MATHEMATICAL MODEL OF THE DEPENDENCE OF THE STARTING TORQUE OF AN ASYNCHRONOUS ELECTRICAL MOTOR ON THE INITIAL ANGULAR POSITION OF THE ROTOR
Authors: Hraniak Valerii , Dudnyk Volodymyr 
Published: June 2023

The current trend of recent decades is the growing role of the automated electric drive built on the basis of asynchronous electric motors. This is connected both with the development of theoretical approaches that allow to model the behavior of the latter with high accuracy, and with a significant increase in reliability and a decrease in the cost of power semiconductor technology, which in turn made it possible to improve operational characteristics and reduce the cost of such systems as a whole. The consequence of this trend is that asynchronous motors are increasingly used not only in classic electric drive systems with easy starting conditions, but also increasingly used in traction electric drives and electric drives with large starting moments, which were traditionally implemented on the basis of direct current motors. This circumstance leads to the appearance of additional technical difficulties in the design and operation of asynchronous electric motors, which is associated with the peculiarities of their natural mechanical characteristics, which have a slightly underestimated value of the starting torque. And although this shortcoming can be eliminated by increasing the power reserve of the engine when designing the electric drive, such a compromise solution will have significant disadvantages associated with a decrease in efficiency and an increase in the cost of the electric drive as a whole. It is obvious that this circumstance determines the need for further theoretical research aimed at improving the starting characteristics of asynchronous motors.
Considering what has been said, today the induction motor remains the most common electric machine used in various fields of activity. Moreover, the share of asynchronous motors used in industry is growing rapidly, and the scope of their use is constantly expanding. A. therefore, the development of a mathematical model of the dependence of the starting torque on the angular position of the rotor, which in the future would allow improving the starting characteristics of asynchronous motors, is an urgent scientific and applied problem that has significant practical value.
In the article, the equation of the dependence of the starting torque of an asynchronous motor on the initial position of its rotor is obtained, which makes it possible, taking into account the design features of the AD, to uniquely calculate the value of the mechanical torque that occurs on the motor shaft when it is started with the nominal supply voltage. The mathematical dependence of the deviation of the AD starting moment on the initial rotation angle of the rotor was obtained, which can be used as a corrective mathematical model of the AD control system. The simulation of the dependence of the torque of an asynchronous motor on the initial position of its rotor was carried out, which made it possible to confirm the adequacy of the obtained mathematical dependence. It is shown that the change of the starting torque during rotation of the AD rotor occurs according to the sinusoidal law. It is theoretically proven that deviations of the starting torque at different initial angular positions of the rotor can reach ± 6.5% of the nominal value.