Introduction to Electrical Engineering - Basic vocational knowledge (Institut für Berufliche Entwicklung, 213 p.) |

4. Electrical Energy |

The conversion of electrical energy into mechanical energy is a frequent utilisation of electrical energy. Thus, electric motors are used for moving air in air-conditioning plants, in water pumps, for the drive of machines and vehicles, and many other electrical equipment. The fact that electrical energy is easily convertible into mechanical energy and the possibility of adapting the motor to be used to the given technical task have led to the preferred use of electric motors in practice. In most cases, electric motors are considerably cheaper and require less maintenance than engines. For the various applications, types of electromotors are available which are optimally adapted to the purpose.

Let us consider at first a few important physical quantities of rotary motion. The shaft of a motor rotates at a certain rotational speed n which is usually measured in revolutions per minute (rpm). Fig. 4.6. shows a belt drive. The smaller belt pulley is mounted on the shaft of the motor and the larger pulley on the machine to be driven. The V-belt transmits the force from the motor to the machine. The force transmitted by the V-belt is an essential quantity for computation. The force multiplied by the radius r is called torque M.

Fig. 4.6. Belt drive

M = F · r

[M] = N · m

(4.7.)

where:

M |
torque |

F |
force |

r |
radius |

The sketch shows that the torque acting at the belt pulley with
the radius r_{1} is smaller than the torque at the belt pulley with the
larger radius r_{2}. For the rotational speeds of the belt pulleys
the** **relation

n_{1:}n_{2}= r_{2}: r_{1 }holds.

(4.8.)

where:

n |
speed of rotation |

r |
radius |

The mechanical power delivered by the motor is expressed by the following formula:

P = 2 · p^{1)}M · n

[P] = Nm/s = W

(4.9)

^{1)}p Greek letter pi

where

P |
power |

M |
torque |

n |
speed of rotation |

Example 4.7.

On the belt pulley of a motor having a radius of 50 mm, a force of 20 N is acting. The rotational speed is 1000 rpm. What is the power delivered by the motor?

Given:

r = 50 mm

F = 20 N

n = 1000 rpm

To be found:

P in W

Solution:

P = 2 · M · n

P = 2 · F · r · n

P = 2 · 3.14 · 20 N · 50 mm · 1000 rpm

P = 2 · 3.14 · 20 N · 0.05 m · 1000/60 · 1/s

P = 105 W

The power delivered by the motor is 105 W.

An important item for judging the performance of a motor is the
dependence of the rotational speed on the torque (and thus on the load) and the
current path at the instant of switching on. The dependence of the efficiency on
the torque should also be taken into consideration for an appropriate use. In
Fig. 4.7. these dependences are represented for a three-phase squirrel-cage
induction motor. This motor, which is the most widely used type, is shown in
Fig. 4.8. The characteristics show that the rotational speed is reduced only
slightly under load. This property is desired in many drives. When, however, the
stalling torque - also known as pull-out torque - M_{k} is reached,
which is above the rated torque M_{n}, the motor will stall suddenly.

Fig. 4.7. Characteristics of the
three-phase asynchronous motor

Fig. 4.8. Three-phase squirrel cage
induction motor

At the instant of switching on, only the starting torque
M_{q} is available which is frequently insufficient for heavy drives to
cause the motor to start up. Additional measures are then required in order to
allow the motor to start up without load at first. This motor is not suited as a
drive motor for vehicles because it cannot produced the required starting
moment. The efficiency h increases with
increasing load. In order to operate the motor with as high an efficiency as
possible, a load with the rated moment should be effected. Therefore, the motor
power for drives should be chosen according to the required power. It should be
noted that at the instant of switching on the input of current I_{an} is
several times higher than for rated operation I_{n}. The fuses in series
with the motor must comply with these conditions. Frequently switching on and
off is unfavorable except for special motors.

As a drive motor for vehicles, the series-wound motor is particularly suitable. The dependence of the rotational speed on the torque is shown in Fig. 4.9. It is evident that the motor produces a very high torque at a low rotational speed; this is conducive to the starting of electric vehicles.

Fig. 4.9. Characteristic of the
series motor

If, for example, a squirrel-cage induction motor is to be used for driving a centrifugal pump which is frequently used as a water pump, a motor having a suitable power must be selected. For this purpose, first we have to know the dependence of the required torque on the rotational speed of a centrifugal pump (Fig. 4.10.). The point of intersection of the pump characteristics and the motor characteristics should coincide with the rated torque of the motor.

Fig. 4.10. Interaction of a
centrifugal pump and a three-phase squirrel cage induction motor

For many drives, the electromotor is an ideal solution. Its construction is sturdy and it calls for limited maintenance only. Various designs enable an optimum adaptation to the different drive requirements in the various fields of application. The mechanical power delivered by the motor is determined by the rotational speed and the torque. Every motor has its typical characteristics from which conclusions can be drawn as to the practical use.

Questions and problems:

1. Quote some examples of devices which are operated by means of electric motors!2. Calculate the power delivered by a motor when its belt pulley having a diameter of 100 mm rotates at a speed of 1350 rpm and a force of 50 N acts on the pulley!

3. Why is a three-phase squirrel-cage induction motor not suitable for driving electric vehicles!

4. Why is a series-wound motor not suitable for driving a drilling machine?