58 lines
2.0 KiB
Markdown
58 lines
2.0 KiB
Markdown
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---
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author: Akbar Rahman
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date: \today
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title: MMME2051 // DC Motors
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tags: [ dc_motors, motors ]
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uuid: b8313ef8-ef1e-486d-8031-52c39ac88751
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lecture_slides: [ ./lecture_slides/MMME2051EMD_Lecture9.pdf ]
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lecture_notes: []
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exercise_sheets: [ ./seminar_worksheets/Exercise Sheet 12 - DC Motors.pdf ]
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---
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Relevant lecture slides are 15-26.
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Two worked examples can be found in the lecture slides 24-26.
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In a simple DC motor, the stator is either a permanent magnet or a coil with a
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current flowing through it.
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Both create a constant magnetic field.
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The rotor is just a coil with current flowing through it by a (different) DC power supply:
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Note the commutator and brushes.
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This flips the current direction inside the coil, flipping the direction of the induced magnetic field,
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and therefore flipping the direction of the resultant force.
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The split in the commutator is placed such that the current flips just as the force would.
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This is [visualised in this video (timestamped to 50s)](https://youtu.be/LAtPHANEfQo?t=50).
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# Torque, $T$
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$$T = rBIl = KI$$
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using $F = BIl$ and $T = rF$, where $B$ is magnetic field strength, $I$ is current flowing through coil, $l$ is length
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of coil in the magnetic field,
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$K$ is a constant which varies with motor designs, and $I$ is the current through the motor.
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# Back EMF, $E_b$
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$$ E_b = Bvl = K\omega $$
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where $B$ is magnetic field strength, $v$ is linear velocity, $l$ is length of coil in field,
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$K$ is a constant defined by the motor, and $\omega$ is angular velocity.
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# Relating Voltage to Motor Performance
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There are two equations which govern the motor's performance:
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$$V_\text{in} = E_b + IR$$
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\begin{equation} \label{eqn_torquespeed}
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V_\text{in} = K\omega + \frac{T}{K}R
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\end{equation}
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