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9.8 Asynchronous Motor Operation

The stator creates a three-phase current system with i1 (t), i2 (t), and i3 (t) flowing through its windings when its three phases receive a balanced three-phase voltage system (as shown in the right figure above). According to Ferraris' theorem, this current system produces a rotating field at a constant speed. We can plot the rotation of the magnetic field that the stator phases generate (Fig. 9.23). The rotor follows the rotating magnetic field but rotates asynchronously, at a lower speed.

A series of circular diagrams at the top illustrate rotational motion with arrows pointing in various directions. Below, a wave pattern is depicted with two overlapping sinusoidal waves, one above the other, intersecting at regular intervals. The image conveys concepts of rotational dynamics and wave interference.

Fig. 9.23 Three phase voltage induction waveform. Source: from wikicommons under free to use license [12]

According to Faraday's and Lenz's law, it appears magnetic flux due to induced rotor current (Fig. 9.24).

Diagram of an electric motor showing a rotating stator field. The outer circle represents the stator with labeled north (N) and south (S) poles. Arrows indicate the direction of the rotating stator field. Inside, a smaller circle represents the rotor, with arrows showing the flux due to induced rotor current. The diagram illustrates the interaction between the stator and rotor fields.

Fig. 9.24 Flux due to induced rotor current. Source: own elaboration

The rotor windings experience electromotive forces because of this rotating field. Current flows through the rotor windings as a result of the connections made between them, either by short-circuiting the windings with the rings in the squirrel cage, or by connecting the ends and beginnings. These groups of currents, under the influence of a magnetic field, generate forces and torques according to Laplace's law. Below we see the forces and components over a squirrel-cage rotor (Fig. 9.25).

Fig. 9.25 Direction of forces in a squirrel-cage induction machine. Source: own elaboration

These forces and torques system rotate the rotor at a speed n2 in similar direction as n1. However, it is important to note that the final rotor speed, n2, never equals n1 due to Faraday's law, which requires a relative speed between the magnetic field and conductor (Fig. 9.26).

Fig. 9.26 Relative speed between rotor and magnetic flux. Source: own elaboration

Keep in mind that the rotor and magnetic flux speed are very close, but they are not similar. When the rotor rotates at n2, the slip velocity (nS) between the rotor and the stator rotating field causes the frequency of the rotor's electromotive forces as well as the frequency of the rotor currents to occur. This frequency is expressed as:

fs = p·ns/60 = p·s·n1/60 = s·f1 (9.5)

In a vacuum, meaning that no load connects the rotor shaft, the rotor speed is almost the same of the magnetic field. Consequently, nS is almost zero. When the machine is loaded, the speed increases but it is still close to zero. A low nS value suggests that the frequency of rotor currents is low, lowering the iron losses in the machine's rotor. Therefore, the sheet of metal that we use to manufacture rotors is of lower quality than the sheet metal we use to make stators.

练习题

Why does the rotor speed $n_{2}$ in an asynchronous motor never equal the synchronous speed $n_{1}$ of the rotating magnetic field?

A. Because the rotor has too much mechanical friction

B. Because Faraday's law requires a relative speed between the magnetic field and conductor to induce EMF

C. Because the stator windings cannot produce a strong enough field

D. Because the squirrel cage rings limit the maximum rotor speed

In an induction motor, if the stator supply frequency is $f_{1} = 50$ Hz and the slip is $s = 0.04$ , what is the frequency of the rotor currents $f_{s}$ ?

f_{s} = 50

f_{s} = 2

f_{s} = 48

f_{s} = 200

Which of the following physical laws are directly involved in the operation of an asynchronous motor?

A. Faraday's law of electromagnetic induction

B. Lenz's law

C. Laplace's law (force on current-carrying conductor)

D. Ohm's law only

E. Ferraris' theorem for rotating magnetic fields

According to Ferraris' theorem, a balanced three-phase current system in the stator windings produces a rotating magnetic field at constant speed.

The rotor of an asynchronous motor rotates in the opposite direction to the rotating stator magnetic field.

When an asynchronous motor operates with no load connected to its rotor shaft, the slip velocity $n_{S}$ is almost zero.

The slip velocity ( $n_{S}$ ) between the rotor and the stator rotating field causes the frequency of the rotor's ___ as well as the frequency of the rotor currents.

Because the frequency of rotor currents is low during normal operation, the iron losses in the machine's rotor are ___, allowing lower quality sheet metal to be used for rotor construction compared to the stator.

Explain why the rotor of an asynchronous motor rotates at a lower speed than the synchronous speed of the stator's rotating magnetic field.

Describe how current flows through the rotor windings of a squirrel-cage induction motor and how this differs from a wound rotor.

A three-phase induction motor has its stator windings distributed in slots and connected in a star configuration. When balanced three-phase voltages are applied, these windings carry currents $i_{1} (t)$ , $i_{2} (t)$ , and $i_{3} (t)$ . According to Ferraris' theorem, what is the direct result of this current system?

A. A pulsating magnetic field that alternates in direction

B. A rotating magnetic field at constant speed

C. Three separate stationary magnetic fields, one per phase

D. A magnetic field that rotates only when the rotor is moving

Which of the following statements correctly describe the relationship between the stator and rotor in an operating asynchronous motor? Select all that apply.

A. The stator winding acts as the inductor and creates the rotating magnetic field

B. The rotor speed n₂ never equals the synchronous speed n₁ due to Faraday's law

C. The wound rotor must have the same number of poles as the stator

D. The rotor rotates in the opposite direction to the stator field

E. A relative speed between the magnetic field and rotor conductor is necessary for EMF induction

In a squirrel-cage induction motor, the rotor bars are short-circuited by end rings, and the stator's rotating field automatically creates an equal number of poles in both the rotor and stator.

When an asynchronous motor operates with no load connected to the rotor shaft, the rotor speed is nearly equal to the magnetic field speed, making the slip velocity $n_{S}$ almost ___.

Explain why the sheet metal used to manufacture rotors can be of lower quality than the sheet metal used for stators in an asynchronous machine.

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9.8 Asynchronous Motor Operation