EE 255 - Chapter 7a

EE 255 - Chapter 7a - 171 Chapter 7 Induction Motors 7-1 A...

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Unformatted text preview: 171 Chapter 7 : Induction Motors 7-1. A dc test is performed on a 460-V Δ-connected 100-hp induction motor. If DC V = 24 V and DC I = 80 A, what is the stator resistance 1 R ? Why is this so? S OLUTION If this motor’s armature is connected in delta, then there will be two phases in parallel with one phase between the lines tested. R 1 R 1 R 1 V DC Therefore, the stator resistance 1 R will be ( ) ( ) 1 1 1 DC 1 DC 1 1 1 2 3 R R R V R I R R R + = = + + DC 1 DC 3 3 24 V 0.45 2 2 80 A V R I = = = Ω 7-2. A 220-V, three-phase, two-pole, 50-Hz induction motor is running at a slip of 5 percent. 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 S OLUTION (a) The speed of the magnetic fields is ( ) sync 120 50 Hz 120 3000 r/min 2 e f n P = = = (b) The speed of the rotor is ( ) ( )( ) sync 1 1 0.05 3000 r/min 2850 r/min m n s n =- =- = (c) The slip speed of the rotor is ( )( ) slip sync 0.05 3000 r/min 150 r/min n sn = = = (d) The rotor frequency is ( )( ) slip 150 r/min 2 2.5 Hz 120 120 r n P f = = = 7-3. Answer the questions in Problem 7-2 for a 480-V, three-phase, four-pole, 60-Hz induction motor running at a slip of 0.035. S OLUTION (a) The speed of the magnetic fields is 172 ( ) sync 120 60 Hz 120 1800 r/min 4 e f n P = = = (b) The speed of the rotor is ( ) ( )( ) sync 1 1 0.035 1800 r/min 1737 r/min m n s n =- =- = (c) The slip speed of the rotor is ( )( ) slip sync 0.035 1800 r/min 63 r/min n sn = = = (d) The rotor frequency is ( )( ) slip 63 r/min 4 2.1 Hz 120 120 r n P f = = = 7-4. A three-phase, 60-Hz induction motor runs at 890 r/min at no load and at 840 r/min at full load. (a) How many poles does this motor have? (b) What is the slip at rated load? (c) What is the speed at one-quarter of the rated load? (d) What is the rotor’s electrical frequency at one-quarter of the rated load? S OLUTION (a) This machine has 8 poles, which produces a synchronous speed of ( ) sync 120 60 Hz 120 900 r/min 8 e f n P = = = (b) The slip at rated load is sync sync 900 840 100% 100% 6.67% 900 m n n s n-- = × = × = (c) The motor is operating in the linear region of its torque-speed curve, so the slip at ¼ load will be 0.25(0.0667) 0.0167 s = = The resulting speed is ( ) ( )( ) sync 1 1 0.0167 900 r/min 885 r/min m n s n =- =- = (d) The electrical frequency at ¼ load is ( )( ) 0.0167 60 Hz 1.00 Hz r e f sf = = = 7-5. A 50-kW, 440-V, 50-Hz, six-pole induction motor has a slip of 6 percent when operating at full-load conditions. At full-load conditions, the friction and windage losses are 300 W, and the core losses are 600 W. Find the following values for full-load conditions: (a) The shaft speed n m (b) The output power in watts (c) The load torque load τ in newton-meters (d) The induced torque ind τ in newton-meters 173 (e) The rotor frequency in hertz S OLUTION (a) The synchronous speed of this machine is ( ) sync 120 50 Hz...
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EE 255 - Chapter 7a - 171 Chapter 7 Induction Motors 7-1 A...

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