Name: dc motor modeling in electromechanical systems
Uploaded: 2024-09-26T13:17:19.000Z
Duration: 1 min 19 s
Channel: JoVE

Los sistemas electromecánicos representan una combinación única de componentes eléctricos y mecánicos que se integran a la perfección.
Un motor de CC es una unidad que transforma el voltaje en desplazamiento angular, produciendo un resultado mecánico a partir de una entrada eléctrica.
A medida que la corriente fluye en el circuito de la armadura ubicada dentro del campo magnético, experimenta una fuerza, lo que conduce a un par que hace girar el rotor.
Dado que la armadura transporta corriente mientras gira en un campo magnético, su voltaje se vuelve proporcional a la velocidad.
La aplicación de una ecuación de bucle al circuito de inducido transformado de Laplace revela una correlación entre la corriente de inducido, el voltaje de inducido aplicado y el EMF posterior.
El par del motor es proporcional a la corriente del inducido, con una constante de proporcionalidad en función de las características del motor y del campo magnético.
El par está relacionado con la inercia y la amortiguación viscosa en la armadura.
La ecuación de par se reescribe primero para expresarla en términos de la posición angular del eje del motor.
Después de esto, se supone que la inductancia de la armadura es considerablemente menor que la resistencia de la armadura.
Tras la simplificación, se obtiene la función de transferencia.

sistemas electromecánicos

Los sistemas electromecánicos son configuraciones complejas que combinan eficazmente elementos eléctricos y mecánicos para lograr un resultado deseado. En muchos de estos sistemas, el motor de CC es un dispositivo que convierte la energía eléctrica en movimiento mecánico, lo que permite diversas aplicaciones que van desde ventiladores simples hasta mecanismos robóticos complejos.

Un componente clave del motor de CC es la armadura, un circuito giratorio ubicado dentro de un campo magnético. Cuando una corriente eléctrica pasa a través de la armadura, encuentra una fuerza debido a la interacción con el campo magnético, lo que produce un par motor. Este par motor inicia la rotación del rotor, convirtiendo así la energía eléctrica en movimiento mecánico.La tensión inducido en la armadura es directamente proporcional a su velocidad, un fenómeno conocido como fuerza contraelectromotriz (FEM).

Para analizar el comportamiento de un motor de CC, aplicamos principios eléctricos al circuito de la armadura. Al emplear una ecuación de bucle y transformarla mediante el método de Laplace, podemos dilucidar la relación entre la corriente de la armadura (i_a), la tensión aplicado a la armadura (V_a) y la FEM (E_b). La ecuación se da por:

<img alt="Equation1" src="/files/ftp_upload/16098/16098_PT%20EQUATION_1.svg" style="text-align: center; height: 32px;">

Donde R_a representa la resistencia de la armadura y E_b representa la fuerza contraelectromotriz.

En el dominio s, el par (T) producido por el motor es directamente proporcional a la corriente de la armadura, descrita por:

<img alt="Equation2" src="/files/ftp_upload/16098/16098_PT%20EQUATION_2.svg" style="text-align: center; height: 20px;">

Aquí, k_t es la constante de par. Este par también se puede escribir en términos de la inercia (J) del rotor:

<img alt="Equation3" src="/files/ftp_upload/16098/16098_PT%20EQUATION_3.svg" style="text-align: center; height: 20px;">

Al expresar el par en términos de la posición angular (θ) del eje del motor y simplificarlo, se puede derivar la función de transferencia. Suponiendo que la inductancia de la armadura es insignificante en comparación con la resistencia de la armadura, la función de transferencia simplificada del motor de CC se convierte en:

<img alt="Equation4" src="/files/ftp_upload/16098/16098_PT%20EQUATION_4.svg" style="text-align: center; height: 64px;">

Esta función de transferencia proporciona una comprensión integral de la respuesta dinámica del motor, vinculando la entrada eléctrica con la salida mecánica y facilitando el diseño y el control de sistemas electromecánicos.

Sistemas electromecánicos

Los sistemas electromecánicos representan una combinación única de componentes eléctricos y mecánicos que se integran a la perfección.
Un motor de corriente continua es una unidad que transforma ...

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Electro-mechanical Systems

dc motor modeling in electromechanical systems

DC motor modeling is a key part of electromechanical systems. These systems combine electrical parts and mechanical parts to produce a useful output. A DC motor is one common example because it turns electrical energy into mechanical motion. It is used in many places, from simple fans to complex robotic mechanisms.

Inside the DC motor, the armature is a rotating circuit placed in a magnetic field. When current flows through the armature, it experiences a force from the magnetic field. That force creates torque, which starts the rotor spinning. As the motor turns, it also produces a voltage in the armature that rises with speed. This voltage is called back electromotive force, or back EMF.

To study how the motor behaves, electrical principles are applied to the armature circuit. A loop equation is written for the armature current, the applied armature voltage, and the back EMF. The equation can then be transformed with the Laplace method to help show the motor response in the s domain. This makes it easier to relate the input voltage to the motor’s electrical and mechanical behavior.

The torque produced by the motor is directly proportional to the armature current in the s domain. The torque constant, k_t, sets that relationship. Torque can also be written in terms of the rotor inertia, J, and the motion of the motor shaft. By expressing the torque through the angular position, θ, and simplifying the result, a transfer function can be derived. When armature inductance is assumed to be negligible compared with armature resistance, the DC motor transfer function becomes simpler and shows how electrical input leads to mechanical output.

DC Motor Modeling in Electromechanical Systems

dc-motor-modeling-electromechanical-systems

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Learn how a DC motor turns electrical input into motion, how back EMF affects armature current, and how Laplace methods help derive the transfer function.

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DC Motor Modeling in Electromechanical Systems

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