DC Motor, Basic Electrical Engineering, Btech first year

DC Motor

Working Principle

The principle on which DC Motor works is:

"When a current carrying conductor is placed in a magnetic field, it experiences a mechanical force"

The construction of both DC Generator and Motor is same, the only difference is here we provide energy to the machine. As we excite the armature, the conductors of the armature, placed in magnetic field, experience a mechanical force and the motor starts moving. The direction of rotation is given by Fleming Left Hand Rule.

"Outstretch three fingers of left hand namely first finger, middle finger and thumb such that they are mutually perpendicular to each other. If we point first finger in direction of magnetic field and middle finger in direction of current, then the thumb gives direction of force experienced by the conductor."

Back EMF

Once motor starts rotating its conductor will cut magnetic flux produced by field winding, so by Faraday's Law of Electromagnetic Induction there will be induced emf just like in case of emf induced in dc generator. This emf is called Back emf. \[ \boxed{E_b = \frac{\phi PNZ}{60A} } \] The role of back emf in starting and running of the motor is important. The presence of back emf makes the DC Motor a self-regulating machine i.e. it makes the dc motor to draw as much armature current as is sufficient to develop the required load torque.

\[ V_t = I_aR_a + E_b + V_{brush} \] V_t is the supply voltage and it has to take care of all the three factors.

Torque Equation of DC Motor

      Mechanical Power = Torque × Angular Velocity
\[ P = T \times \omega \] \[ E_bI_a = T \times \frac{2\pi N}{60} \] \[ \frac{\cancel{N}P\phi Z}{\cancel{60}A} \times I_a = T \times \frac{2\pi \cancel{N}}{\cancel{60}} \] \[ \boxed{T = \frac{1}{2\pi}\phi I_a \frac{PZ}{A} } \] \[ \boxed{T = 0.159 \phi I_a \frac{PZ}{A} } \] The unit is Newton-meter (Nm).

Types of DC Motor

There are three types of motors:

1) Series Motor
2) Shunt Motor
3) Compound Motor : Of 2 types
      a) Long Shunt Compound Motor
      b) Short Shunt Compound Motor

The construction of all these types are similar to dc generator.

DC Series Motor

\[ I_L = I_{se} = I_a \] \[ E_b + I_aR_a + I_{se}R_{se} - V_t = 0 \] \[ E_b + I_aR_a + I_aR_{se} - V_t = 0 \] \[ E_b + I_a(R_a + R_{Se}) - V_t = 0 \] \[ \boxed{V_t = E_b + T_a(R_a + R_{se}) + V_{brush} } \]

DC Shunt Motor

\[ I_L = I_{sh} + I_a \] \[ E_b + I_aR_a - V_t = 0 \] \[ \boxed{V_t = E_b + I_aR_a } \] \[ \boxed{I_{sh} = \frac{V_t}{R_{sh}} = \frac{E_b + I_aR_a}{R_{sh}} } \]

Compound DC Motor

Long Shunt

\[ I_L = I_{se} + I_{sh} \] Or \[ I_L = I_a + I_{sh} \] \[ E_b + I_aR_a + I_{se}R_{se} - V_t = 0 \] \[ \boxed{V_t = E_b + I_aR_a + I_{se}R_{se} } \] \[ \boxed{I_{sh} = \frac{V_t}{R_{sh}} = \frac{E_b + I_a(R_a + R_{se})}{R_{sh}} } \]

Short Shunt

\[ I_L = I_{se} \] \[ I_L = I_{se} = I_a + I_{sh} \] \[ E_b + I_aR_a + I_{se}R_{se} - V_t = 0 \] \[ \boxed{V_t = E_b + I_aR_a + I_{se}R_{se} } \] \[ \boxed{I_{sh} = \frac{V_t}{R_{sh}} = \frac{E_b + I_aR_a + I_{se}R_{se}}{R_{sh}} } \]