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.
Highlights
Mathematical modelling of transient processes in asynchronous drives is important at the stages of both design and operation
A mathematical model of a susceptible motion transmission-based asynchronous drive including the distributed mechanical parameters of a long shaft that contains cardan joints is the chief purpose of our paper
The development of integral a mathematical model of a long-shaft asynchronous drivewith inHamilton–Ostrogradsky variational principle by expanding the Lagrangian cluding cardan joints is approached with an interdisciplinary method that modifies the two components: dissipation energy and energy of non-potential external forces [27,31]
Summary
Mathematical modelling of transient processes in asynchronous drives is important at the stages of both design and operation. The theory of applied mechanics implies that rather complicated motions are present in drive systems containing cardan joints This is caused by the different instantaneous rotational speeds of co-working and interconnected shafts, which results in their different rotation angles [12,13]. A mathematical model of a susceptible motion transmission-based asynchronous drive including the distributed mechanical parameters of a long shaft that contains cardan joints is the chief purpose of our paper. Based on this model, we analyse transient oscillatory electromechanical processes in the drive
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