asic Concepts of A Machine
asic Concepts of A Machine (1) tator: stationary portion of the achine Rotor: rotating portion of the achine haft: the stiff rod that the rotor is ounted on Air gap (Gap): between stator and rotor
asic Concepts of A Machine (2) Load current: the current that varies with load Magnetizing current: provide agnetic field and independent of load Arature: the winding that carries only load current Field: the winding that carries only agnetizing current dc achine: the input/output current is dc ac achine: the input/output current is ac; two categories: synchronous achine induction achine (no field winding, siilar to transforer)
asic Concepts of A Machine (3)
asic Concepts of A Machine (4) round rotor salient pole rotor
Electrical vs Mechanical Frequency N N N N At steady state echanical speed f n f e 2 f revolution/inute (rp) n 1 60 n 60 rev/second
lots and Coils (1) Double Layer Lap Winding botto top tooth slot top botto
lots and Coils (2) coil end coil side coil leads coil side coil end Nc turns, 2Nc conductors
On arature lots and Coils (3) Each slot has 2 positions: top and botto (double layer winding) Each coil needs to occupy 2 positions: top position of one slot and botto position of another slot Nuber of arature coils = Nuber of arature slots () phase achine: Nuber of coils per phase: ph Nc Nuber of turns per phase: Nph phnc Nc 2 Nuber of conductors per phase: Cph 2 Nph = Note: The above three equations are independent of the nuber of poles (). For balanced -phase design, ph should be an integer.
3 phase, 24 slots lots and Coils (4) 8 coils, 8N c turns, 16N c conductors per phase 13 N ph 12 11 8N c 10 9 8 7 6 5 4 1 2 3 turns N ph / 2 4 N c turns 1 2 3 4 7 6 5 2 pole, hase A, full-pitch 4 pole, hase A, full-pitch
lot itch lot pitch in electrical angle is defined by 2 where is the echanical angle between two adjacent slots: 2 The slot pitch is also defined as the arc length between two slots on stator inner circle (with diaeter D): s D 13 12 11 109 8 7 3 phase, 24 slots, 2 pole hase A, full-pitch D 1 23 4 56
360 o ole itch ole itch: angular distance between two adjacent poles on a achine. 2 (in echanical degree) Regardless of the nuber of poles on the achine, a pole pitch is always 180 o or in electrical degrees. The pole pitch is also defined as the arc length between two adjacent poles on stator inner circle (with diaeter D) : D (in eter or inch) Nuber of lots per ole: Note: ay not be an integer. 36s8p 36 4.5 8
Coil itch Full-itch Coil: If the arature coil stretches across the sae angle as the pole pitch, it is called a full-pitch coil. The coil spans across slots, if is an integer. Fractional-itch Coil: If the arature coil stretches across an angle saller than a pole pitch, it is called a fractional-pitch coil (or shortpitched coil, chorded coil). The coil spans less than slots. Let c be the nuber of slots that the coil spans. Let be the echanical angle that the coil spans or c. Coil pitch in electrical angle is defined by c 2
Fractional itch Coil (1) 2 2 2 24 12 12 24 slots, 2 pole, 3 phase 13 12 11 10 9 8 7 6 5 4 1 2 3 12 11 10 9 8 7 6 5 4 1 2 3 hase A, full-pitch hase A, (11/12)-pitch o 180 11 o 165 12
Fractional itch Coil (2) 24 slots, 4 pole, 3 phase 2 2 4 2 24 12 1 2 3 4 hase A, full-pitch o 2 90 7 6 5 o 180 4 2 6 1 2 3 6 5 4 hase A, (5/6)-pitch 5 6 2 5 12 o 75 5 o 150 6
Group (1) 4 pole, 3 phase, 24 slot achine hase A, (5/6)-pitch This group consists of 2 coils. q Nuber of tator lots ( ) Nuber of coils per group: Nuber of phases ( ) Nuber of poles ( ) q Nuber of coils = Nuber of slots for double layer winding Nuber of groups = Nuber of poles () for double layer winding 3 for 3 phase achine
q can take fractional nuber Group (2) 18 q 1.5 3 4 q 9 1.5 3 2 4 pole, 3 phase, 18 slot 2 pole, 3 phase, 9 slot
UCF Torque T T R F 0 R F How to understand torque: ut the thub in the direction of torque. The other four fingers point to the direction of rotation. wrench on a nut
UCF Torque fro a Current Loop loop df1 Idxax Idx( yaz za y) 1 R1 dya y 2 1 dt1 R1 df1 dya y Idx( yaz za y) 2 1 dxdyiya x 2 1 dt3 R 3 df3 dya y ( Idx)( yaz za y) 2 1 dxdyiyax dt1 2 dt dt dxdyi a 1 3 Likewise y x dt2 dt4 dxdyixa y Idxdy( a ) Id z Note: Define d is in the sae direction of loop and both are proportional to I d Id d d dt d = k loop T k loop
UCF Torque roperty of a Machine (1) sin R R k T k T ince R net sin ) ( net R net R R net R k T k k T
UCF Torque roperty of a Machine (2) R net 6 pole synchronous achine
UCF Torque roperty of a Machine (3) otor T k R generator