DC Shunt Motor :Definition,Torque, Equation and Application-Electrical Diary - Electrical Diary -->

# What is DC Shunt Motor?

DC shunt Motors are also self-excited DC Motor. In an electric circuit, if two components are connected in parallel then it is called a shunt. Similar to this, In DC shunt Motor field winding is connected in parallel to the armature winding. Since field winding and armature windings are connected in parallel the applied voltage is the same for both armature and field winding. The connection of Shunt Motors are shown below:
DC Shunt Motor

## DC Shunt Motor Equation (Relation Between Back EMF and Armature Current)

To study the relation between Back Emf and Armature let's consider the simplified circuit diagram given below.
Circuit Diagram For DC Shunt Motor
from above-given Circuit diagram
• V= supply voltage
• I= Current flowing towards the Motor called input current
• Eb = Induced EMF in armature called Back EMF
• Ia = armature Current
• Ish = field Current called Shunt Current.
• Rsh =the net effective resistance of field winding called shunt resistance
• Ra =Armature Resistance
From the above-given Circuit diagram, on applying KCL at node A  then we will find that
I=Ia+Ish-------(1)
V=IaRsh (Voltage Across Shunt Winding)
V=Eb+IaRa ( Voltage Drop Across Armature of Motor)
Eb =V-IaRa------(2)

### Power Equation for DC Shunt Motor

Power Input  = Mechanical Power Developed + Loss(Armature loss+ Field Winding Loss)
VI = PmIa2Ra+Ish2Rsh
VI = PmIa2Ra+VIsh
(As Voltage across Shunt = V)
Pm = VI - Ia2Ra-VIsh
Pm = V(-Ish)- Ia2Ra
Pm = VIa- Ia2Ra
Pm=Ia(V- IaRa)
From equation(2)
Pm=IaEb
(this is mechanical power develop in armature)

Let Developed Torque is T in N-m and Rotor angular Speed is ω radian per second
Developed Mechanical Power = T ω
IaEb= T ω

$E_{b}I_{a} =T\omega$

$T =\frac{E_{b}I_{a}}{\omega} ---(3)$

We Know that back emf is given as

$E_{b}=\frac{NP\phi Z}{60A}$

Now put the value of back emf in equation(3)
$T =\frac{\frac{NP\phi Z}{60A}I_{a}}{\omega}$
After putting the Value Eb in the above equation, we will get
$T =\frac{NP\phi ZI_{a}}{60\omega A}$

As we know that  Angular Velocity ω= 2 πN/60
$T =\frac{NP\phi ZI_{a}}{60\times \frac{2\pi N}{60} \times A}$
$T =\frac{P\phi ZI_{a}}{ 2\pi A}--(4)$
• P= No of Pole,
• Z=No of Conductor Coil
• Φ = is Flux per
• A= Number of Parallel Path
• Ia= is Armature Current
Out of these all parameters Z, P, and A are constant for the given dimension and rating of the DC Shunt Motor.Hence after arranging the above equation it may be like this
$T =(\frac{P Z}{ 2\pi A})\times \phi I_{a}$
$Let \ \frac{P Z}{ 2\pi A} = k(Constant)$

Now Torque equation can be written as
$T =K \times \phi I_{a}$
$T \propto \phi I_{a}----(A)$
From equation (A)it is clear that the Torque of the DC Shunt Motor is Depend on Magnetic Flux and Armature Current. And also, We know that Flux (Φ) also Depend On the Shunt Branch Current
Φ ∝ Ish
if The Supply terminal Voltage is kept Constant then the Current in the Field Winding (Ish) will be Constant then
Φ = Constant and then Developed Torque will be the Function of only Armature Current
$T \propto I_{a}$

### Characteristics of DC Shunt Motors

The relation between two different quantities is represented by a graph and this graphical representation is called the Characteristics and the relation is called the characteristics equation. The variation of independent quantity and its effect on the dependent quantity is shown on the graph. Torgue-Speed and Speed-Armature characteristics of DC shunt Motors are Similar to Separately excited DC motors and you can look it by clicking here.From above given torque equation it is clear that torque of dc shunt motor depends on flux and armature current.If Shunt Current is kept constant then magnetic flux (Φ) will also be constant and Torque will be proportional to Armature Current.When Load will Increase ,load current will also increase and due to this torque will also increase.It means that Graph of Torque to Armature will be straight line.
Image Credit:https://www.electricaldeck.com/2021/01/characteristics-of-dc-motors-shunt-series-compound.html

### Application of DC Shunt Motor

• Lathe Machines
• Centrifugal Pumps
• Fans, Blowers
• Conveyors, Lifts
• Weaving Machine
• Spinning machines