# CHAPTER 4.8: BRAKING¶

## Example 4.8.1, Page number 806¶

In :
#Variable declaration
V = 525.0    #Voltage of motor(V)
I_1 = 50.0   #Current(A)
T_1 = 216.0  #Torque(N-m)
I_2 = 70.0   #Current(A)
T_2 = 344.0  #Torque(N-m)
I_3 = 80.0   #Current(A)
T_3 = 422.0  #Torque(N-m)
I_4 = 90.0   #Current(A)
T_4 = 500.0  #Torque(N-m)
V_m = 26.0   #Speed(kmph)
R_b = 5.5    #Resistance of braking rheostat(ohm)
R_m = 0.5    #Resistance of motor(ohm)

#Calculation
I = 75.0                #Current drawn at 26 kmph(A)
back_emf = V-I*R_m      #Back emf of the motor(V)
R_t = R_b+R_m           #Total resistance(ohm)
I_del = back_emf/R_t    #Current delivered(A)
T_b = T_3*I_del/I_3     #Braking torque(N-m)

#Result
print('Braking torque = %.f N-m' %T_b)

Braking torque = 429 N-m


## Example 4.8.2, Page number 806¶

In :
#Variable declaration
V = 525.0      #Voltage of motor(V)
I_1 = 50.0     #Current(A)
N_1 = 1200.0   #Speed(rpm)
I_2 = 100.0    #Current(A)
N_2 = 950.0    #Speed(rpm)
I_3 = 150.0    #Current(A)
N_3 = 840.0    #Speed(rpm)
I_4 = 200.0    #Current(A)
N_4 = 745.0    #Speed(rpm)
N = 1000.0     #Speed opearting(rpm)
R = 3.0        #Resistance(ohm)
R_m = 0.5      #Resistance of motor(ohm)

#Calculation
I = 85.0                #Current drawn at 1000 rpm(A)
back_emf = V-I*R_m      #Back emf of the motor(V)
R_t = R+R_m             #Total resistance(ohm)
I_del = back_emf/R_t    #Current delivered(A)

#Result
print('Current delivered when motor works as generator = %.f A' %I_del)

Current delivered when motor works as generator = 138 A


## Example 4.8.3, Page number 810¶

In :
#Variable declaration
W = 400.0       #Weight of train(tonne)
t = 120.0       #Time(sec)
V_1 = 80.0      #Speed(km/hr)
V_2 = 50.0      #Speed(km/hr)
r_kg = 5.0      #Tractive resistance(kg/tonne)
I = 7.5         #Rotational inertia(%)
n = 0.75        #Overall efficiency

#Calculation
W_e = W*(100+I)/100                                      #Accelerating weight of train(tonne)
r = r_kg*9.81                                            #Tractive resistance(N-m/tonne)
energy_recuperation = 0.01072*W_e*(V_1**2-V_2**2)/1000   #Energy available for recuperation(kWh)
F_t = W*(r-98.1*G)                                       #Tractive effort during retardation(N)
distance = (V_1+V_2)*1000*t/(2*3600)                     #Distance travelled by train during retardation period(m)
energy_train = abs(F_t)*distance/(3600*1000)             #Energy available during train movement(kWh)
net_energy = n*(energy_recuperation+energy_train)        #Net energy returned to supply system(kWh)

#Result
print('Energy returned to lines = %.2f kWh' %net_energy)
print('\nNOTE: ERROR: Calculation mistakes & more approximation in textbook solution')

Energy returned to lines = 29.93 kWh

NOTE: ERROR: Calculation mistakes & more approximation in textbook solution


## Example 4.8.4, Page number 810¶

In :
#Variable declaration
W = 355.0        #Weight of train(tonne)
V_1 = 80.5       #Speed(km/hr)
V_2 = 48.3       #Speed(km/hr)
D = 1.525        #Distance(km)
I = 10.0         #Rotational inertia(%)
r = 53.0         #Tractive resistance(N/tonne)
n = 0.8          #Overall efficiency

#Calculation
beta = (V_1**2-V_2**2)/(2*D*3600)   #Braking retardation(km phps)
W_e = W*(100+I)/100                 #Accelerating weight of train(tonne)
F_t = 277.8*W_e*beta+98.1*W*G-W*r   #Tractive effort(N)
work_done = F_t*D*1000              #Work done by this effort(N-m)
energy = work_done*n/(1000*3600)    #Energy returned to line(kWh)

#Result
print('Energy returned to the line = %.1f kWh' %energy)

Energy returned to the line = 20.6 kWh


## Example 4.8.5, Page number 811-812¶

In :
import math

#Variable declaration
area = 16.13       #Area of brakes(sq.cm/pole face)
phi = 2.5*10**-3   #Flux(Wb)
u = 0.2            #Co-efficient of friction
W = 10.0           #Weight of car(tonnes)

#Calculation
a = area*10**-4                   #Area of brakes(sq.m/pole face)
F = phi**2/(2*math.pi*10**-7*a)   #Force(N)
beta = u*F/(W*1000)*100           #Beta(cm/sec^2)

#Result
print('Braking effect, β = %.2f cm/sec^2' %beta)

Braking effect, β = 12.33 cm/sec^2