Non-Linear Control and Numerical Analysis Applied in a Non-Linear Model of Cutting Process Subject to Non-Ideal Excitations
This work presents a non-linear mathematical model of a machining system subjected to a non-ideal vibration source. Computer simulations have shown chaotic behavior for specific parameters of the proposed mathematical model. The chaotic behavior is proven using time histories, phase diagrams, bifurc...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-12-01
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| Series: | Modelling |
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| Online Access: | https://www.mdpi.com/2673-3951/5/4/98 |
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| author | Angelo M. Tusset Jonierson A. Cruz Jose M. Balthazar Maria E. K. Fuziki Giane G. Lenzi |
| author_facet | Angelo M. Tusset Jonierson A. Cruz Jose M. Balthazar Maria E. K. Fuziki Giane G. Lenzi |
| author_sort | Angelo M. Tusset |
| collection | DOAJ |
| description | This work presents a non-linear mathematical model of a machining system subjected to a non-ideal vibration source. Computer simulations have shown chaotic behavior for specific parameters of the proposed mathematical model. The chaotic behavior is proven using time histories, phase diagrams, bifurcation diagrams, and the Lyapunov exponent. Considering that cutting tool vibration in the machining process is one of the main problems of productivity and machining accuracy, the introduction of a magnetorheological damper was considered in the proposed model to reduce the vibration amplitudes of the cutting tool and suppress the chaotic behavior. Hysteresis was considered in the magnetorheological damper model and its application in the system as both a passive and active absorber. The active control strategy considered the application of two non-linear control signals: feedforward to maintain the vibration with a desired behavior and state feedback to drive the system to the desired behavior. The numerical results demonstrated that the proposed controls efficiently reduced the vibration amplitude by introducing the MR damper. Active control has proven effective in controlling the force of the MR damper by varying the electrical voltage applied to the damper coil. |
| format | Article |
| id | doaj-art-ad16e60f972d4eb5bd75dfe328c9a8d4 |
| institution | Kabale University |
| issn | 2673-3951 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Modelling |
| spelling | doaj-art-ad16e60f972d4eb5bd75dfe328c9a8d42024-12-27T14:42:08ZengMDPI AGModelling2673-39512024-12-01541889190410.3390/modelling5040098Non-Linear Control and Numerical Analysis Applied in a Non-Linear Model of Cutting Process Subject to Non-Ideal ExcitationsAngelo M. Tusset0Jonierson A. Cruz1Jose M. Balthazar2Maria E. K. Fuziki3Giane G. Lenzi4Department of Production Engineering, Federal University of Technology-Paraná, Paraná-Doutor Washington Subtil Chueire St. 330, Ponta Grossa 84017-220, BrazilDepartment of Production Engineering, Federal University of Technology-Paraná, Paraná-Doutor Washington Subtil Chueire St. 330, Ponta Grossa 84017-220, BrazilDepartment of Production Engineering, Federal University of Technology-Paraná, Paraná-Doutor Washington Subtil Chueire St. 330, Ponta Grossa 84017-220, BrazilDepartment of Chemical Engineering, State University of Maringá, Colombo Ave. 5790, Maringa 87020-900, BrazilDepartment of Production Engineering, Federal University of Technology-Paraná, Paraná-Doutor Washington Subtil Chueire St. 330, Ponta Grossa 84017-220, BrazilThis work presents a non-linear mathematical model of a machining system subjected to a non-ideal vibration source. Computer simulations have shown chaotic behavior for specific parameters of the proposed mathematical model. The chaotic behavior is proven using time histories, phase diagrams, bifurcation diagrams, and the Lyapunov exponent. Considering that cutting tool vibration in the machining process is one of the main problems of productivity and machining accuracy, the introduction of a magnetorheological damper was considered in the proposed model to reduce the vibration amplitudes of the cutting tool and suppress the chaotic behavior. Hysteresis was considered in the magnetorheological damper model and its application in the system as both a passive and active absorber. The active control strategy considered the application of two non-linear control signals: feedforward to maintain the vibration with a desired behavior and state feedback to drive the system to the desired behavior. The numerical results demonstrated that the proposed controls efficiently reduced the vibration amplitude by introducing the MR damper. Active control has proven effective in controlling the force of the MR damper by varying the electrical voltage applied to the damper coil.https://www.mdpi.com/2673-3951/5/4/98vibration dampingmagnetorheological dampersnon-ideal systemsmechanical vibrationsnon-linear controlmodeling |
| spellingShingle | Angelo M. Tusset Jonierson A. Cruz Jose M. Balthazar Maria E. K. Fuziki Giane G. Lenzi Non-Linear Control and Numerical Analysis Applied in a Non-Linear Model of Cutting Process Subject to Non-Ideal Excitations Modelling vibration damping magnetorheological dampers non-ideal systems mechanical vibrations non-linear control modeling |
| title | Non-Linear Control and Numerical Analysis Applied in a Non-Linear Model of Cutting Process Subject to Non-Ideal Excitations |
| title_full | Non-Linear Control and Numerical Analysis Applied in a Non-Linear Model of Cutting Process Subject to Non-Ideal Excitations |
| title_fullStr | Non-Linear Control and Numerical Analysis Applied in a Non-Linear Model of Cutting Process Subject to Non-Ideal Excitations |
| title_full_unstemmed | Non-Linear Control and Numerical Analysis Applied in a Non-Linear Model of Cutting Process Subject to Non-Ideal Excitations |
| title_short | Non-Linear Control and Numerical Analysis Applied in a Non-Linear Model of Cutting Process Subject to Non-Ideal Excitations |
| title_sort | non linear control and numerical analysis applied in a non linear model of cutting process subject to non ideal excitations |
| topic | vibration damping magnetorheological dampers non-ideal systems mechanical vibrations non-linear control modeling |
| url | https://www.mdpi.com/2673-3951/5/4/98 |
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