Application of the Sine-Cosine Algorithm to the Optimal Design of a Closed Coil Helical Spring

This paper proposes the application of the sinecosine algorithm (SCA) to the optimal design of a closed coil helical spring. The optimization problem addressed corresponds to the minimization of total spring volume subject to physical constraints that represents the closed coil helical spring such a...

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Autores:
Rodríguez Cabal, Miguel Ángel
Grisales-Noreña, Luis Fernando
Ramírez Vanegas, Carlos Alberto
Arias Londoño, Andrés
Tipo de recurso:
Article of journal
Fecha de publicación:
2021
Institución:
Universidad Tecnológica de Bolívar
Repositorio:
Repositorio Institucional UTB
Idioma:
eng
OAI Identifier:
oai:repositorio.utb.edu.co:20.500.12585/13497
Acceso en línea:
https://hdl.handle.net/20.500.12585/13497
https://doi.org/10.32397/tesea.vol2.n2.5
Palabra clave:
Mechanical analysis
machine elements design
sine-cosine algorithm
nonlinear optimization model
closed coil helical spring
Rights
openAccess
License
https://creativecommons.org/licenses/by-nc-sa/4.0/
id UTB2_176273504ee6e501158df184ca1b2171
oai_identifier_str oai:repositorio.utb.edu.co:20.500.12585/13497
network_acronym_str UTB2
network_name_str Repositorio Institucional UTB
repository_id_str
dc.title.spa.fl_str_mv Application of the Sine-Cosine Algorithm to the Optimal Design of a Closed Coil Helical Spring
dc.title.translated.spa.fl_str_mv Application of the Sine-Cosine Algorithm to the Optimal Design of a Closed Coil Helical Spring
title Application of the Sine-Cosine Algorithm to the Optimal Design of a Closed Coil Helical Spring
spellingShingle Application of the Sine-Cosine Algorithm to the Optimal Design of a Closed Coil Helical Spring
Mechanical analysis
machine elements design
sine-cosine algorithm
nonlinear optimization model
closed coil helical spring
title_short Application of the Sine-Cosine Algorithm to the Optimal Design of a Closed Coil Helical Spring
title_full Application of the Sine-Cosine Algorithm to the Optimal Design of a Closed Coil Helical Spring
title_fullStr Application of the Sine-Cosine Algorithm to the Optimal Design of a Closed Coil Helical Spring
title_full_unstemmed Application of the Sine-Cosine Algorithm to the Optimal Design of a Closed Coil Helical Spring
title_sort Application of the Sine-Cosine Algorithm to the Optimal Design of a Closed Coil Helical Spring
dc.creator.fl_str_mv Rodríguez Cabal, Miguel Ángel
Grisales-Noreña, Luis Fernando
Ramírez Vanegas, Carlos Alberto
Arias Londoño, Andrés
dc.contributor.author.eng.fl_str_mv Rodríguez Cabal, Miguel Ángel
Grisales-Noreña, Luis Fernando
Ramírez Vanegas, Carlos Alberto
Arias Londoño, Andrés
dc.subject.eng.fl_str_mv Mechanical analysis
machine elements design
sine-cosine algorithm
nonlinear optimization model
closed coil helical spring
topic Mechanical analysis
machine elements design
sine-cosine algorithm
nonlinear optimization model
closed coil helical spring
description This paper proposes the application of the sinecosine algorithm (SCA) to the optimal design of a closed coil helical spring. The optimization problem addressed corresponds to the minimization of total spring volume subject to physical constraints that represents the closed coil helical spring such as maximum working load, shear stress, and minimum diameter requirements, among other. The resulting mathematical formulation is a complex nonlinear and non-convex optimization model that is typically addressed in literature with trial and error methods or heuristic algorithms. To solve this problem efficiently, the SCA is proposed in this research. This optimization algorithm belongs to the family of the metaheuristic optimization techniques, it works with controlled random processes guided by sine and cosine trigonometric functions, that allows exploring and exploiting the solution space in order to find the best solution to the optimization problem. By presenting as main advantage an easy implementation at any programming language using sequential quadratic programming; eliminating the need to uses specialized and costly software. Numerical results demonstrating that the proposes SCA allows reaching lower spring volume values in comparison with literature approaches, such as genetic algorithms, particle swarm optimization methods, among others. All the numerical simulations have been implemented in the MATLAB software.
publishDate 2021
dc.date.accessioned.none.fl_str_mv 2021-12-15 00:00:00
2025-05-21T19:15:44Z
dc.date.available.none.fl_str_mv 2021-12-15 00:00:00
dc.date.issued.none.fl_str_mv 2021-12-15
dc.type.spa.fl_str_mv Artículo de revista
dc.type.coar.fl_str_mv http://purl.org/coar/resource_type/c_2df8fbb1
dc.type.driver.eng.fl_str_mv info:eu-repo/semantics/article
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dc.type.local.eng.fl_str_mv Journal article
dc.type.content.eng.fl_str_mv Text
dc.type.version.eng.fl_str_mv info:eu-repo/semantics/publishedVersion
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dc.identifier.uri.none.fl_str_mv https://hdl.handle.net/20.500.12585/13497
dc.identifier.url.none.fl_str_mv https://doi.org/10.32397/tesea.vol2.n2.5
dc.identifier.doi.none.fl_str_mv 10.32397/tesea.vol2.n2.5
dc.identifier.eissn.none.fl_str_mv 2745-0120
url https://hdl.handle.net/20.500.12585/13497
https://doi.org/10.32397/tesea.vol2.n2.5
identifier_str_mv 10.32397/tesea.vol2.n2.5
2745-0120
dc.language.iso.eng.fl_str_mv eng
language eng
dc.relation.references.eng.fl_str_mv G. P. Garcia, “Una teor´ıa general de an´alisis en el dise˜no de elementos de m´aquinas,” Ingenier´ıa e Investigaci´on, vol. 0, no. 13, pp. 31–42, 2010. [2] M. A. Rodriguez-Cabal, J. A. Mar´ın, L. F. Grisales-Nore˜na, O. D. Montoya, and J. A. S. Del Rio, “Optimization of a drive shaft using PSO algorithm,” WSEAS Transactions on Applied and Theoretical Mechanics, vol. 13, pp. 130–139, 2018. [3] R. G. Budynas and J. K. Nisbett, Shigley´s Mechanical Engineering Design. New York: McGRAW-HILL, 9 ed., 2011. [4] S. Bhaumik, R. Rangaraju, M. Parameswara, M. Venkataswamy, T. Bhaskaran, and R. Krishnan, “Fatigue failure of a hollow power transmission shaft,” Engineering Failure Analysis, vol. 9, pp. 457–467, aug 2002. [5] M. A. Rodriguez-Cabal, L. F. Grisales-Nore˜na, J. G. Ardila-Mar´ın, and O. D. Montoya-Giraldo, “Optimal design of transmission shafts: a continuous genetic algorithm approach,” Statistics, Optimization & Information Computing, vol. 7, dec 2019. [6] H. N. Ghafil and K. J´armai, “Dynamic differential annealed optimization: New metaheuristic optimization algorithm for engineering applications,” Applied Soft Computing, vol. 93, p. 106392, aug 2020. [7] M. Kohli and S. Arora, “Chaotic grey wolf optimization algorithm for constrained optimization problems,” Journal of Computational Design and Engineering, vol. 5, pp. 458–472, mar 2017. [8] M. Taktak, K. Omheni, A. Aloui, F. Dammak, and M. Haddar, “Dynamic optimization design of a cylindrical helical spring,” Applied Acoustics, vol. 77, pp. 178–183, mar 2014. [9] L. Wu, L. Chen, H. Fu, Q. Jiang, X. Wu, and Y. Tang, “Carbon fiber composite multistrand helical springs with adjustable spring constant: design and mechanism studies,” Journal of Materials Research and Technology, vol. 9, pp. 5067–5076, may 2020. [10] J. Ke, Z. yu Wu, Y. sheng Liu, Z. Xiang, and X. dong Hu, “Design method, performance investigation and manufacturing process of composite helical springs: A review,” Composite Structures, vol. 252, p. 112747, nov 2020. [11] B. Thamaraikannan and V. Thirunavukkarasu, “Design Optimization of Mechanical Components Using an Enhanced Teaching-Learning Based Optimization Algorithm with Differential Operator,” Mathematical Problems in Engineering, vol. 2014, pp. 1–10, 2014. [12] L. F. Grisales-Nore˜na, O. D. Garz´on-Rivera, J. A. Ocampo-Toro, C. A. Ramos-Paja, and M. A. Rodriguez-Cabal, “Metaheuristic optimization methods for optimal power flow analysis in DC distribution networks,” Transactions on Energy Systems and Engineering Applications, vol. 1, pp. 13–31, dec 2020. [13] O. D. Montoya, A. Molina-Cabrera, H. R. Chamorro, L. AlvaradoBarrios, and E. Rivas-Trujillo, “A Hybrid Approach Based on SOCP and the Discrete Version of the SCA for Optimal Placement and Sizing DGs in AC Distribution Networks,” Electronics, vol. 10, p. 26, dec 2020. [14] S. Mirjalili, “SCA: A Sine Cosine Algorithm for solving optimization problems,” Knowledge-Based Systems, vol. 96, pp. 120–133, mar 2016. [15] H. Huang, X. Feng, A. A. Heidari, Y. Xu, M. Wang, G. Liang, H. Chen, and X. Cai, “Rationalized Sine Cosine Optimization With Efficient Searching Patterns,” IEEE Access, vol. 8, pp. 61471–61490, 2020. [16] A.-F. Attia, R. A. E. Sehiemy, and H. M. Hasanien, “Optimal power flow solution in power systems using a novel Sine-Cosine algorithm,” Int. J. Electr. Power Energy Syst., vol. 99, pp. 331–343, jul 2018. [17] J. A. Giraldo, O. D. Montoya, L. F. Grisales-Nore˜na, W. Gil-Gonzalez, and M. Holgu´ın, “Optimal power flow solution in direct current grids using Sine-Cosine algorithm,” J. Phys. Conf. Ser., vol. 1403, p. 012009, nov 2019. [18] A. I. Hafez, H. M. Zawbaa, E. Emary, and A. E. Hassanien, “Sine cosine optimization algorithm for feature selection,” in 2016 International Symposium on INnovations in Intelligent SysTems and Applications (INISTA), IEEE, aug 2016. [19] R. M. Rizk-Allah, “An improved sine–cosine algorithm based on orthogonal parallel information for global optimization,” Soft Computing, vol. 23, pp. 7135–7161, jul 2018. [20] S. Gupta, K. Deep, H. Moayedi, L. K. Foong, and A. Assad, “Sine cosine grey wolf optimizer to solve engineering design problems,” Engineering with Computers, feb 2020. [21] M. L. Manrique, O. D. Montoya, V. M. Garrido, L. F. Grisales-Nore˜na, and W. Gil-Gonzalez, “Sine-Cosine Algorithm for OPF Analysis in Distribution Systems to Size Distributed Generators,” in Communications in Computer and Information Science, pp. 28–39, Springer International Publishing, 2019.
dc.relation.ispartofjournal.eng.fl_str_mv Transactions on Energy Systems and Engineering Applications
dc.relation.citationvolume.eng.fl_str_mv 2
dc.relation.citationstartpage.none.fl_str_mv 33
dc.relation.citationendpage.none.fl_str_mv 38
dc.relation.bitstream.none.fl_str_mv https://revistas.utb.edu.co/tesea/article/download/458/360
dc.relation.citationedition.eng.fl_str_mv Núm. 2 , Año 2021 : Transactions on Energy Systems and Engineering Applications
dc.relation.citationissue.eng.fl_str_mv 2
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dc.publisher.eng.fl_str_mv Universidad Tecnológica de Bolívar
dc.source.eng.fl_str_mv https://revistas.utb.edu.co/tesea/article/view/458
institution Universidad Tecnológica de Bolívar
repository.name.fl_str_mv Repositorio Digital Universidad Tecnológica de Bolívar
repository.mail.fl_str_mv bdigital@metabiblioteca.com
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spelling Rodríguez Cabal, Miguel ÁngelGrisales-Noreña, Luis Fernando Ramírez Vanegas, Carlos AlbertoArias Londoño, Andrés2021-12-15 00:00:002025-05-21T19:15:44Z2021-12-15 00:00:002021-12-15https://hdl.handle.net/20.500.12585/13497https://doi.org/10.32397/tesea.vol2.n2.510.32397/tesea.vol2.n2.52745-0120This paper proposes the application of the sinecosine algorithm (SCA) to the optimal design of a closed coil helical spring. The optimization problem addressed corresponds to the minimization of total spring volume subject to physical constraints that represents the closed coil helical spring such as maximum working load, shear stress, and minimum diameter requirements, among other. The resulting mathematical formulation is a complex nonlinear and non-convex optimization model that is typically addressed in literature with trial and error methods or heuristic algorithms. To solve this problem efficiently, the SCA is proposed in this research. This optimization algorithm belongs to the family of the metaheuristic optimization techniques, it works with controlled random processes guided by sine and cosine trigonometric functions, that allows exploring and exploiting the solution space in order to find the best solution to the optimization problem. By presenting as main advantage an easy implementation at any programming language using sequential quadratic programming; eliminating the need to uses specialized and costly software. Numerical results demonstrating that the proposes SCA allows reaching lower spring volume values in comparison with literature approaches, such as genetic algorithms, particle swarm optimization methods, among others. All the numerical simulations have been implemented in the MATLAB software.application/pdfengUniversidad Tecnológica de BolívarMiguel Ángel Rodríguez Cabal, Luis Fernando Grisales Noreña, Carlos Alberto Ramírez Vanegas, Andrés Arias Londoño - 2021https://creativecommons.org/licenses/by-nc-sa/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2https://revistas.utb.edu.co/tesea/article/view/458Mechanical analysismachine elements designsine-cosine algorithmnonlinear optimization modelclosed coil helical springApplication of the Sine-Cosine Algorithm to the Optimal Design of a Closed Coil Helical SpringApplication of the Sine-Cosine Algorithm to the Optimal Design of a Closed Coil Helical SpringArtículo de revistainfo:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Journal articleTextinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/version/c_970fb48d4fbd8a85G. P. Garcia, “Una teor´ıa general de an´alisis en el dise˜no de elementos de m´aquinas,” Ingenier´ıa e Investigaci´on, vol. 0, no. 13, pp. 31–42, 2010. [2] M. A. Rodriguez-Cabal, J. A. Mar´ın, L. F. Grisales-Nore˜na, O. D. Montoya, and J. A. S. Del Rio, “Optimization of a drive shaft using PSO algorithm,” WSEAS Transactions on Applied and Theoretical Mechanics, vol. 13, pp. 130–139, 2018. [3] R. G. Budynas and J. K. Nisbett, Shigley´s Mechanical Engineering Design. New York: McGRAW-HILL, 9 ed., 2011. [4] S. Bhaumik, R. Rangaraju, M. Parameswara, M. Venkataswamy, T. Bhaskaran, and R. Krishnan, “Fatigue failure of a hollow power transmission shaft,” Engineering Failure Analysis, vol. 9, pp. 457–467, aug 2002. [5] M. A. Rodriguez-Cabal, L. F. Grisales-Nore˜na, J. G. Ardila-Mar´ın, and O. D. Montoya-Giraldo, “Optimal design of transmission shafts: a continuous genetic algorithm approach,” Statistics, Optimization & Information Computing, vol. 7, dec 2019. [6] H. N. Ghafil and K. J´armai, “Dynamic differential annealed optimization: New metaheuristic optimization algorithm for engineering applications,” Applied Soft Computing, vol. 93, p. 106392, aug 2020. [7] M. Kohli and S. Arora, “Chaotic grey wolf optimization algorithm for constrained optimization problems,” Journal of Computational Design and Engineering, vol. 5, pp. 458–472, mar 2017. [8] M. Taktak, K. Omheni, A. Aloui, F. Dammak, and M. Haddar, “Dynamic optimization design of a cylindrical helical spring,” Applied Acoustics, vol. 77, pp. 178–183, mar 2014. [9] L. Wu, L. Chen, H. Fu, Q. Jiang, X. Wu, and Y. Tang, “Carbon fiber composite multistrand helical springs with adjustable spring constant: design and mechanism studies,” Journal of Materials Research and Technology, vol. 9, pp. 5067–5076, may 2020. [10] J. Ke, Z. yu Wu, Y. sheng Liu, Z. Xiang, and X. dong Hu, “Design method, performance investigation and manufacturing process of composite helical springs: A review,” Composite Structures, vol. 252, p. 112747, nov 2020. [11] B. Thamaraikannan and V. Thirunavukkarasu, “Design Optimization of Mechanical Components Using an Enhanced Teaching-Learning Based Optimization Algorithm with Differential Operator,” Mathematical Problems in Engineering, vol. 2014, pp. 1–10, 2014. [12] L. F. Grisales-Nore˜na, O. D. Garz´on-Rivera, J. A. Ocampo-Toro, C. A. Ramos-Paja, and M. A. Rodriguez-Cabal, “Metaheuristic optimization methods for optimal power flow analysis in DC distribution networks,” Transactions on Energy Systems and Engineering Applications, vol. 1, pp. 13–31, dec 2020. [13] O. D. Montoya, A. Molina-Cabrera, H. R. Chamorro, L. AlvaradoBarrios, and E. Rivas-Trujillo, “A Hybrid Approach Based on SOCP and the Discrete Version of the SCA for Optimal Placement and Sizing DGs in AC Distribution Networks,” Electronics, vol. 10, p. 26, dec 2020. [14] S. Mirjalili, “SCA: A Sine Cosine Algorithm for solving optimization problems,” Knowledge-Based Systems, vol. 96, pp. 120–133, mar 2016. [15] H. Huang, X. Feng, A. A. Heidari, Y. Xu, M. Wang, G. Liang, H. Chen, and X. Cai, “Rationalized Sine Cosine Optimization With Efficient Searching Patterns,” IEEE Access, vol. 8, pp. 61471–61490, 2020. [16] A.-F. Attia, R. A. E. Sehiemy, and H. M. Hasanien, “Optimal power flow solution in power systems using a novel Sine-Cosine algorithm,” Int. J. Electr. Power Energy Syst., vol. 99, pp. 331–343, jul 2018. [17] J. A. Giraldo, O. D. Montoya, L. F. Grisales-Nore˜na, W. Gil-Gonzalez, and M. Holgu´ın, “Optimal power flow solution in direct current grids using Sine-Cosine algorithm,” J. Phys. Conf. Ser., vol. 1403, p. 012009, nov 2019. [18] A. I. Hafez, H. M. Zawbaa, E. Emary, and A. E. Hassanien, “Sine cosine optimization algorithm for feature selection,” in 2016 International Symposium on INnovations in Intelligent SysTems and Applications (INISTA), IEEE, aug 2016. [19] R. M. Rizk-Allah, “An improved sine–cosine algorithm based on orthogonal parallel information for global optimization,” Soft Computing, vol. 23, pp. 7135–7161, jul 2018. [20] S. Gupta, K. Deep, H. Moayedi, L. K. Foong, and A. Assad, “Sine cosine grey wolf optimizer to solve engineering design problems,” Engineering with Computers, feb 2020. [21] M. L. Manrique, O. D. Montoya, V. M. Garrido, L. F. Grisales-Nore˜na, and W. Gil-Gonzalez, “Sine-Cosine Algorithm for OPF Analysis in Distribution Systems to Size Distributed Generators,” in Communications in Computer and Information Science, pp. 28–39, Springer International Publishing, 2019.Transactions on Energy Systems and Engineering Applications23338https://revistas.utb.edu.co/tesea/article/download/458/360Núm. 2 , Año 2021 : Transactions on Energy Systems and Engineering Applications220.500.12585/13497oai:repositorio.utb.edu.co:20.500.12585/134972025-06-24 10:31:10.157https://creativecommons.org/licenses/by-nc-sa/4.0/Miguel Ángel Rodríguez Cabal, Luis Fernando Grisales Noreña, Carlos Alberto Ramírez Vanegas, Andrés Arias Londoño - 2021metadata.onlyhttps://repositorio.utb.edu.coRepositorio Digital Universidad Tecnológica de Bolívarbdigital@metabiblioteca.com

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