Chapter 3:electromechanical-energy-conversion

Chapter 3: Electromechanical-Energy-Conversion

Principles

This lecture note is based on the textbook # 1. Electric Machinery - A.E. Fitzgerald, Charles Kingsley, Jr., Stephen D. Umans- 6th edition- Mc Graw Hill series in Electrical Engineering. Power and Energy

• The electromechanical-energy-conversion process takes place through the medium of the electric or magnetic field of the conversion device of which the structures depend on their respective functions.

• Transducers: microphone, pickup, sensor, loudspeaker
• Force producing devices: solenoid, relay, electromagnet
• Continuous energy conversion equipment: motor, generator

This chapter is devoted to the principles of electromechanical energy conversion and the analysis of the devices accomplishing this function. Emphasis is placed on the analysis of systems that use magnetic fields as the conversion medium.

• The concepts and techniques can be applied to a wide range of engineering situations involving electromechanical energy conversion.
• Based on the energy method, we are to develop expressions for forces and torques in magnetic-field-based electromechanical systems.

§3.1 Forces and Torques in Magnetic Field Systems

• The Lorentz Force Law gives the force F on a particle of charge q in the presence of electric and magnetic fields.

$F=q(E+v\times B)$ (3.1)

F : newtons, q : coulombs, E : volts/meter, B : telsas, v : meters/second

• In a pure electric-field system,

F  qE (3.2)

• In pure magnetic-field systems,

$F=q(v\times B)$ (3.3)

Figure 3.1 Right-hand rule for F=( q x v) B .

• For situations where large numbers of charged particles are in motion,

$F_v=\rho (E+v\times B)$ (3.4)

$J=\mathrm{\rho v}$ (3.5)

$F_v=J\times B$ (3.6)

 (charge density): coulombs/ $m^3$ , F (force density): newtons/ $m^3$ ,

$J=\mathrm{\rho v}$ (current density): amperes/ $m^2$ .

• Most electromechanical-energy-conversion devices contain magnetic material.

• Forces act directly on the magnetic material of these devices which are constructed of rigid, nondeforming structures.
• The performance of these devices is typically determined by the net force, or torque, acting on the moving component. It is rarely necessary to calculate the details of the internal force distribution.
• Just as a compass needle tries to align with the earth’s magnetic field, the two sets of fields associated with the rotor and the stator of rotating machinery attempt to align, and torque is associated with their displacement from alignment.
  • In a motor, the stator magnetic field rotates ahead of that of the rotor, pulling on it and performing work.
  • For a generator, the rotor does the work on the stator.
    • The Energy Method

• Based on the principle of conservation of energy: energy is neither created nor destroyed; it is merely changed in form.
• Fig. 3.2(a): a magnetic-field-based electromechanical-energy-conversion device.
  • A lossless magnetic-energy-storage system with two terminals
  • The electric terminal has two terminal variables: e (voltage), i (current).
  • The mechanical terminal has two terminal variables: $f_{\text{fld}}$ (force), x (position)
  • The loss mechanism is separated from the energy-storage mechanism.