Jose M. [UNESP]ASME2019-10-04T12:30:11Z2019-10-04T12:30:11Z2014-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObject8Proceedings Of The Asme International Design Engineering Technical Conferences And Computers And Information In Engineering Conference, 2014, Vol 8. New York: Amer Soc Mechanical Engineers, 8 p., 2014.http://hdl.handle.net/11449/184798WOS:000380084200048Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengProceedings Of The Asme International Design Engineering Technical Conferences And Computers And Information In Engineering Conference, 2014, Vol 8info:eu-repo/semantics/openAccess2021-10-22T22:17:22Zoai:repositorio.unesp.br:11449/184798Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462021-10-22T22:17:22Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
MODELING AND ANALYSIS OF A BALL AND BEAM SYSTEM INCLUDING IMPACTS AND DRY FRICTION |
title |
MODELING AND ANALYSIS OF A BALL AND BEAM SYSTEM INCLUDING IMPACTS AND DRY FRICTION |
spellingShingle |
MODELING AND ANALYSIS OF A BALL AND BEAM SYSTEM INCLUDING IMPACTS AND DRY FRICTION Colon, Diego |
title_short |
MODELING AND ANALYSIS OF A BALL AND BEAM SYSTEM INCLUDING IMPACTS AND DRY FRICTION |
title_full |
MODELING AND ANALYSIS OF A BALL AND BEAM SYSTEM INCLUDING IMPACTS AND DRY FRICTION |
title_fullStr |
MODELING AND ANALYSIS OF A BALL AND BEAM SYSTEM INCLUDING IMPACTS AND DRY FRICTION |
title_full_unstemmed |
MODELING AND ANALYSIS OF A BALL AND BEAM SYSTEM INCLUDING IMPACTS AND DRY FRICTION |
title_sort |
MODELING AND ANALYSIS OF A BALL AND BEAM SYSTEM INCLUDING IMPACTS AND DRY FRICTION |
author |
Colon, Diego |
author_facet |
Colon, Diego Bueno, Atila Madureira [UNESP] Diniz, Ivando S. [UNESP] Balthazar, Jose M. [UNESP] ASME |
author_role |
author |
author2 |
Bueno, Atila Madureira [UNESP] Diniz, Ivando S. [UNESP] Balthazar, Jose M. [UNESP] ASME |
author2_role |
author author author author |
dc.contributor.none.fl_str_mv |
Universidade de São Paulo (USP) Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Colon, Diego Bueno, Atila Madureira [UNESP] Diniz, Ivando S. [UNESP] Balthazar, Jose M. [UNESP] ASME |
description |
The Ball and Beam system is a common didactical plant that presents a complex nonlinear dynamics. This comes from the fact that the ball rolls over the beam, which rotates around its barycenter. In order to deduce the system's equations, composition of movement must be applied, using a non-inertial reference frame attached to the beam. In the Literature, a common hypothesis is to suppose that the ball rolls without slipping. If a viscous friction is supposed to be present, a simpler situation is obtained, where Lagrangean mechanics can be applied, and no contact force is known. Even then, the dynamics is very nonlinear: However; this model does not include all the relevant phenomena, such as ball's slipping at higher beam's inclination angles, dry friction between the ball and the beam, and impacts between: 1) the ball and the ends of the beam, and 2) the beam and the base (ground). These additions to the model impose the necessity to calculate, in a simulation setting, the contact forces, and the Newton's approach to determine the system's equations becomes more convenient. Also, discontinuities in the model are introduced, and the simpler mathematical object for model such systems are the differential inclusion systems. In this work, we deduce the Ball and Beam differential inclusion system, including dry friction and the impact between the ball and beam. We also present simulation results for the corresponding differential inclusion system in a typical situation. |
publishDate |
2014 |
dc.date.none.fl_str_mv |
2014-01-01 2019-10-04T12:30:11Z 2019-10-04T12:30:11Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/conferenceObject |
format |
conferenceObject |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
Proceedings Of The Asme International Design Engineering Technical Conferences And Computers And Information In Engineering Conference, 2014, Vol 8. New York: Amer Soc Mechanical Engineers, 8 p., 2014. http://hdl.handle.net/11449/184798 WOS:000380084200048 |
identifier_str_mv |
Proceedings Of The Asme International Design Engineering Technical Conferences And Computers And Information In Engineering Conference, 2014, Vol 8. New York: Amer Soc Mechanical Engineers, 8 p., 2014. WOS:000380084200048 |
url |
http://hdl.handle.net/11449/184798 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Proceedings Of The Asme International Design Engineering Technical Conferences And Computers And Information In Engineering Conference, 2014, Vol 8 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
8 |
dc.publisher.none.fl_str_mv |
Amer Soc Mechanical Engineers |
publisher.none.fl_str_mv |
Amer Soc Mechanical Engineers |
dc.source.none.fl_str_mv |
Web of Science reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
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1803649366189146112 |