0195136047.pdf

506 ELECTROMECHANICS

Electric energy

Motor

→

←

Generator

Mechanical energy

Electromechanical energy converters, simply known as electric machines, embody three essential

features: (1) an electric system, (2) a mechanical system, and (3) a coupling field. Figure 12.1.1

is a schematic representation of an ideal electric machine (or a lossless electromechanical device)

for which the following relations hold:

Electric input (or output) energyvit=mechanical output (or input) energyTωmt

or

Electric input (or output) powervi=mechanical output (or input) powerTωm(12.1.1)

wherevandiare the voltage and the current associated with the electrical port, andTandωmare

the torque and the angular rotational velocity associated with the mechanical port.

The principle ofconservation of energymay be stated as follows: Energy can be neither

created nor destroyed, even though, within an isolated system, energy may be converted from one

form to another form, and transferred from an energy source to an energy sink. The total energy

in the system is constant.

A practical electromechanical system with losses can be represented by adding on the lossy

portion of the electric system and the lossy portion of the mechanical system modeled externally.

Excluding all types of dissipation and losses makes the energy-conversion part to belosslessor

conservativewith a coupling field.

Both electric and magnetic fields store energy, from which useful mechanical forces and

torques can be derived. With a normal working electric field intensity of about 3× 106 V/m, the

stored electric-energy density is on the order of

1

2

ε 0 E^2 =

1

2

10 −^9

36 π

( 3 × 106 )^2 ∼=40 J/m^3

whereε 0 is the permittivity of free space, given by 10−^6 / 36 πor 8. 854 × 10 −^12 F/m, andEis

the electric field intensity. This corresponds to a force density of 40 N/m^2. The stored magnetic

energy density in air, on the other hand, with a normal working magnetic flux density of about

1.6 T, comes to

1

2

B^2

μ 0

=

1

2

1. 62

4 π× 10 −^7

∼= 1 × 106 J/m^3

whereμ 0 is the permeability of free space, andBis the magnetic flux density. As this is nearly

25,000 times as much as for the electric field, almost all industrial electric machines are magnetic

Lossless

electromechanical

device

with coupling

field

Electrical

port

Mechanical

port

Motor

Generator

i

v

v, iT, ωm

ωm, T

Figure 12.1.1Schematic repre-

sentation of a lossless electrome-

chanical device.