Mathematical modeling of vertical movement of the upper shaft in cane mills

This study introduces a mathematical model to describe the floating effects of the top roll in sugarcane mills. The model is developed from experimental data measured during the operation of a sugarcane mill. The measured data is fitted using the top shaft rotation period of the mill and dividing on...

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Autores:
Cabello Ulloa, Mario Javier
Cabello Eras, Juan Jose
Moya Rodriguez, Jorge
Sagastume Gutierrez, Alexis
Hernandez Herrera, Hernan
Tipo de recurso:
Article of journal
Fecha de publicación:
2016
Institución:
Corporación Universidad de la Costa
Repositorio:
REDICUC - Repositorio CUC
Idioma:
eng
OAI Identifier:
oai:repositorio.cuc.edu.co:11323/935
Acceso en línea:
https://hdl.handle.net/11323/935
https://repositorio.cuc.edu.co/
Palabra clave:
Dynamic loads
Instant floating
Sugarcane mill
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openAccess
License
Atribución – No comercial – Compartir igual
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oai_identifier_str oai:repositorio.cuc.edu.co:11323/935
network_acronym_str RCUC2
network_name_str REDICUC - Repositorio CUC
repository_id_str
dc.title.eng.fl_str_mv Mathematical modeling of vertical movement of the upper shaft in cane mills
title Mathematical modeling of vertical movement of the upper shaft in cane mills
spellingShingle Mathematical modeling of vertical movement of the upper shaft in cane mills
Dynamic loads
Instant floating
Sugarcane mill
title_short Mathematical modeling of vertical movement of the upper shaft in cane mills
title_full Mathematical modeling of vertical movement of the upper shaft in cane mills
title_fullStr Mathematical modeling of vertical movement of the upper shaft in cane mills
title_full_unstemmed Mathematical modeling of vertical movement of the upper shaft in cane mills
title_sort Mathematical modeling of vertical movement of the upper shaft in cane mills
dc.creator.fl_str_mv Cabello Ulloa, Mario Javier
Cabello Eras, Juan Jose
Moya Rodriguez, Jorge
Sagastume Gutierrez, Alexis
Hernandez Herrera, Hernan
dc.contributor.author.spa.fl_str_mv Cabello Ulloa, Mario Javier
Cabello Eras, Juan Jose
Moya Rodriguez, Jorge
Sagastume Gutierrez, Alexis
Hernandez Herrera, Hernan
dc.subject.eng.fl_str_mv Dynamic loads
Instant floating
Sugarcane mill
topic Dynamic loads
Instant floating
Sugarcane mill
description This study introduces a mathematical model to describe the floating effects of the top roll in sugarcane mills. The model is developed from experimental data measured during the operation of a sugarcane mill. The measured data is fitted using the top shaft rotation period of the mill and dividing on intervals to individually fit each interval obtaining a function defined by parts. The resulting model shows a correlation coefficient of R2 ≥ 0.97. This allow including the floating effect in the study and design of other elements of sugarcane mills.
publishDate 2016
dc.date.issued.none.fl_str_mv 2016
dc.date.accessioned.none.fl_str_mv 2018-11-14T12:06:53Z
dc.date.available.none.fl_str_mv 2018-11-14T12:06:53Z
dc.type.spa.fl_str_mv Artículo de revista
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dc.identifier.issn.spa.fl_str_mv 19928645
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dc.identifier.instname.spa.fl_str_mv Corporación Universidad de la Costa
dc.identifier.reponame.spa.fl_str_mv REDICUC - Repositorio CUC
dc.identifier.repourl.spa.fl_str_mv https://repositorio.cuc.edu.co/
identifier_str_mv 19928645
Corporación Universidad de la Costa
REDICUC - Repositorio CUC
url https://hdl.handle.net/11323/935
https://repositorio.cuc.edu.co/
dc.language.iso.none.fl_str_mv eng
language eng
dc.relation.references.spa.fl_str_mv [1] A. BERNARD, Societe dite: Compagnie de Fives-Lille, assignee. Sugar Cane Mill. Patent 2612101. Paris, France. February 22. 1946. [2] D.WILDE, Daniel Wilde, of Washington, Iowa, assignee. Cane-Mill. Washington, United States patent 255228. 1881 December 2, 1881. [3] N. ARZOLA, R. GOYTISOLO, A. FERNANDEZ, “Determination of an Optimal Assembly Misalignment in Sugar Cane Mills”. ASME Conference Proceedings, 2005, IMECE2005-80435, pp. 555-559. ISBN 0-7918-4223-1. [4] C. ADAM, J. G. LOUGHRAN, “Finite element prediction of the performance of sugarcane rolling mills”. International Sugar Journal, 2007, 109(1301), pp. 272-284. [5] C. ADAM, J. G. LOUGHRAN, “The effect of blanket thickness on extraction energy in sugarcane rolling mills: a finite element investigation”. Biosystems Engineering, 2005, 92(2), pp. 255-263. [6] A. KANNAPIRAN, “Computational and experimental modelling of the crushing of prepared sugar cane”. PhD thesis: James Cook University of North Queensland, 2003, pp. 237. [7] G.A. KENT, “Increasing the capacity of Australian raw sugar factory milling units”, PhD thesis, James Cook University of North Queensland; 2003, pp. 248 [8] W. MORA, J. RIVAS, J. CORONADO, “Design of two bearings with sealing system for the top roll shaft of sugar cane mill”. Rev. Téc. Ing. Univ. Zulia, Vol.28. No 3, 2005, pp. 219-232. [9] J. RIVAS, S. RODRÍGUEZ, J. CORONADO, “Análisis de la confiabilidad de los ejes de molino de caña de azúcar”. Tecnura, Vol. 8 No 15, 2004 pp. 45-54. [10] S. RODRÍGUEZ, J. CORONADO, N. ARZOLA, “Predicción de vida remanente en ejes de masa superior de molino de caña”. Ingeniería e Investigación, Vol. 26, No 1, 2006, pp.84-91. [11] S. RODRÍGUEZ, J. CORONADO, N. ARZOLA, “Life prediction for the top roller shafts of sugar mills”. Journal of the Mechanical Behavior of Materials, Vol.17. No 5, 2006, pp. 327-336. [12] N. ARZOLA, R. GOYTISOLO, L. SUAREZ, “Efficiency Increase in the Extraction of Sugar Cane Juice in the Sugar Cane Mills by Means of the Regulation of Hydraulic Pressures”. ASME Conference Proceedings, 2005, (42193), pp. 637-641. [13] J. CORONADO, J. RIVAS, A. LEÓN, “Estudio tribológico en chumaceras y ejes de molino de caña de azúcar”. Dyna (Medellin), No 071, 2004, pp. 1-8. [14] J. CORONADO, “Fracture mechanics approach of repaired top roll shafts in cane mill”. Journal of the Mechanical Behavior of Materials, Vol. 16. No 6, 2005, pp. 419-429. [15] G. MUÑOZ, J. LEWINSKY, “Analysis of the mechanical performance of a sugar cane mill. International Sugar Journal”, 98(1175), 1996, pp. 574-578. [16] E. ROSERO, J. RAMIREZ, “Modelado y control de molinos de caña de azúcar usando accionamientos eléctricos”. Revista Iberoamericana de Automática e Informática Industrial (RIAI), Vol. 6. No 3, 2009, pp. 44-53. [17] A. MENDOZA, M. CABELLO, J. CABELLO, R.GOYTIZOLO, J. MOYA, “Modelación del contacto entre dos pares de dientes en las coronas de molinos”. Ingeniería Mecánica, Vol. 16. No 3. 2014, pp 178-185. [18] N. ARZOLA, “Esquema de análisis para los árboles de los molinos de caña de azúcar y aplicación de la Mecánica de la Fractura en la evaluación de la falla por fatiga”. Tesis de Doctorado. Universidad Central de las Villas Santa Clara. Cuba. 2003. pp. 145. [19] N. ARZOLA, R. GOYTISOLO, R. PEREZ,; et al. “Prediction of the Sugar Mill Shaft Failure Using a Fracture Mechanics Method”. ASME Conference Proceedings, 2005, 2005(42150), pp. 749-755. [20] N. ARZOLA, R. GOYTISOLO, R. PEREZ, et al. “Determinación de la vida remanente de los árboles de los molinos de caña de azúcar con grieta semielíptica superficial”. Ingeniería Mecánica, Vol. 6. No 2. 2003, pp. 43-52. [21] N. ARZOLA, R. GOYTISOLO, J. CABELLO, “Utilización del factor de densidad de energía de deformación en el modelo de crecimiento de la grieta en árboles de molinos de caña de azúcar”. Ingeniería Mecánica, Vol.8. No 2, 2005, pp. 7-14. [22] J. ADAM, J. LOUGHRAN, “Multivariate analysis of frictional interaction between grooved rollers and prepared sugarcane. International”. Journal of the American Society of Agricultural and Biological Engineers, Vol. 47 No 5, 2004, pp. 1611- 1618. [23] H. OKAMURA, H. TANAKA, M. TERAO, “Square box couplings in cane mill Drives1”. International Sugar Journal, 74(886), 1972, pp. 291-293. [24] H. OKAMURA, H.; TANAKA, M. TERAO, “Square box couplings in cane mill Drives-2”. International Sugar Journal, 74(887), 1972, pp. 323-327. [25] J. CABELLO, “Cinemática, transmisión de la carga, lubricación y resistencia superficial de las coronas de molinos de caña de azúcar”. Tesis de Doctorado. Santa Clara: Universidad Central de las Villas, Cuba. 1999. [26] J. MOYA, “Diseño de coronas de molinos de caña de azúcar”. Tesis de Doctorado. Santa Clara: Universidad Central de Las Villas; Cuba 1994. [27] L. NEGRÍN, R. FRANCO, “Estudio de las curvas epicicloide y evolvente para formar el perfil de los engranajes que operan con distancia entre centros variable”. Ingeniería Mecánica, Vol. 10 No 3, pp. 71-76. [28] M. CABELLO “Modelo matemático para el análisis cinemático y dinámico de las coronas de molinos de caña de azúcar”. Tesis de Maestría. Universidad de Cienfuegos: Cienfuegos. 2010. [29] A. ARTANEN, R. BITMEAD, “The application of an iterative identification and controller design to a sugar cane crushing mill. Automática”, Vol. 31. No 11, 1995, pp. 1547-1563.
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spelling Cabello Ulloa, Mario JavierCabello Eras, Juan JoseMoya Rodriguez, JorgeSagastume Gutierrez, AlexisHernandez Herrera, Hernan2018-11-14T12:06:53Z2018-11-14T12:06:53Z201619928645https://hdl.handle.net/11323/935Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/This study introduces a mathematical model to describe the floating effects of the top roll in sugarcane mills. The model is developed from experimental data measured during the operation of a sugarcane mill. The measured data is fitted using the top shaft rotation period of the mill and dividing on intervals to individually fit each interval obtaining a function defined by parts. The resulting model shows a correlation coefficient of R2 ≥ 0.97. This allow including the floating effect in the study and design of other elements of sugarcane mills.Cabello Ulloa, Mario Javier-b9a8893b-9abd-4c08-9ddb-452314d3662e-0Cabello Eras, Juan Jose-0000-0003-0949-0862-600Moya Rodriguez, Jorge-2dd60a80-d61d-4b00-bead-6309aef219e4-0Sagastume Gutierrez, Alexis-0000-0003-0188-7101-600Hernandez Herrera, Hernan-d3f0ff8a-ec90-485a-b33b-40d187052285-0engJournal of Theoretical and Applied Information TechnologyAtribución – No comercial – Compartir igualinfo:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Dynamic loadsInstant floatingSugarcane millMathematical modeling of vertical movement of the upper shaft in cane millsArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARTinfo:eu-repo/semantics/acceptedVersion[1] A. BERNARD, Societe dite: Compagnie de Fives-Lille, assignee. Sugar Cane Mill. Patent 2612101. Paris, France. February 22. 1946. [2] D.WILDE, Daniel Wilde, of Washington, Iowa, assignee. Cane-Mill. Washington, United States patent 255228. 1881 December 2, 1881. [3] N. ARZOLA, R. GOYTISOLO, A. FERNANDEZ, “Determination of an Optimal Assembly Misalignment in Sugar Cane Mills”. ASME Conference Proceedings, 2005, IMECE2005-80435, pp. 555-559. ISBN 0-7918-4223-1. [4] C. ADAM, J. G. LOUGHRAN, “Finite element prediction of the performance of sugarcane rolling mills”. International Sugar Journal, 2007, 109(1301), pp. 272-284. [5] C. ADAM, J. G. LOUGHRAN, “The effect of blanket thickness on extraction energy in sugarcane rolling mills: a finite element investigation”. Biosystems Engineering, 2005, 92(2), pp. 255-263. [6] A. KANNAPIRAN, “Computational and experimental modelling of the crushing of prepared sugar cane”. PhD thesis: James Cook University of North Queensland, 2003, pp. 237. [7] G.A. KENT, “Increasing the capacity of Australian raw sugar factory milling units”, PhD thesis, James Cook University of North Queensland; 2003, pp. 248 [8] W. MORA, J. RIVAS, J. CORONADO, “Design of two bearings with sealing system for the top roll shaft of sugar cane mill”. Rev. Téc. Ing. Univ. Zulia, Vol.28. No 3, 2005, pp. 219-232. [9] J. RIVAS, S. RODRÍGUEZ, J. CORONADO, “Análisis de la confiabilidad de los ejes de molino de caña de azúcar”. Tecnura, Vol. 8 No 15, 2004 pp. 45-54. [10] S. RODRÍGUEZ, J. CORONADO, N. ARZOLA, “Predicción de vida remanente en ejes de masa superior de molino de caña”. Ingeniería e Investigación, Vol. 26, No 1, 2006, pp.84-91. [11] S. RODRÍGUEZ, J. CORONADO, N. ARZOLA, “Life prediction for the top roller shafts of sugar mills”. Journal of the Mechanical Behavior of Materials, Vol.17. No 5, 2006, pp. 327-336. [12] N. ARZOLA, R. GOYTISOLO, L. SUAREZ, “Efficiency Increase in the Extraction of Sugar Cane Juice in the Sugar Cane Mills by Means of the Regulation of Hydraulic Pressures”. ASME Conference Proceedings, 2005, (42193), pp. 637-641. [13] J. CORONADO, J. RIVAS, A. LEÓN, “Estudio tribológico en chumaceras y ejes de molino de caña de azúcar”. Dyna (Medellin), No 071, 2004, pp. 1-8. [14] J. CORONADO, “Fracture mechanics approach of repaired top roll shafts in cane mill”. Journal of the Mechanical Behavior of Materials, Vol. 16. No 6, 2005, pp. 419-429. [15] G. MUÑOZ, J. LEWINSKY, “Analysis of the mechanical performance of a sugar cane mill. International Sugar Journal”, 98(1175), 1996, pp. 574-578. [16] E. ROSERO, J. RAMIREZ, “Modelado y control de molinos de caña de azúcar usando accionamientos eléctricos”. Revista Iberoamericana de Automática e Informática Industrial (RIAI), Vol. 6. No 3, 2009, pp. 44-53. [17] A. MENDOZA, M. CABELLO, J. CABELLO, R.GOYTIZOLO, J. MOYA, “Modelación del contacto entre dos pares de dientes en las coronas de molinos”. Ingeniería Mecánica, Vol. 16. No 3. 2014, pp 178-185. [18] N. ARZOLA, “Esquema de análisis para los árboles de los molinos de caña de azúcar y aplicación de la Mecánica de la Fractura en la evaluación de la falla por fatiga”. Tesis de Doctorado. Universidad Central de las Villas Santa Clara. Cuba. 2003. pp. 145. [19] N. ARZOLA, R. GOYTISOLO, R. PEREZ,; et al. “Prediction of the Sugar Mill Shaft Failure Using a Fracture Mechanics Method”. ASME Conference Proceedings, 2005, 2005(42150), pp. 749-755. [20] N. ARZOLA, R. GOYTISOLO, R. PEREZ, et al. “Determinación de la vida remanente de los árboles de los molinos de caña de azúcar con grieta semielíptica superficial”. Ingeniería Mecánica, Vol. 6. No 2. 2003, pp. 43-52. [21] N. ARZOLA, R. GOYTISOLO, J. CABELLO, “Utilización del factor de densidad de energía de deformación en el modelo de crecimiento de la grieta en árboles de molinos de caña de azúcar”. Ingeniería Mecánica, Vol.8. No 2, 2005, pp. 7-14. [22] J. ADAM, J. LOUGHRAN, “Multivariate analysis of frictional interaction between grooved rollers and prepared sugarcane. International”. Journal of the American Society of Agricultural and Biological Engineers, Vol. 47 No 5, 2004, pp. 1611- 1618. [23] H. OKAMURA, H. TANAKA, M. TERAO, “Square box couplings in cane mill Drives1”. International Sugar Journal, 74(886), 1972, pp. 291-293. [24] H. OKAMURA, H.; TANAKA, M. TERAO, “Square box couplings in cane mill Drives-2”. International Sugar Journal, 74(887), 1972, pp. 323-327. [25] J. CABELLO, “Cinemática, transmisión de la carga, lubricación y resistencia superficial de las coronas de molinos de caña de azúcar”. Tesis de Doctorado. Santa Clara: Universidad Central de las Villas, Cuba. 1999. [26] J. MOYA, “Diseño de coronas de molinos de caña de azúcar”. Tesis de Doctorado. Santa Clara: Universidad Central de Las Villas; Cuba 1994. [27] L. NEGRÍN, R. FRANCO, “Estudio de las curvas epicicloide y evolvente para formar el perfil de los engranajes que operan con distancia entre centros variable”. Ingeniería Mecánica, Vol. 10 No 3, pp. 71-76. [28] M. CABELLO “Modelo matemático para el análisis cinemático y dinámico de las coronas de molinos de caña de azúcar”. Tesis de Maestría. Universidad de Cienfuegos: Cienfuegos. 2010. [29] A. ARTANEN, R. BITMEAD, “The application of an iterative identification and controller design to a sugar cane crushing mill. Automática”, Vol. 31. No 11, 1995, pp. 1547-1563.PublicationORIGINALMathematical modeling of vertical movement.pdfMathematical modeling of vertical movement.pdfapplication/pdf3681632https://repositorio.cuc.edu.co/bitstreams/c6d8b89c-93bd-40be-9fe1-456d5a65831d/download194fc4078ac30b98c523ffa426675600MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81748https://repositorio.cuc.edu.co/bitstreams/76fdc316-28fe-4f95-86d9-6ebc308aa453/download8a4605be74aa9ea9d79846c1fba20a33MD52THUMBNAILMathematical modeling of vertical movement.pdf.jpgMathematical modeling of vertical movement.pdf.jpgimage/jpeg61693https://repositorio.cuc.edu.co/bitstreams/1b059462-6343-44db-95b1-03b6ba07c553/download06a770927fb474f8eb7a4890f8852342MD54TEXTMathematical modeling of vertical movement.pdf.txtMathematical modeling of vertical movement.pdf.txttext/plain19226https://repositorio.cuc.edu.co/bitstreams/759762ca-6c39-4d78-a2a3-878aa8ab271a/download117981c33f9c62f6e0ed366628018889MD5511323/935oai:repositorio.cuc.edu.co:11323/9352024-09-17 14:08:57.305open.accesshttps://repositorio.cuc.edu.coRepositorio de la Universidad de la Costa CUCrepdigital@cuc.edu.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