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 ( E_b / Ф )

       N α ( V – I_aR_a ) / Ф

      Where R_a = 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, ……r_n and total resistance at each studs are R₁, R₂, ……R_n+1 ( r_a ) respectively.

Here

R₁ = ( r₁ + r₂ + …….+ r_n ) + r_a

Where

r_a = Armature resistance

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

I₁ = V / R₁    ( As N = 0 , E_b = 0 )

• As the speed increases, back emf E_b1 is developed and hence armature current decreases to value I₂.

I₂ = ( V – E_b1 ) / 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 ( E_b1) is unaltered.

I₁ = ( V – E_b1 ) / R₂……….. ( 2 )

From equation ( 1 ) and ( 2 )

V – E_b1 = I₁R₂ = I₂R₁

Therefore I₁ / I₂ = R₁ / R₂………. ( 3 )

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

I₂ = ( V – E_bn ) / R_n

I₁ = ( V – E_bn ) / R_{n + 1} = ( V – E_bn ) / r_a

Therefore

I₁ / I₂ = R_n / r_a………… ( 4 )

From equation ( 3 ) and ( 4 )

I₁ / I₂ = R₁ / R₂ = R₂ / R₃ = ….. = R_{n – 1} / R_n = R_n / R_{n + 1} = α ( alpha )

Now

 αⁿ = ( R₁ / R₂ ) × ( R₂ / R₃ ) × …..× ( R_{n – 1} / R_n ) × ( R_n / R_{n + 1} )

αⁿ = ( R₁ / R_{n + 1}  )

αⁿ = ( R₁ / r_a )……… ( 5 )

 α = ( R₁ / r_a )^1/n

α = ( I₁R₁ / I₁r_a )^1/n

α = ( V / I₁r_a )^1/n

α = ( V / α I₂r_a )^1/n    (  As I₁ / I₂ = α )

α = ( V / I₂r_a )^{1 / ( n + 1 )}

Where

n = Number of stud resistance

n + 1 = Number of studs

• If the value of r_a, 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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