Question

The temperature rise of a motor when operating for 25 minutes on full load is 25 0 c and becomes 40 0 c when motor operates for another 25 min on the same load. determine heating time constant and steady state temperature rise

Answer 1

T_min=40 # minimum temperature rise in degree Celsius
T_r=15 # temperature rise when the load is declutched continously in degree Celsius
t_c=10 # time for which the motor is clutched to its load in sec
t_d=20 # time for which the motor is declutched to run on no-load in sec
C= 60 # time constants for both heating and cooling

#calculation
x=math.exp(-t_d/C)
y=math.exp(-t_c/C)

theta2= (T_min-T_r*(1-x))/x #since T_min=T_r(1-x)+theta2*x
theta_ss=(theta2-T_min*y)/(1-y) #since theta2=theta_ss(1-y)+T_min*y

#results
print"\n maximum temperature during the duty cycle :",round(theta2,1),"°C"
print"\n temperature when the load is clutched continously :",round(theta_ss,1),"°C"