Розрахунок швидкості обертання якоря колекторного двигуна постійного струму на базі параметричного подання його електричного кола

Abstract

UA: Для визначення швидкості обертання якоря колекторного двигуна постійного струму з послідовним збудженням в коло якоря вводять невелику тестову синусоїдну напругу з відомими параметрами. Показано, що спектр викликаного дією цієї напруги струму якоря складається з трьох компонент, при цьому частоти двох із них певним чином пов’язані зі швидкістю обертання якоря і частотою тестової напруги. Розглянуто шляхи технічної реалізації можливостей розрахунку вказаної швидкості, які випливають із цієї залежності.

EN: The armature rotation speed of a brushed DC motor is a defining characteristic for controlling the train movement layout or the operating mode of any electric drive. In practice, direct and indirect methods are used to measure this speed. The application of the direct method requires installing special sensors on the motor shaft. Such sensors are negatively affected by contamination and ambient temperature. The indirect method is based on monitoring either the armature current and voltage, or only its current. The equipment required for the indirect method is located in more favorable operating conditions. Its algorithmic flexibility and adaptability are prerequisites for creating an optimal motor control system. The objectivity of the speed measurement result increases if it is based on the use of informational signals whose intensity does not depend on the effects caused by the continuous DC supply voltage of the motor. This paper considers a series-wound brushed DC motor. The informational signal is an incremental armature current generated by injecting a small sinusoidal voltage in series into the armature circuit. To determine the time variation law of this current, a mathematical model of the armature electrical circuit of the aforementioned motor is formulated. A formal description of the time dependence of the mutual inductance between the armature winding and the field winding during constant speed armature rotation is provided. This inductance is a positive quantity that periodically varies in time at twice the armature rotation speed. As a result, the total inductance of the armature circuit is time-varying, meaning the specified circuit is a parametric electrical circuit. The intensity of such a parametric effect does not depend on the motor operating mode. The resulting description is integrated into the aforementioned mathematical model. It is shown that the time variation law of the incremental current is determined by a first-order linear non-homogeneous differential equation with variable coefficients. An analytical solution to this equation is obtained. According to this solution, the incremental current consists of three sinusoidal components, the frequencies of which simply depend on the known frequency of the injected voltage and the unknown armature rotation speed. By obtaining estimates of the frequencies of these components, the armature rotation speed can be calculated.