Page 32 - Electric Machinery Fundamentals

8 ELECTRIC MACHINERY FUNDAM ENTALS

Similarly, assuming constant torque, power in rotational motion is given by

p ~ dW ~ !i(T8) ~ T (d8) ~ TW
dt dt dt
p = TUJ (1-15)
Equation (1- 15) is very important in the study of electric machinery, because it
can describe the mechanical power on the shaft of a motor or generator.
Equation (1- 15) is the correct relationship among power, torque, and speed if
power is measured in watts, torque in newton-meters, and speed in radians per
second. If other units are used to measure any of the above quantities, then a
constant must be introduced into the equation for unit conversion factors. It is still
common in U.S. engil.1eering practice to measure torque in pound-feet, speed in rev-
olutions per minute, and power in either watts or horsepower. If the appropriate
conversion factors are included in each term, then Equation (1- 15) becomes
_ T (lb-ft) n (r/min)
P (watts ) - 7.04 (1-16)
{
_ T (Ib-ft) n (r/min)
)
P (h orsepower - 5252 (1-17)
I
where torque is measured in pound-feet and speed is measured in revolutions per 1
minute.

1,4 THE MAGNETIC FIELD
As previously stated, magnetic fields are the fundamental mechanism by which en-
ergy is convel1ed from one form to another in motors, generators, and transform-
ers. Four basic principles describe how magnetic fields are used in these devices:

1. A current-carrying wire produces a magnetic field in the area around it.
2. A time-changing magnetic field induces a voltage in a coil of wire if it passes
through that coil. (This is the basis of transformer action.)
3. A current-carrying wire in the presence of a magnetic field has a force in-
duced on it. (This is the basis of motor action.)
4. A moving wire in the presence of a magnetic field has a voltage induced in it.
(This is the basis of generator action.)
This section describes and elaborates on the production of a magnetic field by a
current-carrying wire, while later sections of this chapter explain the remaining
three principles.

Production of a Magnetic Field (
The basic law governing the production of a magnetic field by a current is
Ampere's law:
(1- 18)