11 Basic Concepts of a Machine
Transcription
11 Basic Concepts of a Machine
Basic Concepts of A Machine Basic Concepts of A Machine (1) Stator: stationary portion of the machine Rotor: rotating portion of the machine Shaft: the stiff rod that the rotor is mounted on Air gap (Gap): between stator and rotor Basic Concepts of A Machine (2) Load current: the current that varies with load Magnetizing current: provide magnetic field and independent of load Armature: the winding that carries only load current Field: the winding that carries only magnetizing current dc machine: the input/output current is dc ac machine: the input/output current is ac; two categories: synchronous machine induction machine (no field winding, similar to transformer) Basic Concepts of A Machine (3) Basic Concepts of A Machine (4) round rotor salient pole rotor Electrical vs Mechanical Frequency N S S N N S S N At steady state mechanical speed n m fm P fe fm 2 revolution/minute (rpm) nm 1 nm 60 60 rev/second Slots and Coils (1) Double Layer Lap Winding bottom top tooth slot top bottom Slots and Coils (2) coil end coil side coil leads coil side coil end Nc turns, 2Nc conductors Slots and Coils (3) On armature Each slot has 2 positions: top and bottom (double layer winding) Each coil needs to occupy 2 positions: top position of one slot and bottom position of another slot Number of armature coils = Number of armature slots (S) S Number of coils per phase : S ph m phase machine: m S Nc Number of turns per phase: N ph S ph Nc m S Nc 2 Number of conductors per phase: C ph 2 N ph = m Note: The above three equations are independent of the number of poles (P). For balanced m-phase design, Sph should be an integer. Slots and Coils (4) 3 phase, 24 slots 8 coils, 8Nc turns, 16Nc conductors per phase 13 12 11 10 9 N ph 8 N c 8 7 6 turns 5 4 3 2 1 2 pole, Phase A, full-pitch 7 6 N ph 4 N c turns 5 P/2 4 2 3 1 4 pole, Phase A, full-pitch Slot Pitch Slot pitch in electrical angle is defined by P m 2 where m is the mechanical angle between two adjacent slots: m 2 S P S The slot pitch is also defined as the arc length between two slots on stator inner circle (with diameter D): s D S 13 1211 10 9 m D 3 phase, 24 slots, 2 pole Phase A, full-pitch 1 2 8 7 6 5 4 3 Pole Pitch Pole Pitch: angular distance between two adjacent poles on a machine. 360 o 2 P P P (in mechanical degree) Regardless of the number of poles on the machine, 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 diameter D) : P D P (in meter or inch) Number of Slots per Pole: SP S P Note: SP may not be an integer. 36s8p SP 36 4.5 8 Coil Pitch Full-Pitch Coil: If the armature coil stretches across the same angle as the pole pitch, it is called a full-pitch coil. The coil spans across SP slots, if SP is an integer. Fractional-Pitch Coil: If the armature coil stretches across an angle smaller than a pole pitch, it is called a fractional-pitch coil (or shortpitched coil, chorded coil) . The coil spans less than SP slots. Let Sc be the number of slots that the coil spans. Let m be the mechanical angle that the coil spans or m Sc m . Coil pitch in electrical angle is defined by m Sc P SP P m 2 Fractional Pitch Coil (1) 24 slots, 2 pole, 3 phase m 13 12 11 10 9 m m 1 2 2 2 2 24 12 P m 8 7 6 5 4 3 Phase A, full-pitch m 180 o 12 12 11 10 9 m 1 2 8 7 6 5 4 3 Phase A, (11/12)-pitch m 11 165o 12 Fractional Pitch Coil (2) 24 slots, 4 pole, 3 phase 2 4 2 2 24 12 P m m 7 6 5 1 2 3 m 4 1 2 4 2 m Phase A, full-pitch m 2 90 o 180 o 6 5 3 4 6 Phase A, (5/6)-pitch 5 5 m 75o 6 2 12 5 6 150 o Group (1) 4 pole, 3 phase, 24 slot machine Phase A, (5/6)-pitch This group consists of 2 coils. Number of coils per group: Number of Stator Slots ( S ) Number of phases (m) Number of poles ( P ) S for 3 phase machine q 3P q Number of coils = Number of slots for double layer winding Number of groups = Number of poles (P) for double layer winding Group (2) q can take fractional number q 18 1. 5 3 4 4 pole, 3 phase, 18 slot q 9 1. 5 3 2 2 pole, 3 phase, 9 slot Torque UCF T RF T 0 F R How to understand torque: Put the thumb in the direction of torque. The other four fingers point to the direction of rotation. wrench on a nut Torque from a Current Loop UCF d F1 Idx a x B Idx ( B y a z B z a y ) R1 1 dy a y 2 1 dy a y Idx ( B y a z B z a y ) 2 d T1 R 1 d F1 1 dxdyIB y a x 2 1 d T3 R 3 d F3 dy a y ( Idx )( B y a z B z a y ) 2 1 dxdyIB y a x d T1 2 d T1 d T3 dxdyIB y a x Bloop Likewise d T2 d T4 dxdyIB x a y Idxdy ( a z B ) Id S B Define d m Id S d T d m B Note: dm is in the same direction of Bloop and both are proportional to I dm = k Bloop d T kB loop B UCF Torque Property of a Machine (1) T kB R B S T kB R BS sin Since B net B R B S T k B R ( B net B R ) k B R B net T kB R Bnet sin UCF Torque Property of a Machine (2) BR Bnet 6 pole synchronous machine Torque Property of a Machine (3) UCF T kB R B S generator motor