BASIC ELECTRICAL TECHNOLOGY DET 2113 Chapter 7 DC

BASIC ELECTRICAL TECHNOLOGY DET 211/3 Chapter 7 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

Construction

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.

Construction - 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.

Construction • 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.

Construction 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.

Armature Windings Cut and unroll of DC machine

Armature Windings Electrical degree and mechanical degree Pole pitch is the distance between the centers of two adjacent poles

Armature Windings Two basic sequences of armature winding connections: a) Lap windings b) Wave windings

Lap Winding

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.

Lap Winding 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.

Wave Winding 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 faces View of field lines Top view

A simple rotating loop between curved poles faces 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 Voltage Induced in a Rotating Loop The induced voltage for one conductor is 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 where Z = the total number of conductors a = the number of current paths We know , v =rω, r = radius of the rotor

The internal generated voltage The flux of the pole is equal to the flux density under the pole times the pole’s area: The rotor of the DC machine is shaped like a cylinder, so its area is If there are P poles on the machine, then the portion of the area associated with each pole is

The internal generated voltage The total flux per pole in the machine is The internal generated voltage is

The internal generated voltage where or

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. Concepts: a current carrying wire in the presence of a magnetic field has a force induced on it Lorentz Law : use right hand rule. Index finger – vector l Middle finger – Magnetic flux density Thumb - Force

The induced torque in the rotating loop The force for one conductor is 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 induced torque in the rotating loop The torque on that segment is 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 If there are “a” current paths in the machine, then the total armature current Ia is split among the “a” current paths, so the current in a single conductor is The torque in a single conductor on the motor is

The induced torque Since there are Z conductors, the total induced torque in rotor is The total flux per pole in the machine is The total induced torque is

The induced torque The total induced torque is where

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

Power flow and losses in DC machines The losses that occur in DC machine can be divided into 5 categories: 1. Copper losses (I 2 R) 2. Brush losses 3. Core losses 4. Mechanical losses 5. Stray load losses Ia = armature current VBD = brush voltage drop If = field current - Usually assumed to be 2 V Ra = armature resistance Rf = field resistance

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 Pout = VTIL For generator

The Power Flow Diagram 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. 5 cm and effective length of 25 cm. 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. 75 T. 1) If the armature is lap wound, determine: 2) a. the armature constant K 3) b. the induced armature voltage when the armature rotates at 1000 rpm. 4) c. the current in the coil and the electromagnetic torque developed when the armature current is 400 A.

Example 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. Z = 2 CNc Always equal number of poles ( 2 x 33 coils x 7 turns)

Example b. c.

d. or 2. Wave wound DC machine a. b. c.

d.

Magnetizing curve of a DC machine The internal generated voltage, Ea of a DC motor or generator is 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 = Nf. If

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