1 Institute of Mechatronics and Information Systems Electric Machines

2 Institute of Mechatronics and Information Systems Witold Kubiak, Ph.D., M.Sc., Eng. www: phone:

3 Institute of Mechatronics and Information Systems Fundamentals of electromagnetic phenomena in electro-mechanic energy conversion 1.Basic electrical quantities and dependencies 2.Basic magnetic quantities and properties 3.Basic mechanical quantities 4.Power conversion 5.Fundamental principles of electromagnetism

4 Institute of Mechatronics and Information Systems Basic electrical quantities E - electromotive force (EMF) – [V] (volt) U - voltage (potential difference) – [V] (volt) I - current – [A] (ampere) DC – direct current: (Ohm’s law) where: R - resistance – [Ω] (ohm)

5 Institute of Mechatronics and Information Systems AC – alternating current - instantaneous value where: - angular frequency - [rad/s]

6 Institute of Mechatronics and Information Systems AC – alternating current - instantaneous value where: - angular frequency - [rad/s] U peak, ( U m )- peak (maximum) value U RMS, ( U )- root mean square value U av - rectified average value

7 Institute of Mechatronics and Information Systems AC – alternating current Ohm’s law: where impedance Z :

8 Institute of Mechatronics and Information Systems AC – alternating current Reactance X depends on the type of reactive element. Inductive reactance: Capacitive reactance:

9 Institute of Mechatronics and Information Systems AC – alternating current Reactance introduces a phase shift between the current and voltage. Voltage lagging current Voltage leading current

10 Institute of Mechatronics and Information Systems Basic electrical circuits dependencies Kirchoff’s circuit laws:

11 Institute of Mechatronics and Information Systems Basic magnetic quantities F - magnetomotive force (MMF) – [A] (ampere) H - magnetic field strenght – [a/m] (ampere per metre) B - magnetic flux density – [T] (tesla)  - magnetic flux – [Wb] (weber) (Hopkinson’s law) where: R - reluctance – [1/h] (1/henry)

12 Institute of Mechatronics and Information Systems Basic magnetic properties Magnetisation curve in ferromagnetic materials μ 0 - permeability of vacuum [H/m] (henry per metre) μ r - relative permeability [-]

13 Institute of Mechatronics and Information Systems Basic magnetic properties Hysteresis in ferromagnetic materials B R - remanence H C - coercivity

14 Institute of Mechatronics and Information Systems Basic magnetic dependencies - magnetomotive force - magnetic flux - analogy to Kirchoff’s law

15 Institute of Mechatronics and Information Systems Basic mechanical quantities Linear movement F - force – [N] (newton) x - position – [m] (metre)] - velocity – [m/s] (metre per second) - acceleration – [m/s2] (metre per second square) (Newton’s law)

16 Institute of Mechatronics and Information Systems Basic mechanical quantities Rotational movement - torque – [Nm] (newton metre) α - angular position – [rad] (radian)] - angular velocity – [rad/s] (radian per second) - angular acceleration – [rad/s 2 ] (radian per second square) (analogy to Newton’s law)

17 Institute of Mechatronics and Information Systems Energy conversion (transformation)

18 Institute of Mechatronics and Information Systems Power conversion Efficiency

19 Institute of Mechatronics and Information Systems Electric power DC – direct current AC – alternating current, single phase apparent power: real power: reactive power:

20 Institute of Mechatronics and Information Systems Electric power AC – alternating current, three phase system

21 Institute of Mechatronics and Information Systems Electric power AC – alternating current, three phase system apparent power: Delta connection (Δ, D, d)Star connection (, Y, y)

22 Institute of Mechatronics and Information Systems Mechanical power Linear movement: Rotational movement:

23 Institute of Mechatronics and Information Systems Fundamental principles of electromagnetism Ampere’s circuital law:

24 Institute of Mechatronics and Information Systems Fundamental principles of electromagnetism Ampere’s circuital law:

25 Institute of Mechatronics and Information Systems Fundamental principles of electromagnetism Faraday’s law of induction:

26 Institute of Mechatronics and Information Systems Fundamental principles of electromagnetism Faraday’s law of induction:

27 Institute of Mechatronics and Information Systems Fundamental principles of electromagnetism Ampere’s force

28 Institute of Mechatronics and Information Systems Fundamental principles of electromagnetism Lorentz (Laplace) force

29 Institute of Mechatronics and Information Systems Thank You for Your attention