Mathematical model for the design of linear asynchronous electric motors and its software implementation

Mathematical models are the main tool for the layout design of linear asynchronous electric motors. Existing design models of linear asynchronous electric motors assume that the device is powered from a source of multiphase symmetrical positive sequence current, which excludes from consideration the asymmetry of the inductor phase currents and the associated reduction in traction force. This approach is not flexible enough, since the operation of linear asynchronous electric motors in a wide range of movement speeds assumes a functional relationship between the current asymmetry coefficient and the movement speed. The study developed a mathematical model for design purposes that implements the functional relationship between the current asymmetry coefficient and the speed of movement. The mathematical model represents 13 linear equations linking geometric dimensions, current loads, electromagnetic field characteristics and mechanical forces with the speed of the secondary element of the electric motor. The current load of an electric motor has a variable degree of ellipticity depending on the speed of movement. An algorithmic study of the mathematical model was carried out and corresponding software modeling tools were developed. The proposed program algorithm, containing two subroutines, is implemented using the Maple symbolic computing software package. In order to expand the range of users, the software model is additionally implemented in C++. In this case, the functional dependence of the asymmetry coefficient of the exciting current wave on the speed of movement is implemented in the form of an iterative procedure for the case of connecting the winding of the linear asynchronous electric motors inductor to a source of symmetrical three-phase voltage according to the “triangle” circuit. Using the example of a three-phase linear asynchronous electric motors, the electromagnetic and mechanical characteristics of the electric motor were simulated. It was stated that the influence of current asymmetry on the mechanical characteristics of the linear asynchronous electric motors is small and is expressed in the region of high speeds. This makes it possible, in design tasks for the layout of an electric motor, to use models that involve powering the linear asynchronous electric motors from a symmetrical current source or to introduce a fixed asymmetry coefficient into them.