# ECE 4411 Quadrature-Field Theory and Induction-Motor Action Single-phase induction motor cannot develop a rotating magnetic field Needs an “auxiliary”

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ECE 4411 Quadrature-Field Theory and Induction-Motor Action Single-phase induction motor cannot develop a rotating magnetic field Needs an “auxiliary” method –That method is another (auxiliary) winding

ECE 4412 Single-Phase Squirrel-Cage Induction Motor There are two “Main Poles” Squirrel-Cage Rotor Single-Phase Mains Supply

ECE 4413 Excite the Main Winding Stator flux is produced across the air gap – as shown, it is increasing in the downward direction. The squirrel-cage rotor responds with a mmf in the opposite (upward) direction. Magnetic axis of the rotor is in line with the magnetic axis of the stator – no rotation!

ECE 4414 “Main” pole flux (Φ) increasing in the downward direction Rotor mmf develops in the upward direction Current “into” the page Current “out of” the page

ECE 4415 Cause the rotor to turn clockwise Rotor conductors cut through the main pole flux. Current is induced in the rotor bars as shown, producing a magnetic flux perpendicular to the main pole flux. This is known as “Quadrature” flux.

ECE 4416 The quadrature flux is sustained as the rotor conductors shift their positions – other conductors replace them.

ECE 4417 Phase Relationship Between the Direct and Quadrature Flux The “speed” voltage is in phase with the flux that created it, and the flux due to current is in phase with the current that caused it. The instantaneous amplitudes of the direct and quadrature flux are shown above.

ECE 4418 Resultant Flux Determine from

ECE 4419 Resultant Flux Rotates CW

ECE 44110 Phase-Splitting Split-Phase Induction Motor

ECE 44111 Provides “direct” flux Provides quadrature flux Ensures phase difference between winding currents Start winding

ECE 44112 Equivalent Circuit

ECE 44113 Purpose of the “Phase-Splitter” Make the current in the Auxiliary Winding out of phase with the current in the Main Winding. This results in the quadrature field and the main field being out of phase. The locked-rotor torque will be given by

ECE 44114 Example 6-1 The main and auxiliary windings of a hypothetical 120 V, 60 Hz, split-phase motor have the following locked-rotor parameters: –R mw =2.00 ΩX mw =3.50 Ω –R aw =9.15 ΩX aw =8.40 Ω The motor is connected to a 120 V system. Determine

ECE 44115 Example 6-1 continued The locked-rotor current in each winding

ECE 44116 Example 6-1 continued

ECE 44117 Example 6-1 continued The phase displacement angle between the main and auxiliary currents

ECE 44118 Example 6-1 continued The locked-rotor torque in terms of the machine constant

ECE 44119 Example 6-1 continued External resistance required in series with the auxiliary winding in order to obtain a 30  phase displacement between the currents in the two windings.

ECE 44120 Example 6-1 continued Phasor diagram for the new conditions

ECE 44121 Example 6-1 continued

ECE 44122 Example 6-1 continued

ECE 44123 Example 6-1 continued Locked-rotor torque for the condition in d

ECE 44124 Example 6-1 continued % increase in locked-rotor torque due to the adding of additional resistance

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