Balanceo Automático de un Sistema Rotor-Cojinete: Identificador Algebraico en Línea del Desbalance Para un Sistema Rotodinámico
Automatic Balancing of a Rotor-Bearing System: On-line Algebraic Identifier for a Rotordynamic Balancing System
J.G. Mendoza Larios
, J. Colín Ocampo, A. Blanco Ortega, A. Abúndez Pliego, E.S. Gutiérrez Wing
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Departamento de Ingeniería Mecánica, CENIDET, Interior Internado Palmira, s/n, 62490, Cuernavaca, Morelos, México
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"apellidos" => "Gutiérrez Wing" ] ] "afiliaciones" => array:1 [ 0 => array:2 [ "entidad" => "Departamento de Ingeniería Mecánica, CENIDET, Interior Internado Palmira, s/n, 62490, Cuernavaca, Morelos, México" "identificador" => "aff0005" ] ] "correspondencia" => array:1 [ 0 => array:3 [ "identificador" => "cor0005" "etiqueta" => "⁎" "correspondencia" => "Autor para correspondencia." ] ] ] ] "titulosAlternativos" => array:1 [ "en" => array:1 [ "titulo" => "Automatic Balancing of a Rotor-Bearing System: On-line Algebraic Identifier for a Rotordynamic Balancing System" ] ] "textoCompleto" => "<span class="elsevierStyleSections"><span id="sec0005" class="elsevierStyleSection elsevierViewall"><span class="elsevierStyleSectionTitle" id="sect0025">Referencias no citadas</span><p id="par0005" class="elsevierStylePara elsevierViewall"><a class="elsevierStyleCrossRef" href="#bib0005">Arredondo et al., 2008</a>, <a class="elsevierStyleCrossRef" href="#bib0010">Beltrán-Carbajal et al., 2013</a>, <a class="elsevierStyleCrossRef" href="#bib0015">Beltrán-Carbajal et al., 2014</a>, <a class="elsevierStyleCrossRef" href="#bib0020">Beltrán-Carbajal et al., 2008</a>, <a class="elsevierStyleCrossRef" href="#bib0025">Beltrán-Carbajal et al., 2005</a>, <a class="elsevierStyleCrossRef" href="#bib0030">Beltrán-Carbajal et al., 2006</a>, <a class="elsevierStyleCrossRef" href="#bib0035">Blanco et al., 2008</a>, <a class="elsevierStyleCrossRef" href="#bib0040">Blanco et al., 2003</a>, <a class="elsevierStyleCrossRef" href="#bib0045">Blanco et al., 2010</a>, <a class="elsevierStyleCrossRef" href="#bib0050">Chong-Won, 2006</a>, <a class="elsevierStyleCrossRef" href="#bib0055">De Queiroz, 2009</a>, <a class="elsevierStyleCrossRef" href="#bib0060">Fliess and Sira-Ramírez, 2003</a>, <a class="elsevierStyleCrossRef" href="#bib0065">Forte et al., 2004</a>, <a class="elsevierStyleCrossRef" href="#bib0070">Green et al., 2008</a>, <a class="elsevierStyleCrossRef" href="#bib0075">Hredzak and Guo, 2006</a>, <a class="elsevierStyleCrossRef" href="#bib0080">Lalanne and Ferraris, 1990</a>, <a class="elsevierStyleCrossRef" href="#bib0085">Ljung, 1987</a>, <a class="elsevierStyleCrossRef" href="#bib0090">Mahfoud et al., 2009</a>, <a class="elsevierStyleCrossRef" href="#bib0095">Manuel Arias et al., 2014</a>, <a class="elsevierStyleCrossRef" href="#bib0100">Sagara and Zhao, 1989</a>, <a class="elsevierStyleCrossRef" href="#bib0105">Sagara and Zhao, 1990</a>, <a class="elsevierStyleCrossRef" href="#bib0110">Sira-Ramírez et al., 2014</a>, <a class="elsevierStyleCrossRef" href="#bib0115">Soderstrom and Stoica, 1989</a>, <a class="elsevierStyleCrossRef" href="#bib0120">Sudhakar and Sekhar, 2011</a>, <a class="elsevierStyleCrossRef" href="#bib0125">Trapero, 2008</a>, <a class="elsevierStyleCrossRef" href="#bib0130">Trapero et al., 2006</a>, <a class="elsevierStyleCrossRef" href="#bib0135">Trapero et al., 2007</a>, <a class="elsevierStyleCrossRef" href="#bib0140">Ward, 2004</a>, <a class="elsevierStyleCrossRef" href="#bib0145">Yuan-Pin and An-Chen, 1997</a> and <a class="elsevierStyleCrossRef" href="#bib0150">Zhou and Shi, 2001</a>.</p></span></span>" "textoCompletoSecciones" => array:1 [ "secciones" => array:6 [ 0 => array:3 [ "identificador" => "xres683608" "titulo" => "Resumen" "secciones" => array:1 [ 0 => array:1 [ "identificador" => "abst0005" ] ] ] 1 => array:2 [ "identificador" => "xpalclavsec689053" "titulo" => "Palabras clave" ] 2 => array:3 [ "identificador" => "xres683609" "titulo" => "Abstract" "secciones" => array:1 [ 0 => array:1 [ "identificador" => "abst0010" ] ] ] 3 => array:2 [ "identificador" => "xpalclavsec689052" "titulo" => "Keywords" ] 4 => array:2 [ "identificador" => "sec0005" "titulo" => "Referencias no citadas" ] 5 => array:1 [ "titulo" => "Referencias" ] ] ] "pdfFichero" => "main.pdf" "tienePdf" => true "PalabrasClave" => array:2 [ "es" => array:1 [ 0 => array:4 [ "clase" => "keyword" "titulo" => "Palabras clave" "identificador" => "xpalclavsec689053" "palabras" => array:6 [ 0 => "Balanceo" 1 => "rotodinámica" 2 => "identificación algebraica" 3 => "rotor-cojinete" 4 => "desbalance" 5 => "vibración" ] ] ] "en" => array:1 [ 0 => array:4 [ "clase" => "keyword" "titulo" => "Keywords" "identificador" => "xpalclavsec689052" "palabras" => array:6 [ 0 => "Balancing" 1 => "rotordynamic" 2 => "algebraic identification" 3 => "rotor-bearing" 4 => "unbalance" 5 => "vibration" ] ] ] ] "tieneResumen" => true "resumen" => array:2 [ "es" => array:2 [ "titulo" => "Resumen" "resumen" => "<span id="abst0005" class="elsevierStyleSection elsevierViewall"><p id="spar0005" class="elsevierStyleSimplePara elsevierViewall">En este artículo, se presenta una metodología para balancear varios modos de vibración a la vez de un sistema rotor-cojinete mediante lo que se denomina discos de balanceo activo. Para determinar la magnitud del desbalance y su posición angular en el rotor, se propone un identificador en línea basado en la técnica de identificación algebraica. Para lo anterior, se desarrolló un modelo matemático en elemento finito para un sistema rotatorio de múltiples grados de libertad, donde se consideró un elemento viga con cuatro grados de libertad por nodo, en este modelo se consideran los efectos de inercia rotatoria, momentos giroscópicos, deformaciones por cortante y amortiguamiento interno y externo, así como la implementación al sistema rotor-cojinete de los discos de balanceo activo. Asimismo, se evaluó y analizó el comportamiento en el tiempo del identificador propuesto para una distribución de masas de desbalance en diferentes puntos a lo largo del rotor, tomando como dato de entrada la respuesta de vibración obtenida de la simulación de un sistema rotodinámico de múltiples grados de libertad, con diferentes rampas de excitación de tipo lineal. De los resultados obtenidos se demuestra, que con dos discos de balanceo activo se puede balancear hasta cuatro modos de vibración al mismo tiempo.</p></span>" ] "en" => array:2 [ "titulo" => "Abstract" "resumen" => "<span id="abst0010" class="elsevierStyleSection elsevierViewall"><p id="spar0010" class="elsevierStyleSimplePara elsevierViewall">A methodology for simultaneously balancing of several modes of vibration for a rotor bearing system by mean the so-called active balancing disk is presented in this paper. In order to determine the magnitude of the unbalance and its angular position on the rotor, it is proposed an on-line identifier based on algebraic identification. A mathematical model was developed for a multiple degrees-of-freedom rotational system for a beam-type finite element with 4 degrees of freedom per node. This model considers the effect of rotating inertia, gyroscope moments, shearing strains, internal-external damping and the presence of active balancing disks. Likewise, the time scale behavior of the proposed algebraic identifier was assessed and analyzed for an unbalanced mass distribution on different locations along the rotor. For this test, the vibration response was obtained from a multiple degrees-of-freedom rotor dynamic system simulation, with several linear coasting up and down. The results show that it is possible to simultaneously balance up to four vibration modes using two active balancing disks.</p></span>" ] ] "bibliografia" => array:2 [ "titulo" => "Referencias" "seccion" => array:1 [ 0 => array:2 [ "identificador" => "bibs0005" "bibliografiaReferencia" => array:30 [ 0 => array:3 [ "identificador" => "bib0005" "etiqueta" => "Arredondo et al., 2008" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "Modelización, análisis y control de sistemas de cojinetes magnéticos activos" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:5 [ 0 => "J. Arredondo" 1 => "J. Jugo" 2 => "S. Alonso-Quesada" 3 => "I. Lizárraga" 4 => "V. Etxebarria" ] ] ] ] ] "host" => array:1 [ 0 => array:2 [ "doi" => "10.4995/S1697-7912(08)70173-0" "Revista" => array:6 [ "tituloSerie" => "Revista Iberoamericana de Automática e Informática Industrial" "fecha" => "2008" "volumen" => "5" "numero" => "4" "paginaInicial" => "17" "paginaFinal" => "27" ] ] ] ] ] ] 1 => array:3 [ "identificador" => "bib0010" "etiqueta" => "Beltrán-Carbajal et al., 2013" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "Active unbalance control of rotor systems using on-line algebraic identification methods" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:3 [ 0 => "F. Beltrán-Carbajal" 1 => "G. Silva-Navarro" 2 => "M. 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Blanco-Ortega" ] ] ] ] ] "host" => array:1 [ 0 => array:1 [ "Revista" => array:6 [ "tituloSerie" => "Computación y Sistemas" "fecha" => "2008" "volumen" => "13" "numero" => "3" "paginaInicial" => "313" "paginaFinal" => "330" ] ] ] ] ] ] 4 => array:3 [ "identificador" => "bib0025" "etiqueta" => "Beltrán-Carbajal et al., 2005" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "Active vibration control using on-line algebraic identification of harmonic vibrations" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:4 [ 0 => "F. Beltrán-Carbajal" 1 => "G. Silva-Navarro" 2 => "H. Sira-Ramírez" 3 => "J. Quezada-Andrade" ] ] ] ] ] "host" => array:1 [ 0 => array:1 [ "Libro" => array:3 [ "fecha" => "2005" "editorial" => "Proceedings of American control conference" "editorialLocalizacion" => "Portland, Oregon" ] ] ] ] ] ] 5 => array:3 [ "identificador" => "bib0030" "etiqueta" => "Beltrán-Carbajal et al., 2006" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "Adaptive-like Active vibration suppression for a nonlinear mechanical system using on-line algebraic identification" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:3 [ 0 => "F. Beltrán-Carbajal" 1 => "H. Sira-Ramírez" 2 => "G. 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Méndez" ] ] ] ] ] "host" => array:1 [ 0 => array:2 [ "doi" => "10.4995/RIAI.2010.04.06" "Revista" => array:6 [ "tituloSerie" => "Revista Iberoamericana de Automática e Informática Industrial" "fecha" => "2010" "volumen" => "7" "numero" => "4" "paginaInicial" => "36" "paginaFinal" => "43" ] ] ] ] ] ] 9 => array:3 [ "identificador" => "bib0050" "etiqueta" => "Chong-Won, 2006" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "Mechatronics in rotating machinery" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:1 [ 0 => "L. Chong-Won" ] ] ] ] ] "host" => array:1 [ 0 => array:1 [ "Libro" => array:5 [ "fecha" => "2006, September" "paginaInicial" => "25" "paginaFinal" => "28" "editorial" => "7th IFToMM-Conference on Rotor Dynamics" "editorialLocalizacion" => "Vienna, Austria" ] ] ] ] ] ] 10 => array:3 [ "identificador" => "bib0055" "etiqueta" => "De Queiroz, 2009" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "An active identification method of rotor unbalance parameters" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:1 [ 0 => "M.S. De Queiroz" ] ] ] ] ] "host" => array:1 [ 0 => array:1 [ "Revista" => array:6 [ "tituloSerie" => "Journal of Vibration and Control" "fecha" => "2009" "volumen" => "15" "numero" => "9" "paginaInicial" => "1365" "paginaFinal" => "1374" ] ] ] ] ] ] 11 => array:3 [ "identificador" => "bib0060" "etiqueta" => "Fliess and Sira-Ramírez, 2003" "referencia" => array:1 [ 0 => array:2 [ "contribucion" => array:1 [ 0 => array:2 [ "titulo" => "An algebraic frame work for linear identification" "autores" => array:1 [ 0 => array:2 [ "etal" => false "autores" => array:2 [ 0 => "M. Fliess" 1 => "H. 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