Torque and speed characteristics of DC motors

The torque developed is T = KΦI_a and the speed is N = (V − I_aR_a)/(KΦ). The shunt and series motors behave differently because the series field carries the armature current.

DC shunt motor (Φ constant)

 T |           /        N |------___
   |         /            |         ---___
   |       /              |
   |     /                |
   +-------------> Ia     +-------------> T
     T-Ia                   N-T

• T–I_a: T ∝ I_a, a straight line through (near) the origin.
• N–T: speed falls only slightly with torque (drooping line), because the drop I_aR_a is small and Φ is constant. It is nearly a constant-speed machine.

DC series motor (Φ ∝ I_a before saturation)

 T |           /        N |\
   |         _/           | \
   |      _-'             |  \__
   |  __-'                |     ---___
   +-------------> Ia     +-------------> T
     T-Ia                   N-T

• T–I_a: T ∝ Φ I_a ∝ I_a² at light loads (parabola). After magnetic saturation Φ is constant, so T ∝ I_a (straight line). It gives a very high starting torque.
• N–T: N ∝ 1/Φ ∝ 1/I_a ∝ 1/√T. Speed is very high at light load and falls rapidly as torque rises (hyperbola-like). On no load the speed becomes dangerously high, so the load must never be removed.