What is Shaft Torque of DC Motor?- Definition, Formula and Solved Problem

The actual torque available at the motor shaft for driving the mechanical equipment is known as shaft torque(Tsh). In fact, the same electromagnetic or gross torque(Ta) developed by the DC motor can not be available at the shaft, however, it is somewhat less than the electromagnetic torque. The reason for this is that some part of it was lost in overcoming the iron and mechanical losses. The shaft torque is the net torque available for driving the mechanical equipment. We shall study about shaft torque of the DC motor in this article.

The below-given expression shows the relation between power and torque.

formula showing relation between power and torque

Formula of shaft torque of DC Motor

derivation of shaft torque formula

Shaft torque is less than the armature torque in the case of DC motor.

The difference between the armature torque and the shaft torque shows the lost torque.

Lost Torque Formula of DC  Motor

Lost Torque = Armature or Gross Torque – Shaft Torque

lost torque formula in DC Motor

The mechanical power available at the shaft is the Brake Horsepower of the motor.

Brake Horse Power (B.H.P) of DC Motor

We can express the motor output power in BHP as follows.

Brake Horse power of DC motor

Solved problem on Shaft Torque of DC Motor

Determine developed torque and shaft torque of 220-V, the 4-pole series motor with 900 conductors wave-connected supplying a load of 9.0 kW by taking 50 A from the mains. The flux per pole is 30 mWb and its armature circuit resistance is 0.5 Ω

Gross torque = Armature torque

Ta = 0.159 X Φ ZIa (P/A)
Ta= 0.159 X  30 x  10-3 x 900 x  50 (4/2) = 429.3 N-m

Eb = V – Ia Ra = 220 – 50 X  0.5 = 195 V
Eb  = 195 Volts


Eb = Φ ZN (P/A)=  195 = 30 x 10-3 x 900 x N x (4/2)
N = 195 /(30 X10-3 X 900 x 2)
N = 3.611  r.p.s.


2πN Tsh = Power output
2π X 3.611  Tsh =9 x 103
Tsh =9 x 103 / (   2π X 3.611)
Tsh   = 396.87 N-m


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