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

Os sistemas eletromecânicos representam uma mistura única de componentes elétricos e mecânicos que se integram perfeitamente.
Um motor CC é uma unidade que transforma tensão em deslocamento angular, produzindo um resultado mecânico a partir de uma entrada elétrica.
À medida que a corrente flui no circuito da armadura colocado dentro do campo magnético, ela experimenta uma força, levando ao torque que gira o rotor.
Como a armadura transporta corrente enquanto gira em um campo magnético, sua tensão se torna proporcional à velocidade.
A aplicação de uma equação de loop ao circuito da armadura transformada de Laplace revela uma correlação entre a corrente da armadura, a tensão da armadura aplicada e o EMF traseiro.
O torque do motor é proporcional à corrente da armadura, com a proporcionalidade constante dependendo das características do motor e do campo magnético.
O torque está relacionado à inércia e ao amortecimento viscoso na armadura.
A equação de torque é primeiro reescrita para expressá-la em termos da posição angular do eixo do motor.
Em seguida, supõe-se que a indutância da armadura seja consideravelmente menor do que a resistência da armadura.
Após a simplificação, a função de transferência é obtida.

sistemas eletromecânicos

Sistemas eletromecânicos são configurações complexas que combinam efetivamente elementos elétricos e mecânicos para atingir um resultado desejado. Central para muitos desses sistemas é o motor CC, um dispositivo que converte energia elétrica em movimento mecânico, permitindo várias aplicações que vão de ventiladores simples a mecanismos robóticos complexos.

Um componente-chave do motor CC é a armadura, um circuito rotativo posicionado dentro de um campo magnético. À medida que uma corrente elétrica passa pela armadura, ela encontra uma força devido à interação com o campo magnético, produzindo torque. Esse torque inicia a rotação do rotor, convertendo assim energia elétrica em movimento mecânico. A voltagem induzida na armadura é diretamente proporcional à sua velocidade, um fenômeno conhecido como força eletromotriz inversa (EMF).

Para analisar o comportamento de um motor CC, aplicamos princípios elétricos ao circuito da armadura. Ao empregar uma equação de loop e transformá-la pelo método de Laplace, podemos elucidar a relação entre a corrente da armadura (i_a), a tensão aplicada da armadura (V_a) e a EMF reversa (E_b). A equação é dada por:

<img alt="Equation1" src="/files/ftp_upload/16098/16098_PT%20EQUATION_1.svg" style="height: 32px;">

Onde R_a representa a resistência da armadura e E_b representa a EMF traseira.

No domínio s, o torque (T) produzido pelo motor é diretamente proporcional à corrente da armadura, descrita por:

<img alt="Equation2" src="/files/ftp_upload/16098/16098_PT%20EQUATION_2.svg" style="height: 20px;">

​Aqui, k_t é a constante de torque. Este torque também pode ser escrito em termos da inércia (J) do rotor:

<img alt="Equation3" src="/files/ftp_upload/16098/16098_PT%20EQUATION_3.svg" style="height: 20px;">

Ao expressar o torque em termos da posição angular (θ) do eixo do motor e simplificá-lo, pode-se derivar a função de transferência. Supondo que a indutância da armadura seja desprezível em comparação com a resistência da armadura, a função de transferência simplificada do motor CC se torna:

<img alt="Equation4" src="/files/ftp_upload/16098/16098_PT%20EQUATION_4.svg" style="height: 64px;">

Esta função de transferência fornece uma compreensão abrangente da resposta dinâmica do motor, ligando a entrada elétrica à saída mecânica e facilitando o projeto e o controle de sistemas eletromecânicos.

Sistemas eletromecânicos

Os sistemas eletromecânicos representam uma mistura única de componentes elétricos e mecânicos que se integram perfeitamente.
Um motor DC é uma unidade que transforma ...

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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

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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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