The Torque of an Induction Motor

By -

The Torque of an Induction Motor

An expression for the torque of an induction motor may be deri­ved from the equation of the mechanical power, Pm , available at. its shaft

T = Pm/ɷrot                              (14.22)

where ɷrot is the angular velocity of the rotor.

Since the angular velocity of the rotor is

ɷrot = 2πn/60

it. follows that the angular velocity of the magnetic field of a motor, ɷf , and that of its rotor, ɷrot are connected by the slip

s = (nl - n)/ nl = (ɷf - ɷrot)/ɷf

or

ɷrot = ɷf (1 - s)

The angular velocity of the rotating magnetic field, ɷf , is equal to the angular frequency of the sinewave current in the stator phase windings, 00, for a two-pole motor (p = 1). In the general case of a multipole motor the angular velocity of the rotating magnetic field is

ɷf = ɷ/p

where p is the number of pole pairs.

On expressing ɷrot in terms of W in Eq. (14.22), we get

T = P/(1-s)*Pm                      (14.23)

From the equivalent circuit of a motor phase, Fig 18 , it fol­lows that the mechanical power at the. shaft is

The Torque of an Induction Motor

Substituting Eq. (14.24) into Eq. (14.23) yields an expression for the torque. of an induction motor

T = m2prw2I22/ɷs (14.25)

Since, on the basis of the phasor diagram in Fig 15

rw2I2 = E2 cos φ2

and

E2/s = E2,st

it follows that

T = E2,stI2 (m2P/ɷ) cos φ2                                               (14.26)

On recalling Eq. (14.12),

E2,st =4.44fw2kw2Φr = ɷw2kw2Φr/√2

Eq. (14.26) may be re-cast as follows

T =(1/√2) m2Pw2kw2ΦrI2 cos φ2=const X ΦrI2 cos φ2                                  (14.27)

That is, the torque of an induction motor is proportional to the pro­duct of the rotating magnetic flux and the current in the rotor win­ding.

Popular posts from this blog

Microelectronics: Introduction, Evolution Of Microelectronics And vacuum-Tube Equipment.

By -
Image
MICROELECTRONICS LEARNING OBJECTIVES Learning objectives are stated at the beginning of each topic. These learning objectives serve as a preview of the information you are expected to learn in the topic. The comprehensive check questions are based on the objectives. By successfully completing the OCC-ECC, you indicate that you have met the objectives and have learned the information. The learning objectives are listed below. Upon completion of this topic, you will be able to: 1. Outline the progress made in the history of microelectronics. 2. Describe the evolution of microelectronics from point-to-point wiring through high element density state-of-the-art microelectronics. 3. List the advantages and disadvantages of point-to-point wiring and high element density state-of- the-art microelectronics. 4. Identify printed circuit boards, diodes, transistors, and the various types of integrated circuits. Describe the fabrication techniques of these components. 5. Define th...
Read more

Summary of direct current generators

By -
Image
SUMMARY This chapter introduced you to the basic principles concerning direct current generators. The different types of dc generators and their characteristics were covered. The following information provides a summary of the major subjects of the chapter for your review. MAGNETIC INDUCTION takes place when a conductor is moved in a magnetic field in such a way that it cuts flux lines, and a voltage (emf) is induced in the conductor. THE LEFT-HAND RULE FOR GENERATORS states that when the thumb, forefinger, and middle finger of the left hand are extended at right angles to each other so that the thumb indicates the direction of movement of the conductor in the magnetic field, and the forefinger points in the direction of the flux lines (north to south), the middle finger shows the direction of induced emf in the conductor. AN ELEMENTARY GENERATOR consists of a single coil rotated in a magnetic field. It produces an ac voltage. A BASI...
Read more

Newton's third law of motion ( Action & Reaction ! )

By -
Image
          To every action there is an equal and opposite reaction In other words, if two objects interact, then the force exerted by object 1 on object 2 is equal in magnitude and opposite in direction to the force exerted by object 2 on object 1. Thus, an isolated force cannot exist in nature.   This law has already been mentioned with reference to the force with a table exerts on a book placed upon it and also in connection with the weight o a body in an accelerating elevator ( see post : Newton' second law of motion.... ). We shall now discuss another aspect of the law.     When a bullet is fired from a gun equal and opposite forces are exerted on the bullet and the gun during the time the bullet is passing down the barrel.Since,therefore,both bullet and gun are acted upon by equal forces for the same time, they will, in accordance with the second law of motion, acquire equal and opposite momemta. The backward momentu...
Read more