DIRECT-CURRENT MACHINERY 211 



If there is a rheostat connected in series with the shunt-field 

 winding the power wasted in it should be included in the field 

 copper loss. 



(b) The series-field copper loss is I 8 2 r a watts, where I a is the 

 current in the series winding and r s is its resistance. This loss 

 increases as the square of the load current of the machine. In 

 interpole machines the resistance r a will include the resistance of 

 the interpole winding. The power loss in the shunts to the series 

 winding or in the series-field rheostat must be included in the 

 series-field loss. 



(c) The armature copper loss may be divided into three parts, 

 first, the loss due to the current I a flowing through the resistance r a 

 of the armature winding, not including the resistance of the brush 

 contacts. This part of the loss is I a 2 r a watts and increases as the 

 square of the load current. Second, there is a loss of power where 

 the current passes from the commutator to the brushes or vice 

 versa. It is el a watts, where e is the drop of voltage at the brush 

 contacts. The voltage e varies directly as the current at light 

 loads when the current density is low but above a density of about 

 30 amperes per square inch of brush contact it remains nearly con- 

 stant at a value of approximately 2 volts for ordinary carbon 

 brushes. Above this point therefore the loss at the brush contacts 

 increases as the first power of the current. This loss is negligible in 

 high-voltage machines but is quite large in low- voltage machines. 

 The third part of the armature copper loss is that caused by short- 

 circuit currents in coils undergoing commutation or by circulating 

 currents in the machine windings which may be produced by^ im- 

 proper spacing of the brushes or by any variation in the depth of 

 the air gaps under different poles in multipolar machines. These 

 losses cannot be calculated. 



(d) The hysteresis loss is due to the reversal of the magnetism 

 in the armature iron as it moves across a pair of poles. Steinmetz 

 found that the loss per cycle of magnetism varies as the 1.6th power 

 of the induction density; it is 



Co* = YjSS 1 - 6 ergs, 



where 9S is the maximum induction in lines per square centimeter 

 and Y) is the hysteretic constant for the iron and w^ is the loss in 

 ergs per cubic centimeter per cycle. The value of TQ for armature 

 iron is about 0.003. 



