Why is the current density in conductors highest in small powered motors as compared to high powered motors?
In small power motors wires in phase coils are thinner. To increase the effective magnetomotive force (current density) the number of turns need to be high. Consequently, the resistances of phase windings are higher than those in high-power notors, and consequently the power loss density is higher and the efficiency lower than in high-power motors.
Work done, is force multiplied by distance travel. For motor torque multiplied by speed with some constant, high power motor with less speed(wire drawing motor etc), low power with high speed(domestic motors) with same H.P.
Hence low power motor, with high speed, would need more magneto motive force, hence will need more coils, with large number of turns with thin wire having higher, current density, than high power motor. As resistance, and the power loss, would be more which would reduce the efficiency too.
In a small motor, the core length as well as diameter is smaller. Hence the core area is smaller. To maintain same flux density as in a larger motor, larger number of turns is needed. However, the mean length of a turn is small due to smaller diameter and length. Current is lesser in a smaller motor, so conductor area is smaller but can have the same current density in an ideal motor. Thus, the resistance is larger, but I2r loss will be almost same percentage as in an ideal larger motor.
Now what happens in a real small motor is that insulation occupies a larger percentage of the slot area due to its smaller size. Thus, conductor areas have to be made further smaller using higher current density so as to fit into the restricted size slots. Further, the airgap cannot be made proportionally very small due to mechanical constraints, hence the air gap consumes more percentage of Amp-turns than in a large motor, causing higher percentage value of no-load current. These real life factors create higher I2r loss in smaller motors, reducing their efficiency.
It is also to be noted that higher losses in smaller motors do not create higher temperatures as their surface area is a larger percentage of their volume - a fact that can be verified in any solid regular shape, a sphere being the simplest (check the ratio as radius is reduced). The volume represents the amount of loss generated while the surface area represents the air natural cooling provided by the surface. Thus cooling improves, permitting higher losses in smaller motor.
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