# Excercises Electric Machinery Fundamentals

## Problem 6-1



In [1]:

%pylab inline




Populating the interactive namespace from numpy and matplotlib



### Description

A 220-V three-phase six-pole 50-Hz induction motor is running at a slip of 3.5 percent.



In [2]:

fse = 50 # [Hz]
p   = 6
s   = 3.5/100



Find:

#### (a)

• The speed of the magnetic fields in revolutions per minute

#### (b)

• The speed of the rotor in revolutions per minute

#### (c)

• The slip speed of the rotor

#### (d)

• The rotor frequency in hertz

### SOLUTION

#### (a)

The speed of the magnetic fields is:

$$n_\text{sync} = \frac{120f_{se}}{P}$$


In [3]:

n_sync = 120*fse / p
print('''
n_sync = {:.0f} r/min
==================='''.format(n_sync))




n_sync = 1000 r/min
===================



#### (b)

The speed of the rotor is:

$$n_m = (1-s)n_\text{sync}$$


In [4]:

n_m = (1 - s) * n_sync
print('''
n_m = {:.0f} r/min
==============='''.format(n_m))




n_m = 965 r/min
===============



#### (c)

The slip speed of the rotor is:

$$n_\text{slip} = s \cdot n_\text{sync}$$


In [5]:

n_slip = s * n_sync
print('''
n_slip = {:.0f} r/min
================='''.format(n_slip))




n_slip = 35 r/min
=================



#### (d)

The rotor frequency is:

$$f_{re} = \frac{p\cdot n_\text{slip}}{120}$$


In [6]:

fre = n_slip*p / 120
print('''
fre = {:.2f} Hz
============='''.format(fre))




fre = 1.75 Hz
=============