Question

Q. A 208 Volts, 10 hp, four-pole, 60 Hertz, star-connected induction motor has a
full-load slip of 5 percent.

1.What is the synchronous speed of this motor?

2.What is the rotor speed of this motor at rated load?

3.What is the rotor frequency of this motor at rated load?

4.What is the shaft torque of this motor at rated load?
​

Answer 1

Answer:

Induction Motors

2. Introduction Three-phase induction motors are the most common and frequently encountered machines in industry - simple design, rugged, low-price, easy maintenance - wide range of power ratings: fractional horsepower to 10 MW - run essentially as constant speed from no-load to full load - Its speed depends on the frequency of the power source • not easy to have variable speed control • requires a variable-frequency power-electronic drive for optimal speed control

3. Construction An induction motor has two main parts - a stationary stator • consisting of a steel frame that supports a hollow, cylindrical core • core, constructed from stacked laminations (why?), having a number of evenly spaced slots, providing the space for the stator winding Stator of IM

4. Construction - a revolving rotor • composed of punched laminations, stacked to create a series of rotor slots, providing space for the rotor winding • one of two types of rotor windings • conventional 3-phase windings made of insulated wire (wound-rotor) » similar to the winding on the stator • aluminum bus bars shorted together at the ends by two aluminum rings, forming a squirrel-cage shaped circuit (squirrel-cage) Two basic design types depending on the rotor design - squirrel-cage: conducting bars laid into slots and shorted at both ends by shorting rings. - wound-rotor: complete set of three-phase windings exactly as the stator. Usually Y-connected, the ends of the three rotor wires are connected to 3 slip rings on the rotor shaft. In this way, the rotor circuit is accessible.

5. Construction Squirrel cage rotor Wound rotor Notice the slip rings

6. Construction Slip rings Cutaway in a typical wound- rotor IM. Notice the brushes and the slip rings Brushes

7. Rotating Magnetic Field Balanced three phase windings, i.e. mechanically displaced 120 degrees form each other, fed by balanced three phase source A rotating magnetic field with constant magnitude is produced, rotating with a speed 120 f e nsync = rpm PWhere fe is the supply frequency andP is the no. of poles and nsync is called the synchronous speed in rpm (revolutions per minute)

Answer 2

Answer:

synchronous speed=1800rpm

rotor speed= 1710rpm

rotor frequency = 3HZ

shaft torque = 41.64rad/s

Explanation:

1. synchronous speed = $N_s = \frac{120*f}{p} = \frac{120*60}{4} = 1800m/s$

2. full load slip = s = 5% = 1/20

rotor speed N = $(1-s)*N_s = (1-\frac{1}{20})*1800 = 1710m/s$

3. rotor frequency = $\frac{(N_s - N_r)*p}{120} = \frac{(1800-1710)*4}{120} = 3Hz$

4. P= output in watts = 10hp = 7456.99 W

shaft torque = $T_sh = \frac{P}{w_m} =\frac{60*P}{2\pi N} = \frac{9.55*7456.99}{1710} = 41.64Nm$

#SPJ3