The shaft torque (Tsh) in a d.c motor is less than total armature torque (Ta) because of ___________

Question

The shaft torque (Tsh) in a d.c motor is less than total armature torque (Ta) because of ____________ in the motor.

Examoogle · Accepted Answer

Iron and Friction losses

Explanation: The shaft torque (T_{sh}) is the useful torque available at the motor shaft, whereas the armature torque (T_a) is the total torque developed by the armature. T_{sh} is less than T_a because rotational losses, comprising iron (hysteresis and eddy current) and mechanical friction/windage losses, consume a portion of the developed power.

Working Principle: The electrical power converted into mechanical power is $P_{conv} = E_b I_a$. This power generates the armature torque $T_a = \frac{P_{conv}}{\omega_m}$. As this torque is transmitted through the shaft, energy is dissipated against frictional forces at the bearings and brushes, and aerodynamic windage losses occur. Additionally, iron losses in the core act as a retarding torque, reducing the net output torque to $T_{sh} = T_a - T_{lost}$, where $T_{lost}$ corresponds to the rotational losses.

Key Formulas: $T_a = 9.55 \frac{E_b I_a}{N}$ — Total armature torque developed in Nm; $T_{sh} = 9.55 \frac{P_{out}}{N}$ — Useful shaft torque in Nm; $T_a - T_{sh} = T_{lost}$ — Torque lost due to mechanical and iron losses

Key Points: Armature torque ($T_a$) is the total electromagnetic torque generated.; Shaft torque ($T_{sh}$) is the net torque available at the output shaft.; The difference ($T_a - T_{sh}$) is known as lost torque or stray torque.; Iron losses include hysteresis and eddy current losses in the armature core.

Advantages: Higher efficiency in larger machines; Understanding these losses is crucial for accurate motor sizing

Disadvantages: Rotational losses reduce the overall efficiency of the DC motor; Increased thermal stress due to loss dissipation

Applications: Industrial motor design; Drive performance evaluation

Additional Info: Copper losses ($I^2R$) affect the armature voltage drop and efficiency but are accounted for in the internal power conversion stage ($E_bI_a$), making rotational losses the primary cause for the difference between internal developed torque and external shaft torque.. Field losses depend on the field winding resistance and supply voltage, having minimal direct impact on the instantaneous torque conversion balance compared to rotational losses.

Answer: C is correct — The shaft torque is lower than the armature torque because rotational losses (iron and friction) consume a part of the torque developed within the armature.

Exam Tip: Always remember that $T_a$ is internal to the armature and $T_{sh}$ is the output; therefore, any loss occurring after the armature surface (mechanical) or within the core (iron) must result in a decrease in the delivered torque.

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