Research into 2D Dynamics and Control of Small Oscillations of a Cross-Beam during Transportation by Two Overhead Cranes
A new mathematical model of a 3DOF 2D mechanical system “transported cross-beam, two moving bridge cranes” has been proposed. Small system oscillations have been derived through the introduction of Lagrange equations. The numerical estimation of 3DOF system motion has been carried out with equation-...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2017-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2017/9605657 |
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| _version_ | 1849305454539177984 |
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| author | Alexander V. Perig Alexander N. Stadnik Alexander A. Kostikov Sergey V. Podlesny |
| author_facet | Alexander V. Perig Alexander N. Stadnik Alexander A. Kostikov Sergey V. Podlesny |
| author_sort | Alexander V. Perig |
| collection | DOAJ |
| description | A new mathematical model of a 3DOF 2D mechanical system “transported cross-beam, two moving bridge cranes” has been proposed. Small system oscillations have been derived through the introduction of Lagrange equations. The numerical estimation of 3DOF system motion has been carried out with equation-based Modelica language. The present article uses the Lagrange method and numerical and optimization methods, realized with JModelica.org and Optimica freeware. The absolute swaying of the cross-beam with respect to the displacement of the two moving bridge cranes was estimated. The phase portraits of the 3DOF system for linear and angular coordinates were presented. An open loop optimal control problem was posed for the motion of the bridge cranes. A “bang-bang” control strategy was implemented for the derivation of an optimal control solution, which enables the travel of two bridge cranes at a prescribed distance for minimum time and minimum swaying of a heavy cross-beam. The derived results of the numerical simulation can be easily practically realized by crane operators with good agreement with simple engineering estimations. The proposed control strategy enables synchronous motion of two bridge cranes with a cross-beam that practically solves the posed problem of unwanted excessive oscillations of a heavy cross-beam during transportation. |
| format | Article |
| id | doaj-art-0a02ab0ff7634f78b1e3055a2318b29d |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-0a02ab0ff7634f78b1e3055a2318b29d2025-08-20T03:55:27ZengWileyShock and Vibration1070-96221875-92032017-01-01201710.1155/2017/96056579605657Research into 2D Dynamics and Control of Small Oscillations of a Cross-Beam during Transportation by Two Overhead CranesAlexander V. Perig0Alexander N. Stadnik1Alexander A. Kostikov2Sergey V. Podlesny3Manufacturing Processes and Automation Engineering Department, Engineering Automation Faculty, Donbass State Engineering Academy, Shkadinova 72, Kramatorsk, Donetsk Region 84313, UkraineDepartment of Technical Mechanics, Engineering Automation Faculty, Donbass State Engineering Academy, Shkadinova 72, Kramatorsk, Donetsk Region 84313, UkraineInformatics and Engineering Graphics Department, Engineering Automation Faculty, Donbass State Engineering Academy, Shkadinova 72, Kramatorsk, Donetsk Region 84313, UkraineDepartment of Technical Mechanics, Engineering Automation Faculty, Donbass State Engineering Academy, Shkadinova 72, Kramatorsk, Donetsk Region 84313, UkraineA new mathematical model of a 3DOF 2D mechanical system “transported cross-beam, two moving bridge cranes” has been proposed. Small system oscillations have been derived through the introduction of Lagrange equations. The numerical estimation of 3DOF system motion has been carried out with equation-based Modelica language. The present article uses the Lagrange method and numerical and optimization methods, realized with JModelica.org and Optimica freeware. The absolute swaying of the cross-beam with respect to the displacement of the two moving bridge cranes was estimated. The phase portraits of the 3DOF system for linear and angular coordinates were presented. An open loop optimal control problem was posed for the motion of the bridge cranes. A “bang-bang” control strategy was implemented for the derivation of an optimal control solution, which enables the travel of two bridge cranes at a prescribed distance for minimum time and minimum swaying of a heavy cross-beam. The derived results of the numerical simulation can be easily practically realized by crane operators with good agreement with simple engineering estimations. The proposed control strategy enables synchronous motion of two bridge cranes with a cross-beam that practically solves the posed problem of unwanted excessive oscillations of a heavy cross-beam during transportation.http://dx.doi.org/10.1155/2017/9605657 |
| spellingShingle | Alexander V. Perig Alexander N. Stadnik Alexander A. Kostikov Sergey V. Podlesny Research into 2D Dynamics and Control of Small Oscillations of a Cross-Beam during Transportation by Two Overhead Cranes Shock and Vibration |
| title | Research into 2D Dynamics and Control of Small Oscillations of a Cross-Beam during Transportation by Two Overhead Cranes |
| title_full | Research into 2D Dynamics and Control of Small Oscillations of a Cross-Beam during Transportation by Two Overhead Cranes |
| title_fullStr | Research into 2D Dynamics and Control of Small Oscillations of a Cross-Beam during Transportation by Two Overhead Cranes |
| title_full_unstemmed | Research into 2D Dynamics and Control of Small Oscillations of a Cross-Beam during Transportation by Two Overhead Cranes |
| title_short | Research into 2D Dynamics and Control of Small Oscillations of a Cross-Beam during Transportation by Two Overhead Cranes |
| title_sort | research into 2d dynamics and control of small oscillations of a cross beam during transportation by two overhead cranes |
| url | http://dx.doi.org/10.1155/2017/9605657 |
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