Mathematical Modelling of Drive System with an Elastic Coupling Based on Formal Analogy between the Transmission Shaft and the Electric Transmission Line

Popenda, Andrzej; Lis, Marek; Nowak, M.; Blecharz, Krzysztof

doi:10.3390/en13051181

Cited by 14 publications

(16 citation statements)

References 15 publications

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“…Approximated functions of velocity and rotation angle were derived from ( 18 Figure 3 depicts instant angular velocity of the left shaft end (towards the motor) during the first experiment, determined according to the shaft Equations ( 5)-( 8) and the mathematical model of motion transmission (18). This dependence is virtually identical in both the cases of modelling.…”

Section: Results Of Computer Simulation For the Dual Mass Modelmentioning

confidence: 99%

“…The logical question arises of a possible similarity between a long shaft in drive motion transmission and a dual mass elastic dissipation system [15][16][17][18]. It is not always the case, since similarity of a lumped and dispersed parameter system does not address velocity of mechanical wave motion, which leads to inaccuracies in determination of real system parameters.…”

Section: Mathematical Model Of An Elastic-dissipation Long Shaft Of Distributed Parametersmentioning

confidence: 99%

“…The mathematical model of electric drive motion transmission including long elastic elements is described with (2) and is the most accurate, which means results of computer simulation of functional dependences sought on its basis can be with great adequacy regarded as an experiment. The functions computed in this way will be approximated by Equation (18).…”

Section: Mathematical Model Of An Elastic-dissipation Long Shaft Of Distributed Parametersmentioning

confidence: 99%

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Application of Genetic Algorithm Elements to Modelling of Rotation Processes in Motion Transmission Including a Long Shaft

et al. 2020

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Genetic algorithms are used to parameter identification of the model of oscillatory processes in complicated motion transmission of electric drives containing long elastic shafts as systems of distributed mechanical parameters. Shaft equations are generated on the basis of a modified Hamilton–Ostrogradski principle, which serves as the foundation to analyse the lumped parameter system and distributed parameter system. They serve to compute basic functions of analytical mechanics of velocity continuum and rotational angles of shaft elements. It is demonstrated that the application of the distributed parameter method to multi-mass rotational systems, that contain long elastic elements and complicated control systems, is not always possible. The genetic algorithm is applied to determine the coefficients of approximation the system of Rotational Transmission with Elastic Shaft by equivalent differential equations. The fitness function is determined as least-square error. The obtained results confirm that application of the genetic algorithms allow one to replace the use of a complicated distributed parameter model of mechanical system by a considerably simpler model, and to eliminate sophisticated calculation procedures and identification of boundary conditions for wave motion equations of long elastic elements.

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Section: Results Of Computer Simulation For the Dual Mass Modelmentioning

confidence: 99%

Section: Mathematical Model Of An Elastic-dissipation Long Shaft Of Distributed Parametersmentioning

confidence: 99%

Section: Mathematical Model Of An Elastic-dissipation Long Shaft Of Distributed Parametersmentioning

confidence: 99%

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Application of Genetic Algorithm Elements to Modelling of Rotation Processes in Motion Transmission Including a Long Shaft

et al. 2020

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“…In drive systems including long shafts, the susceptibility of these elements in distributed parameter systems must be additionally taken into consideration [4,6,[24][25][26]. Only the susceptibility of the middle shaft needs to be addressed in our system, since it is several times longer than the first or third shaft.…”

Section: Drive Systems Including Cardan Jointsmentioning

confidence: 99%

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

et al. 2021

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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.

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“…Several researchers [19][20][21][22][23][24] have undertaken tests of stresses and vibrations of transmission shafts with the use of various methods of analysis, especially mathematical modeling. To model the transmission shafts, classical methods based on the d'Alembert principle and Newton's second law as well as the variational method are used.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Electromechanical Systems Containing Long Elastic Couplings and Safety of Their Operation

2021

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The electromechanical systems under analysis include electric drives, working machines that perform specific tasks in the technological process, and working mechanisms that transmit mechanical power between the electric drive and the working machine. The vast majority of electric motors included in drive systems require rotational speed control. This task is most often performed with the use of closed-loop control structures based on speed controllers. A step or overly rapid change in the speed reference causes a temporary lock of the speed controller due to the applied limitations at its output. Particularly, unfavorable effects of such a lock can be observed in drive systems in which there is a long elastic coupling (transmission shaft) between the electric motor and the working machine. As a consequence, shaft torsion and accompanying twisting moments of considerable amplitudes appear. This article proposes an uncomplicated active torque limiter structure, which enables the uninterrupted operation of the speed controller thanks to the automatic adaptation of the rate of the speed reference change to any moment of inertia of the rotor and attached rotating masses. The results of the investigations confirm the effectiveness of the proposed structure.

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Mathematical Modelling of Drive System with an Elastic Coupling Based on Formal Analogy between the Transmission Shaft and the Electric Transmission Line

Cited by 14 publications

References 15 publications

Application of Genetic Algorithm Elements to Modelling of Rotation Processes in Motion Transmission Including a Long Shaft

Application of Genetic Algorithm Elements to Modelling of Rotation Processes in Motion Transmission Including a Long Shaft

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

Dynamics of Electromechanical Systems Containing Long Elastic Couplings and Safety of Their Operation

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