torque a. the rigid supporting structure of an object

A. No, they aren’t

B. Yes, they are

C. Yes, they do

D. No, they don’t

10. Do typical supply voltages range from 230 volts line-to-line for motors of relatively low power to about 15 kilovolts line-to-line?

A. No, they don’t

B. Yes, they do

C. No, they aren’t

D. Yes, they are

Induction motors

The simplest type of induction motor is shown in cross section in the figure. A three-phase set of stator windings is inserted in slots in the stator iron. These windings may be connected either in a wye configuration, normally without external connection to the neutral point, or in a delta configuration. The rotor consists of a cylindrical iron core with conductors placed in slots around the surface. In the most usual form, these rotor conductors are connected together at each end of the rotor by a conducting end ring.

The basis of operation of the induction motor may be developed by first assuming that the stator windings are connected to a three-phase electric supply and that a set of three sinusoidal currents of the form shown in the figure flow in the stator windings. This figure shows the effect of these currents in producing a magnetic field across the air gap of the machine for six instants in a cycle. For simplicity, only the central conductor loop for each phase winding is shown. At the instant t₁ in the figure, the current in phase a is maximum positive, while that in phases b and c is half that value negative. The result is a magnetic field with an approximately sinusoidal distribution around the air gap with a maximum outward value at the top and a maximum inward value at the bottom. At time t₂ in the figure (i.e., one-sixth of a cycle later), the current in phase c is maximum negative, while that in both phase b and phase a is half value positive. The result, as shown for t₂ in the figure, is again a sinusoidally distributed magnetic field but rotated 60° counterclockwise. Examination of the current distribution for t₃, t₄, t₅, and t₆ shows that the magnetic field continues to rotate as time progresses. The field completes one revolution in one cycle of the stator currents. Thus, the combined effect of three equal sinusoidal currents, uniformly displaced in time and flowing in three stator windings uniformly displaced in angular position, is to produce a rotating magnetic field with a constant magnitude and a mechanical angular velocity that depends on the frequency of the electric supply.

The rotational motion of the magnetic field with respect to the rotor conductors causes a voltage to be induced in each, proportional to the magnitude and the velocity of the field relative to the conductors. Since the rotor conductors are short-circuited together at each end, the effect will be to cause currents to flow in these conductors. In the simplest mode of operation, these currents will be about equal to the induced voltage divided by the conductor resistance. The pattern of rotor currents for the instant t₁ of the figure is shown in this figure. The currents are seen to be approximately sinusoidally distributed around the rotor periphery and to be located so as to produce a counterclockwise torque on the rotor (i.e., a torque in the same direction as the field rotation). This torque acts to accelerate the rotor and to rotate the mechanical load. As the rotational speed of the rotor increases, its speed relative to that of the rotating field decreases. Thus, the induced voltage is reduced, leading to a proportional reduction in rotor conductor current and in torque. The rotor speed reaches a steady value when the torque produced by the rotor currents equals the torque required at that speed by the load with no excess torque available for accelerating the combined inertia of the load and the motor.

The mechanical output power must be provided by an electrical input power. The original stator currents shown in the figure are just sufficient to produce the rotating magnetic field. To maintain this rotating field in the presence of the rotor currents of the figure, it is necessary that the stator windings carry an additional component of sinusoidal current of such a magnitude and phase as to cancel the effect of the magnetic field that would otherwise be produced by the rotor currents in the figure. The total stator current in each phase winding is then the sum of a sinusoidal component to produce the magnetic field and another sinusoid, leading the first by one-quarter of a cycle, or 90°, to provide the required electrical power. The second, or power, component of the current is in phase with the voltage applied to the stator, while the first, or magnetizing, component lags the applied voltage by a quarter cycle, or 90°. At rated load, this magnetizing component is usually in the range of 0.4 to 0.6 of the magnitude of power component.

A majority of three-phase induction motors operate with their stator windings connected directly to a three-phase electric supply of constant voltage and constant frequency. Typical supply voltages range from 230 volts line-to-line for motors of relatively low power (e.g., 0.5 to 50 kilowatts) to about 15 kilovolts line-to-line for high-power motors up to about 10 megawatts.

Except for a small voltage drop in the resistance of the stator winding, the supply voltage is matched by the time rate of change of the magnetic flux in the stator of the machine. Thus, with a constant-frequency, constant-voltage supply, the magnitude of the rotating magnetic field is held constant, and the torque is roughly proportional to the power component of the supply current.

With the induction motor shown in the foregoing figures, the magnetic field rotates through one revolution for each cycle of the supply frequency. For a 60-hertz supply, the field speed is then 60 revolutions per second, or 3,600 per minute. The rotor speed is less than the speed of the field by an amount that is just enough to induce the required voltage in the rotor conductors to produce the rotor current needed for the load torque. At full load, the speed is typically 0.5 to 5 percent lower than the field speed (often called synchronous speed), with the higher percentage applying to smaller motors. This difference in speed is frequently referred to as the slip.

Other synchronous speeds can be obtained with a constant frequency supply by building a machine with a larger number of pairs of magnetic poles, as opposed to the two-pole construction of the figure. The possible values of magnetic-field speed in revolutions per minute are 120 f/p, where f is the frequency in hertz (cycles per second) and p is the number of poles (which must be an even number). A given iron frame can be wound for any one of several possible numbers of pole pairs by using coils that span an angle of approximately (360/p)°. The torque available from the machine frame will remain unchanged, since it is proportional to the product of the magnetic field and the allowable coil current. Thus, the power rating for the frame, being the product of torque and speed, will be roughly inversely proportional to the number of pole pairs. The most common synchronous speeds for 60-hertz motors are 1,800 and 1,200 revolutions per minute.

Exercise 5. Read the text above once again and choose the right answers to the following questions: