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://dx.doi.org/10.1115/DETC201434529 http://hdl.handle.net/11449/171862 |
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.LAC/PTC, University of São Paulo, Polytechnic School, Av. Prof. Luciano Gualberto, trav. 3, 158GASI, São Paulo State University, UNESP, Av. Três de Março 511DEMAC, São Paulo State University, UNESP, Av. 24-A, 1515GASI, São Paulo State University, UNESP, Av. Três de Março 511DEMAC, São Paulo State University, UNESP, Av. 24-A, 1515Universidade de São Paulo (USP)Universidade Estadual Paulista (Unesp)Colón, DiegoDiniz, Ivando S. [UNESP]Bueno, Átila Madureira [UNESP]Balthazar, Jose M. [UNESP]2018-12-11T16:57:29Z2018-12-11T16:57:29Z2014-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/conferenceObjecthttp://dx.doi.org/10.1115/DETC201434529Proceedings of the ASME Design Engineering Technical Conference, v. 8.http://hdl.handle.net/11449/17186210.1115/DETC2014345292-s2.0-84930192307Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengProceedings of the ASME Design Engineering Technical Conferenceinfo:eu-repo/semantics/openAccess2021-10-23T21:47:00Zoai:repositorio.unesp.br:11449/171862Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462021-10-23T21:47Repositório 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 Colón, 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 |
Colón, Diego |
author_facet |
Colón, Diego Diniz, Ivando S. [UNESP] Bueno, Átila Madureira [UNESP] Balthazar, Jose M. [UNESP] |
author_role |
author |
author2 |
Diniz, Ivando S. [UNESP] Bueno, Átila Madureira [UNESP] Balthazar, Jose M. [UNESP] |
author2_role |
author author author |
dc.contributor.none.fl_str_mv |
Universidade de São Paulo (USP) Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Colón, Diego Diniz, Ivando S. [UNESP] Bueno, Átila Madureira [UNESP] Balthazar, Jose M. [UNESP] |
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 2018-12-11T16:57:29Z 2018-12-11T16:57:29Z |
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 |
http://dx.doi.org/10.1115/DETC201434529 Proceedings of the ASME Design Engineering Technical Conference, v. 8. http://hdl.handle.net/11449/171862 10.1115/DETC201434529 2-s2.0-84930192307 |
url |
http://dx.doi.org/10.1115/DETC201434529 http://hdl.handle.net/11449/171862 |
identifier_str_mv |
Proceedings of the ASME Design Engineering Technical Conference, v. 8. 10.1115/DETC201434529 2-s2.0-84930192307 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Proceedings of the ASME Design Engineering Technical Conference |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.source.none.fl_str_mv |
Scopus 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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1803650196684406784 |