Chapter 17: FRACTIONAL HORSE POWER MOTORS

Example 17.1,Page number: 570

In [1]:
#Question:
"""Finding the slip and efficiency of induction motor."""

#Variable Declaration:
f=50                  #Frequency rating of the induction motor(in Hertz) 
P=4                   #Number of poles in the induction motor  
N=1410                #Speed of the motor(in rpm)
Po=375                #Output Power(in Watts)
V=230                 #Voltage rating of the induction motor(in Volts)    
I=2.9                 #Input current(in Amperes)
pf=0.71               #Power factor(lagging) 


#Calculations:
Ns=(120.0*f)/P
slip=(Ns-N)/Ns


#Result:
print "Slip is %.2f percent." %(slip*100)
Pin=V*I*pf
efficiency=Po/Pin
print "The efficiency is %.2f percent." %(efficiency*100)

Slip is 6.00 percent.
The efficiency is 79.19 percent.

Example 17.2,Page number: 570

In [2]:
#Question:

"""Finding the currents and the power factor in the induction motor."""

from cmath import phase,rect,polar
from math import radians,degrees,cos

#Variable Declartion:
V=rect(230,0)        #Voltage rating of the split-phase induction motor(in Volts)   
Z_M=5+ 12*1j         #Impedance of the main winding(in Ohms)
Z_A=12+ 5*1j         #Start-winding impedance(in Ohms)


#Calculations:
mod_Z_M=abs(Z_M)
mod_Z_A=abs(Z_A)
phi_M=phase(Z_M)
phi_A=phase(Z_A)
I_M=V/Z_M
mod_I_M=abs(I_M)
phi_I_M=degrees(phase(I_M))
I_A=V/Z_A
mod_I_A=abs(I_A)
phi_I_A=degrees(phase(I_A))
I_L=I_M+I_A
mod_I_L=abs(I_L)
phi_I_L=degrees(phase(I_L))
phi=phi_I_A-phi_I_M
pf=cos(radians(phi_I_L))


#Result:
print "(a)The current in the main winding is %.2f A at a phase angle of %.2f degrees." %(mod_I_M,phi_I_M)
print "(b)The current in the starting winding is %.2f A at a phase angle of %.2f degrees." %(mod_I_A,phi_I_A)
print "(c)The line current is %.2f A at a phase angle of %.2f degrees." %(mod_I_L,phi_I_L)
print "(d)The phase displacement between the two winding currents is %.2f degrees." %(phi)
print "(e)The power factor is %.4f lagging." %(pf)                

(a)The current in the main winding is 17.69 A at a phase angle of -67.38 degrees.
(b)The current in the starting winding is 17.69 A at a phase angle of -22.62 degrees.
(c)The line current is 32.72 A at a phase angle of -45.00 degrees.
(d)The phase displacement between the two winding currents is 44.76 degrees.
(e)The power factor is 0.7071 lagging.

Example 17.3,Page number: 571

In [3]:
#Question:
"""Finding the capacitance in series with the auxiliary winding to maximize starting torque."""

from math import radians,degrees,atan,pi,tan

#Variable Declaration:
X_M=20                #Inductive reactance of the main winding(in Ohm)
R_M=2                 #Resistance of the main winding(in Ohm)
X_A=5                 #Inductive reactance of the auxiliary winding(in Ohm)
R_A=25                #Resistance of the auxiliary winding(in Ohm)
f=50                  #Frequency rating of the split-phase induction motor(in Hertz)   


#Calculations:
angle_M=atan(X_M/R_M)
angle_A=degrees(angle_M)-90
Xc=X_A-(R_A*tan(radians(angle_A)))


#Result:
C=1/(2*pi*f*Xc)
print "The value of capacitance connected in series with the auxiliary winding to obtain maximum starting torque is %e F." %(C)

The value of capacitance connected in series with the auxiliary winding to obtain maximum starting torque is 4.244132e-04 F.

Example 17.4,Page number: 576

In [6]:
#Question:
"""Finding the resolution and shaft speed of a stepper motor."""

#Variable Declaration:
beta=2.5              #Step-angle of a stepper motor(in degrees)
step_freq=3600        #Stepping frequency(in pps)


#Calculations:
res=360/beta
number_steps=res*25
shaft_speed=(beta*step_freq)/360


#Result:
print "(a)The resolution is %d steps per revolution." %(res)
print "(b)The number of steps required for the shaft to make 25 revolutions=%d." %(number_steps)
print "(c)The shaft speed is %.2f rps." %(shaft_speed)

(a)The resolution is 144 steps per revolution.
(b)The number of steps required for the shaft to make 25 revolutions=3600.
(c)The shaft speed is 25.00 rps.

Example 17.5,Page number:577

In [7]:
#Question:
"""Finding the number of stator and rotor poles in a VR motor."""

#Variable Declaration:
m=3                   #Number of phases
beta=15               #Step angle(in degrees)


#Calculations:
Nr=360/(m*beta)
Ns1=(Nr*360)/(360-(beta*Nr))
Ns2=(Nr*360)/(360+(beta*Nr))


#Result:
print "(a) The number of rotor poles is %d." %(Nr)
print "(b)"
print "   Case 1: Ns>Nr"
print "   The number of stator poles is %d. \n" %(Ns1)
print "   Case 2: Ns<Nr"
print "   The number of stator poles is %d." %(Ns2)

(a) The number of rotor poles is 8.
(b)
   Case 1: Ns>Nr
   The number of stator poles is 12. 

   Case 2: Ns<Nr
   The number of stator poles is 6.

Example 17.6,Page number: 579

In [8]:
#Question:
"""Finding the number of rotor and stator teeth in VR stepper motor."""

#Variable Declaration:
m=4                   #Number of stacks
beta=1.8              #Step angle(in degrees)


#Calculations:
Nr=360/(m*beta)
Ns=Nr


#Result:
print "The number of rotor teeth is %d." %(Nr)
print "The number of stator teeth is %d." %(Ns)
print "\nNOTE: In a multistack stepper motor the number of stator teeth is same as that of the rotor teeth."

The number of rotor teeth is 50.
The number of stator teeth is 50.

NOTE: In a multistack stepper motor the number of stator teeth is same as that of the rotor teeth.