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Mathematical Comparison of Characteristics

Author: E.E. Kimberly

For a shunt motor the following equation may be written to relate speed and load defined in terms of armature current:


in which


n = speed, in rpm; . V = applied voltage; IaRa = resistive voltage drop

Fig. 11-9. Characteristics of Shunt,

in the armature;

ϕ = mam-field mix;

Z' = number of active armature conductors;

k = a constant of the machine. Inasmuch as ϕZf is a constant K1 with constant excitation,


ee_101-133.png (11-6)

This is the equation of a drooping straight line to which the shunt-motor characteristic of Fig. 11-9 is an approximation. Armature reaction pre-

Cumulative Compound, and Series

Motors, All Referred to the Same

Rated Speed and Power



Notes: Starting current is controlled by starting resistor.

This table shows general effects, which will vary somewhat for specific ratings, i Courtesy General Electric Co,

vents exact similarity between the actual and the theoretical characteristics.

In the cumulative compound motor, ϕ is not constant but increases with load. As ϕ of equation (11-5) increases, the value of the fraction decreases; and there is produced a curve with increasing droop, which approximates the cumulative-compound characteristic of Fig. 11-9. The amount of the droop depends on the number of ampere-turns of the shunt field relative to those of the series field when loaded.

In the series motor,

ee_101-135.png (11-7)

If the saturation of the iron is low, ϕ is approximately proportional to I, and

ee_101-136.png (11-8)

The speed of a series motor is proportional to


and may be controlled by altering either V or ϕ. The applied voltage may be reduced by inserting a resiststance in series with the armature, and ϕ may be reduced by shunting part of the current around the field coils. The interaction of ϕ and Ia produces an approximately hyperbolic speed-load characteristic within the operating range of the motor. Tables 11-1 and 11-2 give data relating to characteristics and applications of d-c motors.

Last Update: 2010-10-05