DC MACHINE FORMULAS

V-Ea = Ra Ia

(Eq.1)

= Ka Ia

(Eq. 2)

Ea = Ka m

(Eq. 3)V = terminal voltage, V (sometimes also shown as Vt)

Ea = counter emf, V

Ra = armature resistance,

Ia = armature current, A

= torque, N.m

Ka =constructional constant of machine

= flux due to field windings, Wb

m = rotational speed of machine, rad/s

GENERATORUnder no load Ia = 0, Ra Ia = 0, so Vt = Ea (Eq. 1)

Under load I 0, Ra Ia 0, Vt < Ea (Ia flows out of generator towards load)

To reverse output polarity: Reverse rotation (m in Eq. 3)or (but not both) Reverse field excitation polarity ( in Eq. 3)To increase output voltage (Vt): Increase rotation speed (m in Eq. 3)and/or

Increase field excitation ( in Eq. 3)and/or

Increase load resistance, Ia decreases (OHMs Law), Ra Ia decreases, Vt increases (Eq. 1)To decrease output voltage (Vt): Do the opposite of any of the three steps above.MOTORUnder no load or under load I 0, Ra Ia 0, Vt > Ea (Ia flows into motor)

To reverse rotation: Reverse armature voltage (Ia changes direction, Eq. 1, and then reverses, Eq. 2)or (but not both) Reverse field excitation polarity ( reverses and then reverses, Eq. 2)To speed up motor: Increase applied armature voltage (Vt), Ia increases (Eq. 1) and then increases (Eq. 2). Note, field voltage to be kept constant. This method may be applied to vary speed from zero up to rated speed (or higher provided electrical and mechanical limits are not exceeded).and/or, but typically only one at a time Decrease field excitation, Ea decreases, Ia increases (Eq. 1) and then increases (Eq. 2). Note, applied armature voltage to be kept constant. This method may be applied to vary speed above base (rated) speed, provided electrical and mechanical limits are not exceeded.or While keeping Vt and constant, decrease load torque (), Ia decreases (Eq. 2), Vt-Ea decreases (Eq. 1), since Vt is assumed constant then Ea increases, causing m to increase (Eq. 3).To slow down motor: Do the opposite of any of the three steps above.