WEEK 8-9 ULOc 85fd2a13b63d78f4d5043fae1561e755 PDF

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Education 2 nd Floor, BE Building Matina Campus, Davao City Telefax: (082)296- 1084 Phone No.: (082)300-5456/300-0647 Local 131WEEK 8-9 ULOcBig Picture in Focus: ULOc. Discuss and apply the principles of three phaseinduction motors in solving real-world problems.MetalanguageIn this section, the most...

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College of Engineering Education 2nd Floor, BE Building Matina Campus, Davao City Telefax: (082)296-1084 Phone No.: (082)300-5456/300-0647 Local 131

WEEK 8-9 ULOc Big Picture in Focus: ULOc. Discuss and apply the principles of three phase induction motors in solving real-world problems.

Metalanguage In this section, the most essential principles and concepts of DC and AC machine relevant to the study of electromechanical energy conversion and to demonstrate ULOc will be reviewed to utilize in the analysis of the three-phase induction motors in solving real lworld problems. Please refer to these definitions in case you will encounter difficulty in understanding educational concepts. 1. Stator. It is the stationary part of the induction motor- the stator consists of a cylindrical laminated slotted core that is placed in the frame. 2. Rotor. It is the rotating part of the induction motor. 3. Revolving Field. It is a three-phase stator winding of an induction motor that is connected to a three-phase source. 4. Slip. It is the difference between the synchronous speed and the actual rotor speed expressed as a percent (or per unit) of the synchronous speed. 5. Starting torque. A motor develops it at an instant. 6. Rotor speed. It is the rotor of an induction motor must rotate in the same direction as the revolving field. 7. Rotor power. Is an actual conversion of electrical power into mechanical power always takes place in the rotor of a motor. 8. Blocked-rotor test. It is the value of the rotor resistance and the rotor reactance.

Essential Knowledge To perform the aforesaid big picture (unit learning outcomes) for the third two- (2) weeks of the course, you need to fully understand the following essential knowledge that will be laid down in the succeeding pages. Please note that you are not limited to refer to these resources exclusively. Thus, you are expected to utilize other books, research articles and other resources that are available in the university’s library (refer to the library contact on page 3)

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Three-Phase Motors Induction-motor Principle. In the electric motor, the conversion of electrical power (or energy) to mechanical power (energy) takes place in the rotating part of the machine. In the d-c motor and one type of a-c motor, the electrical is conducted directly to the rotor through brushes and a commutator; in this respect, it is possible to designate such a machine as a conduction motor. In the most common type of a-c motor, electrical power is not conducted to the rotor directly; the rotor receives its power inductively in the same way as the secondary of a transformer receives its power. It is for the reason that motors of this type are known as induction motors. It will become apparent, as the analysis proceeds, that it will be extremely useful to think of an induction motor as a sort of rotating transformer, i.e., one in which a stationary winding is connected to the a-c source. In contrast, the other winding, mounted on a structure that is free to turn, receives its power by transformer action while it rotates. Consider Fig. 8, which represents the edge of a south magnet pole that lies directly over, and close to the edge of a nonmagnetic disk; both may be imagined as being supported on independent vertical pivots and free to rotate in a horizontal plane. Attention should be centered upon a small element of the disk that lies directly below the center of the pole. In (a), the flux passes vertically upward through the disk and is uniformly distributed. If the magnet is moved to the right, as in (b), the flux follows its usual practice of bending around the conductor element of the disk, so that a voltage is generated in the conductor away from the observer. The generated voltage causes a current to flow in the disk element, the path of which extends toward the pivot and then divides to the left and right, returning to the conductor element from both sides near the edge of the disk. (c) the resultant field is next shown in (d), indicates that the field is dense on the left side and weak on the right side of the disk element. Hence, the conductor element and the disk move to the right, in the same direction as the motion of the pole.

College of Engineering Education 2nd Floor, BE Building Matina Campus, Davao City Telefax: (082)296-1084 Phone No.: (082)300-5456/300-0647 Local 131

Fig. 36 Sketches illustrating a principle of the induction motor Percent slip S = Ns – Nr x 100 Ns Synchronous speed Ns = 120f P Rotor speed Nr = 120f ( 1 – s ) P Where: Ns = synchronous speed (rpm) Nr = rotor speed (rpm) f = frequency of the stator voltage (Hertz) P = number of poles Example 37: The rotor speed of a six-pole 50-cycle induction motor is 960 rpm. Calculate the per cent slip.

Solution: Ns = 120 x 50 x 100 = 1,000 rpm 6 Per cent slip = 1000 – 960 x 100 = 4% 1000 Example 38: Calculate the speed of a 60-cycle 14-pole motor if the slip s is 0.05

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Solution: Nr = 120 x 60 (1 – 0.05) = 488 rpm 14 Generated Voltage and Frequency in a rotor Er = s x EBR fR = s x f where Er = generated voltage per phase in rotor at slip s EBR = block rotor generated voltage per phase fR = rotor frequency Rotor Current and Power IR = sEBR /[(RR)2 + s2XBR2]1/2 = EBR /[(RR/s)2 + XBR2]1/2

Fig. 37 Equivalent circuit diagram for IR RR/s = RR + RR[(1 – s)/s]

Fig. 38 Modified equivalent circuit diagram of rotor per phase Where: ZR = rotor impedance per phase RR = rotor resistance

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XBR = rotor reactance RPI (rotor power input) = RCL (rotor copper loss) + RPD (rotor power developed) IR2x RR = IR2RR + IR2RR[ (1 – s)] s s Where: RPI = IR2x RR s RCL = IR2RR = RPI x s RPD = IR2RR[ (1 – s)] s Example 39: A three-phase 60-cycle six-pole 220-volt wound-rotor induction motor has a stator that is connected in delta and a rotor that is connected star. The rotor has half as many turns as the stator. For a rotor speed of 1,110 rpm, calculate: (a) slip; (b) the blocked-rotor voltage per phase EBR; (c) the rotor generated voltage per phase ER; (d) the rotor voltage between terminals; (e) the rotor frequency Solution: (a) s = 1200 - 1110 = 0.075 1200 (b) EBR = 220 x ½ = 110 volts (c) ER = 0.075 x 110 = 8.25 volts (d) Volts between rotor terminals = (3)1/2x 8.25 = 14.25 volts (e) fR = 0.075 x 60 = 4.5 cycles per second Example 40: A three-phase 60-cycle six-pole 220-volt wound-rotor induction motor has a stator that is connected in delta and a rotor that is connected star. The rotor has half as many turns as the stator. For a rotor speed of 1,110 rpm, calculate the rotor current if RR = 0.1 ohm and XBR = 0.5 ohm Solution: IR = 110/[(0.1/0.075)2 + (0.5)2]1/2 = 110/1.42 = 77.5 A Example 41:

College of Engineering Education 2nd Floor, BE Building Matina Campus, Davao City Telefax: (082)296-1084 Phone No.: (082)300-5456/300-0647 Local 131

A three-phase 60-cycle six-pole 220-volt wound-rotor induction motor has a stator that is connected in delta and a rotor that is connected star. The rotor has half as many turns as the stator. For a rotor speed of 1,110 rpm; R R = 0.1 ohms and XBR = 0.5 ohms, calculate: (a) the rotor power input; (b) the rotor copper loss; (c) the rotor power developed by a rotor, in watts; (d) the rotor power developed by the rotor in horsepower.

Solution: (a) RPI = IR2x RR = 3(77.5)2 x 0.1 = 24,000 watts s 0.075 (b) RCL = RPI x s = 24,000 x 0.075 = 1,800 watts (c) RPD = RPD = IR2RR[ (1 – s)] = 3(77.5)2 x 0.1[1 – 0.075] s 0.075 = 22,200 watts (d) RPD = 22,200 w x 1hp = 29.8 hp 746 w Rotor Torque T = 7.04 x RPI rpmsyn Example 42: A three-phase 60-cycle six-pole 220-volt wound-rotor induction motor has a stator that is connected in delta and a rotor that is connected star. The rotor has half as many turns as the stator. For a rotor speed of 1,110 rpm; R R = 0.1 ohms and XBR = 0.5 ohms, calculate the torque developed by the motor.

Solution: T = 7.04 x 24,000 = 140.8 lb-ft 1,200

Self-Help: You can refer to the sources below to help you further understand the lesson Gupta, J.B. (2015). Theory & Performance of Electrical Machines: DC machines

College of Engineering Education 2nd Floor, BE Building Matina Campus, Davao City Telefax: (082)296-1084 Phone No.: (082)300-5456/300-0647 Local 131

and AC machines. New Delhi, India: S.K. Kataria & Sons, 2014 . Chapman, Stephen J. (2012). Electrical Machinery Fundamentals (5th Edition). New York, N.Y.: McGraw-Hill Companies, 2012) Herman, Stephen L. (2017). Electrical Transformers and Rotating Machines (4th Edition). Australia: Cengage Learning, 2017.

Let’s Check Activity 10: Since you are now armed with basic knowledge of three-phase induction motors in solving real-world problems. It is now your turn to prove what you have learned in the previous discussion. Solve the following problems. 1. The name-plate speed of a 25-cycle induction motor is 720 rpm. If the speed at no-load is 745 rpm, calculate (a) the slip; (b) the per cent regulation. Ans.: 0.04; 3.47% 2. A three-phase six-pole 60-cycle 230-volt wound-rotor motor has its stator connected in delta and its rotor in star. There are 75% as many rotor conductors as stator conductors. Calculate the voltage and frequency between slip rings if a normal voltage is applied to the stator when (a) the rotor is at rest; (b) the rotor slip is 0.04; (c) the rotor is driven by another machine at 800 rpm in a direction opposite from that of the revolving field. Ans.: 299 volts, 60 cps; 11.96 volts, 2.4 cps; 500 volts, 100 cps 3. The nameplate of a squirrel-cage induction motor has the following information: 25 hp, 220 volts, three-phase, 60 cycles, 830 rpm, 64 amp per line. If the motor takes 20,800 watts when operating at full-load, calculate: (a) slip; (b) per cent regulation if the no-load speed is 895 rpm; (c) power factor; (d) torque; (e) efficiency. Ans.: 0.078; 7.83%; 0.856; 158 lb-ft; 89.7%

Let’s Analyze Activity 10. Getting acquainted with the principle of three-phase induction motors in solving real-world problems is not enough. This time, you are going to show the circuit diagram and the principle again and explain its step-by-step procedure. 1. A squirrel cage induction motor with nameplate data of 150 Hp, 3-phase, 460-V, 60 Hz, 6-pole, 0.85 pf was subjected to certain performance tests.

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The test result readings were as follows: Full load current = 202 A, Full load torque = 676.8 lb-ft. Solve the percentage slip. Ans.: 3.28% 2. A six-pole, three-phase squirrel-cage induction motor is connected to a 60cps supply. At full load, the rotor’s induced emf makes 72 complete cycles in 1 minute. Find the rotor speed. Ans.: 1176 rpm 3. A 10 hp (nameplate), 6-pole, 60 Hz, three-phase induction motor delivers 9.9 hp with an input of 9200 watts. The core loss is 450 W. The stator copper loss is 650 watts, and the rotational losses are 150 watts. What is the motor speed? Ans.: 1116.36 rpm

In a Nutshell We are now done with the principle of three-phase induction motor which exploring and understanding the concepts of electrical machines, remember that DC and AC machinery is the cornerstone of the engineering industry. Before proceeding to the next unit learning outcomes, be reminded of some important points when dealing with the principle of three-phase induction motor.    

The flux passes vertically upward through the disk and is uniformly distributed. The flux follows its usual practice of bending around the conductor element of the disk so that a voltage is generated in the conductor away from the observer. The field is dense on the left side and weak on the right side of the disk element. Hence, the conductor element and the disk move to the right, in the same direction as the motion of the pole. The values of the rotor resistance and the rotor reactance can be determined by performing the blocked-rotor test.

Q & A List If you have any questions regarding the principle of three-phase induction motor in solving real-world problems, kindly write down on the table provided.

QUESTIONS

ANSWERS

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Key Words Index: rotor reactance, blocked rotor, starting torque, rotor resistance, slip, rotor speed, stator, conduction, induction....