Series motor: speed and power using torque

[KESTRELx]

Homework Statement

when running at its rated load, a 40kW series motor takes 74A and 550V. The rated speed is 750 rev/min. the armature and field resistances are 0.35 Ω and 0.15 Ω respectivly. when the load torque is doubled the rated value, the current is 110A. dertermin the moror speed and the power output at 100% torque overload.

Answers given, worked solution not
ans = 538 Rev/min and 57.4kW

Homework Equations

Work= Torque x (2pi x speed over 60)
torque = K(t) I(a) ψ (k(t) =constant and I(a)= armature current)
EMF =KNψ (k= constant)
EMF= v-IR

The Attempt at a Solution

Work= Torque x (2pi x speed over 60)
40000= T x ((2pi x 750) / 60)
T=509.29


EMF =KNψ (condition 1)
EMF =KNψ (condition 2)

divide both and cancel
k is constant as its the same motor
flux is constant (as flux is not given a value, i assume that its the same)

EMF(1) over EMF(2) = N(1) over N(2)
put both to the power -1 so as to find N(2) easier
EMF(2) over EMF(1) = N(2) over N(1)

((550 - (74 x 0.35+0.15)) over (550 - (74 x 0.35+0.15))) x 750 = N(2)
N(2) = 723.6 rev/min which is not the value of the answer

seeing as i can't get the speed right i can't go onto finding the power developed, however using the speed provided in the answer i have done it and correctly

Work= 2Torque x (2pi x speed over 60)
Work= 2Torque x (2pi x 538 over 60)
=57386W
=57.4kW

 

[KataKoniK]

The issue with your solution is that you have used the wrong formula for calculating torque. The correct formula is T = K(t) I(a) ψ, where K(t) is a constant, I(a) is the armature current, and ψ is the flux. In this case, the flux is not constant because it depends on the speed of the motor.

To find the correct solution, we can use the following steps:

1. Calculate the flux at rated load:
EMF = v - IR
550 = 550 - (74 x 0.35 + 0.15) x 74
EMF = 550 - 55.5 = 494.5 V
EMF = KNψ
494.5 = K x 74 x ψ
ψ = 7.08 Wb

2. Calculate the flux at 100% torque overload:
EMF = v - IR
550 = 550 - (110 x 0.35 + 0.15) x 110
EMF = 550 - 71.5 = 478.5 V
EMF = KNψ
478.5 = K x 110 x ψ
ψ = 4.35 Wb

3. Use the formula for calculating speed:
EMF = KNψ
494.5 = K x 74 x 7.08
K = 1.06

EMF = KNψ
478.5 = 1.06 x 110 x 4.35
N = 538 rev/min

4. Calculate the power output at 100% torque overload:
Work = Torque x (2pi x speed over 60)
Work = 2T x (2pi x 538 over 60)
Work = 2 x (1.06 x 110 x 4.35) x (2pi x 538 over 60)
Work = 116,772 W
Power = Work / Time
Power = 116,772 / 1 sec
Power = 116,772 W
Power = 116.8 kW

Therefore, the correct answers are:
Motor speed = 538 rev/min
Power output = 116.8 kW