# CHAPTER 4.6: MOTORS FOR ELECTRIC TRACTION¶

## Example 4.6.1, Page number 788¶

In :
#Variable declaration
I_1 = 10.0    #Current(A)
T_1 = 54.0    #Torque(N-m)
I_2 = 20.0    #Current(A)
T_2 = 142.0   #Torque(N-m)
I_3 = 30.0    #Current(A)
T_3 = 250.0   #Torque(N-m)
I_4 = 40.0    #Current(A)
T_4 = 365.0   #Torque(N-m)
I_5 = 50.0    #Current(A)
T_5 = 480.0   #Torque(N-m)
I_6 = 60.0    #Current(A)
T_6 = 620.0   #Torque(N-m)
I_7 = 70.0    #Current(A)
T_7 = 810.0   #Torque(N-m)
E = 500.0     #Operating voltage(V)
R_a = 0.6     #Armature resistance(ohm)

#Calculation
N_1 = 9.55*(E-I_1*R_a)*I_1/T_1   #Speed(rpm)
N_2 = 9.55*(E-I_2*R_a)*I_2/T_2   #Speed(rpm)
N_3 = 9.55*(E-I_3*R_a)*I_3/T_3   #Speed(rpm)
N_4 = 9.55*(E-I_4*R_a)*I_4/T_4   #Speed(rpm)
N_5 = 9.55*(E-I_5*R_a)*I_5/T_5   #Speed(rpm)
N_6 = 9.55*(E-I_6*R_a)*I_6/T_6   #Speed(rpm)
N_7 = 9.55*(E-I_7*R_a)*I_7/T_7   #Speed(rpm)

#Result
print('Speed-current of the motor')
print('_______________________________________')
print(' Current(A)        :      Speed(rpm)  ')
print('_______________________________________')
print('   %.f              :        %.f ' %(I_1,N_1))
print('   %.f              :        %.f ' %(I_2,N_2))
print('   %.f              :        %.f ' %(I_3,N_3))
print('   %.f              :        %.f ' %(I_4,N_4))
print('   %.f              :        %.f ' %(I_5,N_5))
print('   %.f              :        %.f ' %(I_6,N_6))
print('   %.f              :        %.f ' %(I_7,N_7))
print('_______________________________________')
print('\nNOTE: ERROR: Calculation mistakes in the textbook solution')

Speed-current of the motor
_______________________________________
Current(A)        :      Speed(rpm)
_______________________________________
10              :        874
20              :        656
30              :        552
40              :        498
50              :        468
60              :        429
70              :        378
_______________________________________

NOTE: ERROR: Calculation mistakes in the textbook solution


## Example 4.6.2, Page number 788-789¶

In :
#Variable declaration
N_1 = 500.0    #Speed(rpm)
I_1 = 50.0     #Current(A)
E_1 = 220.0    #Armature voltage(V)
I_2 = 100.0    #Current(A)
E_2 = 350.0    #Armature voltage(V)
I_3 = 150.0    #Current(A)
E_3 = 440.0    #Armature voltage(V)
I_4 = 200.0    #Current(A)
E_4 = 500.0    #Armature voltage(V)
I_5 = 250.0    #Current(A)
E_5 = 540.0    #Armature voltage(V)
I_6 = 300.0    #Current(A)
E_6 = 570.0    #Armature voltage(V)
R_wb = 0.08    #Armature and brush resistance(ohm)
R_f = 0.05     #Resistance of series field(ohm)
V = 600.0      #Operating voltage(V)

#Calculation
R_a = R_wb+R_f               #Armature resistance(ohm)
N_11 = N_1/E_1*(V-I_1*R_a)   #Speed(rpm)
T_1 = 9.55*E_1*I_1/N_1       #Torque(N-m)
N_2 = N_1/E_2*(V-I_2*R_a)    #Speed(rpm)
T_2 = 9.55*E_2*I_2/N_1       #Torque(N-m)
N_3 = N_1/E_3*(V-I_3*R_a)    #Speed(rpm)
T_3 = 9.55*E_3*I_3/N_1       #Torque(N-m)
N_4 = N_1/E_4*(V-I_4*R_a)    #Speed(rpm)
T_4 = 9.55*E_4*I_4/N_1       #Torque(N-m)
N_5 = N_1/E_5*(V-I_5*R_a)    #Speed(rpm)
T_5 = 9.55*E_5*I_5/N_1       #Torque(N-m)
N_6 = N_1/E_6*(V-I_6*R_a)    #Speed(rpm)
T_6 = 9.55*E_6*I_6/N_1       #Torque(N-m)

#Result
print('Speed-torque curve for motor')
print('_______________________________________')
print(' Speed(rpm)         :      Torque(N-m)  ')
print('_______________________________________')
print('   %.f             :        %.f ' %(N_11,T_1))
print('   %.f              :        %.f ' %(N_2,T_2))
print('   %.f              :        %.f ' %(N_3,T_3))
print('   %.f              :        %.f ' %(N_4,T_4))
print('   %.f              :        %.f ' %(N_5,T_5))
print('   %.f              :        %.f ' %(N_6,T_6))
print('_______________________________________')
print('\nNOTE: ERROR: Calculation mistakes in the textbook solution')

Speed-torque curve for motor
_______________________________________
Speed(rpm)         :      Torque(N-m)
_______________________________________
1349             :        210
839              :        669
660              :        1261
574              :        1910
525              :        2578
492              :        3266
_______________________________________

NOTE: ERROR: Calculation mistakes in the textbook solution


## Example 4.6.3, Page number 790¶

In :
#Variable declaration
V = 650.0      #Voltage supply(V)
r_A = 45.0     #Radius of driving wheel(cm)
r_B = 43.0     #Radius of driving wheel(cm)
N_A = 400.0    #Speed(rpm)
drop = 10.0    #Voltage drop(%)

#Calculation
rho = r_B/r_A
IR = drop*V/100                 #Voltage drop(V)
V_A = (rho*(V-IR)+IR)/(1+rho)   #Voltage(V)
V_B = V-V_A                     #Voltage(V)
N_A_A = N_A*(V_A-IR)/(V-IR)     #N'_A(rpm)
N_B_B = N_A_A*r_A/r_B           #N'_B(rpm)

#Result
print('Speed of first motor when connected in series, N_A = %.f rpm' %N_A_A)
print('Speed of second motor when connected in series, N_B = %.f rpm' %N_B_B)
print('\nNOTE: Changes in the obtained answer from that of textbook is due to more precision here')

Speed of first motor when connected in series, N_A = 174 rpm
Speed of second motor when connected in series, N_B = 182 rpm

NOTE: Changes in the obtained answer from that of textbook is due to more precision here


## Example 4.6.4, Page number 791¶

In :
#Variable declaration
F_t = 33800.0   #Tractive effort(N)
V = 48.3        #Velocity(kmph)
T = 53400.0     #Tractive effort(N)

#Calculation
HP = F_t*V*1000/(60*60*746)    #HP on level track(hp)
HP_i = HP*(T/F_t)**0.5         #hp delivered by locomotive for dc series motor(hp)
HP_ii = HP*T/F_t               #hp delivered by locomotive for induction motor(hp)

#Result
print('hp delivered by the locomotive when dc series motor is used = %.f HP' %HP_i)
print('hp delivered by the locomotive when induction motor is used = %.f HP' %HP_ii)

hp delivered by the locomotive when dc series motor is used = 764 HP
hp delivered by the locomotive when induction motor is used = 960 HP


## Example 4.6.5, Page number 792-793¶

In :
#Variable declaration
I_1 = 100.0                #Current(A)
N_1 = 71.0                 #Speed(kmph)
F_t1 = 2225.0              #Tractive effort(N)
I_2 = 150.0                #Current(A)
N_2 = 57.0                 #Speed(kmph)
F_t2 = 6675.0              #Tractive effort(N)
I_3 = 200.0                #Current(A)
N_3 = 50.0                 #Speed(kmph)
F_t3 = 11600.0             #Tractive effort(N)
I_4 = 250.0                #Current(A)
N_4 = 45.0                 #Speed(kmph)
F_t4 = 17350.0             #Tractive effort(N)
I_5 = 300.0                #Current(A)
N_5 = 42.0                 #Speed(kmph)
F_t5 = 23200.0             #Tractive effort(N)
D_A = 101.6                #Size of wheels(cm)
ratio_gear = 72.0/23       #Gear ratio
D_B = 106.7                #Size of wheels(cm)
ratio_gear_new = 75.0/20   #Gear ratio

#Calculation
N_B = ratio_gear*D_B/(ratio_gear_new*D_A)    #Speed in terms of V(kmph)
F_tB = D_A*ratio_gear_new/(ratio_gear*D_B)   #Tractive effort in terms of F_tA(N)
N_B1 = N_B*N_1                               #Speed(kmph)
F_tB1 = F_tB*F_t1                            #Tractive effort(N)
N_B2 = N_B*N_2                               #Speed(kmph)
F_tB2 = F_tB*F_t2                            #Tractive effort(N)
N_B3 = N_B*N_3                               #Speed(kmph)
F_tB3 = F_tB*F_t3                            #Tractive effort(N)
N_B4 = N_B*N_4                               #Speed(kmph)
F_tB4 = F_tB*F_t4                            #Tractive effort(N)
N_B5 = N_B*N_5                               #Speed(kmph)
F_tB5 = F_tB*F_t5                            #Tractive effort(N)

#Result
print('New characteristics of motor')
print('_______________________________________')
print(' Current(A)  :  Speed(kmph)  :  F_t(N)')
print('_______________________________________')
print('  %.f        :   %.1f        :   %.f '   %(I_1,N_B1,F_tB1))
print('  %.f        :   %.1f        :   %.f '   %(I_2,N_B2,F_tB2))
print('  %.f        :   %.1f        :   %.f '   %(I_3,N_B3,F_tB3))
print('  %.f        :   %.1f        :   %.f '   %(I_4,N_B4,F_tB4))
print('  %.f        :   %.1f        :   %.f '   %(I_5,N_B5,F_tB5))
print('_______________________________________')
print('\nNOTE: Changes in the obtained answer from that of textbook is due to more precision here')

New characteristics of motor
_______________________________________
Current(A)  :  Speed(kmph)  :  F_t(N)
_______________________________________
100        :   62.2        :   2538
150        :   50.0        :   7614
200        :   43.8        :   13232
250        :   39.5        :   19790
300        :   36.8        :   26463
_______________________________________

NOTE: Changes in the obtained answer from that of textbook is due to more precision here