To begin our studies on Electrical Machines, let's introduce some definitions and establish some
basic principles of Electromagnetism. It should be noted that there are several types of motors, and on this site we are
interested in Direct Current motors, Induction motors and the basic principles of motors
Synchronous. From the knowledge of these types of engines, it is very easy to understand the other existing types,
for almost all are derived from those mentioned above.
2. Machine Basics Principles
The study of Electromagnetism brings with it a very complex theory if we want to be exact.
Therefore, in practice, it is desirable to simplify the problem by making some simplifications that
lead to very satisfactory results and very close to the exact values. So, for example,
in the study of Electric Machines, some magnitudes are such that the term of
current of displacement in the Maxwell equations can be disregarded without prejudice to the
final result. This term takes into
counts the magnetic fields produced in space by time-varying electric fields,
and closely associated with the production of electromagnetic waves.
In the course of this study we will come across several definitions and symbols to designate the
variables. So, below is a list of the main ones.
H - Intensidade do Campo Magnético
B - Densidade do Fluxo Magnético (ou Indução Magnética)
μ_{o} - Permeabilidade Magnética no Vácuo
μ_{r} - Permeabilidade Magnética Relativa
F - Força Magnetomotriz
N - Número de espiras do Enrolamento
A_{c} - Área da seção transversal do núcleo
l_{c} - Comprimento do circuito magnético
g - Comprimento do gap (folga) entre circuitos magnéticos
Φ - Intensidade do Fluxo Magnético
To begin the study of electrical machines, let us begin by introducing the concept of a
DC Linear Machine, as it follows the same principles and presents the same behavior as the
real generators and engines.
2.1 DC Linear Machine
Basically, a DC linear machine consists of a battery, a resistor, and a switch connected to
a pair of frictionless tracks. Along the tracks there is a constant magnetic field of uniform density.
and oriented into the page. A conductive metal bar sits on the rails,
having freedom of movement along the rails. A basic schematic of this machine is shown.
in Figure 101-01.
The behavior of this machine can be determined by applying four basic equations to the machine.
The equations are the following:
1 - The equation of the force induced in a conductor in the presence of a magnetic field, given by eq. 76-02,
already studied in chapter 76 and repeated here for clarity.
eq. 101-01
2 - The equation of voltage induced in a conductor moving in the presence of a magnetic field.
eq. 101-02
3 - Kirchhoff's voltage law for this machine. From Figure 101-01, we can write that.
eq. 101-03
4 - Newton's law for the conductor bar lying on the rails.
eq. 101-04
We use these four equations as tools to analyze the basic behavior of this DC machine.
2.1.1 Starting the Linear DC Machine
Closing the key, we are able to start this machine. Thus, when we close the key, there will be a
current flowing through the circuit and we can determine its value using the Kirchhoff's law of voltages,
that is
eq. 101-05
Initially, the bar is at rest, so ε_{ind} = 0, and the equation shown above reduces to
I = V / R. Thus, the current will flow down through the bar and close the circuit through the rails.
However, we know that a current flowing through a conducting wire immersed in a magnetic field induces a force
in the wire, given by eq. 101-01. As a reminder, we have:
eq. 101-01
And that force is directed to the right. Therefore, by Newton's law, the bar will accelerate to the right.
But when accelerating, the bar gains speed and a voltage will be induced on it. The positive polarity of
Voltage induced in the bar is at the top of the bar. Thus, current flows through the circuit in a clockwise direction.
As we saw in the previous item, the induced voltage, for the case of Figure 101-01, is given by eq. 101-02.
As the induced voltage grows due to the movement of the bar, analyzing eq. 101-05 we conclude that
the current through the circuit decreases. Eventually, as a result of this action, the bar will reach a constant velocity.
steady state, such that the net force on the bar becomes zero. This will happen when
ε_{ind} has grown to equal the battery voltage, V. The bar will continue to move
indefinitely at steady state speed as long as there is no load, unless some external force
come to disturb her.
This is precisely the behavior observed when starting real motors.
2.1.2 A Máquina Linear CC como Motor
Let's assume that initially the linear machine is operating at steady state with no load acting on it.
Now let's imagine that a force is applied to the bar, which we call F_{load}, in the sense of opposing the
your movement. The application of this force will result in a net force on the rod in the opposite direction of motion,
that is, F_{liq} = F_{load} - F_{wire}. As a consequence, the force will make the bar lower
your speed.
However, as soon as the bar starts to slow down, the voltage induced in the bar drops, and as the induced voltage decreases,
the current flow in the bar increases, according to eq. 101-05. Thus, the force induced in the bar also increases. The effect
The sum total of all these events is that the induced force grows until it becomes equal and opposite to the loading force and the
bar starts moving again at a steady state, but with a slower speed.
Now, there is a force induced in the direction of movement of the bar. Power is also being converted from electrical form
to mechanical form to keep the bar moving. And how is power converted from electrical form to
mechanical form, so it is operating as an engine. We can express this power as follows: