Q10Electrical Machine Design
Question
Q.10. Write the output equation of the electrical machine giving the relation between output, diameter, and length of the machine.
Answer
The output equation relates machine output Q to the square of bore diameter D, core length L, speed, and specific loadings: Q = Co D²Ln, where Co is the output coefficient depending on specific electric and magnetic loadings.
The output equation of a rotating electrical machine expresses its rated output as a function of its principal dimensions and specific loadings:
where Q is the output (kVA for AC machines, kW for DC machines), D is the armature/stator bore diameter, L is the core (gross iron) length, n is the rotational speed (in revolutions per second), and Co is the output coefficient, itself a function of the specific magnetic loading (Bav, average flux density in the air gap) and specific electric loading (ac, ampere-conductors per meter of periphery), and the winding factor. This equation is the fundamental starting relation of electrical machine design, since fixing the specific loadings (based on cooling and material constraints) and the desired output/speed allows the designer to solve for the D²L product, and hence the principal dimensions of the machine.