Mathematical Intuition behind Electric Motors

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Emanuele Pesaresi

3:34:18

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1 - Introduction

1 - Introduction.mp4

02:46

2 - DC Motor

2 - DC motor stator rotor constants of the motor.mp4

12:41

3 - DC motor equation of the excitation and armature circuit.mp4

09:49

4 - Constitutive equations of the DC motor.mp4

04:36

5 - Angular velocity in stationary conditions.mp4

04:56

3 - 3phase asynchronous motor

6 - 3phase asynchronous motor windings in the stator and rotor.mp4

03:16

7 - Magnetic field generated by the phases of the stator.mp4

06:27

8 - Magnetic field generated by the phases of the stator part 2.mp4

12:29

9 - Total magnetic field generated by the phases of the stator.mp4

07:52

10 - Sinusoidal regime of 3phase asynchronous motors.mp4

15:08

11 - Electrical power in a 3phase asynchronous motor.mp4

11:13

12 - Simplified electrical power star and triangle configuration.mp4

05:02

13 - Circuit equations in the stator.mp4

03:46

14 - Total magnetic field in the air gap.mp4

09:55

15 - Calculation of the flux in the stator.mp4

11:00

16 - Circuit equation of the stator in vector space.mp4

05:03

17 - Fundamental equations of the rotor.mp4

08:16

18 - Isolating the term related to mechanical power.mp4

16:58

19 - Considerations on the terms related to energy conservation in the motor.mp4

05:44

20 - Equations of the 3phase asynchronous motor in the sinusoidal regime.mp4

10:36

21 - Angular velocity and torque.mp4

08:38

22 - Derivation of the equivalent circuit of the 3phase motor part 1.mp4

03:32

23 - Derivation of the equivalent circuit of the 3phase motor part 2.mp4

07:37

24 - Expression for the torque written with respect to frequencies.mp4

07:55

25 - Simplified expression for the torque.mp4

16:43

26 - Curve of the torque with respect to angular velocity.mp4

02:20

Description

DC motors and 3-phase 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

Who is this for?

students who want to understand DC motors and 3-phase asynchronous motors mathematically

More details

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 â€œslipâ€. The characteristic curve of the torque will also be plotted against the angular velocity of the motor.

Prerequisites
Students should be familiar with complex vectors and calculus. Besides, the knowledge of the following concepts from electromagnetism are recommended:

Â· Kirchhoff's laws
Â· Inductance, resistance, impedance
Â· Faraday-Lenz law of electromagnetism (which stems from Maxwell laws)
Who this course is for:
students who want to understand DC motors and 3-phase asynchronous motors mathematically

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I obtained my PhD in "Mechanics and Advanced Engineering Sciences" in 2021.I attained a Bachelor of Science and Master of Science in Mechanical engineering in 2015 and 2017 respectively, with honors from the University of Bologna.I was the teaching tutor for the course of Mechanics of Machines from the academic year 2018 until the end of 2021 at the University of Bologna (branch of Forlì).My passion for mathematics, physics and teaching has motivated me to lecture high school and university students.My approach as a teacher is to prove to students that memory is less important for an engineer, mathematician, or physicist, than learning how to tackle a problem through logical reasoning. I believe that a teacher of scientific subjects should try to develop his students’ curiosity about the subject, rather than just concentrating on acquisition of knowledge, however important that may also be. Students should be encouraged to dig deeper and build on their knowledge by continually questioning it, rather than accepting everything at face value without a thorough understanding.For enquiries (e.g. about tutoring, or advice related to the subjects spanned by my courses), you can either contact me on LinkedIn, or you can post questions in my courses' message boards, or you can also contact me via email or on my website.You can also find the updated versions of my courses on my website.

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