## 05/12/2020

### Starter Step Calculation For DC Shunt Motor

• When the DC shunt motor is started, it is necessary that the speed should increase with constant rate.
• The speed of the DC shunt motor is given by

N α ( Eb / Ф )

N α ( V – IaRa ) / Ф

Where Ra = Total starter resistance and armature resistance

• If the supply voltage V keeps constant, the flux remains constant in the DC shunt motor.
• The resistance of starter is so designed that the armature current remains within limits that does not affect the value of torque for increasing value of speed.

• Figure shows the connection diagram of the starter for DC shunt motor.
• Let I1 is the maximum value of current and I2 is minimum value of current, number of studs are 1, 2, …..n + 1 resistance excluding “ OFF ” stud, stud resistances are r1, r2, ……rn and total resistance at each studs are R1, R2, ……Rn+1 ( ra ) respectively.

Here

R1 = ( r1 + r2 + …….+ rn ) + ra

Where

ra = Armature resistance

• When starter arm makes contact with stud no. 1, the current immediately rise to value I1

I1 = V / R1    ( As N = 0 , Eb = 0 )

• As the speed increases, back emf Eb1 is developed and hence armature current decreases to value I2.

I2 = ( V – Eb1 ) / R1……..( 1 )

• When the starter arm again move to stud no. 2, the current again rises to value I1 because some resistance is cut out. The speed doesn’t change in very short time therefore the back emf ( Eb1) is unaltered.

I1 = ( V – Eb1 ) / R2……….. ( 2 )

From equation ( 1 ) and ( 2 )

V – Eb1 = I1R2 = I2R1

Therefore I1 / I2 = R1 / R2………. ( 3 )

Similarly, the current at nth and ( n + 1 )th studs are I2 and I1 respectively.

I2 = ( V – Ebn ) / Rn

I1 = ( V – Ebn ) / Rn + 1 = ( V – Ebn ) / ra

Therefore

I1 / I2 = Rn / ra………… ( 4 )

From equation ( 3 ) and ( 4 )

I1 / I2 = R1 / R2 = R2 / R3 = ….. = Rn – 1 / Rn = Rn / Rn + 1 = α ( alpha )

Now

αn = ( R1 / R2 ) × ( R2 / R3 ) × …..× ( Rn – 1 / Rn ) × ( Rn / Rn + 1 )

αn = ( R1 / Rn + 1  )

αn = ( R1 / ra )……… ( 5 )

α = ( R1 / ra )1/n

α = ( I1R1 / I1ra )1/n

α = ( V / I1ra )1/n

α = ( V / α I2ra )1/n    (  As I1 / I2 = α )

α = ( V / I2ra )1 / ( n + 1 )

Where

n = Number of stud resistance

n + 1 = Number of studs

• If the value of ra, R1 and α is given, the value of n can find out easily from equation ( 5 ).
• If value of I1 is not given, it is taken as 1.5 times full load current.

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