* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download electrical machines det 204/3
History of electromagnetic theory wikipedia , lookup
Opto-isolator wikipedia , lookup
Current source wikipedia , lookup
Electrification wikipedia , lookup
Switched-mode power supply wikipedia , lookup
Brushless DC electric motor wikipedia , lookup
Power engineering wikipedia , lookup
History of electric power transmission wikipedia , lookup
Three-phase electric power wikipedia , lookup
Skin effect wikipedia , lookup
Transformer wikipedia , lookup
Stray voltage wikipedia , lookup
Rectiverter wikipedia , lookup
Magnetic core wikipedia , lookup
Buck converter wikipedia , lookup
Voltage optimisation wikipedia , lookup
Variable-frequency drive wikipedia , lookup
Mains electricity wikipedia , lookup
Galvanometer wikipedia , lookup
Electric motor wikipedia , lookup
Alternating current wikipedia , lookup
Resonant inductive coupling wikipedia , lookup
Induction motor wikipedia , lookup
Stepper motor wikipedia , lookup
Brushed DC electric motor wikipedia , lookup
CHAPTER 2 DC Machines Fundamentals Introduction • • • A DC Machines can be used as either a DC generator or a DC motor. DC generators - To convert mechanical energy to electrical energy. - Limited use due to solid state rectifier. DC motors - To convert electrical energy to mechanical energy - Widely used - Main feature: speed control is simple and cheap Construction • DC Machine = Stator + Rotor (armature) - Stator: stationary part ~ does not move, the outer frame of the machines is made of ferromagnetic materials. - Rotor (Armature): rotating part ~ free to move, the inner part of the machine is made of ferromagnetic materials. - Field winding: is wound on the stator poles to produce magnetic field (flux) in the air gap. - Armature winding: is composed of coils placed in the armature slots. - Commutator: is composed of copper bars, insulated from each other. The armature winding is connected to the commutator. - Brush: placed against the commutator surface. Brush is used to connect the armature winding to external circuit through commutator. • • • The conductor placed in the slots of the stator or rotor are interconnected to form windings. The winding in which voltage is induced is called the armature winding. The winding through which a current is passed to produce the primary source of flux in the machine is called the field winding. In the DC machine, the field winding is placed on the stator and the armature winding on the rotor. DC motor stator DC motor rotor Cutaway view of a dc motor Details of the commutator of a dc motor Armature Windings A turn consists of two conductors connected to one end by an end connector. A coil is formed by connecting several turns in series. A winding is formed by connecting several coils in series. Cut and unroll of DC machine Pole pitch is the distance between the centers of two adjacent poles Two basic sequences of armature winding connections: a) Lap windings b) Wave windings Lap Winding Consider coil shown by the dark lines with one end connected to the commutator bar no 2. The coil is placed in slots 2 and 7 such that the coils sides are placed in similar positions under adjacent poles. This is called lap winding because as the winding progresses the coils laps back on itself. We can conclude, in a lap winding, the number of parallel paths, “a” is always equal to the number of poles, “P” and also to the number of brushes. Wave Winding The coil arrangement and the end connections are illustrated by the dark lines shown in figure above for two coils. One end of the coil starts at commutator bar 2 and the coil sides are placed in slots 7 and 12. The other end of coil is connected to commutator bar 13. The second coil starts at this commutator bar and is placed in slots 18 and 2 and ends on commutator bar 3. This winding is called a wave winding because the coils are laid down a wave pattern. In wave windings, the number of parallel paths, ”a” is always two and there may be two or more brush positions. DC machines operates as a generator A simple rotating loop between curved poles faces Perspective view Magnetic for DC machine is supplied by the magnetic north and south poles shown on the stator (field winding) A simple rotating loop between curved poles face View of field lines Top view Front view The Voltage Induced in a Rotating Loop If the rotor of this machine is rotated, a voltage will induced in the wire loop. Concepts: A moving wire in the presence of a magnetic field has a voltage induced in it. The loop of wire shown in rectangular, with sides ab and cd perpendicular to the plane of the page and with sides bc and da parallel to the plane of the page. The induced voltage for one conductor is eind vBl where B = magnetic flux density (T) v = velocity of the conductor (ms-1) l = length of conductor (m) The induced voltage depends on three factor: 1. The flux, Ф in the machine 2. The speed ω of the rotor 3. A constant depending on the construction of the machine The internal generated voltage The voltage out of the armature is; ZvBl a EA where Z = the total number of conductors a = the number of current paths We know , v =rω, r = radius of the rotor ZrBl a EA The total flux per pole in the machine is; BA p B(2rl ) 2rlB P P The internal generated voltage is ZrBl a ZP 2rlB 2a P E A EA ZP 2a EA K where K ZP 2a 2n 60 or E A K ' K' ZP 60a DC machines operates as a motor The induced torque in the rotating loop A battery is now connected to the machine. When the switch is closed and a current is allowed into conductor loop. The torque will be induced on the conductor loop. The force for one conductor is F i(lxB) F ilB where i = magnitude of current in the segment l = length of the segment, with direction of I defined to be in the direction of current B = magnetic flux density vector The torque on that segment is (force applied)(p erpendicul ar distance) Fr sin The induced torque depends on three factors: 1. The flux Ф in the machine 2. The armature (or rotor) current IA in the machine 3. A constant depending on the construction of the machine The induced torque The torque in any single conductor under the pole faces is cond rI cond lB Ia a I cond The torque in a single conductor on the motor is cond rI a lB a Since there are Z conductors, the total induced torque in rotor is ind ZrlBI a a The total flux per pole in the machine is B(2rl ) 2rlB P P BA p The total induced torque is ZPI a 2a The total induced torque is ind ind KI a where K ZP 2a Power flow and losses in DC machines DC generators take in mechanical power and produce electric power while DC motors take in electric power and produce mechanical power Efficiency; Pout x100% Pin Pout Ploss x100% Pin The losses that occur in DC machine can be divided into 5 categories: 1. 2. 3. 4. 5. Copper losses (I2R) Brush losses Core losses Mechanical losses Stray load losses Ia = armature current If = field current Ra = armature resistance Rf = field resistance *VBD = brush voltage drop - Usually assumed to be 2V Power Losses Core losses – hysteresis losses and eddy current losses Mechanical losses – the losses that associated with mechanical effects. Two basic types of mechanical losses: friction & windage. Friction losses caused by the friction of the bearings in the machine. Windage are caused by the friction between the moving parts of the machine and the air inside the motor casing’s Stray losses (Miscellaneous losses) – cannot placed in one of the previous categories. The Power Flow Diagram For generator For motor Equivalent circuit of DC generator Vf = field voltage If = field current Rfw = rheostat resistance Rf = Rfc + Rfw = field circuit resistance Ra = armature resistance Ea = KФω where Ф = flux generated by field current, If VT = terminal voltage Ia = armature current Equivalent circuit of DC motor Vf = field voltage If = field current Rfw = rheostat resistance Rf = Rfc + Rfw = field circuit resistance Ra = armature resistance Back EMF, Eb = KФω where Ф = flux generated by field current, If VT = terminal voltage Ia = armature current Example : A 4 pole DC machine has an armature of radius 12.5cm and effective length of 25cm. The poles cover 75% of the armature periphery. The armature winding consists of 33 coils, each coil having seven turns. The coils are accommodated in 33 slots. The average flux density under each pole is 0.75T. 1) If the armature is lap wound, determine: a. the armature constant K b. the induced armature voltage when the armature rotates at 1000 rpm. c. the current in the coil and the electromagnetic torque developed when the armature current is 400A. d. The power developed by the armature. 2) If the armature is wave wound, repeat parts a. to d. above. The current rating of the coils remains the same as in the lap wound armature. Solution : 1. Lap wound DC machine a) K ZP 2a Z 2x33x7 462 K ZP 462 x 4 73.53 2a 2 x 4 Always equal number of poles ( 2 x 33 coils x 7 turns) b) 2rl 2 x 0.125 x 0.25 x 0.75 P 4 -3 2 36.8 x 10 m Ap BA p 36.8 x 10-3 x0.75 0.0276Wb E K 73.53 x 0.0276 x 2 x 1000 60 212.5V c) I coil I a 400 100 A a 4 kI a 73.53 x 0.0276 x 400 811.8Nm d) Pdev Ea I a 212.5 x 400 85kW or Pdev 811.8 x 2x1000 85kW 60 2. Wave wound DC machine a) ZP 462 x 4 K 147.06 2a 2 x 2 b) 2 x 1000 E K 147.06 x 0.0276 x 60 425V c) I a aI coil 2 x 100 200 A kI a 147.06 x 0.0276 x 200 811.8Nm d) Pdev Ea I a 425 x 200 85kW Magnetizing curve of a DC machine The internal generated voltage, Ea of a DC motor or generator is Ea K The internal generated voltage, Ea is proportional to the flux in the machine and the speed of rotation of the machine. Magnetization curve of a ferromagnetic material (Ф vs F) Magnetomotive Force, F = NfIf Most motors and generator are designed to operate near the saturation point on the magnetization curve. This implies that a fairly large increase in field current is often necessary to get a small increase in Ea when operation is near full load. Classification of a DC machine Separately Excited DC Machine Shunt DC Machine Series DC Machine Compounded DC Machine