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Mathematical Modelling of Transient Processes in an Asynchronous Drive with a Long Shaft Including Cardan Joints

Author

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  • Andriy Chaban

    (Faculty of Transport, Electrical Engineering and Computer Science, University of Technology and Humanities in Radom, 26-600 Radom, Poland)

  • Zbigniew Łukasik

    (Faculty of Transport, Electrical Engineering and Computer Science, University of Technology and Humanities in Radom, 26-600 Radom, Poland)

  • Andrzej Popenda

    (Faculty of Electrical Engineering, Częstochowa University of Technology, 42-201 Częstochowa, Poland)

  • Andrzej Szafraniec

    (Faculty of Transport, Electrical Engineering and Computer Science, University of Technology and Humanities in Radom, 26-600 Radom, Poland)

Abstract

Beginning with the classic methods, a mathematical model of an electromechanical system is developed that consists of a deep bar cage induction motor that, via a complex motion transmission with distributed mechanical parameters, drives a working machine, loading the drive system with a constant torque. The electromagnetic field theory serves to create the motor model, which allows addressing the displacement of current in the rotor cage bars. Ordinary and partial differential equations are used to describe the electromechanical processes of energy conversion in the motor. The complex transmission of the drive motion consists of a long shaft with variable geometry cardan joints mounted on its ends. Non-linear electromechanical differential equations are presented as a system of ordinary differential equations combined with a mixed problem of Dirichlet first-type and Poincaré third-type boundary conditions. This system of equations is integrated by discretising partial derivatives by means of the straight-line methods and successive integration as a function of time using the Runge–Kutta fourth-order method. Starting from there, complicated transient processes in the drive system are analysed. Results of computer simulations are presented in the graphic form, which is analysed.

Suggested Citation

  • Andriy Chaban & Zbigniew Łukasik & Andrzej Popenda & Andrzej Szafraniec, 2021. "Mathematical Modelling of Transient Processes in an Asynchronous Drive with a Long Shaft Including Cardan Joints," Energies, MDPI, vol. 14(18), pages 1-17, September.
    • Handle: RePEc:gam:jeners:v:14:y:2021:i:18:p:5692-:d:632624
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    References listed on IDEAS

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    1. Wei Chen & Jiaojiao Liang & Tingna Shi, 2018. "Speed Synchronous Control of Multiple Permanent Magnet Synchronous Motors Based on an Improved Cross-Coupling Structure," Energies, MDPI, vol. 11(2), pages 1-16, January.
    2. Sayed Poorya Rabiei & Reza Azarafza, 2014. "Investigate of Mechanical Fuse in Cardan Shaft Using FEM," Review of Information Engineering and Applications, Conscientia Beam, vol. 1(1), pages 1-10.
    3. Andriy Lozynskyy & Andriy Chaban & Tomasz Perzyński & Andrzej Szafraniec & Lidiia Kasha, 2021. "Application of Fractional-Order Calculus to Improve the Mathematical Model of a Two-Mass System with a Long Shaft," Energies, MDPI, vol. 14(7), pages 1-15, March.
    4. Sayed Poorya Rabiei & Reza Azarafza, 2014. "Investigate of Mechanical Fuse in Cardan Shaft Using FEM," Review of Information Engineering and Applications, Conscientia Beam, vol. 1(1), pages 1-10.
    5. Kanaan, Hadi Youssef & Al-Haddad, Kamal & Roy, Gilles, 2003. "Analysis of the electromechanical vibrations in induction motor drives due to the imperfections of the mechanical transmission system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 63(3), pages 421-433.
    6. Andrzej Popenda & Marek Lis & Marcjan Nowak & Krzysztof Blecharz, 2020. "Mathematical Modelling of Drive System with an Elastic Coupling Based on Formal Analogy between the Transmission Shaft and the Electric Transmission Line," Energies, MDPI, vol. 13(5), pages 1-14, March.
    7. Gabriel Ekemb & Fouad Slaoui-Hasnaoui & Joseph Song-Manguelle & P. M. Lingom & Issouf Fofana, 2021. "Instantaneous Electromagnetic Torque Components in Synchronous Motors Fed by Load-Commutated Inverters," Energies, MDPI, vol. 14(11), pages 1-25, May.
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    Cited by:

    1. Andriy Chaban & Tomasz Perzyński & Andrzej Popenda & Radosław Figura & Vitaliy Levoniuk, 2022. "Mathematical Modeling of Transient Processes in the Susceptible Motion Transmission in a Ship Propulsion System Containing a Shaft Synchronous Generator," Energies, MDPI, vol. 15(9), pages 1-17, April.
    2. Andrzej Popenda & Andrzej Szafraniec & Andriy Chaban, 2021. "Dynamics of Electromechanical Systems Containing Long Elastic Couplings and Safety of Their Operation," Energies, MDPI, vol. 14(23), pages 1-18, November.

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