DESIGN OF DC MACHINE

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DESIGN OF DC MACHINE 1

Transcript of DESIGN OF DC MACHINE

Page 1: DESIGN OF DC MACHINE

DESIGN OF DC MACHINE

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OUTPUT EQUATIONPa = power developed by armature in kW

P = rating of machine in kW

E = generated emf , volts; V = terminal voltage, volts

p = number of poles; Ia = armaure current , A

Iz = current in each conductor, A

a = number of parallel path; Z = number of armature conductor

N = speed in rpm; n= speed in rps

D= armature diameter, m ; L = core length, m

Ф = flux per pole, weber ; τp = pole pitch

Pa = power developed by armature in kW

= E x Ia x 10-3

And E = p Ф Zn/a

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Thus Pa = (p Ф Z n)/a x Ia x 10-3 = (pФ) (IaZ/a) n x 10-3

= (pФ) (Iz Z) n x 10-3 since Ia/a = Iz

Now pФ = total magnetic loading

And Bav = (pФ)/(π D L) or pФ = Bav x π D L

ac = specific electric loading = (Iz x Z)/ π D

or Iz Z = ac π D

From above equations

Pa = (Bav π DL) (ac π D) n x 10-3

= ( π2 Bav ac 10-3) D2 Ln

= co D2 Ln where co = π2 Bav ac 10-3 = output coefficient

Also

D2 L = (1/ co ) (P/η) Pa = P/η η= efficiency of machine3

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Estimation of Pa:

In case of generator

Pa = input power – rotational losses

= (output power/efficiency) – rotational losses

= P/η – rotational losses

Rotational losses = friction, windage and iron losses

In case of motor

Pa = output power + rotational losses

= P – rotational losses

In case of large machines very small difference between P and Pa. So friction, windage and iron losses could be neglected.

Pa = P/η for generator

Pa = P for motor4

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In case of small machines friction, windage and iron losses can not be neglected.

Assume friction, windage and iron losses = 1/3 (total losses)

Total losses = input power – output power

= P/η – P = P(1- η)/ η

Hence friction, windage and iron losses = P(1- η)/ 3η

For small motors

Pa = P +(friction, windage and iron losses)

Pa = P + P(1- η)/ 3η = P(1+2η)/ 3η

For small generators

Pa = P/η - (friction, windage and iron losses)

= P(2+η)/ 3η5

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Choice of specific magnetic loading (Bav):

Flux density in teeth: if a high value of flux density is assumed for airgap, the flux density in armature teeth also becomes high. Themaximum value of flux density in the teeth at minimum sectionshould not exceed a value of 2.2 wb/m2 because at higher fluxdensity i) increased iron losses and ii) higher ampere turns requiresfor passing the flux through teeth leading to increase copper lossesand cost of copper.

Frequency: the frequency of flux reversal in the armature is given by f= np/2. Higher frequency will result increased iron losses in thearmature core and teeth. So there is a limitation in choosing higherBav for a machine having higher frequency.

Voltage: for high voltage machine space required for insulation is large.Thus for a given diameter less space is available for iron leading tonarrower teeth. Therefore lower value of Bav has to be takenotherwise teeth flux density increases beyond the permissible limit.

Value of Bav varies from 0.4 to 0.8 wb/m2.

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Choice of specific electric loading (ac):

Temperature rise: A higher value of ‘ac’ results in a high temperature

rise of windings. A high value of ‘ac’ can be used for machine using

insulating material which withstand high temperature rise.

Speed of machine: for high speed machine, the ventilation is better and

greater losses could be dissipated. Thus a higher value of ‘ac’ can be

used for higher speed machine.

Voltage: machine with high voltage require large space for insulation,

therefore there is less space for conductors. For high voltage

machines use small value of ampere conductors per meter.

Size of machine: in large size machine there is more space for

accommodating copper. There fore high value of ‘ac’ could be used.

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Armature reaction: if using high value of ‘ac’, armature mmfbecomes high. This means under loaded condition there willbe grater distortion of field form resulting in a large reductionin the value of flux. To compensate this field ampere turns areneeded to be increased. Thus over all cost of copper in themachine will increase.

Commutation: a high value of ‘ac’ means either ampereconductors used are more or diameter is small. Reactancevoltage increases with high ampere conductors. With smalldiameter, deeper slots are used. Deeper slots also give higherreactance voltage. Higher reactance voltage results in badcommutation. Thus using higher ‘ac’ affects the commutationbadly.

The value of ‘ac’ varies from 15000 to 50000 ampere conductorsper meter.

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Core length:

Factors affecting the length of core:

i) Cost : the manufacturing cost of a machine with large corelength, is less. This is because the proportion of inactivecopper to active copper is smaller for grater the length ofcore. Therefore it is desirable to have large core length forless cost.

ii) Ventilation: the ventilation of large core length is difficultbecause the central portion of the core tends to attain a hightemperature rise. If long armature are necessary specialmeans for ventilation of core must be provided.

Limiting value of core length: the emf induced in a conductorshould exceed 7.5/TcNc in order that the maximum value atload between adjacent segments limited to 30 V.

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The voltage in a conductor at no load ez = Bav L Va

For a limiting case: Bav L Va = 7.5/ Tc Nc

Limiting value of core length L = 7.5/ ( Bav Va Tc Nc)

Bav = average gap density wb/m2

Va = peripheral speed, m/s

Tc = turns per coil

Nc = number of coils between adjacent segments

Armature diameter:

The peripheral speed lies between 15 to 50 m/s. As the diameter of thearmature increases, the peripheral velocity of the armature v = πDN/60m/s , centrifugal force and its effects increases. Therefore the machinemust be mechanically made robust to withstand the effect of centrifugalforce. This increases the cost of the machine. In general for normalconstruction, peripheral velocity should not be greater than 30 m/s asfor as possible.

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Limiting value of armature diameter:

Output P = E Ia x 10 -3 kW

E = emf per conductor x conductors per parallel path

= ez Z/a

P = ( ez Z/a) Ia x 10-3 = ez (Iz . Z/a ) x 10-3

= ez π D ac x 10-3

D = (P x 10-3)/ (π ac ez)

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Selection of number of poles

Factors affecting the number of poles:

1. Frequency: As the number of poles increases, frequency of theinduced emf f = 120/PN increases, core loss in the armatureincreases and therefore efficiency of the machine decreases.

2. Weight of the iron used for the yoke: Since the flux carried by theyoke is approximately Ф/2 and the total flux ФT = pФ is a constantfor a given machine, flux density in the yoke

It is clear that Ay α 1/P

as By is also almost constant for a given iron. Thus, as the numberof poles increases, Ay and hence the weight of iron used for theyoke reduces.

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3. Weight of iron used for the armature core (from the core loss

point of view):

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Length of air gap:

i) Armature reaction: to prevent excessive distortion of field form byarmature reaction the field mmf must be large as compare to armaturemmf. A machine designed with long air gap requires large field mmf.Thus the distortion effect of armature reaction can be reduced by largeair gap length.

ii) Circulating current: if air gap length is small, a slight irregularity inthe air gap would result large circulating current.

iii) Noise: the operation of machine with large air gap length iscomparatively quite.

iv) Cooling: machine with large air gap length have better ventilation.

v) Pole face losses: if the length of air gap is made large, the variation inair gap flux density due to slotting are small. Therefore pulsation lossin the pole faces decreases.

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Estimation of air gap length:

Mmf required for air gap ATg = 800000 Bg Kg lgAnd armature mmf per pole ATa = acτ/2

The value of gap mmf is normally between 0.5 to 0.7 of armaturemmf. The usual value is 0.55.

ATg = (0.5 to 0.7) ATa = (0.5 to 0.7) acτ/2

From above equations lg = (0.5 to 0.7) acτ/1600000KgBg

Gap contraction factor Kg may assumed as 1.15.

Usually the value of air gap length lies between 0.01 to 0.015 ofpole pitch.

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Number of armature conductors

The generated emf in the armature

E = V + Ia Rm for generator

E = V - Ia Rm for motor

where V = terminal voltage and

Rm = sum of voltage drop in the armature winding, inter-pole winding,series winding and brush contact drop

i) For large 500 volt machine IaRm = 2 to 2.5% of terminal voltage

ii) For small 250 volt machine IaRm = 5 to 10% of terminal voltage

Total number of conductors in series Zc = E/mean emf per conductor

= E/ez

For a simplex lap winding Zc represent total number of armatureconductor per pole. (A=P)

For a simplax wave winding Zc represent half the total number ofconductor on the armature irrespective of number of poles. (A=2)

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Number of armature slots:

The following factors are to be considered while selecting the

number of slots:

1. Flux pulsations:- flux pulsation means changes in the air gap

flux because of changes in the air gap reluctance between he

pole faces and irregular armature core surface. Flux pulsation

losses rise to eddy current losses and produce magnetic noise.

The flux pulsations are reduced with increased number of

slots.

2. Cooling:-for large number of slots, lesser number of

conductors per slot therefore, cooling is better.

3. Commutation:- for commutation point of view, large number

of slots and smaller number of conductors per slot are better.24

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4. Tooth width:- for large number of slots the slot pitch reduces

and also the tooth width. With reduction in tooth width flux

density at the minimum section of tooth increases causing

increase in iron losses.

5. Cost:- cost of punching slots in stampings increases with the

number of slots to be punched.

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