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

Andriy Chaban, Zbigniew Łukasik, Andrzej Popenda and Andrzej Szafraniec
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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

Energies, 2021, vol. 14, issue 18, 1-17

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.

Keywords: cardan joint; electric machine dynamics; mathematical modelling; asynchronous drive; induction machine; torsional vibrations; analytical mechanics; computer simulation (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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