Mathematical Intuition Behind Electric Motors

What you'll learn
The mathematics of the DC motor
The mathematics of the 3-phase asynchronous motor
How to derive the equations of the DC motor and the 3-phase asynchronous motor
The electromagnetic field generated by the DC motor and 3-phase asynchronous motor
the angular velocity and torque of the DC motor and 3-phase asynchronous motor
Requirements
Kirchhoff's laws
the concept of: Inductance, resistance, impedance
Faraday-Lenz law of electromagnetism (also Maxwell laws)
calculus
Description
In this course the mathematics of electric motors are derived. In particular, the constitutive equations of the DC motor and the 3-phase asynchronous motor are constructed starting from the principles of electromagnetism.In the DC motor, the analysis of the stator and the rotor will lead us to equations containing the torque generated by the motor, the angular velocity, the current in the armature circuit, the current in the excitation circuit, the electromotive force generated by induction, the excitation flux, and more. We will explain the behavior of the motor through the equations; their derivation will foster comprehensive understanding of the dynamics of the motor.The theory of the 3-phase asynchronous motor will require more lectures to be developed, due to the greater physical and mathematical difficulty of this type of motors. The stator and the rotor are analyzed using complex vectors. First, the electromagnetic field in the air gap between the stator and the rotor is derived, which will then allow to find the flux. Finding the flux is necessary because this physical quantity appears in the constitutive equations of the motor. Besides, the mechanical and electric power generated by the motor will be discussed and mathematically derived in the course, as well as the torque, angular frequency of the rotor, and the parameter called "slip". The characteristic curve of the torque will also be plotted against the angular velocity of the motor.PrerequisitesStudents should be familiar with complex vectors and calculus. Besides, the knowledge of the following concepts from electromagnetism are recommended:· Kirchhoff's laws· Inductance, resistance, impedance· Faraday-Lenz law of electromagnetism (which stems from Maxwell laws)
Overview
Section 1: Introduction
Lecture 1 Introduction
Section 2: DC Motor
Lecture 2 DC motor, stator, rotor, constants of the motor
Lecture 3 DC motor, equation of the excitation and armature circuit
Lecture 4 Constitutive equations of the DC motor
Lecture 5 Angular velocity in stationary conditions
Section 3: 3-phase asynchronous motor
Lecture 6 3-phase asynchronous motor: windings in the stator and rotor
Lecture 7 Magnetic field generated by the phases of the stator
Lecture 8 Magnetic field generated by the phases of the stator part 2
Lecture 9 Total magnetic field generated by the phases of the stator
Lecture 10 Sinusoidal regime of 3-phase asynchronous motors
Lecture 11 Electrical power in a 3-phase asynchronous motor
Lecture 12 Simplified electrical power, star and triangle configuration
Lecture 13 Circuit equations in the stator
Lecture 14 Total magnetic field in the air gap
Lecture 15 Calculation of the flux in the stator
Lecture 16 Circuit equation of the stator in vector space
Lecture 17 Fundamental equations of the rotor
Lecture 18 Isolating the term related to mechanical power
Lecture 19 Considerations on the terms related to energy conservation in the motor
Lecture 20 Equations of the 3-phase asynchronous motor in the sinusoidal regime
Lecture 21 Angular velocity and torque
Lecture 22 Derivation of the equivalent circuit of the 3-phase motor part 1
Lecture 23 Derivation of the equivalent circuit of the 3-phase motor part 2
Lecture 24 Expression for the torque written with respect to frequencies
Lecture 25 Simplified expression for the torque
Lecture 26 Curve of the torque with respect to angular velocity
students who want to understand DC motors and 3-phase asynchronous motors mathematically


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