Development of a mathematical model of a stacker crane with regard to energy dissipation
Stacker cranes are widely used in automated warehouses. The actual task is to increase their energy efficiency and productivity. Simulation mathematical models are used for the solution of this problem at the stage of research and development works. We have developed a mathematical model of a rack s...
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| Format: | Article |
| Language: | deu |
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Academician I.G. Petrovskii Bryansk State University
2023-06-01
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| Series: | Naučno-Tehničeskij Vestnik Brânskogo Gosudarstvennogo Universiteta |
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| Online Access: | https://ntv-brgu.ru/wp-content/arhiv/2023-N2/2023-02-02.pdf |
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| author | M.S. Korytov A.E. Bezrodina |
| author_facet | M.S. Korytov A.E. Bezrodina |
| author_sort | M.S. Korytov |
| collection | DOAJ |
| description | Stacker cranes are widely used in automated warehouses. The actual task is to increase their energy efficiency and productivity. Simulation mathematical models are used for the solution of this problem at the stage of research and development works. We have developed a mathematical model of a rack stacker crane in long spatial displacements taking into account energy dissipation of linear coordinates of the cart and the cargo carriage. The model is a system of two second-order Lagrange differential equations. Partial derivatives of analytical expressions of kinetic and potential energies of the dynamic stacker crane system as well as dissipative Rayleigh function are used for derivation of the differential equations. Different values of dissipation coefficients for two linear coordinates of the stacker crane can be used. Using SimInTech we develop a simulation model of a conventional stacker crane based on the suggested system of differential equations and represented in the form of a block diagram. The developed simulation model is described and an example of its use is given. A complex model of a shelf stacker crane includes as a constituent part a procedure of determining time intervals of equivalent-accelerated motion of the links. Examples of time dependences of the crane bogie and cargo carriage coordinates, drive forces providing the set coordinate dependences, drives work and total work are given. The developed mathematical model of the stacker-crane can be used for the modelling of the processes of the cargo moving along the rack, its raising to the given height corresponding to the rack target cell, its lowering as well as for the estimation of the energy input of the crane. |
| first_indexed | 2024-03-13T00:52:09Z |
| format | Article |
| id | doaj.art-553a047cd446450f899326549a1d7653 |
| institution | Directory Open Access Journal |
| issn | 2413-9920 |
| language | deu |
| last_indexed | 2024-03-13T00:52:09Z |
| publishDate | 2023-06-01 |
| publisher | Academician I.G. Petrovskii Bryansk State University |
| record_format | Article |
| series | Naučno-Tehničeskij Vestnik Brânskogo Gosudarstvennogo Universiteta |
| spelling | doaj.art-553a047cd446450f899326549a1d76532023-07-07T11:19:57ZdeuAcademician I.G. Petrovskii Bryansk State UniversityNaučno-Tehničeskij Vestnik Brânskogo Gosudarstvennogo Universiteta2413-99202023-06-019213414410.22281/2413-9920-2023-09-02-134-144Development of a mathematical model of a stacker crane with regard to energy dissipationM.S. Korytov0A.E. Bezrodina 1Siberian State-Impact Automobile and Road UniversitySiberian State-Impact Automobile and Road UniversityStacker cranes are widely used in automated warehouses. The actual task is to increase their energy efficiency and productivity. Simulation mathematical models are used for the solution of this problem at the stage of research and development works. We have developed a mathematical model of a rack stacker crane in long spatial displacements taking into account energy dissipation of linear coordinates of the cart and the cargo carriage. The model is a system of two second-order Lagrange differential equations. Partial derivatives of analytical expressions of kinetic and potential energies of the dynamic stacker crane system as well as dissipative Rayleigh function are used for derivation of the differential equations. Different values of dissipation coefficients for two linear coordinates of the stacker crane can be used. Using SimInTech we develop a simulation model of a conventional stacker crane based on the suggested system of differential equations and represented in the form of a block diagram. The developed simulation model is described and an example of its use is given. A complex model of a shelf stacker crane includes as a constituent part a procedure of determining time intervals of equivalent-accelerated motion of the links. Examples of time dependences of the crane bogie and cargo carriage coordinates, drive forces providing the set coordinate dependences, drives work and total work are given. The developed mathematical model of the stacker-crane can be used for the modelling of the processes of the cargo moving along the rack, its raising to the given height corresponding to the rack target cell, its lowering as well as for the estimation of the energy input of the crane.https://ntv-brgu.ru/wp-content/arhiv/2023-N2/2023-02-02.pdfstacker cranerackingmathematical modelenergy |
| spellingShingle | M.S. Korytov A.E. Bezrodina Development of a mathematical model of a stacker crane with regard to energy dissipation Naučno-Tehničeskij Vestnik Brânskogo Gosudarstvennogo Universiteta stacker crane racking mathematical model energy |
| title | Development of a mathematical model of a stacker crane with regard to energy dissipation |
| title_full | Development of a mathematical model of a stacker crane with regard to energy dissipation |
| title_fullStr | Development of a mathematical model of a stacker crane with regard to energy dissipation |
| title_full_unstemmed | Development of a mathematical model of a stacker crane with regard to energy dissipation |
| title_short | Development of a mathematical model of a stacker crane with regard to energy dissipation |
| title_sort | development of a mathematical model of a stacker crane with regard to energy dissipation |
| topic | stacker crane racking mathematical model energy |
| url | https://ntv-brgu.ru/wp-content/arhiv/2023-N2/2023-02-02.pdf |
| work_keys_str_mv | AT mskorytov developmentofamathematicalmodelofastackercranewithregardtoenergydissipation AT aebezrodina developmentofamathematicalmodelofastackercranewithregardtoenergydissipation |