DC Machines Analysis Symbols that will be used. = flux per pole p = no. of poles z = total number of active conductors on the armature a = no. of parallel paths in the armature winding Aside: Lap Winding -> a = p Wave Winding -> a = 2 n = speed of rotation of the armature in rpm w m = speed in radians per second
EMF Equation When the rotor rotates in the field a voltage is developed in the armature. - the flux cut by one conductor in one rotation = p - - - therefore in n rotations, the flux cut by one conductor = np
EMF Equation EMF induced in the armature windings
TORQUE EQUATION E a I a =T e m - In the DC machine losses are expressed as rotational losses due to friction and windage (F&W). - The torque equation can then be rewritten as:- SHAFT OUTPUT TORQUE = (T e - T F&W )
DC Generator Note: V T = V L i.e. Terminal Voltage is the Load Voltage
OPEN CIRCUIT CHARACTERISTICS The Open Circuit characteristic is a graph relating Open-Circuit Armature voltage of a D.C. Generator versus its field current when the machine is driven at it’s rated speed Diagram showing motor connections for the open circuit test, separately excited The D.C. Generator field is excited by a separate D.C. source and the current is varied using a generator Field Regulator (a potential divider).
OPEN CIRCUIT CHARACTERISTICS Diagram showing the D.C. Generator as a self-excited shunt machine R ext is set to its maximum value. The D.C. Generator is driven at rated its speed. R ext is decrease to a lower value so that the machine self-excites ( i.e.. Develop an e.m.f).
EXTERNAL CHARACTERISTIC OF SHUNT GENERATOR This is a graph relating terminal voltage and the load current of a D.C. Generator when driven at its rated speed with the field current maintained at its normal no-load value. Diagram showing connections for load test.
Summary Losses Rotational and f R 2 f I -- Windings(Armature) -- Windings(Field ) a R 2 a I Losses a E n pz a60 a R a I -V n Speed a60 pzn a E a R a I -V a E Note: For motor (Windage and Friction)