## Torque per unit volume

For motors with similar cooling systems, the rated torque is approximately proportional to the rotor volume, which in turn is roughly proportional to the overall motor volume.

This stems from the fact that for a given cooling arrangement, the specific and magnetic loadings of machines of different types will be more or less the same. The torque per unit length therefore depends first and foremost on the square of the diameter, so motors of roughly the same diameter and length can be expected to produce roughly the same torque.

Power per unit volume - importance of speed

Output power per unit volume is directly proportional to speed.

Low-speed motors are unattractive because they are large, and therefore expensive. It is usually much better to use a high-speed motor with a mechanical speed reduction. For example, a direct drive motor for a portable electric screwdriver would be an absurd proposition.

Size effects - specific torque and efficiency

Large motors have a higher specific torque (torqueper unit volume) and are more efficient than small ones.

In large motors the specific electric loading is normally much higher than in small ones, and the specific magnetic loading is somewhat higher. These two factors combine to give the higher specific torque.

Very small motors are inherently very inefficient (e.g. 1% in a wrist-watch), whereas motors of over say 100 kW have efficiencies above 95%. The reasons for this scale effect are complex, but stem from the fact that the resistance volt-drop term can be made relatively small in large electromagnetic devices, whereas in small ones the resistance becomes the dominant term.

Efficiency and speed

### The efficiency of a motor improves with speed.

For a given torque, power output rises in direct proportion to speed, while electrical losses are - broadly speaking - constant. Under these conditions, efficiency rises with speed.

Rated voltage

### A motor can be provided to suit any voltage.

Within limits it is always possible to rewind a motor for a different voltage without affecting its performance. A 200 V, 10 A motor could be rewound for 100 V, 20 A simply by using half as many turns per coil of wire having twice the cross-sectional area. The total amounts of active material, and hence the performance, would be the same.

Most motors can be overloaded for short periods without damage.

The continuous electric loading (i.e. the current) cannot be exceeded without damaging the insulation, but if the motor has been running with reduced current for some time, it is permissible for the current (and hence the torque) to be much greater than normal for a short period of time. The principal factors which influence the magnitude and duration of the permissible overload are the thermal time-constant (which governs the rate of rise of temperature) and the previous pattern of operation. Thermal time constants range from a few seconds for small motors to many minutes or even hours for large ones. Operating patterns are obviously very variable, so rather than rely on a particular pattern being followed, it is usual for motors to be provided with over-temperature protective devices (e.g. thermistors) which trigger an alarm and/or trip the supply if the safe temperature is exceeded.

REVIEW QUESTIONS

1) The current in a coil with 250 turns is 8 A. Calculate the MMF.

2) The coil in (1) is used in a magnetic circuit with a uniform cross-section made of good-quality magnetic steel and with a 2 mm airgap. Estimate the flux density in the air-gap, and in the iron. (m0 = 4p x 10—7H/m.)

How would the answers change if the cross-sectional area of the magnetic circuit was doubled, with all other parameters remaining the same?

3) Calculate the flux in a magnetic circuit that has a cross-sectional area of 18 cm2 when the flux density is 1.4 T.

4) A magnetic circuit of uniform cross-sectional area has two air-gaps of 0.5 and 1 mm respectively in series. The exciting winding provides an MMF of 1200 Amp-turns. Estimate the MMF across each of the air-gaps, and the flux density.

5) The field winding in a motor consumes 25 W when it produces a flux density of 0.4 T at the pole-face. Estimate the power when the pole-face flux density is 0.8 T.

6) The rotor of a d.c. motor had an original diameter of 30 cm and an air-gap under the poles of 2 mm. During refurbishment the rotor diameter was accidentally reground and was then undersized by 0.5 mm. Estimate by how much the field MMF would have to be increased to restore normal performance. How might the extra MMF be provided?

7) Estimate the minimum cross-sectional area of a magnetic circuit that has to carry a flux of 5 mWb. (Don't worry if you think that this question cannot be answered without more information — you are right.)

8) Calculate the electromagnetic force on:

a) a single conductor of length 25 cm, carrying a current of 4 A, exposed to a magnetic flux density of 0.8 T perpendicular to its length.

b) a coil-side consisting of twenty wires of length 25 cm, each carrying a current of 2 A, exposed to a magnetic flux density of 0.8 T perpendicular to its length.

9) Estimate the torque produced by one of the early machines illustrated in Figure 1.11 given the following:- Mean air-gap flux density under pole-face = 0.4 T; pole-arc as a percentage of total circumference = 75%; active length of rotor = 50 cm; rotor diameter = 30 cm; inner diameter of stator pole = 32 cm; total number of rotor conductors = 120; current in each rotor conductor = 50 A.

10) Motor designers often refer to the 'average flux density over the rotor surface'. What do they really mean? If we want to be really pedantic, what would the average flux density over the (whole) rotor surface be?

11) If the field coils of a motor are rewound to operate from 220 V instead of 110 V, how will the new winding compare with the old in terms of number of turns, wire diameter, power consumption and physical size?

12) A catalogue of DIY power tools indicates that most of them are available in 240 V or 110 V versions. What differences would you expect in terms of appearance, size, weight and performance?

13) Given that the field windings of a motor do not contribute to the mechanical output power, why do they consume power continuously?

14) For a given power, which will be larger, a motor or a generator?

15) Explain briefly why low-speed electrical drives often employ a high-speed motor and some form of mechanical speed reduction, rather than a direct-drive motor.